--- a/doc-src/Classes/Thy/document/Classes.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/Classes/Thy/document/Classes.tex Mon Nov 08 14:41:11 2010 +0100
@@ -28,8 +28,8 @@
of overloading\footnote{throughout this tutorial, we are referring
to classical Haskell 1.0 type classes, not considering later
additions in expressiveness}. As a canonical example, a polymorphic
- equality function \isa{eq\ {\isasymColon}\ {\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}\ {\isasymRightarrow}\ bool} which is overloaded on
- different types for \isa{{\isasymalpha}}, which is achieved by splitting
+ equality function \isa{eq\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool} which is overloaded on
+ different types for \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}}, which is achieved by splitting
introduction of the \isa{eq} function from its overloaded
definitions by means of \isa{class} and \isa{instance}
declarations: \footnote{syntax here is a kind of isabellized
@@ -38,20 +38,20 @@
\begin{quote}
\noindent\isa{class\ eq\ where} \\
- \hspace*{2ex}\isa{eq\ {\isasymColon}\ {\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}\ {\isasymRightarrow}\ bool}
+ \hspace*{2ex}\isa{eq\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}
- \medskip\noindent\isa{instance\ nat\ {\isasymColon}\ eq\ where} \\
- \hspace*{2ex}\isa{eq\ {\isadigit{0}}\ {\isadigit{0}}\ {\isacharequal}\ True} \\
- \hspace*{2ex}\isa{eq\ {\isadigit{0}}\ {\isacharunderscore}\ {\isacharequal}\ False} \\
- \hspace*{2ex}\isa{eq\ {\isacharunderscore}\ {\isadigit{0}}\ {\isacharequal}\ False} \\
- \hspace*{2ex}\isa{eq\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharparenleft}Suc\ m{\isacharparenright}\ {\isacharequal}\ eq\ n\ m}
+ \medskip\noindent\isa{instance\ nat\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ eq\ where} \\
+ \hspace*{2ex}\isa{eq\ {\isadigit{0}}\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ True} \\
+ \hspace*{2ex}\isa{eq\ {\isadigit{0}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3D}{\isacharequal}}\ False} \\
+ \hspace*{2ex}\isa{eq\ {\isaliteral{5F}{\isacharunderscore}}\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ False} \\
+ \hspace*{2ex}\isa{eq\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ m{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ eq\ n\ m}
- \medskip\noindent\isa{instance\ {\isacharparenleft}{\isasymalpha}{\isasymColon}eq{\isacharcomma}\ {\isasymbeta}{\isasymColon}eq{\isacharparenright}\ pair\ {\isasymColon}\ eq\ where} \\
- \hspace*{2ex}\isa{eq\ {\isacharparenleft}x{\isadigit{1}}{\isacharcomma}\ y{\isadigit{1}}{\isacharparenright}\ {\isacharparenleft}x{\isadigit{2}}{\isacharcomma}\ y{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ eq\ x{\isadigit{1}}\ x{\isadigit{2}}\ {\isasymand}\ eq\ y{\isadigit{1}}\ y{\isadigit{2}}}
+ \medskip\noindent\isa{instance\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}eq{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}eq{\isaliteral{29}{\isacharparenright}}\ pair\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ eq\ where} \\
+ \hspace*{2ex}\isa{eq\ {\isaliteral{28}{\isacharparenleft}}x{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ y{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}x{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ y{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ eq\ x{\isadigit{1}}\ x{\isadigit{2}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ eq\ y{\isadigit{1}}\ y{\isadigit{2}}}
\medskip\noindent\isa{class\ ord\ extends\ eq\ where} \\
- \hspace*{2ex}\isa{less{\isacharunderscore}eq\ {\isasymColon}\ {\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}\ {\isasymRightarrow}\ bool} \\
- \hspace*{2ex}\isa{less\ {\isasymColon}\ {\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}\ {\isasymRightarrow}\ bool}
+ \hspace*{2ex}\isa{less{\isaliteral{5F}{\isacharunderscore}}eq\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool} \\
+ \hspace*{2ex}\isa{less\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}
\end{quote}
@@ -75,11 +75,11 @@
\begin{quote}
\noindent\isa{class\ eq\ where} \\
- \hspace*{2ex}\isa{eq\ {\isasymColon}\ {\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}\ {\isasymRightarrow}\ bool} \\
+ \hspace*{2ex}\isa{eq\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool} \\
\isa{satisfying} \\
- \hspace*{2ex}\isa{refl{\isacharcolon}\ eq\ x\ x} \\
- \hspace*{2ex}\isa{sym{\isacharcolon}\ eq\ x\ y\ {\isasymlongleftrightarrow}\ eq\ x\ y} \\
- \hspace*{2ex}\isa{trans{\isacharcolon}\ eq\ x\ y\ {\isasymand}\ eq\ y\ z\ {\isasymlongrightarrow}\ eq\ x\ z}
+ \hspace*{2ex}\isa{refl{\isaliteral{3A}{\isacharcolon}}\ eq\ x\ x} \\
+ \hspace*{2ex}\isa{sym{\isaliteral{3A}{\isacharcolon}}\ eq\ x\ y\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ eq\ x\ y} \\
+ \hspace*{2ex}\isa{trans{\isaliteral{3A}{\isacharcolon}}\ eq\ x\ y\ {\isaliteral{5C3C616E643E}{\isasymand}}\ eq\ y\ z\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ eq\ x\ z}
\end{quote}
@@ -119,7 +119,7 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-Depending on an arbitrary type \isa{{\isasymalpha}}, class \isa{semigroup} introduces a binary operator \isa{{\isacharparenleft}{\isasymotimes}{\isacharparenright}} that is
+Depending on an arbitrary type \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}}, class \isa{semigroup} introduces a binary operator \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}{\isaliteral{29}{\isacharparenright}}} that is
assumed to be associative:%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -130,9 +130,9 @@
%
\isatagquote
\isacommand{class}\isamarkupfalse%
-\ semigroup\ {\isacharequal}\isanewline
-\ \ \isakeyword{fixes}\ mult\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}{\isachardoublequoteclose}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasymotimes}{\isachardoublequoteclose}\ {\isadigit{7}}{\isadigit{0}}{\isacharparenright}\isanewline
-\ \ \isakeyword{assumes}\ assoc{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}x\ {\isasymotimes}\ y{\isacharparenright}\ {\isasymotimes}\ z\ {\isacharequal}\ x\ {\isasymotimes}\ {\isacharparenleft}y\ {\isasymotimes}\ z{\isacharparenright}{\isachardoublequoteclose}%
+\ semigroup\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \isakeyword{fixes}\ mult\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{7}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \isakeyword{assumes}\ assoc{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ z\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -144,8 +144,8 @@
\noindent This \hyperlink{command.class}{\mbox{\isa{\isacommand{class}}}} specification consists of two parts:
the \qn{operational} part names the class parameter (\hyperlink{element.fixes}{\mbox{\isa{\isakeyword{fixes}}}}), the \qn{logical} part specifies properties on them
(\hyperlink{element.assumes}{\mbox{\isa{\isakeyword{assumes}}}}). The local \hyperlink{element.fixes}{\mbox{\isa{\isakeyword{fixes}}}} and \hyperlink{element.assumes}{\mbox{\isa{\isakeyword{assumes}}}} are lifted to the theory toplevel, yielding the global
- parameter \isa{{\isachardoublequote}mult\ {\isasymColon}\ {\isasymalpha}{\isasymColon}semigroup\ {\isasymRightarrow}\ {\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}{\isachardoublequote}} and the
- global theorem \hyperlink{fact.semigroup.assoc:}{\mbox{\isa{semigroup{\isachardot}assoc{\isacharcolon}}}}~\isa{{\isachardoublequote}{\isasymAnd}x\ y\ z\ {\isasymColon}\ {\isasymalpha}{\isasymColon}semigroup{\isachardot}\ {\isacharparenleft}x\ {\isasymotimes}\ y{\isacharparenright}\ {\isasymotimes}\ z\ {\isacharequal}\ x\ {\isasymotimes}\ {\isacharparenleft}y\ {\isasymotimes}\ z{\isacharparenright}{\isachardoublequote}}.%
+ parameter \isa{{\isaliteral{22}{\isachardoublequote}}mult\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}semigroup\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{22}{\isachardoublequote}}} and the
+ global theorem \hyperlink{fact.semigroup.assoc:}{\mbox{\isa{semigroup{\isaliteral{2E}{\isachardot}}assoc{\isaliteral{3A}{\isacharcolon}}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y\ z\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}semigroup{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ z\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -155,7 +155,7 @@
%
\begin{isamarkuptext}%
The concrete type \isa{int} is made a \isa{semigroup} instance
- by providing a suitable definition for the class parameter \isa{{\isacharparenleft}{\isasymotimes}{\isacharparenright}} and a proof for the specification of \hyperlink{fact.assoc}{\mbox{\isa{assoc}}}. This is
+ by providing a suitable definition for the class parameter \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}{\isaliteral{29}{\isacharparenright}}} and a proof for the specification of \hyperlink{fact.assoc}{\mbox{\isa{assoc}}}. This is
accomplished by the \hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}} target:%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -166,25 +166,25 @@
%
\isatagquote
\isacommand{instantiation}\isamarkupfalse%
-\ int\ {\isacharcolon}{\isacharcolon}\ semigroup\isanewline
+\ int\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ semigroup\isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{definition}\isamarkupfalse%
\isanewline
-\ \ mult{\isacharunderscore}int{\isacharunderscore}def{\isacharcolon}\ {\isachardoublequoteopen}i\ {\isasymotimes}\ j\ {\isacharequal}\ i\ {\isacharplus}\ {\isacharparenleft}j{\isasymColon}int{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ mult{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}i\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ j\ {\isaliteral{3D}{\isacharequal}}\ i\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}j{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}int{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{instance}\isamarkupfalse%
\ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
-\ i\ j\ k\ {\isacharcolon}{\isacharcolon}\ int\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}i\ {\isacharplus}\ j{\isacharparenright}\ {\isacharplus}\ k\ {\isacharequal}\ i\ {\isacharplus}\ {\isacharparenleft}j\ {\isacharplus}\ k{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ i\ j\ k\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\ \isacommand{have}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{2B}{\isacharplus}}\ j{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ k\ {\isaliteral{3D}{\isacharequal}}\ i\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}j\ {\isaliteral{2B}{\isacharplus}}\ k{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}i\ {\isasymotimes}\ j{\isacharparenright}\ {\isasymotimes}\ k\ {\isacharequal}\ i\ {\isasymotimes}\ {\isacharparenleft}j\ {\isasymotimes}\ k{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ j{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ k\ {\isaliteral{3D}{\isacharequal}}\ i\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{28}{\isacharparenleft}}j\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ k{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{unfolding}\isamarkupfalse%
-\ mult{\isacharunderscore}int{\isacharunderscore}def\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ mult{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
\isanewline
@@ -203,7 +203,7 @@
particular instance using common specification tools (here,
\hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}). The concluding \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}} opens a
proof that the given parameters actually conform to the class
- specification. Note that the first proof step is the \hyperlink{method.default}{\mbox{\isa{default}}} method, which for such instance proofs maps to the \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isacharunderscore}classes}}} method. This reduces an instance judgement to the
+ specification. Note that the first proof step is the \hyperlink{method.default}{\mbox{\isa{default}}} method, which for such instance proofs maps to the \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}classes}}} method. This reduces an instance judgement to the
relevant primitive proof goals; typically it is the first method
applied in an instantiation proof.
@@ -221,23 +221,23 @@
%
\isatagquote
\isacommand{instantiation}\isamarkupfalse%
-\ nat\ {\isacharcolon}{\isacharcolon}\ semigroup\isanewline
+\ nat\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ semigroup\isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{primrec}\isamarkupfalse%
-\ mult{\isacharunderscore}nat\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}{\isacharparenleft}{\isadigit{0}}{\isasymColon}nat{\isacharparenright}\ {\isasymotimes}\ n\ {\isacharequal}\ n{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}Suc\ m\ {\isasymotimes}\ n\ {\isacharequal}\ Suc\ {\isacharparenleft}m\ {\isasymotimes}\ n{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ mult{\isaliteral{5F}{\isacharunderscore}}nat\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ n\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}Suc\ m\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ n\ {\isaliteral{3D}{\isacharequal}}\ Suc\ {\isaliteral{28}{\isacharparenleft}}m\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{instance}\isamarkupfalse%
\ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
-\ m\ n\ q\ {\isacharcolon}{\isacharcolon}\ nat\ \isanewline
+\ m\ n\ q\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat\ \isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}m\ {\isasymotimes}\ n\ {\isasymotimes}\ q\ {\isacharequal}\ m\ {\isasymotimes}\ {\isacharparenleft}n\ {\isasymotimes}\ q{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}m\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ n\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ q\ {\isaliteral{3D}{\isacharequal}}\ m\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ q{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ m{\isacharparenright}\ auto\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ m{\isaliteral{29}{\isacharparenright}}\ auto\isanewline
\isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
@@ -251,11 +251,11 @@
\endisadelimquote
%
\begin{isamarkuptext}%
-\noindent Note the occurence of the name \isa{mult{\isacharunderscore}nat} in the
+\noindent Note the occurence of the name \isa{mult{\isaliteral{5F}{\isacharunderscore}}nat} in the
primrec declaration; by default, the local name of a class operation
- \isa{f} to be instantiated on type constructor \isa{{\isasymkappa}} is
- mangled as \isa{f{\isacharunderscore}{\isasymkappa}}. In case of uncertainty, these names may be
- inspected using the \hyperlink{command.print-context}{\mbox{\isa{\isacommand{print{\isacharunderscore}context}}}} command or the
+ \isa{f} to be instantiated on type constructor \isa{{\isaliteral{5C3C6B617070613E}{\isasymkappa}}} is
+ mangled as \isa{f{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5C3C6B617070613E}{\isasymkappa}}}. In case of uncertainty, these names may be
+ inspected using the \hyperlink{command.print-context}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}context}}}} command or the
corresponding ProofGeneral button.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -277,23 +277,23 @@
%
\isatagquote
\isacommand{instantiation}\isamarkupfalse%
-\ prod\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}semigroup{\isacharcomma}\ semigroup{\isacharparenright}\ semigroup\isanewline
+\ prod\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}semigroup{\isaliteral{2C}{\isacharcomma}}\ semigroup{\isaliteral{29}{\isacharparenright}}\ semigroup\isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{definition}\isamarkupfalse%
\isanewline
-\ \ mult{\isacharunderscore}prod{\isacharunderscore}def{\isacharcolon}\ {\isachardoublequoteopen}p\isactrlisub {\isadigit{1}}\ {\isasymotimes}\ p\isactrlisub {\isadigit{2}}\ {\isacharequal}\ {\isacharparenleft}fst\ p\isactrlisub {\isadigit{1}}\ {\isasymotimes}\ fst\ p\isactrlisub {\isadigit{2}}{\isacharcomma}\ snd\ p\isactrlisub {\isadigit{1}}\ {\isasymotimes}\ snd\ p\isactrlisub {\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ mult{\isaliteral{5F}{\isacharunderscore}}prod{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}fst\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ fst\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ snd\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ snd\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{instance}\isamarkupfalse%
\ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
-\ p\isactrlisub {\isadigit{1}}\ p\isactrlisub {\isadigit{2}}\ p\isactrlisub {\isadigit{3}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymalpha}{\isasymColon}semigroup\ {\isasymtimes}\ {\isasymbeta}{\isasymColon}semigroup{\isachardoublequoteclose}\isanewline
+\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{3}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}semigroup\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}semigroup{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}p\isactrlisub {\isadigit{1}}\ {\isasymotimes}\ p\isactrlisub {\isadigit{2}}\ {\isasymotimes}\ p\isactrlisub {\isadigit{3}}\ {\isacharequal}\ p\isactrlisub {\isadigit{1}}\ {\isasymotimes}\ {\isacharparenleft}p\isactrlisub {\isadigit{2}}\ {\isasymotimes}\ p\isactrlisub {\isadigit{3}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{3}}\ {\isaliteral{3D}{\isacharequal}}\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{28}{\isacharparenleft}}p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{3}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{unfolding}\isamarkupfalse%
-\ mult{\isacharunderscore}prod{\isacharunderscore}def\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ assoc{\isacharparenright}\isanewline
+\ mult{\isaliteral{5F}{\isacharunderscore}}prod{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ assoc{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{qed}\isamarkupfalse%
\ \ \ \ \ \ \isanewline
\isanewline
@@ -308,7 +308,7 @@
%
\begin{isamarkuptext}%
\noindent Associativity of product semigroups is established using
- the definition of \isa{{\isacharparenleft}{\isasymotimes}{\isacharparenright}} on products and the hypothetical
+ the definition of \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}{\isaliteral{29}{\isacharparenright}}} on products and the hypothetical
associativity of the type components; these hypotheses are
legitimate due to the \isa{semigroup} constraints imposed on the
type components by the \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}} proposition. Indeed,
@@ -333,9 +333,9 @@
%
\isatagquote
\isacommand{class}\isamarkupfalse%
-\ monoidl\ {\isacharequal}\ semigroup\ {\isacharplus}\isanewline
-\ \ \isakeyword{fixes}\ neutral\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymalpha}{\isachardoublequoteclose}\ {\isacharparenleft}{\isachardoublequoteopen}{\isasymone}{\isachardoublequoteclose}{\isacharparenright}\isanewline
-\ \ \isakeyword{assumes}\ neutl{\isacharcolon}\ {\isachardoublequoteopen}{\isasymone}\ {\isasymotimes}\ x\ {\isacharequal}\ x{\isachardoublequoteclose}%
+\ monoidl\ {\isaliteral{3D}{\isacharequal}}\ semigroup\ {\isaliteral{2B}{\isacharplus}}\isanewline
+\ \ \isakeyword{fixes}\ neutral\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F6E653E}{\isasymone}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \isakeyword{assumes}\ neutl{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ x\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -357,35 +357,35 @@
%
\isatagquote
\isacommand{instantiation}\isamarkupfalse%
-\ nat\ \isakeyword{and}\ int\ {\isacharcolon}{\isacharcolon}\ monoidl\isanewline
+\ nat\ \isakeyword{and}\ int\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ monoidl\isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{definition}\isamarkupfalse%
\isanewline
-\ \ neutral{\isacharunderscore}nat{\isacharunderscore}def{\isacharcolon}\ {\isachardoublequoteopen}{\isasymone}\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}nat{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ neutral{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{definition}\isamarkupfalse%
\isanewline
-\ \ neutral{\isacharunderscore}int{\isacharunderscore}def{\isacharcolon}\ {\isachardoublequoteopen}{\isasymone}\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}int{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ neutral{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}int{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{instance}\isamarkupfalse%
\ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
-\ n\ {\isacharcolon}{\isacharcolon}\ nat\isanewline
+\ n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymone}\ {\isasymotimes}\ n\ {\isacharequal}\ n{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ n\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{unfolding}\isamarkupfalse%
-\ neutral{\isacharunderscore}nat{\isacharunderscore}def\ \isacommand{by}\isamarkupfalse%
+\ neutral{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
-\ k\ {\isacharcolon}{\isacharcolon}\ int\isanewline
+\ k\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymone}\ {\isasymotimes}\ k\ {\isacharequal}\ k{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ k\ {\isaliteral{3D}{\isacharequal}}\ k{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{unfolding}\isamarkupfalse%
-\ neutral{\isacharunderscore}int{\isacharunderscore}def\ mult{\isacharunderscore}int{\isacharunderscore}def\ \isacommand{by}\isamarkupfalse%
+\ neutral{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{5F}{\isacharunderscore}}def\ mult{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{qed}\isamarkupfalse%
\isanewline
@@ -394,23 +394,23 @@
\isanewline
\isanewline
\isacommand{instantiation}\isamarkupfalse%
-\ prod\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}monoidl{\isacharcomma}\ monoidl{\isacharparenright}\ monoidl\isanewline
+\ prod\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}monoidl{\isaliteral{2C}{\isacharcomma}}\ monoidl{\isaliteral{29}{\isacharparenright}}\ monoidl\isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{definition}\isamarkupfalse%
\isanewline
-\ \ neutral{\isacharunderscore}prod{\isacharunderscore}def{\isacharcolon}\ {\isachardoublequoteopen}{\isasymone}\ {\isacharequal}\ {\isacharparenleft}{\isasymone}{\isacharcomma}\ {\isasymone}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ neutral{\isaliteral{5F}{\isacharunderscore}}prod{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6F6E653E}{\isasymone}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C6F6E653E}{\isasymone}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{instance}\isamarkupfalse%
\ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
-\ p\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymalpha}{\isasymColon}monoidl\ {\isasymtimes}\ {\isasymbeta}{\isasymColon}monoidl{\isachardoublequoteclose}\isanewline
+\ p\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}monoidl\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}monoidl{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymone}\ {\isasymotimes}\ p\ {\isacharequal}\ p{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ p\ {\isaliteral{3D}{\isacharequal}}\ p{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{unfolding}\isamarkupfalse%
-\ neutral{\isacharunderscore}prod{\isacharunderscore}def\ mult{\isacharunderscore}prod{\isacharunderscore}def\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ neutl{\isacharparenright}\isanewline
+\ neutral{\isaliteral{5F}{\isacharunderscore}}prod{\isaliteral{5F}{\isacharunderscore}}def\ mult{\isaliteral{5F}{\isacharunderscore}}prod{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ neutl{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
@@ -435,31 +435,31 @@
%
\isatagquote
\isacommand{class}\isamarkupfalse%
-\ monoid\ {\isacharequal}\ monoidl\ {\isacharplus}\isanewline
-\ \ \isakeyword{assumes}\ neutr{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymotimes}\ {\isasymone}\ {\isacharequal}\ x{\isachardoublequoteclose}\isanewline
+\ monoid\ {\isaliteral{3D}{\isacharequal}}\ monoidl\ {\isaliteral{2B}{\isacharplus}}\isanewline
+\ \ \isakeyword{assumes}\ neutr{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{instantiation}\isamarkupfalse%
-\ nat\ \isakeyword{and}\ int\ {\isacharcolon}{\isacharcolon}\ monoid\ \isanewline
+\ nat\ \isakeyword{and}\ int\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ monoid\ \isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{instance}\isamarkupfalse%
\ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
-\ n\ {\isacharcolon}{\isacharcolon}\ nat\isanewline
+\ n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}n\ {\isasymotimes}\ {\isasymone}\ {\isacharequal}\ n{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}n\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{unfolding}\isamarkupfalse%
-\ neutral{\isacharunderscore}nat{\isacharunderscore}def\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ n{\isacharparenright}\ simp{\isacharunderscore}all\isanewline
+\ neutral{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}induct\ n{\isaliteral{29}{\isacharparenright}}\ simp{\isaliteral{5F}{\isacharunderscore}}all\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
-\ k\ {\isacharcolon}{\isacharcolon}\ int\isanewline
+\ k\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}k\ {\isasymotimes}\ {\isasymone}\ {\isacharequal}\ k{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}k\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{3D}{\isacharequal}}\ k{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{unfolding}\isamarkupfalse%
-\ neutral{\isacharunderscore}int{\isacharunderscore}def\ mult{\isacharunderscore}int{\isacharunderscore}def\ \isacommand{by}\isamarkupfalse%
+\ neutral{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{5F}{\isacharunderscore}}def\ mult{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{qed}\isamarkupfalse%
\isanewline
@@ -468,19 +468,19 @@
\isanewline
\isanewline
\isacommand{instantiation}\isamarkupfalse%
-\ prod\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}monoid{\isacharcomma}\ monoid{\isacharparenright}\ monoid\isanewline
+\ prod\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}monoid{\isaliteral{2C}{\isacharcomma}}\ monoid{\isaliteral{29}{\isacharparenright}}\ monoid\isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{instance}\isamarkupfalse%
\ \isacommand{proof}\isamarkupfalse%
\ \isanewline
\ \ \isacommand{fix}\isamarkupfalse%
-\ p\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymalpha}{\isasymColon}monoid\ {\isasymtimes}\ {\isasymbeta}{\isasymColon}monoid{\isachardoublequoteclose}\isanewline
+\ p\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}monoid\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}monoid{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}p\ {\isasymotimes}\ {\isasymone}\ {\isacharequal}\ p{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}p\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{3D}{\isacharequal}}\ p{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{unfolding}\isamarkupfalse%
-\ neutral{\isacharunderscore}prod{\isacharunderscore}def\ mult{\isacharunderscore}prod{\isacharunderscore}def\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ neutr{\isacharparenright}\isanewline
+\ neutral{\isaliteral{5F}{\isacharunderscore}}prod{\isaliteral{5F}{\isacharunderscore}}def\ mult{\isaliteral{5F}{\isacharunderscore}}prod{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ neutr{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
@@ -504,31 +504,31 @@
%
\isatagquote
\isacommand{class}\isamarkupfalse%
-\ group\ {\isacharequal}\ monoidl\ {\isacharplus}\isanewline
-\ \ \isakeyword{fixes}\ inverse\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}{\isachardoublequoteclose}\ \ \ \ {\isacharparenleft}{\isachardoublequoteopen}{\isacharparenleft}{\isacharunderscore}{\isasymdiv}{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbrackleft}{\isadigit{1}}{\isadigit{0}}{\isadigit{0}}{\isadigit{0}}{\isacharbrackright}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isacharparenright}\isanewline
-\ \ \isakeyword{assumes}\ invl{\isacharcolon}\ {\isachardoublequoteopen}x{\isasymdiv}\ {\isasymotimes}\ x\ {\isacharequal}\ {\isasymone}{\isachardoublequoteclose}\isanewline
+\ group\ {\isaliteral{3D}{\isacharequal}}\ monoidl\ {\isaliteral{2B}{\isacharplus}}\isanewline
+\ \ \isakeyword{fixes}\ inverse\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5C3C6469763E}{\isasymdiv}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isadigit{0}}{\isadigit{0}}{\isadigit{0}}{\isaliteral{5D}{\isacharbrackright}}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \isakeyword{assumes}\ invl{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x{\isaliteral{5C3C6469763E}{\isasymdiv}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6F6E653E}{\isasymone}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{instantiation}\isamarkupfalse%
-\ int\ {\isacharcolon}{\isacharcolon}\ group\isanewline
+\ int\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ group\isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{definition}\isamarkupfalse%
\isanewline
-\ \ inverse{\isacharunderscore}int{\isacharunderscore}def{\isacharcolon}\ {\isachardoublequoteopen}i{\isasymdiv}\ {\isacharequal}\ {\isacharminus}\ {\isacharparenleft}i{\isasymColon}int{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ inverse{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}i{\isaliteral{5C3C6469763E}{\isasymdiv}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{28}{\isacharparenleft}}i{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}int{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{instance}\isamarkupfalse%
\ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
-\ i\ {\isacharcolon}{\isacharcolon}\ int\isanewline
+\ i\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharminus}i\ {\isacharplus}\ i\ {\isacharequal}\ {\isadigit{0}}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{2D}{\isacharminus}}i\ {\isaliteral{2B}{\isacharplus}}\ i\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}i{\isasymdiv}\ {\isasymotimes}\ i\ {\isacharequal}\ {\isasymone}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}i{\isaliteral{5C3C6469763E}{\isasymdiv}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ i\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6F6E653E}{\isasymone}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{unfolding}\isamarkupfalse%
-\ mult{\isacharunderscore}int{\isacharunderscore}def\ neutral{\isacharunderscore}int{\isacharunderscore}def\ inverse{\isacharunderscore}int{\isacharunderscore}def\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ mult{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{5F}{\isacharunderscore}}def\ neutral{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{5F}{\isacharunderscore}}def\ inverse{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
\isanewline
@@ -564,9 +564,9 @@
%
\isatagquote
\isacommand{class}\isamarkupfalse%
-\ idem\ {\isacharequal}\isanewline
-\ \ \isakeyword{fixes}\ f\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{assumes}\ idem{\isacharcolon}\ {\isachardoublequoteopen}f\ {\isacharparenleft}f\ x{\isacharparenright}\ {\isacharequal}\ f\ x{\isachardoublequoteclose}%
+\ idem\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \isakeyword{fixes}\ f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{assumes}\ idem{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}f\ {\isaliteral{28}{\isacharparenleft}}f\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ f\ x{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -598,9 +598,9 @@
%
\isatagquote
\isacommand{locale}\isamarkupfalse%
-\ idem\ {\isacharequal}\isanewline
-\ \ \isakeyword{fixes}\ f\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{assumes}\ idem{\isacharcolon}\ {\isachardoublequoteopen}f\ {\isacharparenleft}f\ x{\isacharparenright}\ {\isacharequal}\ f\ x{\isachardoublequoteclose}%
+\ idem\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \isakeyword{fixes}\ f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{assumes}\ idem{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}f\ {\isaliteral{28}{\isacharparenleft}}f\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ f\ x{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -619,7 +619,7 @@
%
\isatagquote
\isacommand{consts}\isamarkupfalse%
-\ f\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}{\isachardoublequoteclose}%
+\ f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -652,7 +652,7 @@
%
\isatagquote
\isacommand{classes}\isamarkupfalse%
-\ idem\ {\isacharless}\ type%
+\ idem\ {\isaliteral{3C}{\isacharless}}\ type%
\endisatagquote
{\isafoldquote}%
%
@@ -684,8 +684,8 @@
%
\isatagquote
\isacommand{interpretation}\isamarkupfalse%
-\ idem{\isacharunderscore}class{\isacharcolon}\isanewline
-\ \ idem\ {\isachardoublequoteopen}f\ {\isasymColon}\ {\isacharparenleft}{\isasymalpha}{\isasymColon}idem{\isacharparenright}\ {\isasymRightarrow}\ {\isasymalpha}{\isachardoublequoteclose}%
+\ idem{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ idem\ {\isaliteral{22}{\isachardoublequoteopen}}f\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}idem{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -720,8 +720,8 @@
\begin{isamarkuptext}%
Isabelle locales enable reasoning at a general level, while results
are implicitly transferred to all instances. For example, we can
- now establish the \isa{left{\isacharunderscore}cancel} lemma for groups, which
- states that the function \isa{{\isacharparenleft}x\ {\isasymotimes}{\isacharparenright}} is injective:%
+ now establish the \isa{left{\isaliteral{5F}{\isacharunderscore}}cancel} lemma for groups, which
+ states that the function \isa{{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}{\isaliteral{29}{\isacharparenright}}} is injective:%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -731,32 +731,32 @@
%
\isatagquote
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharparenleft}\isakeyword{in}\ group{\isacharparenright}\ left{\isacharunderscore}cancel{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymotimes}\ y\ {\isacharequal}\ x\ {\isasymotimes}\ z\ {\isasymlongleftrightarrow}\ y\ {\isacharequal}\ z{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{in}\ group{\isaliteral{29}{\isacharparenright}}\ left{\isaliteral{5F}{\isacharunderscore}}cancel{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ y\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ z\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ y\ {\isaliteral{3D}{\isacharequal}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymotimes}\ y\ {\isacharequal}\ x\ {\isasymotimes}\ z{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ y\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x{\isasymdiv}\ {\isasymotimes}\ {\isacharparenleft}x\ {\isasymotimes}\ y{\isacharparenright}\ {\isacharequal}\ x{\isasymdiv}\ {\isasymotimes}\ {\isacharparenleft}x\ {\isasymotimes}\ z{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x{\isaliteral{5C3C6469763E}{\isasymdiv}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{5C3C6469763E}{\isasymdiv}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}x{\isasymdiv}\ {\isasymotimes}\ x{\isacharparenright}\ {\isasymotimes}\ y\ {\isacharequal}\ {\isacharparenleft}x{\isasymdiv}\ {\isasymotimes}\ x{\isacharparenright}\ {\isasymotimes}\ z{\isachardoublequoteclose}\ \isacommand{using}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{5C3C6469763E}{\isasymdiv}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{5C3C6469763E}{\isasymdiv}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{using}\isamarkupfalse%
\ assoc\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isacharequal}\ z{\isachardoublequoteclose}\ \isacommand{using}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{3D}{\isacharequal}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{using}\isamarkupfalse%
\ neutl\ \isakeyword{and}\ invl\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isacharequal}\ z{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{3D}{\isacharequal}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymotimes}\ y\ {\isacharequal}\ x\ {\isasymotimes}\ z{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ y\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -771,9 +771,9 @@
\noindent Here the \qt{\hyperlink{keyword.in}{\mbox{\isa{\isakeyword{in}}}} \isa{group}} target
specification indicates that the result is recorded within that
context for later use. This local theorem is also lifted to the
- global one \hyperlink{fact.group.left-cancel:}{\mbox{\isa{group{\isachardot}left{\isacharunderscore}cancel{\isacharcolon}}}} \isa{{\isachardoublequote}{\isasymAnd}x\ y\ z\ {\isasymColon}\ {\isasymalpha}{\isasymColon}group{\isachardot}\ x\ {\isasymotimes}\ y\ {\isacharequal}\ x\ {\isasymotimes}\ z\ {\isasymlongleftrightarrow}\ y\ {\isacharequal}\ z{\isachardoublequote}}. Since type \isa{int} has been
+ global one \hyperlink{fact.group.left-cancel:}{\mbox{\isa{group{\isaliteral{2E}{\isachardot}}left{\isaliteral{5F}{\isacharunderscore}}cancel{\isaliteral{3A}{\isacharcolon}}}}} \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y\ z\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}group{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ y\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ z\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ y\ {\isaliteral{3D}{\isacharequal}}\ z{\isaliteral{22}{\isachardoublequote}}}. Since type \isa{int} has been
made an instance of \isa{group} before, we may refer to that
- fact as well: \isa{{\isachardoublequote}{\isasymAnd}x\ y\ z\ {\isasymColon}\ int{\isachardot}\ x\ {\isasymotimes}\ y\ {\isacharequal}\ x\ {\isasymotimes}\ z\ {\isasymlongleftrightarrow}\ y\ {\isacharequal}\ z{\isachardoublequote}}.%
+ fact as well: \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y\ z\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ int{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ y\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ z\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ y\ {\isaliteral{3D}{\isacharequal}}\ z{\isaliteral{22}{\isachardoublequote}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -792,9 +792,9 @@
%
\isatagquote
\isacommand{primrec}\isamarkupfalse%
-\ {\isacharparenleft}\isakeyword{in}\ monoid{\isacharparenright}\ pow{\isacharunderscore}nat\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ {\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}pow{\isacharunderscore}nat\ {\isadigit{0}}\ x\ {\isacharequal}\ {\isasymone}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}pow{\isacharunderscore}nat\ {\isacharparenleft}Suc\ n{\isacharparenright}\ x\ {\isacharequal}\ x\ {\isasymotimes}\ pow{\isacharunderscore}nat\ n\ x{\isachardoublequoteclose}%
+\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{in}\ monoid{\isaliteral{29}{\isacharparenright}}\ pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isadigit{0}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6F6E653E}{\isasymone}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ x\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ pow{\isaliteral{5F}{\isacharunderscore}}nat\ n\ x{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -804,10 +804,10 @@
%
\begin{isamarkuptext}%
\noindent If the locale \isa{group} is also a class, this local
- definition is propagated onto a global definition of \isa{{\isachardoublequote}pow{\isacharunderscore}nat\ {\isasymColon}\ nat\ {\isasymRightarrow}\ {\isasymalpha}{\isasymColon}monoid\ {\isasymRightarrow}\ {\isasymalpha}{\isasymColon}monoid{\isachardoublequote}} with corresponding theorems
+ definition is propagated onto a global definition of \isa{{\isaliteral{22}{\isachardoublequote}}pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}monoid\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}monoid{\isaliteral{22}{\isachardoublequote}}} with corresponding theorems
- \isa{pow{\isacharunderscore}nat\ {\isadigit{0}}\ x\ {\isacharequal}\ {\isasymone}\isasep\isanewline%
-pow{\isacharunderscore}nat\ {\isacharparenleft}Suc\ n{\isacharparenright}\ x\ {\isacharequal}\ x\ {\isasymotimes}\ pow{\isacharunderscore}nat\ n\ x}.
+ \isa{pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isadigit{0}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6F6E653E}{\isasymone}}\isasep\isanewline%
+pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ x\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ pow{\isaliteral{5F}{\isacharunderscore}}nat\ n\ x}.
\noindent As you can see from this example, for local definitions
you may use any specification tool which works together with
@@ -828,7 +828,7 @@
functors that have a canonical interpretation as type classes.
There is also the possibility of other interpretations. For
example, \isa{list}s also form a monoid with \isa{append} and
- \isa{{\isacharbrackleft}{\isacharbrackright}} as operations, but it seems inappropriate to apply to
+ \isa{{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}} as operations, but it seems inappropriate to apply to
lists the same operations as for genuinely algebraic types. In such
a case, we can simply make a particular interpretation of monoids
for lists:%
@@ -841,7 +841,7 @@
%
\isatagquote
\isacommand{interpretation}\isamarkupfalse%
-\ list{\isacharunderscore}monoid{\isacharcolon}\ monoid\ append\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
+\ list{\isaliteral{5F}{\isacharunderscore}}monoid{\isaliteral{3A}{\isacharcolon}}\ monoid\ append\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ \isacommand{qed}\isamarkupfalse%
\ auto%
@@ -854,7 +854,7 @@
%
\begin{isamarkuptext}%
\noindent This enables us to apply facts on monoids
- to lists, e.g. \isa{{\isacharbrackleft}{\isacharbrackright}\ {\isacharat}\ x\ {\isacharequal}\ x}.
+ to lists, e.g. \isa{{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{40}{\isacharat}}\ x\ {\isaliteral{3D}{\isacharequal}}\ x}.
When using this interpretation pattern, it may also
be appropriate to map derived definitions accordingly:%
@@ -867,32 +867,32 @@
%
\isatagquote
\isacommand{primrec}\isamarkupfalse%
-\ replicate\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ {\isasymalpha}\ list\ {\isasymRightarrow}\ {\isasymalpha}\ list{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}replicate\ {\isadigit{0}}\ {\isacharunderscore}\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}replicate\ {\isacharparenleft}Suc\ n{\isacharparenright}\ xs\ {\isacharequal}\ xs\ {\isacharat}\ replicate\ n\ xs{\isachardoublequoteclose}\isanewline
+\ replicate\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ list{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}replicate\ {\isadigit{0}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}replicate\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ xs\ {\isaliteral{3D}{\isacharequal}}\ xs\ {\isaliteral{40}{\isacharat}}\ replicate\ n\ xs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{interpretation}\isamarkupfalse%
-\ list{\isacharunderscore}monoid{\isacharcolon}\ monoid\ append\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}monoid{\isachardot}pow{\isacharunderscore}nat\ append\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ replicate{\isachardoublequoteclose}\isanewline
+\ list{\isaliteral{5F}{\isacharunderscore}}monoid{\isaliteral{3A}{\isacharcolon}}\ monoid\ append\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}monoid{\isaliteral{2E}{\isachardot}}pow{\isaliteral{5F}{\isacharunderscore}}nat\ append\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ replicate{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{interpret}\isamarkupfalse%
-\ monoid\ append\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ monoid\ append\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}monoid{\isachardot}pow{\isacharunderscore}nat\ append\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ replicate{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}monoid{\isaliteral{2E}{\isachardot}}pow{\isaliteral{5F}{\isacharunderscore}}nat\ append\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ replicate{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ n\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}monoid{\isachardot}pow{\isacharunderscore}nat\ append\ {\isacharbrackleft}{\isacharbrackright}\ n\ {\isacharequal}\ replicate\ n{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}monoid{\isaliteral{2E}{\isachardot}}pow{\isaliteral{5F}{\isacharunderscore}}nat\ append\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ n\ {\isaliteral{3D}{\isacharequal}}\ replicate\ n{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ n{\isacharparenright}\ auto\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ n{\isaliteral{29}{\isacharparenright}}\ auto\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
-\ intro{\isacharunderscore}locales%
+\ intro{\isaliteral{5F}{\isacharunderscore}}locales%
\endisatagquote
{\isafoldquote}%
%
@@ -928,22 +928,22 @@
%
\isatagquote
\isacommand{subclass}\isamarkupfalse%
-\ {\isacharparenleft}\isakeyword{in}\ group{\isacharparenright}\ monoid\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{in}\ group{\isaliteral{29}{\isacharparenright}}\ monoid\isanewline
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
\ x\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ invl\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x{\isasymdiv}\ {\isasymotimes}\ x\ {\isacharequal}\ {\isasymone}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x{\isaliteral{5C3C6469763E}{\isasymdiv}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6F6E653E}{\isasymone}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\ \ \isacommand{with}\isamarkupfalse%
-\ assoc\ {\isacharbrackleft}symmetric{\isacharbrackright}\ neutl\ invl\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x{\isasymdiv}\ {\isasymotimes}\ {\isacharparenleft}x\ {\isasymotimes}\ {\isasymone}{\isacharparenright}\ {\isacharequal}\ x{\isasymdiv}\ {\isasymotimes}\ x{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ assoc\ {\isaliteral{5B}{\isacharbrackleft}}symmetric{\isaliteral{5D}{\isacharbrackright}}\ neutl\ invl\ \isacommand{have}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x{\isaliteral{5C3C6469763E}{\isasymdiv}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{5C3C6F6E653E}{\isasymone}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{5C3C6469763E}{\isasymdiv}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\ \ \isacommand{with}\isamarkupfalse%
-\ left{\isacharunderscore}cancel\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymotimes}\ {\isasymone}\ {\isacharequal}\ x{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ left{\isaliteral{5F}{\isacharunderscore}}cancel\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -985,12 +985,12 @@
\end{picture}
\caption{Subclass relationship of monoids and groups:
before and after establishing the relationship
- \isa{group\ {\isasymsubseteq}\ monoid}; transitive edges are left out.}
+ \isa{group\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ monoid}; transitive edges are left out.}
\label{fig:subclass}
\end{center}
\end{figure}
- For illustration, a derived definition in \isa{group} using \isa{pow{\isacharunderscore}nat}%
+ For illustration, a derived definition in \isa{group} using \isa{pow{\isaliteral{5F}{\isacharunderscore}}nat}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -1000,10 +1000,10 @@
%
\isatagquote
\isacommand{definition}\isamarkupfalse%
-\ {\isacharparenleft}\isakeyword{in}\ group{\isacharparenright}\ pow{\isacharunderscore}int\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}int\ {\isasymRightarrow}\ {\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}pow{\isacharunderscore}int\ k\ x\ {\isacharequal}\ {\isacharparenleft}if\ k\ {\isachargreater}{\isacharequal}\ {\isadigit{0}}\isanewline
-\ \ \ \ then\ pow{\isacharunderscore}nat\ {\isacharparenleft}nat\ k{\isacharparenright}\ x\isanewline
-\ \ \ \ else\ {\isacharparenleft}pow{\isacharunderscore}nat\ {\isacharparenleft}nat\ {\isacharparenleft}{\isacharminus}\ k{\isacharparenright}{\isacharparenright}\ x{\isacharparenright}{\isasymdiv}{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{in}\ group{\isaliteral{29}{\isacharparenright}}\ pow{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}pow{\isaliteral{5F}{\isacharunderscore}}int\ k\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ k\ {\isaliteral{3E}{\isachargreater}}{\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\isanewline
+\ \ \ \ then\ pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}nat\ k{\isaliteral{29}{\isacharparenright}}\ x\isanewline
+\ \ \ \ else\ {\isaliteral{28}{\isacharparenleft}}pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}nat\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}\ k{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C6469763E}{\isasymdiv}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -1012,7 +1012,7 @@
\endisadelimquote
%
\begin{isamarkuptext}%
-\noindent yields the global definition of \isa{{\isachardoublequote}pow{\isacharunderscore}int\ {\isasymColon}\ int\ {\isasymRightarrow}\ {\isasymalpha}{\isasymColon}group\ {\isasymRightarrow}\ {\isasymalpha}{\isasymColon}group{\isachardoublequote}} with the corresponding theorem \isa{pow{\isacharunderscore}int\ k\ x\ {\isacharequal}\ {\isacharparenleft}if\ {\isadigit{0}}\ {\isasymle}\ k\ then\ pow{\isacharunderscore}nat\ {\isacharparenleft}nat\ k{\isacharparenright}\ x\ else\ {\isacharparenleft}pow{\isacharunderscore}nat\ {\isacharparenleft}nat\ {\isacharparenleft}{\isacharminus}\ k{\isacharparenright}{\isacharparenright}\ x{\isacharparenright}{\isasymdiv}{\isacharparenright}}.%
+\noindent yields the global definition of \isa{{\isaliteral{22}{\isachardoublequote}}pow{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}group\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}group{\isaliteral{22}{\isachardoublequote}}} with the corresponding theorem \isa{pow{\isaliteral{5F}{\isacharunderscore}}int\ k\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ {\isadigit{0}}\ {\isaliteral{5C3C6C653E}{\isasymle}}\ k\ then\ pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}nat\ k{\isaliteral{29}{\isacharparenright}}\ x\ else\ {\isaliteral{28}{\isacharparenleft}}pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}nat\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}\ k{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C6469763E}{\isasymdiv}}{\isaliteral{29}{\isacharparenright}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -1037,12 +1037,12 @@
\isakeyword{begin}\isanewline
\isanewline
\isacommand{term}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymotimes}\ y{\isachardoublequoteclose}\ %
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ %
\isamarkupcmt{example 1%
}
\isanewline
\isacommand{term}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}x{\isasymColon}nat{\isacharparenright}\ {\isasymotimes}\ y{\isachardoublequoteclose}\ %
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ %
\isamarkupcmt{example 2%
}
\isanewline
@@ -1051,7 +1051,7 @@
\isanewline
\isanewline
\isacommand{term}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymotimes}\ y{\isachardoublequoteclose}\ %
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ %
\isamarkupcmt{example 3%
}
%
@@ -1064,10 +1064,10 @@
%
\begin{isamarkuptext}%
\noindent Here in example 1, the term refers to the local class
- operation \isa{mult\ {\isacharbrackleft}{\isasymalpha}{\isacharbrackright}}, whereas in example 2 the type
- constraint enforces the global class operation \isa{mult\ {\isacharbrackleft}nat{\isacharbrackright}}.
+ operation \isa{mult\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5D}{\isacharbrackright}}}, whereas in example 2 the type
+ constraint enforces the global class operation \isa{mult\ {\isaliteral{5B}{\isacharbrackleft}}nat{\isaliteral{5D}{\isacharbrackright}}}.
In the global context in example 3, the reference is to the
- polymorphic global class operation \isa{mult\ {\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isasymColon}\ semigroup{\isacharbrackright}}.%
+ polymorphic global class operation \isa{mult\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ semigroup{\isaliteral{5D}{\isacharbrackright}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -1096,8 +1096,8 @@
%
\isatagquote
\isacommand{definition}\isamarkupfalse%
-\ example\ {\isacharcolon}{\isacharcolon}\ int\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}example\ {\isacharequal}\ pow{\isacharunderscore}int\ {\isadigit{1}}{\isadigit{0}}\ {\isacharparenleft}{\isacharminus}{\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}%
+\ example\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}example\ {\isaliteral{3D}{\isacharequal}}\ pow{\isaliteral{5F}{\isacharunderscore}}int\ {\isadigit{1}}{\isadigit{0}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -1130,68 +1130,68 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-module\ Example\ where\ {\isacharbraceleft}\isanewline
+module\ Example\ where\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
\isanewline
-data\ Nat\ {\isacharequal}\ Zero{\isacharunderscore}nat\ {\isacharbar}\ Suc\ Nat{\isacharsemicolon}\isanewline
+data\ Nat\ {\isaliteral{3D}{\isacharequal}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{7C}{\isacharbar}}\ Suc\ Nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-nat{\isacharunderscore}aux\ {\isacharcolon}{\isacharcolon}\ Integer\ {\isacharminus}{\isachargreater}\ Nat\ {\isacharminus}{\isachargreater}\ Nat{\isacharsemicolon}\isanewline
-nat{\isacharunderscore}aux\ i\ n\ {\isacharequal}\ {\isacharparenleft}if\ i\ {\isacharless}{\isacharequal}\ {\isadigit{0}}\ then\ n\ else\ nat{\isacharunderscore}aux\ {\isacharparenleft}i\ {\isacharminus}\ {\isadigit{1}}{\isacharparenright}\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline
+nat{\isaliteral{5F}{\isacharunderscore}}aux\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ Integer\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+nat{\isaliteral{5F}{\isacharunderscore}}aux\ i\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ i\ {\isaliteral{3C}{\isacharless}}{\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\ then\ n\ else\ nat{\isaliteral{5F}{\isacharunderscore}}aux\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-nat\ {\isacharcolon}{\isacharcolon}\ Integer\ {\isacharminus}{\isachargreater}\ Nat{\isacharsemicolon}\isanewline
-nat\ i\ {\isacharequal}\ nat{\isacharunderscore}aux\ i\ Zero{\isacharunderscore}nat{\isacharsemicolon}\isanewline
+nat\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ Integer\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+nat\ i\ {\isaliteral{3D}{\isacharequal}}\ nat{\isaliteral{5F}{\isacharunderscore}}aux\ i\ Zero{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-class\ Semigroup\ a\ where\ {\isacharbraceleft}\isanewline
-\ \ mult\ {\isacharcolon}{\isacharcolon}\ a\ {\isacharminus}{\isachargreater}\ a\ {\isacharminus}{\isachargreater}\ a{\isacharsemicolon}\isanewline
-{\isacharbraceright}{\isacharsemicolon}\isanewline
+class\ Semigroup\ a\ where\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ mult\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-class\ {\isacharparenleft}Semigroup\ a{\isacharparenright}\ {\isacharequal}{\isachargreater}\ Monoidl\ a\ where\ {\isacharbraceleft}\isanewline
-\ \ neutral\ {\isacharcolon}{\isacharcolon}\ a{\isacharsemicolon}\isanewline
-{\isacharbraceright}{\isacharsemicolon}\isanewline
+class\ {\isaliteral{28}{\isacharparenleft}}Semigroup\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ Monoidl\ a\ where\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ neutral\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-class\ {\isacharparenleft}Monoidl\ a{\isacharparenright}\ {\isacharequal}{\isachargreater}\ Monoid\ a\ where\ {\isacharbraceleft}\isanewline
-{\isacharbraceright}{\isacharsemicolon}\isanewline
+class\ {\isaliteral{28}{\isacharparenleft}}Monoidl\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ Monoid\ a\ where\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-class\ {\isacharparenleft}Monoid\ a{\isacharparenright}\ {\isacharequal}{\isachargreater}\ Group\ a\ where\ {\isacharbraceleft}\isanewline
-\ \ inverse\ {\isacharcolon}{\isacharcolon}\ a\ {\isacharminus}{\isachargreater}\ a{\isacharsemicolon}\isanewline
-{\isacharbraceright}{\isacharsemicolon}\isanewline
+class\ {\isaliteral{28}{\isacharparenleft}}Monoid\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ Group\ a\ where\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ inverse\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-pow{\isacharunderscore}nat\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ {\isacharparenleft}Monoid\ a{\isacharparenright}\ {\isacharequal}{\isachargreater}\ Nat\ {\isacharminus}{\isachargreater}\ a\ {\isacharminus}{\isachargreater}\ a{\isacharsemicolon}\isanewline
-pow{\isacharunderscore}nat\ Zero{\isacharunderscore}nat\ x\ {\isacharequal}\ neutral{\isacharsemicolon}\isanewline
-pow{\isacharunderscore}nat\ {\isacharparenleft}Suc\ n{\isacharparenright}\ x\ {\isacharequal}\ mult\ x\ {\isacharparenleft}pow{\isacharunderscore}nat\ n\ x{\isacharparenright}{\isacharsemicolon}\isanewline
+pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}Monoid\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ Nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+pow{\isaliteral{5F}{\isacharunderscore}}nat\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ x\ {\isaliteral{3D}{\isacharequal}}\ neutral{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ x\ {\isaliteral{3D}{\isacharequal}}\ mult\ x\ {\isaliteral{28}{\isacharparenleft}}pow{\isaliteral{5F}{\isacharunderscore}}nat\ n\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-pow{\isacharunderscore}int\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ {\isacharparenleft}Group\ a{\isacharparenright}\ {\isacharequal}{\isachargreater}\ Integer\ {\isacharminus}{\isachargreater}\ a\ {\isacharminus}{\isachargreater}\ a{\isacharsemicolon}\isanewline
-pow{\isacharunderscore}int\ k\ x\ {\isacharequal}\isanewline
-\ \ {\isacharparenleft}if\ {\isadigit{0}}\ {\isacharless}{\isacharequal}\ k\ then\ pow{\isacharunderscore}nat\ {\isacharparenleft}nat\ k{\isacharparenright}\ x\isanewline
-\ \ \ \ else\ inverse\ {\isacharparenleft}pow{\isacharunderscore}nat\ {\isacharparenleft}nat\ {\isacharparenleft}negate\ k{\isacharparenright}{\isacharparenright}\ x{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline
+pow{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}Group\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ Integer\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+pow{\isaliteral{5F}{\isacharunderscore}}int\ k\ x\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}if\ {\isadigit{0}}\ {\isaliteral{3C}{\isacharless}}{\isaliteral{3D}{\isacharequal}}\ k\ then\ pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}nat\ k{\isaliteral{29}{\isacharparenright}}\ x\isanewline
+\ \ \ \ else\ inverse\ {\isaliteral{28}{\isacharparenleft}}pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}nat\ {\isaliteral{28}{\isacharparenleft}}negate\ k{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-mult{\isacharunderscore}int\ {\isacharcolon}{\isacharcolon}\ Integer\ {\isacharminus}{\isachargreater}\ Integer\ {\isacharminus}{\isachargreater}\ Integer{\isacharsemicolon}\isanewline
-mult{\isacharunderscore}int\ i\ j\ {\isacharequal}\ i\ {\isacharplus}\ j{\isacharsemicolon}\isanewline
+mult{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ Integer\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Integer\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Integer{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+mult{\isaliteral{5F}{\isacharunderscore}}int\ i\ j\ {\isaliteral{3D}{\isacharequal}}\ i\ {\isaliteral{2B}{\isacharplus}}\ j{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-instance\ Semigroup\ Integer\ where\ {\isacharbraceleft}\isanewline
-\ \ mult\ {\isacharequal}\ mult{\isacharunderscore}int{\isacharsemicolon}\isanewline
-{\isacharbraceright}{\isacharsemicolon}\isanewline
+instance\ Semigroup\ Integer\ where\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ mult\ {\isaliteral{3D}{\isacharequal}}\ mult{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-neutral{\isacharunderscore}int\ {\isacharcolon}{\isacharcolon}\ Integer{\isacharsemicolon}\isanewline
-neutral{\isacharunderscore}int\ {\isacharequal}\ {\isadigit{0}}{\isacharsemicolon}\isanewline
+neutral{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ Integer{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+neutral{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-instance\ Monoidl\ Integer\ where\ {\isacharbraceleft}\isanewline
-\ \ neutral\ {\isacharequal}\ neutral{\isacharunderscore}int{\isacharsemicolon}\isanewline
-{\isacharbraceright}{\isacharsemicolon}\isanewline
+instance\ Monoidl\ Integer\ where\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ neutral\ {\isaliteral{3D}{\isacharequal}}\ neutral{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-instance\ Monoid\ Integer\ where\ {\isacharbraceleft}\isanewline
-{\isacharbraceright}{\isacharsemicolon}\isanewline
+instance\ Monoid\ Integer\ where\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-inverse{\isacharunderscore}int\ {\isacharcolon}{\isacharcolon}\ Integer\ {\isacharminus}{\isachargreater}\ Integer{\isacharsemicolon}\isanewline
-inverse{\isacharunderscore}int\ i\ {\isacharequal}\ negate\ i{\isacharsemicolon}\isanewline
+inverse{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ Integer\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Integer{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+inverse{\isaliteral{5F}{\isacharunderscore}}int\ i\ {\isaliteral{3D}{\isacharequal}}\ negate\ i{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-instance\ Group\ Integer\ where\ {\isacharbraceleft}\isanewline
-\ \ inverse\ {\isacharequal}\ inverse{\isacharunderscore}int{\isacharsemicolon}\isanewline
-{\isacharbraceright}{\isacharsemicolon}\isanewline
+instance\ Group\ Integer\ where\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ inverse\ {\isaliteral{3D}{\isacharequal}}\ inverse{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-example\ {\isacharcolon}{\isacharcolon}\ Integer{\isacharsemicolon}\isanewline
-example\ {\isacharequal}\ pow{\isacharunderscore}int\ {\isadigit{1}}{\isadigit{0}}\ {\isacharparenleft}{\isacharminus}{\isadigit{2}}{\isacharparenright}{\isacharsemicolon}\isanewline
+example\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ Integer{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+example\ {\isaliteral{3D}{\isacharequal}}\ pow{\isaliteral{5F}{\isacharunderscore}}int\ {\isadigit{1}}{\isadigit{0}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-{\isacharbraceright}\isanewline%
+{\isaliteral{7D}{\isacharbraceright}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -1214,84 +1214,84 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-structure\ Example\ {\isacharcolon}\ sig\isanewline
-\ \ datatype\ nat\ {\isacharequal}\ Zero{\isacharunderscore}nat\ {\isacharbar}\ Suc\ of\ nat\isanewline
-\ \ val\ nat{\isacharunderscore}aux\ {\isacharcolon}\ IntInf{\isachardot}int\ {\isacharminus}{\isachargreater}\ nat\ {\isacharminus}{\isachargreater}\ nat\isanewline
-\ \ val\ nat\ {\isacharcolon}\ IntInf{\isachardot}int\ {\isacharminus}{\isachargreater}\ nat\isanewline
-\ \ type\ {\isacharprime}a\ semigroup\isanewline
-\ \ val\ mult\ {\isacharcolon}\ {\isacharprime}a\ semigroup\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\isanewline
-\ \ type\ {\isacharprime}a\ monoidl\isanewline
-\ \ val\ semigroup{\isacharunderscore}monoidl\ {\isacharcolon}\ {\isacharprime}a\ monoidl\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ semigroup\isanewline
-\ \ val\ neutral\ {\isacharcolon}\ {\isacharprime}a\ monoidl\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\isanewline
-\ \ type\ {\isacharprime}a\ monoid\isanewline
-\ \ val\ monoidl{\isacharunderscore}monoid\ {\isacharcolon}\ {\isacharprime}a\ monoid\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ monoidl\isanewline
-\ \ type\ {\isacharprime}a\ group\isanewline
-\ \ val\ monoid{\isacharunderscore}group\ {\isacharcolon}\ {\isacharprime}a\ group\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ monoid\isanewline
-\ \ val\ inverse\ {\isacharcolon}\ {\isacharprime}a\ group\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\isanewline
-\ \ val\ pow{\isacharunderscore}nat\ {\isacharcolon}\ {\isacharprime}a\ monoid\ {\isacharminus}{\isachargreater}\ nat\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\isanewline
-\ \ val\ pow{\isacharunderscore}int\ {\isacharcolon}\ {\isacharprime}a\ group\ {\isacharminus}{\isachargreater}\ IntInf{\isachardot}int\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\isanewline
-\ \ val\ mult{\isacharunderscore}int\ {\isacharcolon}\ IntInf{\isachardot}int\ {\isacharminus}{\isachargreater}\ IntInf{\isachardot}int\ {\isacharminus}{\isachargreater}\ IntInf{\isachardot}int\isanewline
-\ \ val\ semigroup{\isacharunderscore}int\ {\isacharcolon}\ IntInf{\isachardot}int\ semigroup\isanewline
-\ \ val\ neutral{\isacharunderscore}int\ {\isacharcolon}\ IntInf{\isachardot}int\isanewline
-\ \ val\ monoidl{\isacharunderscore}int\ {\isacharcolon}\ IntInf{\isachardot}int\ monoidl\isanewline
-\ \ val\ monoid{\isacharunderscore}int\ {\isacharcolon}\ IntInf{\isachardot}int\ monoid\isanewline
-\ \ val\ inverse{\isacharunderscore}int\ {\isacharcolon}\ IntInf{\isachardot}int\ {\isacharminus}{\isachargreater}\ IntInf{\isachardot}int\isanewline
-\ \ val\ group{\isacharunderscore}int\ {\isacharcolon}\ IntInf{\isachardot}int\ group\isanewline
-\ \ val\ example\ {\isacharcolon}\ IntInf{\isachardot}int\isanewline
-end\ {\isacharequal}\ struct\isanewline
+structure\ Example\ {\isaliteral{3A}{\isacharcolon}}\ sig\isanewline
+\ \ datatype\ nat\ {\isaliteral{3D}{\isacharequal}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{7C}{\isacharbar}}\ Suc\ of\ nat\isanewline
+\ \ val\ nat{\isaliteral{5F}{\isacharunderscore}}aux\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\isanewline
+\ \ val\ nat\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\isanewline
+\ \ type\ {\isaliteral{27}{\isacharprime}}a\ semigroup\isanewline
+\ \ val\ mult\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ semigroup\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\isanewline
+\ \ type\ {\isaliteral{27}{\isacharprime}}a\ monoidl\isanewline
+\ \ val\ semigroup{\isaliteral{5F}{\isacharunderscore}}monoidl\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ monoidl\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ semigroup\isanewline
+\ \ val\ neutral\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ monoidl\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\isanewline
+\ \ type\ {\isaliteral{27}{\isacharprime}}a\ monoid\isanewline
+\ \ val\ monoidl{\isaliteral{5F}{\isacharunderscore}}monoid\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ monoid\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ monoidl\isanewline
+\ \ type\ {\isaliteral{27}{\isacharprime}}a\ group\isanewline
+\ \ val\ monoid{\isaliteral{5F}{\isacharunderscore}}group\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ group\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ monoid\isanewline
+\ \ val\ inverse\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ group\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\isanewline
+\ \ val\ pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ monoid\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\isanewline
+\ \ val\ pow{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ group\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ IntInf{\isaliteral{2E}{\isachardot}}int\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\isanewline
+\ \ val\ mult{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ IntInf{\isaliteral{2E}{\isachardot}}int\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ IntInf{\isaliteral{2E}{\isachardot}}int\isanewline
+\ \ val\ semigroup{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int\ semigroup\isanewline
+\ \ val\ neutral{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int\isanewline
+\ \ val\ monoidl{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int\ monoidl\isanewline
+\ \ val\ monoid{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int\ monoid\isanewline
+\ \ val\ inverse{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ IntInf{\isaliteral{2E}{\isachardot}}int\isanewline
+\ \ val\ group{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int\ group\isanewline
+\ \ val\ example\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int\isanewline
+end\ {\isaliteral{3D}{\isacharequal}}\ struct\isanewline
\isanewline
-datatype\ nat\ {\isacharequal}\ Zero{\isacharunderscore}nat\ {\isacharbar}\ Suc\ of\ nat{\isacharsemicolon}\isanewline
+datatype\ nat\ {\isaliteral{3D}{\isacharequal}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{7C}{\isacharbar}}\ Suc\ of\ nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ nat{\isacharunderscore}aux\ i\ n\ {\isacharequal}\isanewline
-\ \ {\isacharparenleft}if\ IntInf{\isachardot}{\isacharless}{\isacharequal}\ {\isacharparenleft}i{\isacharcomma}\ {\isacharparenleft}{\isadigit{0}}\ {\isacharcolon}\ IntInf{\isachardot}int{\isacharparenright}{\isacharparenright}\ then\ n\isanewline
-\ \ \ \ else\ nat{\isacharunderscore}aux\ {\isacharparenleft}IntInf{\isachardot}{\isacharminus}\ {\isacharparenleft}i{\isacharcomma}\ {\isacharparenleft}{\isadigit{1}}\ {\isacharcolon}\ IntInf{\isachardot}int{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline
+fun\ nat{\isaliteral{5F}{\isacharunderscore}}aux\ i\ n\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}if\ IntInf{\isaliteral{2E}{\isachardot}}{\isaliteral{3C}{\isacharless}}{\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}i{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ then\ n\isanewline
+\ \ \ \ else\ nat{\isaliteral{5F}{\isacharunderscore}}aux\ {\isaliteral{28}{\isacharparenleft}}IntInf{\isaliteral{2E}{\isachardot}}{\isaliteral{2D}{\isacharminus}}\ {\isaliteral{28}{\isacharparenleft}}i{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ nat\ i\ {\isacharequal}\ nat{\isacharunderscore}aux\ i\ Zero{\isacharunderscore}nat{\isacharsemicolon}\isanewline
+fun\ nat\ i\ {\isaliteral{3D}{\isacharequal}}\ nat{\isaliteral{5F}{\isacharunderscore}}aux\ i\ Zero{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-type\ {\isacharprime}a\ semigroup\ {\isacharequal}\ {\isacharbraceleft}mult\ {\isacharcolon}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a{\isacharbraceright}{\isacharsemicolon}\isanewline
-val\ mult\ {\isacharequal}\ {\isacharhash}mult\ {\isacharcolon}\ {\isacharprime}a\ semigroup\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a{\isacharsemicolon}\isanewline
+type\ {\isaliteral{27}{\isacharprime}}a\ semigroup\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}mult\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+val\ mult\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{23}{\isacharhash}}mult\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ semigroup\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-type\ {\isacharprime}a\ monoidl\ {\isacharequal}\ {\isacharbraceleft}semigroup{\isacharunderscore}monoidl\ {\isacharcolon}\ {\isacharprime}a\ semigroup{\isacharcomma}\ neutral\ {\isacharcolon}\ {\isacharprime}a{\isacharbraceright}{\isacharsemicolon}\isanewline
-val\ semigroup{\isacharunderscore}monoidl\ {\isacharequal}\ {\isacharhash}semigroup{\isacharunderscore}monoidl\ {\isacharcolon}\ {\isacharprime}a\ monoidl\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ semigroup{\isacharsemicolon}\isanewline
-val\ neutral\ {\isacharequal}\ {\isacharhash}neutral\ {\isacharcolon}\ {\isacharprime}a\ monoidl\ {\isacharminus}{\isachargreater}\ {\isacharprime}a{\isacharsemicolon}\isanewline
+type\ {\isaliteral{27}{\isacharprime}}a\ monoidl\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}semigroup{\isaliteral{5F}{\isacharunderscore}}monoidl\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ semigroup{\isaliteral{2C}{\isacharcomma}}\ neutral\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+val\ semigroup{\isaliteral{5F}{\isacharunderscore}}monoidl\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{23}{\isacharhash}}semigroup{\isaliteral{5F}{\isacharunderscore}}monoidl\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ monoidl\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ semigroup{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+val\ neutral\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{23}{\isacharhash}}neutral\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ monoidl\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-type\ {\isacharprime}a\ monoid\ {\isacharequal}\ {\isacharbraceleft}monoidl{\isacharunderscore}monoid\ {\isacharcolon}\ {\isacharprime}a\ monoidl{\isacharbraceright}{\isacharsemicolon}\isanewline
-val\ monoidl{\isacharunderscore}monoid\ {\isacharequal}\ {\isacharhash}monoidl{\isacharunderscore}monoid\ {\isacharcolon}\ {\isacharprime}a\ monoid\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ monoidl{\isacharsemicolon}\isanewline
+type\ {\isaliteral{27}{\isacharprime}}a\ monoid\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}monoidl{\isaliteral{5F}{\isacharunderscore}}monoid\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ monoidl{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+val\ monoidl{\isaliteral{5F}{\isacharunderscore}}monoid\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{23}{\isacharhash}}monoidl{\isaliteral{5F}{\isacharunderscore}}monoid\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ monoid\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ monoidl{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-type\ {\isacharprime}a\ group\ {\isacharequal}\ {\isacharbraceleft}monoid{\isacharunderscore}group\ {\isacharcolon}\ {\isacharprime}a\ monoid{\isacharcomma}\ inverse\ {\isacharcolon}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a{\isacharbraceright}{\isacharsemicolon}\isanewline
-val\ monoid{\isacharunderscore}group\ {\isacharequal}\ {\isacharhash}monoid{\isacharunderscore}group\ {\isacharcolon}\ {\isacharprime}a\ group\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ monoid{\isacharsemicolon}\isanewline
-val\ inverse\ {\isacharequal}\ {\isacharhash}inverse\ {\isacharcolon}\ {\isacharprime}a\ group\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a{\isacharsemicolon}\isanewline
+type\ {\isaliteral{27}{\isacharprime}}a\ group\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}monoid{\isaliteral{5F}{\isacharunderscore}}group\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ monoid{\isaliteral{2C}{\isacharcomma}}\ inverse\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+val\ monoid{\isaliteral{5F}{\isacharunderscore}}group\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{23}{\isacharhash}}monoid{\isaliteral{5F}{\isacharunderscore}}group\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ group\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ monoid{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+val\ inverse\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{23}{\isacharhash}}inverse\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ group\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ pow{\isacharunderscore}nat\ A{\isacharunderscore}\ Zero{\isacharunderscore}nat\ x\ {\isacharequal}\ neutral\ {\isacharparenleft}monoidl{\isacharunderscore}monoid\ A{\isacharunderscore}{\isacharparenright}\isanewline
-\ \ {\isacharbar}\ pow{\isacharunderscore}nat\ A{\isacharunderscore}\ {\isacharparenleft}Suc\ n{\isacharparenright}\ x\ {\isacharequal}\isanewline
-\ \ \ \ mult\ {\isacharparenleft}{\isacharparenleft}semigroup{\isacharunderscore}monoidl\ o\ monoidl{\isacharunderscore}monoid{\isacharparenright}\ A{\isacharunderscore}{\isacharparenright}\ x\ {\isacharparenleft}pow{\isacharunderscore}nat\ A{\isacharunderscore}\ n\ x{\isacharparenright}{\isacharsemicolon}\isanewline
+fun\ pow{\isaliteral{5F}{\isacharunderscore}}nat\ A{\isaliteral{5F}{\isacharunderscore}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ x\ {\isaliteral{3D}{\isacharequal}}\ neutral\ {\isaliteral{28}{\isacharparenleft}}monoidl{\isaliteral{5F}{\isacharunderscore}}monoid\ A{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ pow{\isaliteral{5F}{\isacharunderscore}}nat\ A{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ x\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ mult\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}semigroup{\isaliteral{5F}{\isacharunderscore}}monoidl\ o\ monoidl{\isaliteral{5F}{\isacharunderscore}}monoid{\isaliteral{29}{\isacharparenright}}\ A{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ x\ {\isaliteral{28}{\isacharparenleft}}pow{\isaliteral{5F}{\isacharunderscore}}nat\ A{\isaliteral{5F}{\isacharunderscore}}\ n\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ pow{\isacharunderscore}int\ A{\isacharunderscore}\ k\ x\ {\isacharequal}\isanewline
-\ \ {\isacharparenleft}if\ IntInf{\isachardot}{\isacharless}{\isacharequal}\ {\isacharparenleft}{\isacharparenleft}{\isadigit{0}}\ {\isacharcolon}\ IntInf{\isachardot}int{\isacharparenright}{\isacharcomma}\ k{\isacharparenright}\isanewline
-\ \ \ \ then\ pow{\isacharunderscore}nat\ {\isacharparenleft}monoid{\isacharunderscore}group\ A{\isacharunderscore}{\isacharparenright}\ {\isacharparenleft}nat\ k{\isacharparenright}\ x\isanewline
-\ \ \ \ else\ inverse\ A{\isacharunderscore}\ {\isacharparenleft}pow{\isacharunderscore}nat\ {\isacharparenleft}monoid{\isacharunderscore}group\ A{\isacharunderscore}{\isacharparenright}\ {\isacharparenleft}nat\ {\isacharparenleft}IntInf{\isachardot}{\isachartilde}\ k{\isacharparenright}{\isacharparenright}\ x{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline
+fun\ pow{\isaliteral{5F}{\isacharunderscore}}int\ A{\isaliteral{5F}{\isacharunderscore}}\ k\ x\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}if\ IntInf{\isaliteral{2E}{\isachardot}}{\isaliteral{3C}{\isacharless}}{\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ k{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ then\ pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}monoid{\isaliteral{5F}{\isacharunderscore}}group\ A{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}nat\ k{\isaliteral{29}{\isacharparenright}}\ x\isanewline
+\ \ \ \ else\ inverse\ A{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{28}{\isacharparenleft}}pow{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}monoid{\isaliteral{5F}{\isacharunderscore}}group\ A{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}nat\ {\isaliteral{28}{\isacharparenleft}}IntInf{\isaliteral{2E}{\isachardot}}{\isaliteral{7E}{\isachartilde}}\ k{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ mult{\isacharunderscore}int\ i\ j\ {\isacharequal}\ IntInf{\isachardot}{\isacharplus}\ {\isacharparenleft}i{\isacharcomma}\ j{\isacharparenright}{\isacharsemicolon}\isanewline
+fun\ mult{\isaliteral{5F}{\isacharunderscore}}int\ i\ j\ {\isaliteral{3D}{\isacharequal}}\ IntInf{\isaliteral{2E}{\isachardot}}{\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}i{\isaliteral{2C}{\isacharcomma}}\ j{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-val\ semigroup{\isacharunderscore}int\ {\isacharequal}\ {\isacharbraceleft}mult\ {\isacharequal}\ mult{\isacharunderscore}int{\isacharbraceright}\ {\isacharcolon}\ IntInf{\isachardot}int\ semigroup{\isacharsemicolon}\isanewline
+val\ semigroup{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}mult\ {\isaliteral{3D}{\isacharequal}}\ mult{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{7D}{\isacharbraceright}}\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int\ semigroup{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-val\ neutral{\isacharunderscore}int\ {\isacharcolon}\ IntInf{\isachardot}int\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}\ {\isacharcolon}\ IntInf{\isachardot}int{\isacharparenright}{\isacharsemicolon}\isanewline
+val\ neutral{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-val\ monoidl{\isacharunderscore}int\ {\isacharequal}\isanewline
-\ \ {\isacharbraceleft}semigroup{\isacharunderscore}monoidl\ {\isacharequal}\ semigroup{\isacharunderscore}int{\isacharcomma}\ neutral\ {\isacharequal}\ neutral{\isacharunderscore}int{\isacharbraceright}\ {\isacharcolon}\isanewline
-\ \ IntInf{\isachardot}int\ monoidl{\isacharsemicolon}\isanewline
+val\ monoidl{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ {\isaliteral{7B}{\isacharbraceleft}}semigroup{\isaliteral{5F}{\isacharunderscore}}monoidl\ {\isaliteral{3D}{\isacharequal}}\ semigroup{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{2C}{\isacharcomma}}\ neutral\ {\isaliteral{3D}{\isacharequal}}\ neutral{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{7D}{\isacharbraceright}}\ {\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ IntInf{\isaliteral{2E}{\isachardot}}int\ monoidl{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-val\ monoid{\isacharunderscore}int\ {\isacharequal}\ {\isacharbraceleft}monoidl{\isacharunderscore}monoid\ {\isacharequal}\ monoidl{\isacharunderscore}int{\isacharbraceright}\ {\isacharcolon}\ IntInf{\isachardot}int\ monoid{\isacharsemicolon}\isanewline
+val\ monoid{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}monoidl{\isaliteral{5F}{\isacharunderscore}}monoid\ {\isaliteral{3D}{\isacharequal}}\ monoidl{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{7D}{\isacharbraceright}}\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int\ monoid{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ inverse{\isacharunderscore}int\ i\ {\isacharequal}\ IntInf{\isachardot}{\isachartilde}\ i{\isacharsemicolon}\isanewline
+fun\ inverse{\isaliteral{5F}{\isacharunderscore}}int\ i\ {\isaliteral{3D}{\isacharequal}}\ IntInf{\isaliteral{2E}{\isachardot}}{\isaliteral{7E}{\isachartilde}}\ i{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-val\ group{\isacharunderscore}int\ {\isacharequal}\ {\isacharbraceleft}monoid{\isacharunderscore}group\ {\isacharequal}\ monoid{\isacharunderscore}int{\isacharcomma}\ inverse\ {\isacharequal}\ inverse{\isacharunderscore}int{\isacharbraceright}\ {\isacharcolon}\isanewline
-\ \ IntInf{\isachardot}int\ group{\isacharsemicolon}\isanewline
+val\ group{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}monoid{\isaliteral{5F}{\isacharunderscore}}group\ {\isaliteral{3D}{\isacharequal}}\ monoid{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{2C}{\isacharcomma}}\ inverse\ {\isaliteral{3D}{\isacharequal}}\ inverse{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{7D}{\isacharbraceright}}\ {\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ IntInf{\isaliteral{2E}{\isachardot}}int\ group{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-val\ example\ {\isacharcolon}\ IntInf{\isachardot}int\ {\isacharequal}\isanewline
-\ \ pow{\isacharunderscore}int\ group{\isacharunderscore}int\ {\isacharparenleft}{\isadigit{1}}{\isadigit{0}}\ {\isacharcolon}\ IntInf{\isachardot}int{\isacharparenright}\ {\isacharparenleft}{\isachartilde}{\isadigit{2}}\ {\isacharcolon}\ IntInf{\isachardot}int{\isacharparenright}{\isacharsemicolon}\isanewline
+val\ example\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ pow{\isaliteral{5F}{\isacharunderscore}}int\ group{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isadigit{0}}\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{7E}{\isachartilde}}{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}\ IntInf{\isaliteral{2E}{\isachardot}}int{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-end{\isacharsemicolon}\ {\isacharparenleft}{\isacharasterisk}struct\ Example{\isacharasterisk}{\isacharparenright}\isanewline%
+end{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}struct\ Example{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -1327,74 +1327,74 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-object\ Example\ {\isacharbraceleft}\isanewline
+object\ Example\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
\isanewline
abstract\ sealed\ class\ nat\isanewline
-final\ case\ object\ Zero{\isacharunderscore}nat\ extends\ nat\isanewline
-final\ case\ class\ Suc{\isacharparenleft}a{\isacharcolon}\ nat{\isacharparenright}\ extends\ nat\isanewline
+final\ case\ object\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ extends\ nat\isanewline
+final\ case\ class\ Suc{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{29}{\isacharparenright}}\ extends\ nat\isanewline
\isanewline
-def\ nat{\isacharunderscore}aux{\isacharparenleft}i{\isacharcolon}\ BigInt{\isacharcomma}\ n{\isacharcolon}\ nat{\isacharparenright}{\isacharcolon}\ nat\ {\isacharequal}\isanewline
-\ \ {\isacharparenleft}if\ {\isacharparenleft}i\ {\isacharless}{\isacharequal}\ BigInt{\isacharparenleft}{\isadigit{0}}{\isacharparenright}{\isacharparenright}\ n\ else\ nat{\isacharunderscore}aux{\isacharparenleft}i\ {\isacharminus}\ BigInt{\isacharparenleft}{\isadigit{1}}{\isacharparenright}{\isacharcomma}\ Suc{\isacharparenleft}n{\isacharparenright}{\isacharparenright}{\isacharparenright}\isanewline
+def\ nat{\isaliteral{5F}{\isacharunderscore}}aux{\isaliteral{28}{\isacharparenleft}}i{\isaliteral{3A}{\isacharcolon}}\ BigInt{\isaliteral{2C}{\isacharcomma}}\ n{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}if\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{3C}{\isacharless}}{\isaliteral{3D}{\isacharequal}}\ BigInt{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ n\ else\ nat{\isaliteral{5F}{\isacharunderscore}}aux{\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{2D}{\isacharminus}}\ BigInt{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ Suc{\isaliteral{28}{\isacharparenleft}}n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
-def\ nat{\isacharparenleft}i{\isacharcolon}\ BigInt{\isacharparenright}{\isacharcolon}\ nat\ {\isacharequal}\ nat{\isacharunderscore}aux{\isacharparenleft}i{\isacharcomma}\ Zero{\isacharunderscore}nat{\isacharparenright}\isanewline
+def\ nat{\isaliteral{28}{\isacharparenleft}}i{\isaliteral{3A}{\isacharcolon}}\ BigInt{\isaliteral{29}{\isacharparenright}}{\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{3D}{\isacharequal}}\ nat{\isaliteral{5F}{\isacharunderscore}}aux{\isaliteral{28}{\isacharparenleft}}i{\isaliteral{2C}{\isacharcomma}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
-trait\ semigroup{\isacharbrackleft}A{\isacharbrackright}\ {\isacharbraceleft}\isanewline
-\ \ val\ {\isacharbackquote}Example{\isachardot}mult{\isacharbackquote}{\isacharcolon}\ {\isacharparenleft}A{\isacharcomma}\ A{\isacharparenright}\ {\isacharequal}{\isachargreater}\ A\isanewline
-{\isacharbraceright}\isanewline
-def\ mult{\isacharbrackleft}A{\isacharbrackright}{\isacharparenleft}a{\isacharcolon}\ A{\isacharcomma}\ b{\isacharcolon}\ A{\isacharparenright}{\isacharparenleft}implicit\ A{\isacharcolon}\ semigroup{\isacharbrackleft}A{\isacharbrackright}{\isacharparenright}{\isacharcolon}\ A\ {\isacharequal}\isanewline
-\ \ A{\isachardot}{\isacharbackquote}Example{\isachardot}mult{\isacharbackquote}{\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\isanewline
+trait\ semigroup{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ val\ {\isaliteral{60}{\isacharbackquote}}Example{\isaliteral{2E}{\isachardot}}mult{\isaliteral{60}{\isacharbackquote}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}A{\isaliteral{2C}{\isacharcomma}}\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ A\isanewline
+{\isaliteral{7D}{\isacharbraceright}}\isanewline
+def\ mult{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{28}{\isacharparenleft}}implicit\ A{\isaliteral{3A}{\isacharcolon}}\ semigroup{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3A}{\isacharcolon}}\ A\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ A{\isaliteral{2E}{\isachardot}}{\isaliteral{60}{\isacharbackquote}}Example{\isaliteral{2E}{\isachardot}}mult{\isaliteral{60}{\isacharbackquote}}{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
-trait\ monoidl{\isacharbrackleft}A{\isacharbrackright}\ extends\ semigroup{\isacharbrackleft}A{\isacharbrackright}\ {\isacharbraceleft}\isanewline
-\ \ val\ {\isacharbackquote}Example{\isachardot}neutral{\isacharbackquote}{\isacharcolon}\ A\isanewline
-{\isacharbraceright}\isanewline
-def\ neutral{\isacharbrackleft}A{\isacharbrackright}{\isacharparenleft}implicit\ A{\isacharcolon}\ monoidl{\isacharbrackleft}A{\isacharbrackright}{\isacharparenright}{\isacharcolon}\ A\ {\isacharequal}\ A{\isachardot}{\isacharbackquote}Example{\isachardot}neutral{\isacharbackquote}\isanewline
+trait\ monoidl{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}\ extends\ semigroup{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ val\ {\isaliteral{60}{\isacharbackquote}}Example{\isaliteral{2E}{\isachardot}}neutral{\isaliteral{60}{\isacharbackquote}}{\isaliteral{3A}{\isacharcolon}}\ A\isanewline
+{\isaliteral{7D}{\isacharbraceright}}\isanewline
+def\ neutral{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{28}{\isacharparenleft}}implicit\ A{\isaliteral{3A}{\isacharcolon}}\ monoidl{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3A}{\isacharcolon}}\ A\ {\isaliteral{3D}{\isacharequal}}\ A{\isaliteral{2E}{\isachardot}}{\isaliteral{60}{\isacharbackquote}}Example{\isaliteral{2E}{\isachardot}}neutral{\isaliteral{60}{\isacharbackquote}}\isanewline
\isanewline
-trait\ monoid{\isacharbrackleft}A{\isacharbrackright}\ extends\ monoidl{\isacharbrackleft}A{\isacharbrackright}\ {\isacharbraceleft}\isanewline
-{\isacharbraceright}\isanewline
+trait\ monoid{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}\ extends\ monoidl{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}\isanewline
\isanewline
-trait\ group{\isacharbrackleft}A{\isacharbrackright}\ extends\ monoid{\isacharbrackleft}A{\isacharbrackright}\ {\isacharbraceleft}\isanewline
-\ \ val\ {\isacharbackquote}Example{\isachardot}inverse{\isacharbackquote}{\isacharcolon}\ A\ {\isacharequal}{\isachargreater}\ A\isanewline
-{\isacharbraceright}\isanewline
-def\ inverse{\isacharbrackleft}A{\isacharbrackright}{\isacharparenleft}a{\isacharcolon}\ A{\isacharparenright}{\isacharparenleft}implicit\ A{\isacharcolon}\ group{\isacharbrackleft}A{\isacharbrackright}{\isacharparenright}{\isacharcolon}\ A\ {\isacharequal}\ A{\isachardot}{\isacharbackquote}Example{\isachardot}inverse{\isacharbackquote}{\isacharparenleft}a{\isacharparenright}\isanewline
+trait\ group{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}\ extends\ monoid{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ val\ {\isaliteral{60}{\isacharbackquote}}Example{\isaliteral{2E}{\isachardot}}inverse{\isaliteral{60}{\isacharbackquote}}{\isaliteral{3A}{\isacharcolon}}\ A\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ A\isanewline
+{\isaliteral{7D}{\isacharbraceright}}\isanewline
+def\ inverse{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{28}{\isacharparenleft}}implicit\ A{\isaliteral{3A}{\isacharcolon}}\ group{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3A}{\isacharcolon}}\ A\ {\isaliteral{3D}{\isacharequal}}\ A{\isaliteral{2E}{\isachardot}}{\isaliteral{60}{\isacharbackquote}}Example{\isaliteral{2E}{\isachardot}}inverse{\isaliteral{60}{\isacharbackquote}}{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
-def\ pow{\isacharunderscore}nat{\isacharbrackleft}A{\isacharcolon}\ monoid{\isacharbrackright}{\isacharparenleft}xa{\isadigit{0}}{\isacharcolon}\ nat{\isacharcomma}\ x{\isacharcolon}\ A{\isacharparenright}{\isacharcolon}\ A\ {\isacharequal}\ {\isacharparenleft}xa{\isadigit{0}}{\isacharcomma}\ x{\isacharparenright}\ match\ {\isacharbraceleft}\isanewline
-\ \ case\ {\isacharparenleft}Zero{\isacharunderscore}nat{\isacharcomma}\ x{\isacharparenright}\ {\isacharequal}{\isachargreater}\ neutral{\isacharbrackleft}A{\isacharbrackright}\isanewline
-\ \ case\ {\isacharparenleft}Suc{\isacharparenleft}n{\isacharparenright}{\isacharcomma}\ x{\isacharparenright}\ {\isacharequal}{\isachargreater}\ mult{\isacharbrackleft}A{\isacharbrackright}{\isacharparenleft}x{\isacharcomma}\ pow{\isacharunderscore}nat{\isacharbrackleft}A{\isacharbrackright}{\isacharparenleft}n{\isacharcomma}\ x{\isacharparenright}{\isacharparenright}\isanewline
-{\isacharbraceright}\isanewline
+def\ pow{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{3A}{\isacharcolon}}\ monoid{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{28}{\isacharparenleft}}xa{\isadigit{0}}{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{3A}{\isacharcolon}}\ A\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}xa{\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}\ match\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ case\ {\isaliteral{28}{\isacharparenleft}}Zero{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ neutral{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}\isanewline
+\ \ case\ {\isaliteral{28}{\isacharparenleft}}Suc{\isaliteral{28}{\isacharparenleft}}n{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ mult{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ pow{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{28}{\isacharparenleft}}n{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}\isanewline
\isanewline
-def\ pow{\isacharunderscore}int{\isacharbrackleft}A{\isacharcolon}\ group{\isacharbrackright}{\isacharparenleft}k{\isacharcolon}\ BigInt{\isacharcomma}\ x{\isacharcolon}\ A{\isacharparenright}{\isacharcolon}\ A\ {\isacharequal}\isanewline
-\ \ {\isacharparenleft}if\ {\isacharparenleft}BigInt{\isacharparenleft}{\isadigit{0}}{\isacharparenright}\ {\isacharless}{\isacharequal}\ k{\isacharparenright}\ pow{\isacharunderscore}nat{\isacharbrackleft}A{\isacharbrackright}{\isacharparenleft}nat{\isacharparenleft}k{\isacharparenright}{\isacharcomma}\ x{\isacharparenright}\isanewline
-\ \ \ \ else\ inverse{\isacharbrackleft}A{\isacharbrackright}{\isacharparenleft}pow{\isacharunderscore}nat{\isacharbrackleft}A{\isacharbrackright}{\isacharparenleft}nat{\isacharparenleft}{\isacharparenleft}{\isacharminus}\ k{\isacharparenright}{\isacharparenright}{\isacharcomma}\ x{\isacharparenright}{\isacharparenright}{\isacharparenright}\isanewline
+def\ pow{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{3A}{\isacharcolon}}\ group{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{28}{\isacharparenleft}}k{\isaliteral{3A}{\isacharcolon}}\ BigInt{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{3A}{\isacharcolon}}\ A\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}if\ {\isaliteral{28}{\isacharparenleft}}BigInt{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3C}{\isacharless}}{\isaliteral{3D}{\isacharequal}}\ k{\isaliteral{29}{\isacharparenright}}\ pow{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{28}{\isacharparenleft}}nat{\isaliteral{28}{\isacharparenleft}}k{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ else\ inverse{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{28}{\isacharparenleft}}pow{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{28}{\isacharparenleft}}nat{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}\ k{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
-def\ mult{\isacharunderscore}int{\isacharparenleft}i{\isacharcolon}\ BigInt{\isacharcomma}\ j{\isacharcolon}\ BigInt{\isacharparenright}{\isacharcolon}\ BigInt\ {\isacharequal}\ i\ {\isacharplus}\ j\isanewline
+def\ mult{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{28}{\isacharparenleft}}i{\isaliteral{3A}{\isacharcolon}}\ BigInt{\isaliteral{2C}{\isacharcomma}}\ j{\isaliteral{3A}{\isacharcolon}}\ BigInt{\isaliteral{29}{\isacharparenright}}{\isaliteral{3A}{\isacharcolon}}\ BigInt\ {\isaliteral{3D}{\isacharequal}}\ i\ {\isaliteral{2B}{\isacharplus}}\ j\isanewline
\isanewline
-implicit\ def\ semigroup{\isacharunderscore}int{\isacharcolon}\ semigroup{\isacharbrackleft}BigInt{\isacharbrackright}\ {\isacharequal}\ new\ semigroup{\isacharbrackleft}BigInt{\isacharbrackright}\ {\isacharbraceleft}\isanewline
-\ \ val\ {\isacharbackquote}Example{\isachardot}mult{\isacharbackquote}\ {\isacharequal}\ {\isacharparenleft}a{\isacharcolon}\ BigInt{\isacharcomma}\ b{\isacharcolon}\ BigInt{\isacharparenright}\ {\isacharequal}{\isachargreater}\ mult{\isacharunderscore}int{\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\isanewline
-{\isacharbraceright}\isanewline
+implicit\ def\ semigroup{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{3A}{\isacharcolon}}\ semigroup{\isaliteral{5B}{\isacharbrackleft}}BigInt{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ new\ semigroup{\isaliteral{5B}{\isacharbrackleft}}BigInt{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ val\ {\isaliteral{60}{\isacharbackquote}}Example{\isaliteral{2E}{\isachardot}}mult{\isaliteral{60}{\isacharbackquote}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{3A}{\isacharcolon}}\ BigInt{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{3A}{\isacharcolon}}\ BigInt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ mult{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}\isanewline
\isanewline
-def\ neutral{\isacharunderscore}int{\isacharcolon}\ BigInt\ {\isacharequal}\ BigInt{\isacharparenleft}{\isadigit{0}}{\isacharparenright}\isanewline
+def\ neutral{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{3A}{\isacharcolon}}\ BigInt\ {\isaliteral{3D}{\isacharequal}}\ BigInt{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
-implicit\ def\ monoidl{\isacharunderscore}int{\isacharcolon}\ monoidl{\isacharbrackleft}BigInt{\isacharbrackright}\ {\isacharequal}\ new\ monoidl{\isacharbrackleft}BigInt{\isacharbrackright}\ {\isacharbraceleft}\isanewline
-\ \ val\ {\isacharbackquote}Example{\isachardot}neutral{\isacharbackquote}\ {\isacharequal}\ neutral{\isacharunderscore}int\isanewline
-\ \ val\ {\isacharbackquote}Example{\isachardot}mult{\isacharbackquote}\ {\isacharequal}\ {\isacharparenleft}a{\isacharcolon}\ BigInt{\isacharcomma}\ b{\isacharcolon}\ BigInt{\isacharparenright}\ {\isacharequal}{\isachargreater}\ mult{\isacharunderscore}int{\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\isanewline
-{\isacharbraceright}\isanewline
+implicit\ def\ monoidl{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{3A}{\isacharcolon}}\ monoidl{\isaliteral{5B}{\isacharbrackleft}}BigInt{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ new\ monoidl{\isaliteral{5B}{\isacharbrackleft}}BigInt{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ val\ {\isaliteral{60}{\isacharbackquote}}Example{\isaliteral{2E}{\isachardot}}neutral{\isaliteral{60}{\isacharbackquote}}\ {\isaliteral{3D}{\isacharequal}}\ neutral{\isaliteral{5F}{\isacharunderscore}}int\isanewline
+\ \ val\ {\isaliteral{60}{\isacharbackquote}}Example{\isaliteral{2E}{\isachardot}}mult{\isaliteral{60}{\isacharbackquote}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{3A}{\isacharcolon}}\ BigInt{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{3A}{\isacharcolon}}\ BigInt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ mult{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}\isanewline
\isanewline
-implicit\ def\ monoid{\isacharunderscore}int{\isacharcolon}\ monoid{\isacharbrackleft}BigInt{\isacharbrackright}\ {\isacharequal}\ new\ monoid{\isacharbrackleft}BigInt{\isacharbrackright}\ {\isacharbraceleft}\isanewline
-\ \ val\ {\isacharbackquote}Example{\isachardot}neutral{\isacharbackquote}\ {\isacharequal}\ neutral{\isacharunderscore}int\isanewline
-\ \ val\ {\isacharbackquote}Example{\isachardot}mult{\isacharbackquote}\ {\isacharequal}\ {\isacharparenleft}a{\isacharcolon}\ BigInt{\isacharcomma}\ b{\isacharcolon}\ BigInt{\isacharparenright}\ {\isacharequal}{\isachargreater}\ mult{\isacharunderscore}int{\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\isanewline
-{\isacharbraceright}\isanewline
+implicit\ def\ monoid{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{3A}{\isacharcolon}}\ monoid{\isaliteral{5B}{\isacharbrackleft}}BigInt{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ new\ monoid{\isaliteral{5B}{\isacharbrackleft}}BigInt{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ val\ {\isaliteral{60}{\isacharbackquote}}Example{\isaliteral{2E}{\isachardot}}neutral{\isaliteral{60}{\isacharbackquote}}\ {\isaliteral{3D}{\isacharequal}}\ neutral{\isaliteral{5F}{\isacharunderscore}}int\isanewline
+\ \ val\ {\isaliteral{60}{\isacharbackquote}}Example{\isaliteral{2E}{\isachardot}}mult{\isaliteral{60}{\isacharbackquote}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{3A}{\isacharcolon}}\ BigInt{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{3A}{\isacharcolon}}\ BigInt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ mult{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}\isanewline
\isanewline
-def\ inverse{\isacharunderscore}int{\isacharparenleft}i{\isacharcolon}\ BigInt{\isacharparenright}{\isacharcolon}\ BigInt\ {\isacharequal}\ {\isacharparenleft}{\isacharminus}\ i{\isacharparenright}\isanewline
+def\ inverse{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{28}{\isacharparenleft}}i{\isaliteral{3A}{\isacharcolon}}\ BigInt{\isaliteral{29}{\isacharparenright}}{\isaliteral{3A}{\isacharcolon}}\ BigInt\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}\ i{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
-implicit\ def\ group{\isacharunderscore}int{\isacharcolon}\ group{\isacharbrackleft}BigInt{\isacharbrackright}\ {\isacharequal}\ new\ group{\isacharbrackleft}BigInt{\isacharbrackright}\ {\isacharbraceleft}\isanewline
-\ \ val\ {\isacharbackquote}Example{\isachardot}inverse{\isacharbackquote}\ {\isacharequal}\ {\isacharparenleft}a{\isacharcolon}\ BigInt{\isacharparenright}\ {\isacharequal}{\isachargreater}\ inverse{\isacharunderscore}int{\isacharparenleft}a{\isacharparenright}\isanewline
-\ \ val\ {\isacharbackquote}Example{\isachardot}neutral{\isacharbackquote}\ {\isacharequal}\ neutral{\isacharunderscore}int\isanewline
-\ \ val\ {\isacharbackquote}Example{\isachardot}mult{\isacharbackquote}\ {\isacharequal}\ {\isacharparenleft}a{\isacharcolon}\ BigInt{\isacharcomma}\ b{\isacharcolon}\ BigInt{\isacharparenright}\ {\isacharequal}{\isachargreater}\ mult{\isacharunderscore}int{\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\isanewline
-{\isacharbraceright}\isanewline
+implicit\ def\ group{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{3A}{\isacharcolon}}\ group{\isaliteral{5B}{\isacharbrackleft}}BigInt{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ new\ group{\isaliteral{5B}{\isacharbrackleft}}BigInt{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ val\ {\isaliteral{60}{\isacharbackquote}}Example{\isaliteral{2E}{\isachardot}}inverse{\isaliteral{60}{\isacharbackquote}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{3A}{\isacharcolon}}\ BigInt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ inverse{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ val\ {\isaliteral{60}{\isacharbackquote}}Example{\isaliteral{2E}{\isachardot}}neutral{\isaliteral{60}{\isacharbackquote}}\ {\isaliteral{3D}{\isacharequal}}\ neutral{\isaliteral{5F}{\isacharunderscore}}int\isanewline
+\ \ val\ {\isaliteral{60}{\isacharbackquote}}Example{\isaliteral{2E}{\isachardot}}mult{\isaliteral{60}{\isacharbackquote}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{3A}{\isacharcolon}}\ BigInt{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{3A}{\isacharcolon}}\ BigInt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ mult{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}\isanewline
\isanewline
-def\ example{\isacharcolon}\ BigInt\ {\isacharequal}\ pow{\isacharunderscore}int{\isacharbrackleft}BigInt{\isacharbrackright}{\isacharparenleft}BigInt{\isacharparenleft}{\isadigit{1}}{\isadigit{0}}{\isacharparenright}{\isacharcomma}\ BigInt{\isacharparenleft}{\isacharminus}\ {\isadigit{2}}{\isacharparenright}{\isacharparenright}\isanewline
+def\ example{\isaliteral{3A}{\isacharcolon}}\ BigInt\ {\isaliteral{3D}{\isacharequal}}\ pow{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{5B}{\isacharbrackleft}}BigInt{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{28}{\isacharparenleft}}BigInt{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ BigInt{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
-{\isacharbraceright}\ {\isacharslash}{\isacharasterisk}\ object\ Example\ {\isacharasterisk}{\isacharslash}\isanewline%
+{\isaliteral{7D}{\isacharbraceright}}\ {\isaliteral{2F}{\isacharslash}}{\isaliteral{2A}{\isacharasterisk}}\ object\ Example\ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2F}{\isacharslash}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -1415,10 +1415,10 @@
\begin{description}
- \item[\hyperlink{command.print-classes}{\mbox{\isa{\isacommand{print{\isacharunderscore}classes}}}}] print a list of all classes
+ \item[\hyperlink{command.print-classes}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}classes}}}}] print a list of all classes
together with associated operations etc.
- \item[\hyperlink{command.class-deps}{\mbox{\isa{\isacommand{class{\isacharunderscore}deps}}}}] visualizes the subclass relation
+ \item[\hyperlink{command.class-deps}{\mbox{\isa{\isacommand{class{\isaliteral{5F}{\isacharunderscore}}deps}}}}] visualizes the subclass relation
between all classes as a Hasse diagram.
\end{description}%
--- a/doc-src/Codegen/Thy/document/Adaptation.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/Codegen/Thy/document/Adaptation.tex Mon Nov 08 14:41:11 2010 +0100
@@ -26,8 +26,8 @@
%
\isataginvisible
\isacommand{setup}\isamarkupfalse%
-\ {\isacharverbatimopen}\ Code{\isacharunderscore}Target{\isachardot}extend{\isacharunderscore}target\ {\isacharparenleft}{\isachardoublequote}{\isasymSML}{\isachardoublequote}{\isacharcomma}\ {\isacharparenleft}{\isachardoublequote}SML{\isachardoublequote}{\isacharcomma}\ K\ I{\isacharparenright}{\isacharparenright}\isanewline
-\ \ {\isacharhash}{\isachargreater}\ Code{\isacharunderscore}Target{\isachardot}extend{\isacharunderscore}target\ {\isacharparenleft}{\isachardoublequote}{\isasymSMLdummy}{\isachardoublequote}{\isacharcomma}\ {\isacharparenleft}{\isachardoublequote}Haskell{\isachardoublequote}{\isacharcomma}\ K\ I{\isacharparenright}{\isacharparenright}\ {\isacharverbatimclose}%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ Code{\isaliteral{5F}{\isacharunderscore}}Target{\isaliteral{2E}{\isachardot}}extend{\isaliteral{5F}{\isacharunderscore}}target\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C534D4C3E}{\isasymSML}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}SML{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ K\ I{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ {\isaliteral{23}{\isacharhash}}{\isaliteral{3E}{\isachargreater}}\ Code{\isaliteral{5F}{\isacharunderscore}}Target{\isaliteral{2E}{\isachardot}}extend{\isaliteral{5F}{\isacharunderscore}}target\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C534D4C64756D6D793E}{\isasymSMLdummy}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Haskell{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ K\ I{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisataginvisible
{\isafoldinvisible}%
%
@@ -158,27 +158,27 @@
\begin{description}
- \item[\hyperlink{theory.Code-Integer}{\mbox{\isa{Code{\isacharunderscore}Integer}}}] represents \isa{HOL} integers by
+ \item[\hyperlink{theory.Code-Integer}{\mbox{\isa{Code{\isaliteral{5F}{\isacharunderscore}}Integer}}}] represents \isa{HOL} integers by
big integer literals in target languages.
- \item[\hyperlink{theory.Code-Char}{\mbox{\isa{Code{\isacharunderscore}Char}}}] represents \isa{HOL} characters by
+ \item[\hyperlink{theory.Code-Char}{\mbox{\isa{Code{\isaliteral{5F}{\isacharunderscore}}Char}}}] represents \isa{HOL} characters by
character literals in target languages.
- \item[\hyperlink{theory.Code-Char-chr}{\mbox{\isa{Code{\isacharunderscore}Char{\isacharunderscore}chr}}}] like \isa{Code{\isacharunderscore}Char}, but
- also offers treatment of character codes; includes \hyperlink{theory.Code-Char}{\mbox{\isa{Code{\isacharunderscore}Char}}}.
+ \item[\hyperlink{theory.Code-Char-chr}{\mbox{\isa{Code{\isaliteral{5F}{\isacharunderscore}}Char{\isaliteral{5F}{\isacharunderscore}}chr}}}] like \isa{Code{\isaliteral{5F}{\isacharunderscore}}Char}, but
+ also offers treatment of character codes; includes \hyperlink{theory.Code-Char}{\mbox{\isa{Code{\isaliteral{5F}{\isacharunderscore}}Char}}}.
- \item[\hyperlink{theory.Efficient-Nat}{\mbox{\isa{Efficient{\isacharunderscore}Nat}}}] \label{eff_nat} implements
+ \item[\hyperlink{theory.Efficient-Nat}{\mbox{\isa{Efficient{\isaliteral{5F}{\isacharunderscore}}Nat}}}] \label{eff_nat} implements
natural numbers by integers, which in general will result in
higher efficiency; pattern matching with \isa{{\isadigit{0}}} /
- \isa{Suc} is eliminated; includes \hyperlink{theory.Code-Integer}{\mbox{\isa{Code{\isacharunderscore}Integer}}}
- and \hyperlink{theory.Code-Numeral}{\mbox{\isa{Code{\isacharunderscore}Numeral}}}.
+ \isa{Suc} is eliminated; includes \hyperlink{theory.Code-Integer}{\mbox{\isa{Code{\isaliteral{5F}{\isacharunderscore}}Integer}}}
+ and \hyperlink{theory.Code-Numeral}{\mbox{\isa{Code{\isaliteral{5F}{\isacharunderscore}}Numeral}}}.
- \item[\hyperlink{theory.Code-Numeral}{\mbox{\isa{Code{\isacharunderscore}Numeral}}}] provides an additional datatype
+ \item[\hyperlink{theory.Code-Numeral}{\mbox{\isa{Code{\isaliteral{5F}{\isacharunderscore}}Numeral}}}] provides an additional datatype
\isa{index} which is mapped to target-language built-in
integers. Useful for code setups which involve e.g.~indexing
of target-language arrays.
- \item[\hyperlink{theory.String}{\mbox{\isa{String}}}] provides an additional datatype \isa{String{\isachardot}literal} which is isomorphic to strings; \isa{String{\isachardot}literal}s are mapped to target-language strings. Useful
+ \item[\hyperlink{theory.String}{\mbox{\isa{String}}}] provides an additional datatype \isa{String{\isaliteral{2E}{\isachardot}}literal} which is isomorphic to strings; \isa{String{\isaliteral{2E}{\isachardot}}literal}s are mapped to target-language strings. Useful
for code setups which involve e.g.~printing (error) messages.
\end{description}
@@ -207,8 +207,8 @@
%
\isatagquote
\isacommand{primrec}\isamarkupfalse%
-\ in{\isacharunderscore}interval\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymtimes}\ nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}in{\isacharunderscore}interval\ {\isacharparenleft}k{\isacharcomma}\ l{\isacharparenright}\ n\ {\isasymlongleftrightarrow}\ k\ {\isasymle}\ n\ {\isasymand}\ n\ {\isasymle}\ l{\isachardoublequoteclose}%
+\ in{\isaliteral{5F}{\isacharunderscore}}interval\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}in{\isaliteral{5F}{\isacharunderscore}}interval\ {\isaliteral{28}{\isacharparenleft}}k{\isaliteral{2C}{\isacharcomma}}\ l{\isaliteral{29}{\isacharparenright}}\ n\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ k\ {\isaliteral{5C3C6C653E}{\isasymle}}\ n\ {\isaliteral{5C3C616E643E}{\isasymand}}\ n\ {\isaliteral{5C3C6C653E}{\isasymle}}\ l{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -236,32 +236,32 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-structure\ Example\ {\isacharcolon}\ sig\isanewline
-\ \ datatype\ nat\ {\isacharequal}\ Zero{\isacharunderscore}nat\ {\isacharbar}\ Suc\ of\ nat\isanewline
-\ \ datatype\ boola\ {\isacharequal}\ True\ {\isacharbar}\ False\isanewline
-\ \ val\ conj\ {\isacharcolon}\ boola\ {\isacharminus}{\isachargreater}\ boola\ {\isacharminus}{\isachargreater}\ boola\isanewline
-\ \ val\ less{\isacharunderscore}nat\ {\isacharcolon}\ nat\ {\isacharminus}{\isachargreater}\ nat\ {\isacharminus}{\isachargreater}\ boola\isanewline
-\ \ val\ less{\isacharunderscore}eq{\isacharunderscore}nat\ {\isacharcolon}\ nat\ {\isacharminus}{\isachargreater}\ nat\ {\isacharminus}{\isachargreater}\ boola\isanewline
-\ \ val\ in{\isacharunderscore}interval\ {\isacharcolon}\ nat\ {\isacharasterisk}\ nat\ {\isacharminus}{\isachargreater}\ nat\ {\isacharminus}{\isachargreater}\ boola\isanewline
-end\ {\isacharequal}\ struct\isanewline
+structure\ Example\ {\isaliteral{3A}{\isacharcolon}}\ sig\isanewline
+\ \ datatype\ nat\ {\isaliteral{3D}{\isacharequal}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{7C}{\isacharbar}}\ Suc\ of\ nat\isanewline
+\ \ datatype\ boola\ {\isaliteral{3D}{\isacharequal}}\ True\ {\isaliteral{7C}{\isacharbar}}\ False\isanewline
+\ \ val\ conj\ {\isaliteral{3A}{\isacharcolon}}\ boola\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ boola\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ boola\isanewline
+\ \ val\ less{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ boola\isanewline
+\ \ val\ less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ boola\isanewline
+\ \ val\ in{\isaliteral{5F}{\isacharunderscore}}interval\ {\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{2A}{\isacharasterisk}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ boola\isanewline
+end\ {\isaliteral{3D}{\isacharequal}}\ struct\isanewline
\isanewline
-datatype\ nat\ {\isacharequal}\ Zero{\isacharunderscore}nat\ {\isacharbar}\ Suc\ of\ nat{\isacharsemicolon}\isanewline
+datatype\ nat\ {\isaliteral{3D}{\isacharequal}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{7C}{\isacharbar}}\ Suc\ of\ nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-datatype\ boola\ {\isacharequal}\ True\ {\isacharbar}\ False{\isacharsemicolon}\isanewline
+datatype\ boola\ {\isaliteral{3D}{\isacharequal}}\ True\ {\isaliteral{7C}{\isacharbar}}\ False{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ conj\ p\ True\ {\isacharequal}\ p\isanewline
-\ \ {\isacharbar}\ conj\ p\ False\ {\isacharequal}\ False\isanewline
-\ \ {\isacharbar}\ conj\ True\ p\ {\isacharequal}\ p\isanewline
-\ \ {\isacharbar}\ conj\ False\ p\ {\isacharequal}\ False{\isacharsemicolon}\isanewline
+fun\ conj\ p\ True\ {\isaliteral{3D}{\isacharequal}}\ p\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ conj\ p\ False\ {\isaliteral{3D}{\isacharequal}}\ False\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ conj\ True\ p\ {\isaliteral{3D}{\isacharequal}}\ p\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ conj\ False\ p\ {\isaliteral{3D}{\isacharequal}}\ False{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ less{\isacharunderscore}nat\ m\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ less{\isacharunderscore}eq{\isacharunderscore}nat\ m\ n\isanewline
-\ \ {\isacharbar}\ less{\isacharunderscore}nat\ n\ Zero{\isacharunderscore}nat\ {\isacharequal}\ False\isanewline
-and\ less{\isacharunderscore}eq{\isacharunderscore}nat\ {\isacharparenleft}Suc\ m{\isacharparenright}\ n\ {\isacharequal}\ less{\isacharunderscore}nat\ m\ n\isanewline
-\ \ {\isacharbar}\ less{\isacharunderscore}eq{\isacharunderscore}nat\ Zero{\isacharunderscore}nat\ n\ {\isacharequal}\ True{\isacharsemicolon}\isanewline
+fun\ less{\isaliteral{5F}{\isacharunderscore}}nat\ m\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ m\ n\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ less{\isaliteral{5F}{\isacharunderscore}}nat\ n\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3D}{\isacharequal}}\ False\isanewline
+and\ less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}Suc\ m{\isaliteral{29}{\isacharparenright}}\ n\ {\isaliteral{3D}{\isacharequal}}\ less{\isaliteral{5F}{\isacharunderscore}}nat\ m\ n\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ n\ {\isaliteral{3D}{\isacharequal}}\ True{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ in{\isacharunderscore}interval\ {\isacharparenleft}k{\isacharcomma}\ l{\isacharparenright}\ n\ {\isacharequal}\ conj\ {\isacharparenleft}less{\isacharunderscore}eq{\isacharunderscore}nat\ k\ n{\isacharparenright}\ {\isacharparenleft}less{\isacharunderscore}eq{\isacharunderscore}nat\ n\ l{\isacharparenright}{\isacharsemicolon}\isanewline
+fun\ in{\isaliteral{5F}{\isacharunderscore}}interval\ {\isaliteral{28}{\isacharparenleft}}k{\isaliteral{2C}{\isacharcomma}}\ l{\isaliteral{29}{\isacharparenright}}\ n\ {\isaliteral{3D}{\isacharequal}}\ conj\ {\isaliteral{28}{\isacharparenleft}}less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ k\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ n\ l{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-end{\isacharsemicolon}\ {\isacharparenleft}{\isacharasterisk}struct\ Example{\isacharasterisk}{\isacharparenright}\isanewline%
+end{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}struct\ Example{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -287,12 +287,12 @@
\endisadelimquotett
%
\isatagquotett
-\isacommand{code{\isacharunderscore}type}\isamarkupfalse%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}type}\isamarkupfalse%
\ bool\isanewline
-\ \ {\isacharparenleft}SML\ {\isachardoublequoteopen}bool{\isachardoublequoteclose}{\isacharparenright}\isanewline
-\isacommand{code{\isacharunderscore}const}\isamarkupfalse%
-\ True\ \isakeyword{and}\ False\ \isakeyword{and}\ {\isachardoublequoteopen}op\ {\isasymand}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharparenleft}SML\ {\isachardoublequoteopen}true{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}false{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}{\isacharunderscore}\ andalso\ {\isacharunderscore}{\isachardoublequoteclose}{\isacharparenright}%
+\ \ {\isaliteral{28}{\isacharparenleft}}SML\ {\isaliteral{22}{\isachardoublequoteopen}}bool{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}const}\isamarkupfalse%
+\ True\ \isakeyword{and}\ False\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}op\ {\isaliteral{5C3C616E643E}{\isasymand}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}SML\ {\isaliteral{22}{\isachardoublequoteopen}}true{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}false{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5F}{\isacharunderscore}}\ andalso\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}%
\endisatagquotett
{\isafoldquotett}%
%
@@ -301,12 +301,12 @@
\endisadelimquotett
%
\begin{isamarkuptext}%
-\noindent The \indexdef{}{command}{code\_type}\hypertarget{command.code-type}{\hyperlink{command.code-type}{\mbox{\isa{\isacommand{code{\isacharunderscore}type}}}}} command takes a type constructor
+\noindent The \indexdef{}{command}{code\_type}\hypertarget{command.code-type}{\hyperlink{command.code-type}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}type}}}}} command takes a type constructor
as arguments together with a list of custom serialisations. Each
custom serialisation starts with a target language identifier
followed by an expression, which during code serialisation is
inserted whenever the type constructor would occur. For constants,
- \indexdef{}{command}{code\_const}\hypertarget{command.code-const}{\hyperlink{command.code-const}{\mbox{\isa{\isacommand{code{\isacharunderscore}const}}}}} implements the corresponding mechanism. Each
+ \indexdef{}{command}{code\_const}\hypertarget{command.code-const}{\hyperlink{command.code-const}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}const}}}}} implements the corresponding mechanism. Each
``\verb|_|'' in a serialisation expression is treated as a
placeholder for the type constructor's (the constant's) arguments.%
\end{isamarkuptext}%
@@ -319,23 +319,23 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-structure\ Example\ {\isacharcolon}\ sig\isanewline
-\ \ datatype\ nat\ {\isacharequal}\ Zero{\isacharunderscore}nat\ {\isacharbar}\ Suc\ of\ nat\isanewline
-\ \ val\ less{\isacharunderscore}nat\ {\isacharcolon}\ nat\ {\isacharminus}{\isachargreater}\ nat\ {\isacharminus}{\isachargreater}\ bool\isanewline
-\ \ val\ less{\isacharunderscore}eq{\isacharunderscore}nat\ {\isacharcolon}\ nat\ {\isacharminus}{\isachargreater}\ nat\ {\isacharminus}{\isachargreater}\ bool\isanewline
-\ \ val\ in{\isacharunderscore}interval\ {\isacharcolon}\ nat\ {\isacharasterisk}\ nat\ {\isacharminus}{\isachargreater}\ nat\ {\isacharminus}{\isachargreater}\ bool\isanewline
-end\ {\isacharequal}\ struct\isanewline
+structure\ Example\ {\isaliteral{3A}{\isacharcolon}}\ sig\isanewline
+\ \ datatype\ nat\ {\isaliteral{3D}{\isacharequal}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{7C}{\isacharbar}}\ Suc\ of\ nat\isanewline
+\ \ val\ less{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ bool\isanewline
+\ \ val\ less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ bool\isanewline
+\ \ val\ in{\isaliteral{5F}{\isacharunderscore}}interval\ {\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{2A}{\isacharasterisk}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ bool\isanewline
+end\ {\isaliteral{3D}{\isacharequal}}\ struct\isanewline
\isanewline
-datatype\ nat\ {\isacharequal}\ Zero{\isacharunderscore}nat\ {\isacharbar}\ Suc\ of\ nat{\isacharsemicolon}\isanewline
+datatype\ nat\ {\isaliteral{3D}{\isacharequal}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{7C}{\isacharbar}}\ Suc\ of\ nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ less{\isacharunderscore}nat\ m\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ less{\isacharunderscore}eq{\isacharunderscore}nat\ m\ n\isanewline
-\ \ {\isacharbar}\ less{\isacharunderscore}nat\ n\ Zero{\isacharunderscore}nat\ {\isacharequal}\ false\isanewline
-and\ less{\isacharunderscore}eq{\isacharunderscore}nat\ {\isacharparenleft}Suc\ m{\isacharparenright}\ n\ {\isacharequal}\ less{\isacharunderscore}nat\ m\ n\isanewline
-\ \ {\isacharbar}\ less{\isacharunderscore}eq{\isacharunderscore}nat\ Zero{\isacharunderscore}nat\ n\ {\isacharequal}\ true{\isacharsemicolon}\isanewline
+fun\ less{\isaliteral{5F}{\isacharunderscore}}nat\ m\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ m\ n\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ less{\isaliteral{5F}{\isacharunderscore}}nat\ n\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3D}{\isacharequal}}\ false\isanewline
+and\ less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}Suc\ m{\isaliteral{29}{\isacharparenright}}\ n\ {\isaliteral{3D}{\isacharequal}}\ less{\isaliteral{5F}{\isacharunderscore}}nat\ m\ n\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ n\ {\isaliteral{3D}{\isacharequal}}\ true{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ in{\isacharunderscore}interval\ {\isacharparenleft}k{\isacharcomma}\ l{\isacharparenright}\ n\ {\isacharequal}\ {\isacharparenleft}less{\isacharunderscore}eq{\isacharunderscore}nat\ k\ n{\isacharparenright}\ andalso\ {\isacharparenleft}less{\isacharunderscore}eq{\isacharunderscore}nat\ n\ l{\isacharparenright}{\isacharsemicolon}\isanewline
+fun\ in{\isaliteral{5F}{\isacharunderscore}}interval\ {\isaliteral{28}{\isacharparenleft}}k{\isaliteral{2C}{\isacharcomma}}\ l{\isaliteral{29}{\isacharparenright}}\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ k\ n{\isaliteral{29}{\isacharparenright}}\ andalso\ {\isaliteral{28}{\isacharparenleft}}less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ n\ l{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-end{\isacharsemicolon}\ {\isacharparenleft}{\isacharasterisk}struct\ Example{\isacharasterisk}{\isacharparenright}\isanewline%
+end{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}struct\ Example{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -360,9 +360,9 @@
\endisadelimquotett
%
\isatagquotett
-\isacommand{code{\isacharunderscore}const}\isamarkupfalse%
-\ {\isachardoublequoteopen}op\ {\isasymand}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharparenleft}SML\ \isakeyword{infixl}\ {\isadigit{1}}\ {\isachardoublequoteopen}andalso{\isachardoublequoteclose}{\isacharparenright}%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}const}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}op\ {\isaliteral{5C3C616E643E}{\isasymand}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}SML\ \isakeyword{infixl}\ {\isadigit{1}}\ {\isaliteral{22}{\isachardoublequoteopen}}andalso{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}%
\endisatagquotett
{\isafoldquotett}%
%
@@ -377,23 +377,23 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-structure\ Example\ {\isacharcolon}\ sig\isanewline
-\ \ datatype\ nat\ {\isacharequal}\ Zero{\isacharunderscore}nat\ {\isacharbar}\ Suc\ of\ nat\isanewline
-\ \ val\ less{\isacharunderscore}nat\ {\isacharcolon}\ nat\ {\isacharminus}{\isachargreater}\ nat\ {\isacharminus}{\isachargreater}\ bool\isanewline
-\ \ val\ less{\isacharunderscore}eq{\isacharunderscore}nat\ {\isacharcolon}\ nat\ {\isacharminus}{\isachargreater}\ nat\ {\isacharminus}{\isachargreater}\ bool\isanewline
-\ \ val\ in{\isacharunderscore}interval\ {\isacharcolon}\ nat\ {\isacharasterisk}\ nat\ {\isacharminus}{\isachargreater}\ nat\ {\isacharminus}{\isachargreater}\ bool\isanewline
-end\ {\isacharequal}\ struct\isanewline
+structure\ Example\ {\isaliteral{3A}{\isacharcolon}}\ sig\isanewline
+\ \ datatype\ nat\ {\isaliteral{3D}{\isacharequal}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{7C}{\isacharbar}}\ Suc\ of\ nat\isanewline
+\ \ val\ less{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ bool\isanewline
+\ \ val\ less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ bool\isanewline
+\ \ val\ in{\isaliteral{5F}{\isacharunderscore}}interval\ {\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{2A}{\isacharasterisk}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ bool\isanewline
+end\ {\isaliteral{3D}{\isacharequal}}\ struct\isanewline
\isanewline
-datatype\ nat\ {\isacharequal}\ Zero{\isacharunderscore}nat\ {\isacharbar}\ Suc\ of\ nat{\isacharsemicolon}\isanewline
+datatype\ nat\ {\isaliteral{3D}{\isacharequal}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{7C}{\isacharbar}}\ Suc\ of\ nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ less{\isacharunderscore}nat\ m\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ less{\isacharunderscore}eq{\isacharunderscore}nat\ m\ n\isanewline
-\ \ {\isacharbar}\ less{\isacharunderscore}nat\ n\ Zero{\isacharunderscore}nat\ {\isacharequal}\ false\isanewline
-and\ less{\isacharunderscore}eq{\isacharunderscore}nat\ {\isacharparenleft}Suc\ m{\isacharparenright}\ n\ {\isacharequal}\ less{\isacharunderscore}nat\ m\ n\isanewline
-\ \ {\isacharbar}\ less{\isacharunderscore}eq{\isacharunderscore}nat\ Zero{\isacharunderscore}nat\ n\ {\isacharequal}\ true{\isacharsemicolon}\isanewline
+fun\ less{\isaliteral{5F}{\isacharunderscore}}nat\ m\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ m\ n\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ less{\isaliteral{5F}{\isacharunderscore}}nat\ n\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3D}{\isacharequal}}\ false\isanewline
+and\ less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}Suc\ m{\isaliteral{29}{\isacharparenright}}\ n\ {\isaliteral{3D}{\isacharequal}}\ less{\isaliteral{5F}{\isacharunderscore}}nat\ m\ n\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ n\ {\isaliteral{3D}{\isacharequal}}\ true{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ in{\isacharunderscore}interval\ {\isacharparenleft}k{\isacharcomma}\ l{\isacharparenright}\ n\ {\isacharequal}\ less{\isacharunderscore}eq{\isacharunderscore}nat\ k\ n\ andalso\ less{\isacharunderscore}eq{\isacharunderscore}nat\ n\ l{\isacharsemicolon}\isanewline
+fun\ in{\isaliteral{5F}{\isacharunderscore}}interval\ {\isaliteral{28}{\isacharparenleft}}k{\isaliteral{2C}{\isacharcomma}}\ l{\isaliteral{29}{\isacharparenright}}\ n\ {\isaliteral{3D}{\isacharequal}}\ less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ k\ n\ andalso\ less{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}nat\ n\ l{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-end{\isacharsemicolon}\ {\isacharparenleft}{\isacharasterisk}struct\ Example{\isacharasterisk}{\isacharparenright}\isanewline%
+end{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}struct\ Example{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -411,7 +411,7 @@
avoided to be used for new declarations. Initially, this table
typically contains the keywords of the target language. It can be
extended manually, thus avoiding accidental overwrites, using the
- \indexdef{}{command}{code\_reserved}\hypertarget{command.code-reserved}{\hyperlink{command.code-reserved}{\mbox{\isa{\isacommand{code{\isacharunderscore}reserved}}}}} command:%
+ \indexdef{}{command}{code\_reserved}\hypertarget{command.code-reserved}{\hyperlink{command.code-reserved}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reserved}}}}} command:%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -420,8 +420,8 @@
\endisadelimquote
%
\isatagquote
-\isacommand{code{\isacharunderscore}reserved}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymSMLdummy}{\isachardoublequoteclose}\ bool\ true\ false\ andalso%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reserved}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C534D4C64756D6D793E}{\isasymSMLdummy}}{\isaliteral{22}{\isachardoublequoteclose}}\ bool\ true\ false\ andalso%
\endisatagquote
{\isafoldquote}%
%
@@ -453,12 +453,12 @@
\endisadelimquotett
%
\isatagquotett
-\isacommand{code{\isacharunderscore}type}\isamarkupfalse%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}type}\isamarkupfalse%
\ prod\isanewline
-\ \ {\isacharparenleft}SML\ \isakeyword{infix}\ {\isadigit{2}}\ {\isachardoublequoteopen}{\isacharasterisk}{\isachardoublequoteclose}{\isacharparenright}\isanewline
-\isacommand{code{\isacharunderscore}const}\isamarkupfalse%
+\ \ {\isaliteral{28}{\isacharparenleft}}SML\ \isakeyword{infix}\ {\isadigit{2}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}const}\isamarkupfalse%
\ Pair\isanewline
-\ \ {\isacharparenleft}SML\ {\isachardoublequoteopen}{\isacharbang}{\isacharparenleft}{\isacharparenleft}{\isacharunderscore}{\isacharparenright}{\isacharcomma}{\isacharslash}\ {\isacharparenleft}{\isacharunderscore}{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}{\isacharparenright}%
+\ \ {\isaliteral{28}{\isacharparenleft}}SML\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{21}{\isacharbang}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}%
\endisatagquotett
{\isafoldquotett}%
%
@@ -496,7 +496,7 @@
For convenience, the default \isa{HOL} setup for \isa{Haskell}
maps the \isa{equal} class to its counterpart in \isa{Haskell},
giving custom serialisations for the class \isa{equal} (by command
- \indexdef{}{command}{code\_class}\hypertarget{command.code-class}{\hyperlink{command.code-class}{\mbox{\isa{\isacommand{code{\isacharunderscore}class}}}}}) and its operation \isa{HOL{\isachardot}equal}%
+ \indexdef{}{command}{code\_class}\hypertarget{command.code-class}{\hyperlink{command.code-class}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}class}}}}}) and its operation \isa{HOL{\isaliteral{2E}{\isachardot}}equal}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -505,13 +505,13 @@
\endisadelimquotett
%
\isatagquotett
-\isacommand{code{\isacharunderscore}class}\isamarkupfalse%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}class}\isamarkupfalse%
\ equal\isanewline
-\ \ {\isacharparenleft}Haskell\ {\isachardoublequoteopen}Eq{\isachardoublequoteclose}{\isacharparenright}\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}Haskell\ {\isaliteral{22}{\isachardoublequoteopen}}Eq{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
-\isacommand{code{\isacharunderscore}const}\isamarkupfalse%
-\ {\isachardoublequoteopen}HOL{\isachardot}equal{\isachardoublequoteclose}\isanewline
-\ \ {\isacharparenleft}Haskell\ \isakeyword{infixl}\ {\isadigit{4}}\ {\isachardoublequoteopen}{\isacharequal}{\isacharequal}{\isachardoublequoteclose}{\isacharparenright}%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}const}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}HOL{\isaliteral{2E}{\isachardot}}equal{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}Haskell\ \isakeyword{infixl}\ {\isadigit{4}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}%
\endisatagquotett
{\isafoldquotett}%
%
@@ -535,15 +535,15 @@
\ bar\isanewline
\isanewline
\isacommand{instantiation}\isamarkupfalse%
-\ bar\ {\isacharcolon}{\isacharcolon}\ equal\isanewline
+\ bar\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ equal\isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{definition}\isamarkupfalse%
-\ {\isachardoublequoteopen}HOL{\isachardot}equal\ {\isacharparenleft}x{\isasymColon}bar{\isacharparenright}\ y\ {\isasymlongleftrightarrow}\ x\ {\isacharequal}\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}HOL{\isaliteral{2E}{\isachardot}}equal\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}bar{\isaliteral{29}{\isacharparenright}}\ y\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{instance}\isamarkupfalse%
\ \isacommand{by}\isamarkupfalse%
-\ default\ {\isacharparenleft}simp\ add{\isacharcolon}\ equal{\isacharunderscore}bar{\isacharunderscore}def{\isacharparenright}\isanewline
+\ default\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ equal{\isaliteral{5F}{\isacharunderscore}}bar{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
\isacommand{end}\isamarkupfalse%
%
@@ -559,9 +559,9 @@
\endisadelimquotett
%
\isatagquotett
-\isacommand{code{\isacharunderscore}type}\isamarkupfalse%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}type}\isamarkupfalse%
\ bar\isanewline
-\ \ {\isacharparenleft}Haskell\ {\isachardoublequoteopen}Integer{\isachardoublequoteclose}{\isacharparenright}%
+\ \ {\isaliteral{28}{\isacharparenleft}}Haskell\ {\isaliteral{22}{\isachardoublequoteopen}}Integer{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}%
\endisatagquotett
{\isafoldquotett}%
%
@@ -572,7 +572,7 @@
\begin{isamarkuptext}%
\noindent The code generator would produce an additional instance,
which of course is rejected by the \isa{Haskell} compiler. To
- suppress this additional instance, use \indexdef{}{command}{code\_instance}\hypertarget{command.code-instance}{\hyperlink{command.code-instance}{\mbox{\isa{\isacommand{code{\isacharunderscore}instance}}}}}:%
+ suppress this additional instance, use \indexdef{}{command}{code\_instance}\hypertarget{command.code-instance}{\hyperlink{command.code-instance}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}instance}}}}}:%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -581,9 +581,9 @@
\endisadelimquotett
%
\isatagquotett
-\isacommand{code{\isacharunderscore}instance}\isamarkupfalse%
-\ bar\ {\isacharcolon}{\isacharcolon}\ equal\isanewline
-\ \ {\isacharparenleft}Haskell\ {\isacharminus}{\isacharparenright}%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}instance}\isamarkupfalse%
+\ bar\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ equal\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}Haskell\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{29}{\isacharparenright}}%
\endisatagquotett
{\isafoldquotett}%
%
@@ -597,7 +597,7 @@
%
\begin{isamarkuptext}%
In rare cases it is necessary to \emph{enrich} the context of a
- target language; this is accomplished using the \indexdef{}{command}{code\_include}\hypertarget{command.code-include}{\hyperlink{command.code-include}{\mbox{\isa{\isacommand{code{\isacharunderscore}include}}}}} command:%
+ target language; this is accomplished using the \indexdef{}{command}{code\_include}\hypertarget{command.code-include}{\hyperlink{command.code-include}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}include}}}}} command:%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -606,11 +606,11 @@
\endisadelimquotett
%
\isatagquotett
-\isacommand{code{\isacharunderscore}include}\isamarkupfalse%
-\ Haskell\ {\isachardoublequoteopen}Errno{\isachardoublequoteclose}\isanewline
-{\isacharverbatimopen}errno\ i\ {\isacharequal}\ error\ {\isacharparenleft}{\isachardoublequote}Error\ number{\isacharcolon}\ {\isachardoublequote}\ {\isacharplus}{\isacharplus}\ show\ i{\isacharparenright}{\isacharverbatimclose}\isanewline
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}include}\isamarkupfalse%
+\ Haskell\ {\isaliteral{22}{\isachardoublequoteopen}}Errno{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7B2A}{\isacharverbatimopen}}errno\ i\ {\isaliteral{3D}{\isacharequal}}\ error\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Error\ number{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{2B}{\isacharplus}}{\isaliteral{2B}{\isacharplus}}\ show\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
\isanewline
-\isacommand{code{\isacharunderscore}reserved}\isamarkupfalse%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reserved}\isamarkupfalse%
\ Haskell\ Errno%
\endisatagquotett
{\isafoldquotett}%
@@ -622,7 +622,7 @@
\begin{isamarkuptext}%
\noindent Such named \isa{include}s are then prepended to every
generated code. Inspect such code in order to find out how
- \hyperlink{command.code-include}{\mbox{\isa{\isacommand{code{\isacharunderscore}include}}}} behaves with respect to a particular
+ \hyperlink{command.code-include}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}include}}}} behaves with respect to a particular
target language.%
\end{isamarkuptext}%
\isamarkuptrue%
--- a/doc-src/Codegen/Thy/document/Evaluation.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/Codegen/Thy/document/Evaluation.tex Mon Nov 08 14:41:11 2010 +0100
@@ -27,7 +27,7 @@
equations into a program with the \emph{same} equational semantics.
As a consequence, this program can be used as a \emph{rewrite
engine} for terms: rewriting a term \isa{t} using a program to a
- term \isa{t{\isacharprime}} yields the theorems \isa{t\ {\isasymequiv}\ t{\isacharprime}}. This
+ term \isa{t{\isaliteral{27}{\isacharprime}}} yields the theorems \isa{t\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{27}{\isacharprime}}}. This
application of code generation in the following is referred to as
\emph{evaluation}.%
\end{isamarkuptext}%
@@ -122,7 +122,7 @@
%
\isatagquote
\isacommand{value}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isadigit{4}}{\isadigit{2}}\ {\isacharslash}\ {\isacharparenleft}{\isadigit{1}}{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ rat{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{4}}{\isadigit{2}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ rat{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -143,7 +143,7 @@
%
\isatagquote
\isacommand{value}\isamarkupfalse%
-\ {\isacharbrackleft}nbe{\isacharbrackright}\ {\isachardoublequoteopen}{\isadigit{4}}{\isadigit{2}}\ {\isacharslash}\ {\isacharparenleft}{\isadigit{1}}{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ rat{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{5B}{\isacharbrackleft}}nbe{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{4}}{\isadigit{2}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ rat{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -174,8 +174,8 @@
and therefore trustable.
\item[Conversion.] Evaluates an arbitrary term \isa{t} first
- by plain evaluation and certifies the result \isa{t{\isacharprime}} by
- checking the equation \isa{t\ {\isasymequiv}\ t{\isacharprime}} using property
+ by plain evaluation and certifies the result \isa{t{\isaliteral{27}{\isacharprime}}} by
+ checking the equation \isa{t\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{27}{\isacharprime}}} using property
conversion.
\end{description}
@@ -185,7 +185,7 @@
\begin{itemize}
- \item Evaluation of \isa{t} terminates with a result \isa{t{\isacharprime}}.
+ \item Evaluation of \isa{t} terminates with a result \isa{t{\isaliteral{27}{\isacharprime}}}.
\item Evaluation of \isa{t} terminates which en exception
indicating a pattern match failure or a non-implemented
@@ -196,15 +196,15 @@
\end{itemize}
- \noindent For conversions, the first case yields the equation \isa{t\ {\isacharequal}\ t{\isacharprime}}, the second defaults to reflexivity \isa{t\ {\isacharequal}\ t}.
+ \noindent For conversions, the first case yields the equation \isa{t\ {\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{27}{\isacharprime}}}, the second defaults to reflexivity \isa{t\ {\isaliteral{3D}{\isacharequal}}\ t}.
Exceptions of the third kind are propagated to the user.
By default return values of plain evaluation are optional, yielding
- \isa{SOME\ t{\isacharprime}} in the first case, \isa{NONE} in the
+ \isa{SOME\ t{\isaliteral{27}{\isacharprime}}} in the first case, \isa{NONE} in the
second, and propagating the exception in the third case. A strict
- variant of plain evaluation either yields \isa{t{\isacharprime}} or propagates
+ variant of plain evaluation either yields \isa{t{\isaliteral{27}{\isacharprime}}} or propagates
any exception, a liberal variant caputures any exception in a result
- of type \isa{Exn{\isachardot}result}.
+ of type \isa{Exn{\isaliteral{2E}{\isachardot}}result}.
For property conversion (which coincides with conversion except for
evaluation in ML), methods are provided which solve a given goal by
@@ -223,10 +223,10 @@
& & \isa{simp} & \isa{nbe} & \isa{code} \tabularnewline \hline \hline
\multirow{5}{1ex}{\rotatebox{90}{dynamic}}
& interactive evaluation
- & \hyperlink{command.value}{\mbox{\isa{\isacommand{value}}}} \isa{{\isacharbrackleft}simp{\isacharbrackright}} & \hyperlink{command.value}{\mbox{\isa{\isacommand{value}}}} \isa{{\isacharbrackleft}nbe{\isacharbrackright}} & \hyperlink{command.value}{\mbox{\isa{\isacommand{value}}}} \isa{{\isacharbrackleft}code{\isacharbrackright}}
+ & \hyperlink{command.value}{\mbox{\isa{\isacommand{value}}}} \isa{{\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}} & \hyperlink{command.value}{\mbox{\isa{\isacommand{value}}}} \isa{{\isaliteral{5B}{\isacharbrackleft}}nbe{\isaliteral{5D}{\isacharbrackright}}} & \hyperlink{command.value}{\mbox{\isa{\isacommand{value}}}} \isa{{\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}}
\tabularnewline
& plain evaluation & & & \ttsize\verb|Code_Evaluation.dynamic_value| \tabularnewline \cline{2-5}
- & evaluation method & \hyperlink{method.code-simp}{\mbox{\isa{code{\isacharunderscore}simp}}} & \hyperlink{method.normalization}{\mbox{\isa{normalization}}} & \hyperlink{method.eval}{\mbox{\isa{eval}}} \tabularnewline
+ & evaluation method & \hyperlink{method.code-simp}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}simp}}} & \hyperlink{method.normalization}{\mbox{\isa{normalization}}} & \hyperlink{method.eval}{\mbox{\isa{eval}}} \tabularnewline
& property conversion & & & \ttsize\verb|Code_Runtime.dynamic_holds_conv| \tabularnewline \cline{2-5}
& conversion & \ttsize\verb|Code_Simp.dynamic_eval_conv| & \ttsize\verb|Nbe.dynamic_eval_conv|
& \ttsize\verb|Code_Evaluation.dynamic_eval_conv| \tabularnewline \hline \hline
@@ -269,7 +269,7 @@
%
\isatagquote
\isacommand{datatype}\isamarkupfalse%
-\ form\ {\isacharequal}\ T\ {\isacharbar}\ F\ {\isacharbar}\ And\ form\ form\ {\isacharbar}\ Or\ form\ form\ %
+\ form\ {\isaliteral{3D}{\isacharequal}}\ T\ {\isaliteral{7C}{\isacharbar}}\ F\ {\isaliteral{7C}{\isacharbar}}\ And\ form\ form\ {\isaliteral{7C}{\isacharbar}}\ Or\ form\ form\ %
\endisatagquote
{\isafoldquote}%
%
@@ -283,30 +283,30 @@
%
\isatagquotett
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ fun\ eval{\isacharunderscore}form\ %
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ fun\ eval{\isaliteral{5F}{\isacharunderscore}}form\ %
\isaantiq
-code\ T%
+code\ T{}%
\endisaantiq
-\ {\isacharequal}\ true\isanewline
-\ \ \ \ {\isacharbar}\ eval{\isacharunderscore}form\ %
+\ {\isaliteral{3D}{\isacharequal}}\ true\isanewline
+\ \ \ \ {\isaliteral{7C}{\isacharbar}}\ eval{\isaliteral{5F}{\isacharunderscore}}form\ %
\isaantiq
-code\ F%
+code\ F{}%
\endisaantiq
-\ {\isacharequal}\ false\isanewline
-\ \ \ \ {\isacharbar}\ eval{\isacharunderscore}form\ {\isacharparenleft}%
+\ {\isaliteral{3D}{\isacharequal}}\ false\isanewline
+\ \ \ \ {\isaliteral{7C}{\isacharbar}}\ eval{\isaliteral{5F}{\isacharunderscore}}form\ {\isaliteral{28}{\isacharparenleft}}%
\isaantiq
-code\ And%
+code\ And{}%
\endisaantiq
-\ {\isacharparenleft}p{\isacharcomma}\ q{\isacharparenright}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ \ \ \ \ eval{\isacharunderscore}form\ p\ andalso\ eval{\isacharunderscore}form\ q\isanewline
-\ \ \ \ {\isacharbar}\ eval{\isacharunderscore}form\ {\isacharparenleft}%
+\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}\ q{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ \ \ \ eval{\isaliteral{5F}{\isacharunderscore}}form\ p\ andalso\ eval{\isaliteral{5F}{\isacharunderscore}}form\ q\isanewline
+\ \ \ \ {\isaliteral{7C}{\isacharbar}}\ eval{\isaliteral{5F}{\isacharunderscore}}form\ {\isaliteral{28}{\isacharparenleft}}%
\isaantiq
-code\ Or%
+code\ Or{}%
\endisaantiq
-\ {\isacharparenleft}p{\isacharcomma}\ q{\isacharparenright}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ \ \ \ \ eval{\isacharunderscore}form\ p\ orelse\ eval{\isacharunderscore}form\ q{\isacharsemicolon}\isanewline
-{\isacharverbatimclose}%
+\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}\ q{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ \ \ \ eval{\isaliteral{5F}{\isacharunderscore}}form\ p\ orelse\ eval{\isaliteral{5F}{\isacharunderscore}}form\ q{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagquotett
{\isafoldquotett}%
%
@@ -324,11 +324,11 @@
here you have to refer to the corresponding adapted code directly.
For a less simplistic example, theory \isa{Approximation} in
- the \isa{Decision{\isacharunderscore}Procs} session is a good reference.%
+ the \isa{Decision{\isaliteral{5F}{\isacharunderscore}}Procs} session is a good reference.%
\end{isamarkuptext}%
\isamarkuptrue%
%
-\isamarkupsubsubsection{Static embedding of generated code into system runtime -- \isa{code{\isacharunderscore}reflect}%
+\isamarkupsubsubsection{Static embedding of generated code into system runtime -- \isa{code{\isaliteral{5F}{\isacharunderscore}}reflect}%
}
\isamarkuptrue%
%
@@ -337,7 +337,7 @@
is only accessible while the ML section is processed. Sometimes this
is not appropriate, especially if the generated code contains datatype
declarations which are shared with other parts of the system. In these
- cases, \indexdef{}{command}{code\_reflect}\hypertarget{command.code-reflect}{\hyperlink{command.code-reflect}{\mbox{\isa{\isacommand{code{\isacharunderscore}reflect}}}}} can be used:%
+ cases, \indexdef{}{command}{code\_reflect}\hypertarget{command.code-reflect}{\hyperlink{command.code-reflect}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reflect}}}}} can be used:%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -346,10 +346,10 @@
\endisadelimquote
%
\isatagquote
-\isacommand{code{\isacharunderscore}reflect}\isamarkupfalse%
-\ Sum{\isacharunderscore}Type\isanewline
-\ \ \isakeyword{datatypes}\ sum\ {\isacharequal}\ Inl\ {\isacharbar}\ Inr\isanewline
-\ \ \isakeyword{functions}\ {\isachardoublequoteopen}Sum{\isacharunderscore}Type{\isachardot}Projl{\isachardoublequoteclose}\ {\isachardoublequoteopen}Sum{\isacharunderscore}Type{\isachardot}Projr{\isachardoublequoteclose}%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reflect}\isamarkupfalse%
+\ Sum{\isaliteral{5F}{\isacharunderscore}}Type\isanewline
+\ \ \isakeyword{datatypes}\ sum\ {\isaliteral{3D}{\isacharequal}}\ Inl\ {\isaliteral{7C}{\isacharbar}}\ Inr\isanewline
+\ \ \isakeyword{functions}\ {\isaliteral{22}{\isachardoublequoteopen}}Sum{\isaliteral{5F}{\isacharunderscore}}Type{\isaliteral{2E}{\isachardot}}Projl{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}Sum{\isaliteral{5F}{\isacharunderscore}}Type{\isaliteral{2E}{\isachardot}}Projr{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -358,7 +358,7 @@
\endisadelimquote
%
\begin{isamarkuptext}%
-\noindent \indexdef{}{command}{code\_reflect}\hypertarget{command.code-reflect}{\hyperlink{command.code-reflect}{\mbox{\isa{\isacommand{code{\isacharunderscore}reflect}}}}} takes a structure name and
+\noindent \indexdef{}{command}{code\_reflect}\hypertarget{command.code-reflect}{\hyperlink{command.code-reflect}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reflect}}}}} takes a structure name and
references to datatypes and functions; for these code is compiled
into the named ML structure and the \emph{Eval} target is modified
in a way that future code generation will reference these
@@ -366,19 +366,19 @@
also allows to refer to the referenced datatypes and functions from
arbitrary ML code as well.
- A typical example for \hyperlink{command.code-reflect}{\mbox{\isa{\isacommand{code{\isacharunderscore}reflect}}}} can be found in the
+ A typical example for \hyperlink{command.code-reflect}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reflect}}}} can be found in the
\hyperlink{theory.Predicate}{\mbox{\isa{Predicate}}} theory.%
\end{isamarkuptext}%
\isamarkuptrue%
%
-\isamarkupsubsubsection{Separate compilation -- \isa{code{\isacharunderscore}reflect}%
+\isamarkupsubsubsection{Separate compilation -- \isa{code{\isaliteral{5F}{\isacharunderscore}}reflect}%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
For technical reasons it is sometimes necessary to separate
generation and compilation of code which is supposed to be used in
- the system runtime. For this \hyperlink{command.code-reflect}{\mbox{\isa{\isacommand{code{\isacharunderscore}reflect}}}} with an
+ the system runtime. For this \hyperlink{command.code-reflect}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reflect}}}} with an
optional \isa{file} argument can be used:%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -388,13 +388,13 @@
\endisadelimquote
%
\isatagquote
-\isacommand{code{\isacharunderscore}reflect}\isamarkupfalse%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reflect}\isamarkupfalse%
\ Rat\isanewline
-\ \ \isakeyword{datatypes}\ rat\ {\isacharequal}\ Frct\isanewline
+\ \ \isakeyword{datatypes}\ rat\ {\isaliteral{3D}{\isacharequal}}\ Frct\isanewline
\ \ \isakeyword{functions}\ Fract\isanewline
-\ \ \ \ {\isachardoublequoteopen}{\isacharparenleft}plus\ {\isacharcolon}{\isacharcolon}\ rat\ {\isasymRightarrow}\ rat\ {\isasymRightarrow}\ rat{\isacharparenright}{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isacharparenleft}minus\ {\isacharcolon}{\isacharcolon}\ rat\ {\isasymRightarrow}\ rat\ {\isasymRightarrow}\ rat{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ \ \ {\isachardoublequoteopen}{\isacharparenleft}times\ {\isacharcolon}{\isacharcolon}\ rat\ {\isasymRightarrow}\ rat\ {\isasymRightarrow}\ rat{\isacharparenright}{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isacharparenleft}divide\ {\isacharcolon}{\isacharcolon}\ rat\ {\isasymRightarrow}\ rat\ {\isasymRightarrow}\ rat{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}rat{\isachardot}ML{\isachardoublequoteclose}%
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}plus\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ rat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ rat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ rat{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}minus\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ rat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ rat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ rat{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}times\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ rat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ rat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ rat{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}divide\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ rat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ rat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ rat{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{file}\ {\isaliteral{22}{\isachardoublequoteopen}}examples{\isaliteral{2F}{\isacharslash}}rat{\isaliteral{2E}{\isachardot}}ML{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
--- a/doc-src/Codegen/Thy/document/Foundations.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/Codegen/Thy/document/Foundations.tex Mon Nov 08 14:41:11 2010 +0100
@@ -46,8 +46,8 @@
\noindent Central to code generation is the notion of \emph{code
equations}. A code equation as a first approximation is a theorem
- of the form \isa{f\ t\isactrlisub {\isadigit{1}}\ t\isactrlisub {\isadigit{2}}\ {\isasymdots}\ t\isactrlisub n\ {\isasymequiv}\ t} (an equation headed by a
- constant \isa{f} with arguments \isa{t\isactrlisub {\isadigit{1}}\ t\isactrlisub {\isadigit{2}}\ {\isasymdots}\ t\isactrlisub n} and right
+ of the form \isa{f\ t\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ t\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ t\isaliteral{5C3C5E697375623E}{}\isactrlisub n\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t} (an equation headed by a
+ constant \isa{f} with arguments \isa{t\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ t\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ t\isaliteral{5C3C5E697375623E}{}\isactrlisub n} and right
hand side \isa{t}).
\begin{itemize}
@@ -99,7 +99,7 @@
arguments of the left hand side of an equation, but never to the
constant heading the left hand side. An important special case are
\emph{unfold theorems}, which may be declared and removed using the
- \hyperlink{attribute.code-unfold}{\mbox{\isa{code{\isacharunderscore}unfold}}} or \emph{\hyperlink{attribute.code-unfold}{\mbox{\isa{code{\isacharunderscore}unfold}}} del}
+ \hyperlink{attribute.code-unfold}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}unfold}}} or \emph{\hyperlink{attribute.code-unfold}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}unfold}}} del}
attribute, respectively.
Some common applications:%
@@ -119,9 +119,9 @@
%
\isatagquote
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code{\isacharunderscore}unfold{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}x\ {\isasymin}\ set\ xs\ {\isasymlongleftrightarrow}\ List{\isachardot}member\ xs\ x{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}fact\ in{\isacharunderscore}set{\isacharunderscore}member{\isacharparenright}%
+\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5F}{\isacharunderscore}}unfold{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ set\ xs\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ List{\isaliteral{2E}{\isachardot}}member\ xs\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}fact\ in{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}member{\isaliteral{29}{\isacharparenright}}%
\endisatagquote
{\isafoldquote}%
%
@@ -140,9 +140,9 @@
%
\isatagquote
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code{\isacharunderscore}unfold{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymlongleftrightarrow}\ List{\isachardot}null\ xs{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}fact\ eq{\isacharunderscore}Nil{\isacharunderscore}null{\isacharparenright}%
+\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5F}{\isacharunderscore}}unfold{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ List{\isaliteral{2E}{\isachardot}}null\ xs{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}fact\ eq{\isaliteral{5F}{\isacharunderscore}}Nil{\isaliteral{5F}{\isacharunderscore}}null{\isaliteral{29}{\isacharparenright}}%
\endisatagquote
{\isafoldquote}%
%
@@ -161,9 +161,9 @@
%
\isatagquote
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code{\isacharunderscore}unfold{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}{\isadigit{1}}\ {\isacharequal}\ Suc\ {\isadigit{0}}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}fact\ One{\isacharunderscore}nat{\isacharunderscore}def{\isacharparenright}%
+\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5F}{\isacharunderscore}}unfold{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ Suc\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}fact\ One{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
\endisatagquote
{\isafoldquote}%
%
@@ -178,18 +178,18 @@
interface, transforming a list of function theorems to another list
of function theorems, provided that neither the heading constant nor
its type change. The \isa{{\isadigit{0}}} / \isa{Suc} pattern
- elimination implemented in theory \hyperlink{theory.Efficient-Nat}{\mbox{\isa{Efficient{\isacharunderscore}Nat}}} (see
+ elimination implemented in theory \hyperlink{theory.Efficient-Nat}{\mbox{\isa{Efficient{\isaliteral{5F}{\isacharunderscore}}Nat}}} (see
\secref{eff_nat}) uses this interface.
\noindent The current setup of the preprocessor may be inspected
- using the \indexdef{}{command}{print\_codeproc}\hypertarget{command.print-codeproc}{\hyperlink{command.print-codeproc}{\mbox{\isa{\isacommand{print{\isacharunderscore}codeproc}}}}} command. \indexdef{}{command}{code\_thms}\hypertarget{command.code-thms}{\hyperlink{command.code-thms}{\mbox{\isa{\isacommand{code{\isacharunderscore}thms}}}}} (see \secref{sec:equations}) provides a convenient
+ using the \indexdef{}{command}{print\_codeproc}\hypertarget{command.print-codeproc}{\hyperlink{command.print-codeproc}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}codeproc}}}}} command. \indexdef{}{command}{code\_thms}\hypertarget{command.code-thms}{\hyperlink{command.code-thms}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}thms}}}}} (see \secref{sec:equations}) provides a convenient
mechanism to inspect the impact of a preprocessor setup on code
equations.
\begin{warn}
- Attribute \hyperlink{attribute.code-unfold}{\mbox{\isa{code{\isacharunderscore}unfold}}} also applies to the
+ Attribute \hyperlink{attribute.code-unfold}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}unfold}}} also applies to the
preprocessor of the ancient \isa{SML\ code\ generator}; in case
- this is not what you intend, use \hyperlink{attribute.code-inline}{\mbox{\isa{code{\isacharunderscore}inline}}} instead.
+ this is not what you intend, use \hyperlink{attribute.code-inline}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}inline}}} instead.
\end{warn}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -215,14 +215,14 @@
%
\isatagquote
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}dequeue\ {\isacharparenleft}AQueue\ xs\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ \ {\isacharparenleft}if\ xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ then\ {\isacharparenleft}None{\isacharcomma}\ AQueue\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\isanewline
-\ \ \ \ \ \ \ else\ dequeue\ {\isacharparenleft}AQueue\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharparenleft}rev\ xs{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}dequeue\ {\isacharparenleft}AQueue\ xs\ {\isacharparenleft}y\ {\isacharhash}\ ys{\isacharparenright}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ \ {\isacharparenleft}Some\ y{\isacharcomma}\ AQueue\ xs\ ys{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}if\ xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ then\ {\isaliteral{28}{\isacharparenleft}}None{\isaliteral{2C}{\isacharcomma}}\ AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ \ \ \ else\ dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{23}{\isacharhash}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}Some\ y{\isaliteral{2C}{\isacharcomma}}\ AQueue\ xs\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}cases\ xs{\isacharcomma}\ simp{\isacharunderscore}all{\isacharparenright}\ {\isacharparenleft}cases\ {\isachardoublequoteopen}rev\ xs{\isachardoublequoteclose}{\isacharcomma}\ simp{\isacharunderscore}all{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}cases\ xs{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}cases\ {\isaliteral{22}{\isachardoublequoteopen}}rev\ xs{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{29}{\isacharparenright}}%
\endisatagquote
{\isafoldquote}%
%
@@ -231,7 +231,7 @@
\endisadelimquote
%
\begin{isamarkuptext}%
-\noindent The annotation \isa{{\isacharbrackleft}code{\isacharbrackright}} is an \isa{attribute}
+\noindent The annotation \isa{{\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}} is an \isa{attribute}
which states that the given theorems should be considered as code
equations for a \isa{fun} statement -- the corresponding constant
is determined syntactically. The resulting code:%
@@ -245,11 +245,11 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-dequeue\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ Queue\ a\ {\isacharminus}{\isachargreater}\ {\isacharparenleft}Maybe\ a{\isacharcomma}\ Queue\ a{\isacharparenright}{\isacharsemicolon}\isanewline
-dequeue\ {\isacharparenleft}AQueue\ xs\ {\isacharparenleft}y\ {\isacharcolon}\ ys{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}Just\ y{\isacharcomma}\ AQueue\ xs\ ys{\isacharparenright}{\isacharsemicolon}\isanewline
-dequeue\ {\isacharparenleft}AQueue\ xs\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ {\isacharparenleft}if\ null\ xs\ then\ {\isacharparenleft}Nothing{\isacharcomma}\ AQueue\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\isanewline
-\ \ \ \ else\ dequeue\ {\isacharparenleft}AQueue\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharparenleft}reverse\ xs{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline%
+dequeue\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ Queue\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}Maybe\ a{\isaliteral{2C}{\isacharcomma}}\ Queue\ a{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{3A}{\isacharcolon}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Just\ y{\isaliteral{2C}{\isacharcomma}}\ AQueue\ xs\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}if\ null\ xs\ then\ {\isaliteral{28}{\isacharparenleft}}Nothing{\isaliteral{2C}{\isacharcomma}}\ AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ else\ dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{28}{\isacharparenleft}}reverse\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -261,8 +261,8 @@
\endisadelimquotetypewriter
%
\begin{isamarkuptext}%
-\noindent You may note that the equality test \isa{xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}} has
- been replaced by the predicate \isa{List{\isachardot}null\ xs}. This is due
+\noindent You may note that the equality test \isa{xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}} has
+ been replaced by the predicate \isa{List{\isaliteral{2E}{\isachardot}}null\ xs}. This is due
to the default setup of the \qn{preprocessor}.
This possibility to select arbitrary code equations is the key
@@ -273,10 +273,10 @@
equations (before preprocessing) and code equations (after
preprocessing).
- The first can be listed (among other data) using the \indexdef{}{command}{print\_codesetup}\hypertarget{command.print-codesetup}{\hyperlink{command.print-codesetup}{\mbox{\isa{\isacommand{print{\isacharunderscore}codesetup}}}}} command.
+ The first can be listed (among other data) using the \indexdef{}{command}{print\_codesetup}\hypertarget{command.print-codesetup}{\hyperlink{command.print-codesetup}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}codesetup}}}}} command.
The code equations after preprocessing are already are blueprint of
- the generated program and can be inspected using the \hyperlink{command.code-thms}{\mbox{\isa{\isacommand{code{\isacharunderscore}thms}}}} command:%
+ the generated program and can be inspected using the \hyperlink{command.code-thms}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}thms}}}} command:%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -285,7 +285,7 @@
\endisadelimquote
%
\isatagquote
-\isacommand{code{\isacharunderscore}thms}\isamarkupfalse%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}thms}\isamarkupfalse%
\ dequeue%
\endisatagquote
{\isafoldquote}%
@@ -297,7 +297,7 @@
\begin{isamarkuptext}%
\noindent This prints a table with the code equations for \isa{dequeue}, including \emph{all} code equations those equations depend
on recursively. These dependencies themselves can be visualized using
- the \indexdef{}{command}{code\_deps}\hypertarget{command.code-deps}{\hyperlink{command.code-deps}{\mbox{\isa{\isacommand{code{\isacharunderscore}deps}}}}} command.%
+ the \indexdef{}{command}{code\_deps}\hypertarget{command.code-deps}{\hyperlink{command.code-deps}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}deps}}}}} command.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -317,13 +317,13 @@
%
\isatagquote
\isacommand{primrec}\isamarkupfalse%
-\ collect{\isacharunderscore}duplicates\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}collect{\isacharunderscore}duplicates\ xs\ ys\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ xs{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}collect{\isacharunderscore}duplicates\ xs\ ys\ {\isacharparenleft}z{\isacharhash}zs{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}if\ z\ {\isasymin}\ set\ xs\isanewline
-\ \ \ \ then\ if\ z\ {\isasymin}\ set\ ys\isanewline
-\ \ \ \ \ \ then\ collect{\isacharunderscore}duplicates\ xs\ ys\ zs\isanewline
-\ \ \ \ \ \ else\ collect{\isacharunderscore}duplicates\ xs\ {\isacharparenleft}z{\isacharhash}ys{\isacharparenright}\ zs\isanewline
-\ \ \ \ else\ collect{\isacharunderscore}duplicates\ {\isacharparenleft}z{\isacharhash}xs{\isacharparenright}\ {\isacharparenleft}z{\isacharhash}ys{\isacharparenright}\ zs{\isacharparenright}{\isachardoublequoteclose}%
+\ collect{\isaliteral{5F}{\isacharunderscore}}duplicates\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}collect{\isaliteral{5F}{\isacharunderscore}}duplicates\ xs\ ys\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ xs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}collect{\isaliteral{5F}{\isacharunderscore}}duplicates\ xs\ ys\ {\isaliteral{28}{\isacharparenleft}}z{\isaliteral{23}{\isacharhash}}zs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ z\ {\isaliteral{5C3C696E3E}{\isasymin}}\ set\ xs\isanewline
+\ \ \ \ then\ if\ z\ {\isaliteral{5C3C696E3E}{\isasymin}}\ set\ ys\isanewline
+\ \ \ \ \ \ then\ collect{\isaliteral{5F}{\isacharunderscore}}duplicates\ xs\ ys\ zs\isanewline
+\ \ \ \ \ \ else\ collect{\isaliteral{5F}{\isacharunderscore}}duplicates\ xs\ {\isaliteral{28}{\isacharparenleft}}z{\isaliteral{23}{\isacharhash}}ys{\isaliteral{29}{\isacharparenright}}\ zs\isanewline
+\ \ \ \ else\ collect{\isaliteral{5F}{\isacharunderscore}}duplicates\ {\isaliteral{28}{\isacharparenleft}}z{\isaliteral{23}{\isacharhash}}xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}z{\isaliteral{23}{\isacharhash}}ys{\isaliteral{29}{\isacharparenright}}\ zs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -333,7 +333,7 @@
%
\begin{isamarkuptext}%
\noindent During preprocessing, the membership test is rewritten,
- resulting in \isa{List{\isachardot}member}, which itself performs an explicit
+ resulting in \isa{List{\isaliteral{2E}{\isachardot}}member}, which itself performs an explicit
equality check, as can be seen in the corresponding \isa{SML} code:%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -345,31 +345,31 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-structure\ Example\ {\isacharcolon}\ sig\isanewline
-\ \ type\ {\isacharprime}a\ equal\isanewline
-\ \ val\ equal\ {\isacharcolon}\ {\isacharprime}a\ equal\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ bool\isanewline
-\ \ val\ eq\ {\isacharcolon}\ {\isacharprime}a\ equal\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ bool\isanewline
-\ \ val\ member\ {\isacharcolon}\ {\isacharprime}a\ equal\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ list\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ bool\isanewline
-\ \ val\ collect{\isacharunderscore}duplicates\ {\isacharcolon}\isanewline
-\ \ \ \ {\isacharprime}a\ equal\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ list\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ list\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ list\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ list\isanewline
-end\ {\isacharequal}\ struct\isanewline
+structure\ Example\ {\isaliteral{3A}{\isacharcolon}}\ sig\isanewline
+\ \ type\ {\isaliteral{27}{\isacharprime}}a\ equal\isanewline
+\ \ val\ equal\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ equal\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ bool\isanewline
+\ \ val\ eq\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ equal\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ bool\isanewline
+\ \ val\ member\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ equal\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ bool\isanewline
+\ \ val\ collect{\isaliteral{5F}{\isacharunderscore}}duplicates\ {\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ {\isaliteral{27}{\isacharprime}}a\ equal\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ list\isanewline
+end\ {\isaliteral{3D}{\isacharequal}}\ struct\isanewline
\isanewline
-type\ {\isacharprime}a\ equal\ {\isacharequal}\ {\isacharbraceleft}equal\ {\isacharcolon}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ bool{\isacharbraceright}{\isacharsemicolon}\isanewline
-val\ equal\ {\isacharequal}\ {\isacharhash}equal\ {\isacharcolon}\ {\isacharprime}a\ equal\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ bool{\isacharsemicolon}\isanewline
+type\ {\isaliteral{27}{\isacharprime}}a\ equal\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}equal\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ bool{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+val\ equal\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{23}{\isacharhash}}equal\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ equal\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ bool{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ eq\ A{\isacharunderscore}\ a\ b\ {\isacharequal}\ equal\ A{\isacharunderscore}\ a\ b{\isacharsemicolon}\isanewline
+fun\ eq\ A{\isaliteral{5F}{\isacharunderscore}}\ a\ b\ {\isaliteral{3D}{\isacharequal}}\ equal\ A{\isaliteral{5F}{\isacharunderscore}}\ a\ b{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ member\ A{\isacharunderscore}\ {\isacharbrackleft}{\isacharbrackright}\ y\ {\isacharequal}\ false\isanewline
-\ \ {\isacharbar}\ member\ A{\isacharunderscore}\ {\isacharparenleft}x\ {\isacharcolon}{\isacharcolon}\ xs{\isacharparenright}\ y\ {\isacharequal}\ eq\ A{\isacharunderscore}\ x\ y\ orelse\ member\ A{\isacharunderscore}\ xs\ y{\isacharsemicolon}\isanewline
+fun\ member\ A{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ y\ {\isaliteral{3D}{\isacharequal}}\ false\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ member\ A{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ xs{\isaliteral{29}{\isacharparenright}}\ y\ {\isaliteral{3D}{\isacharequal}}\ eq\ A{\isaliteral{5F}{\isacharunderscore}}\ x\ y\ orelse\ member\ A{\isaliteral{5F}{\isacharunderscore}}\ xs\ y{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ collect{\isacharunderscore}duplicates\ A{\isacharunderscore}\ xs\ ys\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ xs\isanewline
-\ \ {\isacharbar}\ collect{\isacharunderscore}duplicates\ A{\isacharunderscore}\ xs\ ys\ {\isacharparenleft}z\ {\isacharcolon}{\isacharcolon}\ zs{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ {\isacharparenleft}if\ member\ A{\isacharunderscore}\ xs\ z\isanewline
-\ \ \ \ \ \ then\ {\isacharparenleft}if\ member\ A{\isacharunderscore}\ ys\ z\ then\ collect{\isacharunderscore}duplicates\ A{\isacharunderscore}\ xs\ ys\ zs\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ else\ collect{\isacharunderscore}duplicates\ A{\isacharunderscore}\ xs\ {\isacharparenleft}z\ {\isacharcolon}{\isacharcolon}\ ys{\isacharparenright}\ zs{\isacharparenright}\isanewline
-\ \ \ \ \ \ else\ collect{\isacharunderscore}duplicates\ A{\isacharunderscore}\ {\isacharparenleft}z\ {\isacharcolon}{\isacharcolon}\ xs{\isacharparenright}\ {\isacharparenleft}z\ {\isacharcolon}{\isacharcolon}\ ys{\isacharparenright}\ zs{\isacharparenright}{\isacharsemicolon}\isanewline
+fun\ collect{\isaliteral{5F}{\isacharunderscore}}duplicates\ A{\isaliteral{5F}{\isacharunderscore}}\ xs\ ys\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ xs\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ collect{\isaliteral{5F}{\isacharunderscore}}duplicates\ A{\isaliteral{5F}{\isacharunderscore}}\ xs\ ys\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ zs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ {\isaliteral{28}{\isacharparenleft}}if\ member\ A{\isaliteral{5F}{\isacharunderscore}}\ xs\ z\isanewline
+\ \ \ \ \ \ then\ {\isaliteral{28}{\isacharparenleft}}if\ member\ A{\isaliteral{5F}{\isacharunderscore}}\ ys\ z\ then\ collect{\isaliteral{5F}{\isacharunderscore}}duplicates\ A{\isaliteral{5F}{\isacharunderscore}}\ xs\ ys\ zs\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ else\ collect{\isaliteral{5F}{\isacharunderscore}}duplicates\ A{\isaliteral{5F}{\isacharunderscore}}\ xs\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ ys{\isaliteral{29}{\isacharparenright}}\ zs{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ \ \ else\ collect{\isaliteral{5F}{\isacharunderscore}}duplicates\ A{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ ys{\isaliteral{29}{\isacharparenright}}\ zs{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-end{\isacharsemicolon}\ {\isacharparenleft}{\isacharasterisk}struct\ Example{\isacharasterisk}{\isacharparenright}\isanewline%
+end{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}struct\ Example{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -383,7 +383,7 @@
\begin{isamarkuptext}%
\noindent Obviously, polymorphic equality is implemented the Haskell
way using a type class. How is this achieved? HOL introduces an
- explicit class \isa{equal} with a corresponding operation \isa{equal{\isacharunderscore}class{\isachardot}equal} such that \isa{equal{\isacharunderscore}class{\isachardot}equal\ {\isacharequal}\ op\ {\isacharequal}}. The preprocessing
+ explicit class \isa{equal} with a corresponding operation \isa{equal{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}equal} such that \isa{equal{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}equal\ {\isaliteral{3D}{\isacharequal}}\ op\ {\isaliteral{3D}{\isacharequal}}}. The preprocessing
framework does the rest by propagating the \isa{equal} constraints
through all dependent code equations. For datatypes, instances of
\isa{equal} are implicitly derived when possible. For other types,
@@ -407,17 +407,17 @@
%
\isatagquote
\isacommand{definition}\isamarkupfalse%
-\ strict{\isacharunderscore}dequeue\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ queue\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a\ queue{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}strict{\isacharunderscore}dequeue\ q\ {\isacharequal}\ {\isacharparenleft}case\ dequeue\ q\isanewline
-\ \ \ \ of\ {\isacharparenleft}Some\ x{\isacharcomma}\ q{\isacharprime}{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}x{\isacharcomma}\ q{\isacharprime}{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ strict{\isaliteral{5F}{\isacharunderscore}}dequeue\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a\ queue{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}strict{\isaliteral{5F}{\isacharunderscore}}dequeue\ q\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}case\ dequeue\ q\isanewline
+\ \ \ \ of\ {\isaliteral{28}{\isacharparenleft}}Some\ x{\isaliteral{2C}{\isacharcomma}}\ q{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ q{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ strict{\isacharunderscore}dequeue{\isacharunderscore}AQueue\ {\isacharbrackleft}code{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}strict{\isacharunderscore}dequeue\ {\isacharparenleft}AQueue\ xs\ {\isacharparenleft}y\ {\isacharhash}\ ys{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}y{\isacharcomma}\ AQueue\ xs\ ys{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}strict{\isacharunderscore}dequeue\ {\isacharparenleft}AQueue\ xs\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ {\isacharparenleft}case\ rev\ xs\ of\ y\ {\isacharhash}\ ys\ {\isasymRightarrow}\ {\isacharparenleft}y{\isacharcomma}\ AQueue\ {\isacharbrackleft}{\isacharbrackright}\ ys{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ strict{\isaliteral{5F}{\isacharunderscore}}dequeue{\isaliteral{5F}{\isacharunderscore}}AQueue\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}strict{\isaliteral{5F}{\isacharunderscore}}dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{23}{\isacharhash}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ AQueue\ xs\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}strict{\isaliteral{5F}{\isacharunderscore}}dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ {\isaliteral{28}{\isacharparenleft}}case\ rev\ xs\ of\ y\ {\isaliteral{23}{\isacharhash}}\ ys\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}\ strict{\isacharunderscore}dequeue{\isacharunderscore}def{\isacharparenright}\ {\isacharparenleft}cases\ xs{\isacharcomma}\ simp{\isacharunderscore}all\ split{\isacharcolon}\ list{\isachardot}split{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{5F}{\isacharunderscore}}all\ add{\isaliteral{3A}{\isacharcolon}}\ strict{\isaliteral{5F}{\isacharunderscore}}dequeue{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}cases\ xs{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{5F}{\isacharunderscore}}all\ split{\isaliteral{3A}{\isacharcolon}}\ list{\isaliteral{2E}{\isachardot}}split{\isaliteral{29}{\isacharparenright}}%
\endisatagquote
{\isafoldquote}%
%
@@ -427,7 +427,7 @@
%
\begin{isamarkuptext}%
\noindent In the corresponding code, there is no equation
- for the pattern \isa{AQueue\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbrackleft}{\isacharbrackright}}:%
+ for the pattern \isa{AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}}:%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -438,12 +438,12 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-strict{\isacharunderscore}dequeue\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ Queue\ a\ {\isacharminus}{\isachargreater}\ {\isacharparenleft}a{\isacharcomma}\ Queue\ a{\isacharparenright}{\isacharsemicolon}\isanewline
-strict{\isacharunderscore}dequeue\ {\isacharparenleft}AQueue\ xs\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ let\ {\isacharbraceleft}\isanewline
-\ \ \ \ {\isacharparenleft}y\ {\isacharcolon}\ ys{\isacharparenright}\ {\isacharequal}\ reverse\ xs{\isacharsemicolon}\isanewline
-\ \ {\isacharbraceright}\ in\ {\isacharparenleft}y{\isacharcomma}\ AQueue\ {\isacharbrackleft}{\isacharbrackright}\ ys{\isacharparenright}{\isacharsemicolon}\isanewline
-strict{\isacharunderscore}dequeue\ {\isacharparenleft}AQueue\ xs\ {\isacharparenleft}y\ {\isacharcolon}\ ys{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}y{\isacharcomma}\ AQueue\ xs\ ys{\isacharparenright}{\isacharsemicolon}\isanewline%
+strict{\isaliteral{5F}{\isacharunderscore}}dequeue\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ Queue\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ Queue\ a{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+strict{\isaliteral{5F}{\isacharunderscore}}dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ let\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ \ \ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{3A}{\isacharcolon}}\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ reverse\ xs{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ {\isaliteral{7D}{\isacharbraceright}}\ in\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+strict{\isaliteral{5F}{\isacharunderscore}}dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{3A}{\isacharcolon}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ AQueue\ xs\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -466,20 +466,20 @@
%
\isatagquote
\isacommand{axiomatization}\isamarkupfalse%
-\ empty{\isacharunderscore}queue\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a\isanewline
+\ empty{\isaliteral{5F}{\isacharunderscore}}queue\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\isanewline
\isanewline
\isacommand{definition}\isamarkupfalse%
-\ strict{\isacharunderscore}dequeue{\isacharprime}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ queue\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a\ queue{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}strict{\isacharunderscore}dequeue{\isacharprime}\ q\ {\isacharequal}\ {\isacharparenleft}case\ dequeue\ q\ of\ {\isacharparenleft}Some\ x{\isacharcomma}\ q{\isacharprime}{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}x{\isacharcomma}\ q{\isacharprime}{\isacharparenright}\ {\isacharbar}\ {\isacharunderscore}\ {\isasymRightarrow}\ empty{\isacharunderscore}queue{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ strict{\isaliteral{5F}{\isacharunderscore}}dequeue{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a\ queue{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}strict{\isaliteral{5F}{\isacharunderscore}}dequeue{\isaliteral{27}{\isacharprime}}\ q\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}case\ dequeue\ q\ of\ {\isaliteral{28}{\isacharparenleft}}Some\ x{\isaliteral{2C}{\isacharcomma}}\ q{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ q{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ empty{\isaliteral{5F}{\isacharunderscore}}queue{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ strict{\isacharunderscore}dequeue{\isacharprime}{\isacharunderscore}AQueue\ {\isacharbrackleft}code{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}strict{\isacharunderscore}dequeue{\isacharprime}\ {\isacharparenleft}AQueue\ xs\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}if\ xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ then\ empty{\isacharunderscore}queue\isanewline
-\ \ \ \ \ else\ strict{\isacharunderscore}dequeue{\isacharprime}\ {\isacharparenleft}AQueue\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharparenleft}rev\ xs{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}strict{\isacharunderscore}dequeue{\isacharprime}\ {\isacharparenleft}AQueue\ xs\ {\isacharparenleft}y\ {\isacharhash}\ ys{\isacharparenright}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ \ {\isacharparenleft}y{\isacharcomma}\ AQueue\ xs\ ys{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ strict{\isaliteral{5F}{\isacharunderscore}}dequeue{\isaliteral{27}{\isacharprime}}{\isaliteral{5F}{\isacharunderscore}}AQueue\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}strict{\isaliteral{5F}{\isacharunderscore}}dequeue{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ then\ empty{\isaliteral{5F}{\isacharunderscore}}queue\isanewline
+\ \ \ \ \ else\ strict{\isaliteral{5F}{\isacharunderscore}}dequeue{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}strict{\isaliteral{5F}{\isacharunderscore}}dequeue{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{23}{\isacharhash}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ AQueue\ xs\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}\ strict{\isacharunderscore}dequeue{\isacharprime}{\isacharunderscore}def\ split{\isacharcolon}\ list{\isachardot}splits{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{5F}{\isacharunderscore}}all\ add{\isaliteral{3A}{\isacharcolon}}\ strict{\isaliteral{5F}{\isacharunderscore}}dequeue{\isaliteral{27}{\isacharprime}}{\isaliteral{5F}{\isacharunderscore}}def\ split{\isaliteral{3A}{\isacharcolon}}\ list{\isaliteral{2E}{\isachardot}}splits{\isaliteral{29}{\isacharparenright}}%
\endisatagquote
{\isafoldquote}%
%
@@ -488,7 +488,7 @@
\endisadelimquote
%
\begin{isamarkuptext}%
-Observe that on the right hand side of the definition of \isa{strict{\isacharunderscore}dequeue{\isacharprime}}, the unspecified constant \isa{empty{\isacharunderscore}queue} occurs.
+Observe that on the right hand side of the definition of \isa{strict{\isaliteral{5F}{\isacharunderscore}}dequeue{\isaliteral{27}{\isacharprime}}}, the unspecified constant \isa{empty{\isaliteral{5F}{\isacharunderscore}}queue} occurs.
Normally, if constants without any code equations occur in a
program, the code generator complains (since in most cases this is
@@ -496,7 +496,7 @@
of as function definitions which always fail,
since there is never a successful pattern match on the left hand
side. In order to categorise a constant into that category
- explicitly, use \indexdef{}{command}{code\_abort}\hypertarget{command.code-abort}{\hyperlink{command.code-abort}{\mbox{\isa{\isacommand{code{\isacharunderscore}abort}}}}}:%
+ explicitly, use \indexdef{}{command}{code\_abort}\hypertarget{command.code-abort}{\hyperlink{command.code-abort}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}abort}}}}}:%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -505,8 +505,8 @@
\endisadelimquote
%
\isatagquote
-\isacommand{code{\isacharunderscore}abort}\isamarkupfalse%
-\ empty{\isacharunderscore}queue%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}abort}\isamarkupfalse%
+\ empty{\isaliteral{5F}{\isacharunderscore}}queue%
\endisatagquote
{\isafoldquote}%
%
@@ -527,14 +527,14 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-empty{\isacharunderscore}queue\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ a{\isacharsemicolon}\isanewline
-empty{\isacharunderscore}queue\ {\isacharequal}\ error\ {\isachardoublequote}empty{\isacharunderscore}queue{\isachardoublequote}{\isacharsemicolon}\isanewline
+empty{\isaliteral{5F}{\isacharunderscore}}queue\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+empty{\isaliteral{5F}{\isacharunderscore}}queue\ {\isaliteral{3D}{\isacharequal}}\ error\ {\isaliteral{22}{\isachardoublequote}}empty{\isaliteral{5F}{\isacharunderscore}}queue{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-strict{\isacharunderscore}dequeue\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ Queue\ a\ {\isacharminus}{\isachargreater}\ {\isacharparenleft}a{\isacharcomma}\ Queue\ a{\isacharparenright}{\isacharsemicolon}\isanewline
-strict{\isacharunderscore}dequeue\ {\isacharparenleft}AQueue\ xs\ {\isacharparenleft}y\ {\isacharcolon}\ ys{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}y{\isacharcomma}\ AQueue\ xs\ ys{\isacharparenright}{\isacharsemicolon}\isanewline
-strict{\isacharunderscore}dequeue\ {\isacharparenleft}AQueue\ xs\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ {\isacharparenleft}if\ null\ xs\ then\ empty{\isacharunderscore}queue\isanewline
-\ \ \ \ else\ strict{\isacharunderscore}dequeue\ {\isacharparenleft}AQueue\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharparenleft}reverse\ xs{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline%
+strict{\isaliteral{5F}{\isacharunderscore}}dequeue\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ Queue\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ Queue\ a{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+strict{\isaliteral{5F}{\isacharunderscore}}dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{3A}{\isacharcolon}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ AQueue\ xs\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+strict{\isaliteral{5F}{\isacharunderscore}}dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}if\ null\ xs\ then\ empty{\isaliteral{5F}{\isacharunderscore}}queue\isanewline
+\ \ \ \ else\ strict{\isaliteral{5F}{\isacharunderscore}}dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{28}{\isacharparenleft}}reverse\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -548,7 +548,7 @@
\begin{isamarkuptext}%
\noindent This feature however is rarely needed in practice. Note
also that the HOL default setup already declares \isa{undefined}
- as \hyperlink{command.code-abort}{\mbox{\isa{\isacommand{code{\isacharunderscore}abort}}}}, which is most likely to be used in such
+ as \hyperlink{command.code-abort}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}abort}}}}, which is most likely to be used in such
situations.%
\end{isamarkuptext}%
\isamarkuptrue%
--- a/doc-src/Codegen/Thy/document/Further.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/Codegen/Thy/document/Further.tex Mon Nov 08 14:41:11 2010 +0100
@@ -27,8 +27,8 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-When invoking the \hyperlink{command.export-code}{\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}} command it is possible to leave
- out the \hyperlink{keyword.module-name}{\mbox{\isa{\isakeyword{module{\isacharunderscore}name}}}} part; then code is distributed over
+When invoking the \hyperlink{command.export-code}{\mbox{\isa{\isacommand{export{\isaliteral{5F}{\isacharunderscore}}code}}}} command it is possible to leave
+ out the \hyperlink{keyword.module-name}{\mbox{\isa{\isakeyword{module{\isaliteral{5F}{\isacharunderscore}}name}}}} part; then code is distributed over
different modules, where the module name space roughly is induced
by the Isabelle theory name space.
@@ -49,7 +49,7 @@
\endisadelimquote
%
\isatagquote
-\isacommand{code{\isacharunderscore}modulename}\isamarkupfalse%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}modulename}\isamarkupfalse%
\ SML\isanewline
\ \ A\ ABC\isanewline
\ \ B\ ABC\isanewline
@@ -88,9 +88,9 @@
%
\isatagquote
\isacommand{locale}\isamarkupfalse%
-\ power\ {\isacharequal}\isanewline
-\ \ \isakeyword{fixes}\ power\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}b{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{assumes}\ power{\isacharunderscore}commute{\isacharcolon}\ {\isachardoublequoteopen}power\ x\ {\isasymcirc}\ power\ y\ {\isacharequal}\ power\ y\ {\isasymcirc}\ power\ x{\isachardoublequoteclose}\isanewline
+\ power\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \isakeyword{fixes}\ power\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{assumes}\ power{\isaliteral{5F}{\isacharunderscore}}commute{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}power\ x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ power\ y\ {\isaliteral{3D}{\isacharequal}}\ power\ y\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ power\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{begin}%
\endisatagquote
{\isafoldquote}%
@@ -111,29 +111,29 @@
%
\isatagquote
\isacommand{primrec}\isamarkupfalse%
-\ powers\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}b{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}powers\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ id{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}powers\ {\isacharparenleft}x\ {\isacharhash}\ xs{\isacharparenright}\ {\isacharequal}\ power\ x\ {\isasymcirc}\ powers\ xs{\isachardoublequoteclose}\isanewline
+\ powers\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}powers\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ id{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}powers\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ power\ x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ powers\ xs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ powers{\isacharunderscore}append{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}powers\ {\isacharparenleft}xs\ {\isacharat}\ ys{\isacharparenright}\ {\isacharequal}\ powers\ xs\ {\isasymcirc}\ powers\ ys{\isachardoublequoteclose}\isanewline
+\ powers{\isaliteral{5F}{\isacharunderscore}}append{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}powers\ {\isaliteral{28}{\isacharparenleft}}xs\ {\isaliteral{40}{\isacharat}}\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ powers\ xs\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ powers\ ys{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ xs{\isacharparenright}\ simp{\isacharunderscore}all\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ xs{\isaliteral{29}{\isacharparenright}}\ simp{\isaliteral{5F}{\isacharunderscore}}all\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ powers{\isacharunderscore}power{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}powers\ xs\ {\isasymcirc}\ power\ x\ {\isacharequal}\ power\ x\ {\isasymcirc}\ powers\ xs{\isachardoublequoteclose}\isanewline
+\ powers{\isaliteral{5F}{\isacharunderscore}}power{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}powers\ xs\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ power\ x\ {\isaliteral{3D}{\isacharequal}}\ power\ x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ powers\ xs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ xs{\isacharparenright}\isanewline
-\ \ \ \ {\isacharparenleft}simp{\isacharunderscore}all\ del{\isacharcolon}\ o{\isacharunderscore}apply\ id{\isacharunderscore}apply\ add{\isacharcolon}\ o{\isacharunderscore}assoc\ {\isacharbrackleft}symmetric{\isacharbrackright}{\isacharcomma}\isanewline
-\ \ \ \ \ \ simp\ del{\isacharcolon}\ o{\isacharunderscore}apply\ add{\isacharcolon}\ o{\isacharunderscore}assoc\ power{\isacharunderscore}commute{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ xs{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ {\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{5F}{\isacharunderscore}}all\ del{\isaliteral{3A}{\isacharcolon}}\ o{\isaliteral{5F}{\isacharunderscore}}apply\ id{\isaliteral{5F}{\isacharunderscore}}apply\ add{\isaliteral{3A}{\isacharcolon}}\ o{\isaliteral{5F}{\isacharunderscore}}assoc\ {\isaliteral{5B}{\isacharbrackleft}}symmetric{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
+\ \ \ \ \ \ simp\ del{\isaliteral{3A}{\isacharcolon}}\ o{\isaliteral{5F}{\isacharunderscore}}apply\ add{\isaliteral{3A}{\isacharcolon}}\ o{\isaliteral{5F}{\isacharunderscore}}assoc\ power{\isaliteral{5F}{\isacharunderscore}}commute{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ powers{\isacharunderscore}rev{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}powers\ {\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharequal}\ powers\ xs{\isachardoublequoteclose}\isanewline
+\ powers{\isaliteral{5F}{\isacharunderscore}}rev{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}powers\ {\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ powers\ xs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ xs{\isacharparenright}\ {\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}\ powers{\isacharunderscore}append\ powers{\isacharunderscore}power{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{5F}{\isacharunderscore}}all\ add{\isaliteral{3A}{\isacharcolon}}\ powers{\isaliteral{5F}{\isacharunderscore}}append\ powers{\isaliteral{5F}{\isacharunderscore}}power{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
\isacommand{end}\isamarkupfalse%
%
@@ -145,10 +145,10 @@
\endisadelimquote
%
\begin{isamarkuptext}%
-After an interpretation of this locale (say, \indexdef{}{command}{interpretation}\hypertarget{command.interpretation}{\hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}}} \isa{fun{\isacharunderscore}power{\isacharcolon}} \isa{{\isachardoublequote}power\ {\isacharparenleft}{\isasymlambda}n\ {\isacharparenleft}f\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}{\isachardot}\ f\ {\isacharcircum}{\isacharcircum}\ n{\isacharparenright}{\isachardoublequote}}), one would expect to have a constant \isa{fun{\isacharunderscore}power{\isachardot}powers\ {\isacharcolon}{\isacharcolon}\ nat\ list\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a} for which code
+After an interpretation of this locale (say, \indexdef{}{command}{interpretation}\hypertarget{command.interpretation}{\hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}}} \isa{fun{\isaliteral{5F}{\isacharunderscore}}power{\isaliteral{3A}{\isacharcolon}}} \isa{{\isaliteral{22}{\isachardoublequote}}power\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}n\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ f\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}), one would expect to have a constant \isa{fun{\isaliteral{5F}{\isacharunderscore}}power{\isaliteral{2E}{\isachardot}}powers\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a} for which code
can be generated. But this not the case: internally, the term
- \isa{fun{\isacharunderscore}power{\isachardot}powers} is an abbreviation for the foundational
- term \isa{{\isachardoublequote}power{\isachardot}powers\ {\isacharparenleft}{\isasymlambda}n\ {\isacharparenleft}f\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}{\isachardot}\ f\ {\isacharcircum}{\isacharcircum}\ n{\isacharparenright}{\isachardoublequote}}
+ \isa{fun{\isaliteral{5F}{\isacharunderscore}}power{\isaliteral{2E}{\isachardot}}powers} is an abbreviation for the foundational
+ term \isa{{\isaliteral{22}{\isachardoublequote}}power{\isaliteral{2E}{\isachardot}}powers\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}n\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ f\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}
(see \cite{isabelle-locale} for the details behind).
Fortunately, with minor effort the desired behaviour can be achieved.
@@ -163,8 +163,8 @@
%
\isatagquote
\isacommand{definition}\isamarkupfalse%
-\ funpows\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ list\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isacharbrackleft}code\ del{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}funpows\ {\isacharequal}\ power{\isachardot}powers\ {\isacharparenleft}{\isasymlambda}n\ f{\isachardot}\ f\ {\isacharcircum}{\isacharcircum}\ n{\isacharparenright}{\isachardoublequoteclose}%
+\ funpows\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{5B}{\isacharbrackleft}}code\ del{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}funpows\ {\isaliteral{3D}{\isacharequal}}\ power{\isaliteral{2E}{\isachardot}}powers\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}n\ f{\isaliteral{2E}{\isachardot}}\ f\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -173,11 +173,11 @@
\endisadelimquote
%
\begin{isamarkuptext}%
-\noindent In general, the pattern is \isa{c\ {\isacharequal}\ t} where \isa{c} is
+\noindent In general, the pattern is \isa{c\ {\isaliteral{3D}{\isacharequal}}\ t} where \isa{c} is
the name of the future constant and \isa{t} the foundational term
corresponding to the local constant after interpretation.
- The interpretation itself is enriched with an equation \isa{t\ {\isacharequal}\ c}:%
+ The interpretation itself is enriched with an equation \isa{t\ {\isaliteral{3D}{\isacharequal}}\ c}:%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -187,11 +187,11 @@
%
\isatagquote
\isacommand{interpretation}\isamarkupfalse%
-\ fun{\isacharunderscore}power{\isacharcolon}\ power\ {\isachardoublequoteopen}{\isasymlambda}n\ {\isacharparenleft}f\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}{\isachardot}\ f\ {\isacharcircum}{\isacharcircum}\ n{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}power{\isachardot}powers\ {\isacharparenleft}{\isasymlambda}n\ f{\isachardot}\ f\ {\isacharcircum}{\isacharcircum}\ n{\isacharparenright}\ {\isacharequal}\ funpows{\isachardoublequoteclose}\isanewline
+\ fun{\isaliteral{5F}{\isacharunderscore}}power{\isaliteral{3A}{\isacharcolon}}\ power\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}n\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ f\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ n{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}power{\isaliteral{2E}{\isachardot}}powers\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}n\ f{\isaliteral{2E}{\isachardot}}\ f\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ funpows{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
-\ unfold{\isacharunderscore}locales\isanewline
-\ \ \ \ {\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}\ fun{\isacharunderscore}eq{\isacharunderscore}iff\ funpow{\isacharunderscore}mult\ mult{\isacharunderscore}commute\ funpows{\isacharunderscore}def{\isacharparenright}%
+\ unfold{\isaliteral{5F}{\isacharunderscore}}locales\isanewline
+\ \ \ \ {\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{5F}{\isacharunderscore}}all\ add{\isaliteral{3A}{\isacharcolon}}\ fun{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{5F}{\isacharunderscore}}iff\ funpow{\isaliteral{5F}{\isacharunderscore}}mult\ mult{\isaliteral{5F}{\isacharunderscore}}commute\ funpows{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
\endisatagquote
{\isafoldquote}%
%
@@ -214,13 +214,13 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-funpow\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ Nat\ {\isacharminus}{\isachargreater}\ {\isacharparenleft}a\ {\isacharminus}{\isachargreater}\ a{\isacharparenright}\ {\isacharminus}{\isachargreater}\ a\ {\isacharminus}{\isachargreater}\ a{\isacharsemicolon}\isanewline
-funpow\ Zero{\isacharunderscore}nat\ f\ {\isacharequal}\ id{\isacharsemicolon}\isanewline
-funpow\ {\isacharparenleft}Suc\ n{\isacharparenright}\ f\ {\isacharequal}\ f\ {\isachardot}\ funpow\ n\ f{\isacharsemicolon}\isanewline
+funpow\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ Nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+funpow\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ f\ {\isaliteral{3D}{\isacharequal}}\ id{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+funpow\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ f\ {\isaliteral{3D}{\isacharequal}}\ f\ {\isaliteral{2E}{\isachardot}}\ funpow\ n\ f{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-funpows\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ {\isacharbrackleft}Nat{\isacharbrackright}\ {\isacharminus}{\isachargreater}\ {\isacharparenleft}a\ {\isacharminus}{\isachargreater}\ a{\isacharparenright}\ {\isacharminus}{\isachargreater}\ a\ {\isacharminus}{\isachargreater}\ a{\isacharsemicolon}\isanewline
-funpows\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ id{\isacharsemicolon}\isanewline
-funpows\ {\isacharparenleft}x\ {\isacharcolon}\ xs{\isacharparenright}\ {\isacharequal}\ funpow\ x\ {\isachardot}\ funpows\ xs{\isacharsemicolon}\isanewline%
+funpows\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5B}{\isacharbrackleft}}Nat{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+funpows\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ id{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+funpows\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3A}{\isacharcolon}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ funpow\ x\ {\isaliteral{2E}{\isachardot}}\ funpows\ xs{\isaliteral{3B}{\isacharsemicolon}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -240,7 +240,7 @@
specific application, you should consider \emph{Imperative
Functional Programming with Isabelle/HOL}
\cite{bulwahn-et-al:2008:imperative}; the framework described there
- is available in session \isa{Imperative{\isacharunderscore}HOL}, together with a short
+ is available in session \isa{Imperative{\isaliteral{5F}{\isacharunderscore}}HOL}, together with a short
primer document.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -298,7 +298,7 @@
\item \verb|Code_Preproc.map_pre|~\isa{f}~\isa{thy} changes
the preprocessor simpset.
- \item \verb|Code_Preproc.add_functrans|~\isa{{\isacharparenleft}name{\isacharcomma}\ f{\isacharparenright}}~\isa{thy} adds
+ \item \verb|Code_Preproc.add_functrans|~\isa{{\isaliteral{28}{\isacharparenleft}}name{\isaliteral{2C}{\isacharcomma}}\ f{\isaliteral{29}{\isacharparenright}}}~\isa{thy} adds
function transformer \isa{f} (named \isa{name}) to executable content;
\isa{f} is a transformer of the code equations belonging
to a certain function definition, depending on the
@@ -354,7 +354,7 @@
\medskip
\begin{tabular}{l}
\isa{type\ T} \\
- \isa{val\ empty{\isacharcolon}\ T} \\
+ \isa{val\ empty{\isaliteral{3A}{\isacharcolon}}\ T} \\
\end{tabular}
\begin{description}
@@ -370,8 +370,8 @@
\medskip
\begin{tabular}{l}
- \isa{change{\isacharcolon}\ theory\ {\isasymrightarrow}\ {\isacharparenleft}T\ {\isasymrightarrow}\ T{\isacharparenright}\ {\isasymrightarrow}\ T} \\
- \isa{change{\isacharunderscore}yield{\isacharcolon}\ theory\ {\isasymrightarrow}\ {\isacharparenleft}T\ {\isasymrightarrow}\ {\isacharprime}a\ {\isacharasterisk}\ T{\isacharparenright}\ {\isasymrightarrow}\ {\isacharprime}a\ {\isacharasterisk}\ T}
+ \isa{change{\isaliteral{3A}{\isacharcolon}}\ theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}T\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ T{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ T} \\
+ \isa{change{\isaliteral{5F}{\isacharunderscore}}yield{\isaliteral{3A}{\isacharcolon}}\ theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}T\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2A}{\isacharasterisk}}\ T{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2A}{\isacharasterisk}}\ T}
\end{tabular}
\begin{description}
@@ -379,7 +379,7 @@
\item \isa{change} update of current data (cached!)
by giving a continuation.
- \item \isa{change{\isacharunderscore}yield} update with side result.
+ \item \isa{change{\isaliteral{5F}{\isacharunderscore}}yield} update with side result.
\end{description}%
\end{isamarkuptext}%
--- a/doc-src/Codegen/Thy/document/Inductive_Predicate.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/Codegen/Thy/document/Inductive_Predicate.tex Mon Nov 08 14:41:11 2010 +0100
@@ -1,6 +1,6 @@
%
\begin{isabellebody}%
-\def\isabellecontext{Inductive{\isacharunderscore}Predicate}%
+\def\isabellecontext{Inductive{\isaliteral{5F}{\isacharunderscore}}Predicate}%
%
\isadelimtheory
%
@@ -8,7 +8,7 @@
%
\isatagtheory
\isacommand{theory}\isamarkupfalse%
-\ Inductive{\isacharunderscore}Predicate\isanewline
+\ Inductive{\isaliteral{5F}{\isacharunderscore}}Predicate\isanewline
\isakeyword{imports}\ Setup\isanewline
\isakeyword{begin}\isanewline
%
@@ -55,8 +55,8 @@
\isatagquote
%
\begin{isamarkuptext}%
-\isa{append\ {\isacharbrackleft}{\isacharbrackright}\ ys\ ys} \\
- \isa{append\ xs\ ys\ zs\ {\isasymLongrightarrow}\ append\ {\isacharparenleft}x\ {\isacharhash}\ xs{\isacharparenright}\ ys\ {\isacharparenleft}x\ {\isacharhash}\ zs{\isacharparenright}}%
+\isa{append\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ ys\ ys} \\
+ \isa{append\ xs\ ys\ zs\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ append\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}\ ys\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ zs{\isaliteral{29}{\isacharparenright}}}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -68,7 +68,7 @@
\endisadelimquote
%
\begin{isamarkuptext}%
-\noindent To invoke the compiler, simply use \indexdef{}{command}{code\_pred}\hypertarget{command.code-pred}{\hyperlink{command.code-pred}{\mbox{\isa{\isacommand{code{\isacharunderscore}pred}}}}}:%
+\noindent To invoke the compiler, simply use \indexdef{}{command}{code\_pred}\hypertarget{command.code-pred}{\hyperlink{command.code-pred}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}pred}}}}}:%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -77,8 +77,8 @@
\endisadelimquote
%
\isatagquote
-\isacommand{code{\isacharunderscore}pred}\isamarkupfalse%
-\ append\ \isacommand{{\isachardot}}\isamarkupfalse%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}pred}\isamarkupfalse%
+\ append\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\endisatagquote
{\isafoldquote}%
@@ -88,7 +88,7 @@
\endisadelimquote
%
\begin{isamarkuptext}%
-\noindent The \hyperlink{command.code-pred}{\mbox{\isa{\isacommand{code{\isacharunderscore}pred}}}} command takes the name of the
+\noindent The \hyperlink{command.code-pred}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}pred}}}} command takes the name of the
inductive predicate and then you put a period to discharge a trivial
correctness proof. The compiler infers possible modes for the
predicate and produces the derived code equations. Modes annotate
@@ -98,9 +98,9 @@
For \isa{append}, the compiler can infer the following modes:
\begin{itemize}
- \item \isa{i\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ bool}
- \item \isa{i\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool}
- \item \isa{o\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ bool}
+ \item \isa{i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}
+ \item \isa{i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}
+ \item \isa{o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}
\end{itemize}
You can compute sets of predicates using \indexdef{}{command}{values}\hypertarget{command.values}{\hyperlink{command.values}{\mbox{\isa{\isacommand{values}}}}}:%
\end{isamarkuptext}%
@@ -112,7 +112,7 @@
%
\isatagquote
\isacommand{values}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharbraceleft}zs{\isachardot}\ append\ {\isacharbrackleft}{\isacharparenleft}{\isadigit{1}}{\isacharcolon}{\isacharcolon}nat{\isacharparenright}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbrackright}\ {\isacharbrackleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbrackright}\ zs{\isacharbraceright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7B}{\isacharbraceleft}}zs{\isaliteral{2E}{\isachardot}}\ append\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}{\isadigit{3}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{4}}{\isaliteral{2C}{\isacharcomma}}{\isadigit{5}}{\isaliteral{5D}{\isacharbrackright}}\ zs{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -121,7 +121,7 @@
\endisadelimquote
%
\begin{isamarkuptext}%
-\noindent outputs \isa{{\isacharbraceleft}{\isacharbrackleft}{\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isacharcomma}\ {\isadigit{3}}{\isacharcomma}\ {\isadigit{4}}{\isacharcomma}\ {\isadigit{5}}{\isacharbrackright}{\isacharbraceright}}, and%
+\noindent outputs \isa{{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{3}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{4}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{5}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{7D}{\isacharbraceright}}}, and%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -131,7 +131,7 @@
%
\isatagquote
\isacommand{values}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharparenleft}xs{\isacharcomma}\ ys{\isacharparenright}{\isachardot}\ append\ xs\ ys\ {\isacharbrackleft}{\isacharparenleft}{\isadigit{2}}{\isacharcolon}{\isacharcolon}nat{\isacharparenright}{\isacharcomma}{\isadigit{3}}{\isacharbrackright}{\isacharbraceright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{28}{\isacharparenleft}}xs{\isaliteral{2C}{\isacharcomma}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ append\ xs\ ys\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}{\isadigit{3}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -140,7 +140,7 @@
\endisadelimquote
%
\begin{isamarkuptext}%
-\noindent outputs \isa{{\isacharbraceleft}{\isacharparenleft}{\isacharbrackleft}{\isacharbrackright}{\isacharcomma}\ {\isacharbrackleft}{\isadigit{2}}{\isacharcomma}\ {\isadigit{3}}{\isacharbrackright}{\isacharparenright}{\isacharcomma}\ {\isacharparenleft}{\isacharbrackleft}{\isadigit{2}}{\isacharbrackright}{\isacharcomma}\ {\isacharbrackleft}{\isadigit{3}}{\isacharbrackright}{\isacharparenright}{\isacharcomma}\ {\isacharparenleft}{\isacharbrackleft}{\isadigit{2}}{\isacharcomma}\ {\isadigit{3}}{\isacharbrackright}{\isacharcomma}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isacharbraceright}}.%
+\noindent outputs \isa{{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{3}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{2}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{3}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{3}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{7D}{\isacharbraceright}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -158,9 +158,9 @@
%
\isatagquote
\isacommand{values}\isamarkupfalse%
-\ {\isadigit{1}}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharparenleft}xs{\isacharcomma}\ ys{\isacharparenright}{\isachardot}\ append\ xs\ ys\ {\isacharbrackleft}{\isacharparenleft}{\isadigit{1}}{\isacharcolon}{\isacharcolon}nat{\isacharparenright}{\isacharcomma}\ {\isadigit{2}}{\isacharcomma}\ {\isadigit{3}}{\isacharcomma}\ {\isadigit{4}}{\isacharbrackright}{\isacharbraceright}{\isachardoublequoteclose}\isanewline
+\ {\isadigit{1}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{28}{\isacharparenleft}}xs{\isaliteral{2C}{\isacharcomma}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ append\ xs\ ys\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{3}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{4}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isacommand{values}\isamarkupfalse%
-\ {\isadigit{3}}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharparenleft}xs{\isacharcomma}\ ys{\isacharparenright}{\isachardot}\ append\ xs\ ys\ {\isacharbrackleft}{\isacharparenleft}{\isadigit{1}}{\isacharcolon}{\isacharcolon}nat{\isacharparenright}{\isacharcomma}\ {\isadigit{2}}{\isacharcomma}\ {\isadigit{3}}{\isacharcomma}\ {\isadigit{4}}{\isacharbrackright}{\isacharbraceright}{\isachardoublequoteclose}%
+\ {\isadigit{3}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{28}{\isacharparenleft}}xs{\isaliteral{2C}{\isacharcomma}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ append\ xs\ ys\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{3}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{4}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -183,7 +183,7 @@
%
\isatagquote
\isacommand{thm}\isamarkupfalse%
-\ append{\isachardot}equation%
+\ append{\isaliteral{2E}{\isachardot}}equation%
\endisatagquote
{\isafoldquote}%
%
@@ -202,7 +202,7 @@
%
\begin{isamarkuptext}%
By default, the functions generated from a predicate are named after
- the predicate with the mode mangled into the name (e.g., \isa{append{\isacharunderscore}i{\isacharunderscore}i{\isacharunderscore}o}). You can specify your own names as follows:%
+ the predicate with the mode mangled into the name (e.g., \isa{append{\isaliteral{5F}{\isacharunderscore}}i{\isaliteral{5F}{\isacharunderscore}}i{\isaliteral{5F}{\isacharunderscore}}o}). You can specify your own names as follows:%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -211,10 +211,10 @@
\endisadelimquote
%
\isatagquote
-\isacommand{code{\isacharunderscore}pred}\isamarkupfalse%
-\ {\isacharparenleft}modes{\isacharcolon}\ i\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool\ as\ concat{\isacharcomma}\isanewline
-\ \ o\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ bool\ as\ split{\isacharcomma}\isanewline
-\ \ i\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ bool\ as\ suffix{\isacharparenright}\ append\ \isacommand{{\isachardot}}\isamarkupfalse%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}pred}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}modes{\isaliteral{3A}{\isacharcolon}}\ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool\ as\ concat{\isaliteral{2C}{\isacharcomma}}\isanewline
+\ \ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool\ as\ split{\isaliteral{2C}{\isacharcomma}}\isanewline
+\ \ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool\ as\ suffix{\isaliteral{29}{\isacharparenright}}\ append\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\endisatagquote
{\isafoldquote}%
@@ -233,7 +233,7 @@
could not be inferred. It is also possible that the introduction
rules yield a function that loops forever due to the execution in a
depth-first search manner. Therefore, you can declare alternative
- introduction rules for predicates with the attribute \hyperlink{attribute.code-pred-intro}{\mbox{\isa{code{\isacharunderscore}pred{\isacharunderscore}intro}}}. For example, the transitive closure is defined
+ introduction rules for predicates with the attribute \hyperlink{attribute.code-pred-intro}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}pred{\isaliteral{5F}{\isacharunderscore}}intro}}}. For example, the transitive closure is defined
by:%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -245,8 +245,8 @@
\isatagquote
%
\begin{isamarkuptext}%
-\isa{{\isachardoublequote}r\ a\ b\ {\isasymLongrightarrow}\ tranclp\ r\ a\ b{\isachardoublequote}}\\
- \isa{{\isachardoublequote}tranclp\ r\ a\ b\ {\isasymLongrightarrow}\ r\ b\ c\ {\isasymLongrightarrow}\ tranclp\ r\ a\ c{\isachardoublequote}}%
+\isa{{\isaliteral{22}{\isachardoublequote}}r\ a\ b\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ tranclp\ r\ a\ b{\isaliteral{22}{\isachardoublequote}}}\\
+ \isa{{\isaliteral{22}{\isachardoublequote}}tranclp\ r\ a\ b\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ r\ b\ c\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ tranclp\ r\ a\ c{\isaliteral{22}{\isachardoublequote}}}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -259,10 +259,10 @@
%
\begin{isamarkuptext}%
\noindent These rules do not suit well for executing the transitive
- closure with the mode \isa{{\isacharparenleft}i\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool{\isacharparenright}\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool}, as
+ closure with the mode \isa{{\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}, as
the second rule will cause an infinite loop in the recursive call.
This can be avoided using the following alternative rules which are
- declared to the predicate compiler by the attribute \hyperlink{attribute.code-pred-intro}{\mbox{\isa{code{\isacharunderscore}pred{\isacharunderscore}intro}}}:%
+ declared to the predicate compiler by the attribute \hyperlink{attribute.code-pred-intro}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}pred{\isaliteral{5F}{\isacharunderscore}}intro}}}:%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -272,9 +272,9 @@
%
\isatagquote
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code{\isacharunderscore}pred{\isacharunderscore}intro{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}r\ a\ b\ {\isasymLongrightarrow}\ tranclp\ r\ a\ b{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}r\ a\ b\ {\isasymLongrightarrow}\ tranclp\ r\ b\ c\ {\isasymLongrightarrow}\ tranclp\ r\ a\ c{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5F}{\isacharunderscore}}pred{\isaliteral{5F}{\isacharunderscore}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}r\ a\ b\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ tranclp\ r\ a\ b{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}r\ a\ b\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ tranclp\ r\ b\ c\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ tranclp\ r\ a\ c{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isacommand{by}\isamarkupfalse%
\ auto%
\endisatagquote
@@ -286,7 +286,7 @@
%
\begin{isamarkuptext}%
\noindent After declaring all alternative rules for the transitive
- closure, you invoke \hyperlink{command.code-pred}{\mbox{\isa{\isacommand{code{\isacharunderscore}pred}}}} as usual. As you have
+ closure, you invoke \hyperlink{command.code-pred}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}pred}}}} as usual. As you have
declared alternative rules for the predicate, you are urged to prove
that these introduction rules are complete, i.e., that you can
derive an elimination rule for the alternative rules:%
@@ -298,14 +298,14 @@
\endisadelimquote
%
\isatagquote
-\isacommand{code{\isacharunderscore}pred}\isamarkupfalse%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}pred}\isamarkupfalse%
\ tranclp\isanewline
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{case}\isamarkupfalse%
\ tranclp\isanewline
\ \ \isacommand{from}\isamarkupfalse%
-\ this\ converse{\isacharunderscore}tranclpE\ {\isacharbrackleft}OF\ tranclp{\isachardot}prems{\isacharbrackright}\ \isacommand{show}\isamarkupfalse%
+\ this\ converse{\isaliteral{5F}{\isacharunderscore}}tranclpE\ {\isaliteral{5B}{\isacharbrackleft}}OF\ tranclp{\isaliteral{2E}{\isachardot}}prems{\isaliteral{5D}{\isacharbrackright}}\ \isacommand{show}\isamarkupfalse%
\ thesis\ \isacommand{by}\isamarkupfalse%
\ metis\isanewline
\isacommand{qed}\isamarkupfalse%
@@ -332,10 +332,10 @@
%
\begin{isamarkuptext}%
\begin{isabelle}%
-lexord\ r\ {\isacharequal}\isanewline
-{\isacharbraceleft}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\isanewline
-\isaindent{\ }{\isasymexists}a\ v{\isachardot}\ y\ {\isacharequal}\ x\ {\isacharat}\ a\ {\isacharhash}\ v\ {\isasymor}\isanewline
-\isaindent{\ {\isasymexists}a\ v{\isachardot}\ }{\isacharparenleft}{\isasymexists}u\ a\ b\ v\ w{\isachardot}\ {\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\ {\isasymin}\ r\ {\isasymand}\ x\ {\isacharequal}\ u\ {\isacharat}\ a\ {\isacharhash}\ v\ {\isasymand}\ y\ {\isacharequal}\ u\ {\isacharat}\ b\ {\isacharhash}\ w{\isacharparenright}{\isacharbraceright}%
+lexord\ r\ {\isaliteral{3D}{\isacharequal}}\isanewline
+{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ }{\isaliteral{5C3C6578697374733E}{\isasymexists}}a\ v{\isaliteral{2E}{\isachardot}}\ y\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{40}{\isacharat}}\ a\ {\isaliteral{23}{\isacharhash}}\ v\ {\isaliteral{5C3C6F723E}{\isasymor}}\isanewline
+\isaindent{\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}a\ v{\isaliteral{2E}{\isachardot}}\ }{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}u\ a\ b\ v\ w{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r\ {\isaliteral{5C3C616E643E}{\isasymand}}\ x\ {\isaliteral{3D}{\isacharequal}}\ u\ {\isaliteral{40}{\isacharat}}\ a\ {\isaliteral{23}{\isacharhash}}\ v\ {\isaliteral{5C3C616E643E}{\isasymand}}\ y\ {\isaliteral{3D}{\isacharequal}}\ u\ {\isaliteral{40}{\isacharat}}\ b\ {\isaliteral{23}{\isacharhash}}\ w{\isaliteral{29}{\isacharparenright}}{\isaliteral{7D}{\isacharbraceright}}%
\end{isabelle}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -359,13 +359,13 @@
%
\isatagquote
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code{\isacharunderscore}pred{\isacharunderscore}intro{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}append\ xs\ {\isacharparenleft}a\ {\isacharhash}\ v{\isacharparenright}\ ys\ {\isasymLongrightarrow}\ lexord\ r\ {\isacharparenleft}xs{\isacharcomma}\ ys{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5F}{\isacharunderscore}}pred{\isaliteral{5F}{\isacharunderscore}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}append\ xs\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{23}{\isacharhash}}\ v{\isaliteral{29}{\isacharparenright}}\ ys\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ lexord\ r\ {\isaliteral{28}{\isacharparenleft}}xs{\isaliteral{2C}{\isacharcomma}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code{\isacharunderscore}pred{\isacharunderscore}intro{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}append\ u\ {\isacharparenleft}a\ {\isacharhash}\ v{\isacharparenright}\ xs\ {\isasymLongrightarrow}\ append\ u\ {\isacharparenleft}b\ {\isacharhash}\ w{\isacharparenright}\ ys\ {\isasymLongrightarrow}\ r\ {\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\isanewline
-\ \ {\isasymLongrightarrow}\ lexord\ r\ {\isacharparenleft}xs{\isacharcomma}\ ys{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\isacommand{code{\isacharunderscore}pred}\isamarkupfalse%
+\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5F}{\isacharunderscore}}pred{\isaliteral{5F}{\isacharunderscore}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}append\ u\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{23}{\isacharhash}}\ v{\isaliteral{29}{\isacharparenright}}\ xs\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ append\ u\ {\isaliteral{28}{\isacharparenleft}}b\ {\isaliteral{23}{\isacharhash}}\ w{\isaliteral{29}{\isacharparenright}}\ ys\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ r\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ lexord\ r\ {\isaliteral{28}{\isacharparenleft}}xs{\isaliteral{2C}{\isacharcomma}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}pred}\isamarkupfalse%
\ lexord%
\endisatagquote
{\isafoldquote}%
@@ -393,12 +393,12 @@
%
\isatagquote
\isacommand{inductive}\isamarkupfalse%
-\ succ\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}succ\ {\isadigit{0}}\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}succ\ x\ y\ {\isasymLongrightarrow}\ succ\ {\isacharparenleft}Suc\ x{\isacharparenright}\ {\isacharparenleft}Suc\ y{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ succ\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}succ\ {\isadigit{0}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}succ\ x\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ succ\ {\isaliteral{28}{\isacharparenleft}}Suc\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
-\isacommand{code{\isacharunderscore}pred}\isamarkupfalse%
-\ succ\ \isacommand{{\isachardot}}\isamarkupfalse%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}pred}\isamarkupfalse%
+\ succ\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\endisatagquote
{\isafoldquote}%
@@ -408,10 +408,10 @@
\endisadelimquote
%
\begin{isamarkuptext}%
-\noindent For this, the predicate compiler can infer modes \isa{o\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool}, \isa{i\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool}, \isa{o\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ bool} and
- \isa{i\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ bool}. The invocation of \hyperlink{command.values}{\mbox{\isa{\isacommand{values}}}}
- \isa{{\isacharbraceleft}n{\isachardot}\ tranclp\ succ\ {\isadigit{1}}{\isadigit{0}}\ n{\isacharbraceright}} loops, as multiple modes for the
- predicate \isa{succ} are possible and here the first mode \isa{o\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool} is chosen. To choose another mode for the argument,
+\noindent For this, the predicate compiler can infer modes \isa{o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}, \isa{i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}, \isa{o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool} and
+ \isa{i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}. The invocation of \hyperlink{command.values}{\mbox{\isa{\isacommand{values}}}}
+ \isa{{\isaliteral{7B}{\isacharbraceleft}}n{\isaliteral{2E}{\isachardot}}\ tranclp\ succ\ {\isadigit{1}}{\isadigit{0}}\ n{\isaliteral{7D}{\isacharbraceright}}} loops, as multiple modes for the
+ predicate \isa{succ} are possible and here the first mode \isa{o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool} is chosen. To choose another mode for the argument,
you can declare the mode for the argument between the \hyperlink{command.values}{\mbox{\isa{\isacommand{values}}}} and the number of elements.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -422,9 +422,9 @@
%
\isatagquote
\isacommand{values}\isamarkupfalse%
-\ {\isacharbrackleft}mode{\isacharcolon}\ i\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ bool{\isacharbrackright}\ {\isadigit{1}}\ {\isachardoublequoteopen}{\isacharbraceleft}n{\isachardot}\ tranclp\ succ\ {\isadigit{1}}{\isadigit{0}}\ n{\isacharbraceright}{\isachardoublequoteclose}\ \isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}mode{\isaliteral{3A}{\isacharcolon}}\ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{5D}{\isacharbrackright}}\ {\isadigit{1}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7B}{\isacharbraceleft}}n{\isaliteral{2E}{\isachardot}}\ tranclp\ succ\ {\isadigit{1}}{\isadigit{0}}\ n{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isanewline
\isacommand{values}\isamarkupfalse%
-\ {\isacharbrackleft}mode{\isacharcolon}\ o\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ bool{\isacharbrackright}\ {\isadigit{1}}\ {\isachardoublequoteopen}{\isacharbraceleft}n{\isachardot}\ tranclp\ succ\ n\ {\isadigit{1}}{\isadigit{0}}{\isacharbraceright}{\isachardoublequoteclose}%
+\ {\isaliteral{5B}{\isacharbrackleft}}mode{\isaliteral{3A}{\isacharcolon}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{5D}{\isacharbrackright}}\ {\isadigit{1}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7B}{\isacharbraceleft}}n{\isaliteral{2E}{\isachardot}}\ tranclp\ succ\ n\ {\isadigit{1}}{\isadigit{0}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -446,20 +446,20 @@
where all arguments are input. Then you can use the predicate directly, e.g.
\begin{quote}
- \isa{valid{\isacharunderscore}suffix\ ys\ zs\ {\isacharequal}} \\
- \isa{{\isacharparenleft}if\ append\ {\isacharbrackleft}Suc\ {\isadigit{0}}{\isacharcomma}\ {\isadigit{2}}{\isacharbrackright}\ ys\ zs\ then\ Some\ ys\ else\ None{\isacharparenright}}
+ \isa{valid{\isaliteral{5F}{\isacharunderscore}}suffix\ ys\ zs\ {\isaliteral{3D}{\isacharequal}}} \\
+ \isa{{\isaliteral{28}{\isacharparenleft}}if\ append\ {\isaliteral{5B}{\isacharbrackleft}}Suc\ {\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isaliteral{5D}{\isacharbrackright}}\ ys\ zs\ then\ Some\ ys\ else\ None{\isaliteral{29}{\isacharparenright}}}
\end{quote}
\item If you know that the execution returns only one value (it is
- deterministic), then you can use the combinator \isa{Predicate{\isachardot}the}, e.g., a functional concatenation of lists is
+ deterministic), then you can use the combinator \isa{Predicate{\isaliteral{2E}{\isachardot}}the}, e.g., a functional concatenation of lists is
defined with
\begin{quote}
- \isa{functional{\isacharunderscore}concat\ xs\ ys\ {\isacharequal}\ Predicate{\isachardot}the\ {\isacharparenleft}append{\isacharunderscore}i{\isacharunderscore}i{\isacharunderscore}o\ xs\ ys{\isacharparenright}}
+ \isa{functional{\isaliteral{5F}{\isacharunderscore}}concat\ xs\ ys\ {\isaliteral{3D}{\isacharequal}}\ Predicate{\isaliteral{2E}{\isachardot}}the\ {\isaliteral{28}{\isacharparenleft}}append{\isaliteral{5F}{\isacharunderscore}}i{\isaliteral{5F}{\isacharunderscore}}i{\isaliteral{5F}{\isacharunderscore}}o\ xs\ ys{\isaliteral{29}{\isacharparenright}}}
\end{quote}
Note that if the evaluation does not return a unique value, it
- raises a run-time error \isa{not{\isacharunderscore}unique}.
+ raises a run-time error \isa{not{\isaliteral{5F}{\isacharunderscore}}unique}.
\end{itemize}%
\end{isamarkuptext}%
@@ -471,9 +471,9 @@
%
\begin{isamarkuptext}%
Further examples for compiling inductive predicates can be found in
- the \isa{HOL{\isacharslash}ex{\isacharslash}Predicate{\isacharunderscore}Compile{\isacharunderscore}ex{\isachardot}thy} theory file. There are
+ the \isa{HOL{\isaliteral{2F}{\isacharslash}}ex{\isaliteral{2F}{\isacharslash}}Predicate{\isaliteral{5F}{\isacharunderscore}}Compile{\isaliteral{5F}{\isacharunderscore}}ex{\isaliteral{2E}{\isachardot}}thy} theory file. There are
also some examples in the Archive of Formal Proofs, notably in the
- \isa{POPLmark{\isacharminus}deBruijn} and the \isa{FeatherweightJava}
+ \isa{POPLmark{\isaliteral{2D}{\isacharminus}}deBruijn} and the \isa{FeatherweightJava}
sessions.%
\end{isamarkuptext}%
\isamarkuptrue%
--- a/doc-src/Codegen/Thy/document/Introduction.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/Codegen/Thy/document/Introduction.tex Mon Nov 08 14:41:11 2010 +0100
@@ -23,7 +23,7 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-This tutorial introduces the code generator facilities of \isa{Isabelle{\isacharslash}HOL}. It allows to turn (a certain class of) HOL
+This tutorial introduces the code generator facilities of \isa{Isabelle{\isaliteral{2F}{\isacharslash}}HOL}. It allows to turn (a certain class of) HOL
specifications into corresponding executable code in the programming
languages \isa{SML} \cite{SML}, \isa{OCaml} \cite{OCaml},
\isa{Haskell} \cite{haskell-revised-report} and \isa{Scala}
@@ -72,22 +72,22 @@
%
\isatagquote
\isacommand{datatype}\isamarkupfalse%
-\ {\isacharprime}a\ queue\ {\isacharequal}\ AQueue\ {\isachardoublequoteopen}{\isacharprime}a\ list{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isacharprime}a\ list{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{3D}{\isacharequal}}\ AQueue\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{definition}\isamarkupfalse%
-\ empty\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ queue{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}empty\ {\isacharequal}\ AQueue\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
+\ empty\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ queue{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}empty\ {\isaliteral{3D}{\isacharequal}}\ AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{primrec}\isamarkupfalse%
-\ enqueue\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ queue\ {\isasymRightarrow}\ {\isacharprime}a\ queue{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}enqueue\ x\ {\isacharparenleft}AQueue\ xs\ ys{\isacharparenright}\ {\isacharequal}\ AQueue\ {\isacharparenleft}x\ {\isacharhash}\ xs{\isacharparenright}\ ys{\isachardoublequoteclose}\isanewline
+\ enqueue\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ queue{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}enqueue\ x\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ AQueue\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}\ ys{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{fun}\isamarkupfalse%
-\ dequeue\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ queue\ {\isasymRightarrow}\ {\isacharprime}a\ option\ {\isasymtimes}\ {\isacharprime}a\ queue{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ \ \ {\isachardoublequoteopen}dequeue\ {\isacharparenleft}AQueue\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}None{\isacharcomma}\ AQueue\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}dequeue\ {\isacharparenleft}AQueue\ xs\ {\isacharparenleft}y\ {\isacharhash}\ ys{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}Some\ y{\isacharcomma}\ AQueue\ xs\ ys{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}dequeue\ {\isacharparenleft}AQueue\ xs\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ \ \ {\isacharparenleft}case\ rev\ xs\ of\ y\ {\isacharhash}\ ys\ {\isasymRightarrow}\ {\isacharparenleft}Some\ y{\isacharcomma}\ AQueue\ {\isacharbrackleft}{\isacharbrackright}\ ys{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\ %
+\ dequeue\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ option\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a\ queue{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}None{\isaliteral{2C}{\isacharcomma}}\ AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{23}{\isacharhash}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Some\ y{\isaliteral{2C}{\isacharcomma}}\ AQueue\ xs\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}case\ rev\ xs\ of\ y\ {\isaliteral{23}{\isacharhash}}\ ys\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}Some\ y{\isaliteral{2C}{\isacharcomma}}\ AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ %
\endisatagquote
{\isafoldquote}%
%
@@ -118,9 +118,9 @@
\endisadelimquote
%
\isatagquote
-\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
+\isacommand{export{\isaliteral{5F}{\isacharunderscore}}code}\isamarkupfalse%
\ empty\ dequeue\ enqueue\ \isakeyword{in}\ SML\isanewline
-\ \ \isakeyword{module{\isacharunderscore}name}\ Example\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}example{\isachardot}ML{\isachardoublequoteclose}%
+\ \ \isakeyword{module{\isaliteral{5F}{\isacharunderscore}}name}\ Example\ \isakeyword{file}\ {\isaliteral{22}{\isachardoublequoteopen}}examples{\isaliteral{2F}{\isacharslash}}example{\isaliteral{2E}{\isachardot}}ML{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -140,39 +140,39 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-structure\ Example\ {\isacharcolon}\ sig\isanewline
-\ \ val\ id\ {\isacharcolon}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\isanewline
-\ \ val\ fold\ {\isacharcolon}\ {\isacharparenleft}{\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}b\ {\isacharminus}{\isachargreater}\ {\isacharprime}b{\isacharparenright}\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ list\ {\isacharminus}{\isachargreater}\ {\isacharprime}b\ {\isacharminus}{\isachargreater}\ {\isacharprime}b\isanewline
-\ \ val\ rev\ {\isacharcolon}\ {\isacharprime}a\ list\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ list\isanewline
-\ \ datatype\ {\isacharprime}a\ queue\ {\isacharequal}\ AQueue\ of\ {\isacharprime}a\ list\ {\isacharasterisk}\ {\isacharprime}a\ list\isanewline
-\ \ val\ empty\ {\isacharcolon}\ {\isacharprime}a\ queue\isanewline
-\ \ val\ dequeue\ {\isacharcolon}\ {\isacharprime}a\ queue\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ option\ {\isacharasterisk}\ {\isacharprime}a\ queue\isanewline
-\ \ val\ enqueue\ {\isacharcolon}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ queue\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ queue\isanewline
-end\ {\isacharequal}\ struct\isanewline
+structure\ Example\ {\isaliteral{3A}{\isacharcolon}}\ sig\isanewline
+\ \ val\ id\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\isanewline
+\ \ val\ fold\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}b\isanewline
+\ \ val\ rev\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ list\isanewline
+\ \ datatype\ {\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{3D}{\isacharequal}}\ AQueue\ of\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{27}{\isacharprime}}a\ list\isanewline
+\ \ val\ empty\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ queue\isanewline
+\ \ val\ dequeue\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ option\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{27}{\isacharprime}}a\ queue\isanewline
+\ \ val\ enqueue\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ queue\isanewline
+end\ {\isaliteral{3D}{\isacharequal}}\ struct\isanewline
\isanewline
-fun\ id\ x\ {\isacharequal}\ {\isacharparenleft}fn\ xa\ {\isacharequal}{\isachargreater}\ xa{\isacharparenright}\ x{\isacharsemicolon}\isanewline
+fun\ id\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}fn\ xa\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ xa{\isaliteral{29}{\isacharparenright}}\ x{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ fold\ f\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ id\isanewline
-\ \ {\isacharbar}\ fold\ f\ {\isacharparenleft}x\ {\isacharcolon}{\isacharcolon}\ xs{\isacharparenright}\ {\isacharequal}\ fold\ f\ xs\ o\ f\ x{\isacharsemicolon}\isanewline
+fun\ fold\ f\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ id\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ fold\ f\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ fold\ f\ xs\ o\ f\ x{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ rev\ xs\ {\isacharequal}\ fold\ {\isacharparenleft}fn\ a\ {\isacharequal}{\isachargreater}\ fn\ b\ {\isacharequal}{\isachargreater}\ a\ {\isacharcolon}{\isacharcolon}\ b{\isacharparenright}\ xs\ {\isacharbrackleft}{\isacharbrackright}{\isacharsemicolon}\isanewline
+fun\ rev\ xs\ {\isaliteral{3D}{\isacharequal}}\ fold\ {\isaliteral{28}{\isacharparenleft}}fn\ a\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ fn\ b\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ a\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ b{\isaliteral{29}{\isacharparenright}}\ xs\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-datatype\ {\isacharprime}a\ queue\ {\isacharequal}\ AQueue\ of\ {\isacharprime}a\ list\ {\isacharasterisk}\ {\isacharprime}a\ list{\isacharsemicolon}\isanewline
+datatype\ {\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{3D}{\isacharequal}}\ AQueue\ of\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-val\ empty\ {\isacharcolon}\ {\isacharprime}a\ queue\ {\isacharequal}\ AQueue\ {\isacharparenleft}{\isacharbrackleft}{\isacharbrackright}{\isacharcomma}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isacharsemicolon}\isanewline
+val\ empty\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{3D}{\isacharequal}}\ AQueue\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ dequeue\ {\isacharparenleft}AQueue\ {\isacharparenleft}{\isacharbrackleft}{\isacharbrackright}{\isacharcomma}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}NONE{\isacharcomma}\ AQueue\ {\isacharparenleft}{\isacharbrackleft}{\isacharbrackright}{\isacharcomma}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isacharparenright}\isanewline
-\ \ {\isacharbar}\ dequeue\ {\isacharparenleft}AQueue\ {\isacharparenleft}xs{\isacharcomma}\ y\ {\isacharcolon}{\isacharcolon}\ ys{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}SOME\ y{\isacharcomma}\ AQueue\ {\isacharparenleft}xs{\isacharcomma}\ ys{\isacharparenright}{\isacharparenright}\isanewline
-\ \ {\isacharbar}\ dequeue\ {\isacharparenleft}AQueue\ {\isacharparenleft}v\ {\isacharcolon}{\isacharcolon}\ va{\isacharcomma}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isacharparenright}\ {\isacharequal}\isanewline
+fun\ dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}NONE{\isaliteral{2C}{\isacharcomma}}\ AQueue\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ {\isaliteral{28}{\isacharparenleft}}xs{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}SOME\ y{\isaliteral{2C}{\isacharcomma}}\ AQueue\ {\isaliteral{28}{\isacharparenleft}}xs{\isaliteral{2C}{\isacharcomma}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ {\isaliteral{28}{\isacharparenleft}}v\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ va{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
\ \ \ \ let\isanewline
-\ \ \ \ \ \ val\ y\ {\isacharcolon}{\isacharcolon}\ ys\ {\isacharequal}\ rev\ {\isacharparenleft}v\ {\isacharcolon}{\isacharcolon}\ va{\isacharparenright}{\isacharsemicolon}\isanewline
+\ \ \ \ \ \ val\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ ys\ {\isaliteral{3D}{\isacharequal}}\ rev\ {\isaliteral{28}{\isacharparenleft}}v\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ va{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\ \ \ \ in\isanewline
-\ \ \ \ \ \ {\isacharparenleft}SOME\ y{\isacharcomma}\ AQueue\ {\isacharparenleft}{\isacharbrackleft}{\isacharbrackright}{\isacharcomma}\ ys{\isacharparenright}{\isacharparenright}\isanewline
-\ \ \ \ end{\isacharsemicolon}\isanewline
+\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}SOME\ y{\isaliteral{2C}{\isacharcomma}}\ AQueue\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ end{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ enqueue\ x\ {\isacharparenleft}AQueue\ {\isacharparenleft}xs{\isacharcomma}\ ys{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ AQueue\ {\isacharparenleft}x\ {\isacharcolon}{\isacharcolon}\ xs{\isacharcomma}\ ys{\isacharparenright}{\isacharsemicolon}\isanewline
+fun\ enqueue\ x\ {\isaliteral{28}{\isacharparenleft}}AQueue\ {\isaliteral{28}{\isacharparenleft}}xs{\isaliteral{2C}{\isacharcomma}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ AQueue\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ xs{\isaliteral{2C}{\isacharcomma}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-end{\isacharsemicolon}\ {\isacharparenleft}{\isacharasterisk}struct\ Example{\isacharasterisk}{\isacharparenright}\isanewline%
+end{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}struct\ Example{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -184,7 +184,7 @@
\endisadelimquotetypewriter
%
\begin{isamarkuptext}%
-\noindent The \indexdef{}{command}{export\_code}\hypertarget{command.export-code}{\hyperlink{command.export-code}{\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}}} command takes a
+\noindent The \indexdef{}{command}{export\_code}\hypertarget{command.export-code}{\hyperlink{command.export-code}{\mbox{\isa{\isacommand{export{\isaliteral{5F}{\isacharunderscore}}code}}}}} command takes a
space-separated list of constants for which code shall be generated;
anything else needed for those is added implicitly. Then follows a
target language identifier and a freely chosen module name. A file
@@ -192,7 +192,7 @@
the semantics of the destination depends on the target language: for
\isa{SML}, \isa{OCaml} and \isa{Scala} it denotes a \emph{file},
for \isa{Haskell} it denotes a \emph{directory} where a file named as the
- module name (with extension \isa{{\isachardot}hs}) is written:%
+ module name (with extension \isa{{\isaliteral{2E}{\isachardot}}hs}) is written:%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -201,9 +201,9 @@
\endisadelimquote
%
\isatagquote
-\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
+\isacommand{export{\isaliteral{5F}{\isacharunderscore}}code}\isamarkupfalse%
\ empty\ dequeue\ enqueue\ \isakeyword{in}\ Haskell\isanewline
-\ \ \isakeyword{module{\isacharunderscore}name}\ Example\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}{\isachardoublequoteclose}%
+\ \ \isakeyword{module{\isaliteral{5F}{\isacharunderscore}}name}\ Example\ \isakeyword{file}\ {\isaliteral{22}{\isachardoublequoteopen}}examples{\isaliteral{2F}{\isacharslash}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -223,25 +223,25 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-module\ Example\ where\ {\isacharbraceleft}\isanewline
+module\ Example\ where\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
\isanewline
-data\ Queue\ a\ {\isacharequal}\ AQueue\ {\isacharbrackleft}a{\isacharbrackright}\ {\isacharbrackleft}a{\isacharbrackright}{\isacharsemicolon}\isanewline
+data\ Queue\ a\ {\isaliteral{3D}{\isacharequal}}\ AQueue\ {\isaliteral{5B}{\isacharbrackleft}}a{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5B}{\isacharbrackleft}}a{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-empty\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ Queue\ a{\isacharsemicolon}\isanewline
-empty\ {\isacharequal}\ AQueue\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbrackleft}{\isacharbrackright}{\isacharsemicolon}\isanewline
+empty\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ Queue\ a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+empty\ {\isaliteral{3D}{\isacharequal}}\ AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-dequeue\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ Queue\ a\ {\isacharminus}{\isachargreater}\ {\isacharparenleft}Maybe\ a{\isacharcomma}\ Queue\ a{\isacharparenright}{\isacharsemicolon}\isanewline
-dequeue\ {\isacharparenleft}AQueue\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}Nothing{\isacharcomma}\ AQueue\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isacharsemicolon}\isanewline
-dequeue\ {\isacharparenleft}AQueue\ xs\ {\isacharparenleft}y\ {\isacharcolon}\ ys{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}Just\ y{\isacharcomma}\ AQueue\ xs\ ys{\isacharparenright}{\isacharsemicolon}\isanewline
-dequeue\ {\isacharparenleft}AQueue\ {\isacharparenleft}v\ {\isacharcolon}\ va{\isacharparenright}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ let\ {\isacharbraceleft}\isanewline
-\ \ \ \ {\isacharparenleft}y\ {\isacharcolon}\ ys{\isacharparenright}\ {\isacharequal}\ reverse\ {\isacharparenleft}v\ {\isacharcolon}\ va{\isacharparenright}{\isacharsemicolon}\isanewline
-\ \ {\isacharbraceright}\ in\ {\isacharparenleft}Just\ y{\isacharcomma}\ AQueue\ {\isacharbrackleft}{\isacharbrackright}\ ys{\isacharparenright}{\isacharsemicolon}\isanewline
+dequeue\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ Queue\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}Maybe\ a{\isaliteral{2C}{\isacharcomma}}\ Queue\ a{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Nothing{\isaliteral{2C}{\isacharcomma}}\ AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{3A}{\isacharcolon}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Just\ y{\isaliteral{2C}{\isacharcomma}}\ AQueue\ xs\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ {\isaliteral{28}{\isacharparenleft}}v\ {\isaliteral{3A}{\isacharcolon}}\ va{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ let\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ \ \ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{3A}{\isacharcolon}}\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ reverse\ {\isaliteral{28}{\isacharparenleft}}v\ {\isaliteral{3A}{\isacharcolon}}\ va{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ {\isaliteral{7D}{\isacharbraceright}}\ in\ {\isaliteral{28}{\isacharparenleft}}Just\ y{\isaliteral{2C}{\isacharcomma}}\ AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-enqueue\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ a\ {\isacharminus}{\isachargreater}\ Queue\ a\ {\isacharminus}{\isachargreater}\ Queue\ a{\isacharsemicolon}\isanewline
-enqueue\ x\ {\isacharparenleft}AQueue\ xs\ ys{\isacharparenright}\ {\isacharequal}\ AQueue\ {\isacharparenleft}x\ {\isacharcolon}\ xs{\isacharparenright}\ ys{\isacharsemicolon}\isanewline
+enqueue\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Queue\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Queue\ a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+enqueue\ x\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ AQueue\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3A}{\isacharcolon}}\ xs{\isaliteral{29}{\isacharparenright}}\ ys{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-{\isacharbraceright}\isanewline%
+{\isaliteral{7D}{\isacharbraceright}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -253,7 +253,7 @@
\endisadelimquotetypewriter
%
\begin{isamarkuptext}%
-\noindent For more details about \hyperlink{command.export-code}{\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}} see
+\noindent For more details about \hyperlink{command.export-code}{\mbox{\isa{\isacommand{export{\isaliteral{5F}{\isacharunderscore}}code}}}} see
\secref{sec:further}.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -274,53 +274,53 @@
%
\isatagquote
\isacommand{class}\isamarkupfalse%
-\ semigroup\ {\isacharequal}\isanewline
-\ \ \isakeyword{fixes}\ mult\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasymotimes}{\isachardoublequoteclose}\ {\isadigit{7}}{\isadigit{0}}{\isacharparenright}\isanewline
-\ \ \isakeyword{assumes}\ assoc{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}x\ {\isasymotimes}\ y{\isacharparenright}\ {\isasymotimes}\ z\ {\isacharequal}\ x\ {\isasymotimes}\ {\isacharparenleft}y\ {\isasymotimes}\ z{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ semigroup\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \isakeyword{fixes}\ mult\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{7}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \isakeyword{assumes}\ assoc{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ z\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{class}\isamarkupfalse%
-\ monoid\ {\isacharequal}\ semigroup\ {\isacharplus}\isanewline
-\ \ \isakeyword{fixes}\ neutral\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a\ {\isacharparenleft}{\isachardoublequoteopen}{\isasymone}{\isachardoublequoteclose}{\isacharparenright}\isanewline
-\ \ \isakeyword{assumes}\ neutl{\isacharcolon}\ {\isachardoublequoteopen}{\isasymone}\ {\isasymotimes}\ x\ {\isacharequal}\ x{\isachardoublequoteclose}\isanewline
-\ \ \ \ \isakeyword{and}\ neutr{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymotimes}\ {\isasymone}\ {\isacharequal}\ x{\isachardoublequoteclose}\isanewline
+\ monoid\ {\isaliteral{3D}{\isacharequal}}\ semigroup\ {\isaliteral{2B}{\isacharplus}}\isanewline
+\ \ \isakeyword{fixes}\ neutral\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F6E653E}{\isasymone}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \isakeyword{assumes}\ neutl{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ x\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \isakeyword{and}\ neutr{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{instantiation}\isamarkupfalse%
-\ nat\ {\isacharcolon}{\isacharcolon}\ monoid\isanewline
+\ nat\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ monoid\isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{primrec}\isamarkupfalse%
-\ mult{\isacharunderscore}nat\ \isakeyword{where}\isanewline
-\ \ \ \ {\isachardoublequoteopen}{\isadigit{0}}\ {\isasymotimes}\ n\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}nat{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}Suc\ m\ {\isasymotimes}\ n\ {\isacharequal}\ n\ {\isacharplus}\ m\ {\isasymotimes}\ n{\isachardoublequoteclose}\isanewline
+\ mult{\isaliteral{5F}{\isacharunderscore}}nat\ \isakeyword{where}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{0}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}Suc\ m\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ n\ {\isaliteral{3D}{\isacharequal}}\ n\ {\isaliteral{2B}{\isacharplus}}\ m\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ n{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{definition}\isamarkupfalse%
-\ neutral{\isacharunderscore}nat\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}{\isasymone}\ {\isacharequal}\ Suc\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
+\ neutral{\isaliteral{5F}{\isacharunderscore}}nat\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{3D}{\isacharequal}}\ Suc\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ add{\isacharunderscore}mult{\isacharunderscore}distrib{\isacharcolon}\isanewline
-\ \ \isakeyword{fixes}\ n\ m\ q\ {\isacharcolon}{\isacharcolon}\ nat\isanewline
-\ \ \isakeyword{shows}\ {\isachardoublequoteopen}{\isacharparenleft}n\ {\isacharplus}\ m{\isacharparenright}\ {\isasymotimes}\ q\ {\isacharequal}\ n\ {\isasymotimes}\ q\ {\isacharplus}\ m\ {\isasymotimes}\ q{\isachardoublequoteclose}\isanewline
+\ add{\isaliteral{5F}{\isacharunderscore}}mult{\isaliteral{5F}{\isacharunderscore}}distrib{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \isakeyword{fixes}\ n\ m\ q\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat\isanewline
+\ \ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2B}{\isacharplus}}\ m{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ q\ {\isaliteral{3D}{\isacharequal}}\ n\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ q\ {\isaliteral{2B}{\isacharplus}}\ m\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ q{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ n{\isacharparenright}\ simp{\isacharunderscore}all\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ n{\isaliteral{29}{\isacharparenright}}\ simp{\isaliteral{5F}{\isacharunderscore}}all\isanewline
\isanewline
\isacommand{instance}\isamarkupfalse%
\ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
-\ m\ n\ q\ {\isacharcolon}{\isacharcolon}\ nat\isanewline
+\ m\ n\ q\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}m\ {\isasymotimes}\ n\ {\isasymotimes}\ q\ {\isacharequal}\ m\ {\isasymotimes}\ {\isacharparenleft}n\ {\isasymotimes}\ q{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}m\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ n\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ q\ {\isaliteral{3D}{\isacharequal}}\ m\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ q{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ m{\isacharparenright}\ {\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}\ add{\isacharunderscore}mult{\isacharunderscore}distrib{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ m{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{5F}{\isacharunderscore}}all\ add{\isaliteral{3A}{\isacharcolon}}\ add{\isaliteral{5F}{\isacharunderscore}}mult{\isaliteral{5F}{\isacharunderscore}}distrib{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymone}\ {\isasymotimes}\ n\ {\isacharequal}\ n{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ n\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ neutral{\isacharunderscore}nat{\isacharunderscore}def{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ neutral{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}m\ {\isasymotimes}\ {\isasymone}\ {\isacharequal}\ m{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}m\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ {\isaliteral{5C3C6F6E653E}{\isasymone}}\ {\isaliteral{3D}{\isacharequal}}\ m{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ m{\isacharparenright}\ {\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}\ neutral{\isacharunderscore}nat{\isacharunderscore}def{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ m{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{5F}{\isacharunderscore}}all\ add{\isaliteral{3A}{\isacharcolon}}\ neutral{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
@@ -345,9 +345,9 @@
%
\isatagquote
\isacommand{primrec}\isamarkupfalse%
-\ {\isacharparenleft}\isakeyword{in}\ monoid{\isacharparenright}\ pow\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ \ \ {\isachardoublequoteopen}pow\ {\isadigit{0}}\ a\ {\isacharequal}\ {\isasymone}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}pow\ {\isacharparenleft}Suc\ n{\isacharparenright}\ a\ {\isacharequal}\ a\ {\isasymotimes}\ pow\ n\ a{\isachardoublequoteclose}%
+\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{in}\ monoid{\isaliteral{29}{\isacharparenright}}\ pow\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}pow\ {\isadigit{0}}\ a\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6F6E653E}{\isasymone}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}pow\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ a\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}\ pow\ n\ a{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -367,8 +367,8 @@
%
\isatagquote
\isacommand{definition}\isamarkupfalse%
-\ bexp\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}bexp\ n\ {\isacharequal}\ pow\ n\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
+\ bexp\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}bexp\ n\ {\isaliteral{3D}{\isacharequal}}\ pow\ n\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -389,45 +389,45 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-module\ Example\ where\ {\isacharbraceleft}\isanewline
+module\ Example\ where\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
\isanewline
-data\ Nat\ {\isacharequal}\ Zero{\isacharunderscore}nat\ {\isacharbar}\ Suc\ Nat{\isacharsemicolon}\isanewline
+data\ Nat\ {\isaliteral{3D}{\isacharequal}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{7C}{\isacharbar}}\ Suc\ Nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-plus{\isacharunderscore}nat\ {\isacharcolon}{\isacharcolon}\ Nat\ {\isacharminus}{\isachargreater}\ Nat\ {\isacharminus}{\isachargreater}\ Nat{\isacharsemicolon}\isanewline
-plus{\isacharunderscore}nat\ {\isacharparenleft}Suc\ m{\isacharparenright}\ n\ {\isacharequal}\ plus{\isacharunderscore}nat\ m\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharsemicolon}\isanewline
-plus{\isacharunderscore}nat\ Zero{\isacharunderscore}nat\ n\ {\isacharequal}\ n{\isacharsemicolon}\isanewline
+plus{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ Nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+plus{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}Suc\ m{\isaliteral{29}{\isacharparenright}}\ n\ {\isaliteral{3D}{\isacharequal}}\ plus{\isaliteral{5F}{\isacharunderscore}}nat\ m\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+plus{\isaliteral{5F}{\isacharunderscore}}nat\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ n\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-class\ Semigroup\ a\ where\ {\isacharbraceleft}\isanewline
-\ \ mult\ {\isacharcolon}{\isacharcolon}\ a\ {\isacharminus}{\isachargreater}\ a\ {\isacharminus}{\isachargreater}\ a{\isacharsemicolon}\isanewline
-{\isacharbraceright}{\isacharsemicolon}\isanewline
+class\ Semigroup\ a\ where\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ mult\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-class\ {\isacharparenleft}Semigroup\ a{\isacharparenright}\ {\isacharequal}{\isachargreater}\ Monoid\ a\ where\ {\isacharbraceleft}\isanewline
-\ \ neutral\ {\isacharcolon}{\isacharcolon}\ a{\isacharsemicolon}\isanewline
-{\isacharbraceright}{\isacharsemicolon}\isanewline
+class\ {\isaliteral{28}{\isacharparenleft}}Semigroup\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ Monoid\ a\ where\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ neutral\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-pow\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ {\isacharparenleft}Monoid\ a{\isacharparenright}\ {\isacharequal}{\isachargreater}\ Nat\ {\isacharminus}{\isachargreater}\ a\ {\isacharminus}{\isachargreater}\ a{\isacharsemicolon}\isanewline
-pow\ Zero{\isacharunderscore}nat\ a\ {\isacharequal}\ neutral{\isacharsemicolon}\isanewline
-pow\ {\isacharparenleft}Suc\ n{\isacharparenright}\ a\ {\isacharequal}\ mult\ a\ {\isacharparenleft}pow\ n\ a{\isacharparenright}{\isacharsemicolon}\isanewline
+pow\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}Monoid\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ Nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+pow\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ a\ {\isaliteral{3D}{\isacharequal}}\ neutral{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+pow\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ a\ {\isaliteral{3D}{\isacharequal}}\ mult\ a\ {\isaliteral{28}{\isacharparenleft}}pow\ n\ a{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-mult{\isacharunderscore}nat\ {\isacharcolon}{\isacharcolon}\ Nat\ {\isacharminus}{\isachargreater}\ Nat\ {\isacharminus}{\isachargreater}\ Nat{\isacharsemicolon}\isanewline
-mult{\isacharunderscore}nat\ Zero{\isacharunderscore}nat\ n\ {\isacharequal}\ Zero{\isacharunderscore}nat{\isacharsemicolon}\isanewline
-mult{\isacharunderscore}nat\ {\isacharparenleft}Suc\ m{\isacharparenright}\ n\ {\isacharequal}\ plus{\isacharunderscore}nat\ n\ {\isacharparenleft}mult{\isacharunderscore}nat\ m\ n{\isacharparenright}{\isacharsemicolon}\isanewline
+mult{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ Nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+mult{\isaliteral{5F}{\isacharunderscore}}nat\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ n\ {\isaliteral{3D}{\isacharequal}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+mult{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}Suc\ m{\isaliteral{29}{\isacharparenright}}\ n\ {\isaliteral{3D}{\isacharequal}}\ plus{\isaliteral{5F}{\isacharunderscore}}nat\ n\ {\isaliteral{28}{\isacharparenleft}}mult{\isaliteral{5F}{\isacharunderscore}}nat\ m\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-instance\ Semigroup\ Nat\ where\ {\isacharbraceleft}\isanewline
-\ \ mult\ {\isacharequal}\ mult{\isacharunderscore}nat{\isacharsemicolon}\isanewline
-{\isacharbraceright}{\isacharsemicolon}\isanewline
+instance\ Semigroup\ Nat\ where\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ mult\ {\isaliteral{3D}{\isacharequal}}\ mult{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-neutral{\isacharunderscore}nat\ {\isacharcolon}{\isacharcolon}\ Nat{\isacharsemicolon}\isanewline
-neutral{\isacharunderscore}nat\ {\isacharequal}\ Suc\ Zero{\isacharunderscore}nat{\isacharsemicolon}\isanewline
+neutral{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ Nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+neutral{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3D}{\isacharequal}}\ Suc\ Zero{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-instance\ Monoid\ Nat\ where\ {\isacharbraceleft}\isanewline
-\ \ neutral\ {\isacharequal}\ neutral{\isacharunderscore}nat{\isacharsemicolon}\isanewline
-{\isacharbraceright}{\isacharsemicolon}\isanewline
+instance\ Monoid\ Nat\ where\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ neutral\ {\isaliteral{3D}{\isacharequal}}\ neutral{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-bexp\ {\isacharcolon}{\isacharcolon}\ Nat\ {\isacharminus}{\isachargreater}\ Nat{\isacharsemicolon}\isanewline
-bexp\ n\ {\isacharequal}\ pow\ n\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ Zero{\isacharunderscore}nat{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline
+bexp\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ Nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+bexp\ n\ {\isaliteral{3D}{\isacharequal}}\ pow\ n\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ Zero{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-{\isacharbraceright}\isanewline%
+{\isaliteral{7D}{\isacharbraceright}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -452,50 +452,50 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-structure\ Example\ {\isacharcolon}\ sig\isanewline
-\ \ datatype\ nat\ {\isacharequal}\ Zero{\isacharunderscore}nat\ {\isacharbar}\ Suc\ of\ nat\isanewline
-\ \ val\ plus{\isacharunderscore}nat\ {\isacharcolon}\ nat\ {\isacharminus}{\isachargreater}\ nat\ {\isacharminus}{\isachargreater}\ nat\isanewline
-\ \ type\ {\isacharprime}a\ semigroup\isanewline
-\ \ val\ mult\ {\isacharcolon}\ {\isacharprime}a\ semigroup\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\isanewline
-\ \ type\ {\isacharprime}a\ monoid\isanewline
-\ \ val\ semigroup{\isacharunderscore}monoid\ {\isacharcolon}\ {\isacharprime}a\ monoid\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ semigroup\isanewline
-\ \ val\ neutral\ {\isacharcolon}\ {\isacharprime}a\ monoid\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\isanewline
-\ \ val\ pow\ {\isacharcolon}\ {\isacharprime}a\ monoid\ {\isacharminus}{\isachargreater}\ nat\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\isanewline
-\ \ val\ mult{\isacharunderscore}nat\ {\isacharcolon}\ nat\ {\isacharminus}{\isachargreater}\ nat\ {\isacharminus}{\isachargreater}\ nat\isanewline
-\ \ val\ semigroup{\isacharunderscore}nat\ {\isacharcolon}\ nat\ semigroup\isanewline
-\ \ val\ neutral{\isacharunderscore}nat\ {\isacharcolon}\ nat\isanewline
-\ \ val\ monoid{\isacharunderscore}nat\ {\isacharcolon}\ nat\ monoid\isanewline
-\ \ val\ bexp\ {\isacharcolon}\ nat\ {\isacharminus}{\isachargreater}\ nat\isanewline
-end\ {\isacharequal}\ struct\isanewline
+structure\ Example\ {\isaliteral{3A}{\isacharcolon}}\ sig\isanewline
+\ \ datatype\ nat\ {\isaliteral{3D}{\isacharequal}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{7C}{\isacharbar}}\ Suc\ of\ nat\isanewline
+\ \ val\ plus{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\isanewline
+\ \ type\ {\isaliteral{27}{\isacharprime}}a\ semigroup\isanewline
+\ \ val\ mult\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ semigroup\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\isanewline
+\ \ type\ {\isaliteral{27}{\isacharprime}}a\ monoid\isanewline
+\ \ val\ semigroup{\isaliteral{5F}{\isacharunderscore}}monoid\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ monoid\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ semigroup\isanewline
+\ \ val\ neutral\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ monoid\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\isanewline
+\ \ val\ pow\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ monoid\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\isanewline
+\ \ val\ mult{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\isanewline
+\ \ val\ semigroup{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}\ nat\ semigroup\isanewline
+\ \ val\ neutral{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}\ nat\isanewline
+\ \ val\ monoid{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}\ nat\ monoid\isanewline
+\ \ val\ bexp\ {\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ nat\isanewline
+end\ {\isaliteral{3D}{\isacharequal}}\ struct\isanewline
\isanewline
-datatype\ nat\ {\isacharequal}\ Zero{\isacharunderscore}nat\ {\isacharbar}\ Suc\ of\ nat{\isacharsemicolon}\isanewline
+datatype\ nat\ {\isaliteral{3D}{\isacharequal}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{7C}{\isacharbar}}\ Suc\ of\ nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ plus{\isacharunderscore}nat\ {\isacharparenleft}Suc\ m{\isacharparenright}\ n\ {\isacharequal}\ plus{\isacharunderscore}nat\ m\ {\isacharparenleft}Suc\ n{\isacharparenright}\isanewline
-\ \ {\isacharbar}\ plus{\isacharunderscore}nat\ Zero{\isacharunderscore}nat\ n\ {\isacharequal}\ n{\isacharsemicolon}\isanewline
+fun\ plus{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}Suc\ m{\isaliteral{29}{\isacharparenright}}\ n\ {\isaliteral{3D}{\isacharequal}}\ plus{\isaliteral{5F}{\isacharunderscore}}nat\ m\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ plus{\isaliteral{5F}{\isacharunderscore}}nat\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ n\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-type\ {\isacharprime}a\ semigroup\ {\isacharequal}\ {\isacharbraceleft}mult\ {\isacharcolon}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a{\isacharbraceright}{\isacharsemicolon}\isanewline
-val\ mult\ {\isacharequal}\ {\isacharhash}mult\ {\isacharcolon}\ {\isacharprime}a\ semigroup\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a{\isacharsemicolon}\isanewline
+type\ {\isaliteral{27}{\isacharprime}}a\ semigroup\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}mult\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+val\ mult\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{23}{\isacharhash}}mult\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ semigroup\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-type\ {\isacharprime}a\ monoid\ {\isacharequal}\ {\isacharbraceleft}semigroup{\isacharunderscore}monoid\ {\isacharcolon}\ {\isacharprime}a\ semigroup{\isacharcomma}\ neutral\ {\isacharcolon}\ {\isacharprime}a{\isacharbraceright}{\isacharsemicolon}\isanewline
-val\ semigroup{\isacharunderscore}monoid\ {\isacharequal}\ {\isacharhash}semigroup{\isacharunderscore}monoid\ {\isacharcolon}\ {\isacharprime}a\ monoid\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ semigroup{\isacharsemicolon}\isanewline
-val\ neutral\ {\isacharequal}\ {\isacharhash}neutral\ {\isacharcolon}\ {\isacharprime}a\ monoid\ {\isacharminus}{\isachargreater}\ {\isacharprime}a{\isacharsemicolon}\isanewline
+type\ {\isaliteral{27}{\isacharprime}}a\ monoid\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}semigroup{\isaliteral{5F}{\isacharunderscore}}monoid\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ semigroup{\isaliteral{2C}{\isacharcomma}}\ neutral\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+val\ semigroup{\isaliteral{5F}{\isacharunderscore}}monoid\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{23}{\isacharhash}}semigroup{\isaliteral{5F}{\isacharunderscore}}monoid\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ monoid\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ semigroup{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+val\ neutral\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{23}{\isacharhash}}neutral\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ monoid\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ pow\ A{\isacharunderscore}\ Zero{\isacharunderscore}nat\ a\ {\isacharequal}\ neutral\ A{\isacharunderscore}\isanewline
-\ \ {\isacharbar}\ pow\ A{\isacharunderscore}\ {\isacharparenleft}Suc\ n{\isacharparenright}\ a\ {\isacharequal}\ mult\ {\isacharparenleft}semigroup{\isacharunderscore}monoid\ A{\isacharunderscore}{\isacharparenright}\ a\ {\isacharparenleft}pow\ A{\isacharunderscore}\ n\ a{\isacharparenright}{\isacharsemicolon}\isanewline
+fun\ pow\ A{\isaliteral{5F}{\isacharunderscore}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ a\ {\isaliteral{3D}{\isacharequal}}\ neutral\ A{\isaliteral{5F}{\isacharunderscore}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ pow\ A{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ a\ {\isaliteral{3D}{\isacharequal}}\ mult\ {\isaliteral{28}{\isacharparenleft}}semigroup{\isaliteral{5F}{\isacharunderscore}}monoid\ A{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ a\ {\isaliteral{28}{\isacharparenleft}}pow\ A{\isaliteral{5F}{\isacharunderscore}}\ n\ a{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ mult{\isacharunderscore}nat\ Zero{\isacharunderscore}nat\ n\ {\isacharequal}\ Zero{\isacharunderscore}nat\isanewline
-\ \ {\isacharbar}\ mult{\isacharunderscore}nat\ {\isacharparenleft}Suc\ m{\isacharparenright}\ n\ {\isacharequal}\ plus{\isacharunderscore}nat\ n\ {\isacharparenleft}mult{\isacharunderscore}nat\ m\ n{\isacharparenright}{\isacharsemicolon}\isanewline
+fun\ mult{\isaliteral{5F}{\isacharunderscore}}nat\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ n\ {\isaliteral{3D}{\isacharequal}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ mult{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}Suc\ m{\isaliteral{29}{\isacharparenright}}\ n\ {\isaliteral{3D}{\isacharequal}}\ plus{\isaliteral{5F}{\isacharunderscore}}nat\ n\ {\isaliteral{28}{\isacharparenleft}}mult{\isaliteral{5F}{\isacharunderscore}}nat\ m\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-val\ semigroup{\isacharunderscore}nat\ {\isacharequal}\ {\isacharbraceleft}mult\ {\isacharequal}\ mult{\isacharunderscore}nat{\isacharbraceright}\ {\isacharcolon}\ nat\ semigroup{\isacharsemicolon}\isanewline
+val\ semigroup{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}mult\ {\isaliteral{3D}{\isacharequal}}\ mult{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{7D}{\isacharbraceright}}\ {\isaliteral{3A}{\isacharcolon}}\ nat\ semigroup{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-val\ neutral{\isacharunderscore}nat\ {\isacharcolon}\ nat\ {\isacharequal}\ Suc\ Zero{\isacharunderscore}nat{\isacharsemicolon}\isanewline
+val\ neutral{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{3D}{\isacharequal}}\ Suc\ Zero{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-val\ monoid{\isacharunderscore}nat\ {\isacharequal}\ {\isacharbraceleft}semigroup{\isacharunderscore}monoid\ {\isacharequal}\ semigroup{\isacharunderscore}nat{\isacharcomma}\ neutral\ {\isacharequal}\ neutral{\isacharunderscore}nat{\isacharbraceright}\isanewline
-\ \ {\isacharcolon}\ nat\ monoid{\isacharsemicolon}\isanewline
+val\ monoid{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}semigroup{\isaliteral{5F}{\isacharunderscore}}monoid\ {\isaliteral{3D}{\isacharequal}}\ semigroup{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{2C}{\isacharcomma}}\ neutral\ {\isaliteral{3D}{\isacharequal}}\ neutral{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{7D}{\isacharbraceright}}\isanewline
+\ \ {\isaliteral{3A}{\isacharcolon}}\ nat\ monoid{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ bexp\ n\ {\isacharequal}\ pow\ monoid{\isacharunderscore}nat\ n\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ Zero{\isacharunderscore}nat{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline
+fun\ bexp\ n\ {\isaliteral{3D}{\isacharequal}}\ pow\ monoid{\isaliteral{5F}{\isacharunderscore}}nat\ n\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ Zero{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-end{\isacharsemicolon}\ {\isacharparenleft}{\isacharasterisk}struct\ Example{\isacharasterisk}{\isacharparenright}\isanewline%
+end{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}struct\ Example{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
--- a/doc-src/Codegen/Thy/document/Refinement.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/Codegen/Thy/document/Refinement.tex Mon Nov 08 14:41:11 2010 +0100
@@ -48,10 +48,10 @@
%
\isatagquote
\isacommand{fun}\isamarkupfalse%
-\ fib\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ \ \ {\isachardoublequoteopen}fib\ {\isadigit{0}}\ {\isacharequal}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}fib\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}\ {\isacharequal}\ Suc\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}fib\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ fib\ n\ {\isacharplus}\ fib\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isachardoublequoteclose}%
+\ fib\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}fib\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}fib\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Suc\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}fib\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ fib\ n\ {\isaliteral{2B}{\isacharplus}}\ fib\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -72,10 +72,10 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-fib\ {\isacharcolon}{\isacharcolon}\ Nat\ {\isacharminus}{\isachargreater}\ Nat{\isacharsemicolon}\isanewline
-fib\ Zero{\isacharunderscore}nat\ {\isacharequal}\ Zero{\isacharunderscore}nat{\isacharsemicolon}\isanewline
-fib\ {\isacharparenleft}Suc\ Zero{\isacharunderscore}nat{\isacharparenright}\ {\isacharequal}\ Suc\ Zero{\isacharunderscore}nat{\isacharsemicolon}\isanewline
-fib\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ plus{\isacharunderscore}nat\ {\isacharparenleft}fib\ n{\isacharparenright}\ {\isacharparenleft}fib\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline%
+fib\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ Nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+fib\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3D}{\isacharequal}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+fib\ {\isaliteral{28}{\isacharparenleft}}Suc\ Zero{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Suc\ Zero{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+fib\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ plus{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{28}{\isacharparenleft}}fib\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}fib\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -100,8 +100,8 @@
%
\isatagquote
\isacommand{definition}\isamarkupfalse%
-\ fib{\isacharunderscore}step\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat\ {\isasymtimes}\ nat{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}fib{\isacharunderscore}step\ n\ {\isacharequal}\ {\isacharparenleft}fib\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharcomma}\ fib\ n{\isacharparenright}{\isachardoublequoteclose}%
+\ fib{\isaliteral{5F}{\isacharunderscore}}step\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}fib{\isaliteral{5F}{\isacharunderscore}}step\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}fib\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ fib\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -121,11 +121,11 @@
%
\isatagquote
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}fib{\isacharunderscore}step\ {\isadigit{0}}\ {\isacharequal}\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharcomma}\ {\isadigit{0}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}fib{\isacharunderscore}step\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}let\ {\isacharparenleft}m{\isacharcomma}\ q{\isacharparenright}\ {\isacharequal}\ fib{\isacharunderscore}step\ n\ in\ {\isacharparenleft}m\ {\isacharplus}\ q{\isacharcomma}\ m{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}fib{\isaliteral{5F}{\isacharunderscore}}step\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}fib{\isaliteral{5F}{\isacharunderscore}}step\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}let\ {\isaliteral{28}{\isacharparenleft}}m{\isaliteral{2C}{\isacharcomma}}\ q{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ fib{\isaliteral{5F}{\isacharunderscore}}step\ n\ in\ {\isaliteral{28}{\isacharparenleft}}m\ {\isaliteral{2B}{\isacharplus}}\ q{\isaliteral{2C}{\isacharcomma}}\ m{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}\ fib{\isacharunderscore}step{\isacharunderscore}def{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{5F}{\isacharunderscore}}all\ add{\isaliteral{3A}{\isacharcolon}}\ fib{\isaliteral{5F}{\isacharunderscore}}step{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
\endisatagquote
{\isafoldquote}%
%
@@ -134,7 +134,7 @@
\endisadelimquote
%
\begin{isamarkuptext}%
-\noindent What remains is to implement \isa{fib} by \isa{fib{\isacharunderscore}step} as follows:%
+\noindent What remains is to implement \isa{fib} by \isa{fib{\isaliteral{5F}{\isacharunderscore}}step} as follows:%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -144,11 +144,11 @@
%
\isatagquote
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}fib\ {\isadigit{0}}\ {\isacharequal}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}fib\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ fst\ {\isacharparenleft}fib{\isacharunderscore}step\ n{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}fib\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}fib\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ fst\ {\isaliteral{28}{\isacharparenleft}}fib{\isaliteral{5F}{\isacharunderscore}}step\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}\ fib{\isacharunderscore}step{\isacharunderscore}def{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{5F}{\isacharunderscore}}all\ add{\isaliteral{3A}{\isacharcolon}}\ fib{\isaliteral{5F}{\isacharunderscore}}step{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
\endisatagquote
{\isafoldquote}%
%
@@ -168,15 +168,15 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-fib{\isacharunderscore}step\ {\isacharcolon}{\isacharcolon}\ Nat\ {\isacharminus}{\isachargreater}\ {\isacharparenleft}Nat{\isacharcomma}\ Nat{\isacharparenright}{\isacharsemicolon}\isanewline
-fib{\isacharunderscore}step\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ let\ {\isacharbraceleft}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharparenleft}m{\isacharcomma}\ q{\isacharparenright}\ {\isacharequal}\ fib{\isacharunderscore}step\ n{\isacharsemicolon}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbraceright}\ in\ {\isacharparenleft}plus{\isacharunderscore}nat\ m\ q{\isacharcomma}\ m{\isacharparenright}{\isacharsemicolon}\isanewline
-fib{\isacharunderscore}step\ Zero{\isacharunderscore}nat\ {\isacharequal}\ {\isacharparenleft}Suc\ Zero{\isacharunderscore}nat{\isacharcomma}\ Zero{\isacharunderscore}nat{\isacharparenright}{\isacharsemicolon}\isanewline
+fib{\isaliteral{5F}{\isacharunderscore}}step\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ Nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}Nat{\isaliteral{2C}{\isacharcomma}}\ Nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+fib{\isaliteral{5F}{\isacharunderscore}}step\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ let\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}m{\isaliteral{2C}{\isacharcomma}}\ q{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ fib{\isaliteral{5F}{\isacharunderscore}}step\ n{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7D}{\isacharbraceright}}\ in\ {\isaliteral{28}{\isacharparenleft}}plus{\isaliteral{5F}{\isacharunderscore}}nat\ m\ q{\isaliteral{2C}{\isacharcomma}}\ m{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+fib{\isaliteral{5F}{\isacharunderscore}}step\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ Zero{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{2C}{\isacharcomma}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fib\ {\isacharcolon}{\isacharcolon}\ Nat\ {\isacharminus}{\isachargreater}\ Nat{\isacharsemicolon}\isanewline
-fib\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ fst\ {\isacharparenleft}fib{\isacharunderscore}step\ n{\isacharparenright}{\isacharsemicolon}\isanewline
-fib\ Zero{\isacharunderscore}nat\ {\isacharequal}\ Zero{\isacharunderscore}nat{\isacharsemicolon}\isanewline%
+fib\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ Nat\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+fib\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ fst\ {\isaliteral{28}{\isacharparenleft}}fib{\isaliteral{5F}{\isacharunderscore}}step\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+fib\ Zero{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3D}{\isacharequal}}\ Zero{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{3B}{\isacharsemicolon}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -209,20 +209,20 @@
%
\isatagquote
\isacommand{datatype}\isamarkupfalse%
-\ {\isacharprime}a\ queue\ {\isacharequal}\ Queue\ {\isachardoublequoteopen}{\isacharprime}a\ list{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{3D}{\isacharequal}}\ Queue\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{definition}\isamarkupfalse%
-\ empty\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ queue{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}empty\ {\isacharequal}\ Queue\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
+\ empty\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ queue{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}empty\ {\isaliteral{3D}{\isacharequal}}\ Queue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{primrec}\isamarkupfalse%
-\ enqueue\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ queue\ {\isasymRightarrow}\ {\isacharprime}a\ queue{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}enqueue\ x\ {\isacharparenleft}Queue\ xs{\isacharparenright}\ {\isacharequal}\ Queue\ {\isacharparenleft}xs\ {\isacharat}\ {\isacharbrackleft}x{\isacharbrackright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ enqueue\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ queue{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}enqueue\ x\ {\isaliteral{28}{\isacharparenleft}}Queue\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Queue\ {\isaliteral{28}{\isacharparenleft}}xs\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{fun}\isamarkupfalse%
-\ dequeue\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ queue\ {\isasymRightarrow}\ {\isacharprime}a\ option\ {\isasymtimes}\ {\isacharprime}a\ queue{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ \ \ {\isachardoublequoteopen}dequeue\ {\isacharparenleft}Queue\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}None{\isacharcomma}\ Queue\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}dequeue\ {\isacharparenleft}Queue\ {\isacharparenleft}x\ {\isacharhash}\ xs{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}Some\ x{\isacharcomma}\ Queue\ xs{\isacharparenright}{\isachardoublequoteclose}%
+\ dequeue\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ option\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a\ queue{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}dequeue\ {\isaliteral{28}{\isacharparenleft}}Queue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}None{\isaliteral{2C}{\isacharcomma}}\ Queue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}dequeue\ {\isaliteral{28}{\isacharparenleft}}Queue\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Some\ x{\isaliteral{2C}{\isacharcomma}}\ Queue\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagquote
{\isafoldquote}%
%
@@ -242,10 +242,10 @@
%
\isatagquote
\isacommand{definition}\isamarkupfalse%
-\ AQueue\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ queue{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}AQueue\ xs\ ys\ {\isacharequal}\ Queue\ {\isacharparenleft}ys\ {\isacharat}\ rev\ xs{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ AQueue\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ queue{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}AQueue\ xs\ ys\ {\isaliteral{3D}{\isacharequal}}\ Queue\ {\isaliteral{28}{\isacharparenleft}}ys\ {\isaliteral{40}{\isacharat}}\ rev\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
-\isacommand{code{\isacharunderscore}datatype}\isamarkupfalse%
+\isacommand{code{\isaliteral{5F}{\isacharunderscore}}datatype}\isamarkupfalse%
\ AQueue%
\endisatagquote
{\isafoldquote}%
@@ -261,11 +261,11 @@
to be.
The prerequisite for datatype constructors is only syntactical: a
- constructor must be of type \isa{{\isasymtau}\ {\isacharequal}\ {\isasymdots}\ {\isasymRightarrow}\ {\isasymkappa}\ {\isasymalpha}\isactrlisub {\isadigit{1}}\ {\isasymdots}\ {\isasymalpha}\isactrlisub n} where \isa{{\isacharbraceleft}{\isasymalpha}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlisub n{\isacharbraceright}} is exactly the set of \emph{all} type variables in
- \isa{{\isasymtau}}; then \isa{{\isasymkappa}} is its corresponding datatype. The
+ constructor must be of type \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6B617070613E}{\isasymkappa}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n} where \isa{{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{7D}{\isacharbraceright}}} is exactly the set of \emph{all} type variables in
+ \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}}; then \isa{{\isaliteral{5C3C6B617070613E}{\isasymkappa}}} is its corresponding datatype. The
HOL datatype package by default registers any new datatype with its
- constructors, but this may be changed using \indexdef{}{command}{code\_datatype}\hypertarget{command.code-datatype}{\hyperlink{command.code-datatype}{\mbox{\isa{\isacommand{code{\isacharunderscore}datatype}}}}}; the currently chosen constructors can be inspected
- using the \hyperlink{command.print-codesetup}{\mbox{\isa{\isacommand{print{\isacharunderscore}codesetup}}}} command.
+ constructors, but this may be changed using \indexdef{}{command}{code\_datatype}\hypertarget{command.code-datatype}{\hyperlink{command.code-datatype}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}datatype}}}}}; the currently chosen constructors can be inspected
+ using the \hyperlink{command.print-codesetup}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}codesetup}}}} command.
Equipped with this, we are able to prove the following equations
for our primitive queue operations which \qt{implement} the simple
@@ -279,28 +279,28 @@
%
\isatagquote
\isacommand{lemma}\isamarkupfalse%
-\ empty{\isacharunderscore}AQueue\ {\isacharbrackleft}code{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}empty\ {\isacharequal}\ AQueue\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
+\ empty{\isaliteral{5F}{\isacharunderscore}}AQueue\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}empty\ {\isaliteral{3D}{\isacharequal}}\ AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{unfolding}\isamarkupfalse%
-\ AQueue{\isacharunderscore}def\ empty{\isacharunderscore}def\ \isacommand{by}\isamarkupfalse%
+\ AQueue{\isaliteral{5F}{\isacharunderscore}}def\ empty{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ enqueue{\isacharunderscore}AQueue\ {\isacharbrackleft}code{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}enqueue\ x\ {\isacharparenleft}AQueue\ xs\ ys{\isacharparenright}\ {\isacharequal}\ AQueue\ {\isacharparenleft}x\ {\isacharhash}\ xs{\isacharparenright}\ ys{\isachardoublequoteclose}\isanewline
+\ enqueue{\isaliteral{5F}{\isacharunderscore}}AQueue\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}enqueue\ x\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ AQueue\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}\ ys{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{unfolding}\isamarkupfalse%
-\ AQueue{\isacharunderscore}def\ \isacommand{by}\isamarkupfalse%
+\ AQueue{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ dequeue{\isacharunderscore}AQueue\ {\isacharbrackleft}code{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}dequeue\ {\isacharparenleft}AQueue\ xs\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ {\isacharparenleft}if\ xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ then\ {\isacharparenleft}None{\isacharcomma}\ AQueue\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\isanewline
-\ \ \ \ else\ dequeue\ {\isacharparenleft}AQueue\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharparenleft}rev\ xs{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}dequeue\ {\isacharparenleft}AQueue\ xs\ {\isacharparenleft}y\ {\isacharhash}\ ys{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}Some\ y{\isacharcomma}\ AQueue\ xs\ ys{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ dequeue{\isaliteral{5F}{\isacharunderscore}}AQueue\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ {\isaliteral{28}{\isacharparenleft}}if\ xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ then\ {\isaliteral{28}{\isacharparenleft}}None{\isaliteral{2C}{\isacharcomma}}\ AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ else\ dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{23}{\isacharhash}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Some\ y{\isaliteral{2C}{\isacharcomma}}\ AQueue\ xs\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{unfolding}\isamarkupfalse%
-\ AQueue{\isacharunderscore}def\ \isacommand{by}\isamarkupfalse%
-\ simp{\isacharunderscore}all%
+\ AQueue{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{by}\isamarkupfalse%
+\ simp{\isaliteral{5F}{\isacharunderscore}}all%
\endisatagquote
{\isafoldquote}%
%
@@ -320,10 +320,10 @@
%
\isatagquote
\isacommand{lemma}\isamarkupfalse%
-\ queue{\isacharunderscore}case{\isacharunderscore}AQueue\ {\isacharbrackleft}code{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}queue{\isacharunderscore}case\ f\ {\isacharparenleft}AQueue\ xs\ ys{\isacharparenright}\ {\isacharequal}\ f\ {\isacharparenleft}ys\ {\isacharat}\ rev\ xs{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ queue{\isaliteral{5F}{\isacharunderscore}}case{\isaliteral{5F}{\isacharunderscore}}AQueue\ {\isaliteral{5B}{\isacharbrackleft}}code{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}queue{\isaliteral{5F}{\isacharunderscore}}case\ f\ {\isaliteral{28}{\isacharparenleft}}AQueue\ xs\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ f\ {\isaliteral{28}{\isacharparenleft}}ys\ {\isaliteral{40}{\isacharat}}\ rev\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{unfolding}\isamarkupfalse%
-\ AQueue{\isacharunderscore}def\ \isacommand{by}\isamarkupfalse%
+\ AQueue{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{by}\isamarkupfalse%
\ simp%
\endisatagquote
{\isafoldquote}%
@@ -344,39 +344,39 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-structure\ Example\ {\isacharcolon}\ sig\isanewline
-\ \ val\ id\ {\isacharcolon}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\isanewline
-\ \ val\ fold\ {\isacharcolon}\ {\isacharparenleft}{\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}b\ {\isacharminus}{\isachargreater}\ {\isacharprime}b{\isacharparenright}\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ list\ {\isacharminus}{\isachargreater}\ {\isacharprime}b\ {\isacharminus}{\isachargreater}\ {\isacharprime}b\isanewline
-\ \ val\ rev\ {\isacharcolon}\ {\isacharprime}a\ list\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ list\isanewline
-\ \ val\ null\ {\isacharcolon}\ {\isacharprime}a\ list\ {\isacharminus}{\isachargreater}\ bool\isanewline
-\ \ datatype\ {\isacharprime}a\ queue\ {\isacharequal}\ AQueue\ of\ {\isacharprime}a\ list\ {\isacharasterisk}\ {\isacharprime}a\ list\isanewline
-\ \ val\ empty\ {\isacharcolon}\ {\isacharprime}a\ queue\isanewline
-\ \ val\ dequeue\ {\isacharcolon}\ {\isacharprime}a\ queue\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ option\ {\isacharasterisk}\ {\isacharprime}a\ queue\isanewline
-\ \ val\ enqueue\ {\isacharcolon}\ {\isacharprime}a\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ queue\ {\isacharminus}{\isachargreater}\ {\isacharprime}a\ queue\isanewline
-end\ {\isacharequal}\ struct\isanewline
+structure\ Example\ {\isaliteral{3A}{\isacharcolon}}\ sig\isanewline
+\ \ val\ id\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\isanewline
+\ \ val\ fold\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}b\isanewline
+\ \ val\ rev\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ list\isanewline
+\ \ val\ null\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ bool\isanewline
+\ \ datatype\ {\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{3D}{\isacharequal}}\ AQueue\ of\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{27}{\isacharprime}}a\ list\isanewline
+\ \ val\ empty\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ queue\isanewline
+\ \ val\ dequeue\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ option\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{27}{\isacharprime}}a\ queue\isanewline
+\ \ val\ enqueue\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{27}{\isacharprime}}a\ queue\isanewline
+end\ {\isaliteral{3D}{\isacharequal}}\ struct\isanewline
\isanewline
-fun\ id\ x\ {\isacharequal}\ {\isacharparenleft}fn\ xa\ {\isacharequal}{\isachargreater}\ xa{\isacharparenright}\ x{\isacharsemicolon}\isanewline
+fun\ id\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}fn\ xa\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ xa{\isaliteral{29}{\isacharparenright}}\ x{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ fold\ f\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ id\isanewline
-\ \ {\isacharbar}\ fold\ f\ {\isacharparenleft}x\ {\isacharcolon}{\isacharcolon}\ xs{\isacharparenright}\ {\isacharequal}\ fold\ f\ xs\ o\ f\ x{\isacharsemicolon}\isanewline
+fun\ fold\ f\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ id\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ fold\ f\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ fold\ f\ xs\ o\ f\ x{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ rev\ xs\ {\isacharequal}\ fold\ {\isacharparenleft}fn\ a\ {\isacharequal}{\isachargreater}\ fn\ b\ {\isacharequal}{\isachargreater}\ a\ {\isacharcolon}{\isacharcolon}\ b{\isacharparenright}\ xs\ {\isacharbrackleft}{\isacharbrackright}{\isacharsemicolon}\isanewline
+fun\ rev\ xs\ {\isaliteral{3D}{\isacharequal}}\ fold\ {\isaliteral{28}{\isacharparenleft}}fn\ a\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ fn\ b\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ a\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ b{\isaliteral{29}{\isacharparenright}}\ xs\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ null\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ true\isanewline
-\ \ {\isacharbar}\ null\ {\isacharparenleft}x\ {\isacharcolon}{\isacharcolon}\ xs{\isacharparenright}\ {\isacharequal}\ false{\isacharsemicolon}\isanewline
+fun\ null\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ true\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ null\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ false{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-datatype\ {\isacharprime}a\ queue\ {\isacharequal}\ AQueue\ of\ {\isacharprime}a\ list\ {\isacharasterisk}\ {\isacharprime}a\ list{\isacharsemicolon}\isanewline
+datatype\ {\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{3D}{\isacharequal}}\ AQueue\ of\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-val\ empty\ {\isacharcolon}\ {\isacharprime}a\ queue\ {\isacharequal}\ AQueue\ {\isacharparenleft}{\isacharbrackleft}{\isacharbrackright}{\isacharcomma}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isacharsemicolon}\isanewline
+val\ empty\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ queue\ {\isaliteral{3D}{\isacharequal}}\ AQueue\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ dequeue\ {\isacharparenleft}AQueue\ {\isacharparenleft}xs{\isacharcomma}\ y\ {\isacharcolon}{\isacharcolon}\ ys{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}SOME\ y{\isacharcomma}\ AQueue\ {\isacharparenleft}xs{\isacharcomma}\ ys{\isacharparenright}{\isacharparenright}\isanewline
-\ \ {\isacharbar}\ dequeue\ {\isacharparenleft}AQueue\ {\isacharparenleft}xs{\isacharcomma}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ {\isacharparenleft}if\ null\ xs\ then\ {\isacharparenleft}NONE{\isacharcomma}\ AQueue\ {\isacharparenleft}{\isacharbrackleft}{\isacharbrackright}{\isacharcomma}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isacharparenright}\isanewline
-\ \ \ \ \ \ else\ dequeue\ {\isacharparenleft}AQueue\ {\isacharparenleft}{\isacharbrackleft}{\isacharbrackright}{\isacharcomma}\ rev\ xs{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline
+fun\ dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ {\isaliteral{28}{\isacharparenleft}}xs{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}SOME\ y{\isaliteral{2C}{\isacharcomma}}\ AQueue\ {\isaliteral{28}{\isacharparenleft}}xs{\isaliteral{2C}{\isacharcomma}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ {\isaliteral{28}{\isacharparenleft}}xs{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ {\isaliteral{28}{\isacharparenleft}}if\ null\ xs\ then\ {\isaliteral{28}{\isacharparenleft}}NONE{\isaliteral{2C}{\isacharcomma}}\ AQueue\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ \ \ else\ dequeue\ {\isaliteral{28}{\isacharparenleft}}AQueue\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ rev\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-fun\ enqueue\ x\ {\isacharparenleft}AQueue\ {\isacharparenleft}xs{\isacharcomma}\ ys{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ AQueue\ {\isacharparenleft}x\ {\isacharcolon}{\isacharcolon}\ xs{\isacharcomma}\ ys{\isacharparenright}{\isacharsemicolon}\isanewline
+fun\ enqueue\ x\ {\isaliteral{28}{\isacharparenleft}}AQueue\ {\isaliteral{28}{\isacharparenleft}}xs{\isaliteral{2C}{\isacharcomma}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ AQueue\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ xs{\isaliteral{2C}{\isacharcomma}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-end{\isacharsemicolon}\ {\isacharparenleft}{\isacharasterisk}struct\ Example{\isacharasterisk}{\isacharparenright}\isanewline%
+end{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}struct\ Example{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -406,12 +406,12 @@
\begin{isamarkuptext}%
Datatype representation involving invariants require a dedicated
setup for the type and its primitive operations. As a running
- example, we implement a type \isa{{\isacharprime}a\ dlist} of list consisting
+ example, we implement a type \isa{{\isaliteral{27}{\isacharprime}}a\ dlist} of list consisting
of distinct elements.
The first step is to decide on which representation the abstract
- type (in our example \isa{{\isacharprime}a\ dlist}) should be implemented.
- Here we choose \isa{{\isacharprime}a\ list}. Then a conversion from the concrete
+ type (in our example \isa{{\isaliteral{27}{\isacharprime}}a\ dlist}) should be implemented.
+ Here we choose \isa{{\isaliteral{27}{\isacharprime}}a\ list}. Then a conversion from the concrete
type to the abstract type must be specified, here:%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -423,7 +423,7 @@
\isatagquote
%
\begin{isamarkuptext}%
-\isa{Dlist\ {\isasymColon}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ dlist}%
+\isa{Dlist\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ dlist}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -447,7 +447,7 @@
\isatagquote
%
\begin{isamarkuptext}%
-\isa{list{\isacharunderscore}of{\isacharunderscore}dlist\ {\isasymColon}\ {\isacharprime}a\ dlist\ {\isasymRightarrow}\ {\isacharprime}a\ list}%
+\isa{list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ {\isaliteral{27}{\isacharprime}}a\ dlist\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -470,10 +470,10 @@
%
\isatagquote
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code\ abstype{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}Dlist\ {\isacharparenleft}list{\isacharunderscore}of{\isacharunderscore}dlist\ dxs{\isacharparenright}\ {\isacharequal}\ dxs{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}code\ abstype{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}Dlist\ {\isaliteral{28}{\isacharparenleft}}list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist\ dxs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ dxs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}fact\ Dlist{\isacharunderscore}list{\isacharunderscore}of{\isacharunderscore}dlist{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}fact\ Dlist{\isaliteral{5F}{\isacharunderscore}}list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist{\isaliteral{29}{\isacharparenright}}%
\endisatagquote
{\isafoldquote}%
%
@@ -483,14 +483,14 @@
%
\begin{isamarkuptext}%
\noindent Note that so far the invariant on representations
- (\isa{distinct\ {\isasymColon}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ bool}) has never been mentioned explicitly:
+ (\isa{distinct\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}) has never been mentioned explicitly:
the invariant is only referred to implicitly: all values in
- set \isa{{\isacharbraceleft}xs{\isachardot}\ list{\isacharunderscore}of{\isacharunderscore}dlist\ {\isacharparenleft}Dlist\ xs{\isacharparenright}\ {\isacharequal}\ xs{\isacharbraceright}} are invariant,
- and in our example this is exactly \isa{{\isacharbraceleft}xs{\isachardot}\ distinct\ xs{\isacharbraceright}}.
+ set \isa{{\isaliteral{7B}{\isacharbraceleft}}xs{\isaliteral{2E}{\isachardot}}\ list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist\ {\isaliteral{28}{\isacharparenleft}}Dlist\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ xs{\isaliteral{7D}{\isacharbraceright}}} are invariant,
+ and in our example this is exactly \isa{{\isaliteral{7B}{\isacharbraceleft}}xs{\isaliteral{2E}{\isachardot}}\ distinct\ xs{\isaliteral{7D}{\isacharbraceright}}}.
- The primitive operations on \isa{{\isacharprime}a\ dlist} are specified
- indirectly using the projection \isa{list{\isacharunderscore}of{\isacharunderscore}dlist}. For
- the empty \isa{dlist}, \isa{Dlist{\isachardot}empty}, we finally want
+ The primitive operations on \isa{{\isaliteral{27}{\isacharprime}}a\ dlist} are specified
+ indirectly using the projection \isa{list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist}. For
+ the empty \isa{dlist}, \isa{Dlist{\isaliteral{2E}{\isachardot}}empty}, we finally want
the code equation%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -502,7 +502,7 @@
\isatagquote
%
\begin{isamarkuptext}%
-\isa{Dlist{\isachardot}empty\ {\isacharequal}\ Dlist\ {\isacharbrackleft}{\isacharbrackright}}%
+\isa{Dlist{\isaliteral{2E}{\isachardot}}empty\ {\isaliteral{3D}{\isacharequal}}\ Dlist\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -524,10 +524,10 @@
%
\isatagquote
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code\ abstract{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}list{\isacharunderscore}of{\isacharunderscore}dlist\ Dlist{\isachardot}empty\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}code\ abstract{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist\ Dlist{\isaliteral{2E}{\isachardot}}empty\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}fact\ list{\isacharunderscore}of{\isacharunderscore}dlist{\isacharunderscore}empty{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}fact\ list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist{\isaliteral{5F}{\isacharunderscore}}empty{\isaliteral{29}{\isacharparenright}}%
\endisatagquote
{\isafoldquote}%
%
@@ -549,16 +549,16 @@
%
\isatagquote
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code\ abstract{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}list{\isacharunderscore}of{\isacharunderscore}dlist\ {\isacharparenleft}Dlist{\isachardot}insert\ x\ dxs{\isacharparenright}\ {\isacharequal}\ List{\isachardot}insert\ x\ {\isacharparenleft}list{\isacharunderscore}of{\isacharunderscore}dlist\ dxs{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}code\ abstract{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist\ {\isaliteral{28}{\isacharparenleft}}Dlist{\isaliteral{2E}{\isachardot}}insert\ x\ dxs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ List{\isaliteral{2E}{\isachardot}}insert\ x\ {\isaliteral{28}{\isacharparenleft}}list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist\ dxs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}fact\ list{\isacharunderscore}of{\isacharunderscore}dlist{\isacharunderscore}insert{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}fact\ list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist{\isaliteral{5F}{\isacharunderscore}}insert{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code\ abstract{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}list{\isacharunderscore}of{\isacharunderscore}dlist\ {\isacharparenleft}Dlist{\isachardot}remove\ x\ dxs{\isacharparenright}\ {\isacharequal}\ remove{\isadigit{1}}\ x\ {\isacharparenleft}list{\isacharunderscore}of{\isacharunderscore}dlist\ dxs{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}code\ abstract{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist\ {\isaliteral{28}{\isacharparenleft}}Dlist{\isaliteral{2E}{\isachardot}}remove\ x\ dxs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ remove{\isadigit{1}}\ x\ {\isaliteral{28}{\isacharparenleft}}list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist\ dxs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}fact\ list{\isacharunderscore}of{\isacharunderscore}dlist{\isacharunderscore}remove{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}fact\ list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist{\isaliteral{5F}{\isacharunderscore}}remove{\isaliteral{29}{\isacharparenright}}%
\endisatagquote
{\isafoldquote}%
%
@@ -578,34 +578,34 @@
\isatagquotetypewriter
%
\begin{isamarkuptext}%
-module\ Example\ where\ {\isacharbraceleft}\isanewline
+module\ Example\ where\ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
\isanewline
-newtype\ Dlist\ a\ {\isacharequal}\ Dlist\ {\isacharbrackleft}a{\isacharbrackright}{\isacharsemicolon}\isanewline
+newtype\ Dlist\ a\ {\isaliteral{3D}{\isacharequal}}\ Dlist\ {\isaliteral{5B}{\isacharbrackleft}}a{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-empty\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ Dlist\ a{\isacharsemicolon}\isanewline
-empty\ {\isacharequal}\ Dlist\ {\isacharbrackleft}{\isacharbrackright}{\isacharsemicolon}\isanewline
+empty\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ Dlist\ a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+empty\ {\isaliteral{3D}{\isacharequal}}\ Dlist\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-member\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ {\isacharparenleft}Eq\ a{\isacharparenright}\ {\isacharequal}{\isachargreater}\ {\isacharbrackleft}a{\isacharbrackright}\ {\isacharminus}{\isachargreater}\ a\ {\isacharminus}{\isachargreater}\ Bool{\isacharsemicolon}\isanewline
-member\ {\isacharbrackleft}{\isacharbrackright}\ y\ {\isacharequal}\ False{\isacharsemicolon}\isanewline
-member\ {\isacharparenleft}x\ {\isacharcolon}\ xs{\isacharparenright}\ y\ {\isacharequal}\ x\ {\isacharequal}{\isacharequal}\ y\ {\isacharbar}{\isacharbar}\ member\ xs\ y{\isacharsemicolon}\isanewline
+member\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}Eq\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{5B}{\isacharbrackleft}}a{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Bool{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+member\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ y\ {\isaliteral{3D}{\isacharequal}}\ False{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+member\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3A}{\isacharcolon}}\ xs{\isaliteral{29}{\isacharparenright}}\ y\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}\ y\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ member\ xs\ y{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-insert\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ {\isacharparenleft}Eq\ a{\isacharparenright}\ {\isacharequal}{\isachargreater}\ a\ {\isacharminus}{\isachargreater}\ {\isacharbrackleft}a{\isacharbrackright}\ {\isacharminus}{\isachargreater}\ {\isacharbrackleft}a{\isacharbrackright}{\isacharsemicolon}\isanewline
-insert\ x\ xs\ {\isacharequal}\ {\isacharparenleft}if\ member\ xs\ x\ then\ xs\ else\ x\ {\isacharcolon}\ xs{\isacharparenright}{\isacharsemicolon}\isanewline
+insert\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}Eq\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{5B}{\isacharbrackleft}}a{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{5B}{\isacharbrackleft}}a{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+insert\ x\ xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ member\ xs\ x\ then\ xs\ else\ x\ {\isaliteral{3A}{\isacharcolon}}\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-list{\isacharunderscore}of{\isacharunderscore}dlist\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ Dlist\ a\ {\isacharminus}{\isachargreater}\ {\isacharbrackleft}a{\isacharbrackright}{\isacharsemicolon}\isanewline
-list{\isacharunderscore}of{\isacharunderscore}dlist\ {\isacharparenleft}Dlist\ x{\isacharparenright}\ {\isacharequal}\ x{\isacharsemicolon}\isanewline
+list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ Dlist\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{5B}{\isacharbrackleft}}a{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist\ {\isaliteral{28}{\isacharparenleft}}Dlist\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-inserta\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ {\isacharparenleft}Eq\ a{\isacharparenright}\ {\isacharequal}{\isachargreater}\ a\ {\isacharminus}{\isachargreater}\ Dlist\ a\ {\isacharminus}{\isachargreater}\ Dlist\ a{\isacharsemicolon}\isanewline
-inserta\ x\ dxs\ {\isacharequal}\ Dlist\ {\isacharparenleft}insert\ x\ {\isacharparenleft}list{\isacharunderscore}of{\isacharunderscore}dlist\ dxs{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline
+inserta\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}Eq\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Dlist\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Dlist\ a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+inserta\ x\ dxs\ {\isaliteral{3D}{\isacharequal}}\ Dlist\ {\isaliteral{28}{\isacharparenleft}}insert\ x\ {\isaliteral{28}{\isacharparenleft}}list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist\ dxs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-remove{\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ {\isacharparenleft}Eq\ a{\isacharparenright}\ {\isacharequal}{\isachargreater}\ a\ {\isacharminus}{\isachargreater}\ {\isacharbrackleft}a{\isacharbrackright}\ {\isacharminus}{\isachargreater}\ {\isacharbrackleft}a{\isacharbrackright}{\isacharsemicolon}\isanewline
-remove{\isadigit{1}}\ x\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isacharsemicolon}\isanewline
-remove{\isadigit{1}}\ x\ {\isacharparenleft}y\ {\isacharcolon}\ xs{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}if\ x\ {\isacharequal}{\isacharequal}\ y\ then\ xs\ else\ y\ {\isacharcolon}\ remove{\isadigit{1}}\ x\ xs{\isacharparenright}{\isacharsemicolon}\isanewline
+remove{\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}Eq\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{5B}{\isacharbrackleft}}a{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{5B}{\isacharbrackleft}}a{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+remove{\isadigit{1}}\ x\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+remove{\isadigit{1}}\ x\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{3A}{\isacharcolon}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ x\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}\ y\ then\ xs\ else\ y\ {\isaliteral{3A}{\isacharcolon}}\ remove{\isadigit{1}}\ x\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-remove\ {\isacharcolon}{\isacharcolon}\ forall\ a{\isachardot}\ {\isacharparenleft}Eq\ a{\isacharparenright}\ {\isacharequal}{\isachargreater}\ a\ {\isacharminus}{\isachargreater}\ Dlist\ a\ {\isacharminus}{\isachargreater}\ Dlist\ a{\isacharsemicolon}\isanewline
-remove\ x\ dxs\ {\isacharequal}\ Dlist\ {\isacharparenleft}remove{\isadigit{1}}\ x\ {\isacharparenleft}list{\isacharunderscore}of{\isacharunderscore}dlist\ dxs{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline
+remove\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ forall\ a{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}Eq\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Dlist\ a\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Dlist\ a{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+remove\ x\ dxs\ {\isaliteral{3D}{\isacharequal}}\ Dlist\ {\isaliteral{28}{\isacharparenleft}}remove{\isadigit{1}}\ x\ {\isaliteral{28}{\isacharparenleft}}list{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}dlist\ dxs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-{\isacharbraceright}\isanewline%
+{\isaliteral{7D}{\isacharbraceright}}\isanewline%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -618,8 +618,8 @@
%
\begin{isamarkuptext}%
Typical data structures implemented by representations involving
- invariants are available in the library, e.g.~theories \hyperlink{theory.Fset}{\mbox{\isa{Fset}}} and \hyperlink{theory.Mapping}{\mbox{\isa{Mapping}}} specify sets (type \isa{{\isacharprime}a\ fset}) and
- key-value-mappings (type \isa{{\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isacharprime}b{\isacharparenright}\ mapping}) respectively;
+ invariants are available in the library, e.g.~theories \hyperlink{theory.Fset}{\mbox{\isa{Fset}}} and \hyperlink{theory.Mapping}{\mbox{\isa{Mapping}}} specify sets (type \isa{{\isaliteral{27}{\isacharprime}}a\ fset}) and
+ key-value-mappings (type \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ mapping}) respectively;
these can be implemented by distinct lists as presented here as
example (theory \hyperlink{theory.Dlist}{\mbox{\isa{Dlist}}}) and red-black-trees respectively
(theory \hyperlink{theory.RBT}{\mbox{\isa{RBT}}}).%
--- a/doc-src/Functions/Thy/document/Functions.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/Functions/Thy/document/Functions.tex Mon Nov 08 14:41:11 2010 +0100
@@ -29,18 +29,18 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
-\ fib\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\isanewline
+\ fib\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}fib\ {\isadigit{0}}\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}fib\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}fib\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ fib\ n\ {\isacharplus}\ fib\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isachardoublequoteclose}%
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}fib\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}fib\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}fib\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ fib\ n\ {\isaliteral{2B}{\isacharplus}}\ fib\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
The syntax is rather self-explanatory: We introduce a function by
giving its name, its type,
and a set of defining recursive equations.
If we leave out the type, the most general type will be
- inferred, which can sometimes lead to surprises: Since both \isa{{\isadigit{1}}} and \isa{{\isacharplus}} are overloaded, we would end up
- with \isa{fib\ {\isacharcolon}{\isacharcolon}\ nat\ {\isasymRightarrow}\ {\isacharprime}a{\isacharcolon}{\isacharcolon}{\isacharbraceleft}one{\isacharcomma}plus{\isacharbraceright}}.%
+ inferred, which can sometimes lead to surprises: Since both \isa{{\isadigit{1}}} and \isa{{\isaliteral{2B}{\isacharplus}}} are overloaded, we would end up
+ with \isa{fib\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{7B}{\isacharbraceleft}}one{\isaliteral{2C}{\isacharcomma}}plus{\isaliteral{7D}{\isacharbraceright}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -49,8 +49,8 @@
every recursive call.
Since HOL is a logic of total functions, termination is a
fundamental requirement to prevent inconsistencies\footnote{From the
- \qt{definition} \isa{f{\isacharparenleft}n{\isacharparenright}\ {\isacharequal}\ f{\isacharparenleft}n{\isacharparenright}\ {\isacharplus}\ {\isadigit{1}}} we could prove
- \isa{{\isadigit{0}}\ {\isacharequal}\ {\isadigit{1}}} by subtracting \isa{f{\isacharparenleft}n{\isacharparenright}} on both sides.}.
+ \qt{definition} \isa{f{\isaliteral{28}{\isacharparenleft}}n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ f{\isaliteral{28}{\isacharparenleft}}n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}} we could prove
+ \isa{{\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}} by subtracting \isa{f{\isaliteral{28}{\isacharparenleft}}n{\isaliteral{29}{\isacharparenright}}} on both sides.}.
Isabelle tries to prove termination automatically when a definition
is made. In \S\ref{termination}, we will look at cases where this
fails and see what to do then.%
@@ -76,10 +76,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
-\ sep\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequoteclose}\isanewline
+\ sep\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}sep\ a\ {\isacharparenleft}x{\isacharhash}y{\isacharhash}xs{\isacharparenright}\ {\isacharequal}\ x\ {\isacharhash}\ a\ {\isacharhash}\ sep\ a\ {\isacharparenleft}y\ {\isacharhash}\ xs{\isacharparenright}{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}sep\ a\ xs\ \ \ \ \ \ \ {\isacharequal}\ xs{\isachardoublequoteclose}%
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}sep\ a\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{23}{\isacharhash}}y{\isaliteral{23}{\isacharhash}}xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{23}{\isacharhash}}\ a\ {\isaliteral{23}{\isacharhash}}\ sep\ a\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}sep\ a\ xs\ \ \ \ \ \ \ {\isaliteral{3D}{\isacharequal}}\ xs{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
Overlapping patterns are interpreted as \qt{increments} to what is
already there: The second equation is only meant for the cases where
@@ -88,12 +88,12 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{thm}\isamarkupfalse%
-\ sep{\isachardot}simps%
+\ sep{\isaliteral{2E}{\isachardot}}simps%
\begin{isamarkuptext}%
\begin{isabelle}%
-sep\ a\ {\isacharparenleft}x\ {\isacharhash}\ y\ {\isacharhash}\ xs{\isacharparenright}\ {\isacharequal}\ x\ {\isacharhash}\ a\ {\isacharhash}\ sep\ a\ {\isacharparenleft}y\ {\isacharhash}\ xs{\isacharparenright}\isasep\isanewline%
-sep\ a\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\isasep\isanewline%
-sep\ a\ {\isacharbrackleft}v{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}v{\isacharbrackright}%
+sep\ a\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ y\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{23}{\isacharhash}}\ a\ {\isaliteral{23}{\isacharhash}}\ sep\ a\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}\isasep\isanewline%
+sep\ a\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\isasep\isanewline%
+sep\ a\ {\isaliteral{5B}{\isacharbrackleft}}v{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}v{\isaliteral{5D}{\isacharbrackright}}%
\end{isabelle}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -104,7 +104,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}sep\ {\isadigit{0}}\ {\isacharbrackleft}{\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isacharcomma}\ {\isadigit{3}}{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}{\isadigit{1}}{\isacharcomma}\ {\isadigit{0}}{\isacharcomma}\ {\isadigit{2}}{\isacharcomma}\ {\isadigit{0}}{\isacharcomma}\ {\isadigit{3}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}sep\ {\isadigit{0}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{3}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{3}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -127,12 +127,12 @@
\begin{isamarkuptext}%
Isabelle provides customized induction rules for recursive
functions. These rules follow the recursive structure of the
- definition. Here is the rule \isa{sep{\isachardot}induct} arising from the
+ definition. Here is the rule \isa{sep{\isaliteral{2E}{\isachardot}}induct} arising from the
above definition of \isa{sep}:
\begin{isabelle}%
-{\isasymlbrakk}{\isasymAnd}a\ x\ y\ xs{\isachardot}\ {\isacharquery}P\ a\ {\isacharparenleft}y\ {\isacharhash}\ xs{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharquery}P\ a\ {\isacharparenleft}x\ {\isacharhash}\ y\ {\isacharhash}\ xs{\isacharparenright}{\isacharsemicolon}\ {\isasymAnd}a{\isachardot}\ {\isacharquery}P\ a\ {\isacharbrackleft}{\isacharbrackright}{\isacharsemicolon}\ {\isasymAnd}a\ v{\isachardot}\ {\isacharquery}P\ a\ {\isacharbrackleft}v{\isacharbrackright}{\isasymrbrakk}\isanewline
-{\isasymLongrightarrow}\ {\isacharquery}P\ {\isacharquery}a{\isadigit{0}}{\isachardot}{\isadigit{0}}\ {\isacharquery}a{\isadigit{1}}{\isachardot}{\isadigit{0}}%
+{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C416E643E}{\isasymAnd}}a\ x\ y\ xs{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}P\ a\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}P\ a\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ y\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}P\ a\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a\ v{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}P\ a\ {\isaliteral{5B}{\isacharbrackleft}}v{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{3F}{\isacharquery}}a{\isadigit{0}}{\isaliteral{2E}{\isachardot}}{\isadigit{0}}\ {\isaliteral{3F}{\isacharquery}}a{\isadigit{1}}{\isaliteral{2E}{\isachardot}}{\isadigit{0}}%
\end{isabelle}
We have a step case for list with at least two elements, and two
@@ -141,7 +141,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}map\ f\ {\isacharparenleft}sep\ x\ ys{\isacharparenright}\ {\isacharequal}\ sep\ {\isacharparenleft}f\ x{\isacharparenright}\ {\isacharparenleft}map\ f\ ys{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}map\ f\ {\isaliteral{28}{\isacharparenleft}}sep\ x\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ sep\ {\isaliteral{28}{\isacharparenleft}}f\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}map\ f\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -149,16 +149,16 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}induct\ x\ ys\ rule{\isacharcolon}\ sep{\isachardot}induct{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}induct\ x\ ys\ rule{\isaliteral{3A}{\isacharcolon}}\ sep{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
We get three cases, like in the definition.
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}a\ x\ y\ xs{\isachardot}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }map\ f\ {\isacharparenleft}sep\ a\ {\isacharparenleft}y\ {\isacharhash}\ xs{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ sep\ {\isacharparenleft}f\ a{\isacharparenright}\ {\isacharparenleft}map\ f\ {\isacharparenleft}y\ {\isacharhash}\ xs{\isacharparenright}{\isacharparenright}\ {\isasymLongrightarrow}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }map\ f\ {\isacharparenleft}sep\ a\ {\isacharparenleft}x\ {\isacharhash}\ y\ {\isacharhash}\ xs{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ sep\ {\isacharparenleft}f\ a{\isacharparenright}\ {\isacharparenleft}map\ f\ {\isacharparenleft}x\ {\isacharhash}\ y\ {\isacharhash}\ xs{\isacharparenright}{\isacharparenright}\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}a{\isachardot}\ map\ f\ {\isacharparenleft}sep\ a\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\ sep\ {\isacharparenleft}f\ a{\isacharparenright}\ {\isacharparenleft}map\ f\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\isanewline
-\ {\isadigit{3}}{\isachardot}\ {\isasymAnd}a\ v{\isachardot}\ map\ f\ {\isacharparenleft}sep\ a\ {\isacharbrackleft}v{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\ sep\ {\isacharparenleft}f\ a{\isacharparenright}\ {\isacharparenleft}map\ f\ {\isacharbrackleft}v{\isacharbrackright}{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a\ x\ y\ xs{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }map\ f\ {\isaliteral{28}{\isacharparenleft}}sep\ a\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ sep\ {\isaliteral{28}{\isacharparenleft}}f\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}map\ f\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }map\ f\ {\isaliteral{28}{\isacharparenleft}}sep\ a\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ y\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ sep\ {\isaliteral{28}{\isacharparenleft}}f\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}map\ f\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ y\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a{\isaliteral{2E}{\isachardot}}\ map\ f\ {\isaliteral{28}{\isacharparenleft}}sep\ a\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ sep\ {\isaliteral{28}{\isacharparenleft}}f\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}map\ f\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ {\isadigit{3}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a\ v{\isaliteral{2E}{\isachardot}}\ map\ f\ {\isaliteral{28}{\isacharparenleft}}sep\ a\ {\isaliteral{5B}{\isacharbrackleft}}v{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ sep\ {\isaliteral{28}{\isacharparenleft}}f\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}map\ f\ {\isaliteral{5B}{\isacharbrackleft}}v{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
@@ -200,19 +200,19 @@
\[\left[\;\begin{minipage}{0.25\textwidth}\vspace{6pt}
-\cmd{fun} \isa{f\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}}\\%
+\cmd{fun} \isa{f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}}\\%
\cmd{where}\\%
\hspace*{2ex}{\it equations}\\%
\hspace*{2ex}\vdots\vspace*{6pt}
\end{minipage}\right]
\quad\equiv\quad
\left[\;\begin{minipage}{0.48\textwidth}\vspace{6pt}
-\cmd{function} \isa{{\isacharparenleft}}\cmd{sequential}\isa{{\isacharparenright}\ f\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}}\\%
+\cmd{function} \isa{{\isaliteral{28}{\isacharparenleft}}}\cmd{sequential}\isa{{\isaliteral{29}{\isacharparenright}}\ f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}}\\%
\cmd{where}\\%
\hspace*{2ex}{\it equations}\\%
\hspace*{2ex}\vdots\\%
-\cmd{by} \isa{pat{\isacharunderscore}completeness\ auto}\\%
-\cmd{termination by} \isa{lexicographic{\isacharunderscore}order}\vspace{6pt}
+\cmd{by} \isa{pat{\isaliteral{5F}{\isacharunderscore}}completeness\ auto}\\%
+\cmd{termination by} \isa{lexicographic{\isaliteral{5F}{\isacharunderscore}}order}\vspace{6pt}
\end{minipage}
\right]\]
@@ -228,7 +228,7 @@
\item A function definition produces a proof obligation which
expresses completeness and compatibility of patterns (we talk about
- this later). The combination of the methods \isa{pat{\isacharunderscore}completeness} and
+ this later). The combination of the methods \isa{pat{\isaliteral{5F}{\isacharunderscore}}completeness} and
\isa{auto} is used to solve this proof obligation.
\item A termination proof follows the definition, started by the
@@ -246,7 +246,7 @@
%
\begin{isamarkuptext}%
\label{termination}
- The method \isa{lexicographic{\isacharunderscore}order} is the default method for
+ The method \isa{lexicographic{\isaliteral{5F}{\isacharunderscore}}order} is the default method for
termination proofs. It can prove termination of a
certain class of functions by searching for a suitable lexicographic
combination of size measures. Of course, not all functions have such
@@ -265,9 +265,9 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{function}\isamarkupfalse%
-\ sum\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\isanewline
+\ sum\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}sum\ i\ N\ {\isacharequal}\ {\isacharparenleft}if\ i\ {\isachargreater}\ N\ then\ {\isadigit{0}}\ else\ i\ {\isacharplus}\ sum\ {\isacharparenleft}Suc\ i{\isacharparenright}\ N{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}sum\ i\ N\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ i\ {\isaliteral{3E}{\isachargreater}}\ N\ then\ {\isadigit{0}}\ else\ i\ {\isaliteral{2B}{\isacharplus}}\ sum\ {\isaliteral{28}{\isacharparenleft}}Suc\ i{\isaliteral{29}{\isacharparenright}}\ N{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -275,7 +275,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ pat{\isacharunderscore}completeness\ auto%
+\ pat{\isaliteral{5F}{\isacharunderscore}}completeness\ auto%
\endisatagproof
{\isafoldproof}%
%
@@ -284,7 +284,7 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-\noindent The \isa{lexicographic{\isacharunderscore}order} method fails on this example, because none of the
+\noindent The \isa{lexicographic{\isaliteral{5F}{\isacharunderscore}}order} method fails on this example, because none of the
arguments decreases in the recursive call, with respect to the standard size ordering.
To prove termination manually, we must provide a custom wellfounded relation.
@@ -292,7 +292,7 @@
the \emph{difference} between \isa{i} and \isa{N} gets
smaller in every step, and that the recursion stops when \isa{i}
is greater than \isa{N}. Phrased differently, the expression
- \isa{N\ {\isacharplus}\ {\isadigit{1}}\ {\isacharminus}\ i} always decreases.
+ \isa{N\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}\ {\isaliteral{2D}{\isacharminus}}\ i} always decreases.
We can use this expression as a measure function suitable to prove termination.%
\end{isamarkuptext}%
@@ -306,19 +306,19 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}relation\ {\isachardoublequoteopen}measure\ {\isacharparenleft}{\isasymlambda}{\isacharparenleft}i{\isacharcomma}N{\isacharparenright}{\isachardot}\ N\ {\isacharplus}\ {\isadigit{1}}\ {\isacharminus}\ i{\isacharparenright}{\isachardoublequoteclose}{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}relation\ {\isaliteral{22}{\isachardoublequoteopen}}measure\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{28}{\isacharparenleft}}i{\isaliteral{2C}{\isacharcomma}}N{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ N\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}\ {\isaliteral{2D}{\isacharminus}}\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
The \cmd{termination} command sets up the termination goal for the
specified function \isa{sum}. If the function name is omitted, it
implicitly refers to the last function definition.
The \isa{relation} method takes a relation of
- type \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set}, where \isa{{\isacharprime}a} is the argument type of
+ type \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set}, where \isa{{\isaliteral{27}{\isacharprime}}a} is the argument type of
the function. If the function has multiple curried arguments, then
these are packed together into a tuple, as it happened in the above
example.
- The predefined function \isa{{\isachardoublequote}measure\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ nat{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set{\isachardoublequote}} constructs a
+ The predefined function \isa{{\isaliteral{22}{\isachardoublequote}}measure\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set{\isaliteral{22}{\isachardoublequote}}} constructs a
wellfounded relation from a mapping into the natural numbers (a
\emph{measure function}).
@@ -328,8 +328,8 @@
relation:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ wf\ {\isacharparenleft}measure\ {\isacharparenleft}{\isasymlambda}{\isacharparenleft}i{\isacharcomma}\ N{\isacharparenright}{\isachardot}\ N\ {\isacharplus}\ {\isadigit{1}}\ {\isacharminus}\ i{\isacharparenright}{\isacharparenright}\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}i\ N{\isachardot}\ {\isasymnot}\ N\ {\isacharless}\ i\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isacharparenleft}Suc\ i{\isacharcomma}\ N{\isacharparenright}{\isacharcomma}\ i{\isacharcomma}\ N{\isacharparenright}\ {\isasymin}\ measure\ {\isacharparenleft}{\isasymlambda}{\isacharparenleft}i{\isacharcomma}\ N{\isacharparenright}{\isachardot}\ N\ {\isacharplus}\ {\isadigit{1}}\ {\isacharminus}\ i{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ wf\ {\isaliteral{28}{\isacharparenleft}}measure\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{28}{\isacharparenleft}}i{\isaliteral{2C}{\isacharcomma}}\ N{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ N\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}\ {\isaliteral{2D}{\isacharminus}}\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}i\ N{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ N\ {\isaliteral{3C}{\isacharless}}\ i\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}Suc\ i{\isaliteral{2C}{\isacharcomma}}\ N{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ i{\isaliteral{2C}{\isacharcomma}}\ N{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ measure\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{28}{\isacharparenleft}}i{\isaliteral{2C}{\isacharcomma}}\ N{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ N\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}\ {\isaliteral{2D}{\isacharminus}}\ i{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
These goals are all solved by \isa{auto}:%
@@ -352,11 +352,11 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{function}\isamarkupfalse%
-\ foo\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\isanewline
+\ foo\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}foo\ i\ N\ {\isacharequal}\ {\isacharparenleft}if\ i\ {\isachargreater}\ N\ \isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ then\ {\isacharparenleft}if\ N\ {\isacharequal}\ {\isadigit{0}}\ then\ {\isadigit{0}}\ else\ foo\ {\isadigit{0}}\ {\isacharparenleft}N\ {\isacharminus}\ {\isadigit{1}}{\isacharparenright}{\isacharparenright}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ else\ i\ {\isacharplus}\ foo\ {\isacharparenleft}Suc\ i{\isacharparenright}\ N{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}foo\ i\ N\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ i\ {\isaliteral{3E}{\isachargreater}}\ N\ \isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ then\ {\isaliteral{28}{\isacharparenleft}}if\ N\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\ then\ {\isadigit{0}}\ else\ foo\ {\isadigit{0}}\ {\isaliteral{28}{\isacharparenleft}}N\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ else\ i\ {\isaliteral{2B}{\isacharplus}}\ foo\ {\isaliteral{28}{\isacharparenleft}}Suc\ i{\isaliteral{29}{\isacharparenright}}\ N{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -364,7 +364,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ pat{\isacharunderscore}completeness\ auto%
+\ pat{\isaliteral{5F}{\isacharunderscore}}completeness\ auto%
\endisatagproof
{\isafoldproof}%
%
@@ -391,7 +391,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}relation\ {\isachardoublequoteopen}measures\ {\isacharbrackleft}{\isasymlambda}{\isacharparenleft}i{\isacharcomma}\ N{\isacharparenright}{\isachardot}\ N{\isacharcomma}\ {\isasymlambda}{\isacharparenleft}i{\isacharcomma}N{\isacharparenright}{\isachardot}\ N\ {\isacharplus}\ {\isadigit{1}}\ {\isacharminus}\ i{\isacharbrackright}{\isachardoublequoteclose}{\isacharparenright}\ auto%
+\ {\isaliteral{28}{\isacharparenleft}}relation\ {\isaliteral{22}{\isachardoublequoteopen}}measures\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{28}{\isacharparenleft}}i{\isaliteral{2C}{\isacharcomma}}\ N{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ N{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{28}{\isacharparenleft}}i{\isaliteral{2C}{\isacharcomma}}N{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ N\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}\ {\isaliteral{2D}{\isacharminus}}\ i{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\ auto%
\endisatagproof
{\isafoldproof}%
%
@@ -399,7 +399,7 @@
%
\endisadelimproof
%
-\isamarkupsubsection{How \isa{lexicographic{\isacharunderscore}order} works%
+\isamarkupsubsection{How \isa{lexicographic{\isaliteral{5F}{\isacharunderscore}}order} works%
}
\isamarkuptrue%
%
@@ -409,10 +409,10 @@
termination prover, see \cite{bulwahnKN07}}:
\end{isamarkuptext}
-\cmd{fun} \isa{fails\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}nat\ {\isasymRightarrow}\ nat\ list\ {\isasymRightarrow}\ nat{\isachardoublequote}}\\%
+\cmd{fun} \isa{fails\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequote}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequote}}}\\%
\cmd{where}\\%
-\hspace*{2ex}\isa{{\isachardoublequote}fails\ a\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ a{\isachardoublequote}}\\%
-|\hspace*{1.5ex}\isa{{\isachardoublequote}fails\ a\ {\isacharparenleft}x{\isacharhash}xs{\isacharparenright}\ {\isacharequal}\ fails\ {\isacharparenleft}x\ {\isacharplus}\ a{\isacharparenright}\ {\isacharparenleft}x{\isacharhash}xs{\isacharparenright}{\isachardoublequote}}\\
+\hspace*{2ex}\isa{{\isaliteral{22}{\isachardoublequote}}fails\ a\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{22}{\isachardoublequote}}}\\%
+|\hspace*{1.5ex}\isa{{\isaliteral{22}{\isachardoublequote}}fails\ a\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{23}{\isacharhash}}xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ fails\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{2B}{\isacharplus}}\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{23}{\isacharhash}}xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}\\
\begin{isamarkuptext}
\noindent Isabelle responds with the following error:
@@ -420,16 +420,16 @@
\begin{isabelle}
*** Unfinished subgoals:\newline
*** (a, 1, <):\newline
-*** \ 1.~\isa{{\isasymAnd}x{\isachardot}\ x\ {\isacharequal}\ {\isadigit{0}}}\newline
+*** \ 1.~\isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}}\newline
*** (a, 1, <=):\newline
*** \ 1.~False\newline
*** (a, 2, <):\newline
*** \ 1.~False\newline
*** Calls:\newline
-*** a) \isa{{\isacharparenleft}a{\isacharcomma}\ x\ {\isacharhash}\ xs{\isacharparenright}\ {\isacharminus}{\isacharminus}{\isachargreater}{\isachargreater}\ {\isacharparenleft}x\ {\isacharplus}\ a{\isacharcomma}\ x\ {\isacharhash}\ xs{\isacharparenright}}\newline
+*** a) \isa{{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ x\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{2B}{\isacharplus}}\ a{\isaliteral{2C}{\isacharcomma}}\ x\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}}\newline
*** Measures:\newline
-*** 1) \isa{{\isasymlambda}x{\isachardot}\ size\ {\isacharparenleft}fst\ x{\isacharparenright}}\newline
-*** 2) \isa{{\isasymlambda}x{\isachardot}\ size\ {\isacharparenleft}snd\ x{\isacharparenright}}\newline
+*** 1) \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ size\ {\isaliteral{28}{\isacharparenleft}}fst\ x{\isaliteral{29}{\isacharparenright}}}\newline
+*** 2) \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ size\ {\isaliteral{28}{\isacharparenleft}}snd\ x{\isaliteral{29}{\isacharparenright}}}\newline
*** Result matrix:\newline
*** \ \ \ \ 1\ \ 2 \newline
*** a: ? <= \newline
@@ -447,29 +447,29 @@
argument tuple to a natural number).
The contents of the matrix summarize what is known about argument
- descents: The second argument has a weak descent (\isa{{\isacharless}{\isacharequal}}) at the
+ descents: The second argument has a weak descent (\isa{{\isaliteral{3C}{\isacharless}}{\isaliteral{3D}{\isacharequal}}}) at the
recursive call, and for the first argument nothing could be proved,
- which is expressed by \isa{{\isacharquery}}. In general, there are the values
- \isa{{\isacharless}}, \isa{{\isacharless}{\isacharequal}} and \isa{{\isacharquery}}.
+ which is expressed by \isa{{\isaliteral{3F}{\isacharquery}}}. In general, there are the values
+ \isa{{\isaliteral{3C}{\isacharless}}}, \isa{{\isaliteral{3C}{\isacharless}}{\isaliteral{3D}{\isacharequal}}} and \isa{{\isaliteral{3F}{\isacharquery}}}.
For the failed proof attempts, the unfinished subgoals are also
printed. Looking at these will often point to a missing lemma.%
\end{isamarkuptext}%
\isamarkuptrue%
%
-\isamarkupsubsection{The \isa{size{\isacharunderscore}change} method%
+\isamarkupsubsection{The \isa{size{\isaliteral{5F}{\isacharunderscore}}change} method%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
Some termination goals that are beyond the powers of
- \isa{lexicographic{\isacharunderscore}order} can be solved automatically by the
- more powerful \isa{size{\isacharunderscore}change} method, which uses a variant of
+ \isa{lexicographic{\isaliteral{5F}{\isacharunderscore}}order} can be solved automatically by the
+ more powerful \isa{size{\isaliteral{5F}{\isacharunderscore}}change} method, which uses a variant of
the size-change principle, together with some other
techniques. While the details are discussed
elsewhere\cite{krauss_phd},
here are a few typical situations where
- \isa{lexicographic{\isacharunderscore}order} has difficulties and \isa{size{\isacharunderscore}change}
+ \isa{lexicographic{\isaliteral{5F}{\isacharunderscore}}order} has difficulties and \isa{size{\isaliteral{5F}{\isacharunderscore}}change}
may be worth a try:
\begin{itemize}
\item Arguments are permuted in a recursive call.
@@ -478,7 +478,7 @@
occur in sequence).
\end{itemize}
- Loading the theory \isa{Multiset} makes the \isa{size{\isacharunderscore}change}
+ Loading the theory \isa{Multiset} makes the \isa{size{\isaliteral{5F}{\isacharunderscore}}change}
method a bit stronger: it can then use multiset orders internally.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -493,13 +493,13 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{function}\isamarkupfalse%
-\ even\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
-\ \ \ \ \isakeyword{and}\ odd\ \ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
+\ even\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \isakeyword{and}\ odd\ \ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}even\ {\isadigit{0}}\ {\isacharequal}\ True{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}odd\ {\isadigit{0}}\ {\isacharequal}\ False{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}even\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ odd\ n{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}odd\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ even\ n{\isachardoublequoteclose}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}even\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ True{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}odd\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ False{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}even\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ odd\ n{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}odd\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ even\ n{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -507,7 +507,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ pat{\isacharunderscore}completeness\ auto%
+\ pat{\isaliteral{5F}{\isacharunderscore}}completeness\ auto%
\endisatagproof
{\isafoldproof}%
%
@@ -518,7 +518,7 @@
\begin{isamarkuptext}%
To eliminate the mutual dependencies, Isabelle internally
creates a single function operating on the sum
- type \isa{nat\ {\isacharplus}\ nat}. Then, \isa{even} and \isa{odd} are
+ type \isa{nat\ {\isaliteral{2B}{\isacharplus}}\ nat}. Then, \isa{even} and \isa{odd} are
defined as projections. Consequently, termination has to be proved
simultaneously for both functions, by specifying a measure on the
sum type:%
@@ -533,7 +533,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}relation\ {\isachardoublequoteopen}measure\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ case\ x\ of\ Inl\ n\ {\isasymRightarrow}\ n\ {\isacharbar}\ Inr\ n\ {\isasymRightarrow}\ n{\isacharparenright}{\isachardoublequoteclose}{\isacharparenright}\ auto%
+\ {\isaliteral{28}{\isacharparenleft}}relation\ {\isaliteral{22}{\isachardoublequoteopen}}measure\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ case\ x\ of\ Inl\ n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ n\ {\isaliteral{7C}{\isacharbar}}\ Inr\ n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\ auto%
\endisatagproof
{\isafoldproof}%
%
@@ -542,7 +542,7 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-We could also have used \isa{lexicographic{\isacharunderscore}order}, which
+We could also have used \isa{lexicographic{\isaliteral{5F}{\isacharunderscore}}order}, which
supports mutual recursive termination proofs to a certain extent.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -553,16 +553,16 @@
%
\begin{isamarkuptext}%
When functions are mutually recursive, proving properties about them
- generally requires simultaneous induction. The induction rule \isa{even{\isacharunderscore}odd{\isachardot}induct}
+ generally requires simultaneous induction. The induction rule \isa{even{\isaliteral{5F}{\isacharunderscore}}odd{\isaliteral{2E}{\isachardot}}induct}
generated from the above definition reflects this.
Let us prove something about \isa{even} and \isa{odd}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ even{\isacharunderscore}odd{\isacharunderscore}mod{\isadigit{2}}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}even\ n\ {\isacharequal}\ {\isacharparenleft}n\ mod\ {\isadigit{2}}\ {\isacharequal}\ {\isadigit{0}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}odd\ n\ {\isacharequal}\ {\isacharparenleft}n\ mod\ {\isadigit{2}}\ {\isacharequal}\ {\isadigit{1}}{\isacharparenright}{\isachardoublequoteclose}%
+\ even{\isaliteral{5F}{\isacharunderscore}}odd{\isaliteral{5F}{\isacharunderscore}}mod{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}even\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}n\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}odd\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}n\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -575,26 +575,26 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}induct\ n\ \isakeyword{and}\ n\ rule{\isacharcolon}\ even{\isacharunderscore}odd{\isachardot}induct{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}induct\ n\ \isakeyword{and}\ n\ rule{\isaliteral{3A}{\isacharcolon}}\ even{\isaliteral{5F}{\isacharunderscore}}odd{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
We get four subgoals, which correspond to the clauses in the
definition of \isa{even} and \isa{odd}:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ even\ {\isadigit{0}}\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}\ mod\ {\isadigit{2}}\ {\isacharequal}\ {\isadigit{0}}{\isacharparenright}\isanewline
-\ {\isadigit{2}}{\isachardot}\ odd\ {\isadigit{0}}\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}\ mod\ {\isadigit{2}}\ {\isacharequal}\ {\isadigit{1}}{\isacharparenright}\isanewline
-\ {\isadigit{3}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ odd\ n\ {\isacharequal}\ {\isacharparenleft}n\ mod\ {\isadigit{2}}\ {\isacharequal}\ {\isadigit{1}}{\isacharparenright}\ {\isasymLongrightarrow}\ even\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}Suc\ n\ mod\ {\isadigit{2}}\ {\isacharequal}\ {\isadigit{0}}{\isacharparenright}\isanewline
-\ {\isadigit{4}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ even\ n\ {\isacharequal}\ {\isacharparenleft}n\ mod\ {\isadigit{2}}\ {\isacharequal}\ {\isadigit{0}}{\isacharparenright}\ {\isasymLongrightarrow}\ odd\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}Suc\ n\ mod\ {\isadigit{2}}\ {\isacharequal}\ {\isadigit{1}}{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ even\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ odd\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ {\isadigit{3}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ odd\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}n\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ even\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ n\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ {\isadigit{4}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ even\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}n\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ odd\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ n\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
Simplification solves the first two goals, leaving us with two
statements about the \isa{mod} operation to prove:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-\ simp{\isacharunderscore}all%
+\ simp{\isaliteral{5F}{\isacharunderscore}}all%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ odd\ n\ {\isacharequal}\ {\isacharparenleft}n\ mod\ {\isadigit{2}}\ {\isacharequal}\ Suc\ {\isadigit{0}}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}n\ mod\ {\isadigit{2}}\ {\isacharequal}\ Suc\ {\isadigit{0}}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}Suc\ n\ mod\ {\isadigit{2}}\ {\isacharequal}\ {\isadigit{0}}{\isacharparenright}\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ even\ n\ {\isacharequal}\ {\isacharparenleft}n\ mod\ {\isadigit{2}}\ {\isacharequal}\ {\isadigit{0}}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}n\ mod\ {\isadigit{2}}\ {\isacharequal}\ {\isadigit{0}}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}Suc\ n\ mod\ {\isadigit{2}}\ {\isacharequal}\ Suc\ {\isadigit{0}}{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ odd\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}n\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ Suc\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}n\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ Suc\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ n\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ even\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}n\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}n\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ n\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ Suc\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\noindent These can be handled by Isabelle's arithmetic decision procedures.%
@@ -622,9 +622,9 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ failed{\isacharunderscore}attempt{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}even\ n\ {\isacharequal}\ {\isacharparenleft}n\ mod\ {\isadigit{2}}\ {\isacharequal}\ {\isadigit{0}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}True{\isachardoublequoteclose}\isanewline
+\ failed{\isaliteral{5F}{\isacharunderscore}}attempt{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}even\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}n\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}True{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -632,16 +632,16 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}induct\ n\ rule{\isacharcolon}\ even{\isacharunderscore}odd{\isachardot}induct{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}induct\ n\ rule{\isaliteral{3A}{\isacharcolon}}\ even{\isaliteral{5F}{\isacharunderscore}}odd{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent Now the third subgoal is a dead end, since we have no
useful induction hypothesis available:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ even\ {\isadigit{0}}\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}\ mod\ {\isadigit{2}}\ {\isacharequal}\ {\isadigit{0}}{\isacharparenright}\isanewline
-\ {\isadigit{2}}{\isachardot}\ True\isanewline
-\ {\isadigit{3}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ True\ {\isasymLongrightarrow}\ even\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}Suc\ n\ mod\ {\isadigit{2}}\ {\isacharequal}\ {\isadigit{0}}{\isacharparenright}\isanewline
-\ {\isadigit{4}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ even\ n\ {\isacharequal}\ {\isacharparenleft}n\ mod\ {\isadigit{2}}\ {\isacharequal}\ {\isadigit{0}}{\isacharparenright}\ {\isasymLongrightarrow}\ True%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ even\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ True\isanewline
+\ {\isadigit{3}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ True\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ even\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ n\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ {\isadigit{4}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ even\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}n\ mod\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ True%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
@@ -683,19 +683,19 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ P{\isadigit{3}}\ {\isacharequal}\ T\ {\isacharbar}\ F\ {\isacharbar}\ X%
+\ P{\isadigit{3}}\ {\isaliteral{3D}{\isacharequal}}\ T\ {\isaliteral{7C}{\isacharbar}}\ F\ {\isaliteral{7C}{\isacharbar}}\ X%
\begin{isamarkuptext}%
\noindent Then the conjunction of such values can be defined as follows:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
-\ And\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}P{\isadigit{3}}\ {\isasymRightarrow}\ P{\isadigit{3}}\ {\isasymRightarrow}\ P{\isadigit{3}}{\isachardoublequoteclose}\isanewline
+\ And\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}P{\isadigit{3}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ P{\isadigit{3}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ P{\isadigit{3}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}And\ T\ p\ {\isacharequal}\ p{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}And\ p\ T\ {\isacharequal}\ p{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}And\ p\ F\ {\isacharequal}\ F{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}And\ F\ p\ {\isacharequal}\ F{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}And\ X\ X\ {\isacharequal}\ X{\isachardoublequoteclose}%
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}And\ T\ p\ {\isaliteral{3D}{\isacharequal}}\ p{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}And\ p\ T\ {\isaliteral{3D}{\isacharequal}}\ p{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}And\ p\ F\ {\isaliteral{3D}{\isacharequal}}\ F{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}And\ F\ p\ {\isaliteral{3D}{\isacharequal}}\ F{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}And\ X\ X\ {\isaliteral{3D}{\isacharequal}}\ X{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
This definition is useful, because the equations can directly be used
as simplification rules. But the patterns overlap: For example,
@@ -705,15 +705,15 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{thm}\isamarkupfalse%
-\ And{\isachardot}simps%
+\ And{\isaliteral{2E}{\isachardot}}simps%
\begin{isamarkuptext}%
-\isa{And\ T\ {\isacharquery}p\ {\isacharequal}\ {\isacharquery}p\isasep\isanewline%
-And\ F\ T\ {\isacharequal}\ F\isasep\isanewline%
-And\ X\ T\ {\isacharequal}\ X\isasep\isanewline%
-And\ F\ F\ {\isacharequal}\ F\isasep\isanewline%
-And\ X\ F\ {\isacharequal}\ F\isasep\isanewline%
-And\ F\ X\ {\isacharequal}\ F\isasep\isanewline%
-And\ X\ X\ {\isacharequal}\ X}
+\isa{And\ T\ {\isaliteral{3F}{\isacharquery}}p\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}p\isasep\isanewline%
+And\ F\ T\ {\isaliteral{3D}{\isacharequal}}\ F\isasep\isanewline%
+And\ X\ T\ {\isaliteral{3D}{\isacharequal}}\ X\isasep\isanewline%
+And\ F\ F\ {\isaliteral{3D}{\isacharequal}}\ F\isasep\isanewline%
+And\ X\ F\ {\isaliteral{3D}{\isacharequal}}\ F\isasep\isanewline%
+And\ F\ X\ {\isaliteral{3D}{\isacharequal}}\ F\isasep\isanewline%
+And\ X\ X\ {\isaliteral{3D}{\isacharequal}}\ X}
\vspace*{1em}
\noindent There are several problems with this:
@@ -729,7 +729,7 @@
can be simplified to \isa{F} with the original equations, a
(manual) case split on \isa{x} is now necessary.
- \item The splitting also concerns the induction rule \isa{And{\isachardot}induct}. Instead of five premises it now has seven, which
+ \item The splitting also concerns the induction rule \isa{And{\isaliteral{2E}{\isachardot}}induct}. Instead of five premises it now has seven, which
means that our induction proofs will have more cases.
\item In general, it increases clarity if we get the same definition
@@ -739,17 +739,17 @@
If we do not want the automatic splitting, we can switch it off by
leaving out the \cmd{sequential} option. However, we will have to
prove that our pattern matching is consistent\footnote{This prevents
- us from defining something like \isa{f\ x\ {\isacharequal}\ True} and \isa{f\ x\ {\isacharequal}\ False} simultaneously.}:%
+ us from defining something like \isa{f\ x\ {\isaliteral{3D}{\isacharequal}}\ True} and \isa{f\ x\ {\isaliteral{3D}{\isacharequal}}\ False} simultaneously.}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{function}\isamarkupfalse%
-\ And{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}P{\isadigit{3}}\ {\isasymRightarrow}\ P{\isadigit{3}}\ {\isasymRightarrow}\ P{\isadigit{3}}{\isachardoublequoteclose}\isanewline
+\ And{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}P{\isadigit{3}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ P{\isadigit{3}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ P{\isadigit{3}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}And{\isadigit{2}}\ T\ p\ {\isacharequal}\ p{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}And{\isadigit{2}}\ p\ T\ {\isacharequal}\ p{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}And{\isadigit{2}}\ p\ F\ {\isacharequal}\ F{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}And{\isadigit{2}}\ F\ p\ {\isacharequal}\ F{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}And{\isadigit{2}}\ X\ X\ {\isacharequal}\ X{\isachardoublequoteclose}%
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}And{\isadigit{2}}\ T\ p\ {\isaliteral{3D}{\isacharequal}}\ p{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}And{\isadigit{2}}\ p\ T\ {\isaliteral{3D}{\isacharequal}}\ p{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}And{\isadigit{2}}\ p\ F\ {\isaliteral{3D}{\isacharequal}}\ F{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}And{\isadigit{2}}\ F\ p\ {\isaliteral{3D}{\isacharequal}}\ F{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}And{\isadigit{2}}\ X\ X\ {\isaliteral{3D}{\isacharequal}}\ X{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -761,31 +761,31 @@
function definition. In this case, they are:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}P\ x{\isachardot}\ {\isasymlbrakk}{\isasymAnd}p{\isachardot}\ x\ {\isacharequal}\ {\isacharparenleft}T{\isacharcomma}\ p{\isacharparenright}\ {\isasymLongrightarrow}\ P{\isacharsemicolon}\ {\isasymAnd}p{\isachardot}\ x\ {\isacharequal}\ {\isacharparenleft}p{\isacharcomma}\ T{\isacharparenright}\ {\isasymLongrightarrow}\ P{\isacharsemicolon}\ {\isasymAnd}p{\isachardot}\ x\ {\isacharequal}\ {\isacharparenleft}p{\isacharcomma}\ F{\isacharparenright}\ {\isasymLongrightarrow}\ P{\isacharsemicolon}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}P\ x{\isachardot}\ \ }{\isasymAnd}p{\isachardot}\ x\ {\isacharequal}\ {\isacharparenleft}F{\isacharcomma}\ p{\isacharparenright}\ {\isasymLongrightarrow}\ P{\isacharsemicolon}\ x\ {\isacharequal}\ {\isacharparenleft}X{\isacharcomma}\ X{\isacharparenright}\ {\isasymLongrightarrow}\ P{\isasymrbrakk}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}P\ x{\isachardot}\ }{\isasymLongrightarrow}\ P\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}p\ pa{\isachardot}\ {\isacharparenleft}T{\isacharcomma}\ p{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}T{\isacharcomma}\ pa{\isacharparenright}\ {\isasymLongrightarrow}\ p\ {\isacharequal}\ pa\isanewline
-\ {\isadigit{3}}{\isachardot}\ {\isasymAnd}p\ pa{\isachardot}\ {\isacharparenleft}T{\isacharcomma}\ p{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}pa{\isacharcomma}\ T{\isacharparenright}\ {\isasymLongrightarrow}\ p\ {\isacharequal}\ pa\isanewline
-\ {\isadigit{4}}{\isachardot}\ {\isasymAnd}p\ pa{\isachardot}\ {\isacharparenleft}T{\isacharcomma}\ p{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}pa{\isacharcomma}\ F{\isacharparenright}\ {\isasymLongrightarrow}\ p\ {\isacharequal}\ F\isanewline
-\ {\isadigit{5}}{\isachardot}\ {\isasymAnd}p\ pa{\isachardot}\ {\isacharparenleft}T{\isacharcomma}\ p{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}F{\isacharcomma}\ pa{\isacharparenright}\ {\isasymLongrightarrow}\ p\ {\isacharequal}\ F\isanewline
-\ {\isadigit{6}}{\isachardot}\ {\isasymAnd}p{\isachardot}\ {\isacharparenleft}T{\isacharcomma}\ p{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}X{\isacharcomma}\ X{\isacharparenright}\ {\isasymLongrightarrow}\ p\ {\isacharequal}\ X\isanewline
-\ {\isadigit{7}}{\isachardot}\ {\isasymAnd}p\ pa{\isachardot}\ {\isacharparenleft}p{\isacharcomma}\ T{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}pa{\isacharcomma}\ T{\isacharparenright}\ {\isasymLongrightarrow}\ p\ {\isacharequal}\ pa\isanewline
-\ {\isadigit{8}}{\isachardot}\ {\isasymAnd}p\ pa{\isachardot}\ {\isacharparenleft}p{\isacharcomma}\ T{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}pa{\isacharcomma}\ F{\isacharparenright}\ {\isasymLongrightarrow}\ p\ {\isacharequal}\ F\isanewline
-\ {\isadigit{9}}{\isachardot}\ {\isasymAnd}p\ pa{\isachardot}\ {\isacharparenleft}p{\isacharcomma}\ T{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}F{\isacharcomma}\ pa{\isacharparenright}\ {\isasymLongrightarrow}\ p\ {\isacharequal}\ F\isanewline
-\ {\isadigit{1}}{\isadigit{0}}{\isachardot}\ {\isasymAnd}p{\isachardot}\ {\isacharparenleft}p{\isacharcomma}\ T{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}X{\isacharcomma}\ X{\isacharparenright}\ {\isasymLongrightarrow}\ p\ {\isacharequal}\ X%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}P\ x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C416E643E}{\isasymAnd}}p{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}T{\isaliteral{2C}{\isacharcomma}}\ p{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}p{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}\ T{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}p{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}\ F{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}P\ x{\isaliteral{2E}{\isachardot}}\ \ }{\isaliteral{5C3C416E643E}{\isasymAnd}}p{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}F{\isaliteral{2C}{\isacharcomma}}\ p{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{3B}{\isacharsemicolon}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}X{\isaliteral{2C}{\isacharcomma}}\ X{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}P\ x{\isaliteral{2E}{\isachardot}}\ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}p\ pa{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}T{\isaliteral{2C}{\isacharcomma}}\ p{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}T{\isaliteral{2C}{\isacharcomma}}\ pa{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ p\ {\isaliteral{3D}{\isacharequal}}\ pa\isanewline
+\ {\isadigit{3}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}p\ pa{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}T{\isaliteral{2C}{\isacharcomma}}\ p{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}pa{\isaliteral{2C}{\isacharcomma}}\ T{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ p\ {\isaliteral{3D}{\isacharequal}}\ pa\isanewline
+\ {\isadigit{4}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}p\ pa{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}T{\isaliteral{2C}{\isacharcomma}}\ p{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}pa{\isaliteral{2C}{\isacharcomma}}\ F{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ p\ {\isaliteral{3D}{\isacharequal}}\ F\isanewline
+\ {\isadigit{5}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}p\ pa{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}T{\isaliteral{2C}{\isacharcomma}}\ p{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}F{\isaliteral{2C}{\isacharcomma}}\ pa{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ p\ {\isaliteral{3D}{\isacharequal}}\ F\isanewline
+\ {\isadigit{6}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}p{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}T{\isaliteral{2C}{\isacharcomma}}\ p{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}X{\isaliteral{2C}{\isacharcomma}}\ X{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ p\ {\isaliteral{3D}{\isacharequal}}\ X\isanewline
+\ {\isadigit{7}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}p\ pa{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}\ T{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}pa{\isaliteral{2C}{\isacharcomma}}\ T{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ p\ {\isaliteral{3D}{\isacharequal}}\ pa\isanewline
+\ {\isadigit{8}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}p\ pa{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}\ T{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}pa{\isaliteral{2C}{\isacharcomma}}\ F{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ p\ {\isaliteral{3D}{\isacharequal}}\ F\isanewline
+\ {\isadigit{9}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}p\ pa{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}\ T{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}F{\isaliteral{2C}{\isacharcomma}}\ pa{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ p\ {\isaliteral{3D}{\isacharequal}}\ F\isanewline
+\ {\isadigit{1}}{\isadigit{0}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}p{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}\ T{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}X{\isaliteral{2C}{\isacharcomma}}\ X{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ p\ {\isaliteral{3D}{\isacharequal}}\ X%
\end{isabelle}\vspace{-1.2em}\hspace{3cm}\vdots\vspace{1.2em}
The first subgoal expresses the completeness of the patterns. It has
the form of an elimination rule and states that every \isa{x} of
the function's input type must match at least one of the patterns\footnote{Completeness could
be equivalently stated as a disjunction of existential statements:
-\isa{{\isacharparenleft}{\isasymexists}p{\isachardot}\ x\ {\isacharequal}\ {\isacharparenleft}T{\isacharcomma}\ p{\isacharparenright}{\isacharparenright}\ {\isasymor}\ {\isacharparenleft}{\isasymexists}p{\isachardot}\ x\ {\isacharequal}\ {\isacharparenleft}p{\isacharcomma}\ T{\isacharparenright}{\isacharparenright}\ {\isasymor}\ {\isacharparenleft}{\isasymexists}p{\isachardot}\ x\ {\isacharequal}\ {\isacharparenleft}p{\isacharcomma}\ F{\isacharparenright}{\isacharparenright}\ {\isasymor}\ {\isacharparenleft}{\isasymexists}p{\isachardot}\ x\ {\isacharequal}\ {\isacharparenleft}F{\isacharcomma}\ p{\isacharparenright}{\isacharparenright}\ {\isasymor}\ x\ {\isacharequal}\ {\isacharparenleft}X{\isacharcomma}\ X{\isacharparenright}}, and you can use the method \isa{atomize{\isacharunderscore}elim} to get that form instead.}. If the patterns just involve
- datatypes, we can solve it with the \isa{pat{\isacharunderscore}completeness}
+\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}p{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}T{\isaliteral{2C}{\isacharcomma}}\ p{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}p{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}\ T{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}p{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}\ F{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}p{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}F{\isaliteral{2C}{\isacharcomma}}\ p{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}X{\isaliteral{2C}{\isacharcomma}}\ X{\isaliteral{29}{\isacharparenright}}}, and you can use the method \isa{atomize{\isaliteral{5F}{\isacharunderscore}}elim} to get that form instead.}. If the patterns just involve
+ datatypes, we can solve it with the \isa{pat{\isaliteral{5F}{\isacharunderscore}}completeness}
method:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-\ pat{\isacharunderscore}completeness%
+\ pat{\isaliteral{5F}{\isacharunderscore}}completeness%
\begin{isamarkuptxt}%
The remaining subgoals express \emph{pattern compatibility}. We do
allow that an input value matches multiple patterns, but in this
@@ -821,25 +821,11 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{function}\isamarkupfalse%
-\ fib{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\isanewline
+\ fib{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}fib{\isadigit{2}}\ {\isadigit{0}}\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}fib{\isadigit{2}}\ {\isadigit{1}}\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}fib{\isadigit{2}}\ {\isacharparenleft}n\ {\isacharplus}\ {\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ fib{\isadigit{2}}\ n\ {\isacharplus}\ fib{\isadigit{2}}\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isachardoublequoteclose}\isanewline
-%
-\isadelimML
-%
-\endisadelimML
-%
-\isatagML
-%
-\endisatagML
-{\isafoldML}%
-%
-\isadelimML
-%
-\endisadelimML
-%
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}fib{\isadigit{2}}\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}fib{\isadigit{2}}\ {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}fib{\isadigit{2}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ fib{\isadigit{2}}\ n\ {\isaliteral{2B}{\isacharplus}}\ fib{\isadigit{2}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -850,55 +836,21 @@
This kind of matching is again justified by the proof of pattern
completeness and compatibility.
The proof obligation for pattern completeness states that every natural number is
- either \isa{{\isadigit{0}}}, \isa{{\isadigit{1}}} or \isa{n\ {\isacharplus}\ {\isadigit{2}}}:
+ either \isa{{\isadigit{0}}}, \isa{{\isadigit{1}}} or \isa{n\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{2}}}:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}P\ x{\isachardot}\ {\isasymlbrakk}x\ {\isacharequal}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ P{\isacharsemicolon}\ x\ {\isacharequal}\ {\isadigit{1}}\ {\isasymLongrightarrow}\ P{\isacharsemicolon}\ {\isasymAnd}n{\isachardot}\ x\ {\isacharequal}\ n\ {\isacharplus}\ {\isadigit{2}}\ {\isasymLongrightarrow}\ P{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isadigit{0}}\ {\isacharequal}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ {\isadigit{1}}\ {\isacharequal}\ {\isadigit{1}}\isanewline
-\ {\isadigit{3}}{\isachardot}\ {\isadigit{0}}\ {\isacharequal}\ {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isadigit{1}}\ {\isacharequal}\ {\isadigit{1}}\isanewline
-\ {\isadigit{4}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ {\isadigit{0}}\ {\isacharequal}\ n\ {\isacharplus}\ {\isadigit{2}}\ {\isasymLongrightarrow}\ {\isadigit{1}}\ {\isacharequal}\ fib{\isadigit{2}}{\isacharunderscore}sumC\ n\ {\isacharplus}\ fib{\isadigit{2}}{\isacharunderscore}sumC\ {\isacharparenleft}Suc\ n{\isacharparenright}\isanewline
-\ {\isadigit{5}}{\isachardot}\ {\isadigit{1}}\ {\isacharequal}\ {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isadigit{1}}\ {\isacharequal}\ {\isadigit{1}}\isanewline
-\ {\isadigit{6}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ {\isadigit{1}}\ {\isacharequal}\ n\ {\isacharplus}\ {\isadigit{2}}\ {\isasymLongrightarrow}\ {\isadigit{1}}\ {\isacharequal}\ fib{\isadigit{2}}{\isacharunderscore}sumC\ n\ {\isacharplus}\ fib{\isadigit{2}}{\isacharunderscore}sumC\ {\isacharparenleft}Suc\ n{\isacharparenright}\isanewline
-\ {\isadigit{7}}{\isachardot}\ {\isasymAnd}n\ na{\isachardot}\isanewline
-\isaindent{\ {\isadigit{7}}{\isachardot}\ \ \ \ }n\ {\isacharplus}\ {\isadigit{2}}\ {\isacharequal}\ na\ {\isacharplus}\ {\isadigit{2}}\ {\isasymLongrightarrow}\isanewline
-\isaindent{\ {\isadigit{7}}{\isachardot}\ \ \ \ }fib{\isadigit{2}}{\isacharunderscore}sumC\ n\ {\isacharplus}\ fib{\isadigit{2}}{\isacharunderscore}sumC\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ fib{\isadigit{2}}{\isacharunderscore}sumC\ na\ {\isacharplus}\ fib{\isadigit{2}}{\isacharunderscore}sumC\ {\isacharparenleft}Suc\ na{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}P\ x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}x\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{3B}{\isacharsemicolon}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3D}{\isacharequal}}\ n\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{2}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P%
\end{isabelle}
This is an arithmetic triviality, but unfortunately the
\isa{arith} method cannot handle this specific form of an
- elimination rule. However, we can use the method \isa{atomize{\isacharunderscore}elim} to do an ad-hoc conversion to a disjunction of
+ elimination rule. However, we can use the method \isa{atomize{\isaliteral{5F}{\isacharunderscore}}elim} to do an ad-hoc conversion to a disjunction of
existentials, which can then be solved by the arithmetic decision procedure.
Pattern compatibility and termination are automatic as usual.%
\end{isamarkuptxt}%
\isamarkuptrue%
-%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\isadelimML
-%
-\endisadelimML
-%
-\isatagML
-%
-\endisatagML
-{\isafoldML}%
-%
-\isadelimML
-%
-\endisadelimML
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ atomize{\isacharunderscore}elim\isanewline
+\ atomize{\isaliteral{5F}{\isacharunderscore}}elim\isanewline
\isacommand{apply}\isamarkupfalse%
\ arith\isanewline
\isacommand{apply}\isamarkupfalse%
@@ -920,7 +872,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ lexicographic{\isacharunderscore}order%
+\ lexicographic{\isaliteral{5F}{\isacharunderscore}}order%
\endisatagproof
{\isafoldproof}%
%
@@ -935,10 +887,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{function}\isamarkupfalse%
-\ ev\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
+\ ev\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}ev\ {\isacharparenleft}{\isadigit{2}}\ {\isacharasterisk}\ n{\isacharparenright}\ {\isacharequal}\ True{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}ev\ {\isacharparenleft}{\isadigit{2}}\ {\isacharasterisk}\ n\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}\ {\isacharequal}\ False{\isachardoublequoteclose}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}ev\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ True{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}ev\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ n\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ False{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -946,9 +898,9 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ atomize{\isacharunderscore}elim\isanewline
+\ atomize{\isaliteral{5F}{\isacharunderscore}}elim\isanewline
\isacommand{by}\isamarkupfalse%
-\ arith{\isacharplus}%
+\ arith{\isaliteral{2B}{\isacharplus}}%
\endisatagproof
{\isafoldproof}%
%
@@ -964,7 +916,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}relation\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceright}{\isachardoublequoteclose}{\isacharparenright}\ simp%
+\ {\isaliteral{28}{\isacharparenleft}}relation\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\ simp%
\endisatagproof
{\isafoldproof}%
%
@@ -998,12 +950,12 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{function}\isamarkupfalse%
-\ gcd\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\isanewline
+\ gcd\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}gcd\ x\ {\isadigit{0}}\ {\isacharequal}\ x{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}gcd\ {\isadigit{0}}\ y\ {\isacharequal}\ y{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}x\ {\isacharless}\ y\ {\isasymLongrightarrow}\ gcd\ {\isacharparenleft}Suc\ x{\isacharparenright}\ {\isacharparenleft}Suc\ y{\isacharparenright}\ {\isacharequal}\ gcd\ {\isacharparenleft}Suc\ x{\isacharparenright}\ {\isacharparenleft}y\ {\isacharminus}\ x{\isacharparenright}{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}{\isasymnot}\ x\ {\isacharless}\ y\ {\isasymLongrightarrow}\ gcd\ {\isacharparenleft}Suc\ x{\isacharparenright}\ {\isacharparenleft}Suc\ y{\isacharparenright}\ {\isacharequal}\ gcd\ {\isacharparenleft}x\ {\isacharminus}\ y{\isacharparenright}\ {\isacharparenleft}Suc\ y{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}gcd\ x\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}gcd\ {\isadigit{0}}\ y\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3C}{\isacharless}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ gcd\ {\isaliteral{28}{\isacharparenleft}}Suc\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ gcd\ {\isaliteral{28}{\isacharparenleft}}Suc\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{2D}{\isacharminus}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ x\ {\isaliteral{3C}{\isacharless}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ gcd\ {\isaliteral{28}{\isacharparenleft}}Suc\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ gcd\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{2D}{\isacharminus}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1011,7 +963,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}atomize{\isacharunderscore}elim{\isacharcomma}\ auto{\isacharcomma}\ arith{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}atomize{\isaliteral{5F}{\isacharunderscore}}elim{\isaliteral{2C}{\isacharcomma}}\ auto{\isaliteral{2C}{\isacharcomma}}\ arith{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1027,7 +979,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ lexicographic{\isacharunderscore}order%
+\ lexicographic{\isaliteral{5F}{\isacharunderscore}}order%
\endisatagproof
{\isafoldproof}%
%
@@ -1054,10 +1006,10 @@
following definition:
\end{isamarkuptext}
-\noindent\cmd{fun} \isa{check\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}string\ {\isasymRightarrow}\ bool{\isachardoublequote}}\\%
+\noindent\cmd{fun} \isa{check\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequote}}string\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequote}}}\\%
\cmd{where}\\%
-\hspace*{2ex}\isa{{\isachardoublequote}check\ {\isacharparenleft}{\isacharprime}{\isacharprime}good{\isacharprime}{\isacharprime}{\isacharparenright}\ {\isacharequal}\ True{\isachardoublequote}}\\%
-\isa{{\isacharbar}\ {\isachardoublequote}check\ s\ {\isacharequal}\ False{\isachardoublequote}}
+\hspace*{2ex}\isa{{\isaliteral{22}{\isachardoublequote}}check\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}good{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ True{\isaliteral{22}{\isachardoublequote}}}\\%
+\isa{{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequote}}check\ s\ {\isaliteral{3D}{\isacharequal}}\ False{\isaliteral{22}{\isachardoublequote}}}
\begin{isamarkuptext}
\noindent An invocation of the above \cmd{fun} command does not
@@ -1071,10 +1023,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{function}\isamarkupfalse%
-\ check\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}string\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
+\ check\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}string\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}check\ {\isacharparenleft}{\isacharprime}{\isacharprime}good{\isacharprime}{\isacharprime}{\isacharparenright}\ {\isacharequal}\ True{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}s\ {\isasymnoteq}\ {\isacharprime}{\isacharprime}good{\isacharprime}{\isacharprime}\ {\isasymLongrightarrow}\ check\ s\ {\isacharequal}\ False{\isachardoublequoteclose}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}check\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}good{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ True{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}s\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}good{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ check\ s\ {\isaliteral{3D}{\isacharequal}}\ False{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1108,9 +1060,9 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{function}\isamarkupfalse%
-\ findzero\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}nat\ {\isasymRightarrow}\ nat{\isacharparenright}\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\isanewline
+\ findzero\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}findzero\ f\ n\ {\isacharequal}\ {\isacharparenleft}if\ f\ n\ {\isacharequal}\ {\isadigit{0}}\ then\ n\ else\ findzero\ f\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}findzero\ f\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ f\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\ then\ n\ else\ findzero\ f\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1118,7 +1070,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ pat{\isacharunderscore}completeness\ auto%
+\ pat{\isaliteral{5F}{\isacharunderscore}}completeness\ auto%
\endisatagproof
{\isafoldproof}%
%
@@ -1128,8 +1080,8 @@
%
\begin{isamarkuptext}%
\noindent Clearly, any attempt of a termination proof must fail. And without
- that, we do not get the usual rules \isa{findzero{\isachardot}simps} and
- \isa{findzero{\isachardot}induct}. So what was the definition good for at all?%
+ that, we do not get the usual rules \isa{findzero{\isaliteral{2E}{\isachardot}}simps} and
+ \isa{findzero{\isaliteral{2E}{\isachardot}}induct}. So what was the definition good for at all?%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -1139,7 +1091,7 @@
%
\begin{isamarkuptext}%
The trick is that Isabelle has not only defined the function \isa{findzero}, but also
- a predicate \isa{findzero{\isacharunderscore}dom} that characterizes the values where the function
+ a predicate \isa{findzero{\isaliteral{5F}{\isacharunderscore}}dom} that characterizes the values where the function
terminates: the \emph{domain} of the function. If we treat a
partial function just as a total function with an additional domain
predicate, we can derive simplification and
@@ -1150,25 +1102,25 @@
%
\begin{isamarkuptext}%
\noindent\begin{minipage}{0.79\textwidth}\begin{isabelle}%
-findzero{\isacharunderscore}dom\ {\isacharparenleft}{\isacharquery}f{\isacharcomma}\ {\isacharquery}n{\isacharparenright}\ {\isasymLongrightarrow}\isanewline
-findzero\ {\isacharquery}f\ {\isacharquery}n\ {\isacharequal}\ {\isacharparenleft}if\ {\isacharquery}f\ {\isacharquery}n\ {\isacharequal}\ {\isadigit{0}}\ then\ {\isacharquery}n\ else\ findzero\ {\isacharquery}f\ {\isacharparenleft}Suc\ {\isacharquery}n{\isacharparenright}{\isacharparenright}%
+findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}f{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\isanewline
+findzero\ {\isaliteral{3F}{\isacharquery}}f\ {\isaliteral{3F}{\isacharquery}}n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ {\isaliteral{3F}{\isacharquery}}f\ {\isaliteral{3F}{\isacharquery}}n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\ then\ {\isaliteral{3F}{\isacharquery}}n\ else\ findzero\ {\isaliteral{3F}{\isacharquery}}f\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isaliteral{3F}{\isacharquery}}n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}\end{minipage}
- \hfill(\isa{findzero{\isachardot}psimps})
+ \hfill(\isa{findzero{\isaliteral{2E}{\isachardot}}psimps})
\vspace{1em}
\noindent\begin{minipage}{0.79\textwidth}\begin{isabelle}%
-{\isasymlbrakk}findzero{\isacharunderscore}dom\ {\isacharparenleft}{\isacharquery}a{\isadigit{0}}{\isachardot}{\isadigit{0}}{\isacharcomma}\ {\isacharquery}a{\isadigit{1}}{\isachardot}{\isadigit{0}}{\isacharparenright}{\isacharsemicolon}\isanewline
-\isaindent{\ }{\isasymAnd}f\ n{\isachardot}\ {\isasymlbrakk}findzero{\isacharunderscore}dom\ {\isacharparenleft}f{\isacharcomma}\ n{\isacharparenright}{\isacharsemicolon}\ f\ n\ {\isasymnoteq}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ {\isacharquery}P\ f\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}P\ f\ n{\isasymrbrakk}\isanewline
-{\isasymLongrightarrow}\ {\isacharquery}P\ {\isacharquery}a{\isadigit{0}}{\isachardot}{\isadigit{0}}\ {\isacharquery}a{\isadigit{1}}{\isachardot}{\isadigit{0}}%
+{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}a{\isadigit{0}}{\isaliteral{2E}{\isachardot}}{\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}a{\isadigit{1}}{\isaliteral{2E}{\isachardot}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ }{\isaliteral{5C3C416E643E}{\isasymAnd}}f\ n{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}f{\isaliteral{2C}{\isacharcomma}}\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ f\ n\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}P\ f\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}P\ f\ n{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{3F}{\isacharquery}}a{\isadigit{0}}{\isaliteral{2E}{\isachardot}}{\isadigit{0}}\ {\isaliteral{3F}{\isacharquery}}a{\isadigit{1}}{\isaliteral{2E}{\isachardot}}{\isadigit{0}}%
\end{isabelle}\end{minipage}
- \hfill(\isa{findzero{\isachardot}pinduct})%
+ \hfill(\isa{findzero{\isaliteral{2E}{\isachardot}}pinduct})%
\end{isamarkuptext}%
\isamarkuptrue%
%
\begin{isamarkuptext}%
Remember that all we
are doing here is use some tricks to make a total function appear
- as if it was partial. We can still write the term \isa{findzero\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ {\isadigit{1}}{\isacharparenright}\ {\isadigit{0}}} and like any other term of type \isa{nat} it is equal
+ as if it was partial. We can still write the term \isa{findzero\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isadigit{0}}} and like any other term of type \isa{nat} it is equal
to some natural number, although we might not be able to find out
which one. The function is \emph{underdefined}.
@@ -1178,7 +1130,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ findzero{\isacharunderscore}zero{\isacharcolon}\ {\isachardoublequoteopen}findzero{\isacharunderscore}dom\ {\isacharparenleft}f{\isacharcomma}\ n{\isacharparenright}\ {\isasymLongrightarrow}\ f\ {\isacharparenleft}findzero\ f\ n{\isacharparenright}\ {\isacharequal}\ {\isadigit{0}}{\isachardoublequoteclose}%
+\ findzero{\isaliteral{5F}{\isacharunderscore}}zero{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}f{\isaliteral{2C}{\isacharcomma}}\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ f\ {\isaliteral{28}{\isacharparenleft}}findzero\ f\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -1191,24 +1143,23 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}induct\ f\ n\ rule{\isacharcolon}\ findzero{\isachardot}pinduct{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}induct\ f\ n\ rule{\isaliteral{3A}{\isacharcolon}}\ findzero{\isaliteral{2E}{\isachardot}}pinduct{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent This gives the following subgoals:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}f\ n{\isachardot}\ {\isasymlbrakk}findzero{\isacharunderscore}dom\ {\isacharparenleft}f{\isacharcomma}\ n{\isacharparenright}{\isacharsemicolon}\ f\ n\ {\isasymnoteq}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ f\ {\isacharparenleft}findzero\ f\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isadigit{0}}{\isasymrbrakk}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}f\ n{\isachardot}\ }{\isasymLongrightarrow}\ f\ {\isacharparenleft}findzero\ f\ n{\isacharparenright}\ {\isacharequal}\ {\isadigit{0}}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}f\ n{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}f{\isaliteral{2C}{\isacharcomma}}\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ f\ n\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ f\ {\isaliteral{28}{\isacharparenleft}}findzero\ f\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}f\ n{\isaliteral{2E}{\isachardot}}\ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ f\ {\isaliteral{28}{\isacharparenleft}}findzero\ f\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}%
\end{isabelle}
\noindent The hypothesis in our lemma was used to satisfy the first premise in
- the induction rule. However, we also get \isa{findzero{\isacharunderscore}dom\ {\isacharparenleft}f{\isacharcomma}\ n{\isacharparenright}} as a local assumption in the induction step. This
- allows to unfold \isa{findzero\ f\ n} using the \isa{psimps}
- rule, and the rest is trivial. Since the \isa{psimps} rules carry the
- \isa{{\isacharbrackleft}simp{\isacharbrackright}} attribute by default, we just need a single step:%
+ the induction rule. However, we also get \isa{findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}f{\isaliteral{2C}{\isacharcomma}}\ n{\isaliteral{29}{\isacharparenright}}} as a local assumption in the induction step. This
+ allows unfolding \isa{findzero\ f\ n} using the \isa{psimps}
+ rule, and the rest is trivial.%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-\ simp\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ findzero{\isaliteral{2E}{\isachardot}}psimps{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -1234,7 +1185,7 @@
\isabellestyle{it}
\isastyle\isamarkuptrue
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymlbrakk}findzero{\isacharunderscore}dom\ {\isacharparenleft}f{\isacharcomma}\ n{\isacharparenright}{\isacharsemicolon}\ x\ {\isasymin}\ {\isacharbraceleft}n\ {\isachardot}{\isachardot}{\isacharless}\ findzero\ f\ n{\isacharbraceright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ f\ x\ {\isasymnoteq}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}f{\isaliteral{2C}{\isacharcomma}}\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{7B}{\isacharbraceleft}}n\ {\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{3C}{\isacharless}}\ findzero\ f\ n{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ f\ x\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1242,55 +1193,55 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}induct\ rule{\isacharcolon}\ findzero{\isachardot}pinduct{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ rule{\isaliteral{3A}{\isacharcolon}}\ findzero{\isaliteral{2E}{\isachardot}}pinduct{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
\ f\ n\ \isacommand{assume}\isamarkupfalse%
-\ dom{\isacharcolon}\ {\isachardoublequoteopen}findzero{\isacharunderscore}dom\ {\isacharparenleft}f{\isacharcomma}\ n{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \isakeyword{and}\ IH{\isacharcolon}\ {\isachardoublequoteopen}{\isasymlbrakk}f\ n\ {\isasymnoteq}\ {\isadigit{0}}{\isacharsemicolon}\ x\ {\isasymin}\ {\isacharbraceleft}Suc\ n\ {\isachardot}{\isachardot}{\isacharless}\ findzero\ f\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharbraceright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ f\ x\ {\isasymnoteq}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \isakeyword{and}\ x{\isacharunderscore}range{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymin}\ {\isacharbraceleft}n\ {\isachardot}{\isachardot}{\isacharless}\ findzero\ f\ n{\isacharbraceright}{\isachardoublequoteclose}\isanewline
+\ dom{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}f{\isaliteral{2C}{\isacharcomma}}\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \isakeyword{and}\ IH{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}f\ n\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}{\isaliteral{3B}{\isacharsemicolon}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{7B}{\isacharbraceleft}}Suc\ n\ {\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{3C}{\isacharless}}\ findzero\ f\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ f\ x\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \isakeyword{and}\ x{\isaliteral{5F}{\isacharunderscore}}range{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{7B}{\isacharbraceleft}}n\ {\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{3C}{\isacharless}}\ findzero\ f\ n{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}f\ n\ {\isasymnoteq}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}f\ n\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ \isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}f\ n\ {\isacharequal}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}f\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{with}\isamarkupfalse%
\ dom\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}findzero\ f\ n\ {\isacharequal}\ n{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ simp\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}findzero\ f\ n\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ findzero{\isaliteral{2E}{\isachardot}}psimps{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{with}\isamarkupfalse%
-\ x{\isacharunderscore}range\ \isacommand{show}\isamarkupfalse%
+\ x{\isaliteral{5F}{\isacharunderscore}}range\ \isacommand{show}\isamarkupfalse%
\ False\ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isanewline
\ \ \isacommand{from}\isamarkupfalse%
-\ x{\isacharunderscore}range\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isacharequal}\ n\ {\isasymor}\ x\ {\isasymin}\ {\isacharbraceleft}Suc\ n\ {\isachardot}{\isachardot}{\isacharless}\ findzero\ f\ n{\isacharbraceright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ x{\isaliteral{5F}{\isacharunderscore}}range\ \isacommand{have}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ n\ {\isaliteral{5C3C6F723E}{\isasymor}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{7B}{\isacharbraceleft}}Suc\ n\ {\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{3C}{\isacharless}}\ findzero\ f\ n{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{thus}\isamarkupfalse%
-\ {\isachardoublequoteopen}f\ x\ {\isasymnoteq}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}f\ x\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isacharequal}\ n{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{with}\isamarkupfalse%
-\ {\isacharbackquoteopen}f\ n\ {\isasymnoteq}\ {\isadigit{0}}{\isacharbackquoteclose}\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}f\ n\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymin}\ {\isacharbraceleft}Suc\ n\ {\isachardot}{\isachardot}{\isacharless}\ findzero\ f\ n{\isacharbraceright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{7B}{\isacharbraceleft}}Suc\ n\ {\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{3C}{\isacharless}}\ findzero\ f\ n{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{with}\isamarkupfalse%
-\ dom\ \isakeyword{and}\ {\isacharbackquoteopen}f\ n\ {\isasymnoteq}\ {\isadigit{0}}{\isacharbackquoteclose}\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymin}\ {\isacharbraceleft}Suc\ n\ {\isachardot}{\isachardot}{\isacharless}\ findzero\ f\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharbraceright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ simp\isanewline
+\ dom\ \isakeyword{and}\ {\isaliteral{60}{\isacharbackquoteopen}}f\ n\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{have}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{7B}{\isacharbraceleft}}Suc\ n\ {\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{3C}{\isacharless}}\ findzero\ f\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ findzero{\isaliteral{2E}{\isachardot}}psimps{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{with}\isamarkupfalse%
-\ IH\ \isakeyword{and}\ {\isacharbackquoteopen}f\ n\ {\isasymnoteq}\ {\isadigit{0}}{\isacharbackquoteclose}\isanewline
+\ IH\ \isakeyword{and}\ {\isaliteral{60}{\isacharbackquoteopen}}f\ n\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}{\isaliteral{60}{\isacharbackquoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
@@ -1318,25 +1269,25 @@
actually true for some values. Otherwise we would have just proved
lemmas with \isa{False} as a premise.
- Essentially, we need some introduction rules for \isa{findzero{\isacharunderscore}dom}. The function package can prove such domain
+ Essentially, we need some introduction rules for \isa{findzero{\isaliteral{5F}{\isacharunderscore}}dom}. The function package can prove such domain
introduction rules automatically. But since they are not used very
often (they are almost never needed if the function is total), this
functionality is disabled by default for efficiency reasons. So we have to go
- back and ask for them explicitly by passing the \isa{{\isacharparenleft}domintros{\isacharparenright}} option to the function package:
+ back and ask for them explicitly by passing the \isa{{\isaliteral{28}{\isacharparenleft}}domintros{\isaliteral{29}{\isacharparenright}}} option to the function package:
\vspace{1ex}
-\noindent\cmd{function} \isa{{\isacharparenleft}domintros{\isacharparenright}\ findzero\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharparenleft}nat\ {\isasymRightarrow}\ nat{\isacharparenright}\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat{\isachardoublequote}}\\%
+\noindent\cmd{function} \isa{{\isaliteral{28}{\isacharparenleft}}domintros{\isaliteral{29}{\isacharparenright}}\ findzero\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequote}}}\\%
\cmd{where}\isanewline%
\ \ \ldots\\
- \noindent Now the package has proved an introduction rule for \isa{findzero{\isacharunderscore}dom}:%
+ \noindent Now the package has proved an introduction rule for \isa{findzero{\isaliteral{5F}{\isacharunderscore}}dom}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{thm}\isamarkupfalse%
-\ findzero{\isachardot}domintros%
+\ findzero{\isaliteral{2E}{\isachardot}}domintros%
\begin{isamarkuptext}%
\begin{isabelle}%
-{\isacharparenleft}{\isadigit{0}}\ {\isacharless}\ {\isacharquery}f\ {\isacharquery}n\ {\isasymLongrightarrow}\ findzero{\isacharunderscore}dom\ {\isacharparenleft}{\isacharquery}f{\isacharcomma}\ Suc\ {\isacharquery}n{\isacharparenright}{\isacharparenright}\ {\isasymLongrightarrow}\ findzero{\isacharunderscore}dom\ {\isacharparenleft}{\isacharquery}f{\isacharcomma}\ {\isacharquery}n{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}\ {\isaliteral{3C}{\isacharless}}\ {\isaliteral{3F}{\isacharquery}}f\ {\isaliteral{3F}{\isacharquery}}n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}f{\isaliteral{2C}{\isacharcomma}}\ Suc\ {\isaliteral{3F}{\isacharquery}}n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}f{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}n{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
Domain introduction rules allow to show that a given value lies in the
@@ -1347,10 +1298,10 @@
Since our function increases its argument at recursive calls, we
need an induction principle which works \qt{backwards}. We will use
- \isa{inc{\isacharunderscore}induct}, which allows to do induction from a fixed number
+ \isa{inc{\isaliteral{5F}{\isacharunderscore}}induct}, which allows to do induction from a fixed number
\qt{downwards}:
- \begin{center}\isa{{\isasymlbrakk}{\isacharquery}i\ {\isasymle}\ {\isacharquery}j{\isacharsemicolon}\ {\isacharquery}P\ {\isacharquery}j{\isacharsemicolon}\ {\isasymAnd}i{\isachardot}\ {\isasymlbrakk}i\ {\isacharless}\ {\isacharquery}j{\isacharsemicolon}\ {\isacharquery}P\ {\isacharparenleft}Suc\ i{\isacharparenright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}P\ i{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}P\ {\isacharquery}i}\hfill(\isa{inc{\isacharunderscore}induct})\end{center}
+ \begin{center}\isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{3F}{\isacharquery}}i\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3F}{\isacharquery}}j{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{3F}{\isacharquery}}j{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}i{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}i\ {\isaliteral{3C}{\isacharless}}\ {\isaliteral{3F}{\isacharquery}}j{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{28}{\isacharparenleft}}Suc\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}P\ i{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{3F}{\isacharquery}}i}\hfill(\isa{inc{\isaliteral{5F}{\isacharunderscore}}induct})\end{center}
Figure \ref{findzero_term} gives a detailed Isar proof of the fact
that \isa{findzero} terminates if there is a zero which is greater
@@ -1367,9 +1318,9 @@
\isabellestyle{it}
\isastyle\isamarkuptrue
\isacommand{lemma}\isamarkupfalse%
-\ findzero{\isacharunderscore}termination{\isacharcolon}\isanewline
-\ \ \isakeyword{assumes}\ {\isachardoublequoteopen}x\ {\isasymge}\ n{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}f\ x\ {\isacharequal}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{shows}\ {\isachardoublequoteopen}findzero{\isacharunderscore}dom\ {\isacharparenleft}f{\isacharcomma}\ n{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ findzero{\isaliteral{5F}{\isacharunderscore}}termination{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \isakeyword{assumes}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C67653E}{\isasymge}}\ n{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}f\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}f{\isaliteral{2C}{\isacharcomma}}\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1377,34 +1328,34 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\ \isanewline
+\ {\isaliteral{2D}{\isacharminus}}\ \isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ base{\isacharcolon}\ {\isachardoublequoteopen}findzero{\isacharunderscore}dom\ {\isacharparenleft}f{\isacharcomma}\ x{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ base{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}f{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ findzero{\isachardot}domintros{\isacharparenright}\ {\isacharparenleft}simp\ add{\isacharcolon}{\isacharbackquoteopen}f\ x\ {\isacharequal}\ {\isadigit{0}}{\isacharbackquoteclose}{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ findzero{\isaliteral{2E}{\isachardot}}domintros{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}{\isaliteral{60}{\isacharbackquoteopen}}f\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{60}{\isacharbackquoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ step{\isacharcolon}\ {\isachardoublequoteopen}{\isasymAnd}i{\isachardot}\ findzero{\isacharunderscore}dom\ {\isacharparenleft}f{\isacharcomma}\ Suc\ i{\isacharparenright}\ \isanewline
-\ \ \ \ {\isasymLongrightarrow}\ findzero{\isacharunderscore}dom\ {\isacharparenleft}f{\isacharcomma}\ i{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ step{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C416E643E}{\isasymAnd}}i{\isaliteral{2E}{\isachardot}}\ findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}f{\isaliteral{2C}{\isacharcomma}}\ Suc\ i{\isaliteral{29}{\isacharparenright}}\ \isanewline
+\ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}f{\isaliteral{2C}{\isacharcomma}}\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ findzero{\isachardot}domintros{\isacharparenright}\ simp\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ findzero{\isaliteral{2E}{\isachardot}}domintros{\isaliteral{29}{\isacharparenright}}\ simp\isanewline
\isanewline
\ \ \isacommand{from}\isamarkupfalse%
-\ {\isacharbackquoteopen}x\ {\isasymge}\ n{\isacharbackquoteclose}\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\isanewline
+\ {\isaliteral{60}{\isacharbackquoteopen}}x\ {\isaliteral{5C3C67653E}{\isasymge}}\ n{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}induct\ rule{\isacharcolon}inc{\isacharunderscore}induct{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ rule{\isaliteral{3A}{\isacharcolon}}inc{\isaliteral{5F}{\isacharunderscore}}induct{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}findzero{\isacharunderscore}dom\ {\isacharparenleft}f{\isacharcomma}\ x{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ base{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}f{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ base{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ i\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}findzero{\isacharunderscore}dom\ {\isacharparenleft}f{\isacharcomma}\ Suc\ i{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}f{\isaliteral{2C}{\isacharcomma}}\ Suc\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{thus}\isamarkupfalse%
-\ {\isachardoublequoteopen}findzero{\isacharunderscore}dom\ {\isacharparenleft}f{\isacharcomma}\ i{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ step{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}f{\isaliteral{2C}{\isacharcomma}}\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ step{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
@@ -1428,10 +1379,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ findzero{\isacharunderscore}termination{\isacharunderscore}short{\isacharcolon}\isanewline
-\ \ \isakeyword{assumes}\ zero{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isachargreater}{\isacharequal}\ n{\isachardoublequoteclose}\ \isanewline
-\ \ \isakeyword{assumes}\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}f\ x\ {\isacharequal}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{shows}\ {\isachardoublequoteopen}findzero{\isacharunderscore}dom\ {\isacharparenleft}f{\isacharcomma}\ n{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ findzero{\isaliteral{5F}{\isacharunderscore}}termination{\isaliteral{5F}{\isacharunderscore}}short{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \isakeyword{assumes}\ zero{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3E}{\isachargreater}}{\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{22}{\isachardoublequoteclose}}\ \isanewline
+\ \ \isakeyword{assumes}\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}f\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}f{\isaliteral{2C}{\isacharcomma}}\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1441,7 +1392,7 @@
\isacommand{using}\isamarkupfalse%
\ zero\isanewline
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ rule{\isacharcolon}inc{\isacharunderscore}induct{\isacharparenright}\ {\isacharparenleft}auto\ intro{\isacharcolon}\ findzero{\isachardot}domintros{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}induct\ rule{\isaliteral{3A}{\isacharcolon}}inc{\isaliteral{5F}{\isacharunderscore}}induct{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}auto\ intro{\isaliteral{3A}{\isacharcolon}}\ findzero{\isaliteral{2E}{\isachardot}}domintros{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1455,8 +1406,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ findzero{\isacharunderscore}total{\isacharunderscore}correctness{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}f\ x\ {\isacharequal}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ f\ {\isacharparenleft}findzero\ f\ {\isadigit{0}}{\isacharparenright}\ {\isacharequal}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
+\ findzero{\isaliteral{5F}{\isacharunderscore}}total{\isaliteral{5F}{\isacharunderscore}}correctness{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}f\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ f\ {\isaliteral{28}{\isacharparenleft}}findzero\ f\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1464,7 +1415,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}blast\ intro{\isacharcolon}\ findzero{\isacharunderscore}zero\ findzero{\isacharunderscore}termination{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}blast\ intro{\isaliteral{3A}{\isacharcolon}}\ findzero{\isaliteral{5F}{\isacharunderscore}}zero\ findzero{\isaliteral{5F}{\isacharunderscore}}termination{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1478,38 +1429,38 @@
%
\begin{isamarkuptext}%
Sometimes it is useful to know what the definition of the domain
- predicate looks like. Actually, \isa{findzero{\isacharunderscore}dom} is just an
+ predicate looks like. Actually, \isa{findzero{\isaliteral{5F}{\isacharunderscore}}dom} is just an
abbreviation:
\begin{isabelle}%
-findzero{\isacharunderscore}dom\ {\isasymequiv}\ accp\ findzero{\isacharunderscore}rel%
+findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ accp\ findzero{\isaliteral{5F}{\isacharunderscore}}rel%
\end{isabelle}
- The domain predicate is the \emph{accessible part} of a relation \isa{findzero{\isacharunderscore}rel}, which was also created internally by the function
- package. \isa{findzero{\isacharunderscore}rel} is just a normal
+ The domain predicate is the \emph{accessible part} of a relation \isa{findzero{\isaliteral{5F}{\isacharunderscore}}rel}, which was also created internally by the function
+ package. \isa{findzero{\isaliteral{5F}{\isacharunderscore}}rel} is just a normal
inductive predicate, so we can inspect its definition by
- looking at the introduction rules \isa{findzero{\isacharunderscore}rel{\isachardot}intros}.
+ looking at the introduction rules \isa{findzero{\isaliteral{5F}{\isacharunderscore}}rel{\isaliteral{2E}{\isachardot}}intros}.
In our case there is just a single rule:
\begin{isabelle}%
-{\isacharquery}f\ {\isacharquery}n\ {\isasymnoteq}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ findzero{\isacharunderscore}rel\ {\isacharparenleft}{\isacharquery}f{\isacharcomma}\ Suc\ {\isacharquery}n{\isacharparenright}\ {\isacharparenleft}{\isacharquery}f{\isacharcomma}\ {\isacharquery}n{\isacharparenright}%
+{\isaliteral{3F}{\isacharquery}}f\ {\isaliteral{3F}{\isacharquery}}n\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ findzero{\isaliteral{5F}{\isacharunderscore}}rel\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}f{\isaliteral{2C}{\isacharcomma}}\ Suc\ {\isaliteral{3F}{\isacharquery}}n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}f{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}n{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
- The predicate \isa{findzero{\isacharunderscore}rel}
+ The predicate \isa{findzero{\isaliteral{5F}{\isacharunderscore}}rel}
describes the \emph{recursion relation} of the function
definition. The recursion relation is a binary relation on
the arguments of the function that relates each argument to its
recursive calls. In general, there is one introduction rule for each
recursive call.
- The predicate \isa{findzero{\isacharunderscore}dom} is the accessible part of
+ The predicate \isa{findzero{\isaliteral{5F}{\isacharunderscore}}dom} is the accessible part of
that relation. An argument belongs to the accessible part, if it can
- be reached in a finite number of steps (cf.~its definition in \isa{Wellfounded{\isachardot}thy}).
+ be reached in a finite number of steps (cf.~its definition in \isa{Wellfounded{\isaliteral{2E}{\isachardot}}thy}).
Since the domain predicate is just an abbreviation, you can use
- lemmas for \isa{accp} and \isa{findzero{\isacharunderscore}rel} directly. Some
- lemmas which are occasionally useful are \isa{accpI}, \isa{accp{\isacharunderscore}downward}, and of course the introduction and elimination rules
- for the recursion relation \isa{findzero{\isachardot}intros} and \isa{findzero{\isachardot}cases}.%
+ lemmas for \isa{accp} and \isa{findzero{\isaliteral{5F}{\isacharunderscore}}rel} directly. Some
+ lemmas which are occasionally useful are \isa{accpI}, \isa{accp{\isaliteral{5F}{\isacharunderscore}}downward}, and of course the introduction and elimination rules
+ for the recursion relation \isa{findzero{\isaliteral{2E}{\isachardot}}intros} and \isa{findzero{\isaliteral{2E}{\isachardot}}cases}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -1521,8 +1472,8 @@
The domain predicate is our trick that allows us to model partiality
in a world of total functions. The downside of this is that we have
to carry it around all the time. The termination proof above allowed
- us to replace the abstract \isa{findzero{\isacharunderscore}dom\ {\isacharparenleft}f{\isacharcomma}\ n{\isacharparenright}} by the more
- concrete \isa{n\ {\isasymle}\ x\ {\isasymand}\ f\ x\ {\isacharequal}\ {\isadigit{0}}}, but the condition is still
+ us to replace the abstract \isa{findzero{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}f{\isaliteral{2C}{\isacharcomma}}\ n{\isaliteral{29}{\isacharparenright}}} by the more
+ concrete \isa{n\ {\isaliteral{5C3C6C653E}{\isasymle}}\ x\ {\isaliteral{5C3C616E643E}{\isasymand}}\ f\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}}, but the condition is still
there and can only be discharged for special cases.
In particular, the domain predicate guards the unfolding of our
function, since it is there as a condition in the \isa{psimp}
@@ -1550,7 +1501,7 @@
back and add another option to the \cmd{function} command:
\vspace{1ex}
-\noindent\cmd{function} \isa{{\isacharparenleft}domintros{\isacharcomma}\ tailrec{\isacharparenright}\ findzero\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharparenleft}nat\ {\isasymRightarrow}\ nat{\isacharparenright}\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat{\isachardoublequote}}\\%
+\noindent\cmd{function} \isa{{\isaliteral{28}{\isacharparenleft}}domintros{\isaliteral{2C}{\isacharcomma}}\ tailrec{\isaliteral{29}{\isacharparenright}}\ findzero\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequote}}}\\%
\cmd{where}\isanewline%
\ \ \ldots\\%
@@ -1560,10 +1511,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{thm}\isamarkupfalse%
-\ findzero{\isachardot}simps%
+\ findzero{\isaliteral{2E}{\isachardot}}simps%
\begin{isamarkuptext}%
\begin{isabelle}%
-findzero\ {\isacharquery}f\ {\isacharquery}n\ {\isacharequal}\ {\isacharparenleft}if\ {\isacharquery}f\ {\isacharquery}n\ {\isacharequal}\ {\isadigit{0}}\ then\ {\isacharquery}n\ else\ findzero\ {\isacharquery}f\ {\isacharparenleft}Suc\ {\isacharquery}n{\isacharparenright}{\isacharparenright}%
+findzero\ {\isaliteral{3F}{\isacharquery}}f\ {\isaliteral{3F}{\isacharquery}}n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ {\isaliteral{3F}{\isacharquery}}f\ {\isaliteral{3F}{\isacharquery}}n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\ then\ {\isaliteral{3F}{\isacharquery}}n\ else\ findzero\ {\isaliteral{3F}{\isacharquery}}f\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isaliteral{3F}{\isacharquery}}n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\noindent Of course these would make the simplifier loop, so we better remove
@@ -1571,7 +1522,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{declare}\isamarkupfalse%
-\ findzero{\isachardot}simps{\isacharbrackleft}simp\ del{\isacharbrackright}%
+\ findzero{\isaliteral{2E}{\isachardot}}simps{\isaliteral{5B}{\isacharbrackleft}}simp\ del{\isaliteral{5D}{\isacharbrackright}}%
\begin{isamarkuptext}%
Getting rid of the domain conditions in the simplification rules is
not only useful because it simplifies proofs. It is also required in
@@ -1598,10 +1549,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{function}\isamarkupfalse%
-\ nz\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\isanewline
+\ nz\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}nz\ {\isadigit{0}}\ {\isacharequal}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}nz\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ nz\ {\isacharparenleft}nz\ n{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}nz\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}nz\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ nz\ {\isaliteral{28}{\isacharparenleft}}nz\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1609,7 +1560,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ pat{\isacharunderscore}completeness\ auto%
+\ pat{\isaliteral{5F}{\isacharunderscore}}completeness\ auto%
\endisatagproof
{\isafoldproof}%
%
@@ -1631,14 +1582,14 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}relation\ {\isachardoublequoteopen}measure\ {\isacharparenleft}{\isasymlambda}n{\isachardot}\ n{\isacharparenright}{\isachardoublequoteclose}{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}relation\ {\isaliteral{22}{\isachardoublequoteopen}}measure\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}n{\isaliteral{2E}{\isachardot}}\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{apply}\isamarkupfalse%
\ auto%
\begin{isamarkuptxt}%
We get stuck with the subgoal
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ nz{\isacharunderscore}dom\ n\ {\isasymLongrightarrow}\ nz\ n\ {\isacharless}\ Suc\ n%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ nz{\isaliteral{5F}{\isacharunderscore}}dom\ n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ nz\ n\ {\isaliteral{3C}{\isacharless}}\ Suc\ n%
\end{isabelle}
Of course this statement is true, since we know that \isa{nz} is
@@ -1654,7 +1605,7 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ nz{\isacharunderscore}is{\isacharunderscore}zero{\isacharcolon}\ {\isachardoublequoteopen}nz{\isacharunderscore}dom\ n\ {\isasymLongrightarrow}\ nz\ n\ {\isacharequal}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
+\ nz{\isaliteral{5F}{\isacharunderscore}}is{\isaliteral{5F}{\isacharunderscore}}zero{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nz{\isaliteral{5F}{\isacharunderscore}}dom\ n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ nz\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -1662,7 +1613,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ rule{\isacharcolon}nz{\isachardot}pinduct{\isacharparenright}\ auto%
+\ {\isaliteral{28}{\isacharparenleft}}induct\ rule{\isaliteral{3A}{\isacharcolon}}nz{\isaliteral{2E}{\isachardot}}pinduct{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}auto\ simp{\isaliteral{3A}{\isacharcolon}}\ nz{\isaliteral{2E}{\isachardot}}psimps{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1672,7 +1623,7 @@
%
\begin{isamarkuptext}%
We formulate this as a partial correctness lemma with the condition
- \isa{nz{\isacharunderscore}dom\ n}. This allows us to prove it with the \isa{pinduct} rule before we have proved termination. With this lemma,
+ \isa{nz{\isaliteral{5F}{\isacharunderscore}}dom\ n}. This allows us to prove it with the \isa{pinduct} rule before we have proved termination. With this lemma,
the termination proof works as expected:%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -1685,7 +1636,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}relation\ {\isachardoublequoteopen}measure\ {\isacharparenleft}{\isasymlambda}n{\isachardot}\ n{\isacharparenright}{\isachardoublequoteclose}{\isacharparenright}\ {\isacharparenleft}auto\ simp{\isacharcolon}\ nz{\isacharunderscore}is{\isacharunderscore}zero{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}relation\ {\isaliteral{22}{\isachardoublequoteopen}}measure\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}n{\isaliteral{2E}{\isachardot}}\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}auto\ simp{\isaliteral{3A}{\isacharcolon}}\ nz{\isaliteral{5F}{\isacharunderscore}}is{\isaliteral{5F}{\isacharunderscore}}zero{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1708,9 +1659,9 @@
\isabellestyle{it}
\isastyle\isamarkuptrue
\isacommand{function}\isamarkupfalse%
-\ f{\isadigit{9}}{\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\isanewline
+\ f{\isadigit{9}}{\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}f{\isadigit{9}}{\isadigit{1}}\ n\ {\isacharequal}\ {\isacharparenleft}if\ {\isadigit{1}}{\isadigit{0}}{\isadigit{0}}\ {\isacharless}\ n\ then\ n\ {\isacharminus}\ {\isadigit{1}}{\isadigit{0}}\ else\ f{\isadigit{9}}{\isadigit{1}}\ {\isacharparenleft}f{\isadigit{9}}{\isadigit{1}}\ {\isacharparenleft}n\ {\isacharplus}\ {\isadigit{1}}{\isadigit{1}}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}f{\isadigit{9}}{\isadigit{1}}\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ {\isadigit{1}}{\isadigit{0}}{\isadigit{0}}\ {\isaliteral{3C}{\isacharless}}\ n\ then\ n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isadigit{0}}\ else\ f{\isadigit{9}}{\isadigit{1}}\ {\isaliteral{28}{\isacharparenleft}}f{\isadigit{9}}{\isadigit{1}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1718,7 +1669,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ pat{\isacharunderscore}completeness\ auto%
+\ pat{\isaliteral{5F}{\isacharunderscore}}completeness\ auto%
\endisatagproof
{\isafoldproof}%
%
@@ -1728,9 +1679,9 @@
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ f{\isadigit{9}}{\isadigit{1}}{\isacharunderscore}estimate{\isacharcolon}\ \isanewline
-\ \ \isakeyword{assumes}\ trm{\isacharcolon}\ {\isachardoublequoteopen}f{\isadigit{9}}{\isadigit{1}}{\isacharunderscore}dom\ n{\isachardoublequoteclose}\ \isanewline
-\ \ \isakeyword{shows}\ {\isachardoublequoteopen}n\ {\isacharless}\ f{\isadigit{9}}{\isadigit{1}}\ n\ {\isacharplus}\ {\isadigit{1}}{\isadigit{1}}{\isachardoublequoteclose}\isanewline
+\ f{\isadigit{9}}{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}estimate{\isaliteral{3A}{\isacharcolon}}\ \isanewline
+\ \ \isakeyword{assumes}\ trm{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}f{\isadigit{9}}{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}dom\ n{\isaliteral{22}{\isachardoublequoteclose}}\ \isanewline
+\ \ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}n\ {\isaliteral{3C}{\isacharless}}\ f{\isadigit{9}}{\isadigit{1}}\ n\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1739,7 +1690,7 @@
\isatagproof
\isacommand{using}\isamarkupfalse%
\ trm\ \isacommand{by}\isamarkupfalse%
-\ induct\ auto%
+\ induct\ {\isaliteral{28}{\isacharparenleft}}auto\ simp{\isaliteral{3A}{\isacharcolon}}\ f{\isadigit{9}}{\isadigit{1}}{\isaliteral{2E}{\isachardot}}psimps{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1759,37 +1710,37 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{let}\isamarkupfalse%
-\ {\isacharquery}R\ {\isacharequal}\ {\isachardoublequoteopen}measure\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ {\isadigit{1}}{\isadigit{0}}{\isadigit{1}}\ {\isacharminus}\ x{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{3F}{\isacharquery}}R\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequoteopen}}measure\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ {\isadigit{1}}{\isadigit{0}}{\isadigit{1}}\ {\isaliteral{2D}{\isacharminus}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}wf\ {\isacharquery}R{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}wf\ {\isaliteral{3F}{\isacharquery}}R{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
-\ n\ {\isacharcolon}{\isacharcolon}\ nat\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymnot}\ {\isadigit{1}}{\isadigit{0}}{\isadigit{0}}\ {\isacharless}\ n{\isachardoublequoteclose}\ %
+\ n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat\ \isacommand{assume}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isadigit{1}}{\isadigit{0}}{\isadigit{0}}\ {\isaliteral{3C}{\isacharless}}\ n{\isaliteral{22}{\isachardoublequoteclose}}\ %
\isamarkupcmt{Assumptions for both calls%
}
\isanewline
\isanewline
\ \ \isacommand{thus}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}n\ {\isacharplus}\ {\isadigit{1}}{\isadigit{1}}{\isacharcomma}\ n{\isacharparenright}\ {\isasymin}\ {\isacharquery}R{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{3F}{\isacharquery}}R{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\ %
\isamarkupcmt{Inner call%
}
\isanewline
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ inner{\isacharunderscore}trm{\isacharcolon}\ {\isachardoublequoteopen}f{\isadigit{9}}{\isadigit{1}}{\isacharunderscore}dom\ {\isacharparenleft}n\ {\isacharplus}\ {\isadigit{1}}{\isadigit{1}}{\isacharparenright}{\isachardoublequoteclose}\ %
+\ inner{\isaliteral{5F}{\isacharunderscore}}trm{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}f{\isadigit{9}}{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}dom\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ %
\isamarkupcmt{Outer call%
}
\isanewline
\ \ \isacommand{with}\isamarkupfalse%
-\ f{\isadigit{9}}{\isadigit{1}}{\isacharunderscore}estimate\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}n\ {\isacharplus}\ {\isadigit{1}}{\isadigit{1}}\ {\isacharless}\ f{\isadigit{9}}{\isadigit{1}}\ {\isacharparenleft}n\ {\isacharplus}\ {\isadigit{1}}{\isadigit{1}}{\isacharparenright}\ {\isacharplus}\ {\isadigit{1}}{\isadigit{1}}{\isachardoublequoteclose}\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ f{\isadigit{9}}{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}estimate\ \isacommand{have}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}n\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isadigit{1}}\ {\isaliteral{3C}{\isacharless}}\ f{\isadigit{9}}{\isadigit{1}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{with}\isamarkupfalse%
-\ {\isacharbackquoteopen}{\isasymnot}\ {\isadigit{1}}{\isadigit{0}}{\isadigit{0}}\ {\isacharless}\ n{\isacharbackquoteclose}\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}f{\isadigit{9}}{\isadigit{1}}\ {\isacharparenleft}n\ {\isacharplus}\ {\isadigit{1}}{\isadigit{1}}{\isacharparenright}{\isacharcomma}\ n{\isacharparenright}\ {\isasymin}\ {\isacharquery}R{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isadigit{1}}{\isadigit{0}}{\isadigit{0}}\ {\isaliteral{3C}{\isacharless}}\ n{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}f{\isadigit{9}}{\isadigit{1}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{3F}{\isacharquery}}R{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -1817,19 +1768,19 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ {\isacharprime}a\ tree\ {\isacharequal}\ \isanewline
-\ \ Leaf\ {\isacharprime}a\ \isanewline
-{\isacharbar}\ Branch\ {\isachardoublequoteopen}{\isacharprime}a\ tree\ list{\isachardoublequoteclose}%
+\ {\isaliteral{27}{\isacharprime}}a\ tree\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
+\ \ Leaf\ {\isaliteral{27}{\isacharprime}}a\ \isanewline
+{\isaliteral{7C}{\isacharbar}}\ Branch\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ tree\ list{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent We can define a function which swaps the left and right subtrees recursively, using the
list functions \isa{rev} and \isa{map}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
-\ mirror\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ tree\ {\isasymRightarrow}\ {\isacharprime}a\ tree{\isachardoublequoteclose}\isanewline
+\ mirror\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ tree\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ tree{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}mirror\ {\isacharparenleft}Leaf\ n{\isacharparenright}\ {\isacharequal}\ Leaf\ n{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}mirror\ {\isacharparenleft}Branch\ l{\isacharparenright}\ {\isacharequal}\ Branch\ {\isacharparenleft}rev\ {\isacharparenleft}map\ mirror\ l{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}mirror\ {\isaliteral{28}{\isacharparenleft}}Leaf\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Leaf\ n{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}mirror\ {\isaliteral{28}{\isacharparenleft}}Branch\ l{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Branch\ {\isaliteral{28}{\isacharparenleft}}rev\ {\isaliteral{28}{\isacharparenleft}}map\ mirror\ l{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
Although the definition is accepted without problems, let us look at the termination proof:%
\end{isamarkuptext}%
@@ -1851,8 +1802,8 @@
subgoals
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ wf\ {\isacharquery}R\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}l\ x{\isachardot}\ x\ {\isasymin}\ set\ l\ {\isasymLongrightarrow}\ {\isacharparenleft}x{\isacharcomma}\ Branch\ l{\isacharparenright}\ {\isasymin}\ {\isacharquery}R%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ wf\ {\isaliteral{3F}{\isacharquery}}R\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}l\ x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ set\ l\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ Branch\ l{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{3F}{\isacharquery}}R%
\end{isabelle}
So the system seems to know that \isa{map} only
@@ -1864,7 +1815,7 @@
rule for \isa{map} is
\begin{isabelle}%
-{\isasymlbrakk}{\isacharquery}xs\ {\isacharequal}\ {\isacharquery}ys{\isacharsemicolon}\ {\isasymAnd}x{\isachardot}\ x\ {\isasymin}\ set\ {\isacharquery}ys\ {\isasymLongrightarrow}\ {\isacharquery}f\ x\ {\isacharequal}\ {\isacharquery}g\ x{\isasymrbrakk}\ {\isasymLongrightarrow}\ map\ {\isacharquery}f\ {\isacharquery}xs\ {\isacharequal}\ map\ {\isacharquery}g\ {\isacharquery}ys%
+{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{3F}{\isacharquery}}xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}ys{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ set\ {\isaliteral{3F}{\isacharquery}}ys\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}f\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}g\ x{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ map\ {\isaliteral{3F}{\isacharquery}}f\ {\isaliteral{3F}{\isacharquery}}xs\ {\isaliteral{3D}{\isacharequal}}\ map\ {\isaliteral{3F}{\isacharquery}}g\ {\isaliteral{3F}{\isacharquery}}ys%
\end{isabelle}
You can read this in the following way: Two applications of \isa{map} are equal, if the list arguments are equal and the functions
@@ -1880,12 +1831,12 @@
is false:
\begin{isabelle}%
-{\isasymlbrakk}{\isacharquery}b\ {\isacharequal}\ {\isacharquery}c{\isacharsemicolon}\ {\isacharquery}c\ {\isasymLongrightarrow}\ {\isacharquery}x\ {\isacharequal}\ {\isacharquery}u{\isacharsemicolon}\ {\isasymnot}\ {\isacharquery}c\ {\isasymLongrightarrow}\ {\isacharquery}y\ {\isacharequal}\ {\isacharquery}v{\isasymrbrakk}\isanewline
-{\isasymLongrightarrow}\ {\isacharparenleft}if\ {\isacharquery}b\ then\ {\isacharquery}x\ else\ {\isacharquery}y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}if\ {\isacharquery}c\ then\ {\isacharquery}u\ else\ {\isacharquery}v{\isacharparenright}%
+{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{3F}{\isacharquery}}b\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}c{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{3F}{\isacharquery}}c\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}u{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{3F}{\isacharquery}}c\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}v{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}if\ {\isaliteral{3F}{\isacharquery}}b\ then\ {\isaliteral{3F}{\isacharquery}}x\ else\ {\isaliteral{3F}{\isacharquery}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ {\isaliteral{3F}{\isacharquery}}c\ then\ {\isaliteral{3F}{\isacharquery}}u\ else\ {\isaliteral{3F}{\isacharquery}}v{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
Congruence rules can be added to the
- function package by giving them the \isa{fundef{\isacharunderscore}cong} attribute.
+ function package by giving them the \isa{fundef{\isaliteral{5F}{\isacharunderscore}}cong} attribute.
The constructs that are predefined in Isabelle, usually
come with the respective congruence rules.
@@ -1921,9 +1872,9 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{function}\isamarkupfalse%
-\ f\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
+\ f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}f\ n\ {\isacharequal}\ {\isacharparenleft}n\ {\isacharequal}\ {\isadigit{0}}\ {\isasymor}\ f\ {\isacharparenleft}n\ {\isacharminus}\ {\isadigit{1}}{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}f\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ f\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -1943,7 +1894,7 @@
congruence rule that specifies left-to-right evaluation order:
\vspace{1ex}
- \noindent \isa{{\isasymlbrakk}{\isacharquery}P\ {\isacharequal}\ {\isacharquery}P{\isacharprime}{\isacharsemicolon}\ {\isasymnot}\ {\isacharquery}P{\isacharprime}\ {\isasymLongrightarrow}\ {\isacharquery}Q\ {\isacharequal}\ {\isacharquery}Q{\isacharprime}{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isacharquery}P\ {\isasymor}\ {\isacharquery}Q{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isacharquery}P{\isacharprime}\ {\isasymor}\ {\isacharquery}Q{\isacharprime}{\isacharparenright}}\hfill(\isa{disj{\isacharunderscore}cong})
+ \noindent \isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}P{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{3F}{\isacharquery}}P{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}Q\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}Q{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{3F}{\isacharquery}}Q{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}P{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{3F}{\isacharquery}}Q{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}}\hfill(\isa{disj{\isaliteral{5F}{\isacharunderscore}}cong})
\vspace{1ex}
Now the definition works without problems. Note how the termination
@@ -1956,8 +1907,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ disj{\isacharunderscore}cong{\isadigit{2}}{\isacharbrackleft}fundef{\isacharunderscore}cong{\isacharbrackright}{\isacharcolon}\ \isanewline
-\ \ {\isachardoublequoteopen}{\isacharparenleft}{\isasymnot}\ Q{\isacharprime}\ {\isasymLongrightarrow}\ P\ {\isacharequal}\ P{\isacharprime}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}Q\ {\isacharequal}\ Q{\isacharprime}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}P\ {\isasymor}\ Q{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}P{\isacharprime}\ {\isasymor}\ Q{\isacharprime}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ disj{\isaliteral{5F}{\isacharunderscore}}cong{\isadigit{2}}{\isaliteral{5B}{\isacharbrackleft}}fundef{\isaliteral{5F}{\isacharunderscore}}cong{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ \isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ Q{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ {\isaliteral{3D}{\isacharequal}}\ P{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}Q\ {\isaliteral{3D}{\isacharequal}}\ Q{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}P\ {\isaliteral{5C3C6F723E}{\isasymor}}\ Q{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}P{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ Q{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -1975,9 +1926,9 @@
\endisadelimproof
\isanewline
\isacommand{fun}\isamarkupfalse%
-\ f{\isacharprime}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
+\ f{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}f{\isacharprime}\ n\ {\isacharequal}\ {\isacharparenleft}f{\isacharprime}\ {\isacharparenleft}n\ {\isacharminus}\ {\isadigit{1}}{\isacharparenright}\ {\isasymor}\ n\ {\isacharequal}\ {\isadigit{0}}{\isacharparenright}{\isachardoublequoteclose}%
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}f{\isaliteral{27}{\isacharprime}}\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}f{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent These examples show that, in general, there is no \qt{best} set of
congruence rules.
--- a/doc-src/IsarImplementation/Thy/document/Base.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarImplementation/Thy/document/Base.tex Mon Nov 08 14:41:11 2010 +0100
@@ -10,7 +10,7 @@
\isacommand{theory}\isamarkupfalse%
\ Base\isanewline
\isakeyword{imports}\ Main\isanewline
-\isakeyword{uses}\ {\isachardoublequoteopen}{\isachardot}{\isachardot}{\isacharslash}{\isachardot}{\isachardot}{\isacharslash}antiquote{\isacharunderscore}setup{\isachardot}ML{\isachardoublequoteclose}\isanewline
+\isakeyword{uses}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2F}{\isacharslash}}antiquote{\isaliteral{5F}{\isacharunderscore}}setup{\isaliteral{2E}{\isachardot}}ML{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{end}\isamarkupfalse%
--- a/doc-src/IsarImplementation/Thy/document/Integration.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarImplementation/Thy/document/Integration.tex Mon Nov 08 14:41:11 2010 +0100
@@ -54,14 +54,14 @@
The toplevel state is a disjoint sum of empty \isa{toplevel}, or
\isa{theory}, or \isa{proof}. On entering the main Isar loop we
start with an empty toplevel. A theory is commenced by giving a
- \isa{{\isasymTHEORY}} header; within a theory we may issue theory
- commands such as \isa{{\isasymDEFINITION}}, or state a \isa{{\isasymTHEOREM}} to be proven. Now we are within a proof state, with a
+ \isa{{\isaliteral{5C3C5448454F52593E}{\isasymTHEORY}}} header; within a theory we may issue theory
+ commands such as \isa{{\isaliteral{5C3C444546494E4954494F4E3E}{\isasymDEFINITION}}}, or state a \isa{{\isaliteral{5C3C5448454F52454D3E}{\isasymTHEOREM}}} to be proven. Now we are within a proof state, with a
rich collection of Isar proof commands for structured proof
composition, or unstructured proof scripts. When the proof is
concluded we get back to the theory, which is then updated by
storing the resulting fact. Further theory declarations or theorem
statements with proofs may follow, until we eventually conclude the
- theory development by issuing \isa{{\isasymEND}}. The resulting theory
+ theory development by issuing \isa{{\isaliteral{5C3C454E443E}{\isasymEND}}}. The resulting theory
is then stored within the theory database and we are back to the
empty toplevel.
@@ -121,7 +121,7 @@
\item \verb|Toplevel.profiling|~\verb|:=|~\isa{n} controls
low-level profiling of the underlying ML runtime system. For
- Poly/ML, \isa{n\ {\isacharequal}\ {\isadigit{1}}} means time and \isa{n\ {\isacharequal}\ {\isadigit{2}}} space
+ Poly/ML, \isa{n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}} means time and \isa{n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{2}}} space
profiling.
\end{description}%
@@ -143,15 +143,15 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{ML antiquotation}{Isar.state}\hypertarget{ML antiquotation.Isar.state}{\hyperlink{ML antiquotation.Isar.state}{\mbox{\isa{Isar{\isachardot}state}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
+ \indexdef{}{ML antiquotation}{Isar.state}\hypertarget{ML antiquotation.Isar.state}{\hyperlink{ML antiquotation.Isar.state}{\mbox{\isa{Isar{\isaliteral{2E}{\isachardot}}state}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
\end{matharray}
\begin{description}
- \item \isa{{\isacharat}{\isacharbraceleft}Isar{\isachardot}state{\isacharbraceright}} refers to Isar toplevel state at that
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}Isar{\isaliteral{2E}{\isachardot}}state{\isaliteral{7D}{\isacharbraceright}}} refers to Isar toplevel state at that
point --- as abstract value.
- This only works for diagnostic ML commands, such as \hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isacharunderscore}val}}}} or \hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isacharunderscore}command}}}}.
+ This only works for diagnostic ML commands, such as \hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}}}} or \hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}command}}}}.
\end{description}%
\end{isamarkuptext}%
@@ -279,7 +279,7 @@
Theory \isa{A} is associated with the main theory file \isa{A}\verb,.thy,, which needs to be accessible through the theory
loader path. Any number of additional ML source files may be
associated with each theory, by declaring these dependencies in the
- theory header as \isa{{\isasymUSES}}, and loading them consecutively
+ theory header as \isa{{\isaliteral{5C3C555345533E}{\isasymUSES}}}, and loading them consecutively
within the theory context. The system keeps track of incoming ML
sources and associates them with the current theory.
@@ -306,8 +306,8 @@
\medskip There are separate user-level interfaces to operate on the
theory database directly or indirectly. The primitive actions then
just happen automatically while working with the system. In
- particular, processing a theory header \isa{{\isasymTHEORY}\ A\ {\isasymIMPORTS}\ B\isactrlsub {\isadigit{1}}\ {\isasymdots}\ B\isactrlsub n\ {\isasymBEGIN}} ensures that the
- sub-graph of the collective imports \isa{B\isactrlsub {\isadigit{1}}\ {\isasymdots}\ B\isactrlsub n}
+ particular, processing a theory header \isa{{\isaliteral{5C3C5448454F52593E}{\isasymTHEORY}}\ A\ {\isaliteral{5C3C494D504F5254533E}{\isasymIMPORTS}}\ B\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ B\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C424547494E3E}{\isasymBEGIN}}} ensures that the
+ sub-graph of the collective imports \isa{B\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ B\isaliteral{5C3C5E7375623E}{}\isactrlsub n}
is up-to-date, too. Earlier theories are reloaded as required, with
\isa{update} actions proceeding in topological order according to
theory dependencies. There may be also a wave of implied \isa{remove} actions for derived theory nodes until a stable situation
--- a/doc-src/IsarImplementation/Thy/document/Isar.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarImplementation/Thy/document/Isar.tex Mon Nov 08 14:41:11 2010 +0100
@@ -120,7 +120,7 @@
defined by the proof method that is applied in that situation.
\item \verb|Proof.assert_forward|, \verb|Proof.assert_chain|, \verb|Proof.assert_backward| are partial identity functions that fail
- unless a certain linguistic mode is active, namely ``\isa{proof{\isacharparenleft}state{\isacharparenright}}'', ``\isa{proof{\isacharparenleft}chain{\isacharparenright}}'', ``\isa{proof{\isacharparenleft}prove{\isacharparenright}}'', respectively (using the terminology of
+ unless a certain linguistic mode is active, namely ``\isa{proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}}'', ``\isa{proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}}'', ``\isa{proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}}'', respectively (using the terminology of
\cite{isabelle-isar-ref}).
It is advisable study the implementations of existing proof commands
@@ -143,14 +143,14 @@
for dignostic tools; \verb|Proof.simple_goal| or \verb|Proof.goal|
should be used in most situations.
- \item \verb|Proof.theorem|~\isa{before{\isacharunderscore}qed\ after{\isacharunderscore}qed\ statement\ ctxt}
+ \item \verb|Proof.theorem|~\isa{before{\isaliteral{5F}{\isacharunderscore}}qed\ after{\isaliteral{5F}{\isacharunderscore}}qed\ statement\ ctxt}
initializes a toplevel Isar proof state within a given context.
- The optional \isa{before{\isacharunderscore}qed} method is applied at the end of
+ The optional \isa{before{\isaliteral{5F}{\isacharunderscore}}qed} method is applied at the end of
the proof, just before extracting the result (this feature is rarely
used).
- The \isa{after{\isacharunderscore}qed} continuation receives the extracted result
+ The \isa{after{\isaliteral{5F}{\isacharunderscore}}qed} continuation receives the extracted result
in order to apply it to the final context in a suitable way (e.g.\
storing named facts). Note that at this generic level the target
context is specified as \verb|Proof.context|, but the usual
@@ -161,7 +161,7 @@
The \isa{statement} is given as a nested list of terms, each
associated with optional \hyperlink{keyword.is}{\mbox{\isa{\isakeyword{is}}}} patterns as usual in the
Isar source language. The original nested list structure over terms
- is turned into one over theorems when \isa{after{\isacharunderscore}qed} is
+ is turned into one over theorems when \isa{after{\isaliteral{5F}{\isacharunderscore}}qed} is
invoked.
\end{description}%
@@ -183,16 +183,16 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{ML antiquotation}{Isar.goal}\hypertarget{ML antiquotation.Isar.goal}{\hyperlink{ML antiquotation.Isar.goal}{\mbox{\isa{Isar{\isachardot}goal}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
+ \indexdef{}{ML antiquotation}{Isar.goal}\hypertarget{ML antiquotation.Isar.goal}{\hyperlink{ML antiquotation.Isar.goal}{\mbox{\isa{Isar{\isaliteral{2E}{\isachardot}}goal}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
\end{matharray}
\begin{description}
- \item \isa{{\isacharat}{\isacharbraceleft}Isar{\isachardot}goal{\isacharbraceright}} refers to the regular goal state (if
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}Isar{\isaliteral{2E}{\isachardot}}goal{\isaliteral{7D}{\isacharbraceright}}} refers to the regular goal state (if
available) of the current proof state managed by the Isar toplevel
--- as abstract value.
- This only works for diagnostic ML commands, such as \hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isacharunderscore}val}}}} or \hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isacharunderscore}command}}}}.
+ This only works for diagnostic ML commands, such as \hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}}}} or \hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}command}}}}.
\end{description}%
\end{isamarkuptext}%
@@ -222,7 +222,7 @@
\isadelimmlex
%
\endisadelimmlex
-\isacommand{example{\isacharunderscore}proof}\isamarkupfalse%
+\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}\isamarkupfalse%
\isanewline
%
\isadelimproof
@@ -245,19 +245,19 @@
\endisadelimML
%
\isatagML
-\isacommand{ML{\isacharunderscore}val}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ \ \ \ \ val\ n\ {\isacharequal}\ Thm{\isachardot}nprems{\isacharunderscore}of\ {\isacharparenleft}{\isacharhash}goal\ %
+\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ \ \ \ \ val\ n\ {\isaliteral{3D}{\isacharequal}}\ Thm{\isaliteral{2E}{\isachardot}}nprems{\isaliteral{5F}{\isacharunderscore}}of\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{23}{\isacharhash}}goal\ %
\isaantiq
-Isar{\isachardot}goal%
+Isar{\isaliteral{2E}{\isachardot}}goal{}%
\endisaantiq
-{\isacharparenright}{\isacharsemicolon}\isanewline
+{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\ \ \ \ \ \ %
\isaantiq
-assert%
+assert{}%
\endisaantiq
-\ {\isacharparenleft}n\ {\isacharequal}\ {\isadigit{3}}{\isacharparenright}{\isacharsemicolon}\isanewline
-\ \ \ \ {\isacharverbatimclose}%
+\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{3}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ {\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -291,7 +291,7 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-A \isa{method} is a function \isa{context\ {\isasymrightarrow}\ thm\isactrlsup {\isacharasterisk}\ {\isasymrightarrow}\ goal\ {\isasymrightarrow}\ {\isacharparenleft}cases\ {\isasymtimes}\ goal{\isacharparenright}\isactrlsup {\isacharasterisk}\isactrlsup {\isacharasterisk}} that operates on the full Isar goal
+A \isa{method} is a function \isa{context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ thm\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ goal\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}cases\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ goal{\isaliteral{29}{\isacharparenright}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}} that operates on the full Isar goal
configuration with context, goal facts, and tactical goal state and
enumerates possible follow-up goal states, with the potential
addition of named extensions of the proof context (\emph{cases}).
@@ -309,15 +309,15 @@
\emph{first} subgoal.
Exception: old-style tactic emulations that are embedded into the
- method space, e.g.\ \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isacharunderscore}tac}}}.
+ method space, e.g.\ \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}tac}}}.
\item A non-trivial method always needs to make progress: an
identical follow-up goal state has to be avoided.\footnote{This
- enables the user to write method expressions like \isa{meth\isactrlsup {\isacharplus}}
+ enables the user to write method expressions like \isa{meth\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2B}{\isacharplus}}}
without looping, while the trivial do-nothing case can be recovered
- via \isa{meth\isactrlsup {\isacharquery}}.}
+ via \isa{meth\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{3F}{\isacharquery}}}.}
- Exception: trivial stuttering steps, such as ``\hyperlink{method.-}{\mbox{\isa{{\isacharminus}}}}'' or
+ Exception: trivial stuttering steps, such as ``\hyperlink{method.-}{\mbox{\isa{{\isaliteral{2D}{\isacharminus}}}}}'' or
\hyperlink{method.succeed}{\mbox{\isa{succeed}}}.
\item Goal facts passed to the method must not be ignored. If there
@@ -330,7 +330,7 @@
arguments to Isar commands like \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}} or \hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}.
User-space additions are reasonably easy by plugging suitable
method-valued parser functions into the framework, using the
- \hyperlink{command.method-setup}{\mbox{\isa{\isacommand{method{\isacharunderscore}setup}}}} command, for example.
+ \hyperlink{command.method-setup}{\mbox{\isa{\isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}}}} command, for example.
To get a better idea about the range of possibilities, consider the
following Isar proof schemes. This is the general form of
@@ -338,17 +338,17 @@
\medskip
\begin{tabular}{l}
- \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{facts\isactrlsub {\isadigit{1}}}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{props}~\hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{facts\isactrlsub {\isadigit{2}}} \\
- \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isacharparenleft}initial{\isacharunderscore}method{\isacharparenright}} \\
+ \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{facts\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{props}~\hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{facts\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}} \\
+ \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{28}{\isacharparenleft}}initial{\isaliteral{5F}{\isacharunderscore}}method{\isaliteral{29}{\isacharparenright}}} \\
\quad\isa{body} \\
- \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isacharparenleft}terminal{\isacharunderscore}method{\isacharparenright}} \\
+ \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isaliteral{28}{\isacharparenleft}}terminal{\isaliteral{5F}{\isacharunderscore}}method{\isaliteral{29}{\isacharparenright}}} \\
\end{tabular}
\medskip
- The goal configuration consists of \isa{facts\isactrlsub {\isadigit{1}}} and
- \isa{facts\isactrlsub {\isadigit{2}}} appended in that order, and various \isa{props} being claimed. The \isa{initial{\isacharunderscore}method} is invoked
+ The goal configuration consists of \isa{facts\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}} and
+ \isa{facts\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}} appended in that order, and various \isa{props} being claimed. The \isa{initial{\isaliteral{5F}{\isacharunderscore}}method} is invoked
with facts and goals together and refines the problem to something
- that is handled recursively in the proof \isa{body}. The \isa{terminal{\isacharunderscore}method} has another chance to finish any remaining
+ that is handled recursively in the proof \isa{body}. The \isa{terminal{\isaliteral{5F}{\isacharunderscore}}method} has another chance to finish any remaining
subgoals, but it does not see the facts of the initial step.
\medskip This pattern illustrates unstructured proof scripts:
@@ -356,17 +356,17 @@
\medskip
\begin{tabular}{l}
\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{props} \\
- \quad\hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{facts\isactrlsub {\isadigit{1}}}~\hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}~\isa{method\isactrlsub {\isadigit{1}}} \\
- \quad\hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}~\isa{method\isactrlsub {\isadigit{2}}} \\
- \quad\hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{facts\isactrlsub {\isadigit{3}}}~\hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}~\isa{method\isactrlsub {\isadigit{3}}} \\
+ \quad\hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{facts\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}}~\hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}~\isa{method\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}} \\
+ \quad\hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}~\isa{method\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}} \\
+ \quad\hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{facts\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{3}}}~\hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}~\isa{method\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{3}}} \\
\quad\hyperlink{command.done}{\mbox{\isa{\isacommand{done}}}} \\
\end{tabular}
\medskip
- The \isa{method\isactrlsub {\isadigit{1}}} operates on the original claim while
- using \isa{facts\isactrlsub {\isadigit{1}}}. Since the \hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}} command
- structurally resets the facts, the \isa{method\isactrlsub {\isadigit{2}}} will
- operate on the remaining goal state without facts. The \isa{method\isactrlsub {\isadigit{3}}} will see again a collection of \isa{facts\isactrlsub {\isadigit{3}}} that has been inserted into the script explicitly.
+ The \isa{method\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}} operates on the original claim while
+ using \isa{facts\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}}. Since the \hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}} command
+ structurally resets the facts, the \isa{method\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}} will
+ operate on the remaining goal state without facts. The \isa{method\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{3}}} will see again a collection of \isa{facts\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{3}}} that has been inserted into the script explicitly.
\medskip Empirically, any Isar proof method can be categorized as
follows.
@@ -396,10 +396,10 @@
\item \emph{Old-style tactic emulation} with detailed numeric goal
addressing and explicit references to entities of the internal goal
state (which are otherwise invisible from proper Isar proof text).
- The naming convention \isa{foo{\isacharunderscore}tac} makes this special
+ The naming convention \isa{foo{\isaliteral{5F}{\isacharunderscore}}tac} makes this special
non-standard status clear.
- Example: \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isacharunderscore}tac}}}.
+ Example: \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}tac}}}.
\end{enumerate}
@@ -438,11 +438,11 @@
\item Type \verb|Proof.method| represents proof methods as
abstract type.
- \item \verb|METHOD_CASES|~\isa{{\isacharparenleft}fn\ facts\ {\isacharequal}{\isachargreater}\ cases{\isacharunderscore}tactic{\isacharparenright}} wraps
- \isa{cases{\isacharunderscore}tactic} depending on goal facts as proof method with
+ \item \verb|METHOD_CASES|~\isa{{\isaliteral{28}{\isacharparenleft}}fn\ facts\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ cases{\isaliteral{5F}{\isacharunderscore}}tactic{\isaliteral{29}{\isacharparenright}}} wraps
+ \isa{cases{\isaliteral{5F}{\isacharunderscore}}tactic} depending on goal facts as proof method with
cases; the goal context is passed via method syntax.
- \item \verb|METHOD|~\isa{{\isacharparenleft}fn\ facts\ {\isacharequal}{\isachargreater}\ tactic{\isacharparenright}} wraps \isa{tactic} depending on goal facts as regular proof method; the goal
+ \item \verb|METHOD|~\isa{{\isaliteral{28}{\isacharparenleft}}fn\ facts\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ tactic{\isaliteral{29}{\isacharparenright}}} wraps \isa{tactic} depending on goal facts as regular proof method; the goal
context is passed via method syntax.
\item \verb|SIMPLE_METHOD|~\isa{tactic} wraps a tactic that
@@ -463,7 +463,7 @@
within regular \verb|METHOD|, for example.
\item \verb|Method.setup|~\isa{name\ parser\ description} provides
- the functionality of the Isar command \hyperlink{command.method-setup}{\mbox{\isa{\isacommand{method{\isacharunderscore}setup}}}} as ML
+ the functionality of the Isar command \hyperlink{command.method-setup}{\mbox{\isa{\isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}}}} as ML
function.
\end{description}%
@@ -484,7 +484,7 @@
\isatagmlex
%
\begin{isamarkuptext}%
-See also \hyperlink{command.method-setup}{\mbox{\isa{\isacommand{method{\isacharunderscore}setup}}}} in
+See also \hyperlink{command.method-setup}{\mbox{\isa{\isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}}}} in
\cite{isabelle-isar-ref} which includes some abstract examples.
\medskip The following toy examples illustrate how the goal facts
@@ -500,7 +500,7 @@
\isadelimmlex
%
\endisadelimmlex
-\isacommand{example{\isacharunderscore}proof}\isamarkupfalse%
+\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}\isamarkupfalse%
\isanewline
%
\isadelimproof
@@ -509,27 +509,27 @@
%
\isatagproof
\isacommand{assume}\isamarkupfalse%
-\ a{\isacharcolon}\ A\ \isakeyword{and}\ b{\isacharcolon}\ B\isanewline
+\ a{\isaliteral{3A}{\isacharcolon}}\ A\ \isakeyword{and}\ b{\isaliteral{3A}{\isacharcolon}}\ B\isanewline
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymand}\ B{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ rtac\ %
+\ {\isaliteral{28}{\isacharparenleft}}tactic\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ rtac\ %
\isaantiq
-thm\ conjI%
+thm\ conjI{}%
\endisaantiq
-\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
+\ {\isadigit{1}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{using}\isamarkupfalse%
\ a\ \isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ resolve{\isacharunderscore}tac\ facts\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}tactic\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ resolve{\isaliteral{5F}{\isacharunderscore}}tac\ facts\ {\isadigit{1}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{using}\isamarkupfalse%
\ b\ \isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ resolve{\isacharunderscore}tac\ facts\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}tactic\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ resolve{\isaliteral{5F}{\isacharunderscore}}tac\ facts\ {\isadigit{1}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{done}\isamarkupfalse%
\isanewline
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymand}\ B{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{using}\isamarkupfalse%
\ a\ \isakeyword{and}\ b%
\endisatagproof
@@ -545,8 +545,8 @@
\endisadelimML
%
\isatagML
-\isacommand{ML{\isacharunderscore}val}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharat}{\isacharbraceleft}Isar{\isachardot}goal{\isacharbraceright}{\isachardoublequoteclose}%
+\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}Isar{\isaliteral{2E}{\isachardot}}goal{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagML
{\isafoldML}%
%
@@ -561,13 +561,13 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ Method{\isachardot}insert{\isacharunderscore}tac\ facts\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}tactic\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ Method{\isaliteral{2E}{\isachardot}}insert{\isaliteral{5F}{\isacharunderscore}}tac\ facts\ {\isadigit{1}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ {\isacharparenleft}rtac\ %
+\ {\isaliteral{28}{\isacharparenleft}}tactic\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ {\isaliteral{28}{\isacharparenleft}}rtac\ %
\isaantiq
-thm\ conjI%
+thm\ conjI{}%
\endisaantiq
-\ THEN{\isacharunderscore}ALL{\isacharunderscore}NEW\ atac{\isacharparenright}\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
+\ THEN{\isaliteral{5F}{\isacharunderscore}}ALL{\isaliteral{5F}{\isacharunderscore}}NEW\ atac{\isaliteral{29}{\isacharparenright}}\ {\isadigit{1}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{done}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
@@ -590,13 +590,13 @@
\endisadelimML
%
\isatagML
-\isacommand{method{\isacharunderscore}setup}\isamarkupfalse%
-\ my{\isacharunderscore}simp\ {\isacharequal}\ {\isacharverbatimopen}\isanewline
-\ \ Attrib{\isachardot}thms\ {\isachargreater}{\isachargreater}\ {\isacharparenleft}fn\ thms\ {\isacharequal}{\isachargreater}\ fn\ ctxt\ {\isacharequal}{\isachargreater}\isanewline
-\ \ \ \ SIMPLE{\isacharunderscore}METHOD{\isacharprime}\ {\isacharparenleft}fn\ i\ {\isacharequal}{\isachargreater}\isanewline
-\ \ \ \ \ \ CHANGED\ {\isacharparenleft}asm{\isacharunderscore}full{\isacharunderscore}simp{\isacharunderscore}tac\isanewline
-\ \ \ \ \ \ \ \ {\isacharparenleft}HOL{\isacharunderscore}basic{\isacharunderscore}ss\ addsimps\ thms{\isacharparenright}\ i{\isacharparenright}{\isacharparenright}{\isacharparenright}\isanewline
-{\isacharverbatimclose}\ {\isachardoublequoteopen}rewrite\ subgoal\ by\ given\ rules{\isachardoublequoteclose}%
+\isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}\isamarkupfalse%
+\ my{\isaliteral{5F}{\isacharunderscore}}simp\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ Attrib{\isaliteral{2E}{\isachardot}}thms\ {\isaliteral{3E}{\isachargreater}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}fn\ thms\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ fn\ ctxt\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline
+\ \ \ \ SIMPLE{\isaliteral{5F}{\isacharunderscore}}METHOD{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}fn\ i\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline
+\ \ \ \ \ \ CHANGED\ {\isaliteral{28}{\isacharparenleft}}asm{\isaliteral{5F}{\isacharunderscore}}full{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{5F}{\isacharunderscore}}tac\isanewline
+\ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}HOL{\isaliteral{5F}{\isacharunderscore}}basic{\isaliteral{5F}{\isacharunderscore}}ss\ addsimps\ thms{\isaliteral{29}{\isacharparenright}}\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}rewrite\ subgoal\ by\ given\ rules{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagML
{\isafoldML}%
%
@@ -605,7 +605,7 @@
\endisadelimML
%
\begin{isamarkuptext}%
-The concrete syntax wrapping of \hyperlink{command.method-setup}{\mbox{\isa{\isacommand{method{\isacharunderscore}setup}}}} always
+The concrete syntax wrapping of \hyperlink{command.method-setup}{\mbox{\isa{\isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}}}} always
passes-through the proof context at the end of parsing, but it is
not used in this example.
@@ -620,11 +620,11 @@
states are filtered out explicitly to make the raw tactic conform to
standard Isar method behaviour.
- \medskip Method \hyperlink{method.my-simp}{\mbox{\isa{my{\isacharunderscore}simp}}} can be used in Isar proofs like
+ \medskip Method \hyperlink{method.my-simp}{\mbox{\isa{my{\isaliteral{5F}{\isacharunderscore}}simp}}} can be used in Isar proofs like
this:%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{example{\isacharunderscore}proof}\isamarkupfalse%
+\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}\isamarkupfalse%
\isanewline
%
\isadelimproof
@@ -635,12 +635,12 @@
\isacommand{fix}\isamarkupfalse%
\ a\ b\ c\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ a{\isacharcolon}\ {\isachardoublequoteopen}a\ {\isacharequal}\ b{\isachardoublequoteclose}\isanewline
+\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}a\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ b{\isacharcolon}\ {\isachardoublequoteopen}b\ {\isacharequal}\ c{\isachardoublequoteclose}\isanewline
+\ b{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}b\ {\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}a\ {\isacharequal}\ c{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}my{\isacharunderscore}simp\ a\ b{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}a\ {\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}my{\isaliteral{5F}{\isacharunderscore}}simp\ a\ b{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
@@ -661,14 +661,14 @@
\endisadelimML
%
\isatagML
-\isacommand{method{\isacharunderscore}setup}\isamarkupfalse%
-\ my{\isacharunderscore}simp{\isacharunderscore}all\ {\isacharequal}\ {\isacharverbatimopen}\isanewline
-\ \ Attrib{\isachardot}thms\ {\isachargreater}{\isachargreater}\ {\isacharparenleft}fn\ thms\ {\isacharequal}{\isachargreater}\ fn\ ctxt\ {\isacharequal}{\isachargreater}\isanewline
-\ \ \ \ SIMPLE{\isacharunderscore}METHOD\isanewline
-\ \ \ \ \ \ {\isacharparenleft}CHANGED\isanewline
-\ \ \ \ \ \ \ \ {\isacharparenleft}ALLGOALS\ {\isacharparenleft}asm{\isacharunderscore}full{\isacharunderscore}simp{\isacharunderscore}tac\isanewline
-\ \ \ \ \ \ \ \ \ \ {\isacharparenleft}HOL{\isacharunderscore}basic{\isacharunderscore}ss\ addsimps\ thms{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}\isanewline
-{\isacharverbatimclose}\ {\isachardoublequoteopen}rewrite\ all\ subgoals\ by\ given\ rules{\isachardoublequoteclose}%
+\isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}\isamarkupfalse%
+\ my{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{5F}{\isacharunderscore}}all\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ Attrib{\isaliteral{2E}{\isachardot}}thms\ {\isaliteral{3E}{\isachargreater}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}fn\ thms\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ fn\ ctxt\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline
+\ \ \ \ SIMPLE{\isaliteral{5F}{\isacharunderscore}}METHOD\isanewline
+\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}CHANGED\isanewline
+\ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}ALLGOALS\ {\isaliteral{28}{\isacharparenleft}}asm{\isaliteral{5F}{\isacharunderscore}}full{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{5F}{\isacharunderscore}}tac\isanewline
+\ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}HOL{\isaliteral{5F}{\isacharunderscore}}basic{\isaliteral{5F}{\isacharunderscore}}ss\ addsimps\ thms{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}rewrite\ all\ subgoals\ by\ given\ rules{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagML
{\isafoldML}%
%
@@ -677,7 +677,7 @@
\endisadelimML
\isanewline
\isanewline
-\isacommand{example{\isacharunderscore}proof}\isamarkupfalse%
+\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}\isamarkupfalse%
\isanewline
%
\isadelimproof
@@ -688,12 +688,12 @@
\isacommand{fix}\isamarkupfalse%
\ a\ b\ c\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ a{\isacharcolon}\ {\isachardoublequoteopen}a\ {\isacharequal}\ b{\isachardoublequoteclose}\isanewline
+\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}a\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ b{\isacharcolon}\ {\isachardoublequoteopen}b\ {\isacharequal}\ c{\isachardoublequoteclose}\isanewline
+\ b{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}b\ {\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}a\ {\isacharequal}\ c{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}c\ {\isacharequal}\ b{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}my{\isacharunderscore}simp{\isacharunderscore}all\ a\ b{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}a\ {\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}c\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}my{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{5F}{\isacharunderscore}}all\ a\ b{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -708,7 +708,7 @@
\medskip Apart from explicit arguments, common proof methods
typically work with a default configuration provided by the context.
As a shortcut to rule management we use a cheap solution via functor
- \verb|Named_Thms| (see also \hyperlink{file.~~/src/Pure/Tools/named-thms.ML}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}Pure{\isacharslash}Tools{\isacharslash}named{\isacharunderscore}thms{\isachardot}ML}}}}).%
+ \verb|Named_Thms| (see also \hyperlink{file.~~/src/Pure/Tools/named-thms.ML}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}Pure{\isaliteral{2F}{\isacharslash}}Tools{\isaliteral{2F}{\isacharslash}}named{\isaliteral{5F}{\isacharunderscore}}thms{\isaliteral{2E}{\isachardot}}ML}}}}).%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -718,13 +718,13 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ structure\ My{\isacharunderscore}Simps\ {\isacharequal}\isanewline
-\ \ \ \ Named{\isacharunderscore}Thms\isanewline
-\ \ \ \ \ \ {\isacharparenleft}val\ name\ {\isacharequal}\ {\isachardoublequote}my{\isacharunderscore}simp{\isachardoublequote}\ val\ description\ {\isacharequal}\ {\isachardoublequote}my{\isacharunderscore}simp\ rule{\isachardoublequote}{\isacharparenright}\isanewline
-{\isacharverbatimclose}\isanewline
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ structure\ My{\isaliteral{5F}{\isacharunderscore}}Simps\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ Named{\isaliteral{5F}{\isacharunderscore}}Thms\isanewline
+\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}val\ name\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}my{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{22}{\isachardoublequote}}\ val\ description\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}my{\isaliteral{5F}{\isacharunderscore}}simp\ rule{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
\isacommand{setup}\isamarkupfalse%
-\ My{\isacharunderscore}Simps{\isachardot}setup%
+\ My{\isaliteral{5F}{\isacharunderscore}}Simps{\isaliteral{2E}{\isachardot}}setup%
\endisatagML
{\isafoldML}%
%
@@ -735,7 +735,7 @@
\begin{isamarkuptext}%
This provides ML access to a list of theorems in canonical
declaration order via \verb|My_Simps.get|. The user can add or
- delete rules via the attribute \hyperlink{attribute.my-simp}{\mbox{\isa{my{\isacharunderscore}simp}}}. The actual
+ delete rules via the attribute \hyperlink{attribute.my-simp}{\mbox{\isa{my{\isaliteral{5F}{\isacharunderscore}}simp}}}. The actual
proof method is now defined as before, but we append the explicit
arguments and the rules from the context.%
\end{isamarkuptext}%
@@ -746,13 +746,13 @@
\endisadelimML
%
\isatagML
-\isacommand{method{\isacharunderscore}setup}\isamarkupfalse%
-\ my{\isacharunderscore}simp{\isacharprime}\ {\isacharequal}\ {\isacharverbatimopen}\isanewline
-\ \ Attrib{\isachardot}thms\ {\isachargreater}{\isachargreater}\ {\isacharparenleft}fn\ thms\ {\isacharequal}{\isachargreater}\ fn\ ctxt\ {\isacharequal}{\isachargreater}\isanewline
-\ \ \ \ SIMPLE{\isacharunderscore}METHOD{\isacharprime}\ {\isacharparenleft}fn\ i\ {\isacharequal}{\isachargreater}\isanewline
-\ \ \ \ \ \ CHANGED\ {\isacharparenleft}asm{\isacharunderscore}full{\isacharunderscore}simp{\isacharunderscore}tac\isanewline
-\ \ \ \ \ \ \ \ {\isacharparenleft}HOL{\isacharunderscore}basic{\isacharunderscore}ss\ addsimps\ {\isacharparenleft}thms\ {\isacharat}\ My{\isacharunderscore}Simps{\isachardot}get\ ctxt{\isacharparenright}{\isacharparenright}\ i{\isacharparenright}{\isacharparenright}{\isacharparenright}\isanewline
-{\isacharverbatimclose}\ {\isachardoublequoteopen}rewrite\ subgoal\ by\ given\ rules\ and\ my{\isacharunderscore}simp\ rules\ from\ the\ context{\isachardoublequoteclose}%
+\isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}\isamarkupfalse%
+\ my{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ Attrib{\isaliteral{2E}{\isachardot}}thms\ {\isaliteral{3E}{\isachargreater}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}fn\ thms\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ fn\ ctxt\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline
+\ \ \ \ SIMPLE{\isaliteral{5F}{\isacharunderscore}}METHOD{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}fn\ i\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline
+\ \ \ \ \ \ CHANGED\ {\isaliteral{28}{\isacharparenleft}}asm{\isaliteral{5F}{\isacharunderscore}}full{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{5F}{\isacharunderscore}}tac\isanewline
+\ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}HOL{\isaliteral{5F}{\isacharunderscore}}basic{\isaliteral{5F}{\isacharunderscore}}ss\ addsimps\ {\isaliteral{28}{\isacharparenleft}}thms\ {\isaliteral{40}{\isacharat}}\ My{\isaliteral{5F}{\isacharunderscore}}Simps{\isaliteral{2E}{\isachardot}}get\ ctxt{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}rewrite\ subgoal\ by\ given\ rules\ and\ my{\isaliteral{5F}{\isacharunderscore}}simp\ rules\ from\ the\ context{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagML
{\isafoldML}%
%
@@ -761,11 +761,11 @@
\endisadelimML
%
\begin{isamarkuptext}%
-\medskip Method \hyperlink{method.my-simp'}{\mbox{\isa{my{\isacharunderscore}simp{\isacharprime}}}} can be used in Isar proofs
+\medskip Method \hyperlink{method.my-simp'}{\mbox{\isa{my{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{27}{\isacharprime}}}}} can be used in Isar proofs
like this:%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{example{\isacharunderscore}proof}\isamarkupfalse%
+\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}\isamarkupfalse%
\isanewline
%
\isadelimproof
@@ -776,12 +776,12 @@
\isacommand{fix}\isamarkupfalse%
\ a\ b\ c\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isacharbrackleft}my{\isacharunderscore}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}a\ {\isasymequiv}\ b{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}my{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}a\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ b{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isacharbrackleft}my{\isacharunderscore}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}b\ {\isasymequiv}\ c{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}my{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}b\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ c{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}a\ {\isasymequiv}\ c{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ my{\isacharunderscore}simp{\isacharprime}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}a\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ c{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ my{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{27}{\isacharprime}}\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
@@ -792,7 +792,7 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-\medskip The \hyperlink{method.my-simp}{\mbox{\isa{my{\isacharunderscore}simp}}} variants defined above are
+\medskip The \hyperlink{method.my-simp}{\mbox{\isa{my{\isaliteral{5F}{\isacharunderscore}}simp}}} variants defined above are
``simple'' methods, i.e.\ the goal facts are merely inserted as goal
premises by the \verb|SIMPLE_METHOD'| or \verb|SIMPLE_METHOD| wrapper.
For proof methods that are similar to the standard collection of
@@ -803,7 +803,7 @@
method arguments obtained via concrete syntax or the context does
not meet the requirement of ``strong emphasis on facts'' of regular
proof methods, because rewrite rules as used above can be easily
- ignored. A proof text ``\hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{foo}~\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{my{\isacharunderscore}simp}'' where \isa{foo} is not used would
+ ignored. A proof text ``\hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{foo}~\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{my{\isaliteral{5F}{\isacharunderscore}}simp}'' where \isa{foo} is not used would
deceive the reader.
\medskip The technical treatment of rules from the context requires
@@ -830,11 +830,11 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-An \emph{attribute} is a function \isa{context\ {\isasymtimes}\ thm\ {\isasymrightarrow}\ context\ {\isasymtimes}\ thm}, which means both a (generic) context and a theorem
+An \emph{attribute} is a function \isa{context\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ thm\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ context\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ thm}, which means both a (generic) context and a theorem
can be modified simultaneously. In practice this fully general form
is very rare, instead attributes are presented either as
- \emph{declaration attribute:} \isa{thm\ {\isasymrightarrow}\ context\ {\isasymrightarrow}\ context} or
- \emph{rule attribute:} \isa{context\ {\isasymrightarrow}\ thm\ {\isasymrightarrow}\ thm}.
+ \emph{declaration attribute:} \isa{thm\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ context} or
+ \emph{rule attribute:} \isa{context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ thm\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ thm}.
Attributes can have additional arguments via concrete syntax. There
is a collection of context-sensitive parsers for various logical
@@ -871,14 +871,14 @@
\item Type \verb|attribute| represents attributes as concrete
type alias.
- \item \verb|Thm.rule_attribute|~\isa{{\isacharparenleft}fn\ context\ {\isacharequal}{\isachargreater}\ rule{\isacharparenright}} wraps
+ \item \verb|Thm.rule_attribute|~\isa{{\isaliteral{28}{\isacharparenleft}}fn\ context\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ rule{\isaliteral{29}{\isacharparenright}}} wraps
a context-dependent rule (mapping on \verb|thm|) as attribute.
- \item \verb|Thm.declaration_attribute|~\isa{{\isacharparenleft}fn\ thm\ {\isacharequal}{\isachargreater}\ decl{\isacharparenright}}
+ \item \verb|Thm.declaration_attribute|~\isa{{\isaliteral{28}{\isacharparenleft}}fn\ thm\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ decl{\isaliteral{29}{\isacharparenright}}}
wraps a theorem-dependent declaration (mapping on \verb|Context.generic|) as attribute.
\item \verb|Attrib.setup|~\isa{name\ parser\ description} provides
- the functionality of the Isar command \hyperlink{command.attribute-setup}{\mbox{\isa{\isacommand{attribute{\isacharunderscore}setup}}}} as
+ the functionality of the Isar command \hyperlink{command.attribute-setup}{\mbox{\isa{\isacommand{attribute{\isaliteral{5F}{\isacharunderscore}}setup}}}} as
ML function.
\end{description}%
@@ -899,7 +899,7 @@
\isatagmlex
%
\begin{isamarkuptext}%
-See also \hyperlink{command.attribute-setup}{\mbox{\isa{\isacommand{attribute{\isacharunderscore}setup}}}} in
+See also \hyperlink{command.attribute-setup}{\mbox{\isa{\isacommand{attribute{\isaliteral{5F}{\isacharunderscore}}setup}}}} in
\cite{isabelle-isar-ref} which includes some abstract examples.%
\end{isamarkuptext}%
\isamarkuptrue%
--- a/doc-src/IsarImplementation/Thy/document/Local_Theory.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarImplementation/Thy/document/Local_Theory.tex Mon Nov 08 14:41:11 2010 +0100
@@ -1,6 +1,6 @@
%
\begin{isabellebody}%
-\def\isabellecontext{Local{\isacharunderscore}Theory}%
+\def\isabellecontext{Local{\isaliteral{5F}{\isacharunderscore}}Theory}%
%
\isadelimtheory
%
@@ -8,7 +8,7 @@
%
\isatagtheory
\isacommand{theory}\isamarkupfalse%
-\ Local{\isacharunderscore}Theory\isanewline
+\ Local{\isaliteral{5F}{\isacharunderscore}}Theory\isanewline
\isakeyword{imports}\ Base\isanewline
\isakeyword{begin}%
\endisatagtheory
@@ -31,11 +31,11 @@
context}.
The target is usually derived from the background theory by adding
- local \isa{{\isasymFIX}} and \isa{{\isasymASSUME}} elements, plus
+ local \isa{{\isaliteral{5C3C4649583E}{\isasymFIX}}} and \isa{{\isaliteral{5C3C415353554D453E}{\isasymASSUME}}} elements, plus
suitable modifications of non-logical context data (e.g.\ a special
type-checking discipline). Once initialized, the target is ready to
- absorb definitional primitives: \isa{{\isasymDEFINE}} for terms and
- \isa{{\isasymNOTE}} for theorems. Such definitions may get
+ absorb definitional primitives: \isa{{\isaliteral{5C3C444546494E453E}{\isasymDEFINE}}} for terms and
+ \isa{{\isaliteral{5C3C4E4F54453E}{\isasymNOTE}}} for theorems. Such definitions may get
transformed in a target-specific way, but the programming interface
hides such details.
@@ -59,13 +59,13 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-There are separate elements \isa{{\isasymDEFINE}\ c\ {\isasymequiv}\ t} for terms, and
- \isa{{\isasymNOTE}\ b\ {\isacharequal}\ thm} for theorems. Types are treated
+There are separate elements \isa{{\isaliteral{5C3C444546494E453E}{\isasymDEFINE}}\ c\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t} for terms, and
+ \isa{{\isaliteral{5C3C4E4F54453E}{\isasymNOTE}}\ b\ {\isaliteral{3D}{\isacharequal}}\ thm} for theorems. Types are treated
implicitly, according to Hindley-Milner discipline (cf.\
\secref{sec:variables}). These definitional primitives essentially
act like \isa{let}-bindings within a local context that may
already contain earlier \isa{let}-bindings and some initial
- \isa{{\isasymlambda}}-bindings. Thus we gain \emph{dependent definitions}
+ \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}}-bindings. Thus we gain \emph{dependent definitions}
that are relative to an initial axiomatic context. The following
diagram illustrates this idea of axiomatic elements versus
definitional elements:
@@ -73,28 +73,28 @@
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
- & \isa{{\isasymlambda}}-binding & \isa{let}-binding \\
+ & \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}}-binding & \isa{let}-binding \\
\hline
- types & fixed \isa{{\isasymalpha}} & arbitrary \isa{{\isasymbeta}} \\
- terms & \isa{{\isasymFIX}\ x\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}} & \isa{{\isasymDEFINE}\ c\ {\isasymequiv}\ t} \\
- theorems & \isa{{\isasymASSUME}\ a{\isacharcolon}\ A} & \isa{{\isasymNOTE}\ b\ {\isacharequal}\ \isactrlBG B\isactrlEN } \\
+ types & fixed \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}} & arbitrary \isa{{\isaliteral{5C3C626574613E}{\isasymbeta}}} \\
+ terms & \isa{{\isaliteral{5C3C4649583E}{\isasymFIX}}\ x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}} & \isa{{\isaliteral{5C3C444546494E453E}{\isasymDEFINE}}\ c\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t} \\
+ theorems & \isa{{\isaliteral{5C3C415353554D453E}{\isasymASSUME}}\ a{\isaliteral{3A}{\isacharcolon}}\ A} & \isa{{\isaliteral{5C3C4E4F54453E}{\isasymNOTE}}\ b\ {\isaliteral{3D}{\isacharequal}}\ \isaliteral{5C3C5E42473E}{}\isactrlBG B\isaliteral{5C3C5E454E3E}{}\isactrlEN } \\
\hline
\end{tabular}
\end{center}
- A user package merely needs to produce suitable \isa{{\isasymDEFINE}}
- and \isa{{\isasymNOTE}} elements according to the application. For
- example, a package for inductive definitions might first \isa{{\isasymDEFINE}} a certain predicate as some fixed-point construction,
- then \isa{{\isasymNOTE}} a proven result about monotonicity of the
+ A user package merely needs to produce suitable \isa{{\isaliteral{5C3C444546494E453E}{\isasymDEFINE}}}
+ and \isa{{\isaliteral{5C3C4E4F54453E}{\isasymNOTE}}} elements according to the application. For
+ example, a package for inductive definitions might first \isa{{\isaliteral{5C3C444546494E453E}{\isasymDEFINE}}} a certain predicate as some fixed-point construction,
+ then \isa{{\isaliteral{5C3C4E4F54453E}{\isasymNOTE}}} a proven result about monotonicity of the
functor involved here, and then produce further derived concepts via
- additional \isa{{\isasymDEFINE}} and \isa{{\isasymNOTE}} elements.
+ additional \isa{{\isaliteral{5C3C444546494E453E}{\isasymDEFINE}}} and \isa{{\isaliteral{5C3C4E4F54453E}{\isasymNOTE}}} elements.
- The cumulative sequence of \isa{{\isasymDEFINE}} and \isa{{\isasymNOTE}}
+ The cumulative sequence of \isa{{\isaliteral{5C3C444546494E453E}{\isasymDEFINE}}} and \isa{{\isaliteral{5C3C4E4F54453E}{\isasymNOTE}}}
produced at package runtime is managed by the local theory
infrastructure by means of an \emph{auxiliary context}. Thus the
system holds up the impression of working within a fully abstract
- situation with hypothetical entities: \isa{{\isasymDEFINE}\ c\ {\isasymequiv}\ t}
- always results in a literal fact \isa{\isactrlBG c\ {\isasymequiv}\ t\isactrlEN }, where
+ situation with hypothetical entities: \isa{{\isaliteral{5C3C444546494E453E}{\isasymDEFINE}}\ c\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t}
+ always results in a literal fact \isa{\isaliteral{5C3C5E42473E}{}\isactrlBG c\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t\isaliteral{5C3C5E454E3E}{}\isactrlEN }, where
\isa{c} is a fixed variable \isa{c}. The details about
global constants, name spaces etc. are handled internally.
@@ -107,7 +107,7 @@
When a definitional package is finished, the auxiliary context is
reset to the target context. The target now holds definitions for
- terms and theorems that stem from the hypothetical \isa{{\isasymDEFINE}} and \isa{{\isasymNOTE}} elements, transformed by the
+ terms and theorems that stem from the hypothetical \isa{{\isaliteral{5C3C444546494E453E}{\isasymDEFINE}}} and \isa{{\isaliteral{5C3C4E4F54453E}{\isasymNOTE}}} elements, transformed by the
particular target policy (see \cite[\S4--5]{Haftmann-Wenzel:2009}
for details).%
\end{isamarkuptext}%
@@ -135,8 +135,8 @@
Although this is merely an alias for \verb|Proof.context|, it is
semantically a subtype of the same: a \verb|local_theory| holds
target information as special context data. Subtyping means that
- any value \isa{lthy{\isacharcolon}}~\verb|local_theory| can be also used
- with operations on expecting a regular \isa{ctxt{\isacharcolon}}~\verb|Proof.context|.
+ any value \isa{lthy{\isaliteral{3A}{\isacharcolon}}}~\verb|local_theory| can be also used
+ with operations on expecting a regular \isa{ctxt{\isaliteral{3A}{\isacharcolon}}}~\verb|Proof.context|.
\item \verb|Named_Target.init|~\isa{name\ thy} initializes a local
theory derived from the given background theory. An empty name
@@ -146,7 +146,7 @@
experimentation --- normally the Isar toplevel already takes care to
initialize the local theory context.
- \item \verb|Local_Theory.define|~\isa{{\isacharparenleft}{\isacharparenleft}b{\isacharcomma}\ mx{\isacharparenright}{\isacharcomma}\ {\isacharparenleft}a{\isacharcomma}\ rhs{\isacharparenright}{\isacharparenright}\ lthy} defines a local entity according to the specification that is
+ \item \verb|Local_Theory.define|~\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}b{\isaliteral{2C}{\isacharcomma}}\ mx{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ rhs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ lthy} defines a local entity according to the specification that is
given relatively to the current \isa{lthy} context. In
particular the term of the RHS may refer to earlier local entities
from the auxiliary context, or hypothetical parameters from the
@@ -156,7 +156,7 @@
definition as a hypothetical fact.
Unless an explicit name binding is given for the RHS, the resulting
- fact will be called \isa{b{\isacharunderscore}def}. Any given attributes are
+ fact will be called \isa{b{\isaliteral{5F}{\isacharunderscore}}def}. Any given attributes are
applied to that same fact --- immediately in the auxiliary context
\emph{and} in any transformed versions stemming from target-specific
policies or any later interpretations of results from the target
@@ -165,7 +165,7 @@
declarations such as \hyperlink{attribute.simp}{\mbox{\isa{simp}}}, while non-trivial rules like
\hyperlink{attribute.simplified}{\mbox{\isa{simplified}}} are better avoided.
- \item \verb|Local_Theory.note|~\isa{{\isacharparenleft}a{\isacharcomma}\ ths{\isacharparenright}\ lthy} is
+ \item \verb|Local_Theory.note|~\isa{{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ ths{\isaliteral{29}{\isacharparenright}}\ lthy} is
analogous to \verb|Local_Theory.define|, but defines facts instead of
terms. There is also a slightly more general variant \verb|Local_Theory.notes| that defines several facts (with attribute
expressions) simultaneously.
--- a/doc-src/IsarImplementation/Thy/document/Logic.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarImplementation/Thy/document/Logic.tex Mon Nov 08 14:41:11 2010 +0100
@@ -25,20 +25,20 @@
\begin{isamarkuptext}%
The logical foundations of Isabelle/Isar are that of the Pure logic,
which has been introduced as a Natural Deduction framework in
- \cite{paulson700}. This is essentially the same logic as ``\isa{{\isasymlambda}HOL}'' in the more abstract setting of Pure Type Systems (PTS)
+ \cite{paulson700}. This is essentially the same logic as ``\isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}HOL}'' in the more abstract setting of Pure Type Systems (PTS)
\cite{Barendregt-Geuvers:2001}, although there are some key
differences in the specific treatment of simple types in
Isabelle/Pure.
Following type-theoretic parlance, the Pure logic consists of three
- levels of \isa{{\isasymlambda}}-calculus with corresponding arrows, \isa{{\isasymRightarrow}} for syntactic function space (terms depending on terms), \isa{{\isasymAnd}} for universal quantification (proofs depending on terms), and
- \isa{{\isasymLongrightarrow}} for implication (proofs depending on proofs).
+ levels of \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}}-calculus with corresponding arrows, \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} for syntactic function space (terms depending on terms), \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}} for universal quantification (proofs depending on terms), and
+ \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}} for implication (proofs depending on proofs).
Derivations are relative to a logical theory, which declares type
constructors, constants, and axioms. Theory declarations support
schematic polymorphism, which is strictly speaking outside the
logic.\footnote{This is the deeper logical reason, why the theory
- context \isa{{\isasymTheta}} is separate from the proof context \isa{{\isasymGamma}}
+ context \isa{{\isaliteral{5C3C54686574613E}{\isasymTheta}}} is separate from the proof context \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}}
of the core calculus: type constructors, term constants, and facts
(proof constants) may involve arbitrary type schemes, but the type
of a locally fixed term parameter is also fixed!}%
@@ -54,27 +54,27 @@
algebra; types are qualified by ordered type classes.
\medskip A \emph{type class} is an abstract syntactic entity
- declared in the theory context. The \emph{subclass relation} \isa{c\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlisub {\isadigit{2}}} is specified by stating an acyclic
+ declared in the theory context. The \emph{subclass relation} \isa{c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}} is specified by stating an acyclic
generating relation; the transitive closure is maintained
internally. The resulting relation is an ordering: reflexive,
transitive, and antisymmetric.
- A \emph{sort} is a list of type classes written as \isa{s\ {\isacharequal}\ {\isacharbraceleft}c\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlisub m{\isacharbraceright}}, it represents symbolic intersection. Notationally, the
+ A \emph{sort} is a list of type classes written as \isa{s\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E697375623E}{}\isactrlisub m{\isaliteral{7D}{\isacharbraceright}}}, it represents symbolic intersection. Notationally, the
curly braces are omitted for singleton intersections, i.e.\ any
- class \isa{c} may be read as a sort \isa{{\isacharbraceleft}c{\isacharbraceright}}. The ordering
+ class \isa{c} may be read as a sort \isa{{\isaliteral{7B}{\isacharbraceleft}}c{\isaliteral{7D}{\isacharbraceright}}}. The ordering
on type classes is extended to sorts according to the meaning of
- intersections: \isa{{\isacharbraceleft}c\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}\ c\isactrlisub m{\isacharbraceright}\ {\isasymsubseteq}\ {\isacharbraceleft}d\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ d\isactrlisub n{\isacharbraceright}} iff \isa{{\isasymforall}j{\isachardot}\ {\isasymexists}i{\isachardot}\ c\isactrlisub i\ {\isasymsubseteq}\ d\isactrlisub j}. The empty intersection \isa{{\isacharbraceleft}{\isacharbraceright}} refers to
+ intersections: \isa{{\isaliteral{7B}{\isacharbraceleft}}c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ c\isaliteral{5C3C5E697375623E}{}\isactrlisub m{\isaliteral{7D}{\isacharbraceright}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ {\isaliteral{7B}{\isacharbraceleft}}d\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ d\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{7D}{\isacharbraceright}}} iff \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}j{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}i{\isaliteral{2E}{\isachardot}}\ c\isaliteral{5C3C5E697375623E}{}\isactrlisub i\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ d\isaliteral{5C3C5E697375623E}{}\isactrlisub j}. The empty intersection \isa{{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{7D}{\isacharbraceright}}} refers to
the universal sort, which is the largest element wrt.\ the sort
- order. Thus \isa{{\isacharbraceleft}{\isacharbraceright}} represents the ``full sort'', not the
+ order. Thus \isa{{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{7D}{\isacharbraceright}}} represents the ``full sort'', not the
empty one! The intersection of all (finitely many) classes declared
in the current theory is the least element wrt.\ the sort ordering.
\medskip A \emph{fixed type variable} is a pair of a basic name
- (starting with a \isa{{\isacharprime}} character) and a sort constraint, e.g.\
- \isa{{\isacharparenleft}{\isacharprime}a{\isacharcomma}\ s{\isacharparenright}} which is usually printed as \isa{{\isasymalpha}\isactrlisub s}.
+ (starting with a \isa{{\isaliteral{27}{\isacharprime}}} character) and a sort constraint, e.g.\
+ \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ s{\isaliteral{29}{\isacharparenright}}} which is usually printed as \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub s}.
A \emph{schematic type variable} is a pair of an indexname and a
- sort constraint, e.g.\ \isa{{\isacharparenleft}{\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isadigit{0}}{\isacharparenright}{\isacharcomma}\ s{\isacharparenright}} which is usually
- printed as \isa{{\isacharquery}{\isasymalpha}\isactrlisub s}.
+ sort constraint, e.g.\ \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ s{\isaliteral{29}{\isacharparenright}}} which is usually
+ printed as \isa{{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub s}.
Note that \emph{all} syntactic components contribute to the identity
of type variables: basic name, index, and sort constraint. The core
@@ -82,38 +82,38 @@
as different, although the type-inference layer (which is outside
the core) rejects anything like that.
- A \emph{type constructor} \isa{{\isasymkappa}} is a \isa{k}-ary operator
+ A \emph{type constructor} \isa{{\isaliteral{5C3C6B617070613E}{\isasymkappa}}} is a \isa{k}-ary operator
on types declared in the theory. Type constructor application is
- written postfix as \isa{{\isacharparenleft}{\isasymalpha}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlisub k{\isacharparenright}{\isasymkappa}}. For
- \isa{k\ {\isacharequal}\ {\isadigit{0}}} the argument tuple is omitted, e.g.\ \isa{prop}
- instead of \isa{{\isacharparenleft}{\isacharparenright}prop}. For \isa{k\ {\isacharequal}\ {\isadigit{1}}} the parentheses
- are omitted, e.g.\ \isa{{\isasymalpha}\ list} instead of \isa{{\isacharparenleft}{\isasymalpha}{\isacharparenright}list}.
+ written postfix as \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub k{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C6B617070613E}{\isasymkappa}}}. For
+ \isa{k\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}} the argument tuple is omitted, e.g.\ \isa{prop}
+ instead of \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}prop}. For \isa{k\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}} the parentheses
+ are omitted, e.g.\ \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ list} instead of \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}list}.
Further notation is provided for specific constructors, notably the
- right-associative infix \isa{{\isasymalpha}\ {\isasymRightarrow}\ {\isasymbeta}} instead of \isa{{\isacharparenleft}{\isasymalpha}{\isacharcomma}\ {\isasymbeta}{\isacharparenright}fun}.
+ right-associative infix \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}} instead of \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{29}{\isacharparenright}}fun}.
The logical category \emph{type} is defined inductively over type
- variables and type constructors as follows: \isa{{\isasymtau}\ {\isacharequal}\ {\isasymalpha}\isactrlisub s\ {\isacharbar}\ {\isacharquery}{\isasymalpha}\isactrlisub s\ {\isacharbar}\ {\isacharparenleft}{\isasymtau}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymtau}\isactrlsub k{\isacharparenright}{\isasymkappa}}.
+ variables and type constructors as follows: \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub s\ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub s\ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C6B617070613E}{\isasymkappa}}}.
- A \emph{type abbreviation} is a syntactic definition \isa{{\isacharparenleft}\isactrlvec {\isasymalpha}{\isacharparenright}{\isasymkappa}\ {\isacharequal}\ {\isasymtau}} of an arbitrary type expression \isa{{\isasymtau}} over
- variables \isa{\isactrlvec {\isasymalpha}}. Type abbreviations appear as type
+ A \emph{type abbreviation} is a syntactic definition \isa{{\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C6B617070613E}{\isasymkappa}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}} of an arbitrary type expression \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} over
+ variables \isa{\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C616C7068613E}{\isasymalpha}}}. Type abbreviations appear as type
constructors in the syntax, but are expanded before entering the
logical core.
A \emph{type arity} declares the image behavior of a type
- constructor wrt.\ the algebra of sorts: \isa{{\isasymkappa}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}s\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s\isactrlisub k{\isacharparenright}s} means that \isa{{\isacharparenleft}{\isasymtau}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymtau}\isactrlisub k{\isacharparenright}{\isasymkappa}} is
- of sort \isa{s} if every argument type \isa{{\isasymtau}\isactrlisub i} is
- of sort \isa{s\isactrlisub i}. Arity declarations are implicitly
- completed, i.e.\ \isa{{\isasymkappa}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s{\isacharparenright}c} entails \isa{{\isasymkappa}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s{\isacharparenright}c{\isacharprime}} for any \isa{c{\isacharprime}\ {\isasymsupseteq}\ c}.
+ constructor wrt.\ the algebra of sorts: \isa{{\isaliteral{5C3C6B617070613E}{\isasymkappa}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}s\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ s\isaliteral{5C3C5E697375623E}{}\isactrlisub k{\isaliteral{29}{\isacharparenright}}s} means that \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub k{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C6B617070613E}{\isasymkappa}}} is
+ of sort \isa{s} if every argument type \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub i} is
+ of sort \isa{s\isaliteral{5C3C5E697375623E}{}\isactrlisub i}. Arity declarations are implicitly
+ completed, i.e.\ \isa{{\isaliteral{5C3C6B617070613E}{\isasymkappa}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec s{\isaliteral{29}{\isacharparenright}}c} entails \isa{{\isaliteral{5C3C6B617070613E}{\isasymkappa}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec s{\isaliteral{29}{\isacharparenright}}c{\isaliteral{27}{\isacharprime}}} for any \isa{c{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C73757073657465713E}{\isasymsupseteq}}\ c}.
\medskip The sort algebra is always maintained as \emph{coregular},
which means that type arities are consistent with the subclass
- relation: for any type constructor \isa{{\isasymkappa}}, and classes \isa{c\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlisub {\isadigit{2}}}, and arities \isa{{\isasymkappa}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s\isactrlisub {\isadigit{1}}{\isacharparenright}c\isactrlisub {\isadigit{1}}} and \isa{{\isasymkappa}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s\isactrlisub {\isadigit{2}}{\isacharparenright}c\isactrlisub {\isadigit{2}}} holds \isa{\isactrlvec s\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ \isactrlvec s\isactrlisub {\isadigit{2}}} component-wise.
+ relation: for any type constructor \isa{{\isaliteral{5C3C6B617070613E}{\isasymkappa}}}, and classes \isa{c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}, and arities \isa{{\isaliteral{5C3C6B617070613E}{\isasymkappa}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec s\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}} and \isa{{\isaliteral{5C3C6B617070613E}{\isasymkappa}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec s\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}} holds \isa{\isaliteral{5C3C5E7665633E}{}\isactrlvec s\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec s\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}} component-wise.
The key property of a coregular order-sorted algebra is that sort
constraints can be solved in a most general fashion: for each type
- constructor \isa{{\isasymkappa}} and sort \isa{s} there is a most general
- vector of argument sorts \isa{{\isacharparenleft}s\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s\isactrlisub k{\isacharparenright}} such
- that a type scheme \isa{{\isacharparenleft}{\isasymalpha}\isactrlbsub s\isactrlisub {\isadigit{1}}\isactrlesub {\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlbsub s\isactrlisub k\isactrlesub {\isacharparenright}{\isasymkappa}} is of sort \isa{s}.
+ constructor \isa{{\isaliteral{5C3C6B617070613E}{\isasymkappa}}} and sort \isa{s} there is a most general
+ vector of argument sorts \isa{{\isaliteral{28}{\isacharparenleft}}s\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ s\isaliteral{5C3C5E697375623E}{}\isactrlisub k{\isaliteral{29}{\isacharparenright}}} such
+ that a type scheme \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E627375623E}{}\isactrlbsub s\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\isaliteral{5C3C5E657375623E}{}\isactrlesub {\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E627375623E}{}\isactrlbsub s\isaliteral{5C3C5E697375623E}{}\isactrlisub k\isaliteral{5C3C5E657375623E}{}\isactrlesub {\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C6B617070613E}{\isasymkappa}}} is of sort \isa{s}.
Consequently, type unification has most general solutions (modulo
equivalence of sorts), so type-inference produces primary types as
expected \cite{nipkow-prehofer}.%
@@ -154,37 +154,37 @@
the empty class intersection, i.e.\ the ``full sort''.
\item Type \verb|arity| represents type arities. A triple
- \isa{{\isacharparenleft}{\isasymkappa}{\isacharcomma}\ \isactrlvec s{\isacharcomma}\ s{\isacharparenright}\ {\isacharcolon}\ arity} represents \isa{{\isasymkappa}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s{\isacharparenright}s} as described above.
+ \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6B617070613E}{\isasymkappa}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec s{\isaliteral{2C}{\isacharcomma}}\ s{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3A}{\isacharcolon}}\ arity} represents \isa{{\isaliteral{5C3C6B617070613E}{\isasymkappa}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec s{\isaliteral{29}{\isacharparenright}}s} as described above.
\item Type \verb|typ| represents types; this is a datatype with
constructors \verb|TFree|, \verb|TVar|, \verb|Type|.
- \item \verb|Term.map_atyps|~\isa{f\ {\isasymtau}} applies the mapping \isa{f} to all atomic types (\verb|TFree|, \verb|TVar|) occurring in
- \isa{{\isasymtau}}.
+ \item \verb|Term.map_atyps|~\isa{f\ {\isaliteral{5C3C7461753E}{\isasymtau}}} applies the mapping \isa{f} to all atomic types (\verb|TFree|, \verb|TVar|) occurring in
+ \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}}.
- \item \verb|Term.fold_atyps|~\isa{f\ {\isasymtau}} iterates the operation
- \isa{f} over all occurrences of atomic types (\verb|TFree|, \verb|TVar|) in \isa{{\isasymtau}}; the type structure is traversed from left to
+ \item \verb|Term.fold_atyps|~\isa{f\ {\isaliteral{5C3C7461753E}{\isasymtau}}} iterates the operation
+ \isa{f} over all occurrences of atomic types (\verb|TFree|, \verb|TVar|) in \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}}; the type structure is traversed from left to
right.
- \item \verb|Sign.subsort|~\isa{thy\ {\isacharparenleft}s\isactrlisub {\isadigit{1}}{\isacharcomma}\ s\isactrlisub {\isadigit{2}}{\isacharparenright}}
- tests the subsort relation \isa{s\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ s\isactrlisub {\isadigit{2}}}.
+ \item \verb|Sign.subsort|~\isa{thy\ {\isaliteral{28}{\isacharparenleft}}s\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ s\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}}
+ tests the subsort relation \isa{s\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ s\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}.
- \item \verb|Sign.of_sort|~\isa{thy\ {\isacharparenleft}{\isasymtau}{\isacharcomma}\ s{\isacharparenright}} tests whether type
- \isa{{\isasymtau}} is of sort \isa{s}.
+ \item \verb|Sign.of_sort|~\isa{thy\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{2C}{\isacharcomma}}\ s{\isaliteral{29}{\isacharparenright}}} tests whether type
+ \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} is of sort \isa{s}.
- \item \verb|Sign.add_types|~\isa{{\isacharbrackleft}{\isacharparenleft}{\isasymkappa}{\isacharcomma}\ k{\isacharcomma}\ mx{\isacharparenright}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}} declares a new
- type constructors \isa{{\isasymkappa}} with \isa{k} arguments and
+ \item \verb|Sign.add_types|~\isa{{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6B617070613E}{\isasymkappa}}{\isaliteral{2C}{\isacharcomma}}\ k{\isaliteral{2C}{\isacharcomma}}\ mx{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5D}{\isacharbrackright}}} declares a new
+ type constructors \isa{{\isaliteral{5C3C6B617070613E}{\isasymkappa}}} with \isa{k} arguments and
optional mixfix syntax.
- \item \verb|Sign.add_type_abbrev|~\isa{{\isacharparenleft}{\isasymkappa}{\isacharcomma}\ \isactrlvec {\isasymalpha}{\isacharcomma}\ {\isasymtau}{\isacharparenright}} defines a new type abbreviation \isa{{\isacharparenleft}\isactrlvec {\isasymalpha}{\isacharparenright}{\isasymkappa}\ {\isacharequal}\ {\isasymtau}}.
+ \item \verb|Sign.add_type_abbrev|~\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6B617070613E}{\isasymkappa}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{29}{\isacharparenright}}} defines a new type abbreviation \isa{{\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C6B617070613E}{\isasymkappa}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}}.
- \item \verb|Sign.primitive_class|~\isa{{\isacharparenleft}c{\isacharcomma}\ {\isacharbrackleft}c\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlisub n{\isacharbrackright}{\isacharparenright}} declares a new class \isa{c}, together with class
- relations \isa{c\ {\isasymsubseteq}\ c\isactrlisub i}, for \isa{i\ {\isacharequal}\ {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ n}.
+ \item \verb|Sign.primitive_class|~\isa{{\isaliteral{28}{\isacharparenleft}}c{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}} declares a new class \isa{c}, together with class
+ relations \isa{c\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c\isaliteral{5C3C5E697375623E}{}\isactrlisub i}, for \isa{i\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ n}.
- \item \verb|Sign.primitive_classrel|~\isa{{\isacharparenleft}c\isactrlisub {\isadigit{1}}{\isacharcomma}\ c\isactrlisub {\isadigit{2}}{\isacharparenright}} declares the class relation \isa{c\isactrlisub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlisub {\isadigit{2}}}.
+ \item \verb|Sign.primitive_classrel|~\isa{{\isaliteral{28}{\isacharparenleft}}c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}} declares the class relation \isa{c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}.
- \item \verb|Sign.primitive_arity|~\isa{{\isacharparenleft}{\isasymkappa}{\isacharcomma}\ \isactrlvec s{\isacharcomma}\ s{\isacharparenright}} declares
- the arity \isa{{\isasymkappa}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s{\isacharparenright}s}.
+ \item \verb|Sign.primitive_arity|~\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6B617070613E}{\isasymkappa}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec s{\isaliteral{2C}{\isacharcomma}}\ s{\isaliteral{29}{\isacharparenright}}} declares
+ the arity \isa{{\isaliteral{5C3C6B617070613E}{\isasymkappa}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec s{\isaliteral{29}{\isacharparenright}}s}.
\end{description}%
\end{isamarkuptext}%
@@ -205,12 +205,12 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{ML antiquotation}{class}\hypertarget{ML antiquotation.class}{\hyperlink{ML antiquotation.class}{\mbox{\isa{class}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{sort}\hypertarget{ML antiquotation.sort}{\hyperlink{ML antiquotation.sort}{\mbox{\isa{sort}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{type\_name}\hypertarget{ML antiquotation.type-name}{\hyperlink{ML antiquotation.type-name}{\mbox{\isa{type{\isacharunderscore}name}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{type\_abbrev}\hypertarget{ML antiquotation.type-abbrev}{\hyperlink{ML antiquotation.type-abbrev}{\mbox{\isa{type{\isacharunderscore}abbrev}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{nonterminal}\hypertarget{ML antiquotation.nonterminal}{\hyperlink{ML antiquotation.nonterminal}{\mbox{\isa{nonterminal}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{typ}\hypertarget{ML antiquotation.typ}{\hyperlink{ML antiquotation.typ}{\mbox{\isa{typ}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
+ \indexdef{}{ML antiquotation}{class}\hypertarget{ML antiquotation.class}{\hyperlink{ML antiquotation.class}{\mbox{\isa{class}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{sort}\hypertarget{ML antiquotation.sort}{\hyperlink{ML antiquotation.sort}{\mbox{\isa{sort}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{type\_name}\hypertarget{ML antiquotation.type-name}{\hyperlink{ML antiquotation.type-name}{\mbox{\isa{type{\isaliteral{5F}{\isacharunderscore}}name}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{type\_abbrev}\hypertarget{ML antiquotation.type-abbrev}{\hyperlink{ML antiquotation.type-abbrev}{\mbox{\isa{type{\isaliteral{5F}{\isacharunderscore}}abbrev}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{nonterminal}\hypertarget{ML antiquotation.nonterminal}{\hyperlink{ML antiquotation.nonterminal}{\mbox{\isa{nonterminal}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{typ}\hypertarget{ML antiquotation.typ}{\hyperlink{ML antiquotation.typ}{\mbox{\isa{typ}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
\end{matharray}
\begin{rail}
@@ -226,22 +226,22 @@
\begin{description}
- \item \isa{{\isacharat}{\isacharbraceleft}class\ c{\isacharbraceright}} inlines the internalized class \isa{c} --- as \verb|string| literal.
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}class\ c{\isaliteral{7D}{\isacharbraceright}}} inlines the internalized class \isa{c} --- as \verb|string| literal.
- \item \isa{{\isacharat}{\isacharbraceleft}sort\ s{\isacharbraceright}} inlines the internalized sort \isa{s}
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}sort\ s{\isaliteral{7D}{\isacharbraceright}}} inlines the internalized sort \isa{s}
--- as \verb|string list| literal.
- \item \isa{{\isacharat}{\isacharbraceleft}type{\isacharunderscore}name\ c{\isacharbraceright}} inlines the internalized type
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}type{\isaliteral{5F}{\isacharunderscore}}name\ c{\isaliteral{7D}{\isacharbraceright}}} inlines the internalized type
constructor \isa{c} --- as \verb|string| literal.
- \item \isa{{\isacharat}{\isacharbraceleft}type{\isacharunderscore}abbrev\ c{\isacharbraceright}} inlines the internalized type
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}type{\isaliteral{5F}{\isacharunderscore}}abbrev\ c{\isaliteral{7D}{\isacharbraceright}}} inlines the internalized type
abbreviation \isa{c} --- as \verb|string| literal.
- \item \isa{{\isacharat}{\isacharbraceleft}nonterminal\ c{\isacharbraceright}} inlines the internalized syntactic
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}nonterminal\ c{\isaliteral{7D}{\isacharbraceright}}} inlines the internalized syntactic
type~/ grammar nonterminal \isa{c} --- as \verb|string|
literal.
- \item \isa{{\isacharat}{\isacharbraceleft}typ\ {\isasymtau}{\isacharbraceright}} inlines the internalized type \isa{{\isasymtau}}
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}typ\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{7D}{\isacharbraceright}}} inlines the internalized type \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}}
--- as constructor term for datatype \verb|typ|.
\end{description}%
@@ -260,7 +260,7 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-The language of terms is that of simply-typed \isa{{\isasymlambda}}-calculus
+The language of terms is that of simply-typed \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}}-calculus
with de-Bruijn indices for bound variables (cf.\ \cite{debruijn72}
or \cite{paulson-ml2}), with the types being determined by the
corresponding binders. In contrast, free variables and constants
@@ -269,8 +269,8 @@
\medskip A \emph{bound variable} is a natural number \isa{b},
which accounts for the number of intermediate binders between the
variable occurrence in the body and its binding position. For
- example, the de-Bruijn term \isa{{\isasymlambda}\isactrlbsub bool\isactrlesub {\isachardot}\ {\isasymlambda}\isactrlbsub bool\isactrlesub {\isachardot}\ {\isadigit{1}}\ {\isasymand}\ {\isadigit{0}}} would
- correspond to \isa{{\isasymlambda}x\isactrlbsub bool\isactrlesub {\isachardot}\ {\isasymlambda}y\isactrlbsub bool\isactrlesub {\isachardot}\ x\ {\isasymand}\ y} in a named
+ example, the de-Bruijn term \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}\isaliteral{5C3C5E627375623E}{}\isactrlbsub bool\isaliteral{5C3C5E657375623E}{}\isactrlesub {\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}\isaliteral{5C3C5E627375623E}{}\isactrlbsub bool\isaliteral{5C3C5E657375623E}{}\isactrlesub {\isaliteral{2E}{\isachardot}}\ {\isadigit{1}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isadigit{0}}} would
+ correspond to \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x\isaliteral{5C3C5E627375623E}{}\isactrlbsub bool\isaliteral{5C3C5E657375623E}{}\isactrlesub {\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}y\isaliteral{5C3C5E627375623E}{}\isactrlbsub bool\isaliteral{5C3C5E657375623E}{}\isactrlesub {\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C616E643E}{\isasymand}}\ y} in a named
representation. Note that a bound variable may be represented by
different de-Bruijn indices at different occurrences, depending on
the nesting of abstractions.
@@ -282,26 +282,26 @@
without any loose variables.
A \emph{fixed variable} is a pair of a basic name and a type, e.g.\
- \isa{{\isacharparenleft}x{\isacharcomma}\ {\isasymtau}{\isacharparenright}} which is usually printed \isa{x\isactrlisub {\isasymtau}} here. A
+ \isa{{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{29}{\isacharparenright}}} which is usually printed \isa{x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}} here. A
\emph{schematic variable} is a pair of an indexname and a type,
- e.g.\ \isa{{\isacharparenleft}{\isacharparenleft}x{\isacharcomma}\ {\isadigit{0}}{\isacharparenright}{\isacharcomma}\ {\isasymtau}{\isacharparenright}} which is likewise printed as \isa{{\isacharquery}x\isactrlisub {\isasymtau}}.
+ e.g.\ \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{29}{\isacharparenright}}} which is likewise printed as \isa{{\isaliteral{3F}{\isacharquery}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}}.
\medskip A \emph{constant} is a pair of a basic name and a type,
- e.g.\ \isa{{\isacharparenleft}c{\isacharcomma}\ {\isasymtau}{\isacharparenright}} which is usually printed as \isa{c\isactrlisub {\isasymtau}}
+ e.g.\ \isa{{\isaliteral{28}{\isacharparenleft}}c{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{29}{\isacharparenright}}} which is usually printed as \isa{c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}}
here. Constants are declared in the context as polymorphic families
- \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}}, meaning that all substitution instances \isa{c\isactrlisub {\isasymtau}} for \isa{{\isasymtau}\ {\isacharequal}\ {\isasymsigma}{\isasymvartheta}} are valid.
+ \isa{c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}}, meaning that all substitution instances \isa{c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}} for \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}} are valid.
- The vector of \emph{type arguments} of constant \isa{c\isactrlisub {\isasymtau}} wrt.\
- the declaration \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}} is defined as the codomain of the
- matcher \isa{{\isasymvartheta}\ {\isacharequal}\ {\isacharbraceleft}{\isacharquery}{\isasymalpha}\isactrlisub {\isadigit{1}}\ {\isasymmapsto}\ {\isasymtau}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isacharquery}{\isasymalpha}\isactrlisub n\ {\isasymmapsto}\ {\isasymtau}\isactrlisub n{\isacharbraceright}} presented in
- canonical order \isa{{\isacharparenleft}{\isasymtau}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymtau}\isactrlisub n{\isacharparenright}}, corresponding to the
- left-to-right occurrences of the \isa{{\isasymalpha}\isactrlisub i} in \isa{{\isasymsigma}}.
+ The vector of \emph{type arguments} of constant \isa{c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}} wrt.\
+ the declaration \isa{c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}} is defined as the codomain of the
+ matcher \isa{{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{7D}{\isacharbraceright}}} presented in
+ canonical order \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}}, corresponding to the
+ left-to-right occurrences of the \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub i} in \isa{{\isaliteral{5C3C7369676D613E}{\isasymsigma}}}.
Within a given theory context, there is a one-to-one correspondence
- between any constant \isa{c\isactrlisub {\isasymtau}} and the application \isa{c{\isacharparenleft}{\isasymtau}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymtau}\isactrlisub n{\isacharparenright}} of its type arguments. For example, with \isa{plus\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}}, the instance \isa{plus\isactrlbsub nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat\isactrlesub } corresponds to
- \isa{plus{\isacharparenleft}nat{\isacharparenright}}.
+ between any constant \isa{c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}} and the application \isa{c{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}} of its type arguments. For example, with \isa{plus\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}}, the instance \isa{plus\isaliteral{5C3C5E627375623E}{}\isactrlbsub nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\isaliteral{5C3C5E657375623E}{}\isactrlesub } corresponds to
+ \isa{plus{\isaliteral{28}{\isacharparenleft}}nat{\isaliteral{29}{\isacharparenright}}}.
- Constant declarations \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}} may contain sort constraints
- for type variables in \isa{{\isasymsigma}}. These are observed by
+ Constant declarations \isa{c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}} may contain sort constraints
+ for type variables in \isa{{\isaliteral{5C3C7369676D613E}{\isasymsigma}}}. These are observed by
type-inference as expected, but \emph{ignored} by the core logic.
This means the primitive logic is able to reason with instances of
polymorphic constants that the user-level type-checker would reject
@@ -309,20 +309,20 @@
\medskip An \emph{atomic term} is either a variable or constant.
The logical category \emph{term} is defined inductively over atomic
- terms, with abstraction and application as follows: \isa{t\ {\isacharequal}\ b\ {\isacharbar}\ x\isactrlisub {\isasymtau}\ {\isacharbar}\ {\isacharquery}x\isactrlisub {\isasymtau}\ {\isacharbar}\ c\isactrlisub {\isasymtau}\ {\isacharbar}\ {\isasymlambda}\isactrlisub {\isasymtau}{\isachardot}\ t\ {\isacharbar}\ t\isactrlisub {\isadigit{1}}\ t\isactrlisub {\isadigit{2}}}. Parsing and printing takes care of
+ terms, with abstraction and application as follows: \isa{t\ {\isaliteral{3D}{\isacharequal}}\ b\ {\isaliteral{7C}{\isacharbar}}\ x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}\ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3F}{\isacharquery}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}\ {\isaliteral{7C}{\isacharbar}}\ c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}\ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{2E}{\isachardot}}\ t\ {\isaliteral{7C}{\isacharbar}}\ t\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ t\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}. Parsing and printing takes care of
converting between an external representation with named bound
variables. Subsequently, we shall use the latter notation instead
of internal de-Bruijn representation.
- The inductive relation \isa{t\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}} assigns a (unique) type to a
+ The inductive relation \isa{t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}} assigns a (unique) type to a
term according to the structure of atomic terms, abstractions, and
applicatins:
\[
- \infer{\isa{a\isactrlisub {\isasymtau}\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}}}{}
+ \infer{\isa{a\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}}}{}
\qquad
- \infer{\isa{{\isacharparenleft}{\isasymlambda}x\isactrlsub {\isasymtau}{\isachardot}\ t{\isacharparenright}\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}\ {\isasymRightarrow}\ {\isasymsigma}}}{\isa{t\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}}}
+ \infer{\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{2E}{\isachardot}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}}}{\isa{t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}}}
\qquad
- \infer{\isa{t\ u\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}}}{\isa{t\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}\ {\isasymRightarrow}\ {\isasymsigma}} & \isa{u\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}}}
+ \infer{\isa{t\ u\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}}}{\isa{t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}} & \isa{u\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}}}
\]
A \emph{well-typed term} is a term that can be typed according to these rules.
@@ -333,35 +333,35 @@
variables, and declarations for polymorphic constants.
The identity of atomic terms consists both of the name and the type
- component. This means that different variables \isa{x\isactrlbsub {\isasymtau}\isactrlisub {\isadigit{1}}\isactrlesub } and \isa{x\isactrlbsub {\isasymtau}\isactrlisub {\isadigit{2}}\isactrlesub } may become the same after
+ component. This means that different variables \isa{x\isaliteral{5C3C5E627375623E}{}\isactrlbsub {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\isaliteral{5C3C5E657375623E}{}\isactrlesub } and \isa{x\isaliteral{5C3C5E627375623E}{}\isactrlbsub {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}\isaliteral{5C3C5E657375623E}{}\isactrlesub } may become the same after
type instantiation. Type-inference rejects variables of the same
name, but different types. In contrast, mixed instances of
polymorphic constants occur routinely.
- \medskip The \emph{hidden polymorphism} of a term \isa{t\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}}
+ \medskip The \emph{hidden polymorphism} of a term \isa{t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}}
is the set of type variables occurring in \isa{t}, but not in
- its type \isa{{\isasymsigma}}. This means that the term implicitly depends
+ its type \isa{{\isaliteral{5C3C7369676D613E}{\isasymsigma}}}. This means that the term implicitly depends
on type arguments that are not accounted in the result type, i.e.\
- there are different type instances \isa{t{\isasymvartheta}\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}} and
- \isa{t{\isasymvartheta}{\isacharprime}\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}} with the same type. This slightly
+ there are different type instances \isa{t{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}} and
+ \isa{t{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}} with the same type. This slightly
pathological situation notoriously demands additional care.
- \medskip A \emph{term abbreviation} is a syntactic definition \isa{c\isactrlisub {\isasymsigma}\ {\isasymequiv}\ t} of a closed term \isa{t} of type \isa{{\isasymsigma}},
+ \medskip A \emph{term abbreviation} is a syntactic definition \isa{c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t} of a closed term \isa{t} of type \isa{{\isaliteral{5C3C7369676D613E}{\isasymsigma}}},
without any hidden polymorphism. A term abbreviation looks like a
constant in the syntax, but is expanded before entering the logical
core. Abbreviations are usually reverted when printing terms, using
- \isa{t\ {\isasymrightarrow}\ c\isactrlisub {\isasymsigma}} as rules for higher-order rewriting.
+ \isa{t\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7369676D613E}{\isasymsigma}}} as rules for higher-order rewriting.
- \medskip Canonical operations on \isa{{\isasymlambda}}-terms include \isa{{\isasymalpha}{\isasymbeta}{\isasymeta}}-conversion: \isa{{\isasymalpha}}-conversion refers to capture-free
- renaming of bound variables; \isa{{\isasymbeta}}-conversion contracts an
+ \medskip Canonical operations on \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}}-terms include \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{5C3C6574613E}{\isasymeta}}}-conversion: \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}}-conversion refers to capture-free
+ renaming of bound variables; \isa{{\isaliteral{5C3C626574613E}{\isasymbeta}}}-conversion contracts an
abstraction applied to an argument term, substituting the argument
- in the body: \isa{{\isacharparenleft}{\isasymlambda}x{\isachardot}\ b{\isacharparenright}a} becomes \isa{b{\isacharbrackleft}a{\isacharslash}x{\isacharbrackright}}; \isa{{\isasymeta}}-conversion contracts vacuous application-abstraction: \isa{{\isasymlambda}x{\isachardot}\ f\ x} becomes \isa{f}, provided that the bound variable
+ in the body: \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ b{\isaliteral{29}{\isacharparenright}}a} becomes \isa{b{\isaliteral{5B}{\isacharbrackleft}}a{\isaliteral{2F}{\isacharslash}}x{\isaliteral{5D}{\isacharbrackright}}}; \isa{{\isaliteral{5C3C6574613E}{\isasymeta}}}-conversion contracts vacuous application-abstraction: \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ f\ x} becomes \isa{f}, provided that the bound variable
does not occur in \isa{f}.
- Terms are normally treated modulo \isa{{\isasymalpha}}-conversion, which is
+ Terms are normally treated modulo \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}}-conversion, which is
implicit in the de-Bruijn representation. Names for bound variables
in abstractions are maintained separately as (meaningless) comments,
- mostly for parsing and printing. Full \isa{{\isasymalpha}{\isasymbeta}{\isasymeta}}-conversion is
+ mostly for parsing and printing. Full \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{5C3C6574613E}{\isasymeta}}}-conversion is
commonplace in various standard operations (\secref{sec:obj-rules})
that are based on higher-order unification and matching.%
\end{isamarkuptext}%
@@ -400,7 +400,7 @@
in abstractions, and explicitly named free variables and constants;
this is a datatype with constructors \verb|Bound|, \verb|Free|, \verb|Var|, \verb|Const|, \verb|Abs|, \verb|op $|.
- \item \isa{t}~\verb|aconv|~\isa{u} checks \isa{{\isasymalpha}}-equivalence of two terms. This is the basic equality relation
+ \item \isa{t}~\verb|aconv|~\isa{u} checks \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}}-equivalence of two terms. This is the basic equality relation
on type \verb|term|; raw datatype equality should only be used
for operations related to parsing or printing!
@@ -420,20 +420,20 @@
well-typed term. This operation is relatively slow, despite the
omission of any sanity checks.
- \item \verb|lambda|~\isa{a\ b} produces an abstraction \isa{{\isasymlambda}a{\isachardot}\ b}, where occurrences of the atomic term \isa{a} in the
+ \item \verb|lambda|~\isa{a\ b} produces an abstraction \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}a{\isaliteral{2E}{\isachardot}}\ b}, where occurrences of the atomic term \isa{a} in the
body \isa{b} are replaced by bound variables.
- \item \verb|betapply|~\isa{{\isacharparenleft}t{\isacharcomma}\ u{\isacharparenright}} produces an application \isa{t\ u}, with topmost \isa{{\isasymbeta}}-conversion if \isa{t} is an
+ \item \verb|betapply|~\isa{{\isaliteral{28}{\isacharparenleft}}t{\isaliteral{2C}{\isacharcomma}}\ u{\isaliteral{29}{\isacharparenright}}} produces an application \isa{t\ u}, with topmost \isa{{\isaliteral{5C3C626574613E}{\isasymbeta}}}-conversion if \isa{t} is an
abstraction.
- \item \verb|Sign.declare_const|~\isa{{\isacharparenleft}{\isacharparenleft}c{\isacharcomma}\ {\isasymsigma}{\isacharparenright}{\isacharcomma}\ mx{\isacharparenright}}
- declares a new constant \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}} with optional mixfix
+ \item \verb|Sign.declare_const|~\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}c{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ mx{\isaliteral{29}{\isacharparenright}}}
+ declares a new constant \isa{c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}} with optional mixfix
syntax.
- \item \verb|Sign.add_abbrev|~\isa{print{\isacharunderscore}mode\ {\isacharparenleft}c{\isacharcomma}\ t{\isacharparenright}}
- introduces a new term abbreviation \isa{c\ {\isasymequiv}\ t}.
+ \item \verb|Sign.add_abbrev|~\isa{print{\isaliteral{5F}{\isacharunderscore}}mode\ {\isaliteral{28}{\isacharparenleft}}c{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}}
+ introduces a new term abbreviation \isa{c\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t}.
- \item \verb|Sign.const_typargs|~\isa{thy\ {\isacharparenleft}c{\isacharcomma}\ {\isasymtau}{\isacharparenright}} and \verb|Sign.const_instance|~\isa{thy\ {\isacharparenleft}c{\isacharcomma}\ {\isacharbrackleft}{\isasymtau}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymtau}\isactrlisub n{\isacharbrackright}{\isacharparenright}}
+ \item \verb|Sign.const_typargs|~\isa{thy\ {\isaliteral{28}{\isacharparenleft}}c{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{29}{\isacharparenright}}} and \verb|Sign.const_instance|~\isa{thy\ {\isaliteral{28}{\isacharparenleft}}c{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}}
convert between two representations of polymorphic constants: full
type instance vs.\ compact type arguments form.
@@ -456,11 +456,11 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{ML antiquotation}{const\_name}\hypertarget{ML antiquotation.const-name}{\hyperlink{ML antiquotation.const-name}{\mbox{\isa{const{\isacharunderscore}name}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{const\_abbrev}\hypertarget{ML antiquotation.const-abbrev}{\hyperlink{ML antiquotation.const-abbrev}{\mbox{\isa{const{\isacharunderscore}abbrev}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{const}\hypertarget{ML antiquotation.const}{\hyperlink{ML antiquotation.const}{\mbox{\isa{const}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{term}\hypertarget{ML antiquotation.term}{\hyperlink{ML antiquotation.term}{\mbox{\isa{term}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{prop}\hypertarget{ML antiquotation.prop}{\hyperlink{ML antiquotation.prop}{\mbox{\isa{prop}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
+ \indexdef{}{ML antiquotation}{const\_name}\hypertarget{ML antiquotation.const-name}{\hyperlink{ML antiquotation.const-name}{\mbox{\isa{const{\isaliteral{5F}{\isacharunderscore}}name}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{const\_abbrev}\hypertarget{ML antiquotation.const-abbrev}{\hyperlink{ML antiquotation.const-abbrev}{\mbox{\isa{const{\isaliteral{5F}{\isacharunderscore}}abbrev}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{const}\hypertarget{ML antiquotation.const}{\hyperlink{ML antiquotation.const}{\mbox{\isa{const}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{term}\hypertarget{ML antiquotation.term}{\hyperlink{ML antiquotation.term}{\mbox{\isa{term}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{prop}\hypertarget{ML antiquotation.prop}{\hyperlink{ML antiquotation.prop}{\mbox{\isa{prop}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
\end{matharray}
\begin{rail}
@@ -476,23 +476,23 @@
\begin{description}
- \item \isa{{\isacharat}{\isacharbraceleft}const{\isacharunderscore}name\ c{\isacharbraceright}} inlines the internalized logical
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}const{\isaliteral{5F}{\isacharunderscore}}name\ c{\isaliteral{7D}{\isacharbraceright}}} inlines the internalized logical
constant name \isa{c} --- as \verb|string| literal.
- \item \isa{{\isacharat}{\isacharbraceleft}const{\isacharunderscore}abbrev\ c{\isacharbraceright}} inlines the internalized
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}const{\isaliteral{5F}{\isacharunderscore}}abbrev\ c{\isaliteral{7D}{\isacharbraceright}}} inlines the internalized
abbreviated constant name \isa{c} --- as \verb|string|
literal.
- \item \isa{{\isacharat}{\isacharbraceleft}const\ c{\isacharparenleft}\isactrlvec {\isasymtau}{\isacharparenright}{\isacharbraceright}} inlines the internalized
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}const\ c{\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{7D}{\isacharbraceright}}} inlines the internalized
constant \isa{c} with precise type instantiation in the sense of
\verb|Sign.const_instance| --- as \verb|Const| constructor term for
datatype \verb|term|.
- \item \isa{{\isacharat}{\isacharbraceleft}term\ t{\isacharbraceright}} inlines the internalized term \isa{t}
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}term\ t{\isaliteral{7D}{\isacharbraceright}}} inlines the internalized term \isa{t}
--- as constructor term for datatype \verb|term|.
- \item \isa{{\isacharat}{\isacharbraceleft}prop\ {\isasymphi}{\isacharbraceright}} inlines the internalized proposition
- \isa{{\isasymphi}} --- as constructor term for datatype \verb|term|.
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}prop\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{7D}{\isacharbraceright}}} inlines the internalized proposition
+ \isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} --- as constructor term for datatype \verb|term|.
\end{description}%
\end{isamarkuptext}%
@@ -513,8 +513,8 @@
A \emph{proposition} is a well-typed term of type \isa{prop}, a
\emph{theorem} is a proven proposition (depending on a context of
hypotheses and the background theory). Primitive inferences include
- plain Natural Deduction rules for the primary connectives \isa{{\isasymAnd}} and \isa{{\isasymLongrightarrow}} of the framework. There is also a builtin
- notion of equality/equivalence \isa{{\isasymequiv}}.%
+ plain Natural Deduction rules for the primary connectives \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}} and \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}} of the framework. There is also a builtin
+ notion of equality/equivalence \isa{{\isaliteral{5C3C65717569763E}{\isasymequiv}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -524,9 +524,9 @@
%
\begin{isamarkuptext}%
The theory \isa{Pure} contains constant declarations for the
- primitive connectives \isa{{\isasymAnd}}, \isa{{\isasymLongrightarrow}}, and \isa{{\isasymequiv}} of
+ primitive connectives \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}}, \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}}, and \isa{{\isaliteral{5C3C65717569763E}{\isasymequiv}}} of
the logical framework, see \figref{fig:pure-connectives}. The
- derivability judgment \isa{A\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ A\isactrlisub n\ {\isasymturnstile}\ B} is
+ derivability judgment \isa{A\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ A\isaliteral{5C3C5E697375623E}{}\isactrlisub n\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B} is
defined inductively by the primitive inferences given in
\figref{fig:prim-rules}, with the global restriction that the
hypotheses must \emph{not} contain any schematic variables. The
@@ -537,9 +537,9 @@
\begin{figure}[htb]
\begin{center}
\begin{tabular}{ll}
- \isa{all\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}{\isasymalpha}\ {\isasymRightarrow}\ prop{\isacharparenright}\ {\isasymRightarrow}\ prop} & universal quantification (binder \isa{{\isasymAnd}}) \\
- \isa{{\isasymLongrightarrow}\ {\isacharcolon}{\isacharcolon}\ prop\ {\isasymRightarrow}\ prop\ {\isasymRightarrow}\ prop} & implication (right associative infix) \\
- \isa{{\isasymequiv}\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}\ {\isasymRightarrow}\ prop} & equality relation (infix) \\
+ \isa{all\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ prop{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ prop} & universal quantification (binder \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}}) \\
+ \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ prop\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ prop\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ prop} & implication (right associative infix) \\
+ \isa{{\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ prop} & equality relation (infix) \\
\end{tabular}
\caption{Primitive connectives of Pure}\label{fig:pure-connectives}
\end{center}
@@ -548,19 +548,19 @@
\begin{figure}[htb]
\begin{center}
\[
- \infer[\isa{{\isacharparenleft}axiom{\isacharparenright}}]{\isa{{\isasymturnstile}\ A}}{\isa{A\ {\isasymin}\ {\isasymTheta}}}
+ \infer[\isa{{\isaliteral{28}{\isacharparenleft}}axiom{\isaliteral{29}{\isacharparenright}}}]{\isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A}}{\isa{A\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C54686574613E}{\isasymTheta}}}}
\qquad
- \infer[\isa{{\isacharparenleft}assume{\isacharparenright}}]{\isa{A\ {\isasymturnstile}\ A}}{}
+ \infer[\isa{{\isaliteral{28}{\isacharparenleft}}assume{\isaliteral{29}{\isacharparenright}}}]{\isa{A\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A}}{}
\]
\[
- \infer[\isa{{\isacharparenleft}{\isasymAnd}{\isasymdash}intro{\isacharparenright}}]{\isa{{\isasymGamma}\ {\isasymturnstile}\ {\isasymAnd}x{\isachardot}\ b{\isacharbrackleft}x{\isacharbrackright}}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ b{\isacharbrackleft}x{\isacharbrackright}} & \isa{x\ {\isasymnotin}\ {\isasymGamma}}}
+ \infer[\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{5C3C646173683E}{\isasymdash}}intro{\isaliteral{29}{\isacharparenright}}}]{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ b{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}}}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ b{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}} & \isa{x\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ {\isaliteral{5C3C47616D6D613E}{\isasymGamma}}}}
\qquad
- \infer[\isa{{\isacharparenleft}{\isasymAnd}{\isasymdash}elim{\isacharparenright}}]{\isa{{\isasymGamma}\ {\isasymturnstile}\ b{\isacharbrackleft}a{\isacharbrackright}}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ {\isasymAnd}x{\isachardot}\ b{\isacharbrackleft}x{\isacharbrackright}}}
+ \infer[\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{5C3C646173683E}{\isasymdash}}elim{\isaliteral{29}{\isacharparenright}}}]{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ b{\isaliteral{5B}{\isacharbrackleft}}a{\isaliteral{5D}{\isacharbrackright}}}}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ b{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}}}
\]
\[
- \infer[\isa{{\isacharparenleft}{\isasymLongrightarrow}{\isasymdash}intro{\isacharparenright}}]{\isa{{\isasymGamma}\ {\isacharminus}\ A\ {\isasymturnstile}\ A\ {\isasymLongrightarrow}\ B}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B}}
+ \infer[\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{5C3C646173683E}{\isasymdash}}intro{\isaliteral{29}{\isacharparenright}}}]{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{2D}{\isacharminus}}\ A\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B}}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B}}
\qquad
- \infer[\isa{{\isacharparenleft}{\isasymLongrightarrow}{\isasymdash}elim{\isacharparenright}}]{\isa{{\isasymGamma}\isactrlsub {\isadigit{1}}\ {\isasymunion}\ {\isasymGamma}\isactrlsub {\isadigit{2}}\ {\isasymturnstile}\ B}}{\isa{{\isasymGamma}\isactrlsub {\isadigit{1}}\ {\isasymturnstile}\ A\ {\isasymLongrightarrow}\ B} & \isa{{\isasymGamma}\isactrlsub {\isadigit{2}}\ {\isasymturnstile}\ A}}
+ \infer[\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{5C3C646173683E}{\isasymdash}}elim{\isaliteral{29}{\isacharparenright}}}]{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ {\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B}}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B} & \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A}}
\]
\caption{Primitive inferences of Pure}\label{fig:prim-rules}
\end{center}
@@ -569,61 +569,61 @@
\begin{figure}[htb]
\begin{center}
\begin{tabular}{ll}
- \isa{{\isasymturnstile}\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ b{\isacharbrackleft}x{\isacharbrackright}{\isacharparenright}\ a\ {\isasymequiv}\ b{\isacharbrackleft}a{\isacharbrackright}} & \isa{{\isasymbeta}}-conversion \\
- \isa{{\isasymturnstile}\ x\ {\isasymequiv}\ x} & reflexivity \\
- \isa{{\isasymturnstile}\ x\ {\isasymequiv}\ y\ {\isasymLongrightarrow}\ P\ x\ {\isasymLongrightarrow}\ P\ y} & substitution \\
- \isa{{\isasymturnstile}\ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ f\ x\ {\isasymequiv}\ g\ x{\isacharparenright}\ {\isasymLongrightarrow}\ f\ {\isasymequiv}\ g} & extensionality \\
- \isa{{\isasymturnstile}\ {\isacharparenleft}A\ {\isasymLongrightarrow}\ B{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}B\ {\isasymLongrightarrow}\ A{\isacharparenright}\ {\isasymLongrightarrow}\ A\ {\isasymequiv}\ B} & logical equivalence \\
+ \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ b{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ a\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ b{\isaliteral{5B}{\isacharbrackleft}}a{\isaliteral{5D}{\isacharbrackright}}} & \isa{{\isaliteral{5C3C626574613E}{\isasymbeta}}}-conversion \\
+ \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ x} & reflexivity \\
+ \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ y} & substitution \\
+ \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ f\ x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ g\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ f\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ g} & extensionality \\
+ \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ B} & logical equivalence \\
\end{tabular}
\caption{Conceptual axiomatization of Pure equality}\label{fig:pure-equality}
\end{center}
\end{figure}
- The introduction and elimination rules for \isa{{\isasymAnd}} and \isa{{\isasymLongrightarrow}} are analogous to formation of dependently typed \isa{{\isasymlambda}}-terms representing the underlying proof objects. Proof terms
+ The introduction and elimination rules for \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}} and \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}} are analogous to formation of dependently typed \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}}-terms representing the underlying proof objects. Proof terms
are irrelevant in the Pure logic, though; they cannot occur within
propositions. The system provides a runtime option to record
explicit proof terms for primitive inferences. Thus all three
- levels of \isa{{\isasymlambda}}-calculus become explicit: \isa{{\isasymRightarrow}} for
- terms, and \isa{{\isasymAnd}{\isacharslash}{\isasymLongrightarrow}} for proofs (cf.\
+ levels of \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}}-calculus become explicit: \isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} for
+ terms, and \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}} for proofs (cf.\
\cite{Berghofer-Nipkow:2000:TPHOL}).
- Observe that locally fixed parameters (as in \isa{{\isasymAnd}{\isasymdash}intro}) need not be recorded in the hypotheses, because
+ Observe that locally fixed parameters (as in \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{5C3C646173683E}{\isasymdash}}intro}) need not be recorded in the hypotheses, because
the simple syntactic types of Pure are always inhabitable.
- ``Assumptions'' \isa{x\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}} for type-membership are only
- present as long as some \isa{x\isactrlisub {\isasymtau}} occurs in the statement
- body.\footnote{This is the key difference to ``\isa{{\isasymlambda}HOL}'' in
+ ``Assumptions'' \isa{x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}} for type-membership are only
+ present as long as some \isa{x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}} occurs in the statement
+ body.\footnote{This is the key difference to ``\isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}HOL}'' in
the PTS framework \cite{Barendregt-Geuvers:2001}, where hypotheses
- \isa{x\ {\isacharcolon}\ A} are treated uniformly for propositions and types.}
+ \isa{x\ {\isaliteral{3A}{\isacharcolon}}\ A} are treated uniformly for propositions and types.}
\medskip The axiomatization of a theory is implicitly closed by
- forming all instances of type and term variables: \isa{{\isasymturnstile}\ A{\isasymvartheta}} holds for any substitution instance of an axiom
- \isa{{\isasymturnstile}\ A}. By pushing substitutions through derivations
+ forming all instances of type and term variables: \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}} holds for any substitution instance of an axiom
+ \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A}. By pushing substitutions through derivations
inductively, we also get admissible \isa{generalize} and \isa{instantiate} rules as shown in \figref{fig:subst-rules}.
\begin{figure}[htb]
\begin{center}
\[
- \infer{\isa{{\isasymGamma}\ {\isasymturnstile}\ B{\isacharbrackleft}{\isacharquery}{\isasymalpha}{\isacharbrackright}}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}} & \isa{{\isasymalpha}\ {\isasymnotin}\ {\isasymGamma}}}
+ \infer{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5D}{\isacharbrackright}}}}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5D}{\isacharbrackright}}} & \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ {\isaliteral{5C3C47616D6D613E}{\isasymGamma}}}}
\quad
- \infer[\quad\isa{{\isacharparenleft}generalize{\isacharparenright}}]{\isa{{\isasymGamma}\ {\isasymturnstile}\ B{\isacharbrackleft}{\isacharquery}x{\isacharbrackright}}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B{\isacharbrackleft}x{\isacharbrackright}} & \isa{x\ {\isasymnotin}\ {\isasymGamma}}}
+ \infer[\quad\isa{{\isaliteral{28}{\isacharparenleft}}generalize{\isaliteral{29}{\isacharparenright}}}]{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{5D}{\isacharbrackright}}}}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}} & \isa{x\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ {\isaliteral{5C3C47616D6D613E}{\isasymGamma}}}}
\]
\[
- \infer{\isa{{\isasymGamma}\ {\isasymturnstile}\ B{\isacharbrackleft}{\isasymtau}{\isacharbrackright}}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B{\isacharbrackleft}{\isacharquery}{\isasymalpha}{\isacharbrackright}}}
+ \infer{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{5D}{\isacharbrackright}}}}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5D}{\isacharbrackright}}}}
\quad
- \infer[\quad\isa{{\isacharparenleft}instantiate{\isacharparenright}}]{\isa{{\isasymGamma}\ {\isasymturnstile}\ B{\isacharbrackleft}t{\isacharbrackright}}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B{\isacharbrackleft}{\isacharquery}x{\isacharbrackright}}}
+ \infer[\quad\isa{{\isaliteral{28}{\isacharparenleft}}instantiate{\isaliteral{29}{\isacharparenright}}}]{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{5B}{\isacharbrackleft}}t{\isaliteral{5D}{\isacharbrackright}}}}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{5D}{\isacharbrackright}}}}
\]
\caption{Admissible substitution rules}\label{fig:subst-rules}
\end{center}
\end{figure}
Note that \isa{instantiate} does not require an explicit
- side-condition, because \isa{{\isasymGamma}} may never contain schematic
+ side-condition, because \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}} may never contain schematic
variables.
In principle, variables could be substituted in hypotheses as well,
but this would disrupt the monotonicity of reasoning: deriving
- \isa{{\isasymGamma}{\isasymvartheta}\ {\isasymturnstile}\ B{\isasymvartheta}} from \isa{{\isasymGamma}\ {\isasymturnstile}\ B} is
- correct, but \isa{{\isasymGamma}{\isasymvartheta}\ {\isasymsupseteq}\ {\isasymGamma}} does not necessarily hold:
+ \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}} from \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B} is
+ correct, but \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}\ {\isaliteral{5C3C73757073657465713E}{\isasymsupseteq}}\ {\isaliteral{5C3C47616D6D613E}{\isasymGamma}}} does not necessarily hold:
the result belongs to a different proof context.
\medskip An \emph{oracle} is a function that produces axioms on the
@@ -637,14 +637,14 @@
Later on, theories are usually developed in a strictly definitional
fashion, by stating only certain equalities over new constants.
- A \emph{simple definition} consists of a constant declaration \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}} together with an axiom \isa{{\isasymturnstile}\ c\ {\isasymequiv}\ t}, where \isa{t\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}} is a closed term without any hidden polymorphism. The RHS
+ A \emph{simple definition} consists of a constant declaration \isa{c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}} together with an axiom \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ c\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t}, where \isa{t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}} is a closed term without any hidden polymorphism. The RHS
may depend on further defined constants, but not \isa{c} itself.
- Definitions of functions may be presented as \isa{c\ \isactrlvec x\ {\isasymequiv}\ t} instead of the puristic \isa{c\ {\isasymequiv}\ {\isasymlambda}\isactrlvec x{\isachardot}\ t}.
+ Definitions of functions may be presented as \isa{c\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t} instead of the puristic \isa{c\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ t}.
An \emph{overloaded definition} consists of a collection of axioms
- for the same constant, with zero or one equations \isa{c{\isacharparenleft}{\isacharparenleft}\isactrlvec {\isasymalpha}{\isacharparenright}{\isasymkappa}{\isacharparenright}\ {\isasymequiv}\ t} for each type constructor \isa{{\isasymkappa}} (for
- distinct variables \isa{\isactrlvec {\isasymalpha}}). The RHS may mention
- previously defined constants as above, or arbitrary constants \isa{d{\isacharparenleft}{\isasymalpha}\isactrlisub i{\isacharparenright}} for some \isa{{\isasymalpha}\isactrlisub i} projected from \isa{\isactrlvec {\isasymalpha}}. Thus overloaded definitions essentially work by
+ for the same constant, with zero or one equations \isa{c{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C6B617070613E}{\isasymkappa}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t} for each type constructor \isa{{\isaliteral{5C3C6B617070613E}{\isasymkappa}}} (for
+ distinct variables \isa{\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C616C7068613E}{\isasymalpha}}}). The RHS may mention
+ previously defined constants as above, or arbitrary constants \isa{d{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub i{\isaliteral{29}{\isacharparenright}}} for some \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub i} projected from \isa{\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C616C7068613E}{\isasymalpha}}}. Thus overloaded definitions essentially work by
primitive recursion over the syntactic structure of a single type
argument. See also \cite[\S4.3]{Haftmann-Wenzel:2006:classes}.%
\end{isamarkuptext}%
@@ -692,7 +692,7 @@
well-typedness) checks, relative to the declarations of type
constructors, constants etc. in the theory.
- \item \verb|Thm.ctyp_of|~\isa{thy\ {\isasymtau}} and \verb|Thm.cterm_of|~\isa{thy\ t} explicitly checks types and terms,
+ \item \verb|Thm.ctyp_of|~\isa{thy\ {\isaliteral{5C3C7461753E}{\isasymtau}}} and \verb|Thm.cterm_of|~\isa{thy\ t} explicitly checks types and terms,
respectively. This also involves some basic normalizations, such
expansion of type and term abbreviations from the theory context.
@@ -715,36 +715,36 @@
\item \verb|Thm.assume|, \verb|Thm.forall_intr|, \verb|Thm.forall_elim|, \verb|Thm.implies_intr|, and \verb|Thm.implies_elim|
correspond to the primitive inferences of \figref{fig:prim-rules}.
- \item \verb|Thm.generalize|~\isa{{\isacharparenleft}\isactrlvec {\isasymalpha}{\isacharcomma}\ \isactrlvec x{\isacharparenright}}
+ \item \verb|Thm.generalize|~\isa{{\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{29}{\isacharparenright}}}
corresponds to the \isa{generalize} rules of
\figref{fig:subst-rules}. Here collections of type and term
variables are generalized simultaneously, specified by the given
basic names.
- \item \verb|Thm.instantiate|~\isa{{\isacharparenleft}\isactrlvec {\isasymalpha}\isactrlisub s{\isacharcomma}\ \isactrlvec x\isactrlisub {\isasymtau}{\isacharparenright}} corresponds to the \isa{instantiate} rules
+ \item \verb|Thm.instantiate|~\isa{{\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub s{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{29}{\isacharparenright}}} corresponds to the \isa{instantiate} rules
of \figref{fig:subst-rules}. Type variables are substituted before
- term variables. Note that the types in \isa{\isactrlvec x\isactrlisub {\isasymtau}}
+ term variables. Note that the types in \isa{\isaliteral{5C3C5E7665633E}{}\isactrlvec x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}}
refer to the instantiated versions.
- \item \verb|Thm.add_axiom|~\isa{{\isacharparenleft}name{\isacharcomma}\ A{\isacharparenright}\ thy} declares an
+ \item \verb|Thm.add_axiom|~\isa{{\isaliteral{28}{\isacharparenleft}}name{\isaliteral{2C}{\isacharcomma}}\ A{\isaliteral{29}{\isacharparenright}}\ thy} declares an
arbitrary proposition as axiom, and retrieves it as a theorem from
the resulting theory, cf.\ \isa{axiom} in
\figref{fig:prim-rules}. Note that the low-level representation in
the axiom table may differ slightly from the returned theorem.
- \item \verb|Thm.add_oracle|~\isa{{\isacharparenleft}binding{\isacharcomma}\ oracle{\isacharparenright}} produces a named
+ \item \verb|Thm.add_oracle|~\isa{{\isaliteral{28}{\isacharparenleft}}binding{\isaliteral{2C}{\isacharcomma}}\ oracle{\isaliteral{29}{\isacharparenright}}} produces a named
oracle rule, essentially generating arbitrary axioms on the fly,
cf.\ \isa{axiom} in \figref{fig:prim-rules}.
- \item \verb|Thm.add_def|~\isa{unchecked\ overloaded\ {\isacharparenleft}name{\isacharcomma}\ c\ \isactrlvec x\ {\isasymequiv}\ t{\isacharparenright}} states a definitional axiom for an existing constant
+ \item \verb|Thm.add_def|~\isa{unchecked\ overloaded\ {\isaliteral{28}{\isacharparenleft}}name{\isaliteral{2C}{\isacharcomma}}\ c\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{29}{\isacharparenright}}} states a definitional axiom for an existing constant
\isa{c}. Dependencies are recorded via \verb|Theory.add_deps|,
unless the \isa{unchecked} option is set. Note that the
low-level representation in the axiom table may differ slightly from
the returned theorem.
- \item \verb|Theory.add_deps|~\isa{name\ c\isactrlisub {\isasymtau}\ \isactrlvec d\isactrlisub {\isasymsigma}} declares dependencies of a named specification
- for constant \isa{c\isactrlisub {\isasymtau}}, relative to existing
- specifications for constants \isa{\isactrlvec d\isactrlisub {\isasymsigma}}.
+ \item \verb|Theory.add_deps|~\isa{name\ c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec d\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7369676D613E}{\isasymsigma}}} declares dependencies of a named specification
+ for constant \isa{c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}}, relative to existing
+ specifications for constants \isa{\isaliteral{5C3C5E7665633E}{}\isactrlvec d\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7369676D613E}{\isasymsigma}}}.
\end{description}%
\end{isamarkuptext}%
@@ -765,12 +765,12 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{ML antiquotation}{ctyp}\hypertarget{ML antiquotation.ctyp}{\hyperlink{ML antiquotation.ctyp}{\mbox{\isa{ctyp}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{cterm}\hypertarget{ML antiquotation.cterm}{\hyperlink{ML antiquotation.cterm}{\mbox{\isa{cterm}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{cprop}\hypertarget{ML antiquotation.cprop}{\hyperlink{ML antiquotation.cprop}{\mbox{\isa{cprop}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{thm}\hypertarget{ML antiquotation.thm}{\hyperlink{ML antiquotation.thm}{\mbox{\isa{thm}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{thms}\hypertarget{ML antiquotation.thms}{\hyperlink{ML antiquotation.thms}{\mbox{\isa{thms}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{lemma}\hypertarget{ML antiquotation.lemma}{\hyperlink{ML antiquotation.lemma}{\mbox{\isa{lemma}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
+ \indexdef{}{ML antiquotation}{ctyp}\hypertarget{ML antiquotation.ctyp}{\hyperlink{ML antiquotation.ctyp}{\mbox{\isa{ctyp}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{cterm}\hypertarget{ML antiquotation.cterm}{\hyperlink{ML antiquotation.cterm}{\mbox{\isa{cterm}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{cprop}\hypertarget{ML antiquotation.cprop}{\hyperlink{ML antiquotation.cprop}{\mbox{\isa{cprop}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{thm}\hypertarget{ML antiquotation.thm}{\hyperlink{ML antiquotation.thm}{\mbox{\isa{thm}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{thms}\hypertarget{ML antiquotation.thms}{\hyperlink{ML antiquotation.thms}{\mbox{\isa{thms}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{lemma}\hypertarget{ML antiquotation.lemma}{\hyperlink{ML antiquotation.lemma}{\mbox{\isa{lemma}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
\end{matharray}
\begin{rail}
@@ -789,27 +789,27 @@
\begin{description}
- \item \isa{{\isacharat}{\isacharbraceleft}ctyp\ {\isasymtau}{\isacharbraceright}} produces a certified type wrt.\ the
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}ctyp\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{7D}{\isacharbraceright}}} produces a certified type wrt.\ the
current background theory --- as abstract value of type \verb|ctyp|.
- \item \isa{{\isacharat}{\isacharbraceleft}cterm\ t{\isacharbraceright}} and \isa{{\isacharat}{\isacharbraceleft}cprop\ {\isasymphi}{\isacharbraceright}} produce a
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}cterm\ t{\isaliteral{7D}{\isacharbraceright}}} and \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}cprop\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{7D}{\isacharbraceright}}} produce a
certified term wrt.\ the current background theory --- as abstract
value of type \verb|cterm|.
- \item \isa{{\isacharat}{\isacharbraceleft}thm\ a{\isacharbraceright}} produces a singleton fact --- as abstract
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}thm\ a{\isaliteral{7D}{\isacharbraceright}}} produces a singleton fact --- as abstract
value of type \verb|thm|.
- \item \isa{{\isacharat}{\isacharbraceleft}thms\ a{\isacharbraceright}} produces a general fact --- as abstract
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}thms\ a{\isaliteral{7D}{\isacharbraceright}}} produces a general fact --- as abstract
value of type \verb|thm list|.
- \item \isa{{\isacharat}{\isacharbraceleft}lemma\ {\isasymphi}\ by\ meth{\isacharbraceright}} produces a fact that is proven on
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}lemma\ {\isaliteral{5C3C7068693E}{\isasymphi}}\ by\ meth{\isaliteral{7D}{\isacharbraceright}}} produces a fact that is proven on
the spot according to the minimal proof, which imitates a terminal
Isar proof. The result is an abstract value of type \verb|thm|
or \verb|thm list|, depending on the number of propositions
given here.
The internal derivation object lacks a proper theorem name, but it
- is formally closed, unless the \isa{{\isacharparenleft}open{\isacharparenright}} option is specified
+ is formally closed, unless the \isa{{\isaliteral{28}{\isacharparenleft}}open{\isaliteral{29}{\isacharparenright}}} option is specified
(this may impact performance of applications with proof terms).
Since ML antiquotations are always evaluated at compile-time, there
@@ -841,47 +841,47 @@
\begin{figure}[htb]
\begin{center}
\begin{tabular}{ll}
- \isa{conjunction\ {\isacharcolon}{\isacharcolon}\ prop\ {\isasymRightarrow}\ prop\ {\isasymRightarrow}\ prop} & (infix \isa{{\isacharampersand}{\isacharampersand}{\isacharampersand}}) \\
- \isa{{\isasymturnstile}\ A\ {\isacharampersand}{\isacharampersand}{\isacharampersand}\ B\ {\isasymequiv}\ {\isacharparenleft}{\isasymAnd}C{\isachardot}\ {\isacharparenleft}A\ {\isasymLongrightarrow}\ B\ {\isasymLongrightarrow}\ C{\isacharparenright}\ {\isasymLongrightarrow}\ C{\isacharparenright}} \\[1ex]
- \isa{prop\ {\isacharcolon}{\isacharcolon}\ prop\ {\isasymRightarrow}\ prop} & (prefix \isa{{\isacharhash}}, suppressed) \\
- \isa{{\isacharhash}A\ {\isasymequiv}\ A} \\[1ex]
- \isa{term\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ {\isasymRightarrow}\ prop} & (prefix \isa{TERM}) \\
- \isa{term\ x\ {\isasymequiv}\ {\isacharparenleft}{\isasymAnd}A{\isachardot}\ A\ {\isasymLongrightarrow}\ A{\isacharparenright}} \\[1ex]
- \isa{TYPE\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ itself} & (prefix \isa{TYPE}) \\
- \isa{{\isacharparenleft}unspecified{\isacharparenright}} \\
+ \isa{conjunction\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ prop\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ prop\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ prop} & (infix \isa{{\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}}) \\
+ \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A\ {\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}\ B\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}C{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{29}{\isacharparenright}}} \\[1ex]
+ \isa{prop\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ prop\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ prop} & (prefix \isa{{\isaliteral{23}{\isacharhash}}}, suppressed) \\
+ \isa{{\isaliteral{23}{\isacharhash}}A\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ A} \\[1ex]
+ \isa{term\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ prop} & (prefix \isa{TERM}) \\
+ \isa{term\ x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}A{\isaliteral{2E}{\isachardot}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A{\isaliteral{29}{\isacharparenright}}} \\[1ex]
+ \isa{TYPE\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ itself} & (prefix \isa{TYPE}) \\
+ \isa{{\isaliteral{28}{\isacharparenleft}}unspecified{\isaliteral{29}{\isacharparenright}}} \\
\end{tabular}
\caption{Definitions of auxiliary connectives}\label{fig:pure-aux}
\end{center}
\end{figure}
- The introduction \isa{A\ {\isasymLongrightarrow}\ B\ {\isasymLongrightarrow}\ A\ {\isacharampersand}{\isacharampersand}{\isacharampersand}\ B}, and eliminations
- (projections) \isa{A\ {\isacharampersand}{\isacharampersand}{\isacharampersand}\ B\ {\isasymLongrightarrow}\ A} and \isa{A\ {\isacharampersand}{\isacharampersand}{\isacharampersand}\ B\ {\isasymLongrightarrow}\ B} are
+ The introduction \isa{A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ {\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}\ B}, and eliminations
+ (projections) \isa{A\ {\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A} and \isa{A\ {\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B} are
available as derived rules. Conjunction allows to treat
simultaneous assumptions and conclusions uniformly, e.g.\ consider
- \isa{A\ {\isasymLongrightarrow}\ B\ {\isasymLongrightarrow}\ C\ {\isacharampersand}{\isacharampersand}{\isacharampersand}\ D}. In particular, the goal mechanism
+ \isa{A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C\ {\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}\ D}. In particular, the goal mechanism
represents multiple claims as explicit conjunction internally, but
this is refined (via backwards introduction) into separate sub-goals
before the user commences the proof; the final result is projected
into a list of theorems using eliminations (cf.\
\secref{sec:tactical-goals}).
- The \isa{prop} marker (\isa{{\isacharhash}}) makes arbitrarily complex
- propositions appear as atomic, without changing the meaning: \isa{{\isasymGamma}\ {\isasymturnstile}\ A} and \isa{{\isasymGamma}\ {\isasymturnstile}\ {\isacharhash}A} are interchangeable. See
+ The \isa{prop} marker (\isa{{\isaliteral{23}{\isacharhash}}}) makes arbitrarily complex
+ propositions appear as atomic, without changing the meaning: \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A} and \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{23}{\isacharhash}}A} are interchangeable. See
\secref{sec:tactical-goals} for specific operations.
The \isa{term} marker turns any well-typed term into a derivable
- proposition: \isa{{\isasymturnstile}\ TERM\ t} holds unconditionally. Although
+ proposition: \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ TERM\ t} holds unconditionally. Although
this is logically vacuous, it allows to treat terms and proofs
uniformly, similar to a type-theoretic framework.
The \isa{TYPE} constructor is the canonical representative of
- the unspecified type \isa{{\isasymalpha}\ itself}; it essentially injects the
+ the unspecified type \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ itself}; it essentially injects the
language of types into that of terms. There is specific notation
- \isa{TYPE{\isacharparenleft}{\isasymtau}{\isacharparenright}} for \isa{TYPE\isactrlbsub {\isasymtau}\ itself\isactrlesub }.
- Although being devoid of any particular meaning, the term \isa{TYPE{\isacharparenleft}{\isasymtau}{\isacharparenright}} accounts for the type \isa{{\isasymtau}} within the term
- language. In particular, \isa{TYPE{\isacharparenleft}{\isasymalpha}{\isacharparenright}} may be used as formal
+ \isa{TYPE{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{29}{\isacharparenright}}} for \isa{TYPE\isaliteral{5C3C5E627375623E}{}\isactrlbsub {\isaliteral{5C3C7461753E}{\isasymtau}}\ itself\isaliteral{5C3C5E657375623E}{}\isactrlesub }.
+ Although being devoid of any particular meaning, the term \isa{TYPE{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{29}{\isacharparenright}}} accounts for the type \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} within the term
+ language. In particular, \isa{TYPE{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}} may be used as formal
argument in primitive definitions, in order to circumvent hidden
- polymorphism (cf.\ \secref{sec:terms}). For example, \isa{c\ TYPE{\isacharparenleft}{\isasymalpha}{\isacharparenright}\ {\isasymequiv}\ A{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}} defines \isa{c\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ itself\ {\isasymRightarrow}\ prop} in terms of
+ polymorphism (cf.\ \secref{sec:terms}). For example, \isa{c\ TYPE{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ A{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5D}{\isacharbrackright}}} defines \isa{c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ itself\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ prop} in terms of
a proposition \isa{A} that depends on an additional type
argument, which is essentially a predicate on types.%
\end{isamarkuptext}%
@@ -905,19 +905,19 @@
\begin{description}
- \item \verb|Conjunction.intr| derives \isa{A\ {\isacharampersand}{\isacharampersand}{\isacharampersand}\ B} from \isa{A} and \isa{B}.
+ \item \verb|Conjunction.intr| derives \isa{A\ {\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}\ B} from \isa{A} and \isa{B}.
\item \verb|Conjunction.elim| derives \isa{A} and \isa{B}
- from \isa{A\ {\isacharampersand}{\isacharampersand}{\isacharampersand}\ B}.
+ from \isa{A\ {\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}\ B}.
\item \verb|Drule.mk_term| derives \isa{TERM\ t}.
\item \verb|Drule.dest_term| recovers term \isa{t} from \isa{TERM\ t}.
- \item \verb|Logic.mk_type|~\isa{{\isasymtau}} produces the term \isa{TYPE{\isacharparenleft}{\isasymtau}{\isacharparenright}}.
+ \item \verb|Logic.mk_type|~\isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} produces the term \isa{TYPE{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{29}{\isacharparenright}}}.
- \item \verb|Logic.dest_type|~\isa{TYPE{\isacharparenleft}{\isasymtau}{\isacharparenright}} recovers the type
- \isa{{\isasymtau}}.
+ \item \verb|Logic.dest_type|~\isa{TYPE{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{29}{\isacharparenright}}} recovers the type
+ \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}}.
\end{description}%
\end{isamarkuptext}%
@@ -939,8 +939,8 @@
purposes. User-level reasoning usually works via object-level rules
that are represented as theorems of Pure. Composition of rules
involves \emph{backchaining}, \emph{higher-order unification} modulo
- \isa{{\isasymalpha}{\isasymbeta}{\isasymeta}}-conversion of \isa{{\isasymlambda}}-terms, and so-called
- \emph{lifting} of rules into a context of \isa{{\isasymAnd}} and \isa{{\isasymLongrightarrow}} connectives. Thus the full power of higher-order Natural
+ \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{5C3C6574613E}{\isasymeta}}}-conversion of \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}}-terms, and so-called
+ \emph{lifting} of rules into a context of \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}} and \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}} connectives. Thus the full power of higher-order Natural
Deduction in Isabelle/Pure becomes readily available.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -955,23 +955,23 @@
arbitrary nesting similar to \cite{extensions91}. The most basic
rule format is that of a \emph{Horn Clause}:
\[
- \infer{\isa{A}}{\isa{A\isactrlsub {\isadigit{1}}} & \isa{{\isasymdots}} & \isa{A\isactrlsub n}}
+ \infer{\isa{A}}{\isa{A\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}} & \isa{{\isaliteral{5C3C646F74733E}{\isasymdots}}} & \isa{A\isaliteral{5C3C5E7375623E}{}\isactrlsub n}}
\]
- where \isa{A{\isacharcomma}\ A\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ A\isactrlsub n} are atomic propositions
+ where \isa{A{\isaliteral{2C}{\isacharcomma}}\ A\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ A\isaliteral{5C3C5E7375623E}{}\isactrlsub n} are atomic propositions
of the framework, usually of the form \isa{Trueprop\ B}, where
\isa{B} is a (compound) object-level statement. This
object-level inference corresponds to an iterated implication in
Pure like this:
\[
- \isa{A\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ A\isactrlsub n\ {\isasymLongrightarrow}\ A}
+ \isa{A\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ A\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A}
\]
- As an example consider conjunction introduction: \isa{A\ {\isasymLongrightarrow}\ B\ {\isasymLongrightarrow}\ A\ {\isasymand}\ B}. Any parameters occurring in such rule statements are
+ As an example consider conjunction introduction: \isa{A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B}. Any parameters occurring in such rule statements are
conceptionally treated as arbitrary:
\[
- \isa{{\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ A\isactrlsub {\isadigit{1}}\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m\ {\isasymLongrightarrow}\ {\isasymdots}\ A\isactrlsub n\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m\ {\isasymLongrightarrow}\ A\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m}
+ \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{2E}{\isachardot}}\ A\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ A\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m}
\]
- Nesting of rules means that the positions of \isa{A\isactrlsub i} may
+ Nesting of rules means that the positions of \isa{A\isaliteral{5C3C5E7375623E}{}\isactrlsub i} may
again hold compound rules, not just atomic propositions.
Propositions of this format are called \emph{Hereditary Harrop
Formulae} in the literature \cite{Miller:1991}. Here we give an
@@ -979,17 +979,17 @@
\medskip
\begin{tabular}{ll}
- \isa{\isactrlbold x} & set of variables \\
- \isa{\isactrlbold A} & set of atomic propositions \\
- \isa{\isactrlbold H\ \ {\isacharequal}\ \ {\isasymAnd}\isactrlbold x\isactrlsup {\isacharasterisk}{\isachardot}\ \isactrlbold H\isactrlsup {\isacharasterisk}\ {\isasymLongrightarrow}\ \isactrlbold A} & set of Hereditary Harrop Formulas \\
+ \isa{\isaliteral{5C3C5E626F6C643E}{}\isactrlbold x} & set of variables \\
+ \isa{\isaliteral{5C3C5E626F6C643E}{}\isactrlbold A} & set of atomic propositions \\
+ \isa{\isaliteral{5C3C5E626F6C643E}{}\isactrlbold H\ \ {\isaliteral{3D}{\isacharequal}}\ \ {\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E626F6C643E}{}\isactrlbold x\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2E}{\isachardot}}\ \isaliteral{5C3C5E626F6C643E}{}\isactrlbold H\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ \isaliteral{5C3C5E626F6C643E}{}\isactrlbold A} & set of Hereditary Harrop Formulas \\
\end{tabular}
\medskip
Thus we essentially impose nesting levels on propositions formed
- from \isa{{\isasymAnd}} and \isa{{\isasymLongrightarrow}}. At each level there is a prefix
+ from \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}} and \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}}. At each level there is a prefix
of parameters and compound premises, concluding an atomic
- proposition. Typical examples are \isa{{\isasymlongrightarrow}}-introduction \isa{{\isacharparenleft}A\ {\isasymLongrightarrow}\ B{\isacharparenright}\ {\isasymLongrightarrow}\ A\ {\isasymlongrightarrow}\ B} or mathematical induction \isa{P\ {\isadigit{0}}\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymAnd}n{\isachardot}\ P\ n\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}\ {\isasymLongrightarrow}\ P\ n}. Even deeper nesting occurs in well-founded
- induction \isa{{\isacharparenleft}{\isasymAnd}x{\isachardot}\ {\isacharparenleft}{\isasymAnd}y{\isachardot}\ y\ {\isasymprec}\ x\ {\isasymLongrightarrow}\ P\ y{\isacharparenright}\ {\isasymLongrightarrow}\ P\ x{\isacharparenright}\ {\isasymLongrightarrow}\ P\ x}, but this
+ proposition. Typical examples are \isa{{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}}-introduction \isa{{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B} or mathematical induction \isa{P\ {\isadigit{0}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ P\ n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ n}. Even deeper nesting occurs in well-founded
+ induction \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}y{\isaliteral{2E}{\isachardot}}\ y\ {\isaliteral{5C3C707265633E}{\isasymprec}}\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ x}, but this
already marks the limit of rule complexity that is usually seen in
practice.
@@ -998,13 +998,13 @@
\begin{itemize}
- \item Normalization by \isa{{\isacharparenleft}A\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ B\ x{\isacharparenright}{\isacharparenright}\ {\isasymequiv}\ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ A\ {\isasymLongrightarrow}\ B\ x{\isacharparenright}},
+ \item Normalization by \isa{{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ x{\isaliteral{29}{\isacharparenright}}},
which is a theorem of Pure, means that quantifiers are pushed in
front of implication at each level of nesting. The normal form is a
Hereditary Harrop Formula.
\item The outermost prefix of parameters is represented via
- schematic variables: instead of \isa{{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec H\ \isactrlvec x\ {\isasymLongrightarrow}\ A\ \isactrlvec x} we have \isa{\isactrlvec H\ {\isacharquery}\isactrlvec x\ {\isasymLongrightarrow}\ A\ {\isacharquery}\isactrlvec x}.
+ schematic variables: instead of \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec H\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x} we have \isa{\isaliteral{5C3C5E7665633E}{}\isactrlvec H\ {\isaliteral{3F}{\isacharquery}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ {\isaliteral{3F}{\isacharquery}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x}.
Note that this representation looses information about the order of
parameters, and vacuous quantifiers vanish automatically.
@@ -1050,42 +1050,42 @@
\hyperlink{inference.resolution}{\mbox{\isa{resolution}}} (i.e.\ back-chaining of rules) and
\hyperlink{inference.assumption}{\mbox{\isa{assumption}}} (i.e.\ closing a branch), both modulo
higher-order unification. There are also combined variants, notably
- \hyperlink{inference.elim-resolution}{\mbox{\isa{elim{\isacharunderscore}resolution}}} and \hyperlink{inference.dest-resolution}{\mbox{\isa{dest{\isacharunderscore}resolution}}}.
+ \hyperlink{inference.elim-resolution}{\mbox{\isa{elim{\isaliteral{5F}{\isacharunderscore}}resolution}}} and \hyperlink{inference.dest-resolution}{\mbox{\isa{dest{\isaliteral{5F}{\isacharunderscore}}resolution}}}.
To understand the all-important \hyperlink{inference.resolution}{\mbox{\isa{resolution}}} principle,
we first consider raw \indexdef{}{inference}{composition}\hypertarget{inference.composition}{\hyperlink{inference.composition}{\mbox{\isa{composition}}}} (modulo
- higher-order unification with substitution \isa{{\isasymvartheta}}):
+ higher-order unification with substitution \isa{{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}}):
\[
- \infer[(\indexdef{}{inference}{composition}\hypertarget{inference.composition}{\hyperlink{inference.composition}{\mbox{\isa{composition}}}})]{\isa{\isactrlvec A{\isasymvartheta}\ {\isasymLongrightarrow}\ C{\isasymvartheta}}}
- {\isa{\isactrlvec A\ {\isasymLongrightarrow}\ B} & \isa{B{\isacharprime}\ {\isasymLongrightarrow}\ C} & \isa{B{\isasymvartheta}\ {\isacharequal}\ B{\isacharprime}{\isasymvartheta}}}
+ \infer[(\indexdef{}{inference}{composition}\hypertarget{inference.composition}{\hyperlink{inference.composition}{\mbox{\isa{composition}}}})]{\isa{\isaliteral{5C3C5E7665633E}{}\isactrlvec A{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}}}
+ {\isa{\isaliteral{5C3C5E7665633E}{}\isactrlvec A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B} & \isa{B{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C} & \isa{B{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}\ {\isaliteral{3D}{\isacharequal}}\ B{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}}}
\]
Here the conclusion of the first rule is unified with the premise of
the second; the resulting rule instance inherits the premises of the
first and conclusion of the second. Note that \isa{C} can again
consist of iterated implications. We can also permute the premises
- of the second rule back-and-forth in order to compose with \isa{B{\isacharprime}} in any position (subsequently we shall always refer to
+ of the second rule back-and-forth in order to compose with \isa{B{\isaliteral{27}{\isacharprime}}} in any position (subsequently we shall always refer to
position 1 w.l.o.g.).
In \hyperlink{inference.composition}{\mbox{\isa{composition}}} the internal structure of the common
- part \isa{B} and \isa{B{\isacharprime}} is not taken into account. For
+ part \isa{B} and \isa{B{\isaliteral{27}{\isacharprime}}} is not taken into account. For
proper \hyperlink{inference.resolution}{\mbox{\isa{resolution}}} we require \isa{B} to be atomic,
- and explicitly observe the structure \isa{{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec H\ \isactrlvec x\ {\isasymLongrightarrow}\ B{\isacharprime}\ \isactrlvec x} of the premise of the second rule. The
+ and explicitly observe the structure \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec H\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{27}{\isacharprime}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x} of the premise of the second rule. The
idea is to adapt the first rule by ``lifting'' it into this context,
by means of iterated application of the following inferences:
\[
- \infer[(\indexdef{}{inference}{imp\_lift}\hypertarget{inference.imp-lift}{\hyperlink{inference.imp-lift}{\mbox{\isa{imp{\isacharunderscore}lift}}}})]{\isa{{\isacharparenleft}\isactrlvec H\ {\isasymLongrightarrow}\ \isactrlvec A{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}\isactrlvec H\ {\isasymLongrightarrow}\ B{\isacharparenright}}}{\isa{\isactrlvec A\ {\isasymLongrightarrow}\ B}}
+ \infer[(\indexdef{}{inference}{imp\_lift}\hypertarget{inference.imp-lift}{\hyperlink{inference.imp-lift}{\mbox{\isa{imp{\isaliteral{5F}{\isacharunderscore}}lift}}}})]{\isa{{\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec H\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec H\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{29}{\isacharparenright}}}}{\isa{\isaliteral{5C3C5E7665633E}{}\isactrlvec A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B}}
\]
\[
- \infer[(\indexdef{}{inference}{all\_lift}\hypertarget{inference.all-lift}{\hyperlink{inference.all-lift}{\mbox{\isa{all{\isacharunderscore}lift}}}})]{\isa{{\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec A\ {\isacharparenleft}{\isacharquery}\isactrlvec a\ \isactrlvec x{\isacharparenright}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ B\ {\isacharparenleft}{\isacharquery}\isactrlvec a\ \isactrlvec x{\isacharparenright}{\isacharparenright}}}{\isa{\isactrlvec A\ {\isacharquery}\isactrlvec a\ {\isasymLongrightarrow}\ B\ {\isacharquery}\isactrlvec a}}
+ \infer[(\indexdef{}{inference}{all\_lift}\hypertarget{inference.all-lift}{\hyperlink{inference.all-lift}{\mbox{\isa{all{\isaliteral{5F}{\isacharunderscore}}lift}}}})]{\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec A\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}\isaliteral{5C3C5E7665633E}{}\isactrlvec a\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ B\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}\isaliteral{5C3C5E7665633E}{}\isactrlvec a\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}}}{\isa{\isaliteral{5C3C5E7665633E}{}\isactrlvec A\ {\isaliteral{3F}{\isacharquery}}\isaliteral{5C3C5E7665633E}{}\isactrlvec a\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{3F}{\isacharquery}}\isaliteral{5C3C5E7665633E}{}\isactrlvec a}}
\]
By combining raw composition with lifting, we get full \hyperlink{inference.resolution}{\mbox{\isa{resolution}}} as follows:
\[
\infer[(\indexdef{}{inference}{resolution}\hypertarget{inference.resolution}{\hyperlink{inference.resolution}{\mbox{\isa{resolution}}}})]
- {\isa{{\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec H\ \isactrlvec x\ {\isasymLongrightarrow}\ \isactrlvec A\ {\isacharparenleft}{\isacharquery}\isactrlvec a\ \isactrlvec x{\isacharparenright}{\isacharparenright}{\isasymvartheta}\ {\isasymLongrightarrow}\ C{\isasymvartheta}}}
+ {\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec H\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec A\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}\isaliteral{5C3C5E7665633E}{}\isactrlvec a\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}}}
{\begin{tabular}{l}
- \isa{\isactrlvec A\ {\isacharquery}\isactrlvec a\ {\isasymLongrightarrow}\ B\ {\isacharquery}\isactrlvec a} \\
- \isa{{\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec H\ \isactrlvec x\ {\isasymLongrightarrow}\ B{\isacharprime}\ \isactrlvec x{\isacharparenright}\ {\isasymLongrightarrow}\ C} \\
- \isa{{\isacharparenleft}{\isasymlambda}\isactrlvec x{\isachardot}\ B\ {\isacharparenleft}{\isacharquery}\isactrlvec a\ \isactrlvec x{\isacharparenright}{\isacharparenright}{\isasymvartheta}\ {\isacharequal}\ B{\isacharprime}{\isasymvartheta}} \\
+ \isa{\isaliteral{5C3C5E7665633E}{}\isactrlvec A\ {\isaliteral{3F}{\isacharquery}}\isaliteral{5C3C5E7665633E}{}\isactrlvec a\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{3F}{\isacharquery}}\isaliteral{5C3C5E7665633E}{}\isactrlvec a} \\
+ \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec H\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{27}{\isacharprime}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C} \\
+ \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ B\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}\isaliteral{5C3C5E7665633E}{}\isactrlvec a\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}\ {\isaliteral{3D}{\isacharequal}}\ B{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}} \\
\end{tabular}}
\]
@@ -1094,11 +1094,11 @@
a rule of 0 premises, or by producing a ``short-circuit'' within a
solved situation (again modulo unification):
\[
- \infer[(\indexdef{}{inference}{assumption}\hypertarget{inference.assumption}{\hyperlink{inference.assumption}{\mbox{\isa{assumption}}}})]{\isa{C{\isasymvartheta}}}
- {\isa{{\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec H\ \isactrlvec x\ {\isasymLongrightarrow}\ A\ \isactrlvec x{\isacharparenright}\ {\isasymLongrightarrow}\ C} & \isa{A{\isasymvartheta}\ {\isacharequal}\ H\isactrlsub i{\isasymvartheta}}~~\text{(for some~\isa{i})}}
+ \infer[(\indexdef{}{inference}{assumption}\hypertarget{inference.assumption}{\hyperlink{inference.assumption}{\mbox{\isa{assumption}}}})]{\isa{C{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}}}
+ {\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec H\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C} & \isa{A{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}\ {\isaliteral{3D}{\isacharequal}}\ H\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}}~~\text{(for some~\isa{i})}}
\]
- FIXME \indexdef{}{inference}{elim\_resolution}\hypertarget{inference.elim-resolution}{\hyperlink{inference.elim-resolution}{\mbox{\isa{elim{\isacharunderscore}resolution}}}}, \indexdef{}{inference}{dest\_resolution}\hypertarget{inference.dest-resolution}{\hyperlink{inference.dest-resolution}{\mbox{\isa{dest{\isacharunderscore}resolution}}}}%
+ FIXME \indexdef{}{inference}{elim\_resolution}\hypertarget{inference.elim-resolution}{\hyperlink{inference.elim-resolution}{\mbox{\isa{elim{\isaliteral{5F}{\isacharunderscore}}resolution}}}}, \indexdef{}{inference}{dest\_resolution}\hypertarget{inference.dest-resolution}{\hyperlink{inference.dest-resolution}{\mbox{\isa{dest{\isaliteral{5F}{\isacharunderscore}}resolution}}}}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -1116,15 +1116,15 @@
\begin{description}
- \item \isa{rule\isactrlsub {\isadigit{1}}\ RS\ rule\isactrlsub {\isadigit{2}}} resolves \isa{rule\isactrlsub {\isadigit{1}}} with \isa{rule\isactrlsub {\isadigit{2}}} according to the \hyperlink{inference.resolution}{\mbox{\isa{resolution}}} principle
+ \item \isa{rule\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ RS\ rule\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}} resolves \isa{rule\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}} with \isa{rule\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}} according to the \hyperlink{inference.resolution}{\mbox{\isa{resolution}}} principle
explained above. Note that the corresponding rule attribute in the
Isar language is called \hyperlink{attribute.THEN}{\mbox{\isa{THEN}}}.
\item \isa{rule\ OF\ rules} resolves a list of rules with the
- first rule, addressing its premises \isa{{\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ length\ rules}
+ first rule, addressing its premises \isa{{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ length\ rules}
(operating from last to first). This means the newly emerging
premises are all concatenated, without interfering. Also note that
- compared to \isa{RS}, the rule argument order is swapped: \isa{rule\isactrlsub {\isadigit{1}}\ RS\ rule\isactrlsub {\isadigit{2}}\ {\isacharequal}\ rule\isactrlsub {\isadigit{2}}\ OF\ {\isacharbrackleft}rule\isactrlsub {\isadigit{1}}{\isacharbrackright}}.
+ compared to \isa{RS}, the rule argument order is swapped: \isa{rule\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ RS\ rule\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ rule\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ OF\ {\isaliteral{5B}{\isacharbrackleft}}rule\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}}.
\end{description}%
\end{isamarkuptext}%
--- a/doc-src/IsarImplementation/Thy/document/ML.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarImplementation/Thy/document/ML.tex Mon Nov 08 14:41:11 2010 +0100
@@ -8,7 +8,7 @@
%
\isatagtheory
\isacommand{theory}\isamarkupfalse%
-\ {\isachardoublequoteopen}ML{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}ML{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{imports}\ Base\isanewline
\isakeyword{begin}%
\endisatagtheory
@@ -89,7 +89,7 @@
Isabelle source files have a certain standardized header
format (with precise spacing) that follows ancient traditions
reaching back to the earliest versions of the system by Larry
- Paulson. See \hyperlink{file.~~/src/Pure/thm.ML}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}Pure{\isacharslash}thm{\isachardot}ML}}}}, for example.
+ Paulson. See \hyperlink{file.~~/src/Pure/thm.ML}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}Pure{\isaliteral{2F}{\isacharslash}}thm{\isaliteral{2E}{\isachardot}}ML}}}}, for example.
The header includes at least \verb|Title| and \verb|Author| entries, followed by a prose description of the purpose of
the module. The latter can range from a single line to several
@@ -350,7 +350,7 @@
Some special infixes (e.g.\ \verb||\verb,|,\verb|>|) work better at the
start of the line, but punctuation is always at the end.
- Function application follows the tradition of \isa{{\isasymlambda}}-calculus,
+ Function application follows the tradition of \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}}-calculus,
not informal mathematics. For example: \verb|f a b| for a
curried function, or \verb|g (a, b)| for a tupled function.
Note that the space between \verb|g| and the pair \verb|(a, b)| follows the important principle of
@@ -599,10 +599,10 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ fun\ factorial\ {\isadigit{0}}\ {\isacharequal}\ {\isadigit{1}}\isanewline
-\ \ \ \ {\isacharbar}\ factorial\ n\ {\isacharequal}\ n\ {\isacharasterisk}\ factorial\ {\isacharparenleft}n\ {\isacharminus}\ {\isadigit{1}}{\isacharparenright}\isanewline
-{\isacharverbatimclose}%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ fun\ factorial\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}\isanewline
+\ \ \ \ {\isaliteral{7C}{\isacharbar}}\ factorial\ n\ {\isaliteral{3D}{\isacharequal}}\ n\ {\isaliteral{2A}{\isacharasterisk}}\ factorial\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -625,12 +625,12 @@
nodes of the implicit theory development graph.}
\medskip The next example shows how to embed ML into Isar proofs, using
- \indexref{}{command}{ML\_prf}\hyperlink{command.ML-prf}{\mbox{\isa{\isacommand{ML{\isacharunderscore}prf}}}} instead of Instead of \indexref{}{command}{ML}\hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}}.
+ \indexref{}{command}{ML\_prf}\hyperlink{command.ML-prf}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}prf}}}} instead of Instead of \indexref{}{command}{ML}\hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}}.
As illustrated below, the effect on the ML environment is local to
the whole proof body, ignoring the block structure.%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{example{\isacharunderscore}proof}\isamarkupfalse%
+\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}\isamarkupfalse%
\isanewline
%
\isadelimML
@@ -638,19 +638,19 @@
\endisadelimML
%
\isatagML
-\isacommand{ML{\isacharunderscore}prf}\isamarkupfalse%
-\ {\isacharverbatimopen}\ val\ a\ {\isacharequal}\ {\isadigit{1}}\ {\isacharverbatimclose}\isanewline
-\ \ \isacommand{{\isacharbraceleft}}\isamarkupfalse%
+\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}prf}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ val\ a\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
+\ \ \isacommand{{\isaliteral{7B}{\isacharbraceleft}}}\isamarkupfalse%
\isanewline
-\ \ \ \ \isacommand{ML{\isacharunderscore}prf}\isamarkupfalse%
-\ {\isacharverbatimopen}\ val\ b\ {\isacharequal}\ a\ {\isacharplus}\ {\isadigit{1}}\ {\isacharverbatimclose}\isanewline
-\ \ \isacommand{{\isacharbraceright}}\isamarkupfalse%
+\ \ \ \ \isacommand{ML{\isaliteral{5F}{\isacharunderscore}}prf}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ val\ b\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
+\ \ \isacommand{{\isaliteral{7D}{\isacharbraceright}}}\isamarkupfalse%
\ %
\isamarkupcmt{Isar block structure ignored by ML environment%
}
\isanewline
-\ \ \isacommand{ML{\isacharunderscore}prf}\isamarkupfalse%
-\ {\isacharverbatimopen}\ val\ c\ {\isacharequal}\ b\ {\isacharplus}\ {\isadigit{1}}\ {\isacharverbatimclose}\isanewline
+\ \ \isacommand{ML{\isaliteral{5F}{\isacharunderscore}}prf}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ val\ c\ {\isaliteral{3D}{\isacharequal}}\ b\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagML
@@ -667,12 +667,12 @@
context.
\medskip Two further ML commands are useful in certain situations:
- \indexref{}{command}{ML\_val}\hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isacharunderscore}val}}}} and \indexref{}{command}{ML\_command}\hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isacharunderscore}command}}}} are
+ \indexref{}{command}{ML\_val}\hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}}}} and \indexref{}{command}{ML\_command}\hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}command}}}} are
\emph{diagnostic} in the sense that there is no effect on the
underlying environment, and can thus used anywhere (even outside a
theory). The examples below produce long strings of digits by
- invoking \verb|factorial|: \hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isacharunderscore}val}}}} already takes care of
- printing the ML toplevel result, but \hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isacharunderscore}command}}}} is silent
+ invoking \verb|factorial|: \hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}}}} already takes care of
+ printing the ML toplevel result, but \hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}command}}}} is silent
so we produce an explicit output message.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -682,10 +682,10 @@
\endisadelimML
%
\isatagML
-\isacommand{ML{\isacharunderscore}val}\isamarkupfalse%
-\ {\isacharverbatimopen}\ factorial\ {\isadigit{1}}{\isadigit{0}}{\isadigit{0}}\ {\isacharverbatimclose}\isanewline
-\isacommand{ML{\isacharunderscore}command}\isamarkupfalse%
-\ {\isacharverbatimopen}\ writeln\ {\isacharparenleft}string{\isacharunderscore}of{\isacharunderscore}int\ {\isacharparenleft}factorial\ {\isadigit{1}}{\isadigit{0}}{\isadigit{0}}{\isacharparenright}{\isacharparenright}\ {\isacharverbatimclose}%
+\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ factorial\ {\isadigit{1}}{\isadigit{0}}{\isadigit{0}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
+\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}command}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ writeln\ {\isaliteral{28}{\isacharparenleft}}string{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{28}{\isacharparenleft}}factorial\ {\isadigit{1}}{\isadigit{0}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -694,7 +694,7 @@
\endisadelimML
\isanewline
\isanewline
-\isacommand{example{\isacharunderscore}proof}\isamarkupfalse%
+\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}\isamarkupfalse%
\isanewline
%
\isadelimML
@@ -702,10 +702,10 @@
\endisadelimML
%
\isatagML
-\isacommand{ML{\isacharunderscore}val}\isamarkupfalse%
-\ {\isacharverbatimopen}\ factorial\ {\isadigit{1}}{\isadigit{0}}{\isadigit{0}}\ {\isacharverbatimclose}\ \ \isanewline
-\ \ \isacommand{ML{\isacharunderscore}command}\isamarkupfalse%
-\ {\isacharverbatimopen}\ writeln\ {\isacharparenleft}string{\isacharunderscore}of{\isacharunderscore}int\ {\isacharparenleft}factorial\ {\isadigit{1}}{\isadigit{0}}{\isadigit{0}}{\isacharparenright}{\isacharparenright}\ {\isacharverbatimclose}%
+\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ factorial\ {\isadigit{1}}{\isadigit{0}}{\isadigit{0}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}\ \ \isanewline
+\ \ \isacommand{ML{\isaliteral{5F}{\isacharunderscore}}command}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ writeln\ {\isaliteral{28}{\isacharparenleft}}string{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}int\ {\isaliteral{28}{\isacharparenleft}}factorial\ {\isadigit{1}}{\isadigit{0}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -767,7 +767,7 @@
\item \verb|Context.>>|~\isa{f} applies context transformation
\isa{f} to the implicit context of the ML toplevel.
- \item \verb|bind_thms|~\isa{{\isacharparenleft}name{\isacharcomma}\ thms{\isacharparenright}} stores a list of
+ \item \verb|bind_thms|~\isa{{\isaliteral{28}{\isacharparenleft}}name{\isaliteral{2C}{\isacharcomma}}\ thms{\isaliteral{29}{\isacharparenright}}} stores a list of
theorems produced in ML both in the (global) theory context and the
ML toplevel, associating it with the provided name. Theorems are
put into a global ``standard'' format before being stored.
@@ -811,17 +811,17 @@
categories \cite{isabelle-isar-ref}. Attributes and proof methods
use similar syntax.
- \medskip A regular antiquotation \isa{{\isacharat}{\isacharbraceleft}name\ args{\isacharbraceright}} processes
+ \medskip A regular antiquotation \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}name\ args{\isaliteral{7D}{\isacharbraceright}}} processes
its arguments by the usual means of the Isar source language, and
produces corresponding ML source text, either as literal
- \emph{inline} text (e.g. \isa{{\isacharat}{\isacharbraceleft}term\ t{\isacharbraceright}}) or abstract
- \emph{value} (e.g. \isa{{\isacharat}{\isacharbraceleft}thm\ th{\isacharbraceright}}). This pre-compilation
+ \emph{inline} text (e.g. \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}term\ t{\isaliteral{7D}{\isacharbraceright}}}) or abstract
+ \emph{value} (e.g. \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}thm\ th{\isaliteral{7D}{\isacharbraceright}}}). This pre-compilation
scheme allows to refer to formal entities in a robust manner, with
proper static scoping and with some degree of logical checking of
small portions of the code.
- Special antiquotations like \isa{{\isacharat}{\isacharbraceleft}let\ {\isasymdots}{\isacharbraceright}} or \isa{{\isacharat}{\isacharbraceleft}note\ {\isasymdots}{\isacharbraceright}} augment the compilation context without generating code. The
- non-ASCII braces \isa{{\isasymlbrace}} and \isa{{\isasymrbrace}} allow to delimit the
+ Special antiquotations like \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}let\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{7D}{\isacharbraceright}}} or \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}note\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{7D}{\isacharbraceright}}} augment the compilation context without generating code. The
+ non-ASCII braces \isa{{\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}} and \isa{{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}} allow to delimit the
effect by introducing local blocks within the pre-compilation
environment.
@@ -838,8 +838,8 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{ML antiquotation}{let}\hypertarget{ML antiquotation.let}{\hyperlink{ML antiquotation.let}{\mbox{\isa{let}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{note}\hypertarget{ML antiquotation.note}{\hyperlink{ML antiquotation.note}{\mbox{\isa{note}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
+ \indexdef{}{ML antiquotation}{let}\hypertarget{ML antiquotation.let}{\hyperlink{ML antiquotation.let}{\mbox{\isa{let}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{note}\hypertarget{ML antiquotation.note}{\hyperlink{ML antiquotation.note}{\mbox{\isa{note}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
\end{matharray}
\begin{rail}
@@ -852,12 +852,12 @@
\begin{description}
- \item \isa{{\isacharat}{\isacharbraceleft}let\ p\ {\isacharequal}\ t{\isacharbraceright}} binds schematic variables in the
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}let\ p\ {\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{7D}{\isacharbraceright}}} binds schematic variables in the
pattern \isa{p} by higher-order matching against the term \isa{t}. This is analogous to the regular \indexref{}{command}{let}\hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}} command
in the Isar proof language. The pre-compilation environment is
augmented by auxiliary term bindings, without emitting ML source.
- \item \isa{{\isacharat}{\isacharbraceleft}note\ a\ {\isacharequal}\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isacharbraceright}} recalls existing facts \isa{b\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ b\isactrlsub n}, binding the result as \isa{a}. This is analogous to
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}note\ a\ {\isaliteral{3D}{\isacharequal}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{7D}{\isacharbraceright}}} recalls existing facts \isa{b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n}, binding the result as \isa{a}. This is analogous to
the regular \indexref{}{command}{note}\hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}} command in the Isar proof language.
The pre-compilation environment is augmented by auxiliary fact
bindings, without emitting ML source.
@@ -882,7 +882,7 @@
\begin{isamarkuptext}%
The following artificial example gives some impression
about the antiquotation elements introduced so far, together with
- the important \isa{{\isacharat}{\isacharbraceleft}thm{\isacharbraceright}} antiquotation defined later.%
+ the important \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}thm{\isaliteral{7D}{\isacharbraceright}}} antiquotation defined later.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -899,25 +899,25 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ {\isaantiqopen}\isanewline
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ {\isaliteral{5C3C6C62726163653E}{\isaantiqopen}}\isanewline
\ \ \ \ %
\isaantiq
-let\ {\isacharquery}t\ {\isacharequal}\ my{\isacharunderscore}term%
+let\ {\isaliteral{3F}{\isacharquery}}t\ {\isaliteral{3D}{\isacharequal}}\ my{\isaliteral{5F}{\isacharunderscore}}term{}%
\endisaantiq
\isanewline
\ \ \ \ %
\isaantiq
-note\ my{\isacharunderscore}refl\ {\isacharequal}\ reflexive\ {\isacharbrackleft}of\ {\isacharquery}t{\isacharbrackright}%
+note\ my{\isaliteral{5F}{\isacharunderscore}}refl\ {\isaliteral{3D}{\isacharequal}}\ reflexive\ {\isaliteral{5B}{\isacharbrackleft}}of\ {\isaliteral{3F}{\isacharquery}}t{\isaliteral{5D}{\isacharbrackright}}{}%
\endisaantiq
\isanewline
-\ \ \ \ fun\ foo\ th\ {\isacharequal}\ Thm{\isachardot}transitive\ th\ %
+\ \ \ \ fun\ foo\ th\ {\isaliteral{3D}{\isacharequal}}\ Thm{\isaliteral{2E}{\isachardot}}transitive\ th\ %
\isaantiq
-thm\ my{\isacharunderscore}refl%
+thm\ my{\isaliteral{5F}{\isacharunderscore}}refl{}%
\endisaantiq
\isanewline
-\ \ {\isaantiqclose}\isanewline
-{\isacharverbatimclose}%
+\ \ {\isaliteral{5C3C7262726163653E}{\isaantiqclose}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -937,25 +937,25 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-Standard ML is a language in the tradition of \isa{{\isasymlambda}}-calculus and \emph{higher-order functional programming},
+Standard ML is a language in the tradition of \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}}-calculus and \emph{higher-order functional programming},
similar to OCaml, Haskell, or Isabelle/Pure and HOL as logical
languages. Getting acquainted with the native style of representing
functions in that setting can save a lot of extra boiler-plate of
redundant shuffling of arguments, auxiliary abstractions etc.
Functions are usually \emph{curried}: the idea of turning arguments
- of type \isa{{\isasymtau}\isactrlsub i} (for \isa{i\ {\isasymin}\ {\isacharbraceleft}{\isadigit{1}}{\isacharcomma}\ {\isasymdots}\ n{\isacharbraceright}}) into a result of
- type \isa{{\isasymtau}} is represented by the iterated function space
- \isa{{\isasymtau}\isactrlsub {\isadigit{1}}\ {\isasymrightarrow}\ {\isasymdots}\ {\isasymrightarrow}\ {\isasymtau}\isactrlsub n\ {\isasymrightarrow}\ {\isasymtau}}. This is isomorphic to the well-known
- encoding via tuples \isa{{\isasymtau}\isactrlsub {\isadigit{1}}\ {\isasymtimes}\ {\isasymdots}\ {\isasymtimes}\ {\isasymtau}\isactrlsub n\ {\isasymrightarrow}\ {\isasymtau}}, but the curried
+ of type \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i} (for \isa{i\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{7B}{\isacharbraceleft}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ n{\isaliteral{7D}{\isacharbraceright}}}) into a result of
+ type \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} is represented by the iterated function space
+ \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}}. This is isomorphic to the well-known
+ encoding via tuples \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}}, but the curried
version fits more smoothly into the basic calculus.\footnote{The
difference is even more significant in higher-order logic, because
the redundant tuple structure needs to be accommodated by formal
reasoning.}
Currying gives some flexiblity due to \emph{partial application}. A
- function \isa{f{\isacharcolon}\ {\isasymtau}\isactrlsub {\isadigit{1}}\ {\isasymrightarrow}\ {\isasymtau}\isactrlbsub {\isadigit{2}}\isactrlesub \ {\isasymrightarrow}\ {\isasymtau}} can be applied to \isa{x{\isacharcolon}\ {\isasymtau}\isactrlsub {\isadigit{1}}}
- and the remaining \isa{{\isacharparenleft}f\ x{\isacharparenright}{\isacharcolon}\ {\isasymtau}\isactrlsub {\isadigit{2}}\ {\isasymrightarrow}\ {\isasymtau}} passed to another function
+ function \isa{f{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E627375623E}{}\isactrlbsub {\isadigit{2}}\isaliteral{5C3C5E657375623E}{}\isactrlesub \ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}} can be applied to \isa{x{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}}
+ and the remaining \isa{{\isaliteral{28}{\isacharparenleft}}f\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}} passed to another function
etc. How well this works in practice depends on the order of
arguments. In the worst case, arguments are arranged erratically,
and using a function in a certain situation always requires some
@@ -965,8 +965,8 @@
This can be avoided by \emph{canonical argument order}, which
observes certain standard patterns and minimizes adhoc permutations
in their application. In Isabelle/ML, large portions of text can be
- written without ever using \isa{swap{\isacharcolon}\ {\isasymalpha}\ {\isasymtimes}\ {\isasymbeta}\ {\isasymrightarrow}\ {\isasymbeta}\ {\isasymtimes}\ {\isasymalpha}}, or the
- combinator \isa{C{\isacharcolon}\ {\isacharparenleft}{\isasymalpha}\ {\isasymrightarrow}\ {\isasymbeta}\ {\isasymrightarrow}\ {\isasymgamma}{\isacharparenright}\ {\isasymrightarrow}\ {\isacharparenleft}{\isasymbeta}\ {\isasymrightarrow}\ {\isasymalpha}\ {\isasymrightarrow}\ {\isasymgamma}{\isacharparenright}} that is not even
+ written without ever using \isa{swap{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}}, or the
+ combinator \isa{C{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C67616D6D613E}{\isasymgamma}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C626574613E}{\isasymbeta}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C67616D6D613E}{\isasymgamma}}{\isaliteral{29}{\isacharparenright}}} that is not even
defined in our library.
\medskip The basic idea is that arguments that vary less are moved
@@ -975,30 +975,30 @@
\emph{updates}.
The subsequent scheme is based on a hypothetical set-like container
- of type \isa{{\isasymbeta}} that manages elements of type \isa{{\isasymalpha}}. Both
+ of type \isa{{\isaliteral{5C3C626574613E}{\isasymbeta}}} that manages elements of type \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}}. Both
the names and types of the associated operations are canonical for
Isabelle/ML.
\medskip
\begin{tabular}{ll}
kind & canonical name and type \\\hline
- selector & \isa{member{\isacharcolon}\ {\isasymbeta}\ {\isasymrightarrow}\ {\isasymalpha}\ {\isasymrightarrow}\ bool} \\
- update & \isa{insert{\isacharcolon}\ {\isasymalpha}\ {\isasymrightarrow}\ {\isasymbeta}\ {\isasymrightarrow}\ {\isasymbeta}} \\
+ selector & \isa{member{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ bool} \\
+ update & \isa{insert{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}} \\
\end{tabular}
\medskip
- Given a container \isa{B{\isacharcolon}\ {\isasymbeta}}, the partially applied \isa{member\ B} is a predicate over elements \isa{{\isasymalpha}\ {\isasymrightarrow}\ bool}, and
+ Given a container \isa{B{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}}, the partially applied \isa{member\ B} is a predicate over elements \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ bool}, and
thus represents the intended denotation directly. It is customary
to pass the abstract predicate to further operations, not the
concrete container. The argument order makes it easy to use other
- combinators: \isa{forall\ {\isacharparenleft}member\ B{\isacharparenright}\ list} will check a list of
+ combinators: \isa{forall\ {\isaliteral{28}{\isacharparenleft}}member\ B{\isaliteral{29}{\isacharparenright}}\ list} will check a list of
elements for membership in \isa{B} etc. Often the explicit
- \isa{list} is pointless and can be contracted to \isa{forall\ {\isacharparenleft}member\ B{\isacharparenright}} to get directly a predicate again.
+ \isa{list} is pointless and can be contracted to \isa{forall\ {\isaliteral{28}{\isacharparenleft}}member\ B{\isaliteral{29}{\isacharparenright}}} to get directly a predicate again.
In contrast, an update operation varies the container, so it moves
- to the right: \isa{insert\ a} is a function \isa{{\isasymbeta}\ {\isasymrightarrow}\ {\isasymbeta}} to
+ to the right: \isa{insert\ a} is a function \isa{{\isaliteral{5C3C626574613E}{\isasymbeta}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}} to
insert a value \isa{a}. These can be composed naturally as
- \isa{insert\ c\ {\isasymcirc}\ insert\ b\ {\isasymcirc}\ insert\ a}. The slightly awkward
+ \isa{insert\ c\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ insert\ b\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ insert\ a}. The slightly awkward
inversion of the composition order is due to conventional
mathematical notation, which can be easily amended as explained
below.%
@@ -1011,8 +1011,8 @@
%
\begin{isamarkuptext}%
Regular function application and infix notation works best for
- relatively deeply structured expressions, e.g.\ \isa{h\ {\isacharparenleft}f\ x\ y\ {\isacharplus}\ g\ z{\isacharparenright}}. The important special case of \emph{linear transformation}
- applies a cascade of functions \isa{f\isactrlsub n\ {\isacharparenleft}{\isasymdots}\ {\isacharparenleft}f\isactrlsub {\isadigit{1}}\ x{\isacharparenright}{\isacharparenright}}. This
+ relatively deeply structured expressions, e.g.\ \isa{h\ {\isaliteral{28}{\isacharparenleft}}f\ x\ y\ {\isaliteral{2B}{\isacharplus}}\ g\ z{\isaliteral{29}{\isacharparenright}}}. The important special case of \emph{linear transformation}
+ applies a cascade of functions \isa{f\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{28}{\isacharparenleft}}f\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}}. This
becomes hard to read and maintain if the functions are themselves
given as complex expressions. The notation can be significantly
improved by introducing \emph{forward} versions of application and
@@ -1020,13 +1020,13 @@
\medskip
\begin{tabular}{lll}
- \isa{x\ {\isacharbar}{\isachargreater}\ f} & \isa{{\isasymequiv}} & \isa{f\ x} \\
- \isa{f\ {\isacharhash}{\isachargreater}\ g} & \isa{{\isasymequiv}} & \isa{x\ {\isacharbar}{\isachargreater}\ f\ {\isacharbar}{\isachargreater}\ g} \\
+ \isa{x\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ f} & \isa{{\isaliteral{5C3C65717569763E}{\isasymequiv}}} & \isa{f\ x} \\
+ \isa{f\ {\isaliteral{23}{\isacharhash}}{\isaliteral{3E}{\isachargreater}}\ g} & \isa{{\isaliteral{5C3C65717569763E}{\isasymequiv}}} & \isa{x\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ f\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ g} \\
\end{tabular}
\medskip
- This enables to write conveniently \isa{x\ {\isacharbar}{\isachargreater}\ f\isactrlsub {\isadigit{1}}\ {\isacharbar}{\isachargreater}\ {\isasymdots}\ {\isacharbar}{\isachargreater}\ f\isactrlsub n} or
- \isa{f\isactrlsub {\isadigit{1}}\ {\isacharhash}{\isachargreater}\ {\isasymdots}\ {\isacharhash}{\isachargreater}\ f\isactrlsub n} for its functional abstraction over \isa{x}.
+ This enables to write conveniently \isa{x\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ f\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ f\isaliteral{5C3C5E7375623E}{}\isactrlsub n} or
+ \isa{f\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{23}{\isacharhash}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{23}{\isacharhash}}{\isaliteral{3E}{\isachargreater}}\ f\isaliteral{5C3C5E7375623E}{}\isactrlsub n} for its functional abstraction over \isa{x}.
\medskip There is an additional set of combinators to accommodate
multiple results (via pairs) that are passed on as multiple
@@ -1034,8 +1034,8 @@
\medskip
\begin{tabular}{lll}
- \isa{{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isacharbar}{\isacharminus}{\isachargreater}\ f} & \isa{{\isasymequiv}} & \isa{f\ x\ y} \\
- \isa{f\ {\isacharhash}{\isacharminus}{\isachargreater}\ g} & \isa{{\isasymequiv}} & \isa{x\ {\isacharbar}{\isachargreater}\ f\ {\isacharbar}{\isacharminus}{\isachargreater}\ g} \\
+ \isa{{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ f} & \isa{{\isaliteral{5C3C65717569763E}{\isasymequiv}}} & \isa{f\ x\ y} \\
+ \isa{f\ {\isaliteral{23}{\isacharhash}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ g} & \isa{{\isaliteral{5C3C65717569763E}{\isasymequiv}}} & \isa{x\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ f\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ g} \\
\end{tabular}
\medskip%
\end{isamarkuptext}%
@@ -1071,24 +1071,24 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-As explained above, a function \isa{f{\isacharcolon}\ {\isasymalpha}\ {\isasymrightarrow}\ {\isasymbeta}\ {\isasymrightarrow}\ {\isasymbeta}} can be
- understood as update on a configuration of type \isa{{\isasymbeta}},
- parametrized by arguments of type \isa{{\isasymalpha}}. Given \isa{a{\isacharcolon}\ {\isasymalpha}}
- the partial application \isa{{\isacharparenleft}f\ a{\isacharparenright}{\isacharcolon}\ {\isasymbeta}\ {\isasymrightarrow}\ {\isasymbeta}} operates
- homogeneously on \isa{{\isasymbeta}}. This can be iterated naturally over a
- list of parameters \isa{{\isacharbrackleft}a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n{\isacharbrackright}} as \isa{f\ a\isactrlsub {\isadigit{1}}\ {\isacharhash}{\isachargreater}\ {\isasymdots}\ {\isacharhash}{\isachargreater}\ f\ a\isactrlbsub n\isactrlesub \isactrlbsub \isactrlesub }. The latter expression is again a function \isa{{\isasymbeta}\ {\isasymrightarrow}\ {\isasymbeta}}.
- It can be applied to an initial configuration \isa{b{\isacharcolon}\ {\isasymbeta}} to
- start the iteration over the given list of arguments: each \isa{a} in \isa{a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n} is applied consecutively by updating a
+As explained above, a function \isa{f{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}} can be
+ understood as update on a configuration of type \isa{{\isaliteral{5C3C626574613E}{\isasymbeta}}},
+ parametrized by arguments of type \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}}. Given \isa{a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}}
+ the partial application \isa{{\isaliteral{28}{\isacharparenleft}}f\ a{\isaliteral{29}{\isacharparenright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}} operates
+ homogeneously on \isa{{\isaliteral{5C3C626574613E}{\isasymbeta}}}. This can be iterated naturally over a
+ list of parameters \isa{{\isaliteral{5B}{\isacharbrackleft}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{5D}{\isacharbrackright}}} as \isa{f\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{23}{\isacharhash}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{23}{\isacharhash}}{\isaliteral{3E}{\isachargreater}}\ f\ a\isaliteral{5C3C5E627375623E}{}\isactrlbsub n\isaliteral{5C3C5E657375623E}{}\isactrlesub \isaliteral{5C3C5E627375623E}{}\isactrlbsub \isaliteral{5C3C5E657375623E}{}\isactrlesub }. The latter expression is again a function \isa{{\isaliteral{5C3C626574613E}{\isasymbeta}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}}.
+ It can be applied to an initial configuration \isa{b{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}} to
+ start the iteration over the given list of arguments: each \isa{a} in \isa{a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n} is applied consecutively by updating a
cumulative configuration.
The \isa{fold} combinator in Isabelle/ML lifts a function \isa{f} as above to its iterated version over a list of arguments.
- Lifting can be repeated, e.g.\ \isa{{\isacharparenleft}fold\ {\isasymcirc}\ fold{\isacharparenright}\ f} iterates
+ Lifting can be repeated, e.g.\ \isa{{\isaliteral{28}{\isacharparenleft}}fold\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ fold{\isaliteral{29}{\isacharparenright}}\ f} iterates
over a list of lists as expected.
- The variant \isa{fold{\isacharunderscore}rev} works inside-out over the list of
- arguments, such that \isa{fold{\isacharunderscore}rev\ f\ {\isasymequiv}\ fold\ f\ {\isasymcirc}\ rev} holds.
+ The variant \isa{fold{\isaliteral{5F}{\isacharunderscore}}rev} works inside-out over the list of
+ arguments, such that \isa{fold{\isaliteral{5F}{\isacharunderscore}}rev\ f\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ fold\ f\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ rev} holds.
- The \isa{fold{\isacharunderscore}map} combinator essentially performs \isa{fold} and \isa{map} simultaneously: each application of \isa{f} produces an updated configuration together with a side-result;
+ The \isa{fold{\isaliteral{5F}{\isacharunderscore}}map} combinator essentially performs \isa{fold} and \isa{map} simultaneously: each application of \isa{f} produces an updated configuration together with a side-result;
the iteration collects all such side-results as a separate list.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -1163,19 +1163,19 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ val\ s\ {\isacharequal}\isanewline
-\ \ \ \ Buffer{\isachardot}empty\isanewline
-\ \ \ \ {\isacharbar}{\isachargreater}\ Buffer{\isachardot}add\ {\isachardoublequote}digits{\isacharcolon}\ {\isachardoublequote}\isanewline
-\ \ \ \ {\isacharbar}{\isachargreater}\ fold\ {\isacharparenleft}Buffer{\isachardot}add\ o\ string{\isacharunderscore}of{\isacharunderscore}int{\isacharparenright}\ {\isacharparenleft}{\isadigit{0}}\ upto\ {\isadigit{9}}{\isacharparenright}\isanewline
-\ \ \ \ {\isacharbar}{\isachargreater}\ Buffer{\isachardot}content{\isacharsemicolon}\isanewline
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ val\ s\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ Buffer{\isaliteral{2E}{\isachardot}}empty\isanewline
+\ \ \ \ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ Buffer{\isaliteral{2E}{\isachardot}}add\ {\isaliteral{22}{\isachardoublequote}}digits{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequote}}\isanewline
+\ \ \ \ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ fold\ {\isaliteral{28}{\isacharparenleft}}Buffer{\isaliteral{2E}{\isachardot}}add\ o\ string{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}\ upto\ {\isadigit{9}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ Buffer{\isaliteral{2E}{\isachardot}}content{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
\ \ %
\isaantiq
-assert%
+assert{}%
\endisaantiq
-\ {\isacharparenleft}s\ {\isacharequal}\ {\isachardoublequote}digits{\isacharcolon}\ {\isadigit{0}}{\isadigit{1}}{\isadigit{2}}{\isadigit{3}}{\isadigit{4}}{\isadigit{5}}{\isadigit{6}}{\isadigit{7}}{\isadigit{8}}{\isadigit{9}}{\isachardoublequote}{\isacharparenright}{\isacharsemicolon}\isanewline
-{\isacharverbatimclose}%
+\ {\isaliteral{28}{\isacharparenleft}}s\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}digits{\isaliteral{3A}{\isacharcolon}}\ {\isadigit{0}}{\isadigit{1}}{\isadigit{2}}{\isadigit{3}}{\isadigit{4}}{\isadigit{5}}{\isadigit{6}}{\isadigit{7}}{\isadigit{8}}{\isadigit{9}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -1202,24 +1202,24 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ datatype\ tree\ {\isacharequal}\ Text\ of\ string\ {\isacharbar}\ Elem\ of\ string\ {\isacharasterisk}\ tree\ list{\isacharsemicolon}\isanewline
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ datatype\ tree\ {\isaliteral{3D}{\isacharequal}}\ Text\ of\ string\ {\isaliteral{7C}{\isacharbar}}\ Elem\ of\ string\ {\isaliteral{2A}{\isacharasterisk}}\ tree\ list{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ fun\ slow{\isacharunderscore}content\ {\isacharparenleft}Text\ txt{\isacharparenright}\ {\isacharequal}\ txt\isanewline
-\ \ \ \ {\isacharbar}\ slow{\isacharunderscore}content\ {\isacharparenleft}Elem\ {\isacharparenleft}name{\isacharcomma}\ ts{\isacharparenright}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ \ \ \ \ {\isachardoublequote}{\isacharless}{\isachardoublequote}\ {\isacharcircum}\ name\ {\isacharcircum}\ {\isachardoublequote}{\isachargreater}{\isachardoublequote}\ {\isacharcircum}\isanewline
-\ \ \ \ \ \ \ \ implode\ {\isacharparenleft}map\ slow{\isacharunderscore}content\ ts{\isacharparenright}\ {\isacharcircum}\isanewline
-\ \ \ \ \ \ \ \ {\isachardoublequote}{\isacharless}{\isacharslash}{\isachardoublequote}\ {\isacharcircum}\ name\ {\isacharcircum}\ {\isachardoublequote}{\isachargreater}{\isachardoublequote}\isanewline
+\ \ fun\ slow{\isaliteral{5F}{\isacharunderscore}}content\ {\isaliteral{28}{\isacharparenleft}}Text\ txt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ txt\isanewline
+\ \ \ \ {\isaliteral{7C}{\isacharbar}}\ slow{\isaliteral{5F}{\isacharunderscore}}content\ {\isaliteral{28}{\isacharparenleft}}Elem\ {\isaliteral{28}{\isacharparenleft}}name{\isaliteral{2C}{\isacharcomma}}\ ts{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{3C}{\isacharless}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ name\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{3E}{\isachargreater}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline
+\ \ \ \ \ \ \ \ implode\ {\isaliteral{28}{\isacharparenleft}}map\ slow{\isaliteral{5F}{\isacharunderscore}}content\ ts{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline
+\ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{3C}{\isacharless}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ name\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{3E}{\isachargreater}}{\isaliteral{22}{\isachardoublequote}}\isanewline
\isanewline
-\ \ fun\ add{\isacharunderscore}content\ {\isacharparenleft}Text\ txt{\isacharparenright}\ {\isacharequal}\ Buffer{\isachardot}add\ txt\isanewline
-\ \ \ \ {\isacharbar}\ add{\isacharunderscore}content\ {\isacharparenleft}Elem\ {\isacharparenleft}name{\isacharcomma}\ ts{\isacharparenright}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ \ \ \ \ Buffer{\isachardot}add\ {\isacharparenleft}{\isachardoublequote}{\isacharless}{\isachardoublequote}\ {\isacharcircum}\ name\ {\isacharcircum}\ {\isachardoublequote}{\isachargreater}{\isachardoublequote}{\isacharparenright}\ {\isacharhash}{\isachargreater}\isanewline
-\ \ \ \ \ \ \ \ fold\ add{\isacharunderscore}content\ ts\ {\isacharhash}{\isachargreater}\isanewline
-\ \ \ \ \ \ \ \ Buffer{\isachardot}add\ {\isacharparenleft}{\isachardoublequote}{\isacharless}{\isacharslash}{\isachardoublequote}\ {\isacharcircum}\ name\ {\isacharcircum}\ {\isachardoublequote}{\isachargreater}{\isachardoublequote}{\isacharparenright}{\isacharsemicolon}\isanewline
+\ \ fun\ add{\isaliteral{5F}{\isacharunderscore}}content\ {\isaliteral{28}{\isacharparenleft}}Text\ txt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Buffer{\isaliteral{2E}{\isachardot}}add\ txt\isanewline
+\ \ \ \ {\isaliteral{7C}{\isacharbar}}\ add{\isaliteral{5F}{\isacharunderscore}}content\ {\isaliteral{28}{\isacharparenleft}}Elem\ {\isaliteral{28}{\isacharparenleft}}name{\isaliteral{2C}{\isacharcomma}}\ ts{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ \ \ \ Buffer{\isaliteral{2E}{\isachardot}}add\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3C}{\isacharless}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ name\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{3E}{\isachargreater}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{23}{\isacharhash}}{\isaliteral{3E}{\isachargreater}}\isanewline
+\ \ \ \ \ \ \ \ fold\ add{\isaliteral{5F}{\isacharunderscore}}content\ ts\ {\isaliteral{23}{\isacharhash}}{\isaliteral{3E}{\isachargreater}}\isanewline
+\ \ \ \ \ \ \ \ Buffer{\isaliteral{2E}{\isachardot}}add\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3C}{\isacharless}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ name\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{3E}{\isachargreater}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ fun\ fast{\isacharunderscore}content\ tree\ {\isacharequal}\isanewline
-\ \ \ \ Buffer{\isachardot}empty\ {\isacharbar}{\isachargreater}\ add{\isacharunderscore}content\ tree\ {\isacharbar}{\isachargreater}\ Buffer{\isachardot}content{\isacharsemicolon}\isanewline
-{\isacharverbatimclose}%
+\ \ fun\ fast{\isaliteral{5F}{\isacharunderscore}}content\ tree\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ Buffer{\isaliteral{2E}{\isachardot}}empty\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ add{\isaliteral{5F}{\isacharunderscore}}content\ tree\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ Buffer{\isaliteral{2E}{\isachardot}}content{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -1381,14 +1381,14 @@
\endisadelimML
%
\isatagML
-\isacommand{ML{\isacharunderscore}command}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ warning\ {\isacharparenleft}cat{\isacharunderscore}lines\isanewline
-\ \ \ {\isacharbrackleft}{\isachardoublequote}Beware\ the\ Jabberwock{\isacharcomma}\ my\ son{\isacharbang}{\isachardoublequote}{\isacharcomma}\isanewline
-\ \ \ \ {\isachardoublequote}The\ jaws\ that\ bite{\isacharcomma}\ the\ claws\ that\ catch{\isacharbang}{\isachardoublequote}{\isacharcomma}\isanewline
-\ \ \ \ {\isachardoublequote}Beware\ the\ Jubjub\ Bird{\isacharcomma}\ and\ shun{\isachardoublequote}{\isacharcomma}\isanewline
-\ \ \ \ {\isachardoublequote}The\ frumious\ Bandersnatch{\isacharbang}{\isachardoublequote}{\isacharbrackright}{\isacharparenright}{\isacharsemicolon}\isanewline
-{\isacharverbatimclose}%
+\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}command}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ warning\ {\isaliteral{28}{\isacharparenleft}}cat{\isaliteral{5F}{\isacharunderscore}}lines\isanewline
+\ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}Beware\ the\ Jabberwock{\isaliteral{2C}{\isacharcomma}}\ my\ son{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequote}}The\ jaws\ that\ bite{\isaliteral{2C}{\isacharcomma}}\ the\ claws\ that\ catch{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequote}}Beware\ the\ Jubjub\ Bird{\isaliteral{2C}{\isacharcomma}}\ and\ shun{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequote}}The\ frumious\ Bandersnatch{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -1548,12 +1548,12 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{ML antiquotation}{assert}\hypertarget{ML antiquotation.assert}{\hyperlink{ML antiquotation.assert}{\mbox{\isa{assert}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
+ \indexdef{}{ML antiquotation}{assert}\hypertarget{ML antiquotation.assert}{\hyperlink{ML antiquotation.assert}{\mbox{\isa{assert}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
\end{matharray}
\begin{description}
- \item \isa{{\isacharat}{\isacharbraceleft}assert{\isacharbraceright}} inlines a function
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}assert{\isaliteral{7D}{\isacharbraceright}}} inlines a function
\verb|bool -> unit| that raises \verb|Fail| if the argument is
\verb|false|. Due to inlining the source position of failed
assertions is included in the error output.
@@ -1645,7 +1645,7 @@
integer type --- overloading of SML97 is disabled.
Structure \verb|IntInf| of SML97 is obsolete and superseded by
- \verb|Int|. Structure \verb|Integer| in \hyperlink{file.~~/src/Pure/General/integer.ML}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}Pure{\isacharslash}General{\isacharslash}integer{\isachardot}ML}}}} provides some additional
+ \verb|Int|. Structure \verb|Integer| in \hyperlink{file.~~/src/Pure/General/integer.ML}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}Pure{\isaliteral{2F}{\isacharslash}}General{\isaliteral{2F}{\isacharslash}}integer{\isaliteral{2E}{\isachardot}}ML}}}} provides some additional
operations.
\end{description}%
@@ -1730,7 +1730,7 @@
\begin{isamarkuptext}%
Apart from \verb|Option.map| most operations defined in
structure \verb|Option| are alien to Isabelle/ML. The
- operations shown above are defined in \hyperlink{file.~~/src/Pure/General/basics.ML}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}Pure{\isacharslash}General{\isacharslash}basics{\isachardot}ML}}}}, among others.%
+ operations shown above are defined in \hyperlink{file.~~/src/Pure/General/basics.ML}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}Pure{\isaliteral{2F}{\isacharslash}}General{\isaliteral{2F}{\isacharslash}}basics{\isaliteral{2E}{\isachardot}}ML}}}}, among others.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -1763,7 +1763,7 @@
\begin{description}
- \item \verb|cons|~\isa{x\ xs} evaluates to \isa{x\ {\isacharcolon}{\isacharcolon}\ xs}.
+ \item \verb|cons|~\isa{x\ xs} evaluates to \isa{x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ xs}.
Tupled infix operators are a historical accident in Standard ML.
The curried \verb|cons| amends this, but it should be only used when
@@ -1771,7 +1771,7 @@
\item \verb|member|, \verb|insert|, \verb|remove|, \verb|update| treat
lists as a set-like container that maintains the order of elements.
- See \hyperlink{file.~~/src/Pure/library.ML}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}Pure{\isacharslash}library{\isachardot}ML}}}} for the full specifications
+ See \hyperlink{file.~~/src/Pure/library.ML}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}Pure{\isaliteral{2F}{\isacharslash}}library{\isaliteral{2E}{\isachardot}}ML}}}} for the full specifications
(written in ML). There are some further derived operations like
\verb|union| or \verb|inter|.
@@ -1823,23 +1823,23 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ val\ items\ {\isacharequal}\ {\isacharbrackleft}{\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isacharcomma}\ {\isadigit{3}}{\isacharcomma}\ {\isadigit{4}}{\isacharcomma}\ {\isadigit{5}}{\isacharcomma}\ {\isadigit{6}}{\isacharcomma}\ {\isadigit{7}}{\isacharcomma}\ {\isadigit{8}}{\isacharcomma}\ {\isadigit{9}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{0}}{\isacharbrackright}{\isacharsemicolon}\isanewline
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ val\ items\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{3}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{4}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{5}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{6}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{7}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{8}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{9}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{1}}{\isadigit{0}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ val\ list{\isadigit{1}}\ {\isacharequal}\ fold\ cons\ items\ {\isacharbrackleft}{\isacharbrackright}{\isacharsemicolon}\isanewline
+\ \ val\ list{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ fold\ cons\ items\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\ \ %
\isaantiq
-assert%
+assert{}%
\endisaantiq
-\ {\isacharparenleft}list{\isadigit{1}}\ {\isacharequal}\ rev\ items{\isacharparenright}{\isacharsemicolon}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}list{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ rev\ items{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ val\ list{\isadigit{2}}\ {\isacharequal}\ fold{\isacharunderscore}rev\ cons\ items\ {\isacharbrackleft}{\isacharbrackright}{\isacharsemicolon}\isanewline
+\ \ val\ list{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ fold{\isaliteral{5F}{\isacharunderscore}}rev\ cons\ items\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\ \ %
\isaantiq
-assert%
+assert{}%
\endisaantiq
-\ {\isacharparenleft}list{\isadigit{2}}\ {\isacharequal}\ items{\isacharparenright}{\isacharsemicolon}\isanewline
-{\isacharverbatimclose}%
+\ {\isaliteral{28}{\isacharparenleft}}list{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ items{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -1859,9 +1859,9 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ fun\ merge{\isacharunderscore}lists\ eq\ {\isacharparenleft}xs{\isacharcomma}\ ys{\isacharparenright}\ {\isacharequal}\ fold{\isacharunderscore}rev\ {\isacharparenleft}insert\ eq{\isacharparenright}\ ys\ xs{\isacharsemicolon}\isanewline
-{\isacharverbatimclose}%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ fun\ merge{\isaliteral{5F}{\isacharunderscore}}lists\ eq\ {\isaliteral{28}{\isacharparenleft}}xs{\isaliteral{2C}{\isacharcomma}}\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ fold{\isaliteral{5F}{\isacharunderscore}}rev\ {\isaliteral{28}{\isacharparenleft}}insert\ eq{\isaliteral{29}{\isacharparenright}}\ ys\ xs{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -1877,7 +1877,7 @@
This way of merging lists is typical for context data
(\secref{sec:context-data}). See also \verb|merge| as defined in
- \hyperlink{file.~~/src/Pure/library.ML}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}Pure{\isacharslash}library{\isachardot}ML}}}}.%
+ \hyperlink{file.~~/src/Pure/library.ML}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}Pure{\isaliteral{2F}{\isacharslash}}library{\isaliteral{2E}{\isachardot}}ML}}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -1911,7 +1911,7 @@
Note that a function called \isa{lookup} is obliged to express its
partiality via an explicit option element. There is no choice to
raise an exception, without changing the name to something like
- \isa{the{\isacharunderscore}element} or \isa{get}.
+ \isa{the{\isaliteral{5F}{\isacharunderscore}}element} or \isa{get}.
The \isa{defined} operation is essentially a contraction of \verb|is_some| and \isa{lookup}, but this is sufficiently frequent to
justify its independent existence. This also gives the
@@ -1921,7 +1921,7 @@
Association lists are adequate as simple and light-weight
implementation of finite mappings in many practical situations. A
- more heavy-duty table structure is defined in \hyperlink{file.~~/src/Pure/General/table.ML}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}Pure{\isacharslash}General{\isacharslash}table{\isachardot}ML}}}}; that version scales easily to
+ more heavy-duty table structure is defined in \hyperlink{file.~~/src/Pure/General/table.ML}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}Pure{\isaliteral{2F}{\isacharslash}}General{\isaliteral{2F}{\isacharslash}}table{\isaliteral{2E}{\isachardot}}ML}}}}; that version scales easily to
thousands or millions of elements.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -2145,7 +2145,7 @@
component of \isa{path} into the unique temporary directory of
the running Isabelle/ML process.
- \item \verb|serial_string|~\isa{{\isacharparenleft}{\isacharparenright}} creates a new serial number
+ \item \verb|serial_string|~\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}} creates a new serial number
that is unique over the runtime of the Isabelle/ML process.
\end{description}%
@@ -2184,15 +2184,15 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ val\ tmp{\isadigit{1}}\ {\isacharequal}\ File{\isachardot}tmp{\isacharunderscore}path\ {\isacharparenleft}Path{\isachardot}basic\ {\isacharparenleft}{\isachardoublequote}foo{\isachardoublequote}\ {\isacharcircum}\ serial{\isacharunderscore}string\ {\isacharparenleft}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline
-\ \ val\ tmp{\isadigit{2}}\ {\isacharequal}\ File{\isachardot}tmp{\isacharunderscore}path\ {\isacharparenleft}Path{\isachardot}basic\ {\isacharparenleft}{\isachardoublequote}foo{\isachardoublequote}\ {\isacharcircum}\ serial{\isacharunderscore}string\ {\isacharparenleft}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ val\ tmp{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ File{\isaliteral{2E}{\isachardot}}tmp{\isaliteral{5F}{\isacharunderscore}}path\ {\isaliteral{28}{\isacharparenleft}}Path{\isaliteral{2E}{\isachardot}}basic\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}foo{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ serial{\isaliteral{5F}{\isacharunderscore}}string\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ val\ tmp{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ File{\isaliteral{2E}{\isachardot}}tmp{\isaliteral{5F}{\isacharunderscore}}path\ {\isaliteral{28}{\isacharparenleft}}Path{\isaliteral{2E}{\isachardot}}basic\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}foo{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ serial{\isaliteral{5F}{\isacharunderscore}}string\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\ \ %
\isaantiq
-assert%
+assert{}%
\endisaantiq
-\ {\isacharparenleft}tmp{\isadigit{1}}\ {\isacharless}{\isachargreater}\ tmp{\isadigit{2}}{\isacharparenright}{\isacharsemicolon}\isanewline
-{\isacharverbatimclose}%
+\ {\isaliteral{28}{\isacharparenleft}}tmp{\isadigit{1}}\ {\isaliteral{3C}{\isacharless}}{\isaliteral{3E}{\isachargreater}}\ tmp{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -2253,7 +2253,7 @@
\begin{description}
- \item \verb|NAMED_CRITICAL|~\isa{name\ e} evaluates \isa{e\ {\isacharparenleft}{\isacharparenright}}
+ \item \verb|NAMED_CRITICAL|~\isa{name\ e} evaluates \isa{e\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}}
within the central critical section of Isabelle/ML. No other thread
may do so at the same time, but non-critical parallel execution will
continue. The \isa{name} argument is used for tracing and might
@@ -2278,14 +2278,14 @@
\isa{x} as follows: if \isa{f\ x} produces \verb|NONE|, it
continues to wait on the internal condition variable, expecting that
some other thread will eventually change the content in a suitable
- manner; if \isa{f\ x} produces \verb|SOME|~\isa{{\isacharparenleft}y{\isacharcomma}\ x{\isacharprime}{\isacharparenright}} it is
- satisfied and assigns the new state value \isa{x{\isacharprime}}, broadcasts a
+ manner; if \isa{f\ x} produces \verb|SOME|~\isa{{\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}} it is
+ satisfied and assigns the new state value \isa{x{\isaliteral{27}{\isacharprime}}}, broadcasts a
signal to all waiting threads on the associated condition variable,
and returns the result \isa{y}.
\end{description}
- There are some further variants of the \verb|Synchronized.guarded_access| combinator, see \hyperlink{file.~~/src/Pure/Concurrent/synchronized.ML}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}Pure{\isacharslash}Concurrent{\isacharslash}synchronized{\isachardot}ML}}}} for details.%
+ There are some further variants of the \verb|Synchronized.guarded_access| combinator, see \hyperlink{file.~~/src/Pure/Concurrent/synchronized.ML}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}Pure{\isaliteral{2F}{\isacharslash}}Concurrent{\isaliteral{2F}{\isacharslash}}synchronized{\isaliteral{2E}{\isachardot}}ML}}}} for details.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -2322,28 +2322,28 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
\ \ local\isanewline
-\ \ \ \ val\ counter\ {\isacharequal}\ Synchronized{\isachardot}var\ {\isachardoublequote}counter{\isachardoublequote}\ {\isadigit{0}}{\isacharsemicolon}\isanewline
+\ \ \ \ val\ counter\ {\isaliteral{3D}{\isacharequal}}\ Synchronized{\isaliteral{2E}{\isachardot}}var\ {\isaliteral{22}{\isachardoublequote}}counter{\isaliteral{22}{\isachardoublequote}}\ {\isadigit{0}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\ \ in\isanewline
-\ \ \ \ fun\ next\ {\isacharparenleft}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ \ \ Synchronized{\isachardot}guarded{\isacharunderscore}access\ counter\isanewline
-\ \ \ \ \ \ \ \ {\isacharparenleft}fn\ i\ {\isacharequal}{\isachargreater}\isanewline
-\ \ \ \ \ \ \ \ \ \ let\ val\ j\ {\isacharequal}\ i\ {\isacharplus}\ {\isadigit{1}}\isanewline
-\ \ \ \ \ \ \ \ \ \ in\ SOME\ {\isacharparenleft}j{\isacharcomma}\ j{\isacharparenright}\ end{\isacharparenright}{\isacharsemicolon}\isanewline
-\ \ end{\isacharsemicolon}\isanewline
-{\isacharverbatimclose}\isanewline
+\ \ \ \ fun\ next\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ \ Synchronized{\isaliteral{2E}{\isachardot}}guarded{\isaliteral{5F}{\isacharunderscore}}access\ counter\isanewline
+\ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}fn\ i\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline
+\ \ \ \ \ \ \ \ \ \ let\ val\ j\ {\isaliteral{3D}{\isacharequal}}\ i\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}\isanewline
+\ \ \ \ \ \ \ \ \ \ in\ SOME\ {\isaliteral{28}{\isacharparenleft}}j{\isaliteral{2C}{\isacharcomma}}\ j{\isaliteral{29}{\isacharparenright}}\ end{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ end{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
\isanewline
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ val\ a\ {\isacharequal}\ next\ {\isacharparenleft}{\isacharparenright}{\isacharsemicolon}\isanewline
-\ \ val\ b\ {\isacharequal}\ next\ {\isacharparenleft}{\isacharparenright}{\isacharsemicolon}\isanewline
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ val\ a\ {\isaliteral{3D}{\isacharequal}}\ next\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ val\ b\ {\isaliteral{3D}{\isacharequal}}\ next\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\ \ %
\isaantiq
-assert%
+assert{}%
\endisaantiq
-\ {\isacharparenleft}a\ {\isacharless}{\isachargreater}\ b{\isacharparenright}{\isacharsemicolon}\isanewline
-{\isacharverbatimclose}%
+\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{3C}{\isacharless}}{\isaliteral{3E}{\isachargreater}}\ b{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -2352,7 +2352,7 @@
\endisadelimML
%
\begin{isamarkuptext}%
-\medskip See \hyperlink{file.~~/src/Pure/Concurrent/mailbox.ML}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}Pure{\isacharslash}Concurrent{\isacharslash}mailbox{\isachardot}ML}}}} how
+\medskip See \hyperlink{file.~~/src/Pure/Concurrent/mailbox.ML}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}Pure{\isaliteral{2F}{\isacharslash}}Concurrent{\isaliteral{2F}{\isacharslash}}mailbox{\isaliteral{2E}{\isachardot}}ML}}}} how
to implement a mailbox as synchronized variable over a purely
functional queue.%
\end{isamarkuptext}%
--- a/doc-src/IsarImplementation/Thy/document/Prelim.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarImplementation/Thy/document/Prelim.tex Mon Nov 08 14:41:11 2010 +0100
@@ -33,13 +33,13 @@
results etc.).
For example, derivations within the Isabelle/Pure logic can be
- described as a judgment \isa{{\isasymGamma}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\ {\isasymphi}}, which means that a
- proposition \isa{{\isasymphi}} is derivable from hypotheses \isa{{\isasymGamma}}
- within the theory \isa{{\isasymTheta}}. There are logical reasons for
- keeping \isa{{\isasymTheta}} and \isa{{\isasymGamma}} separate: theories can be
+ described as a judgment \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{5C3C54686574613E}{\isasymTheta}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}}, which means that a
+ proposition \isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} is derivable from hypotheses \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}}
+ within the theory \isa{{\isaliteral{5C3C54686574613E}{\isasymTheta}}}. There are logical reasons for
+ keeping \isa{{\isaliteral{5C3C54686574613E}{\isasymTheta}}} and \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}} separate: theories can be
liberal about supporting type constructors and schematic
polymorphism of constants and axioms, while the inner calculus of
- \isa{{\isasymGamma}\ {\isasymturnstile}\ {\isasymphi}} is strictly limited to Simple Type Theory (with
+ \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}} is strictly limited to Simple Type Theory (with
fixed type variables in the assumptions).
\medskip Contexts and derivations are linked by the following key
@@ -48,18 +48,18 @@
\begin{itemize}
\item Transfer: monotonicity of derivations admits results to be
- transferred into a \emph{larger} context, i.e.\ \isa{{\isasymGamma}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\ {\isasymphi}} implies \isa{{\isasymGamma}{\isacharprime}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\isactrlsub {\isacharprime}\ {\isasymphi}} for contexts \isa{{\isasymTheta}{\isacharprime}\ {\isasymsupseteq}\ {\isasymTheta}} and \isa{{\isasymGamma}{\isacharprime}\ {\isasymsupseteq}\ {\isasymGamma}}.
+ transferred into a \emph{larger} context, i.e.\ \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{5C3C54686574613E}{\isasymTheta}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}} implies \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{5C3C54686574613E}{\isasymTheta}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}} for contexts \isa{{\isaliteral{5C3C54686574613E}{\isasymTheta}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C73757073657465713E}{\isasymsupseteq}}\ {\isaliteral{5C3C54686574613E}{\isasymTheta}}} and \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C73757073657465713E}{\isasymsupseteq}}\ {\isaliteral{5C3C47616D6D613E}{\isasymGamma}}}.
\item Export: discharge of hypotheses admits results to be exported
- into a \emph{smaller} context, i.e.\ \isa{{\isasymGamma}{\isacharprime}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\ {\isasymphi}}
- implies \isa{{\isasymGamma}\ {\isasymturnstile}\isactrlsub {\isasymTheta}\ {\isasymDelta}\ {\isasymLongrightarrow}\ {\isasymphi}} where \isa{{\isasymGamma}{\isacharprime}\ {\isasymsupseteq}\ {\isasymGamma}} and
- \isa{{\isasymDelta}\ {\isacharequal}\ {\isasymGamma}{\isacharprime}\ {\isacharminus}\ {\isasymGamma}}. Note that \isa{{\isasymTheta}} remains unchanged here,
- only the \isa{{\isasymGamma}} part is affected.
+ into a \emph{smaller} context, i.e.\ \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{5C3C54686574613E}{\isasymTheta}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}}
+ implies \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{5C3C54686574613E}{\isasymTheta}}\ {\isaliteral{5C3C44656C74613E}{\isasymDelta}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}} where \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C73757073657465713E}{\isasymsupseteq}}\ {\isaliteral{5C3C47616D6D613E}{\isasymGamma}}} and
+ \isa{{\isaliteral{5C3C44656C74613E}{\isasymDelta}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{5C3C47616D6D613E}{\isasymGamma}}}. Note that \isa{{\isaliteral{5C3C54686574613E}{\isasymTheta}}} remains unchanged here,
+ only the \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}} part is affected.
\end{itemize}
\medskip By modeling the main characteristics of the primitive
- \isa{{\isasymTheta}} and \isa{{\isasymGamma}} above, and abstracting over any
+ \isa{{\isaliteral{5C3C54686574613E}{\isasymTheta}}} and \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}} above, and abstracting over any
particular logical content, we arrive at the fundamental notions of
\emph{theory context} and \emph{proof context} in Isabelle/Isar.
These implement a certain policy to manage arbitrary \emph{context
@@ -67,7 +67,7 @@
data at compile time.
The internal bootstrap process of Isabelle/Pure eventually reaches a
- stage where certain data slots provide the logical content of \isa{{\isasymTheta}} and \isa{{\isasymGamma}} sketched above, but this does not stop there!
+ stage where certain data slots provide the logical content of \isa{{\isaliteral{5C3C54686574613E}{\isasymTheta}}} and \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}} sketched above, but this does not stop there!
Various additional data slots support all kinds of mechanisms that
are not necessarily part of the core logic.
@@ -138,7 +138,7 @@
\begin{center}
\begin{tabular}{rcccl}
& & \isa{Pure} \\
- & & \isa{{\isasymdown}} \\
+ & & \isa{{\isaliteral{5C3C646F776E3E}{\isasymdown}}} \\
& & \isa{FOL} \\
& $\swarrow$ & & $\searrow$ & \\
\isa{Nat} & & & & \isa{List} \\
@@ -147,9 +147,9 @@
& & \multicolumn{3}{l}{~~\hyperlink{keyword.imports}{\mbox{\isa{\isakeyword{imports}}}}} \\
& & \multicolumn{3}{l}{~~\hyperlink{keyword.begin}{\mbox{\isa{\isakeyword{begin}}}}} \\
& & $\vdots$~~ \\
- & & \isa{{\isasymbullet}}~~ \\
+ & & \isa{{\isaliteral{5C3C62756C6C65743E}{\isasymbullet}}}~~ \\
& & $\vdots$~~ \\
- & & \isa{{\isasymbullet}}~~ \\
+ & & \isa{{\isaliteral{5C3C62756C6C65743E}{\isasymbullet}}}~~ \\
& & $\vdots$~~ \\
& & \multicolumn{3}{l}{~~\hyperlink{command.end}{\mbox{\isa{\isacommand{end}}}}} \\
\end{tabular}
@@ -202,13 +202,13 @@
which the system does at least at the boundary of toplevel command
transactions \secref{sec:isar-toplevel}.
- \item \verb|Theory.eq_thy|~\isa{{\isacharparenleft}thy\isactrlsub {\isadigit{1}}{\isacharcomma}\ thy\isactrlsub {\isadigit{2}}{\isacharparenright}} check strict
+ \item \verb|Theory.eq_thy|~\isa{{\isaliteral{28}{\isacharparenleft}}thy\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ thy\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}} check strict
identity of two theories.
- \item \verb|Theory.subthy|~\isa{{\isacharparenleft}thy\isactrlsub {\isadigit{1}}{\isacharcomma}\ thy\isactrlsub {\isadigit{2}}{\isacharparenright}} compares theories
+ \item \verb|Theory.subthy|~\isa{{\isaliteral{28}{\isacharparenleft}}thy\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ thy\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}} compares theories
according to the intrinsic graph structure of the construction.
This sub-theory relation is a nominal approximation of inclusion
- (\isa{{\isasymsubseteq}}) of the corresponding content (according to the
+ (\isa{{\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}}) of the corresponding content (according to the
semantics of the ML modules that implement the data).
\item \verb|Theory.checkpoint|~\isa{thy} produces a safe
@@ -219,8 +219,8 @@
\item \verb|Theory.copy|~\isa{thy} produces a variant of \isa{thy} with the same data. The copy is not related to the original,
but the original is unchanged.
- \item \verb|Theory.merge|~\isa{{\isacharparenleft}thy\isactrlsub {\isadigit{1}}{\isacharcomma}\ thy\isactrlsub {\isadigit{2}}{\isacharparenright}} absorbs one theory
- into the other, without changing \isa{thy\isactrlsub {\isadigit{1}}} or \isa{thy\isactrlsub {\isadigit{2}}}.
+ \item \verb|Theory.merge|~\isa{{\isaliteral{28}{\isacharparenleft}}thy\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ thy\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}} absorbs one theory
+ into the other, without changing \isa{thy\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}} or \isa{thy\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}}.
This version of ad-hoc theory merge fails for unrelated theories!
\item \verb|Theory.begin_theory|~\isa{name\ parents} constructs
@@ -237,7 +237,7 @@
an always valid theory; updates on the original are propagated
automatically.
- \item \verb|Theory.deref|~\isa{thy{\isacharunderscore}ref} turns a \verb|theory_ref| into an \verb|theory| value. As the referenced
+ \item \verb|Theory.deref|~\isa{thy{\isaliteral{5F}{\isacharunderscore}}ref} turns a \verb|theory_ref| into an \verb|theory| value. As the referenced
theory evolves monotonically over time, later invocations of \verb|Theory.deref| may refer to a larger context.
\item \verb|Theory.check_thy|~\isa{thy} produces a \verb|theory_ref| from a valid \verb|theory| value.
@@ -261,7 +261,7 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{ML antiquotation}{theory}\hypertarget{ML antiquotation.theory}{\hyperlink{ML antiquotation.theory}{\mbox{\isa{theory}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
+ \indexdef{}{ML antiquotation}{theory}\hypertarget{ML antiquotation.theory}{\hyperlink{ML antiquotation.theory}{\mbox{\isa{theory}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
\end{matharray}
\begin{rail}
@@ -271,10 +271,10 @@
\begin{description}
- \item \isa{{\isacharat}{\isacharbraceleft}theory{\isacharbraceright}} refers to the background theory of the
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}theory{\isaliteral{7D}{\isacharbraceright}}} refers to the background theory of the
current context --- as abstract value.
- \item \isa{{\isacharat}{\isacharbraceleft}theory\ A{\isacharbraceright}} refers to an explicitly named ancestor
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}theory\ A{\isaliteral{7D}{\isacharbraceright}}} refers to an explicitly named ancestor
theory \isa{A} of the background theory of the current context
--- as abstract value.
@@ -305,7 +305,7 @@
requirements explicitly, since there is no separate context
identification or symbolic inclusion as for theories. For example,
hypotheses used in primitive derivations (cf.\ \secref{sec:thms})
- are recorded separately within the sequent \isa{{\isasymGamma}\ {\isasymturnstile}\ {\isasymphi}}, just to
+ are recorded separately within the sequent \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}}, just to
make double sure. Results could still leak into an alien proof
context due to programming errors, but Isabelle/Isar includes some
extra validity checks in critical positions, notably at the end of a
@@ -371,12 +371,12 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{ML antiquotation}{context}\hypertarget{ML antiquotation.context}{\hyperlink{ML antiquotation.context}{\mbox{\isa{context}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
+ \indexdef{}{ML antiquotation}{context}\hypertarget{ML antiquotation.context}{\hyperlink{ML antiquotation.context}{\mbox{\isa{context}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
\end{matharray}
\begin{description}
- \item \isa{{\isacharat}{\isacharbraceleft}context{\isacharbraceright}} refers to \emph{the} context at
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}context{\isaliteral{7D}{\isacharbraceright}}} refers to \emph{the} context at
compile-time --- as abstract value. Independently of (local) theory
or proof mode, this always produces a meaningful result.
@@ -406,7 +406,7 @@
and combinators for lifting operations on either component of the
disjoint sum.
- Moreover, there are total operations \isa{theory{\isacharunderscore}of} and \isa{proof{\isacharunderscore}of} to convert a generic context into either kind: a theory
+ Moreover, there are total operations \isa{theory{\isaliteral{5F}{\isacharunderscore}}of} and \isa{proof{\isaliteral{5F}{\isacharunderscore}}of} to convert a generic context into either kind: a theory
can always be selected from the sum, while a proof context might
have to be constructed by an ad-hoc \isa{init} operation, which
incurs a small runtime overhead.%
@@ -464,10 +464,10 @@
\medskip
\begin{tabular}{ll}
- \isa{{\isasymtype}\ T} & representing type \\
- \isa{{\isasymval}\ empty{\isacharcolon}\ T} & empty default value \\
- \isa{{\isasymval}\ extend{\isacharcolon}\ T\ {\isasymrightarrow}\ T} & re-initialize on import \\
- \isa{{\isasymval}\ merge{\isacharcolon}\ T\ {\isasymtimes}\ T\ {\isasymrightarrow}\ T} & join on import \\
+ \isa{{\isaliteral{5C3C747970653E}{\isasymtype}}\ T} & representing type \\
+ \isa{{\isaliteral{5C3C76616C3E}{\isasymval}}\ empty{\isaliteral{3A}{\isacharcolon}}\ T} & empty default value \\
+ \isa{{\isaliteral{5C3C76616C3E}{\isasymval}}\ extend{\isaliteral{3A}{\isacharcolon}}\ T\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ T} & re-initialize on import \\
+ \isa{{\isaliteral{5C3C76616C3E}{\isasymval}}\ merge{\isaliteral{3A}{\isacharcolon}}\ T\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ T\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ T} & join on import \\
\end{tabular}
\medskip
@@ -476,7 +476,7 @@
is acts like a unitary version of \isa{merge}.
Implementing \isa{merge} can be tricky. The general idea is
- that \isa{merge\ {\isacharparenleft}data\isactrlsub {\isadigit{1}}{\isacharcomma}\ data\isactrlsub {\isadigit{2}}{\isacharparenright}} inserts those parts of \isa{data\isactrlsub {\isadigit{2}}} into \isa{data\isactrlsub {\isadigit{1}}} that are not yet present, while
+ that \isa{merge\ {\isaliteral{28}{\isacharparenleft}}data\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ data\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}} inserts those parts of \isa{data\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}} into \isa{data\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}} that are not yet present, while
keeping the general order of things. The \verb|Library.merge|
function on plain lists may serve as canonical template.
@@ -489,8 +489,8 @@
\medskip
\begin{tabular}{ll}
- \isa{{\isasymtype}\ T} & representing type \\
- \isa{{\isasymval}\ init{\isacharcolon}\ theory\ {\isasymrightarrow}\ T} & produce initial value \\
+ \isa{{\isaliteral{5C3C747970653E}{\isasymtype}}\ T} & representing type \\
+ \isa{{\isaliteral{5C3C76616C3E}{\isasymval}}\ init{\isaliteral{3A}{\isacharcolon}}\ theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ T} & produce initial value \\
\end{tabular}
\medskip
@@ -515,9 +515,9 @@
\medskip
\begin{tabular}{ll}
- \isa{get{\isacharcolon}\ context\ {\isasymrightarrow}\ T} \\
- \isa{put{\isacharcolon}\ T\ {\isasymrightarrow}\ context\ {\isasymrightarrow}\ context} \\
- \isa{map{\isacharcolon}\ {\isacharparenleft}T\ {\isasymrightarrow}\ T{\isacharparenright}\ {\isasymrightarrow}\ context\ {\isasymrightarrow}\ context} \\
+ \isa{get{\isaliteral{3A}{\isacharcolon}}\ context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ T} \\
+ \isa{put{\isaliteral{3A}{\isacharcolon}}\ T\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ context} \\
+ \isa{map{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}T\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ T{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ context} \\
\end{tabular}
\medskip
@@ -545,15 +545,15 @@
\begin{description}
- \item \verb|Theory_Data|\isa{{\isacharparenleft}spec{\isacharparenright}} declares data for
+ \item \verb|Theory_Data|\isa{{\isaliteral{28}{\isacharparenleft}}spec{\isaliteral{29}{\isacharparenright}}} declares data for
type \verb|theory| according to the specification provided as
argument structure. The resulting structure provides data init and
access operations as described above.
- \item \verb|Proof_Data|\isa{{\isacharparenleft}spec{\isacharparenright}} is analogous to
+ \item \verb|Proof_Data|\isa{{\isaliteral{28}{\isacharparenleft}}spec{\isaliteral{29}{\isacharparenright}}} is analogous to
\verb|Theory_Data| for type \verb|Proof.context|.
- \item \verb|Generic_Data|\isa{{\isacharparenleft}spec{\isacharparenright}} is analogous to
+ \item \verb|Generic_Data|\isa{{\isaliteral{28}{\isacharparenleft}}spec{\isaliteral{29}{\isacharparenright}}} is analogous to
\verb|Theory_Data| for type \verb|Context.generic|.
\end{description}%
@@ -593,13 +593,13 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ signature\ WELLFORMED{\isacharunderscore}TERMS\ {\isacharequal}\isanewline
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ signature\ WELLFORMED{\isaliteral{5F}{\isacharunderscore}}TERMS\ {\isaliteral{3D}{\isacharequal}}\isanewline
\ \ sig\isanewline
-\ \ \ \ val\ get{\isacharcolon}\ theory\ {\isacharminus}{\isachargreater}\ term\ list\isanewline
-\ \ \ \ val\ add{\isacharcolon}\ term\ {\isacharminus}{\isachargreater}\ theory\ {\isacharminus}{\isachargreater}\ theory\isanewline
-\ \ end{\isacharsemicolon}\isanewline
-{\isacharverbatimclose}%
+\ \ \ \ val\ get{\isaliteral{3A}{\isacharcolon}}\ theory\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ term\ list\isanewline
+\ \ \ \ val\ add{\isaliteral{3A}{\isacharcolon}}\ term\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ theory\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ theory\isanewline
+\ \ end{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -620,30 +620,30 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ structure\ Wellformed{\isacharunderscore}Terms{\isacharcolon}\ WELLFORMED{\isacharunderscore}TERMS\ {\isacharequal}\isanewline
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ structure\ Wellformed{\isaliteral{5F}{\isacharunderscore}}Terms{\isaliteral{3A}{\isacharcolon}}\ WELLFORMED{\isaliteral{5F}{\isacharunderscore}}TERMS\ {\isaliteral{3D}{\isacharequal}}\isanewline
\ \ struct\isanewline
\isanewline
-\ \ structure\ Terms\ {\isacharequal}\ Theory{\isacharunderscore}Data\isanewline
-\ \ {\isacharparenleft}\isanewline
-\ \ \ \ type\ T\ {\isacharequal}\ term\ Ord{\isacharunderscore}List{\isachardot}T{\isacharsemicolon}\isanewline
-\ \ \ \ val\ empty\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isacharsemicolon}\isanewline
-\ \ \ \ val\ extend\ {\isacharequal}\ I{\isacharsemicolon}\isanewline
-\ \ \ \ fun\ merge\ {\isacharparenleft}ts{\isadigit{1}}{\isacharcomma}\ ts{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ \ \ Ord{\isacharunderscore}List{\isachardot}union\ Term{\isacharunderscore}Ord{\isachardot}fast{\isacharunderscore}term{\isacharunderscore}ord\ ts{\isadigit{1}}\ ts{\isadigit{2}}{\isacharsemicolon}\isanewline
-\ \ {\isacharparenright}{\isacharsemicolon}\isanewline
+\ \ structure\ Terms\ {\isaliteral{3D}{\isacharequal}}\ Theory{\isaliteral{5F}{\isacharunderscore}}Data\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}\isanewline
+\ \ \ \ type\ T\ {\isaliteral{3D}{\isacharequal}}\ term\ Ord{\isaliteral{5F}{\isacharunderscore}}List{\isaliteral{2E}{\isachardot}}T{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ val\ empty\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ val\ extend\ {\isaliteral{3D}{\isacharequal}}\ I{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ fun\ merge\ {\isaliteral{28}{\isacharparenleft}}ts{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ ts{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ \ Ord{\isaliteral{5F}{\isacharunderscore}}List{\isaliteral{2E}{\isachardot}}union\ Term{\isaliteral{5F}{\isacharunderscore}}Ord{\isaliteral{2E}{\isachardot}}fast{\isaliteral{5F}{\isacharunderscore}}term{\isaliteral{5F}{\isacharunderscore}}ord\ ts{\isadigit{1}}\ ts{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ {\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ val\ get\ {\isacharequal}\ Terms{\isachardot}get{\isacharsemicolon}\isanewline
+\ \ val\ get\ {\isaliteral{3D}{\isacharequal}}\ Terms{\isaliteral{2E}{\isachardot}}get{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ fun\ add\ raw{\isacharunderscore}t\ thy\ {\isacharequal}\isanewline
+\ \ fun\ add\ raw{\isaliteral{5F}{\isacharunderscore}}t\ thy\ {\isaliteral{3D}{\isacharequal}}\isanewline
\ \ \ \ let\isanewline
-\ \ \ \ \ \ val\ t\ {\isacharequal}\ Sign{\isachardot}cert{\isacharunderscore}term\ thy\ raw{\isacharunderscore}t{\isacharsemicolon}\isanewline
+\ \ \ \ \ \ val\ t\ {\isaliteral{3D}{\isacharequal}}\ Sign{\isaliteral{2E}{\isachardot}}cert{\isaliteral{5F}{\isacharunderscore}}term\ thy\ raw{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\ \ \ \ in\isanewline
-\ \ \ \ \ \ Terms{\isachardot}map\ {\isacharparenleft}Ord{\isacharunderscore}List{\isachardot}insert\ Term{\isacharunderscore}Ord{\isachardot}fast{\isacharunderscore}term{\isacharunderscore}ord\ t{\isacharparenright}\ thy\isanewline
-\ \ \ \ end{\isacharsemicolon}\isanewline
+\ \ \ \ \ \ Terms{\isaliteral{2E}{\isachardot}}map\ {\isaliteral{28}{\isacharparenleft}}Ord{\isaliteral{5F}{\isacharunderscore}}List{\isaliteral{2E}{\isachardot}}insert\ Term{\isaliteral{5F}{\isacharunderscore}}Ord{\isaliteral{2E}{\isachardot}}fast{\isaliteral{5F}{\isacharunderscore}}term{\isaliteral{5F}{\isacharunderscore}}ord\ t{\isaliteral{29}{\isacharparenright}}\ thy\isanewline
+\ \ \ \ end{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ end{\isacharsemicolon}\isanewline
-{\isacharverbatimclose}%
+\ \ end{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -705,19 +705,19 @@
end-users using existing notation for attributes (cf.\
\secref{sec:attributes}).
- For example, the predefined configuration option \hyperlink{attribute.show-types}{\mbox{\isa{show{\isacharunderscore}types}}} controls output of explicit type constraints for
+ For example, the predefined configuration option \hyperlink{attribute.show-types}{\mbox{\isa{show{\isaliteral{5F}{\isacharunderscore}}types}}} controls output of explicit type constraints for
variables in printed terms (cf.\ \secref{sec:read-print}). Its
value can be modified within Isar text like this:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{declare}\isamarkupfalse%
-\ {\isacharbrackleft}{\isacharbrackleft}show{\isacharunderscore}types\ {\isacharequal}\ false{\isacharbrackright}{\isacharbrackright}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5B}{\isacharbrackleft}}show{\isaliteral{5F}{\isacharunderscore}}types\ {\isaliteral{3D}{\isacharequal}}\ false{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5D}{\isacharbrackright}}\isanewline
\ \ %
\isamarkupcmt{declaration within (local) theory context%
}
\isanewline
\isanewline
-\isacommand{example{\isacharunderscore}proof}\isamarkupfalse%
+\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}\isamarkupfalse%
\isanewline
%
\isadelimproof
@@ -726,7 +726,7 @@
%
\isatagproof
\isacommand{note}\isamarkupfalse%
-\ {\isacharbrackleft}{\isacharbrackleft}show{\isacharunderscore}types\ {\isacharequal}\ true{\isacharbrackright}{\isacharbrackright}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5B}{\isacharbrackleft}}show{\isaliteral{5F}{\isacharunderscore}}types\ {\isaliteral{3D}{\isacharequal}}\ true{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5D}{\isacharbrackright}}\isanewline
\ \ \ \ %
\isamarkupcmt{declaration within proof (forward mode)%
}
@@ -748,14 +748,14 @@
%
\isatagproof
\isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isacharequal}\ x{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{using}\isamarkupfalse%
-\ {\isacharbrackleft}{\isacharbrackleft}show{\isacharunderscore}types\ {\isacharequal}\ false{\isacharbrackright}{\isacharbrackright}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5B}{\isacharbrackleft}}show{\isaliteral{5F}{\isacharunderscore}}types\ {\isaliteral{3D}{\isacharequal}}\ false{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5D}{\isacharbrackright}}\isanewline
\ \ \ \ \ \ %
\isamarkupcmt{declaration within proof (backward mode)%
}
\isanewline
-\ \ \ \ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ \ \ \ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -808,7 +808,7 @@
\item \verb|Config.map|~\isa{config\ f\ ctxt} updates the context
by updating the value of \isa{config}.
- \item \isa{{\isacharparenleft}config{\isacharcomma}\ setup{\isacharparenright}\ {\isacharequal}}~\verb|Attrib.config_bool|~\isa{name\ default} creates a named configuration option of type
+ \item \isa{{\isaliteral{28}{\isacharparenleft}}config{\isaliteral{2C}{\isacharcomma}}\ setup{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}}~\verb|Attrib.config_bool|~\isa{name\ default} creates a named configuration option of type
\verb|bool|, with the given \isa{default} depending on the
application context. The resulting \isa{config} can be used to
get/map its value in a given context. The \isa{setup} function
@@ -837,7 +837,7 @@
%
\begin{isamarkuptext}%
The following example shows how to declare and use a
- Boolean configuration option called \isa{my{\isacharunderscore}flag} with constant
+ Boolean configuration option called \isa{my{\isaliteral{5F}{\isacharunderscore}}flag} with constant
default value \verb|false|.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -855,12 +855,12 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ val\ {\isacharparenleft}my{\isacharunderscore}flag{\isacharcomma}\ my{\isacharunderscore}flag{\isacharunderscore}setup{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ Attrib{\isachardot}config{\isacharunderscore}bool\ {\isachardoublequote}my{\isacharunderscore}flag{\isachardoublequote}\ {\isacharparenleft}K\ false{\isacharparenright}\isanewline
-{\isacharverbatimclose}\isanewline
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ val\ {\isaliteral{28}{\isacharparenleft}}my{\isaliteral{5F}{\isacharunderscore}}flag{\isaliteral{2C}{\isacharcomma}}\ my{\isaliteral{5F}{\isacharunderscore}}flag{\isaliteral{5F}{\isacharunderscore}}setup{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ Attrib{\isaliteral{2E}{\isachardot}}config{\isaliteral{5F}{\isacharunderscore}}bool\ {\isaliteral{22}{\isachardoublequote}}my{\isaliteral{5F}{\isacharunderscore}}flag{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}K\ false{\isaliteral{29}{\isacharparenright}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
\isacommand{setup}\isamarkupfalse%
-\ my{\isacharunderscore}flag{\isacharunderscore}setup%
+\ my{\isaliteral{5F}{\isacharunderscore}}flag{\isaliteral{5F}{\isacharunderscore}}setup%
\endisatagML
{\isafoldML}%
%
@@ -869,7 +869,7 @@
\endisadelimML
%
\begin{isamarkuptext}%
-Now the user can refer to \hyperlink{attribute.my-flag}{\mbox{\isa{my{\isacharunderscore}flag}}} in
+Now the user can refer to \hyperlink{attribute.my-flag}{\mbox{\isa{my{\isaliteral{5F}{\isacharunderscore}}flag}}} in
declarations, while ML tools can retrieve the current value from the
context via \verb|Config.get|.%
\end{isamarkuptext}%
@@ -880,16 +880,16 @@
\endisadelimML
%
\isatagML
-\isacommand{ML{\isacharunderscore}val}\isamarkupfalse%
-\ {\isacharverbatimopen}\ %
+\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ %
\isaantiq
-assert%
+assert{}%
\endisaantiq
-\ {\isacharparenleft}Config{\isachardot}get\ %
+\ {\isaliteral{28}{\isacharparenleft}}Config{\isaliteral{2E}{\isachardot}}get\ %
\isaantiq
-context%
+context{}%
\endisaantiq
-\ my{\isacharunderscore}flag\ {\isacharequal}\ false{\isacharparenright}\ {\isacharverbatimclose}%
+\ my{\isaliteral{5F}{\isacharunderscore}}flag\ {\isaliteral{3D}{\isacharequal}}\ false{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -899,7 +899,7 @@
\isanewline
\isanewline
\isacommand{declare}\isamarkupfalse%
-\ {\isacharbrackleft}{\isacharbrackleft}my{\isacharunderscore}flag\ {\isacharequal}\ true{\isacharbrackright}{\isacharbrackright}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5B}{\isacharbrackleft}}my{\isaliteral{5F}{\isacharunderscore}}flag\ {\isaliteral{3D}{\isacharequal}}\ true{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5D}{\isacharbrackright}}\isanewline
%
\isadelimML
\isanewline
@@ -907,16 +907,16 @@
\endisadelimML
%
\isatagML
-\isacommand{ML{\isacharunderscore}val}\isamarkupfalse%
-\ {\isacharverbatimopen}\ %
+\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ %
\isaantiq
-assert%
+assert{}%
\endisaantiq
-\ {\isacharparenleft}Config{\isachardot}get\ %
+\ {\isaliteral{28}{\isacharparenleft}}Config{\isaliteral{2E}{\isachardot}}get\ %
\isaantiq
-context%
+context{}%
\endisaantiq
-\ my{\isacharunderscore}flag\ {\isacharequal}\ true{\isacharparenright}\ {\isacharverbatimclose}%
+\ my{\isaliteral{5F}{\isacharunderscore}}flag\ {\isaliteral{3D}{\isacharequal}}\ true{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -925,7 +925,7 @@
%
\endisadelimML
\isanewline
-\isacommand{example{\isacharunderscore}proof}\isamarkupfalse%
+\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}\isamarkupfalse%
\isanewline
%
\isadelimproof
@@ -933,10 +933,10 @@
\endisadelimproof
%
\isatagproof
-\isacommand{{\isacharbraceleft}}\isamarkupfalse%
+\isacommand{{\isaliteral{7B}{\isacharbraceleft}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{note}\isamarkupfalse%
-\ {\isacharbrackleft}{\isacharbrackleft}my{\isacharunderscore}flag\ {\isacharequal}\ false{\isacharbrackright}{\isacharbrackright}%
+\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5B}{\isacharbrackleft}}my{\isaliteral{5F}{\isacharunderscore}}flag\ {\isaliteral{3D}{\isacharequal}}\ false{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5D}{\isacharbrackright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -950,16 +950,16 @@
\endisadelimML
%
\isatagML
-\isacommand{ML{\isacharunderscore}val}\isamarkupfalse%
-\ {\isacharverbatimopen}\ %
+\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ %
\isaantiq
-assert%
+assert{}%
\endisaantiq
-\ {\isacharparenleft}Config{\isachardot}get\ %
+\ {\isaliteral{28}{\isacharparenleft}}Config{\isaliteral{2E}{\isachardot}}get\ %
\isaantiq
-context%
+context{}%
\endisaantiq
-\ my{\isacharunderscore}flag\ {\isacharequal}\ false{\isacharparenright}\ {\isacharverbatimclose}%
+\ my{\isaliteral{5F}{\isacharunderscore}}flag\ {\isaliteral{3D}{\isacharequal}}\ false{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -973,7 +973,7 @@
\endisadelimproof
%
\isatagproof
-\isacommand{{\isacharbraceright}}\isamarkupfalse%
+\isacommand{{\isaliteral{7D}{\isacharbraceright}}}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
@@ -988,16 +988,16 @@
\endisadelimML
%
\isatagML
-\isacommand{ML{\isacharunderscore}val}\isamarkupfalse%
-\ {\isacharverbatimopen}\ %
+\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ %
\isaantiq
-assert%
+assert{}%
\endisaantiq
-\ {\isacharparenleft}Config{\isachardot}get\ %
+\ {\isaliteral{28}{\isacharparenleft}}Config{\isaliteral{2E}{\isachardot}}get\ %
\isaantiq
-context%
+context{}%
\endisaantiq
-\ my{\isacharunderscore}flag\ {\isacharequal}\ true{\isacharparenright}\ {\isacharverbatimclose}%
+\ my{\isaliteral{5F}{\isacharunderscore}}flag\ {\isaliteral{3D}{\isacharequal}}\ true{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -1032,12 +1032,12 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ val\ {\isacharparenleft}airspeed{\isacharunderscore}velocity{\isacharcomma}\ airspeed{\isacharunderscore}velocity{\isacharunderscore}setup{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ Attrib{\isachardot}config{\isacharunderscore}real\ {\isachardoublequote}airspeed{\isacharunderscore}velocity{\isachardoublequote}\ {\isacharparenleft}K\ {\isadigit{0}}{\isachardot}{\isadigit{0}}{\isacharparenright}\isanewline
-{\isacharverbatimclose}\isanewline
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ val\ {\isaliteral{28}{\isacharparenleft}}airspeed{\isaliteral{5F}{\isacharunderscore}}velocity{\isaliteral{2C}{\isacharcomma}}\ airspeed{\isaliteral{5F}{\isacharunderscore}}velocity{\isaliteral{5F}{\isacharunderscore}}setup{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ Attrib{\isaliteral{2E}{\isachardot}}config{\isaliteral{5F}{\isacharunderscore}}real\ {\isaliteral{22}{\isachardoublequote}}airspeed{\isaliteral{5F}{\isacharunderscore}}velocity{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}K\ {\isadigit{0}}{\isaliteral{2E}{\isachardot}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
\isacommand{setup}\isamarkupfalse%
-\ airspeed{\isacharunderscore}velocity{\isacharunderscore}setup%
+\ airspeed{\isaliteral{5F}{\isacharunderscore}}velocity{\isaliteral{5F}{\isacharunderscore}}setup%
\endisatagML
{\isafoldML}%
%
@@ -1047,9 +1047,9 @@
\isanewline
\isanewline
\isacommand{declare}\isamarkupfalse%
-\ {\isacharbrackleft}{\isacharbrackleft}airspeed{\isacharunderscore}velocity\ {\isacharequal}\ {\isadigit{1}}{\isadigit{0}}{\isacharbrackright}{\isacharbrackright}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5B}{\isacharbrackleft}}airspeed{\isaliteral{5F}{\isacharunderscore}}velocity\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isadigit{0}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5D}{\isacharbrackright}}\isanewline
\isacommand{declare}\isamarkupfalse%
-\ {\isacharbrackleft}{\isacharbrackleft}airspeed{\isacharunderscore}velocity\ {\isacharequal}\ {\isadigit{9}}{\isachardot}{\isadigit{9}}{\isacharbrackright}{\isacharbrackright}%
+\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5B}{\isacharbrackleft}}airspeed{\isaliteral{5F}{\isacharunderscore}}velocity\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{9}}{\isaliteral{2E}{\isachardot}}{\isadigit{9}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5D}{\isacharbrackright}}%
\isamarkupsection{Names \label{sec:names}%
}
\isamarkuptrue%
@@ -1057,8 +1057,8 @@
\begin{isamarkuptext}%
In principle, a name is just a string, but there are various
conventions for representing additional structure. For example,
- ``\isa{Foo{\isachardot}bar{\isachardot}baz}'' is considered as a long name consisting of
- qualifier \isa{Foo{\isachardot}bar} and base name \isa{baz}. The
+ ``\isa{Foo{\isaliteral{2E}{\isachardot}}bar{\isaliteral{2E}{\isachardot}}baz}'' is considered as a long name consisting of
+ qualifier \isa{Foo{\isaliteral{2E}{\isachardot}}bar} and base name \isa{baz}. The
individual constituents of a name may have further substructure,
e.g.\ the string ``\verb,\,\verb,<alpha>,'' encodes as a single
symbol.
@@ -1116,7 +1116,7 @@
\end{enumerate}
- The \isa{ident} syntax for symbol names is \isa{letter\ {\isacharparenleft}letter\ {\isacharbar}\ digit{\isacharparenright}\isactrlsup {\isacharasterisk}}, where \isa{letter\ {\isacharequal}\ A{\isachardot}{\isachardot}Za{\isachardot}{\isachardot}z} and \isa{digit\ {\isacharequal}\ {\isadigit{0}}{\isachardot}{\isachardot}{\isadigit{9}}}. There are infinitely many regular symbols and
+ The \isa{ident} syntax for symbol names is \isa{letter\ {\isaliteral{28}{\isacharparenleft}}letter\ {\isaliteral{7C}{\isacharbar}}\ digit{\isaliteral{29}{\isacharparenright}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}}, where \isa{letter\ {\isaliteral{3D}{\isacharequal}}\ A{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}Za{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}z} and \isa{digit\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isadigit{9}}}. There are infinitely many regular symbols and
control symbols, but a fixed collection of standard symbols is
treated specifically. For example, ``\verb,\,\verb,<alpha>,'' is
classified as a letter, which means it may occur within regular
@@ -1137,8 +1137,8 @@
\medskip Output of Isabelle symbols depends on the print mode
(\secref{print-mode}). For example, the standard {\LaTeX} setup of
the Isabelle document preparation system would present
- ``\verb,\,\verb,<alpha>,'' as \isa{{\isasymalpha}}, and
- ``\verb,\,\verb,<^bold>,\verb,\,\verb,<alpha>,'' as \isa{\isactrlbold {\isasymalpha}}. On-screen rendering usually works by mapping a finite
+ ``\verb,\,\verb,<alpha>,'' as \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}}, and
+ ``\verb,\,\verb,<^bold>,\verb,\,\verb,<alpha>,'' as \isa{\isaliteral{5C3C5E626F6C643E}{}\isactrlbold {\isaliteral{5C3C616C7068613E}{\isasymalpha}}}. On-screen rendering usually works by mapping a finite
subset of Isabelle symbols to suitable Unicode characters.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -1217,7 +1217,7 @@
three underscores means \emph{internal Skolem name}.
For example, the basic name \isa{foo} has the internal version
- \isa{foo{\isacharunderscore}}, with Skolem versions \isa{foo{\isacharunderscore}{\isacharunderscore}} and \isa{foo{\isacharunderscore}{\isacharunderscore}{\isacharunderscore}}, respectively.
+ \isa{foo{\isaliteral{5F}{\isacharunderscore}}}, with Skolem versions \isa{foo{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5F}{\isacharunderscore}}} and \isa{foo{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5F}{\isacharunderscore}}}, respectively.
These special versions provide copies of the basic name space, apart
from anything that normally appears in the user text. For example,
@@ -1235,7 +1235,7 @@
from \isa{a} are \isa{a}, \isa{b}, \isa{c}.
The \isa{variants} operation produces fresh names by
- incrementing tentative names as base-26 numbers (with digits \isa{a{\isachardot}{\isachardot}z}) until all clashes are resolved. For example, name \isa{foo} results in variants \isa{fooa}, \isa{foob}, \isa{fooc}, \dots, \isa{fooaa}, \isa{fooab} etc.; each renaming
+ incrementing tentative names as base-26 numbers (with digits \isa{a{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}z}) until all clashes are resolved. For example, name \isa{foo} results in variants \isa{fooa}, \isa{foob}, \isa{fooc}, \dots, \isa{fooaa}, \isa{fooab} etc.; each renaming
step picks the next unused variant from this sequence.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -1325,22 +1325,22 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ val\ list{\isadigit{1}}\ {\isacharequal}\ Name{\isachardot}invents\ Name{\isachardot}context\ {\isachardoublequote}a{\isachardoublequote}\ {\isadigit{5}}{\isacharsemicolon}\isanewline
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ val\ list{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ Name{\isaliteral{2E}{\isachardot}}invents\ Name{\isaliteral{2E}{\isachardot}}context\ {\isaliteral{22}{\isachardoublequote}}a{\isaliteral{22}{\isachardoublequote}}\ {\isadigit{5}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\ \ %
\isaantiq
-assert%
+assert{}%
\endisaantiq
-\ {\isacharparenleft}list{\isadigit{1}}\ {\isacharequal}\ {\isacharbrackleft}{\isachardoublequote}a{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}b{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}c{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}d{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}e{\isachardoublequote}{\isacharbrackright}{\isacharparenright}{\isacharsemicolon}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}list{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}b{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}c{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}d{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}e{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ val\ list{\isadigit{2}}\ {\isacharequal}\isanewline
-\ \ \ \ {\isacharhash}{\isadigit{1}}\ {\isacharparenleft}Name{\isachardot}variants\ {\isacharbrackleft}{\isachardoublequote}x{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}x{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}a{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}a{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}{\isacharprime}a{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}{\isacharprime}a{\isachardoublequote}{\isacharbrackright}\ Name{\isachardot}context{\isacharparenright}{\isacharsemicolon}\isanewline
+\ \ val\ list{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ {\isaliteral{23}{\isacharhash}}{\isadigit{1}}\ {\isaliteral{28}{\isacharparenleft}}Name{\isaliteral{2E}{\isachardot}}variants\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}a{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}a{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}\ Name{\isaliteral{2E}{\isachardot}}context{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\ \ %
\isaantiq
-assert%
+assert{}%
\endisaantiq
-\ {\isacharparenleft}list{\isadigit{2}}\ {\isacharequal}\ {\isacharbrackleft}{\isachardoublequote}x{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}xa{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}a{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}aa{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}{\isacharprime}a{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}{\isacharprime}aa{\isachardoublequote}{\isacharbrackright}{\isacharparenright}{\isacharsemicolon}\isanewline
-{\isacharverbatimclose}%
+\ {\isaliteral{28}{\isacharparenleft}}list{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}xa{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}a{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}aa{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}aa{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -1354,7 +1354,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{locale}\isamarkupfalse%
-\ ex\ {\isacharequal}\ \isakeyword{fixes}\ a\ b\ c\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a\isanewline
+\ ex\ {\isaliteral{3D}{\isacharequal}}\ \isakeyword{fixes}\ a\ b\ c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\isanewline
\isakeyword{begin}\isanewline
%
\isadelimML
@@ -1364,28 +1364,28 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ val\ names\ {\isacharequal}\ Variable{\isachardot}names{\isacharunderscore}of\ %
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ val\ names\ {\isaliteral{3D}{\isacharequal}}\ Variable{\isaliteral{2E}{\isachardot}}names{\isaliteral{5F}{\isacharunderscore}}of\ %
\isaantiq
-context%
+context{}%
\endisaantiq
-{\isacharsemicolon}\isanewline
+{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ val\ list{\isadigit{1}}\ {\isacharequal}\ Name{\isachardot}invents\ names\ {\isachardoublequote}a{\isachardoublequote}\ {\isadigit{5}}{\isacharsemicolon}\isanewline
+\ \ val\ list{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ Name{\isaliteral{2E}{\isachardot}}invents\ names\ {\isaliteral{22}{\isachardoublequote}}a{\isaliteral{22}{\isachardoublequote}}\ {\isadigit{5}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\ \ %
\isaantiq
-assert%
+assert{}%
\endisaantiq
-\ {\isacharparenleft}list{\isadigit{1}}\ {\isacharequal}\ {\isacharbrackleft}{\isachardoublequote}d{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}e{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}f{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}g{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}h{\isachardoublequote}{\isacharbrackright}{\isacharparenright}{\isacharsemicolon}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}list{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}d{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}e{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}f{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}g{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}h{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ val\ list{\isadigit{2}}\ {\isacharequal}\isanewline
-\ \ \ \ {\isacharhash}{\isadigit{1}}\ {\isacharparenleft}Name{\isachardot}variants\ {\isacharbrackleft}{\isachardoublequote}x{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}x{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}a{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}a{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}{\isacharprime}a{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}{\isacharprime}a{\isachardoublequote}{\isacharbrackright}\ names{\isacharparenright}{\isacharsemicolon}\isanewline
+\ \ val\ list{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ {\isaliteral{23}{\isacharhash}}{\isadigit{1}}\ {\isaliteral{28}{\isacharparenleft}}Name{\isaliteral{2E}{\isachardot}}variants\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}a{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}a{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}\ names{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\ \ %
\isaantiq
-assert%
+assert{}%
\endisaantiq
-\ {\isacharparenleft}list{\isadigit{2}}\ {\isacharequal}\ {\isacharbrackleft}{\isachardoublequote}x{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}xa{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}aa{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}ab{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}{\isacharprime}aa{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}{\isacharprime}ab{\isachardoublequote}{\isacharbrackright}{\isacharparenright}{\isacharsemicolon}\isanewline
-{\isacharverbatimclose}%
+\ {\isaliteral{28}{\isacharparenleft}}list{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}xa{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}aa{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}ab{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}aa{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}ab{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -1407,23 +1407,23 @@
way to rename two collections of indexnames apart from each other is
this: determine the maximum index \isa{maxidx} of the first
collection, then increment all indexes of the second collection by
- \isa{maxidx\ {\isacharplus}\ {\isadigit{1}}}; the maximum index of an empty collection is
- \isa{{\isacharminus}{\isadigit{1}}}.
+ \isa{maxidx\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}}; the maximum index of an empty collection is
+ \isa{{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}}.
Occasionally, basic names are injected into the same pair type of
- indexed names: then \isa{{\isacharparenleft}x{\isacharcomma}\ {\isacharminus}{\isadigit{1}}{\isacharparenright}} is used to encode the basic
+ indexed names: then \isa{{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}} is used to encode the basic
name \isa{x}.
\medskip Isabelle syntax observes the following rules for
- representing an indexname \isa{{\isacharparenleft}x{\isacharcomma}\ i{\isacharparenright}} as a packed string:
+ representing an indexname \isa{{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ i{\isaliteral{29}{\isacharparenright}}} as a packed string:
\begin{itemize}
- \item \isa{{\isacharquery}x} if \isa{x} does not end with a digit and \isa{i\ {\isacharequal}\ {\isadigit{0}}},
+ \item \isa{{\isaliteral{3F}{\isacharquery}}x} if \isa{x} does not end with a digit and \isa{i\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}},
- \item \isa{{\isacharquery}xi} if \isa{x} does not end with a digit,
+ \item \isa{{\isaliteral{3F}{\isacharquery}}xi} if \isa{x} does not end with a digit,
- \item \isa{{\isacharquery}x{\isachardot}i} otherwise.
+ \item \isa{{\isaliteral{3F}{\isacharquery}}x{\isaliteral{2E}{\isachardot}}i} otherwise.
\end{itemize}
@@ -1431,8 +1431,8 @@
shifts have been applied. Results are usually normalized towards
\isa{{\isadigit{0}}} at certain checkpoints, notably at the end of a proof.
This works by producing variants of the corresponding basic name
- components. For example, the collection \isa{{\isacharquery}x{\isadigit{1}}{\isacharcomma}\ {\isacharquery}x{\isadigit{7}}{\isacharcomma}\ {\isacharquery}x{\isadigit{4}}{\isadigit{2}}}
- becomes \isa{{\isacharquery}x{\isacharcomma}\ {\isacharquery}xa{\isacharcomma}\ {\isacharquery}xb}.%
+ components. For example, the collection \isa{{\isaliteral{3F}{\isacharquery}}x{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}x{\isadigit{7}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}x{\isadigit{4}}{\isadigit{2}}}
+ becomes \isa{{\isaliteral{3F}{\isacharquery}}x{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}xa{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}xb}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -1451,7 +1451,7 @@
\item Type \verb|indexname| represents indexed names. This is
an abbreviation for \verb|string * int|. The second component
- is usually non-negative, except for situations where \isa{{\isacharparenleft}x{\isacharcomma}\ {\isacharminus}{\isadigit{1}}{\isacharparenright}} is used to inject basic names into this type. Other negative
+ is usually non-negative, except for situations where \isa{{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}} is used to inject basic names into this type. Other negative
indexes should not be used.
\end{description}%
@@ -1472,14 +1472,14 @@
\begin{isamarkuptext}%
A \emph{long name} consists of a sequence of non-empty name
components. The packed representation uses a dot as separator, as
- in ``\isa{A{\isachardot}b{\isachardot}c}''. The last component is called \emph{base
+ in ``\isa{A{\isaliteral{2E}{\isachardot}}b{\isaliteral{2E}{\isachardot}}c}''. The last component is called \emph{base
name}, the remaining prefix is called \emph{qualifier} (which may be
empty). The qualifier can be understood as the access path to the
named entity while passing through some nested block-structure,
although our free-form long names do not really enforce any strict
discipline.
- For example, an item named ``\isa{A{\isachardot}b{\isachardot}c}'' may be understood as
+ For example, an item named ``\isa{A{\isaliteral{2E}{\isachardot}}b{\isaliteral{2E}{\isachardot}}c}'' may be understood as
a local entity \isa{c}, within a local structure \isa{b},
within a global structure \isa{A}. In practice, long names
usually represent 1--3 levels of qualification. User ML code should
@@ -1516,7 +1516,7 @@
\item \verb|Long_Name.qualifier|~\isa{name} returns the qualifier
of a long name.
- \item \verb|Long_Name.append|~\isa{name\isactrlisub {\isadigit{1}}\ name\isactrlisub {\isadigit{2}}} appends two long
+ \item \verb|Long_Name.append|~\isa{name\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ name\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}} appends two long
names.
\item \verb|Long_Name.implode|~\isa{names} and \verb|Long_Name.explode|~\isa{name} convert between the packed string
@@ -1561,7 +1561,7 @@
\medskip
\begin{tabular}{l}
- \isa{binding\ {\isacharplus}\ naming\ {\isasymlongrightarrow}\ long\ name\ {\isacharplus}\ name\ space\ accesses}
+ \isa{binding\ {\isaliteral{2B}{\isacharplus}}\ naming\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ long\ name\ {\isaliteral{2B}{\isacharplus}}\ name\ space\ accesses}
\end{tabular}
\bigskip As a general principle, there is a separate name space for
@@ -1573,7 +1573,7 @@
There are common schemes to name derived entities systematically
according to the name of the main logical entity involved, e.g.\
- fact \isa{c{\isachardot}intro} for a canonical introduction rule related to
+ fact \isa{c{\isaliteral{2E}{\isachardot}}intro} for a canonical introduction rule related to
constant \isa{c}. This technique of mapping names from one
space into another requires some care in order to avoid conflicts.
In particular, theorem names derived from a type constructor or type
@@ -1584,9 +1584,9 @@
\medskip
\begin{tabular}{ll}
logical entity & fact name \\\hline
- constant \isa{c} & \isa{c{\isachardot}intro} \\
- type \isa{c} & \isa{c{\isacharunderscore}type{\isachardot}intro} \\
- class \isa{c} & \isa{c{\isacharunderscore}class{\isachardot}intro} \\
+ constant \isa{c} & \isa{c{\isaliteral{2E}{\isachardot}}intro} \\
+ type \isa{c} & \isa{c{\isaliteral{5F}{\isacharunderscore}}type{\isaliteral{2E}{\isachardot}}intro} \\
+ class \isa{c} & \isa{c{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}intro} \\
\end{tabular}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -1672,7 +1672,7 @@
\item Type \verb|Name_Space.T| represents name spaces.
- \item \verb|Name_Space.empty|~\isa{kind} and \verb|Name_Space.merge|~\isa{{\isacharparenleft}space\isactrlisub {\isadigit{1}}{\isacharcomma}\ space\isactrlisub {\isadigit{2}}{\isacharparenright}} are the canonical operations for
+ \item \verb|Name_Space.empty|~\isa{kind} and \verb|Name_Space.merge|~\isa{{\isaliteral{28}{\isacharparenleft}}space\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ space\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}} are the canonical operations for
maintaining name spaces according to theory data management
(\secref{sec:context-data}); \isa{kind} is a formal comment
to characterize the purpose of a name space.
@@ -1718,7 +1718,7 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{ML antiquotation}{binding}\hypertarget{ML antiquotation.binding}{\hyperlink{ML antiquotation.binding}{\mbox{\isa{binding}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
+ \indexdef{}{ML antiquotation}{binding}\hypertarget{ML antiquotation.binding}{\hyperlink{ML antiquotation.binding}{\mbox{\isa{binding}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
\end{matharray}
\begin{rail}
@@ -1728,7 +1728,7 @@
\begin{description}
- \item \isa{{\isacharat}{\isacharbraceleft}binding\ name{\isacharbraceright}} produces a binding with base name
+ \item \isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}binding\ name{\isaliteral{7D}{\isacharbraceright}}} produces a binding with base name
\isa{name} and the source position taken from the concrete
syntax of this antiquotation. In many situations this is more
appropriate than the more basic \verb|Binding.name| function.
@@ -1769,11 +1769,11 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\ Binding{\isachardot}pos{\isacharunderscore}of\ %
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ Binding{\isaliteral{2E}{\isachardot}}pos{\isaliteral{5F}{\isacharunderscore}}of\ %
\isaantiq
-binding\ here%
+binding\ here{}%
\endisaantiq
-\ {\isacharverbatimclose}%
+\ {\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -1792,15 +1792,15 @@
\endisadelimML
%
\isatagML
-\isacommand{ML{\isacharunderscore}command}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
+\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}command}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
\ \ writeln\isanewline
-\ \ \ \ {\isacharparenleft}{\isachardoublequote}Look\ here{\isachardoublequote}\ {\isacharcircum}\ Position{\isachardot}str{\isacharunderscore}of\ {\isacharparenleft}Binding{\isachardot}pos{\isacharunderscore}of\ %
+\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Look\ here{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ Position{\isaliteral{2E}{\isachardot}}str{\isaliteral{5F}{\isacharunderscore}}of\ {\isaliteral{28}{\isacharparenleft}}Binding{\isaliteral{2E}{\isachardot}}pos{\isaliteral{5F}{\isacharunderscore}}of\ %
\isaantiq
-binding\ here%
+binding\ here{}%
\endisaantiq
-{\isacharparenright}{\isacharparenright}\isanewline
-{\isacharverbatimclose}%
+{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
--- a/doc-src/IsarImplementation/Thy/document/Proof.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarImplementation/Thy/document/Proof.tex Mon Nov 08 14:41:11 2010 +0100
@@ -27,24 +27,24 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-Any variable that is not explicitly bound by \isa{{\isasymlambda}}-abstraction
+Any variable that is not explicitly bound by \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}}-abstraction
is considered as ``free''. Logically, free variables act like
- outermost universal quantification at the sequent level: \isa{A\isactrlisub {\isadigit{1}}{\isacharparenleft}x{\isacharparenright}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ A\isactrlisub n{\isacharparenleft}x{\isacharparenright}\ {\isasymturnstile}\ B{\isacharparenleft}x{\isacharparenright}} means that the result
+ outermost universal quantification at the sequent level: \isa{A\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ A\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}} means that the result
holds \emph{for all} values of \isa{x}. Free variables for
- terms (not types) can be fully internalized into the logic: \isa{{\isasymturnstile}\ B{\isacharparenleft}x{\isacharparenright}} and \isa{{\isasymturnstile}\ {\isasymAnd}x{\isachardot}\ B{\isacharparenleft}x{\isacharparenright}} are interchangeable, provided
+ terms (not types) can be fully internalized into the logic: \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}} and \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ B{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}} are interchangeable, provided
that \isa{x} does not occur elsewhere in the context.
- Inspecting \isa{{\isasymturnstile}\ {\isasymAnd}x{\isachardot}\ B{\isacharparenleft}x{\isacharparenright}} more closely, we see that inside the
+ Inspecting \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ B{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}} more closely, we see that inside the
quantifier, \isa{x} is essentially ``arbitrary, but fixed'',
while from outside it appears as a place-holder for instantiation
- (thanks to \isa{{\isasymAnd}} elimination).
+ (thanks to \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}} elimination).
The Pure logic represents the idea of variables being either inside
or outside the current scope by providing separate syntactic
categories for \emph{fixed variables} (e.g.\ \isa{x}) vs.\
- \emph{schematic variables} (e.g.\ \isa{{\isacharquery}x}). Incidently, a
- universal result \isa{{\isasymturnstile}\ {\isasymAnd}x{\isachardot}\ B{\isacharparenleft}x{\isacharparenright}} has the HHF normal form \isa{{\isasymturnstile}\ B{\isacharparenleft}{\isacharquery}x{\isacharparenright}}, which represents its generality without requiring an
+ \emph{schematic variables} (e.g.\ \isa{{\isaliteral{3F}{\isacharquery}}x}). Incidently, a
+ universal result \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ B{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}} has the HHF normal form \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{29}{\isacharparenright}}}, which represents its generality without requiring an
explicit quantifier. The same principle works for type variables:
- \isa{{\isasymturnstile}\ B{\isacharparenleft}{\isacharquery}{\isasymalpha}{\isacharparenright}} represents the idea of ``\isa{{\isasymturnstile}\ {\isasymforall}{\isasymalpha}{\isachardot}\ B{\isacharparenleft}{\isasymalpha}{\isacharparenright}}''
+ \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}} represents the idea of ``\isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{2E}{\isachardot}}\ B{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}}''
without demanding a truly polymorphic framework.
\medskip Additional care is required to treat type variables in a
@@ -52,27 +52,27 @@
depend on type variables, which means that type variables would have
to be declared first. For example, a raw type-theoretic framework
would demand the context to be constructed in stages as follows:
- \isa{{\isasymGamma}\ {\isacharequal}\ {\isasymalpha}{\isacharcolon}\ type{\isacharcomma}\ x{\isacharcolon}\ {\isasymalpha}{\isacharcomma}\ a{\isacharcolon}\ A{\isacharparenleft}x\isactrlisub {\isasymalpha}{\isacharparenright}}.
+ \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{3A}{\isacharcolon}}\ type{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{2C}{\isacharcomma}}\ a{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{28}{\isacharparenleft}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}}.
We allow a slightly less formalistic mode of operation: term
variables \isa{x} are fixed without specifying a type yet
(essentially \emph{all} potential occurrences of some instance
- \isa{x\isactrlisub {\isasymtau}} are fixed); the first occurrence of \isa{x}
+ \isa{x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C7461753E}{\isasymtau}}} are fixed); the first occurrence of \isa{x}
within a specific term assigns its most general type, which is then
maintained consistently in the context. The above example becomes
- \isa{{\isasymGamma}\ {\isacharequal}\ x{\isacharcolon}\ term{\isacharcomma}\ {\isasymalpha}{\isacharcolon}\ type{\isacharcomma}\ A{\isacharparenleft}x\isactrlisub {\isasymalpha}{\isacharparenright}}, where type \isa{{\isasymalpha}} is fixed \emph{after} term \isa{x}, and the constraint
- \isa{x\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}} is an implicit consequence of the occurrence of
- \isa{x\isactrlisub {\isasymalpha}} in the subsequent proposition.
+ \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{3A}{\isacharcolon}}\ term{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{3A}{\isacharcolon}}\ type{\isaliteral{2C}{\isacharcomma}}\ A{\isaliteral{28}{\isacharparenleft}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}}, where type \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}} is fixed \emph{after} term \isa{x}, and the constraint
+ \isa{x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}} is an implicit consequence of the occurrence of
+ \isa{x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C616C7068613E}{\isasymalpha}}} in the subsequent proposition.
This twist of dependencies is also accommodated by the reverse
operation of exporting results from a context: a type variable
- \isa{{\isasymalpha}} is considered fixed as long as it occurs in some fixed
- term variable of the context. For example, exporting \isa{x{\isacharcolon}\ term{\isacharcomma}\ {\isasymalpha}{\isacharcolon}\ type\ {\isasymturnstile}\ x\isactrlisub {\isasymalpha}\ {\isasymequiv}\ x\isactrlisub {\isasymalpha}} produces in the first step \isa{x{\isacharcolon}\ term\ {\isasymturnstile}\ x\isactrlisub {\isasymalpha}\ {\isasymequiv}\ x\isactrlisub {\isasymalpha}} for fixed \isa{{\isasymalpha}}, and only in the second step
- \isa{{\isasymturnstile}\ {\isacharquery}x\isactrlisub {\isacharquery}\isactrlisub {\isasymalpha}\ {\isasymequiv}\ {\isacharquery}x\isactrlisub {\isacharquery}\isactrlisub {\isasymalpha}} for schematic \isa{{\isacharquery}x} and \isa{{\isacharquery}{\isasymalpha}}.
+ \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}} is considered fixed as long as it occurs in some fixed
+ term variable of the context. For example, exporting \isa{x{\isaliteral{3A}{\isacharcolon}}\ term{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{3A}{\isacharcolon}}\ type\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C616C7068613E}{\isasymalpha}}} produces in the first step \isa{x{\isaliteral{3A}{\isacharcolon}}\ term\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C616C7068613E}{\isasymalpha}}} for fixed \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}}, and only in the second step
+ \isa{{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{3F}{\isacharquery}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{3F}{\isacharquery}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{3F}{\isacharquery}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{3F}{\isacharquery}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isaliteral{5C3C616C7068613E}{\isasymalpha}}} for schematic \isa{{\isaliteral{3F}{\isacharquery}}x} and \isa{{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}}.
The following Isar source text illustrates this scenario.%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{example{\isacharunderscore}proof}\isamarkupfalse%
+\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}\isamarkupfalse%
\isanewline
%
\isadelimproof
@@ -80,23 +80,23 @@
\endisadelimproof
%
\isatagproof
-\isacommand{{\isacharbraceleft}}\isamarkupfalse%
+\isacommand{{\isaliteral{7B}{\isacharbraceleft}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ x\ \ %
-\isamarkupcmt{all potential occurrences of some \isa{x{\isacharcolon}{\isacharcolon}{\isasymtau}} are fixed%
+\isamarkupcmt{all potential occurrences of some \isa{x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{5C3C7461753E}{\isasymtau}}} are fixed%
}
\isanewline
-\ \ \ \ \isacommand{{\isacharbraceleft}}\isamarkupfalse%
+\ \ \ \ \isacommand{{\isaliteral{7B}{\isacharbraceleft}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x{\isacharcolon}{\isacharcolon}{\isacharprime}a\ {\isasymequiv}\ x{\isachardoublequoteclose}\ \ %
+\ {\isaliteral{22}{\isachardoublequoteopen}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \ %
\isamarkupcmt{implicit type assigment by concrete occurrence%
}
\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ reflexive{\isacharparenright}\isanewline
-\ \ \ \ \isacommand{{\isacharbraceright}}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ reflexive{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ \isacommand{{\isaliteral{7D}{\isacharbraceright}}}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
@@ -107,7 +107,7 @@
\endisadelimproof
\ \ \ \ \isacommand{thm}\isamarkupfalse%
\ this\ \ %
-\isamarkupcmt{result still with fixed type \isa{{\isacharprime}a}%
+\isamarkupcmt{result still with fixed type \isa{{\isaliteral{27}{\isacharprime}}a}%
}
\isanewline
%
@@ -116,7 +116,7 @@
\endisadelimproof
%
\isatagproof
-\isacommand{{\isacharbraceright}}\isamarkupfalse%
+\isacommand{{\isaliteral{7D}{\isacharbraceright}}}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
@@ -127,7 +127,7 @@
\endisadelimproof
\ \ \isacommand{thm}\isamarkupfalse%
\ this\ \ %
-\isamarkupcmt{fully general result for arbitrary \isa{{\isacharquery}x{\isacharcolon}{\isacharcolon}{\isacharquery}{\isacharprime}a}%
+\isamarkupcmt{fully general result for arbitrary \isa{{\isaliteral{3F}{\isacharquery}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{27}{\isacharprime}}a}%
}
\isanewline
%
@@ -150,8 +150,8 @@
vs.\ type variables, with high-level principles for moving the
frontier between fixed and schematic variables.
- The \isa{add{\isacharunderscore}fixes} operation explictly declares fixed
- variables; the \isa{declare{\isacharunderscore}term} operation absorbs a term into
+ The \isa{add{\isaliteral{5F}{\isacharunderscore}}fixes} operation explictly declares fixed
+ variables; the \isa{declare{\isaliteral{5F}{\isacharunderscore}}term} operation absorbs a term into
a context by fixing new type variables and adding syntactic
constraints.
@@ -166,8 +166,8 @@
the original modulo renaming of schematic variables.
The \isa{focus} operation provides a variant of \isa{import}
- for nested propositions (with explicit quantification): \isa{{\isasymAnd}x\isactrlisub {\isadigit{1}}\ {\isasymdots}\ x\isactrlisub n{\isachardot}\ B{\isacharparenleft}x\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlisub n{\isacharparenright}} is
- decomposed by inventing fixed variables \isa{x\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlisub n} for the body.%
+ for nested propositions (with explicit quantification): \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{2E}{\isachardot}}\ B{\isaliteral{28}{\isacharparenleft}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}} is
+ decomposed by inventing fixed variables \isa{x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E697375623E}{}\isactrlisub n} for the body.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -231,7 +231,7 @@
should be accessible to the user, otherwise newly introduced names
are marked as ``internal'' (\secref{sec:names}).
- \item \verb|Variable.focus|~\isa{B} decomposes the outermost \isa{{\isasymAnd}} prefix of proposition \isa{B}.
+ \item \verb|Variable.focus|~\isa{B} decomposes the outermost \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}} prefix of proposition \isa{B}.
\end{description}%
\end{isamarkuptext}%
@@ -269,28 +269,28 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ {\isacharparenleft}{\isacharasterisk}static\ compile{\isacharminus}time\ context\ {\isacharminus}{\isacharminus}\ for\ testing\ only{\isacharasterisk}{\isacharparenright}\isanewline
-\ \ val\ ctxt{\isadigit{0}}\ {\isacharequal}\ %
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}static\ compile{\isaliteral{2D}{\isacharminus}}time\ context\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}\ for\ testing\ only{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ val\ ctxt{\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ %
\isaantiq
-context%
+context{}%
\endisaantiq
-{\isacharsemicolon}\isanewline
+{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ {\isacharparenleft}{\isacharasterisk}locally\ fixed\ parameters\ {\isacharminus}{\isacharminus}\ no\ type\ assignment\ yet{\isacharasterisk}{\isacharparenright}\isanewline
-\ \ val\ {\isacharparenleft}{\isacharbrackleft}x{\isacharcomma}\ y{\isacharbrackright}{\isacharcomma}\ ctxt{\isadigit{1}}{\isacharparenright}\ {\isacharequal}\ ctxt{\isadigit{0}}\ {\isacharbar}{\isachargreater}\ Variable{\isachardot}add{\isacharunderscore}fixes\ {\isacharbrackleft}{\isachardoublequote}x{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}y{\isachardoublequote}{\isacharbrackright}{\isacharsemicolon}\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}locally\ fixed\ parameters\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}\ no\ type\ assignment\ yet{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ val\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ ctxt{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ ctxt{\isadigit{0}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ Variable{\isaliteral{2E}{\isachardot}}add{\isaliteral{5F}{\isacharunderscore}}fixes\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}y{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ {\isacharparenleft}{\isacharasterisk}t{\isadigit{1}}{\isacharcolon}\ most\ general\ fixed\ type{\isacharsemicolon}\ t{\isadigit{1}}{\isacharprime}{\isacharcolon}\ most\ general\ arbitrary\ type{\isacharasterisk}{\isacharparenright}\isanewline
-\ \ val\ t{\isadigit{1}}\ {\isacharequal}\ Syntax{\isachardot}read{\isacharunderscore}term\ ctxt{\isadigit{1}}\ {\isachardoublequote}x{\isachardoublequote}{\isacharsemicolon}\isanewline
-\ \ val\ t{\isadigit{1}}{\isacharprime}\ {\isacharequal}\ singleton\ {\isacharparenleft}Variable{\isachardot}polymorphic\ ctxt{\isadigit{1}}{\isacharparenright}\ t{\isadigit{1}}{\isacharsemicolon}\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}t{\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}\ most\ general\ fixed\ type{\isaliteral{3B}{\isacharsemicolon}}\ t{\isadigit{1}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3A}{\isacharcolon}}\ most\ general\ arbitrary\ type{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ val\ t{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ Syntax{\isaliteral{2E}{\isachardot}}read{\isaliteral{5F}{\isacharunderscore}}term\ ctxt{\isadigit{1}}\ {\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ val\ t{\isadigit{1}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ singleton\ {\isaliteral{28}{\isacharparenleft}}Variable{\isaliteral{2E}{\isachardot}}polymorphic\ ctxt{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ t{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ {\isacharparenleft}{\isacharasterisk}term\ u\ enforces\ specific\ type\ assignment{\isacharasterisk}{\isacharparenright}\isanewline
-\ \ val\ u\ {\isacharequal}\ Syntax{\isachardot}read{\isacharunderscore}term\ ctxt{\isadigit{1}}\ {\isachardoublequote}{\isacharparenleft}x{\isacharcolon}{\isacharcolon}nat{\isacharparenright}\ {\isasymequiv}\ y{\isachardoublequote}{\isacharsemicolon}\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}term\ u\ enforces\ specific\ type\ assignment{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ val\ u\ {\isaliteral{3D}{\isacharequal}}\ Syntax{\isaliteral{2E}{\isachardot}}read{\isaliteral{5F}{\isacharunderscore}}term\ ctxt{\isadigit{1}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ y{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ {\isacharparenleft}{\isacharasterisk}official\ declaration\ of\ u\ {\isacharminus}{\isacharminus}\ propagates\ constraints\ etc{\isachardot}{\isacharasterisk}{\isacharparenright}\isanewline
-\ \ val\ ctxt{\isadigit{2}}\ {\isacharequal}\ ctxt{\isadigit{1}}\ {\isacharbar}{\isachargreater}\ Variable{\isachardot}declare{\isacharunderscore}term\ u{\isacharsemicolon}\isanewline
-\ \ val\ t{\isadigit{2}}\ {\isacharequal}\ Syntax{\isachardot}read{\isacharunderscore}term\ ctxt{\isadigit{2}}\ {\isachardoublequote}x{\isachardoublequote}{\isacharsemicolon}\ \ {\isacharparenleft}{\isacharasterisk}x{\isacharcolon}{\isacharcolon}nat\ is\ enforced{\isacharasterisk}{\isacharparenright}\isanewline
-{\isacharverbatimclose}%
+\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}official\ declaration\ of\ u\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}\ propagates\ constraints\ etc{\isaliteral{2E}{\isachardot}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ val\ ctxt{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ ctxt{\isadigit{1}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ Variable{\isaliteral{2E}{\isachardot}}declare{\isaliteral{5F}{\isacharunderscore}}term\ u{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ val\ t{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ Syntax{\isaliteral{2E}{\isachardot}}read{\isaliteral{5F}{\isacharunderscore}}term\ ctxt{\isadigit{2}}\ {\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat\ is\ enforced{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -314,15 +314,15 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ val\ ctxt{\isadigit{0}}\ {\isacharequal}\ %
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ val\ ctxt{\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ %
\isaantiq
-context%
+context{}%
\endisaantiq
-{\isacharsemicolon}\isanewline
-\ \ val\ {\isacharparenleft}{\isacharbrackleft}x{\isadigit{1}}{\isacharcomma}\ x{\isadigit{2}}{\isacharcomma}\ x{\isadigit{3}}{\isacharbrackright}{\isacharcomma}\ ctxt{\isadigit{1}}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ ctxt{\isadigit{0}}\ {\isacharbar}{\isachargreater}\ Variable{\isachardot}variant{\isacharunderscore}fixes\ {\isacharbrackleft}{\isachardoublequote}x{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}x{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}x{\isachardoublequote}{\isacharbrackright}{\isacharsemicolon}\isanewline
-{\isacharverbatimclose}%
+{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ val\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}x{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ x{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ x{\isadigit{3}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ ctxt{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ ctxt{\isadigit{0}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ Variable{\isaliteral{2E}{\isachardot}}variant{\isaliteral{5F}{\isacharunderscore}}fixes\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -338,7 +338,7 @@
``skolem constants'', e.g.\ as follows:%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{example{\isacharunderscore}proof}\isamarkupfalse%
+\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}\isamarkupfalse%
\isanewline
%
\isadelimML
@@ -346,21 +346,21 @@
\endisadelimML
%
\isatagML
-\isacommand{ML{\isacharunderscore}prf}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ \ \ val\ ctxt{\isadigit{0}}\ {\isacharequal}\ %
+\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}prf}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ \ \ val\ ctxt{\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ %
\isaantiq
-context%
+context{}%
\endisaantiq
-{\isacharsemicolon}\isanewline
+{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ \ \ val\ {\isacharparenleft}{\isacharbrackleft}x{\isadigit{1}}{\isacharbrackright}{\isacharcomma}\ ctxt{\isadigit{1}}{\isacharparenright}\ {\isacharequal}\ ctxt{\isadigit{0}}\ {\isacharbar}{\isachargreater}\ Variable{\isachardot}add{\isacharunderscore}fixes\ {\isacharbrackleft}{\isachardoublequote}x{\isachardoublequote}{\isacharbrackright}{\isacharsemicolon}\isanewline
-\ \ \ \ val\ {\isacharparenleft}{\isacharbrackleft}x{\isadigit{2}}{\isacharbrackright}{\isacharcomma}\ ctxt{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ ctxt{\isadigit{1}}\ {\isacharbar}{\isachargreater}\ Variable{\isachardot}add{\isacharunderscore}fixes\ {\isacharbrackleft}{\isachardoublequote}x{\isachardoublequote}{\isacharbrackright}{\isacharsemicolon}\isanewline
-\ \ \ \ val\ {\isacharparenleft}{\isacharbrackleft}x{\isadigit{3}}{\isacharbrackright}{\isacharcomma}\ ctxt{\isadigit{3}}{\isacharparenright}\ {\isacharequal}\ ctxt{\isadigit{2}}\ {\isacharbar}{\isachargreater}\ Variable{\isachardot}add{\isacharunderscore}fixes\ {\isacharbrackleft}{\isachardoublequote}x{\isachardoublequote}{\isacharbrackright}{\isacharsemicolon}\isanewline
+\ \ \ \ val\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}x{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ ctxt{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ ctxt{\isadigit{0}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ Variable{\isaliteral{2E}{\isachardot}}add{\isaliteral{5F}{\isacharunderscore}}fixes\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ val\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}x{\isadigit{2}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ ctxt{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ ctxt{\isadigit{1}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ Variable{\isaliteral{2E}{\isachardot}}add{\isaliteral{5F}{\isacharunderscore}}fixes\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ val\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}x{\isadigit{3}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ ctxt{\isadigit{3}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ ctxt{\isadigit{2}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ Variable{\isaliteral{2E}{\isachardot}}add{\isaliteral{5F}{\isacharunderscore}}fixes\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ \ \ val\ {\isacharparenleft}{\isacharbrackleft}y{\isadigit{1}}{\isacharcomma}\ y{\isadigit{2}}{\isacharbrackright}{\isacharcomma}\ ctxt{\isadigit{4}}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ \ \ ctxt{\isadigit{3}}\ {\isacharbar}{\isachargreater}\ Variable{\isachardot}variant{\isacharunderscore}fixes\ {\isacharbrackleft}{\isachardoublequote}y{\isachardoublequote}{\isacharcomma}\ {\isachardoublequote}y{\isachardoublequote}{\isacharbrackright}{\isacharsemicolon}\isanewline
-\ \ {\isacharverbatimclose}\isanewline
+\ \ \ \ val\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}y{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ y{\isadigit{2}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ ctxt{\isadigit{4}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ \ ctxt{\isadigit{3}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ Variable{\isaliteral{2E}{\isachardot}}variant{\isaliteral{5F}{\isacharunderscore}}fixes\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}y{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}y{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
\ \ \isacommand{oops}\isamarkupfalse%
%
\endisatagML
@@ -389,12 +389,12 @@
Assumptions are restricted to fixed non-schematic statements, i.e.\
all generality needs to be expressed by explicit quantifiers.
Nevertheless, the result will be in HHF normal form with outermost
- quantifiers stripped. For example, by assuming \isa{{\isasymAnd}x\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}{\isachardot}\ P\ x} we get \isa{{\isasymAnd}x\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}{\isachardot}\ P\ x\ {\isasymturnstile}\ P\ {\isacharquery}x} for schematic \isa{{\isacharquery}x}
- of fixed type \isa{{\isasymalpha}}. Local derivations accumulate more and
- more explicit references to hypotheses: \isa{A\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ A\isactrlisub n\ {\isasymturnstile}\ B} where \isa{A\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ A\isactrlisub n} needs to
+ quantifiers stripped. For example, by assuming \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{2E}{\isachardot}}\ P\ x} we get \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{2E}{\isachardot}}\ P\ x\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ P\ {\isaliteral{3F}{\isacharquery}}x} for schematic \isa{{\isaliteral{3F}{\isacharquery}}x}
+ of fixed type \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}}. Local derivations accumulate more and
+ more explicit references to hypotheses: \isa{A\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ A\isaliteral{5C3C5E697375623E}{}\isactrlisub n\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B} where \isa{A\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ A\isaliteral{5C3C5E697375623E}{}\isactrlisub n} needs to
be covered by the assumptions of the current context.
- \medskip The \isa{add{\isacharunderscore}assms} operation augments the context by
+ \medskip The \isa{add{\isaliteral{5F}{\isacharunderscore}}assms} operation augments the context by
local assumptions, which are parameterized by an arbitrary \isa{export} rule (see below).
The \isa{export} operation moves facts from a (larger) inner
@@ -406,29 +406,29 @@
to refine an enclosing sub-goal of a structured proof state.
\medskip The most basic export rule discharges assumptions directly
- by means of the \isa{{\isasymLongrightarrow}} introduction rule:
+ by means of the \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}} introduction rule:
\[
- \infer[(\isa{{\isasymLongrightarrow}{\isasymdash}intro})]{\isa{{\isasymGamma}\ {\isacharminus}\ A\ {\isasymturnstile}\ A\ {\isasymLongrightarrow}\ B}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B}}
+ \infer[(\isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{5C3C646173683E}{\isasymdash}}intro})]{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{2D}{\isacharminus}}\ A\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B}}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B}}
\]
The variant for goal refinements marks the newly introduced
premises, which causes the canonical Isar goal refinement scheme to
enforce unification with local premises within the goal:
\[
- \infer[(\isa{{\isacharhash}{\isasymLongrightarrow}{\isasymdash}intro})]{\isa{{\isasymGamma}\ {\isacharminus}\ A\ {\isasymturnstile}\ {\isacharhash}A\ {\isasymLongrightarrow}\ B}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B}}
+ \infer[(\isa{{\isaliteral{23}{\isacharhash}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{5C3C646173683E}{\isasymdash}}intro})]{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{2D}{\isacharminus}}\ A\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{23}{\isacharhash}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B}}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B}}
\]
\medskip Alternative versions of assumptions may perform arbitrary
transformations on export, as long as the corresponding portion of
hypotheses is removed from the given facts. For example, a local
- definition works by fixing \isa{x} and assuming \isa{x\ {\isasymequiv}\ t},
+ definition works by fixing \isa{x} and assuming \isa{x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t},
with the following export rule to reverse the effect:
\[
- \infer[(\isa{{\isasymequiv}{\isasymdash}expand})]{\isa{{\isasymGamma}\ {\isacharminus}\ {\isacharparenleft}x\ {\isasymequiv}\ t{\isacharparenright}\ {\isasymturnstile}\ B\ t}}{\isa{{\isasymGamma}\ {\isasymturnstile}\ B\ x}}
+ \infer[(\isa{{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{5C3C646173683E}{\isasymdash}}expand})]{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B\ t}}{\isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B\ x}}
\]
- This works, because the assumption \isa{x\ {\isasymequiv}\ t} was introduced in
+ This works, because the assumption \isa{x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t} was introduced in
a context with \isa{x} being fresh, so \isa{x} does not
- occur in \isa{{\isasymGamma}} here.%
+ occur in \isa{{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}} here.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -457,8 +457,8 @@
and the \verb|cterm list| the collection of assumptions to be
discharged simultaneously.
- \item \verb|Assumption.assume|~\isa{A} turns proposition \isa{A} into a primitive assumption \isa{A\ {\isasymturnstile}\ A{\isacharprime}}, where the
- conclusion \isa{A{\isacharprime}} is in HHF normal form.
+ \item \verb|Assumption.assume|~\isa{A} turns proposition \isa{A} into a primitive assumption \isa{A\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A{\isaliteral{27}{\isacharprime}}}, where the
+ conclusion \isa{A{\isaliteral{27}{\isacharprime}}} is in HHF normal form.
\item \verb|Assumption.add_assms|~\isa{r\ As} augments the context
by assumptions \isa{As} with export rule \isa{r}. The
@@ -466,12 +466,12 @@
\verb|Assumption.assume|.
\item \verb|Assumption.add_assumes|~\isa{As} is a special case of
- \verb|Assumption.add_assms| where the export rule performs \isa{{\isasymLongrightarrow}{\isasymdash}intro} or \isa{{\isacharhash}{\isasymLongrightarrow}{\isasymdash}intro}, depending on goal
+ \verb|Assumption.add_assms| where the export rule performs \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{5C3C646173683E}{\isasymdash}}intro} or \isa{{\isaliteral{23}{\isacharhash}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{5C3C646173683E}{\isasymdash}}intro}, depending on goal
mode.
- \item \verb|Assumption.export|~\isa{is{\isacharunderscore}goal\ inner\ outer\ thm}
+ \item \verb|Assumption.export|~\isa{is{\isaliteral{5F}{\isacharunderscore}}goal\ inner\ outer\ thm}
exports result \isa{thm} from the the \isa{inner} context
- back into the \isa{outer} one; \isa{is{\isacharunderscore}goal\ {\isacharequal}\ true} means
+ back into the \isa{outer} one; \isa{is{\isaliteral{5F}{\isacharunderscore}}goal\ {\isaliteral{3D}{\isacharequal}}\ true} means
this is a goal context. The result is in HHF normal form. Note
that \verb|ProofContext.export| combines \verb|Variable.export|
and \verb|Assumption.export| in the canonical way.
@@ -514,25 +514,25 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ {\isacharparenleft}{\isacharasterisk}static\ compile{\isacharminus}time\ context\ {\isacharminus}{\isacharminus}\ for\ testing\ only{\isacharasterisk}{\isacharparenright}\isanewline
-\ \ val\ ctxt{\isadigit{0}}\ {\isacharequal}\ %
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}static\ compile{\isaliteral{2D}{\isacharminus}}time\ context\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}\ for\ testing\ only{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ val\ ctxt{\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ %
\isaantiq
-context%
+context{}%
\endisaantiq
-{\isacharsemicolon}\isanewline
+{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ val\ {\isacharparenleft}{\isacharbrackleft}eq{\isacharbrackright}{\isacharcomma}\ ctxt{\isadigit{1}}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ ctxt{\isadigit{0}}\ {\isacharbar}{\isachargreater}\ Assumption{\isachardot}add{\isacharunderscore}assumes\ {\isacharbrackleft}%
+\ \ val\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}eq{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ ctxt{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ ctxt{\isadigit{0}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ Assumption{\isaliteral{2E}{\isachardot}}add{\isaliteral{5F}{\isacharunderscore}}assumes\ {\isaliteral{5B}{\isacharbrackleft}}%
\isaantiq
-cprop\ {\isachardoublequote}x\ {\isasymequiv}\ y{\isachardoublequote}%
+cprop\ {\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ y{\isaliteral{22}{\isachardoublequote}}{}%
\endisaantiq
-{\isacharbrackright}{\isacharsemicolon}\isanewline
-\ \ val\ eq{\isacharprime}\ {\isacharequal}\ Thm{\isachardot}symmetric\ eq{\isacharsemicolon}\isanewline
+{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ val\ eq{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ Thm{\isaliteral{2E}{\isachardot}}symmetric\ eq{\isaliteral{3B}{\isacharsemicolon}}\isanewline
\isanewline
-\ \ {\isacharparenleft}{\isacharasterisk}back\ to\ original\ context\ {\isacharminus}{\isacharminus}\ discharges\ assumption{\isacharasterisk}{\isacharparenright}\isanewline
-\ \ val\ r\ {\isacharequal}\ Assumption{\isachardot}export\ false\ ctxt{\isadigit{1}}\ ctxt{\isadigit{0}}\ eq{\isacharprime}{\isacharsemicolon}\isanewline
-{\isacharverbatimclose}%
+\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}back\ to\ original\ context\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}\ discharges\ assumption{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ val\ r\ {\isaliteral{3D}{\isacharequal}}\ Assumption{\isaliteral{2E}{\isachardot}}export\ false\ ctxt{\isadigit{1}}\ ctxt{\isadigit{0}}\ eq{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+{\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -554,16 +554,16 @@
\begin{isamarkuptext}%
Local results are established by monotonic reasoning from facts
within a context. This allows common combinations of theorems,
- e.g.\ via \isa{{\isasymAnd}{\isacharslash}{\isasymLongrightarrow}} elimination, resolution rules, or equational
+ e.g.\ via \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}} elimination, resolution rules, or equational
reasoning, see \secref{sec:thms}. Unaccounted context manipulations
- should be avoided, notably raw \isa{{\isasymAnd}{\isacharslash}{\isasymLongrightarrow}} introduction or ad-hoc
+ should be avoided, notably raw \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}} introduction or ad-hoc
references to free variables or assumptions not present in the proof
context.
\medskip The \isa{SUBPROOF} combinator allows to structure a
tactical proof recursively by decomposing a selected sub-goal:
- \isa{{\isacharparenleft}{\isasymAnd}x{\isachardot}\ A{\isacharparenleft}x{\isacharparenright}\ {\isasymLongrightarrow}\ B{\isacharparenleft}x{\isacharparenright}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymdots}} is turned into \isa{B{\isacharparenleft}x{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymdots}}
- after fixing \isa{x} and assuming \isa{A{\isacharparenleft}x{\isacharparenright}}. This means
+ \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ A{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}} is turned into \isa{B{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}}
+ after fixing \isa{x} and assuming \isa{A{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}}. This means
the tactic needs to solve the conclusion, but may use the premise as
a local fact, for locally fixed variables.
@@ -685,7 +685,7 @@
\isadelimmlex
%
\endisadelimmlex
-\isacommand{example{\isacharunderscore}proof}\isamarkupfalse%
+\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}\isamarkupfalse%
\isanewline
%
\isadelimproof
@@ -694,10 +694,10 @@
%
\isatagproof
\isacommand{fix}\isamarkupfalse%
-\ A\ B\ C\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
+\ A\ B\ C\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymAnd}x{\isachardot}\ A\ x\ {\isasymLongrightarrow}\ B\ x\ {\isasymLongrightarrow}\ C\ x{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ A\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C\ x{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -711,19 +711,19 @@
\endisadelimML
%
\isatagML
-\isacommand{ML{\isacharunderscore}val}\isamarkupfalse%
+\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}\isamarkupfalse%
\isanewline
-\ \ \ \ {\isacharverbatimopen}\isanewline
-\ \ \ \ \ \ val\ {\isacharbraceleft}goal{\isacharcomma}\ context\ {\isacharequal}\ goal{\isacharunderscore}ctxt{\isacharcomma}\ {\isachardot}{\isachardot}{\isachardot}{\isacharbraceright}\ {\isacharequal}\ %
+\ \ \ \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ \ \ \ \ val\ {\isaliteral{7B}{\isacharbraceleft}}goal{\isaliteral{2C}{\isacharcomma}}\ context\ {\isaliteral{3D}{\isacharequal}}\ goal{\isaliteral{5F}{\isacharunderscore}}ctxt{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{7D}{\isacharbraceright}}\ {\isaliteral{3D}{\isacharequal}}\ %
\isaantiq
-Isar{\isachardot}goal%
+Isar{\isaliteral{2E}{\isachardot}}goal{}%
\endisaantiq
-{\isacharsemicolon}\isanewline
-\ \ \ \ \ \ val\ {\isacharparenleft}focus\ as\ {\isacharbraceleft}params{\isacharcomma}\ asms{\isacharcomma}\ concl{\isacharcomma}\ {\isachardot}{\isachardot}{\isachardot}{\isacharbraceright}{\isacharcomma}\ goal{\isacharprime}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ \ \ \ \ Subgoal{\isachardot}focus\ goal{\isacharunderscore}ctxt\ {\isadigit{1}}\ goal{\isacharsemicolon}\isanewline
-\ \ \ \ \ \ val\ {\isacharbrackleft}A{\isacharcomma}\ B{\isacharbrackright}\ {\isacharequal}\ {\isacharhash}prems\ focus{\isacharsemicolon}\isanewline
-\ \ \ \ \ \ val\ {\isacharbrackleft}{\isacharparenleft}{\isacharunderscore}{\isacharcomma}\ x{\isacharparenright}{\isacharbrackright}\ {\isacharequal}\ {\isacharhash}params\ focus{\isacharsemicolon}\isanewline
-\ \ \ \ {\isacharverbatimclose}%
+{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ \ \ val\ {\isaliteral{28}{\isacharparenleft}}focus\ as\ {\isaliteral{7B}{\isacharbraceleft}}params{\isaliteral{2C}{\isacharcomma}}\ asms{\isaliteral{2C}{\isacharcomma}}\ concl{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{2C}{\isacharcomma}}\ goal{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ \ \ \ Subgoal{\isaliteral{2E}{\isachardot}}focus\ goal{\isaliteral{5F}{\isacharunderscore}}ctxt\ {\isadigit{1}}\ goal{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ \ \ val\ {\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{2C}{\isacharcomma}}\ B{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{23}{\isacharhash}}prems\ focus{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ \ \ val\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{23}{\isacharhash}}params\ focus{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ {\isaliteral{2A7D}{\isacharverbatimclose}}%
\endisatagML
{\isafoldML}%
%
@@ -751,7 +751,7 @@
a local context, using \verb|Obtain.result|.%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{example{\isacharunderscore}proof}\isamarkupfalse%
+\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}\isamarkupfalse%
\isanewline
%
\isadelimproof
@@ -760,7 +760,7 @@
%
\isatagproof
\isacommand{assume}\isamarkupfalse%
-\ ex{\isacharcolon}\ {\isachardoublequoteopen}{\isasymexists}x{\isachardot}\ B\ x{\isachardoublequoteclose}%
+\ ex{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -775,37 +775,37 @@
\endisadelimML
%
\isatagML
-\isacommand{ML{\isacharunderscore}prf}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ \ \ val\ ctxt{\isadigit{0}}\ {\isacharequal}\ %
+\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}prf}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ \ \ val\ ctxt{\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ %
\isaantiq
-context%
+context{}%
\endisaantiq
-{\isacharsemicolon}\isanewline
-\ \ \ \ val\ {\isacharparenleft}{\isacharparenleft}{\isacharbrackleft}{\isacharparenleft}{\isacharunderscore}{\isacharcomma}\ x{\isacharparenright}{\isacharbrackright}{\isacharcomma}\ {\isacharbrackleft}B{\isacharbrackright}{\isacharparenright}{\isacharcomma}\ ctxt{\isadigit{1}}{\isacharparenright}\ {\isacharequal}\ ctxt{\isadigit{0}}\isanewline
-\ \ \ \ \ \ {\isacharbar}{\isachargreater}\ Obtain{\isachardot}result\ {\isacharparenleft}fn\ {\isacharunderscore}\ {\isacharequal}{\isachargreater}\ etac\ %
+{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ val\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}B{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ ctxt{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ ctxt{\isadigit{0}}\isanewline
+\ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ Obtain{\isaliteral{2E}{\isachardot}}result\ {\isaliteral{28}{\isacharparenleft}}fn\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ etac\ %
\isaantiq
-thm\ exE%
+thm\ exE{}%
\endisaantiq
-\ {\isadigit{1}}{\isacharparenright}\ {\isacharbrackleft}%
+\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5B}{\isacharbrackleft}}%
\isaantiq
-thm\ ex%
+thm\ ex{}%
\endisaantiq
-{\isacharbrackright}{\isacharsemicolon}\isanewline
-\ \ {\isacharverbatimclose}\isanewline
-\ \ \isacommand{ML{\isacharunderscore}prf}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ \ \ singleton\ {\isacharparenleft}ProofContext{\isachardot}export\ ctxt{\isadigit{1}}\ ctxt{\isadigit{0}}{\isacharparenright}\ %
+{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
+\ \ \isacommand{ML{\isaliteral{5F}{\isacharunderscore}}prf}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ \ \ singleton\ {\isaliteral{28}{\isacharparenleft}}ProofContext{\isaliteral{2E}{\isachardot}}export\ ctxt{\isadigit{1}}\ ctxt{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ %
\isaantiq
-thm\ refl%
+thm\ refl{}%
\endisaantiq
-{\isacharsemicolon}\isanewline
-\ \ {\isacharverbatimclose}\isanewline
-\ \ \isacommand{ML{\isacharunderscore}prf}\isamarkupfalse%
-\ {\isacharverbatimopen}\isanewline
-\ \ \ \ ProofContext{\isachardot}export\ ctxt{\isadigit{1}}\ ctxt{\isadigit{0}}\ {\isacharbrackleft}Thm{\isachardot}reflexive\ x{\isacharbrackright}\isanewline
-\ \ \ \ \ \ handle\ ERROR\ msg\ {\isacharequal}{\isachargreater}\ {\isacharparenleft}warning\ msg{\isacharsemicolon}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isacharsemicolon}\isanewline
-\ \ {\isacharverbatimclose}\isanewline
+{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
+\ \ \isacommand{ML{\isaliteral{5F}{\isacharunderscore}}prf}\isamarkupfalse%
+\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ \ \ ProofContext{\isaliteral{2E}{\isachardot}}export\ ctxt{\isadigit{1}}\ ctxt{\isadigit{0}}\ {\isaliteral{5B}{\isacharbrackleft}}Thm{\isaliteral{2E}{\isachardot}}reflexive\ x{\isaliteral{5D}{\isacharbrackright}}\isanewline
+\ \ \ \ \ \ handle\ ERROR\ msg\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}warning\ msg{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagML
--- a/doc-src/IsarImplementation/Thy/document/Syntax.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarImplementation/Thy/document/Syntax.tex Mon Nov 08 14:41:11 2010 +0100
@@ -161,10 +161,10 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{ML antiquotation}{class\_syntax}\hypertarget{ML antiquotation.class-syntax}{\hyperlink{ML antiquotation.class-syntax}{\mbox{\isa{class{\isacharunderscore}syntax}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{type\_syntax}\hypertarget{ML antiquotation.type-syntax}{\hyperlink{ML antiquotation.type-syntax}{\mbox{\isa{type{\isacharunderscore}syntax}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{const\_syntax}\hypertarget{ML antiquotation.const-syntax}{\hyperlink{ML antiquotation.const-syntax}{\mbox{\isa{const{\isacharunderscore}syntax}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
- \indexdef{}{ML antiquotation}{syntax\_const}\hypertarget{ML antiquotation.syntax-const}{\hyperlink{ML antiquotation.syntax-const}{\mbox{\isa{syntax{\isacharunderscore}const}}}} & : & \isa{ML{\isacharunderscore}antiquotation} \\
+ \indexdef{}{ML antiquotation}{class\_syntax}\hypertarget{ML antiquotation.class-syntax}{\hyperlink{ML antiquotation.class-syntax}{\mbox{\isa{class{\isaliteral{5F}{\isacharunderscore}}syntax}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{type\_syntax}\hypertarget{ML antiquotation.type-syntax}{\hyperlink{ML antiquotation.type-syntax}{\mbox{\isa{type{\isaliteral{5F}{\isacharunderscore}}syntax}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{const\_syntax}\hypertarget{ML antiquotation.const-syntax}{\hyperlink{ML antiquotation.const-syntax}{\mbox{\isa{const{\isaliteral{5F}{\isacharunderscore}}syntax}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
+ \indexdef{}{ML antiquotation}{syntax\_const}\hypertarget{ML antiquotation.syntax-const}{\hyperlink{ML antiquotation.syntax-const}{\mbox{\isa{syntax{\isaliteral{5F}{\isacharunderscore}}const}}}} & : & \isa{ML{\isaliteral{5F}{\isacharunderscore}}antiquotation} \\
\end{matharray}
\begin{rail}
--- a/doc-src/IsarImplementation/Thy/document/Tactic.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarImplementation/Thy/document/Tactic.tex Mon Nov 08 14:41:11 2010 +0100
@@ -38,39 +38,39 @@
%
\begin{isamarkuptext}%
Isabelle/Pure represents a goal as a theorem stating that the
- subgoals imply the main goal: \isa{A\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymLongrightarrow}\ A\isactrlsub n\ {\isasymLongrightarrow}\ C}. The outermost goal structure is that of a Horn Clause: i.e.\
+ subgoals imply the main goal: \isa{A\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C}. The outermost goal structure is that of a Horn Clause: i.e.\
an iterated implication without any quantifiers\footnote{Recall that
- outermost \isa{{\isasymAnd}x{\isachardot}\ {\isasymphi}{\isacharbrackleft}x{\isacharbrackright}} is always represented via schematic
- variables in the body: \isa{{\isasymphi}{\isacharbrackleft}{\isacharquery}x{\isacharbrackright}}. These variables may get
- instantiated during the course of reasoning.}. For \isa{n\ {\isacharequal}\ {\isadigit{0}}}
+ outermost \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}} is always represented via schematic
+ variables in the body: \isa{{\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{5D}{\isacharbrackright}}}. These variables may get
+ instantiated during the course of reasoning.}. For \isa{n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}}
a goal is called ``solved''.
- The structure of each subgoal \isa{A\isactrlsub i} is that of a
- general Hereditary Harrop Formula \isa{{\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymAnd}x\isactrlsub k{\isachardot}\ H\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymLongrightarrow}\ H\isactrlsub m\ {\isasymLongrightarrow}\ B}. Here \isa{x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub k} are goal parameters, i.e.\
- arbitrary-but-fixed entities of certain types, and \isa{H\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ H\isactrlsub m} are goal hypotheses, i.e.\ facts that may
+ The structure of each subgoal \isa{A\isaliteral{5C3C5E7375623E}{}\isactrlsub i} is that of a
+ general Hereditary Harrop Formula \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{2E}{\isachardot}}\ H\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ H\isaliteral{5C3C5E7375623E}{}\isactrlsub m\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B}. Here \isa{x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub k} are goal parameters, i.e.\
+ arbitrary-but-fixed entities of certain types, and \isa{H\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ H\isaliteral{5C3C5E7375623E}{}\isactrlsub m} are goal hypotheses, i.e.\ facts that may
be assumed locally. Together, this forms the goal context of the
conclusion \isa{B} to be established. The goal hypotheses may be
again arbitrary Hereditary Harrop Formulas, although the level of
nesting rarely exceeds 1--2 in practice.
The main conclusion \isa{C} is internally marked as a protected
- proposition, which is represented explicitly by the notation \isa{{\isacharhash}C} here. This ensures that the decomposition into subgoals and
+ proposition, which is represented explicitly by the notation \isa{{\isaliteral{23}{\isacharhash}}C} here. This ensures that the decomposition into subgoals and
main conclusion is well-defined for arbitrarily structured claims.
\medskip Basic goal management is performed via the following
Isabelle/Pure rules:
\[
- \infer[\isa{{\isacharparenleft}init{\isacharparenright}}]{\isa{C\ {\isasymLongrightarrow}\ {\isacharhash}C}}{} \qquad
- \infer[\isa{{\isacharparenleft}finish{\isacharparenright}}]{\isa{C}}{\isa{{\isacharhash}C}}
+ \infer[\isa{{\isaliteral{28}{\isacharparenleft}}init{\isaliteral{29}{\isacharparenright}}}]{\isa{C\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{23}{\isacharhash}}C}}{} \qquad
+ \infer[\isa{{\isaliteral{28}{\isacharparenleft}}finish{\isaliteral{29}{\isacharparenright}}}]{\isa{C}}{\isa{{\isaliteral{23}{\isacharhash}}C}}
\]
\medskip The following low-level variants admit general reasoning
with protected propositions:
\[
- \infer[\isa{{\isacharparenleft}protect{\isacharparenright}}]{\isa{{\isacharhash}C}}{\isa{C}} \qquad
- \infer[\isa{{\isacharparenleft}conclude{\isacharparenright}}]{\isa{A\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymLongrightarrow}\ A\isactrlsub n\ {\isasymLongrightarrow}\ C}}{\isa{A\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymLongrightarrow}\ A\isactrlsub n\ {\isasymLongrightarrow}\ {\isacharhash}C}}
+ \infer[\isa{{\isaliteral{28}{\isacharparenleft}}protect{\isaliteral{29}{\isacharparenright}}}]{\isa{{\isaliteral{23}{\isacharhash}}C}}{\isa{C}} \qquad
+ \infer[\isa{{\isaliteral{28}{\isacharparenleft}}conclude{\isaliteral{29}{\isacharparenright}}}]{\isa{A\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C}}{\isa{A\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{23}{\isacharhash}}C}}
\]%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -121,7 +121,7 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-A \isa{tactic} is a function \isa{goal\ {\isasymrightarrow}\ goal\isactrlsup {\isacharasterisk}\isactrlsup {\isacharasterisk}} that
+A \isa{tactic} is a function \isa{goal\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ goal\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}} that
maps a given goal state (represented as a theorem, cf.\
\secref{sec:tactical-goals}) to a lazy sequence of potential
successor states. The underlying sequence implementation is lazy
@@ -152,7 +152,7 @@
schematic goal variables).
Tactics with explicit \emph{subgoal addressing} are of the form
- \isa{int\ {\isasymrightarrow}\ tactic} and may be applied to a particular subgoal
+ \isa{int\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ tactic} and may be applied to a particular subgoal
(counting from 1). If the subgoal number is out of range, the
tactic should fail with an empty result sequence, but must not raise
an exception!
@@ -222,7 +222,7 @@
\item Type \verb|tactic| represents tactics. The
well-formedness conditions described above need to be observed. See
- also \hyperlink{file.~~/src/Pure/General/seq.ML}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}Pure{\isacharslash}General{\isacharslash}seq{\isachardot}ML}}}} for the underlying
+ also \hyperlink{file.~~/src/Pure/General/seq.ML}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}Pure{\isaliteral{2F}{\isacharslash}}General{\isaliteral{2F}{\isacharslash}}seq{\isaliteral{2E}{\isachardot}}ML}}}} for the underlying
implementation of lazy sequences.
\item Type \verb|int -> tactic| represents tactics with
@@ -244,7 +244,7 @@
a regular tactic failure and produces an empty result; other
exceptions are passed through.
- \item \verb|SUBGOAL|~\isa{{\isacharparenleft}fn\ {\isacharparenleft}subgoal{\isacharcomma}\ i{\isacharparenright}\ {\isacharequal}{\isachargreater}\ tactic{\isacharparenright}} is the
+ \item \verb|SUBGOAL|~\isa{{\isaliteral{28}{\isacharparenleft}}fn\ {\isaliteral{28}{\isacharparenleft}}subgoal{\isaliteral{2C}{\isacharcomma}}\ i{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ tactic{\isaliteral{29}{\isacharparenright}}} is the
most basic form to produce a tactic with subgoal addressing. The
given abstraction over the subgoal term and subgoal number allows to
peek at the relevant information of the full goal state. The
@@ -279,7 +279,7 @@
\emph{Destruct-resolution} is like elim-resolution, but the given
destruction rules are first turned into canonical elimination
format. \emph{Forward-resolution} is like destruct-resolution, but
- without deleting the selected assumption. The \isa{r{\isacharslash}e{\isacharslash}d{\isacharslash}f}
+ without deleting the selected assumption. The \isa{r{\isaliteral{2F}{\isacharslash}}e{\isaliteral{2F}{\isacharslash}}d{\isaliteral{2F}{\isacharslash}}f}
naming convention is maintained for several different kinds of
resolution rules and tactics.
@@ -353,7 +353,7 @@
by assumption (modulo higher-order unification).
\item \verb|eq_assume_tac| is similar to \verb|assume_tac|, but checks
- only for immediate \isa{{\isasymalpha}}-convertibility instead of using
+ only for immediate \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}}-convertibility instead of using
unification. It succeeds (with a unique next state) if one of the
assumptions is equal to the subgoal's conclusion. Since it does not
instantiate variables, it cannot make other subgoals unprovable.
@@ -390,18 +390,18 @@
higher-order unification is not so useful. This typically involves
rules like universal elimination, existential introduction, or
equational substitution. Here the unification problem involves
- fully flexible \isa{{\isacharquery}P\ {\isacharquery}x} schemes, which are hard to manage
+ fully flexible \isa{{\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{3F}{\isacharquery}}x} schemes, which are hard to manage
without further hints.
- By providing a (small) rigid term for \isa{{\isacharquery}x} explicitly, the
- remaining unification problem is to assign a (large) term to \isa{{\isacharquery}P}, according to the shape of the given subgoal. This is
+ By providing a (small) rigid term for \isa{{\isaliteral{3F}{\isacharquery}}x} explicitly, the
+ remaining unification problem is to assign a (large) term to \isa{{\isaliteral{3F}{\isacharquery}}P}, according to the shape of the given subgoal. This is
sufficiently well-behaved in most practical situations.
- \medskip Isabelle provides separate versions of the standard \isa{r{\isacharslash}e{\isacharslash}d{\isacharslash}f} resolution tactics that allow to provide explicit
+ \medskip Isabelle provides separate versions of the standard \isa{r{\isaliteral{2F}{\isacharslash}}e{\isaliteral{2F}{\isacharslash}}d{\isaliteral{2F}{\isacharslash}}f} resolution tactics that allow to provide explicit
instantiations of unknowns of the given rule, wrt.\ terms that refer
to the implicit context of the selected subgoal.
- An instantiation consists of a list of pairs of the form \isa{{\isacharparenleft}{\isacharquery}x{\isacharcomma}\ t{\isacharparenright}}, where \isa{{\isacharquery}x} is a schematic variable occurring in
+ An instantiation consists of a list of pairs of the form \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}}, where \isa{{\isaliteral{3F}{\isacharquery}}x} is a schematic variable occurring in
the given rule, and \isa{t} is a term from the current proof
context, augmented by the local goal parameters of the selected
subgoal; cf.\ the \isa{focus} operation described in
@@ -413,7 +413,7 @@
global names. Explicit renaming of subgoal parameters prior to
explicit instantiation might help to achieve a bit more robustness.
- Type instantiations may be given as well, via pairs like \isa{{\isacharparenleft}{\isacharquery}{\isacharprime}a{\isacharcomma}\ {\isasymtau}{\isacharparenright}}. Type instantiations are distinguished from term
+ Type instantiations may be given as well, via pairs like \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{29}{\isacharparenright}}}. Type instantiations are distinguished from term
instantiations by the syntactic form of the schematic variable.
Types are instantiated before terms are. Since term instantiation
already performs simple type-inference, so explicit type
--- a/doc-src/IsarImplementation/style.sty Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarImplementation/style.sty Mon Nov 08 14:41:11 2010 +0100
@@ -24,6 +24,9 @@
\renewcommand{\isadigit}[1]{\isamath{#1}}
+\renewcommand{\isaantiqopen}{\isasymlbrace}
+\renewcommand{\isaantiqclose}{\isasymrbrace}
+
\newenvironment{mldecls}{\par\noindent\begingroup\footnotesize\def\isanewline{\\}\begin{tabular}{l}}{\end{tabular}\smallskip\endgroup}
\isafoldtag{FIXME}
--- a/doc-src/IsarOverview/Isar/document/Induction.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarOverview/Isar/document/Induction.tex Mon Nov 08 14:41:11 2010 +0100
@@ -23,7 +23,7 @@
Computer science applications abound with inductively defined
structures, which is why we treat them in more detail. HOL already
comes with a datatype of lists with the two constructors \isa{Nil}
-and \isa{Cons}. \isa{Nil} is written \isa{{\isacharbrackleft}{\isacharbrackright}} and \isa{Cons\ x\ xs} is written \isa{x\ {\isacharhash}\ xs}.%
+and \isa{Cons}. \isa{Nil} is written \isa{{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}} and \isa{Cons\ x\ xs} is written \isa{x\ {\isaliteral{23}{\isacharhash}}\ xs}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -37,7 +37,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymnot}\ A\ {\isasymor}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -47,14 +47,14 @@
\isacommand{proof}\isamarkupfalse%
\ cases\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}A{\isachardoublequoteclose}\ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{thus}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymnot}\ A{\isachardoublequoteclose}\ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{thus}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -66,11 +66,11 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-\noindent The two cases must come in this order because \isa{cases} merely abbreviates \isa{{\isacharparenleft}rule\ case{\isacharunderscore}split{\isacharparenright}} where
-\isa{case{\isacharunderscore}split} is \isa{{\isasymlbrakk}{\isacharquery}P\ {\isasymLongrightarrow}\ {\isacharquery}Q{\isacharsemicolon}\ {\isasymnot}\ {\isacharquery}P\ {\isasymLongrightarrow}\ {\isacharquery}Q{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}Q}. If we reverse
+\noindent The two cases must come in this order because \isa{cases} merely abbreviates \isa{{\isaliteral{28}{\isacharparenleft}}rule\ case{\isaliteral{5F}{\isacharunderscore}}split{\isaliteral{29}{\isacharparenright}}} where
+\isa{case{\isaliteral{5F}{\isacharunderscore}}split} is \isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}Q{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}Q{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}Q}. If we reverse
the order of the two cases in the proof, the first case would prove
-\isa{{\isasymnot}\ A\ {\isasymLongrightarrow}\ {\isasymnot}\ A\ {\isasymor}\ A} which would solve the first premise of
-\isa{case{\isacharunderscore}split}, instantiating \isa{{\isacharquery}P} with \isa{{\isasymnot}\ A}, thus making the second premise \isa{{\isasymnot}\ {\isasymnot}\ A\ {\isasymLongrightarrow}\ {\isasymnot}\ A\ {\isasymor}\ A}.
+\isa{{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ A} which would solve the first premise of
+\isa{case{\isaliteral{5F}{\isacharunderscore}}split}, instantiating \isa{{\isaliteral{3F}{\isacharquery}}P} with \isa{{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A}, thus making the second premise \isa{{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ A}.
Therefore the order of subgoals is not always completely arbitrary.
The above proof is appropriate if \isa{A} is textually small.
@@ -79,7 +79,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymnot}\ A\ {\isasymor}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -87,16 +87,16 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}cases\ {\isachardoublequoteopen}A{\isachardoublequoteclose}{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}cases\ {\isaliteral{22}{\isachardoublequoteopen}}A{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{case}\isamarkupfalse%
\ True\ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{case}\isamarkupfalse%
\ False\ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -109,10 +109,10 @@
%
\begin{isamarkuptext}%
\noindent which is like the previous proof but instantiates
-\isa{{\isacharquery}P} right away with \isa{A}. Thus we could prove the two
+\isa{{\isaliteral{3F}{\isacharquery}}P} right away with \isa{A}. Thus we could prove the two
cases in any order. The phrase \isakeyword{case}~\isa{True}
-abbreviates \isakeyword{assume}~\isa{True{\isacharcolon}\ A} and analogously for
-\isa{False} and \isa{{\isasymnot}\ A}.
+abbreviates \isakeyword{assume}~\isa{True{\isaliteral{3A}{\isacharcolon}}\ A} and analogously for
+\isa{False} and \isa{{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A}.
The same game can be played with other datatypes, for example lists,
where \isa{tl} is the tail of a list, and \isa{length} returns a
@@ -120,7 +120,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}length{\isacharparenleft}tl\ xs{\isacharparenright}\ {\isacharequal}\ length\ xs\ {\isacharminus}\ {\isadigit{1}}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}length{\isaliteral{28}{\isacharparenleft}}tl\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ length\ xs\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -128,16 +128,16 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}cases\ xs{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}cases\ xs{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{case}\isamarkupfalse%
\ Nil\ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{case}\isamarkupfalse%
\ Cons\ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -150,17 +150,17 @@
%
\begin{isamarkuptext}%
\noindent Here \isakeyword{case}~\isa{Nil} abbreviates
-\isakeyword{assume}~\isa{Nil{\isacharcolon}}~\isa{xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}} and
-\isakeyword{case}~\isa{Cons} abbreviates \isakeyword{fix}~\isa{{\isacharquery}\ {\isacharquery}{\isacharquery}}
-\isakeyword{assume}~\isa{Cons{\isacharcolon}}~\isa{xs\ {\isacharequal}\ {\isacharquery}\ {\isacharhash}\ {\isacharquery}{\isacharquery}},
-where \isa{{\isacharquery}} and \isa{{\isacharquery}{\isacharquery}}
+\isakeyword{assume}~\isa{Nil{\isaliteral{3A}{\isacharcolon}}}~\isa{xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}} and
+\isakeyword{case}~\isa{Cons} abbreviates \isakeyword{fix}~\isa{{\isaliteral{3F}{\isacharquery}}\ {\isaliteral{3F}{\isacharquery}}{\isaliteral{3F}{\isacharquery}}}
+\isakeyword{assume}~\isa{Cons{\isaliteral{3A}{\isacharcolon}}}~\isa{xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}\ {\isaliteral{23}{\isacharhash}}\ {\isaliteral{3F}{\isacharquery}}{\isaliteral{3F}{\isacharquery}}},
+where \isa{{\isaliteral{3F}{\isacharquery}}} and \isa{{\isaliteral{3F}{\isacharquery}}{\isaliteral{3F}{\isacharquery}}}
stand for variable names that have been chosen by the system.
Therefore we cannot refer to them.
Luckily, this proof is simple enough we do not need to refer to them.
However, sometimes one may have to. Hence Isar offers a simple scheme for
naming those variables: replace the anonymous \isa{Cons} by
-\isa{{\isacharparenleft}Cons\ y\ ys{\isacharparenright}}, which abbreviates \isakeyword{fix}~\isa{y\ ys}
-\isakeyword{assume}~\isa{Cons{\isacharcolon}}~\isa{xs\ {\isacharequal}\ y\ {\isacharhash}\ ys}.
+\isa{{\isaliteral{28}{\isacharparenleft}}Cons\ y\ ys{\isaliteral{29}{\isacharparenright}}}, which abbreviates \isakeyword{fix}~\isa{y\ ys}
+\isakeyword{assume}~\isa{Cons{\isaliteral{3A}{\isacharcolon}}}~\isa{xs\ {\isaliteral{3D}{\isacharequal}}\ y\ {\isaliteral{23}{\isacharhash}}\ ys}.
In each \isakeyword{case} the assumption can be
referred to inside the proof by the name of the constructor. In
Section~\ref{sec:full-Ind} below we will come across an example
@@ -172,7 +172,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isadigit{2}}\ {\isacharasterisk}\ {\isacharparenleft}{\isasymSum}i{\isacharcolon}{\isacharcolon}nat{\isasymle}n{\isachardot}\ i{\isacharparenright}\ {\isacharequal}\ n{\isacharasterisk}{\isacharparenleft}n{\isacharplus}{\isadigit{1}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C53756D3E}{\isasymSum}}i{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{5C3C6C653E}{\isasymle}}n{\isaliteral{2E}{\isachardot}}\ i{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}n{\isaliteral{2B}{\isacharplus}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -180,7 +180,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ n{\isacharparenright}\ simp{\isacharunderscore}all%
+\ {\isaliteral{28}{\isacharparenleft}}induct\ n{\isaliteral{29}{\isacharparenright}}\ simp{\isaliteral{5F}{\isacharunderscore}}all%
\endisatagproof
{\isafoldproof}%
%
@@ -189,7 +189,7 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-\noindent The constraint \isa{{\isacharcolon}{\isacharcolon}nat} is needed because all of
+\noindent The constraint \isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat} is needed because all of
the operations involved are overloaded.
This proof also demonstrates that \isakeyword{by} can take two arguments,
one to start and one to finish the proof --- the latter is optional.
@@ -200,7 +200,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isadigit{2}}\ {\isacharasterisk}\ {\isacharparenleft}{\isasymSum}i{\isacharcolon}{\isacharcolon}nat{\isasymle}n{\isachardot}\ i{\isacharparenright}\ {\isacharequal}\ n{\isacharasterisk}{\isacharparenleft}n{\isacharplus}{\isadigit{1}}{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isacharquery}P\ n{\isachardoublequoteclose}{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C53756D3E}{\isasymSum}}i{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{5C3C6C653E}{\isasymle}}n{\isaliteral{2E}{\isachardot}}\ i{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}n{\isaliteral{2B}{\isacharplus}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{is}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}P\ n{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
%
\isadelimproof
%
@@ -208,17 +208,17 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}induct\ n{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ n{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}P\ {\isadigit{0}}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}P\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
\ n\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}P\ n{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}P\ n{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{thus}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}P{\isacharparenleft}Suc\ n{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}P{\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -236,7 +236,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isadigit{2}}\ {\isacharasterisk}\ {\isacharparenleft}{\isasymSum}i{\isacharcolon}{\isacharcolon}nat\ {\isasymle}\ n{\isachardot}\ i{\isacharparenright}\ {\isacharequal}\ n{\isacharasterisk}{\isacharparenleft}n{\isacharplus}{\isadigit{1}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C53756D3E}{\isasymSum}}i{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat\ {\isaliteral{5C3C6C653E}{\isasymle}}\ n{\isaliteral{2E}{\isachardot}}\ i{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}n{\isaliteral{2B}{\isacharplus}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -244,16 +244,16 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}induct\ n{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ n{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{case}\isamarkupfalse%
\ {\isadigit{0}}\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}case\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}case\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{case}\isamarkupfalse%
\ Suc\ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}case\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}case\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -265,18 +265,18 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-\noindent The implicitly defined \isa{{\isacharquery}case} refers to the
-corresponding case to be proved, i.e.\ \isa{{\isacharquery}P\ {\isadigit{0}}} in the first case and
-\isa{{\isacharquery}P{\isacharparenleft}Suc\ n{\isacharparenright}} in the second case. Context \isakeyword{case}~\isa{{\isadigit{0}}} is
-empty whereas \isakeyword{case}~\isa{Suc} assumes \isa{{\isacharquery}P\ n}. Again we
+\noindent The implicitly defined \isa{{\isaliteral{3F}{\isacharquery}}case} refers to the
+corresponding case to be proved, i.e.\ \isa{{\isaliteral{3F}{\isacharquery}}P\ {\isadigit{0}}} in the first case and
+\isa{{\isaliteral{3F}{\isacharquery}}P{\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}} in the second case. Context \isakeyword{case}~\isa{{\isadigit{0}}} is
+empty whereas \isakeyword{case}~\isa{Suc} assumes \isa{{\isaliteral{3F}{\isacharquery}}P\ n}. Again we
have the same problem as with case distinctions: we cannot refer to an anonymous \isa{n}
in the induction step because it has not been introduced via \isakeyword{fix}
(in contrast to the previous proof). The solution is the one outlined for
-\isa{Cons} above: replace \isa{Suc} by \isa{{\isacharparenleft}Suc\ i{\isacharparenright}}:%
+\isa{Cons} above: replace \isa{Suc} by \isa{{\isaliteral{28}{\isacharparenleft}}Suc\ i{\isaliteral{29}{\isacharparenright}}}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ \isakeyword{fixes}\ n{\isacharcolon}{\isacharcolon}nat\ \isakeyword{shows}\ {\isachardoublequoteopen}n\ {\isacharless}\ n{\isacharasterisk}n\ {\isacharplus}\ {\isadigit{1}}{\isachardoublequoteclose}\isanewline
+\ \isakeyword{fixes}\ n{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat\ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}n\ {\isaliteral{3C}{\isacharless}}\ n{\isaliteral{2A}{\isacharasterisk}}n\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -284,16 +284,16 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}induct\ n{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ n{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{case}\isamarkupfalse%
\ {\isadigit{0}}\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}case\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}case\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{case}\isamarkupfalse%
-\ {\isacharparenleft}Suc\ i{\isacharparenright}\ \isacommand{thus}\isamarkupfalse%
-\ {\isachardoublequoteopen}Suc\ i\ {\isacharless}\ Suc\ i\ {\isacharasterisk}\ Suc\ i\ {\isacharplus}\ {\isadigit{1}}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}Suc\ i{\isaliteral{29}{\isacharparenright}}\ \isacommand{thus}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}Suc\ i\ {\isaliteral{3C}{\isacharless}}\ Suc\ i\ {\isaliteral{2A}{\isacharasterisk}}\ Suc\ i\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -306,22 +306,22 @@
%
\begin{isamarkuptext}%
\noindent Of course we could again have written
-\isakeyword{thus}~\isa{{\isacharquery}case} instead of giving the term explicitly
+\isakeyword{thus}~\isa{{\isaliteral{3F}{\isacharquery}}case} instead of giving the term explicitly
but we wanted to use \isa{i} somewhere.
\subsection{Generalization via \isa{arbitrary}}
It is frequently necessary to generalize a claim before it becomes
provable by induction. The tutorial~\cite{LNCS2283} demonstrates this
-with \isa{itrev\ xs\ ys\ {\isacharequal}\ rev\ xs\ {\isacharat}\ ys}, where \isa{ys}
-needs to be universally quantified before induction succeeds.\footnote{\isa{rev\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}},\quad \isa{rev\ {\isacharparenleft}x\ {\isacharhash}\ xs{\isacharparenright}\ {\isacharequal}\ rev\ xs\ {\isacharat}\ {\isacharbrackleft}x{\isacharbrackright}},\\ \isa{itrev\ {\isacharbrackleft}{\isacharbrackright}\ ys\ {\isacharequal}\ ys},\quad \isa{itrev\ {\isacharparenleft}x\ {\isacharhash}\ xs{\isacharparenright}\ ys\ {\isacharequal}\ itrev\ xs\ {\isacharparenleft}x\ {\isacharhash}\ ys{\isacharparenright}}} But
+with \isa{itrev\ xs\ ys\ {\isaliteral{3D}{\isacharequal}}\ rev\ xs\ {\isaliteral{40}{\isacharat}}\ ys}, where \isa{ys}
+needs to be universally quantified before induction succeeds.\footnote{\isa{rev\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}},\quad \isa{rev\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rev\ xs\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}},\\ \isa{itrev\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ ys\ {\isaliteral{3D}{\isacharequal}}\ ys},\quad \isa{itrev\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}\ ys\ {\isaliteral{3D}{\isacharequal}}\ itrev\ xs\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ ys{\isaliteral{29}{\isacharparenright}}}} But
strictly speaking, this quantification step is already part of the
proof and the quantifiers should not clutter the original claim. This
is how the quantification step can be combined with induction:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}itrev\ xs\ ys\ {\isacharequal}\ rev\ xs\ {\isacharat}\ ys{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}itrev\ xs\ ys\ {\isaliteral{3D}{\isacharequal}}\ rev\ xs\ {\isaliteral{40}{\isacharat}}\ ys{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -329,7 +329,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ xs\ arbitrary{\isacharcolon}\ ys{\isacharparenright}\ simp{\isacharunderscore}all%
+\ {\isaliteral{28}{\isacharparenleft}}induct\ xs\ arbitrary{\isaliteral{3A}{\isacharcolon}}\ ys{\isaliteral{29}{\isacharparenright}}\ simp{\isaliteral{5F}{\isacharunderscore}}all%
\endisatagproof
{\isafoldproof}%
%
@@ -338,27 +338,27 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-\noindent The annotation \isa{arbitrary{\isacharcolon}}~\emph{vars}
+\noindent The annotation \isa{arbitrary{\isaliteral{3A}{\isacharcolon}}}~\emph{vars}
universally quantifies all \emph{vars} before the induction. Hence
they can be replaced by \emph{arbitrary} values in the proof.
Generalization via \isa{arbitrary} is particularly convenient
if the induction step is a structured proof as opposed to the automatic
example above. Then the claim is available in unquantified form but
-with the generalized variables replaced by \isa{{\isacharquery}}-variables, ready
+with the generalized variables replaced by \isa{{\isaliteral{3F}{\isacharquery}}}-variables, ready
for instantiation. In the above example, in the \isa{Cons} case the
-induction hypothesis is \isa{itrev\ xs\ {\isacharquery}ys\ {\isacharequal}\ rev\ xs\ {\isacharat}\ {\isacharquery}ys} (available
+induction hypothesis is \isa{itrev\ xs\ {\isaliteral{3F}{\isacharquery}}ys\ {\isaliteral{3D}{\isacharequal}}\ rev\ xs\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{3F}{\isacharquery}}ys} (available
under the name \isa{Cons}).
\subsection{Inductive proofs of conditional formulae}
\label{sec:full-Ind}
-Induction also copes well with formulae involving \isa{{\isasymLongrightarrow}}, for example%
+Induction also copes well with formulae involving \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}}, for example%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymLongrightarrow}\ hd{\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharequal}\ last\ xs{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}xs\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ hd{\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ last\ xs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -366,7 +366,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ xs{\isacharparenright}\ simp{\isacharunderscore}all%
+\ {\isaliteral{28}{\isacharparenleft}}induct\ xs{\isaliteral{29}{\isacharparenright}}\ simp{\isaliteral{5F}{\isacharunderscore}}all%
\endisatagproof
{\isafoldproof}%
%
@@ -376,12 +376,12 @@
%
\begin{isamarkuptext}%
\noindent This is an improvement over that style the
-tutorial~\cite{LNCS2283} advises, which requires \isa{{\isasymlongrightarrow}}.
+tutorial~\cite{LNCS2283} advises, which requires \isa{{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}}.
A further improvement is shown in the following proof:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ \ {\isachardoublequoteopen}map\ f\ xs\ {\isacharequal}\ map\ f\ ys\ {\isasymLongrightarrow}\ length\ xs\ {\isacharequal}\ length\ ys{\isachardoublequoteclose}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}map\ f\ xs\ {\isaliteral{3D}{\isacharequal}}\ map\ f\ ys\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ length\ xs\ {\isaliteral{3D}{\isacharequal}}\ length\ ys{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -389,40 +389,40 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}induct\ ys\ arbitrary{\isacharcolon}\ xs{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ ys\ arbitrary{\isaliteral{3A}{\isacharcolon}}\ xs{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{case}\isamarkupfalse%
\ Nil\ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}case\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}case\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{case}\isamarkupfalse%
-\ {\isacharparenleft}Cons\ y\ ys{\isacharparenright}\ \ \isacommand{note}\isamarkupfalse%
-\ Asm\ {\isacharequal}\ Cons\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}Cons\ y\ ys{\isaliteral{29}{\isacharparenright}}\ \ \isacommand{note}\isamarkupfalse%
+\ Asm\ {\isaliteral{3D}{\isacharequal}}\ Cons\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}case\isanewline
+\ {\isaliteral{3F}{\isacharquery}}case\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}cases\ xs{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}cases\ xs{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{case}\isamarkupfalse%
\ Nil\isanewline
\ \ \ \ \isacommand{hence}\isamarkupfalse%
\ False\ \isacommand{using}\isamarkupfalse%
-\ Asm{\isacharparenleft}{\isadigit{2}}{\isacharparenright}\ \isacommand{by}\isamarkupfalse%
+\ Asm{\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\ \ \ \ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{case}\isamarkupfalse%
-\ {\isacharparenleft}Cons\ x\ xs{\isacharprime}{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}Cons\ x\ xs{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{with}\isamarkupfalse%
-\ Asm{\isacharparenleft}{\isadigit{2}}{\isacharparenright}\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}map\ f\ xs{\isacharprime}\ {\isacharequal}\ map\ f\ ys{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ Asm{\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ \isacommand{have}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}map\ f\ xs{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ map\ f\ ys{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\ \ \ \ \isacommand{from}\isamarkupfalse%
-\ Asm{\isacharparenleft}{\isadigit{1}}{\isacharparenright}{\isacharbrackleft}OF\ this{\isacharbrackright}\ {\isacharbackquoteopen}xs\ {\isacharequal}\ x{\isacharhash}xs{\isacharprime}{\isacharbackquoteclose}\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{by}\isamarkupfalse%
+\ Asm{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5B}{\isacharbrackleft}}OF\ this{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{60}{\isacharbackquoteopen}}xs\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{23}{\isacharhash}}xs{\isaliteral{27}{\isacharprime}}{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
@@ -441,32 +441,32 @@
(under the name \isa{Cons}) two propositions:
\begin{center}
\begin{tabular}{l}
-\isa{map\ f\ {\isacharquery}xs\ {\isacharequal}\ map\ f\ ys\ {\isasymLongrightarrow}\ length\ {\isacharquery}xs\ {\isacharequal}\ length\ ys}\\
-\isa{map\ f\ xs\ {\isacharequal}\ map\ f\ {\isacharparenleft}y\ {\isacharhash}\ ys{\isacharparenright}}
+\isa{map\ f\ {\isaliteral{3F}{\isacharquery}}xs\ {\isaliteral{3D}{\isacharequal}}\ map\ f\ ys\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ length\ {\isaliteral{3F}{\isacharquery}}xs\ {\isaliteral{3D}{\isacharequal}}\ length\ ys}\\
+\isa{map\ f\ xs\ {\isaliteral{3D}{\isacharequal}}\ map\ f\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{23}{\isacharhash}}\ ys{\isaliteral{29}{\isacharparenright}}}
\end{tabular}
\end{center}
The first is the induction hypothesis, the second, and this is new,
is the premise of the induction step. The actual goal at this point is merely
-\isa{length\ xs\ {\isacharequal}\ length\ {\isacharparenleft}y\ {\isacharhash}\ ys{\isacharparenright}}. The assumptions are given the new name
-\isa{Asm} to avoid a name clash further down. The proof procedes with a case distinction on \isa{xs}. In the case \isa{xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}}, the second of our two
-assumptions (\isa{Asm{\isacharparenleft}{\isadigit{2}}{\isacharparenright}}) implies the contradiction \isa{{\isadigit{0}}\ {\isacharequal}\ Suc{\isacharparenleft}{\isasymdots}{\isacharparenright}}.
- In the case \isa{xs\ {\isacharequal}\ x\ {\isacharhash}\ xs{\isacharprime}}, we first obtain
-\isa{map\ f\ xs{\isacharprime}\ {\isacharequal}\ map\ f\ ys}, from which a forward step with the first assumption (\isa{Asm{\isacharparenleft}{\isadigit{1}}{\isacharparenright}{\isacharbrackleft}OF\ this{\isacharbrackright}}) yields \isa{length\ xs{\isacharprime}\ {\isacharequal}\ length\ ys}. Together
-with \isa{xs\ {\isacharequal}\ x\ {\isacharhash}\ xs} this yields the goal
-\isa{length\ xs\ {\isacharequal}\ length\ {\isacharparenleft}y\ {\isacharhash}\ ys{\isacharparenright}}.
+\isa{length\ xs\ {\isaliteral{3D}{\isacharequal}}\ length\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{23}{\isacharhash}}\ ys{\isaliteral{29}{\isacharparenright}}}. The assumptions are given the new name
+\isa{Asm} to avoid a name clash further down. The proof procedes with a case distinction on \isa{xs}. In the case \isa{xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}}, the second of our two
+assumptions (\isa{Asm{\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}}) implies the contradiction \isa{{\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ Suc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{29}{\isacharparenright}}}.
+ In the case \isa{xs\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{27}{\isacharprime}}}, we first obtain
+\isa{map\ f\ xs{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ map\ f\ ys}, from which a forward step with the first assumption (\isa{Asm{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5B}{\isacharbrackleft}}OF\ this{\isaliteral{5D}{\isacharbrackright}}}) yields \isa{length\ xs{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ length\ ys}. Together
+with \isa{xs\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{23}{\isacharhash}}\ xs} this yields the goal
+\isa{length\ xs\ {\isaliteral{3D}{\isacharequal}}\ length\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{23}{\isacharhash}}\ ys{\isaliteral{29}{\isacharparenright}}}.
-\subsection{Induction formulae involving \isa{{\isasymAnd}} or \isa{{\isasymLongrightarrow}}}
+\subsection{Induction formulae involving \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}} or \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}}}
Let us now consider abstractly the situation where the goal to be proved
-contains both \isa{{\isasymAnd}} and \isa{{\isasymLongrightarrow}}, say \isa{{\isasymAnd}x{\isachardot}\ P\ x\ {\isasymLongrightarrow}\ Q\ x}.
+contains both \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}} and \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}}, say \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ P\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Q\ x}.
This means that in each case of the induction,
-\isa{{\isacharquery}case} would be of the form \isa{{\isasymAnd}x{\isachardot}\ P{\isacharprime}\ x\ {\isasymLongrightarrow}\ Q{\isacharprime}\ x}. Thus the
+\isa{{\isaliteral{3F}{\isacharquery}}case} would be of the form \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ P{\isaliteral{27}{\isacharprime}}\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Q{\isaliteral{27}{\isacharprime}}\ x}. Thus the
first proof steps will be the canonical ones, fixing \isa{x} and assuming
-\isa{P{\isacharprime}\ x}. To avoid this tedium, induction performs the canonical steps
+\isa{P{\isaliteral{27}{\isacharprime}}\ x}. To avoid this tedium, induction performs the canonical steps
automatically: in each step case, the assumptions contain both the
-usual induction hypothesis and \isa{P{\isacharprime}\ x}, whereas \isa{{\isacharquery}case} is only
-\isa{Q{\isacharprime}\ x}.
+usual induction hypothesis and \isa{P{\isaliteral{27}{\isacharprime}}\ x}, whereas \isa{{\isaliteral{3F}{\isacharquery}}case} is only
+\isa{Q{\isaliteral{27}{\isacharprime}}\ x}.
\subsection{Rule induction}
@@ -475,22 +475,22 @@
transitive closure of a relation --- HOL provides a predefined one as well.%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{inductive{\isacharunderscore}set}\isamarkupfalse%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse%
\isanewline
-\ \ rtc\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}set{\isachardoublequoteclose}\ \ \ {\isacharparenleft}{\isachardoublequoteopen}{\isacharunderscore}{\isacharasterisk}{\isachardoublequoteclose}\ {\isacharbrackleft}{\isadigit{1}}{\isadigit{0}}{\isadigit{0}}{\isadigit{0}}{\isacharbrackright}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isacharparenright}\isanewline
-\ \ \isakeyword{for}\ r\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}set{\isachardoublequoteclose}\isanewline
+\ \ rtc\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}set{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isadigit{0}}{\isadigit{0}}{\isadigit{0}}{\isaliteral{5D}{\isacharbrackright}}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \isakeyword{for}\ r\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ refl{\isacharcolon}\ \ {\isachardoublequoteopen}{\isacharparenleft}x{\isacharcomma}x{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ step{\isacharcolon}\ \ {\isachardoublequoteopen}{\isasymlbrakk}\ {\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ r{\isacharsemicolon}\ {\isacharparenleft}y{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharparenleft}x{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}%
+\ \ refl{\isaliteral{3A}{\isacharcolon}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ step{\isaliteral{3A}{\isacharcolon}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
First the constant is declared as a function on binary
-relations (with concrete syntax \isa{r{\isacharasterisk}} instead of \isa{rtc\ r}), then the defining clauses are given. We will now prove that
-\isa{r{\isacharasterisk}} is indeed transitive:%
+relations (with concrete syntax \isa{r{\isaliteral{2A}{\isacharasterisk}}} instead of \isa{rtc\ r}), then the defining clauses are given. We will now prove that
+\isa{r{\isaliteral{2A}{\isacharasterisk}}} is indeed transitive:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ \isakeyword{assumes}\ A{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}\ \isakeyword{shows}\ {\isachardoublequoteopen}{\isacharparenleft}y{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymLongrightarrow}\ {\isacharparenleft}x{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}\isanewline
+\ \isakeyword{assumes}\ A{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -503,14 +503,14 @@
\ induct\isanewline
\ \ \isacommand{case}\isamarkupfalse%
\ refl\ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}case\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}case\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{case}\isamarkupfalse%
\ step\ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}case\ \isacommand{by}\isamarkupfalse%
-{\isacharparenleft}blast\ intro{\isacharcolon}\ rtc{\isachardot}step{\isacharparenright}\isanewline
+\ {\isaliteral{3F}{\isacharquery}}case\ \isacommand{by}\isamarkupfalse%
+{\isaliteral{28}{\isacharparenleft}}blast\ intro{\isaliteral{3A}{\isacharcolon}}\ rtc{\isaliteral{2E}{\isachardot}}step{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
@@ -531,7 +531,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ \isakeyword{assumes}\ {\isachardoublequoteopen}{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}{\isacharparenleft}y{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}\ \isakeyword{shows}\ {\isachardoublequoteopen}{\isacharparenleft}x{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}\isanewline
+\ \isakeyword{assumes}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -544,25 +544,25 @@
\ induct\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
\ x\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}x{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}\ \ %
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\ \ %
\isamarkupcmt{\isa{B}[\isa{y} := \isa{x}]%
}
\isanewline
\ \ \isacommand{thus}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}x{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
-\ x{\isacharprime}\ x\ y\isanewline
+\ x{\isaliteral{27}{\isacharprime}}\ x\ y\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isadigit{1}}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}x{\isacharprime}{\isacharcomma}x{\isacharparenright}\ {\isasymin}\ r{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-\ \ \ \ \ \ \ \ \ IH{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}y{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymLongrightarrow}\ {\isacharparenleft}x{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-\ \ \ \ \ \ \ \ \ B{\isacharcolon}\ \ {\isachardoublequoteopen}{\isacharparenleft}y{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}\isanewline
+\ {\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+\ \ \ \ \ \ \ \ \ IH{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+\ \ \ \ \ \ \ \ \ B{\isaliteral{3A}{\isacharcolon}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
-\ {\isadigit{1}}\ IH{\isacharbrackleft}OF\ B{\isacharbrackright}\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}x{\isacharprime}{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-{\isacharparenleft}rule\ rtc{\isachardot}step{\isacharparenright}\isanewline
+\ {\isadigit{1}}\ IH{\isaliteral{5B}{\isacharbrackleft}}OF\ B{\isaliteral{5D}{\isacharbrackright}}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+{\isaliteral{28}{\isacharparenleft}}rule\ rtc{\isaliteral{2E}{\isachardot}}step{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
@@ -577,11 +577,11 @@
This time, merely for a change, we start the proof with by feeding both
assumptions into the inductive proof. Only the first assumption is
``consumed'' by the induction.
-Since the second one is left over we don't just prove \isa{{\isacharquery}thesis} but
-\isa{{\isacharparenleft}y{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymLongrightarrow}\ {\isacharquery}thesis}, just as in the previous proof.
+Since the second one is left over we don't just prove \isa{{\isaliteral{3F}{\isacharquery}}thesis} but
+\isa{{\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}thesis}, just as in the previous proof.
The base case is trivial. In the assumptions for the induction step we can
see very clearly how things fit together and permit ourselves the
-obvious forward step \isa{IH{\isacharbrackleft}OF\ B{\isacharbrackright}}.
+obvious forward step \isa{IH{\isaliteral{5B}{\isacharbrackleft}}OF\ B{\isaliteral{5D}{\isacharbrackright}}}.
The notation \isakeyword{case}~\isa{(}\emph{constructor} \emph{vars}\isa{)}
is also supported for inductive definitions. The \emph{constructor} is the
@@ -590,7 +590,7 @@
left-to-right order of the variables as they appear in the rule.
For example, we could start the above detailed proof of the induction
with \isakeyword{case}~\isa{(step x' x y)}. In that case we don't need
-to spell out the assumptions but can refer to them by \isa{step{\isacharparenleft}{\isachardot}{\isacharparenright}},
+to spell out the assumptions but can refer to them by \isa{step{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2E}{\isachardot}}{\isaliteral{29}{\isacharparenright}}},
although the resulting text will be quite cryptic.
\subsection{More induction}
@@ -605,14 +605,14 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
-\ rot\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}rot\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}rot\ {\isacharbrackleft}x{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}x{\isacharbrackright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}rot\ {\isacharparenleft}x{\isacharhash}y{\isacharhash}zs{\isacharparenright}\ {\isacharequal}\ y\ {\isacharhash}\ rot{\isacharparenleft}x{\isacharhash}zs{\isacharparenright}{\isachardoublequoteclose}%
+\ rot\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}rot\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}rot\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}rot\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{23}{\isacharhash}}y{\isaliteral{23}{\isacharhash}}zs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ y\ {\isaliteral{23}{\isacharhash}}\ rot{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{23}{\isacharhash}}zs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent This yields, among other things, the induction rule
-\isa{rot{\isachardot}induct}: \begin{isabelle}%
-{\isasymlbrakk}P\ {\isacharbrackleft}{\isacharbrackright}{\isacharsemicolon}\ {\isasymAnd}x{\isachardot}\ P\ {\isacharbrackleft}x{\isacharbrackright}{\isacharsemicolon}\ {\isasymAnd}x\ y\ zs{\isachardot}\ P\ {\isacharparenleft}x\ {\isacharhash}\ zs{\isacharparenright}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}x\ {\isacharhash}\ y\ {\isacharhash}\ zs{\isacharparenright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ a{\isadigit{0}}%
+\isa{rot{\isaliteral{2E}{\isachardot}}induct}: \begin{isabelle}%
+{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}P\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ P\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y\ zs{\isaliteral{2E}{\isachardot}}\ P\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ zs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ y\ {\isaliteral{23}{\isacharhash}}\ zs{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ a{\isadigit{0}}%
\end{isabelle}
The following proof relies on a default naming scheme for cases: they are
called 1, 2, etc, unless they have been named explicitly. The latter happens
@@ -621,7 +621,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymLongrightarrow}\ rot\ xs\ {\isacharequal}\ tl\ xs\ {\isacharat}\ {\isacharbrackleft}hd\ xs{\isacharbrackright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}xs\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ rot\ xs\ {\isaliteral{3D}{\isacharequal}}\ tl\ xs\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{5B}{\isacharbrackleft}}hd\ xs{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -629,35 +629,35 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}induct\ xs\ rule{\isacharcolon}\ rot{\isachardot}induct{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ xs\ rule{\isaliteral{3A}{\isacharcolon}}\ rot{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{case}\isamarkupfalse%
\ {\isadigit{1}}\ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}case\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}case\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{case}\isamarkupfalse%
\ {\isadigit{2}}\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}case\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}case\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{case}\isamarkupfalse%
-\ {\isacharparenleft}{\isadigit{3}}\ a\ b\ cs{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}\ a\ b\ cs{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}rot\ {\isacharparenleft}a\ {\isacharhash}\ b\ {\isacharhash}\ cs{\isacharparenright}\ {\isacharequal}\ b\ {\isacharhash}\ rot{\isacharparenleft}a\ {\isacharhash}\ cs{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}rot\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{23}{\isacharhash}}\ b\ {\isaliteral{23}{\isacharhash}}\ cs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ b\ {\isaliteral{23}{\isacharhash}}\ rot{\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{23}{\isacharhash}}\ cs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdots}\ {\isacharequal}\ b\ {\isacharhash}\ tl{\isacharparenleft}a\ {\isacharhash}\ cs{\isacharparenright}\ {\isacharat}\ {\isacharbrackleft}hd{\isacharparenleft}a\ {\isacharhash}\ cs{\isacharparenright}{\isacharbrackright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-{\isacharparenleft}simp\ add{\isacharcolon}{\isadigit{3}}{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ b\ {\isaliteral{23}{\isacharhash}}\ tl{\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{23}{\isacharhash}}\ cs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{5B}{\isacharbrackleft}}hd{\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{23}{\isacharhash}}\ cs{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+{\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}{\isadigit{3}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdots}\ {\isacharequal}\ tl\ {\isacharparenleft}a\ {\isacharhash}\ b\ {\isacharhash}\ cs{\isacharparenright}\ {\isacharat}\ {\isacharbrackleft}hd\ {\isacharparenleft}a\ {\isacharhash}\ b\ {\isacharhash}\ cs{\isacharparenright}{\isacharbrackright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ tl\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{23}{\isacharhash}}\ b\ {\isaliteral{23}{\isacharhash}}\ cs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{5B}{\isacharbrackleft}}hd\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{23}{\isacharhash}}\ b\ {\isaliteral{23}{\isacharhash}}\ cs{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}case\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}case\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -675,7 +675,7 @@
\isakeyword{case}~\isa{(}\emph{constructor} \emph{vars}\isa{)} notation also
works for arbitrary induction theorems with numbered cases. The order
of the \emph{vars} corresponds to the order of the
-\isa{{\isasymAnd}}-quantified variables in each case of the induction
+\isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}}-quantified variables in each case of the induction
theorem. For induction theorems produced by \isakeyword{fun} it is
the order in which the variables appear on the left-hand side of the
equation.
@@ -690,7 +690,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ xs\ rule{\isacharcolon}\ rot{\isachardot}induct{\isacharparenright}\ simp{\isacharunderscore}all\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ xs\ rule{\isaliteral{3A}{\isacharcolon}}\ rot{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}\ simp{\isaliteral{5F}{\isacharunderscore}}all\isanewline
%
\endisatagproof
{\isafoldproof}%
--- a/doc-src/IsarOverview/Isar/document/Logic.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarOverview/Isar/document/Logic.tex Mon Nov 08 14:41:11 2010 +0100
@@ -33,7 +33,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymlongrightarrow}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -41,12 +41,12 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ impI{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ impI{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ a{\isacharcolon}\ {\isachardoublequoteopen}A{\isachardoublequoteclose}\isanewline
+\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}A{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-{\isacharparenleft}rule\ a{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+{\isaliteral{28}{\isacharparenleft}}rule\ a{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
@@ -59,9 +59,9 @@
\begin{isamarkuptext}%
\noindent
The operational reading: the \isakeyword{assume}-\isakeyword{show}
-block proves \isa{A\ {\isasymLongrightarrow}\ A} (\isa{a} is a degenerate rule (no
+block proves \isa{A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A} (\isa{a} is a degenerate rule (no
assumptions) that proves \isa{A} outright), which rule
-\isa{impI} (\isa{{\isacharparenleft}{\isacharquery}P\ {\isasymLongrightarrow}\ {\isacharquery}Q{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharquery}P\ {\isasymlongrightarrow}\ {\isacharquery}Q}) turns into the desired \isa{A\ {\isasymlongrightarrow}\ A}. However, this text is much too detailed for comfort. Therefore
+\isa{impI} (\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}Q{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}Q}) turns into the desired \isa{A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ A}. However, this text is much too detailed for comfort. Therefore
Isar implements the following principle: \begin{quote}\em Command
\isakeyword{proof} automatically tries to select an introduction rule
based on the goal and a predefined list of rules. \end{quote} Here
@@ -69,7 +69,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymlongrightarrow}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -79,10 +79,10 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ a{\isacharcolon}\ A\isanewline
+\ a{\isaliteral{3A}{\isacharcolon}}\ A\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ A\ \isacommand{by}\isamarkupfalse%
-{\isacharparenleft}rule\ a{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule\ a{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
@@ -103,7 +103,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymlongrightarrow}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -113,10 +113,10 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ a{\isacharcolon}\ {\isachardoublequoteopen}A{\isachardoublequoteclose}\isanewline
+\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ a\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}A{\isachardoublequoteclose}\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -134,7 +134,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymlongrightarrow}\ A\ {\isasymand}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -144,11 +144,11 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ a{\isacharcolon}\ {\isachardoublequoteopen}A{\isachardoublequoteclose}\isanewline
+\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ a\ \isakeyword{and}\ a\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymand}\ A{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-{\isacharparenleft}rule\ conjI{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+{\isaliteral{28}{\isacharparenleft}}rule\ conjI{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
@@ -159,15 +159,15 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-\noindent Rule \isa{conjI} is of course \isa{{\isasymlbrakk}{\isacharquery}P{\isacharsemicolon}\ {\isacharquery}Q{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}P\ {\isasymand}\ {\isacharquery}Q}.
+\noindent Rule \isa{conjI} is of course \isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{3F}{\isacharquery}}P{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{3F}{\isacharquery}}Q{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{3F}{\isacharquery}}Q}.
-Proofs of the form \isakeyword{by}\isa{{\isacharparenleft}rule}~\emph{name}\isa{{\isacharparenright}}
+Proofs of the form \isakeyword{by}\isa{{\isaliteral{28}{\isacharparenleft}}rule}~\emph{name}\isa{{\isaliteral{29}{\isacharparenright}}}
can be abbreviated to ``..'' if \emph{name} refers to one of the
predefined introduction rules (or elimination rules, see below):%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymlongrightarrow}\ A\ {\isasymand}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -177,10 +177,10 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ a{\isacharcolon}\ {\isachardoublequoteopen}A{\isachardoublequoteclose}\isanewline
+\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ a\ \isakeyword{and}\ a\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymand}\ A{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -205,14 +205,14 @@
\begin{isamarkuptext}%
A typical elimination rule is \isa{conjE}, $\land$-elimination:
\begin{isabelle}%
-\ \ \ \ \ {\isasymlbrakk}{\isacharquery}P\ {\isasymand}\ {\isacharquery}Q{\isacharsemicolon}\ {\isasymlbrakk}{\isacharquery}P{\isacharsemicolon}\ {\isacharquery}Q{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}R{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}R%
+\ \ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{3F}{\isacharquery}}Q{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{3F}{\isacharquery}}P{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{3F}{\isacharquery}}Q{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}R{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}R%
\end{isabelle} In the following proof it is applied
by hand, after its first (\emph{major}) premise has been eliminated via
-\isa{{\isacharbrackleft}OF\ ab{\isacharbrackright}}:%
+\isa{{\isaliteral{5B}{\isacharbrackleft}}OF\ ab{\isaliteral{5D}{\isacharbrackright}}}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymand}\ B\ {\isasymlongrightarrow}\ B\ {\isasymand}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -222,19 +222,19 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ ab{\isacharcolon}\ {\isachardoublequoteopen}A\ {\isasymand}\ B{\isachardoublequoteclose}\isanewline
+\ ab{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}B\ {\isasymand}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ conjE{\isacharbrackleft}OF\ ab{\isacharbrackright}{\isacharparenright}\ \ %
-\isamarkupcmt{\isa{conjE{\isacharbrackleft}OF\ ab{\isacharbrackright}}: \isa{{\isacharparenleft}{\isasymlbrakk}A{\isacharsemicolon}\ B{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}R{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharquery}R}%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ conjE{\isaliteral{5B}{\isacharbrackleft}}OF\ ab{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ \ %
+\isamarkupcmt{\isa{conjE{\isaliteral{5B}{\isacharbrackleft}}OF\ ab{\isaliteral{5D}{\isacharbrackright}}}: \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}A{\isaliteral{3B}{\isacharsemicolon}}\ B{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}R{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}R}%
}
\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ a{\isacharcolon}\ {\isachardoublequoteopen}A{\isachardoublequoteclose}\ \isakeyword{and}\ b{\isacharcolon}\ {\isachardoublequoteopen}B{\isachardoublequoteclose}\isanewline
+\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ b{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{from}\isamarkupfalse%
\ b\ \isakeyword{and}\ a\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
@@ -248,7 +248,7 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-\noindent Note that the term \isa{{\isacharquery}thesis} always stands for the
+\noindent Note that the term \isa{{\isaliteral{3F}{\isacharquery}}thesis} always stands for the
``current goal'', i.e.\ the enclosing \isakeyword{show} (or
\isakeyword{have}) statement.
@@ -270,7 +270,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymand}\ B\ {\isasymlongrightarrow}\ B\ {\isasymand}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -280,17 +280,17 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ ab{\isacharcolon}\ {\isachardoublequoteopen}A\ {\isasymand}\ B{\isachardoublequoteclose}\isanewline
+\ ab{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ ab\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}B\ {\isasymand}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ a{\isacharcolon}\ {\isachardoublequoteopen}A{\isachardoublequoteclose}\ \isakeyword{and}\ b{\isacharcolon}\ {\isachardoublequoteopen}B{\isachardoublequoteclose}\isanewline
+\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ b{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{from}\isamarkupfalse%
\ b\ \isakeyword{and}\ a\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
@@ -315,7 +315,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymand}\ B\ {\isasymlongrightarrow}\ B\ {\isasymand}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -325,17 +325,17 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymand}\ B{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ this\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}B\ {\isasymand}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}B{\isachardoublequoteclose}\ {\isachardoublequoteopen}A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}B{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{from}\isamarkupfalse%
\ this\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
@@ -361,7 +361,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymand}\ B\ {\isasymlongrightarrow}\ B\ {\isasymand}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -371,18 +371,18 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ ab{\isacharcolon}\ {\isachardoublequoteopen}A\ {\isasymand}\ B{\isachardoublequoteclose}\isanewline
+\ ab{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ ab\ \isacommand{have}\isamarkupfalse%
-\ a{\isacharcolon}\ {\isachardoublequoteopen}A{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ ab\ \isacommand{have}\isamarkupfalse%
-\ b{\isacharcolon}\ {\isachardoublequoteopen}B{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ b{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}B{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ b\ a\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}B\ {\isasymand}\ A{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -404,17 +404,17 @@
\begin{itemize}
\item
Method \isa{rule} can be given a list of rules, in which case
-\isa{{\isacharparenleft}rule}~\textit{rules}\isa{{\isacharparenright}} applies the first matching
+\isa{{\isaliteral{28}{\isacharparenleft}}rule}~\textit{rules}\isa{{\isaliteral{29}{\isacharparenright}}} applies the first matching
rule in the list \textit{rules}.
\item Command \isakeyword{from} can be
followed by any number of facts. Given \isakeyword{from}~\isa{f}$_1$~\dots~\isa{f}$_n$, the proof step
-\isa{{\isacharparenleft}rule}~\textit{rules}\isa{{\isacharparenright}} following a \isakeyword{have}
+\isa{{\isaliteral{28}{\isacharparenleft}}rule}~\textit{rules}\isa{{\isaliteral{29}{\isacharparenright}}} following a \isakeyword{have}
or \isakeyword{show} searches \textit{rules} for a rule whose first
$n$ premises can be proved by \isa{f}$_1$~\dots~\isa{f}$_n$ in the
given order.
\item ``..'' is short for
-\isa{by{\isacharparenleft}rule}~\textit{elim-rules intro-rules}\isa{{\isacharparenright}}\footnote{or
-merely \isa{{\isacharparenleft}rule}~\textit{intro-rules}\isa{{\isacharparenright}} if there are no facts
+\isa{by{\isaliteral{28}{\isacharparenleft}}rule}~\textit{elim-rules intro-rules}\isa{{\isaliteral{29}{\isacharparenright}}}\footnote{or
+merely \isa{{\isaliteral{28}{\isacharparenleft}}rule}~\textit{intro-rules}\isa{{\isaliteral{29}{\isacharparenright}}} if there are no facts
fed into the proof}, where \textit{elim-rules} and \textit{intro-rules}
are the predefined elimination and introduction rule. Thus
elimination rules are tried first (if there are incoming facts).
@@ -427,7 +427,7 @@
\isakeyword{from}~\isa{b\ a}.
A plain \isakeyword{proof} with no argument is short for
-\isakeyword{proof}~\isa{{\isacharparenleft}rule}~\textit{elim-rules intro-rules}\isa{{\isacharparenright}}\footnotemark[1].
+\isakeyword{proof}~\isa{{\isaliteral{28}{\isacharparenleft}}rule}~\textit{elim-rules intro-rules}\isa{{\isaliteral{29}{\isacharparenright}}}\footnotemark[1].
This means that the matching rule is selected by the incoming facts and the goal exactly as just explained.
Although we have only seen a few introduction and elimination rules so
@@ -437,7 +437,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymnot}\ {\isacharparenleft}A\ {\isasymand}\ B{\isacharparenright}\ {\isasymlongrightarrow}\ {\isasymnot}\ A\ {\isasymor}\ {\isasymnot}\ B{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -447,50 +447,50 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ n{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ {\isacharparenleft}A\ {\isasymand}\ B{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ n{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymnot}\ A\ {\isasymor}\ {\isasymnot}\ B{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ ccontr{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ ccontr{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ nn{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ {\isacharparenleft}{\isasymnot}\ A\ {\isasymor}\ {\isasymnot}\ B{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ nn{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymnot}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ a{\isacharcolon}\ {\isachardoublequoteopen}A{\isachardoublequoteclose}\isanewline
+\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymnot}\ B{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ b{\isacharcolon}\ {\isachardoublequoteopen}B{\isachardoublequoteclose}\isanewline
+\ b{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{from}\isamarkupfalse%
\ a\ \isakeyword{and}\ b\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymand}\ B{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{with}\isamarkupfalse%
\ n\ \isacommand{show}\isamarkupfalse%
-\ False\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ False\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{hence}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymnot}\ A\ {\isasymor}\ {\isasymnot}\ B{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{with}\isamarkupfalse%
\ nn\ \isacommand{show}\isamarkupfalse%
-\ False\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ False\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{hence}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymnot}\ A\ {\isasymor}\ {\isasymnot}\ B{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{with}\isamarkupfalse%
\ nn\ \isacommand{show}\isamarkupfalse%
-\ False\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ False\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
@@ -506,7 +506,7 @@
\begin{isamarkuptext}%
\noindent
Rule \isa{ccontr} (``classical contradiction'') is
-\isa{{\isacharparenleft}{\isasymnot}\ P\ {\isasymLongrightarrow}\ False{\isacharparenright}\ {\isasymLongrightarrow}\ P}.
+\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ P\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ False{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P}.
Apart from demonstrating the strangeness of classical
arguments by contradiction, this example also introduces two new
abbreviations:
@@ -526,11 +526,11 @@
%
\begin{isamarkuptext}%
So far our examples have been a bit unnatural: normally we want to
-prove rules expressed with \isa{{\isasymLongrightarrow}}, not \isa{{\isasymlongrightarrow}}. Here is an example:%
+prove rules expressed with \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}}, not \isa{{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}}. Here is an example:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymand}\ B\ {\isasymLongrightarrow}\ B\ {\isasymand}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -540,14 +540,14 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymand}\ B{\isachardoublequoteclose}\ \isacommand{thus}\isamarkupfalse%
-\ {\isachardoublequoteopen}B{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{thus}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}B{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymand}\ B{\isachardoublequoteclose}\ \isacommand{thus}\isamarkupfalse%
-\ {\isachardoublequoteopen}A{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{thus}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -560,12 +560,12 @@
%
\begin{isamarkuptext}%
\noindent The \isakeyword{proof} always works on the conclusion,
-\isa{B\ {\isasymand}\ A} in our case, thus selecting $\land$-introduction. Hence
+\isa{B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A} in our case, thus selecting $\land$-introduction. Hence
we must show \isa{B} and \isa{A}; both are proved by
$\land$-elimination and the proofs are separated by \isakeyword{next}:
\begin{description}
\item[\isakeyword{next}] deals with multiple subgoals. For example,
-when showing \isa{A\ {\isasymand}\ B} we need to show both \isa{A} and \isa{B}. Each subgoal is proved separately, in \emph{any} order. The
+when showing \isa{A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B} we need to show both \isa{A} and \isa{B}. Each subgoal is proved separately, in \emph{any} order. The
individual proofs are separated by \isakeyword{next}. \footnote{Each
\isakeyword{show} must prove one of the pending subgoals. If a
\isakeyword{show} matches multiple subgoals, e.g.\ if the subgoals
@@ -585,8 +585,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}large{\isacharunderscore}A\ {\isasymand}\ large{\isacharunderscore}B\ {\isasymLongrightarrow}\ large{\isacharunderscore}B\ {\isasymand}\ large{\isacharunderscore}A{\isachardoublequoteclose}\isanewline
-\ \ \ \ \ \ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isacharquery}AB\ {\isasymLongrightarrow}\ {\isacharquery}B\ {\isasymand}\ {\isacharquery}A{\isachardoublequoteclose}{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}large{\isaliteral{5F}{\isacharunderscore}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ large{\isaliteral{5F}{\isacharunderscore}}B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ large{\isaliteral{5F}{\isacharunderscore}}B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ large{\isaliteral{5F}{\isacharunderscore}}A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{is}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}AB\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{3F}{\isacharquery}}A{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
%
\isadelimproof
%
@@ -596,14 +596,14 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}AB{\isachardoublequoteclose}\ \isacommand{thus}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}B{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}AB{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{thus}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}B{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}AB{\isachardoublequoteclose}\ \isacommand{thus}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}A{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}AB{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{thus}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}A{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -616,8 +616,8 @@
%
\begin{isamarkuptext}%
\noindent Any formula may be followed by
-\isa{{\isacharparenleft}}\isakeyword{is}~\emph{pattern}\isa{{\isacharparenright}} which causes the pattern
-to be matched against the formula, instantiating the \isa{{\isacharquery}}-variables in
+\isa{{\isaliteral{28}{\isacharparenleft}}}\isakeyword{is}~\emph{pattern}\isa{{\isaliteral{29}{\isacharparenright}}} which causes the pattern
+to be matched against the formula, instantiating the \isa{{\isaliteral{3F}{\isacharquery}}}-variables in
the pattern. Subsequent uses of these variables in other terms causes
them to be replaced by the terms they stand for.
@@ -627,8 +627,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ \isakeyword{assumes}\ ab{\isacharcolon}\ {\isachardoublequoteopen}large{\isacharunderscore}A\ {\isasymand}\ large{\isacharunderscore}B{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{shows}\ {\isachardoublequoteopen}large{\isacharunderscore}B\ {\isasymand}\ large{\isacharunderscore}A{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isacharquery}B\ {\isasymand}\ {\isacharquery}A{\isachardoublequoteclose}{\isacharparenright}\isanewline
+\ \isakeyword{assumes}\ ab{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}large{\isaliteral{5F}{\isacharunderscore}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ large{\isaliteral{5F}{\isacharunderscore}}B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}large{\isaliteral{5F}{\isacharunderscore}}B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ large{\isaliteral{5F}{\isacharunderscore}}A{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{is}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{3F}{\isacharquery}}A{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
%
\isadelimproof
%
@@ -639,13 +639,13 @@
\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ ab\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}B{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}B{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ ab\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}A{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}A{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -657,7 +657,7 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-\noindent Note the difference between \isa{{\isacharquery}AB}, a term, and
+\noindent Note the difference between \isa{{\isaliteral{3F}{\isacharquery}}AB}, a term, and
\isa{ab}, a fact.
Finally we want to start the proof with $\land$-elimination so we
@@ -666,8 +666,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ \isakeyword{assumes}\ ab{\isacharcolon}\ {\isachardoublequoteopen}large{\isacharunderscore}A\ {\isasymand}\ large{\isacharunderscore}B{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{shows}\ {\isachardoublequoteopen}large{\isacharunderscore}B\ {\isasymand}\ large{\isacharunderscore}A{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isacharquery}B\ {\isasymand}\ {\isacharquery}A{\isachardoublequoteclose}{\isacharparenright}\isanewline
+\ \isakeyword{assumes}\ ab{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}large{\isaliteral{5F}{\isacharunderscore}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ large{\isaliteral{5F}{\isacharunderscore}}B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}large{\isaliteral{5F}{\isacharunderscore}}B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ large{\isaliteral{5F}{\isacharunderscore}}A{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{is}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{3F}{\isacharquery}}A{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
%
\isadelimproof
%
@@ -679,8 +679,8 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}B{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isacharquery}A{\isachardoublequoteclose}\ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}B{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}A{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{thus}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -704,14 +704,14 @@
\end{center}
Sometimes it is necessary to suppress the implicit application of rules in a
-\isakeyword{proof}. For example \isakeyword{show(s)}~\isa{{\isachardoublequote}P\ {\isasymor}\ Q{\isachardoublequote}}
+\isakeyword{proof}. For example \isakeyword{show(s)}~\isa{{\isaliteral{22}{\isachardoublequote}}P\ {\isaliteral{5C3C6F723E}{\isasymor}}\ Q{\isaliteral{22}{\isachardoublequote}}}
would trigger $\lor$-introduction, requiring us to prove \isa{P}, which may
not be what we had in mind.
-A simple ``\isa{{\isacharminus}}'' prevents this \emph{faux pas}:%
+A simple ``\isa{{\isaliteral{2D}{\isacharminus}}}'' prevents this \emph{faux pas}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ \isakeyword{assumes}\ ab{\isacharcolon}\ {\isachardoublequoteopen}A\ {\isasymor}\ B{\isachardoublequoteclose}\ \isakeyword{shows}\ {\isachardoublequoteopen}B\ {\isasymor}\ A{\isachardoublequoteclose}\isanewline
+\ \isakeyword{assumes}\ ab{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ {\isaliteral{5C3C6F723E}{\isasymor}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -719,21 +719,21 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ ab\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\isanewline
+\ {\isaliteral{3F}{\isacharquery}}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
\ A\ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
\ B\ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
@@ -747,12 +747,12 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-\noindent Alternatively one can feed \isa{A\ {\isasymor}\ B} directly
+\noindent Alternatively one can feed \isa{A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B} directly
into the proof, thus triggering the elimination rule:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ \isakeyword{assumes}\ ab{\isacharcolon}\ {\isachardoublequoteopen}A\ {\isasymor}\ B{\isachardoublequoteclose}\ \isakeyword{shows}\ {\isachardoublequoteopen}B\ {\isasymor}\ A{\isachardoublequoteclose}\isanewline
+\ \isakeyword{assumes}\ ab{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ {\isaliteral{5C3C6F723E}{\isasymor}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -765,13 +765,13 @@
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
\ A\ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
\ B\ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -791,14 +791,14 @@
Too many names can easily clutter a proof. We already learned
about \isa{this} as a means of avoiding explicit names. Another
handy device is to refer to a fact not by name but by contents: for
-example, writing \isa{{\isacharbackquote}A\ {\isasymor}\ B{\isacharbackquote}} (enclosing the formula in back quotes)
-refers to the fact \isa{A\ {\isasymor}\ B}
+example, writing \isa{{\isaliteral{60}{\isacharbackquote}}A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B{\isaliteral{60}{\isacharbackquote}}} (enclosing the formula in back quotes)
+refers to the fact \isa{A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B}
without the need to name it. Here is a simple example, a revised version
of the previous proof%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ \isakeyword{assumes}\ {\isachardoublequoteopen}A\ {\isasymor}\ B{\isachardoublequoteclose}\ \isakeyword{shows}\ {\isachardoublequoteopen}B\ {\isasymor}\ A{\isachardoublequoteclose}\isanewline
+\ \isakeyword{assumes}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ {\isaliteral{5C3C6F723E}{\isasymor}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -806,7 +806,7 @@
%
\isatagproof
\isacommand{using}\isamarkupfalse%
-\ {\isacharbackquoteopen}A\ {\isasymor}\ B{\isacharbackquoteclose}%
+\ {\isaliteral{60}{\isacharbackquoteopen}}A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B{\isaliteral{60}{\isacharbackquoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -823,12 +823,12 @@
it in the preceding proof text.
The assumptions of a lemma can also be referred to via their
-predefined name \isa{assms}. Hence the \isa{{\isacharbackquote}A\ {\isasymor}\ B{\isacharbackquote}} in the
+predefined name \isa{assms}. Hence the \isa{{\isaliteral{60}{\isacharbackquote}}A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B{\isaliteral{60}{\isacharbackquote}}} in the
previous proof can also be replaced by \isa{assms}. Note that \isa{assms} refers to the list of \emph{all} assumptions. To pick out a
-specific one, say the second, write \isa{assms{\isacharparenleft}{\isadigit{2}}{\isacharparenright}}.
+specific one, say the second, write \isa{assms{\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}}.
This indexing notation $name(.)$ works for any $name$ that stands for
-a list of facts, for example $f$\isa{{\isachardot}simps}, the equations of the
+a list of facts, for example $f$\isa{{\isaliteral{2E}{\isachardot}}simps}, the equations of the
recursively defined function $f$. You may also select sublists by writing
$name(2-3)$.
@@ -840,7 +840,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ \isakeyword{assumes}\ {\isachardoublequoteopen}A\ {\isasymand}\ B{\isachardoublequoteclose}\ \isakeyword{shows}\ {\isachardoublequoteopen}B\ {\isasymand}\ A{\isachardoublequoteclose}\isanewline
+\ \isakeyword{assumes}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -848,20 +848,20 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
-\ {\isacharbackquoteopen}A\ {\isasymand}\ B{\isacharbackquoteclose}\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}B{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{have}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}B{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \isacommand{from}\isamarkupfalse%
-\ {\isacharbackquoteopen}A\ {\isasymand}\ B{\isacharbackquoteclose}\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}A{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{have}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{ultimately}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}B\ {\isasymand}\ A{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -882,15 +882,15 @@
\subsection{Predicate calculus}
Command \isakeyword{fix} introduces new local variables into a
-proof. The pair \isakeyword{fix}-\isakeyword{show} corresponds to \isa{{\isasymAnd}}
+proof. The pair \isakeyword{fix}-\isakeyword{show} corresponds to \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}}
(the universal quantifier at the
meta-level) just like \isakeyword{assume}-\isakeyword{show} corresponds to
-\isa{{\isasymLongrightarrow}}. Here is a sample proof, annotated with the rules that are
+\isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}}. Here is a sample proof, annotated with the rules that are
applied implicitly:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ \isakeyword{assumes}\ P{\isacharcolon}\ {\isachardoublequoteopen}{\isasymforall}x{\isachardot}\ P\ x{\isachardoublequoteclose}\ \isakeyword{shows}\ {\isachardoublequoteopen}{\isasymforall}x{\isachardot}\ P{\isacharparenleft}f\ x{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \isakeyword{assumes}\ P{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ P{\isaliteral{28}{\isacharparenleft}}f\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -899,16 +899,16 @@
\isatagproof
\isacommand{proof}\isamarkupfalse%
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ %
-\isamarkupcmt{\isa{allI}: \isa{{\isacharparenleft}{\isasymAnd}x{\isachardot}\ {\isacharquery}P\ x{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymforall}x{\isachardot}\ {\isacharquery}P\ x}%
+\isamarkupcmt{\isa{allI}: \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}P\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}P\ x}%
}
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
\ a\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ P\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}P{\isacharparenleft}f\ a{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}P{\isaliteral{28}{\isacharparenleft}}f\ a{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\ \ %
-\isamarkupcmt{\isa{allE}: \isa{{\isasymlbrakk}{\isasymforall}x{\isachardot}\ {\isacharquery}P\ x{\isacharsemicolon}\ {\isacharquery}P\ {\isacharquery}x\ {\isasymLongrightarrow}\ {\isacharquery}R{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}R}%
+\isamarkupcmt{\isa{allE}: \isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}P\ x{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}R{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}R}%
}
\isanewline
\isacommand{qed}\isamarkupfalse%
@@ -925,11 +925,11 @@
variable \isa{a} instead of \isa{x} merely to show that the choice of
local names is irrelevant.
-Next we look at \isa{{\isasymexists}} which is a bit more tricky.%
+Next we look at \isa{{\isaliteral{5C3C6578697374733E}{\isasymexists}}} which is a bit more tricky.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ \isakeyword{assumes}\ Pf{\isacharcolon}\ {\isachardoublequoteopen}{\isasymexists}x{\isachardot}\ P{\isacharparenleft}f\ x{\isacharparenright}{\isachardoublequoteclose}\ \isakeyword{shows}\ {\isachardoublequoteopen}{\isasymexists}y{\isachardot}\ P\ y{\isachardoublequoteclose}\isanewline
+\ \isakeyword{assumes}\ Pf{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ P{\isaliteral{28}{\isacharparenleft}}f\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}y{\isaliteral{2E}{\isachardot}}\ P\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -937,23 +937,23 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ Pf\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\isanewline
+\ {\isaliteral{3F}{\isacharquery}}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ \ \ \ \ \ \ \ \ \ \ \ \ \ %
-\isamarkupcmt{\isa{exE}: \isa{{\isasymlbrakk}{\isasymexists}x{\isachardot}\ {\isacharquery}P\ x{\isacharsemicolon}\ {\isasymAnd}x{\isachardot}\ {\isacharquery}P\ x\ {\isasymLongrightarrow}\ {\isacharquery}Q{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}Q}%
+\isamarkupcmt{\isa{exE}: \isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}P\ x{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}P\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}Q{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}Q}%
}
\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ x\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}P{\isacharparenleft}f\ x{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}P{\isaliteral{28}{\isacharparenleft}}f\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\ \ %
-\isamarkupcmt{\isa{exI}: \isa{{\isacharquery}P\ {\isacharquery}x\ {\isasymLongrightarrow}\ {\isasymexists}x{\isachardot}\ {\isacharquery}P\ x}%
+\isamarkupcmt{\isa{exI}: \isa{{\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}P\ x}%
}
\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
@@ -975,7 +975,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ \isakeyword{assumes}\ Pf{\isacharcolon}\ {\isachardoublequoteopen}{\isasymexists}x{\isachardot}\ P{\isacharparenleft}f\ x{\isacharparenright}{\isachardoublequoteclose}\ \isakeyword{shows}\ {\isachardoublequoteopen}{\isasymexists}y{\isachardot}\ P\ y{\isachardoublequoteclose}\isanewline
+\ \isakeyword{assumes}\ Pf{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ P{\isaliteral{28}{\isacharparenleft}}f\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}y{\isaliteral{2E}{\isachardot}}\ P\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -983,13 +983,13 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ Pf\ \isacommand{obtain}\isamarkupfalse%
-\ x\ \isakeyword{where}\ {\isachardoublequoteopen}P{\isacharparenleft}f\ x{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ x\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}P{\isaliteral{28}{\isacharparenleft}}f\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{thus}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymexists}y{\isachardot}\ P\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}y{\isaliteral{2E}{\isachardot}}\ P\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -1012,7 +1012,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ \isakeyword{assumes}\ ex{\isacharcolon}\ {\isachardoublequoteopen}{\isasymexists}x{\isachardot}\ {\isasymforall}y{\isachardot}\ P\ x\ y{\isachardoublequoteclose}\ \isakeyword{shows}\ {\isachardoublequoteopen}{\isasymforall}y{\isachardot}\ {\isasymexists}x{\isachardot}\ P\ x\ y{\isachardoublequoteclose}\isanewline
+\ \isakeyword{assumes}\ ex{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}y{\isaliteral{2E}{\isachardot}}\ P\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}y{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ P\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1025,13 +1025,13 @@
\ y\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ ex\ \isacommand{obtain}\isamarkupfalse%
-\ x\ \isakeyword{where}\ {\isachardoublequoteopen}{\isasymforall}y{\isachardot}\ P\ x\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ x\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}y{\isaliteral{2E}{\isachardot}}\ P\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{hence}\isamarkupfalse%
-\ {\isachardoublequoteopen}P\ x\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}P\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{thus}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymexists}x{\isachardot}\ P\ x\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ P\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -1054,7 +1054,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymexists}S{\isachardot}\ S\ {\isasymnotin}\ range\ {\isacharparenleft}f\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ set{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}S{\isaliteral{2E}{\isachardot}}\ S\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ range\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1064,33 +1064,33 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{let}\isamarkupfalse%
-\ {\isacharquery}S\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}x{\isachardot}\ x\ {\isasymnotin}\ f\ x{\isacharbraceright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{3F}{\isacharquery}}S\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7B}{\isacharbraceleft}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ f\ x{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}S\ {\isasymnotin}\ range\ f{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}S\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ range\ f{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}S\ {\isasymin}\ range\ f{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}S\ {\isaliteral{5C3C696E3E}{\isasymin}}\ range\ f{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{obtain}\isamarkupfalse%
-\ y\ \isakeyword{where}\ {\isachardoublequoteopen}{\isacharquery}S\ {\isacharequal}\ f\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ y\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}S\ {\isaliteral{3D}{\isacharequal}}\ f\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ False\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
\ cases\isanewline
\ \ \ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymin}\ {\isacharquery}S{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{3F}{\isacharquery}}S{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{with}\isamarkupfalse%
-\ {\isacharbackquoteopen}{\isacharquery}S\ {\isacharequal}\ f\ y{\isacharbackquoteclose}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}{\isaliteral{3F}{\isacharquery}}S\ {\isaliteral{3D}{\isacharequal}}\ f\ y{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{show}\isamarkupfalse%
\ False\ \isacommand{by}\isamarkupfalse%
\ blast\isanewline
\ \ \ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymnotin}\ {\isacharquery}S{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ {\isaliteral{3F}{\isacharquery}}S{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{with}\isamarkupfalse%
-\ {\isacharbackquoteopen}{\isacharquery}S\ {\isacharequal}\ f\ y{\isacharbackquoteclose}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}{\isaliteral{3F}{\isacharquery}}S\ {\isaliteral{3D}{\isacharequal}}\ f\ y{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{show}\isamarkupfalse%
\ False\ \isacommand{by}\isamarkupfalse%
\ blast\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
@@ -1114,11 +1114,11 @@
the witness for the claim.
\item Proof by \isa{cases} starts a proof by cases. Note that it remains
implicit what the two cases are: it is merely expected that the two subproofs
-prove \isa{P\ {\isasymLongrightarrow}\ {\isacharquery}thesis} and \isa{{\isasymnot}P\ {\isasymLongrightarrow}\ {\isacharquery}thesis} (in that order)
+prove \isa{P\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}thesis} and \isa{{\isaliteral{5C3C6E6F743E}{\isasymnot}}P\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}thesis} (in that order)
for some \isa{P}.
\end{itemize}
If you wonder how to \isakeyword{obtain} \isa{y}:
-via the predefined elimination rule \isa{{\isasymlbrakk}b\ {\isasymin}\ range\ f{\isacharsemicolon}\ {\isasymAnd}x{\isachardot}\ b\ {\isacharequal}\ f\ x\ {\isasymLongrightarrow}\ P{\isasymrbrakk}\ {\isasymLongrightarrow}\ P}.
+via the predefined elimination rule \isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}b\ {\isaliteral{5C3C696E3E}{\isasymin}}\ range\ f{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ b\ {\isaliteral{3D}{\isacharequal}}\ f\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P}.
Method \isa{blast} is used because the contradiction does not follow easily
by just a single rule. If you find the proof too cryptic for human
@@ -1127,7 +1127,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymexists}S{\isachardot}\ S\ {\isasymnotin}\ range\ {\isacharparenleft}f\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ set{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}S{\isaliteral{2E}{\isachardot}}\ S\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ range\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1137,45 +1137,45 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{let}\isamarkupfalse%
-\ {\isacharquery}S\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}x{\isachardot}\ x\ {\isasymnotin}\ f\ x{\isacharbraceright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{3F}{\isacharquery}}S\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7B}{\isacharbraceleft}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ f\ x{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}S\ {\isasymnotin}\ range\ f{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}S\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ range\ f{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}S\ {\isasymin}\ range\ f{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}S\ {\isaliteral{5C3C696E3E}{\isasymin}}\ range\ f{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{obtain}\isamarkupfalse%
-\ y\ \isakeyword{where}\ {\isachardoublequoteopen}{\isacharquery}S\ {\isacharequal}\ f\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ y\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}S\ {\isaliteral{3D}{\isacharequal}}\ f\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ False\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
\ cases\isanewline
\ \ \ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymin}\ {\isacharquery}S{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{3F}{\isacharquery}}S{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{hence}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymnotin}\ f\ y{\isachardoublequoteclose}\ \ \ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ f\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\ \ \ \ \ \ \isacommand{hence}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymnotin}\ {\isacharquery}S{\isachardoublequoteclose}\ \ \ \ \isacommand{by}\isamarkupfalse%
-{\isacharparenleft}simp\ add{\isacharcolon}\ {\isacharbackquoteopen}{\isacharquery}S\ {\isacharequal}\ f\ y{\isacharbackquoteclose}{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ {\isaliteral{3F}{\isacharquery}}S{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ \ \isacommand{by}\isamarkupfalse%
+{\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{60}{\isacharbackquoteopen}}{\isaliteral{3F}{\isacharquery}}S\ {\isaliteral{3D}{\isacharequal}}\ f\ y{\isaliteral{60}{\isacharbackquoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \ \ \isacommand{with}\isamarkupfalse%
-\ {\isacharbackquoteopen}y\ {\isasymin}\ {\isacharquery}S{\isacharbackquoteclose}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{3F}{\isacharquery}}S{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{show}\isamarkupfalse%
\ False\ \isacommand{by}\isamarkupfalse%
\ contradiction\isanewline
\ \ \ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymnotin}\ {\isacharquery}S{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ {\isaliteral{3F}{\isacharquery}}S{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{hence}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymin}\ f\ y{\isachardoublequoteclose}\ \ \ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ f\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\ \ \ \ \ \ \isacommand{hence}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymin}\ {\isacharquery}S{\isachardoublequoteclose}\ \ \ \ \isacommand{by}\isamarkupfalse%
-{\isacharparenleft}simp\ add{\isacharcolon}\ {\isacharbackquoteopen}{\isacharquery}S\ {\isacharequal}\ f\ y{\isacharbackquoteclose}{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{3F}{\isacharquery}}S{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ \ \isacommand{by}\isamarkupfalse%
+{\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{60}{\isacharbackquoteopen}}{\isaliteral{3F}{\isacharquery}}S\ {\isaliteral{3D}{\isacharequal}}\ f\ y{\isaliteral{60}{\isacharbackquoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \ \ \isacommand{with}\isamarkupfalse%
-\ {\isacharbackquoteopen}y\ {\isasymnotin}\ {\isacharquery}S{\isacharbackquoteclose}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}y\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ {\isaliteral{3F}{\isacharquery}}S{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{show}\isamarkupfalse%
\ False\ \isacommand{by}\isamarkupfalse%
\ contradiction\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
@@ -1201,7 +1201,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymexists}S{\isachardot}\ S\ {\isasymnotin}\ range\ {\isacharparenleft}f\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ set{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}S{\isaliteral{2E}{\isachardot}}\ S\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ range\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1229,7 +1229,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymforall}x\ y{\isachardot}\ A\ x\ y\ {\isasymand}\ B\ x\ y\ {\isasymlongrightarrow}\ C\ x\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x\ y{\isaliteral{2E}{\isachardot}}\ A\ x\ y\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ x\ y\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1240,18 +1240,18 @@
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
\ x\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymforall}y{\isachardot}\ A\ x\ y\ {\isasymand}\ B\ x\ y\ {\isasymlongrightarrow}\ C\ x\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}y{\isaliteral{2E}{\isachardot}}\ A\ x\ y\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ x\ y\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ y\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ x\ y\ {\isasymand}\ B\ x\ y\ {\isasymlongrightarrow}\ C\ x\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ x\ y\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ x\ y\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ x\ y\ {\isasymand}\ B\ x\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ x\ y\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}C\ x\ y{\isachardoublequoteclose}\ \isacommand{sorry}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{sorry}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
@@ -1277,7 +1277,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymforall}x\ y{\isachardot}\ A\ x\ y\ {\isasymand}\ B\ x\ y\ {\isasymlongrightarrow}\ C\ x\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x\ y{\isaliteral{2E}{\isachardot}}\ A\ x\ y\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ x\ y\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1285,21 +1285,21 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymAnd}x\ y{\isachardot}\ {\isasymlbrakk}\ A\ x\ y{\isacharsemicolon}\ B\ x\ y\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ C\ x\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ A\ x\ y{\isaliteral{3B}{\isacharsemicolon}}\ B\ x\ y\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ x\ y\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ x\ y{\isachardoublequoteclose}\ {\isachardoublequoteopen}B\ x\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}C\ x\ y{\isachardoublequoteclose}\ \isacommand{sorry}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{sorry}\isamarkupfalse%
\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{by}\isamarkupfalse%
\ blast\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -1317,7 +1317,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymforall}x\ y{\isachardot}\ A\ x\ y\ {\isasymand}\ B\ x\ y\ {\isasymlongrightarrow}\ C\ x\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x\ y{\isaliteral{2E}{\isachardot}}\ A\ x\ y\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ x\ y\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1325,17 +1325,17 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
-\ \ \isacommand{{\isacharbraceleft}}\isamarkupfalse%
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
+\ \ \isacommand{{\isaliteral{7B}{\isacharbraceleft}}}\isamarkupfalse%
\ \isacommand{fix}\isamarkupfalse%
\ x\ y\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ x\ y{\isachardoublequoteclose}\ {\isachardoublequoteopen}B\ x\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}C\ x\ y{\isachardoublequoteclose}\ \isacommand{sorry}\isamarkupfalse%
-\ \isacommand{{\isacharbraceright}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{sorry}\isamarkupfalse%
+\ \isacommand{{\isaliteral{7D}{\isacharbraceright}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{thus}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{by}\isamarkupfalse%
\ blast\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -1348,7 +1348,7 @@
%
\begin{isamarkuptext}%
\noindent The result of the raw proof block is the same theorem
-as above, namely \isa{{\isasymAnd}x\ y{\isachardot}\ {\isasymlbrakk}A\ x\ y{\isacharsemicolon}\ B\ x\ y{\isasymrbrakk}\ {\isasymLongrightarrow}\ C\ x\ y}. Raw
+as above, namely \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}A\ x\ y{\isaliteral{3B}{\isacharsemicolon}}\ B\ x\ y{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C\ x\ y}. Raw
proof blocks are like ordinary proofs except that they do not prove
some explicitly stated property but that the property emerges directly
out of the \isakeyword{fixe}s, \isakeyword{assume}s and
@@ -1386,60 +1386,60 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}P\isactrlisub {\isadigit{1}}\ {\isasymor}\ P\isactrlisub {\isadigit{2}}\ {\isasymor}\ P\isactrlisub {\isadigit{3}}{\isachardoublequoteclose}\ \ %
+\ {\isaliteral{22}{\isachardoublequoteopen}}P\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ P\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ P\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{3}}{\isaliteral{22}{\isachardoublequoteclose}}\ \ %
\isamarkupcmt{\dots%
}
\isanewline
\ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
-\ \ \isacommand{{\isacharbraceleft}}\isamarkupfalse%
+\ \ \isacommand{{\isaliteral{7B}{\isacharbraceleft}}}\isamarkupfalse%
\ \isacommand{assume}\isamarkupfalse%
-\ P\isactrlisub {\isadigit{1}}\isanewline
+\ P\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\isanewline
\ \ \ \ %
\isamarkupcmt{\dots%
}
\isanewline
\ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isacharquery}thesis\ \ %
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \ %
\isamarkupcmt{\dots%
}
-\ \isacommand{{\isacharbraceright}}\isamarkupfalse%
+\ \isacommand{{\isaliteral{7D}{\isacharbraceright}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
-\ \ \isacommand{{\isacharbraceleft}}\isamarkupfalse%
+\ \ \isacommand{{\isaliteral{7B}{\isacharbraceleft}}}\isamarkupfalse%
\ \isacommand{assume}\isamarkupfalse%
-\ P\isactrlisub {\isadigit{2}}\isanewline
+\ P\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}\isanewline
\ \ \ \ %
\isamarkupcmt{\dots%
}
\isanewline
\ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isacharquery}thesis\ \ %
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \ %
\isamarkupcmt{\dots%
}
-\ \isacommand{{\isacharbraceright}}\isamarkupfalse%
+\ \isacommand{{\isaliteral{7D}{\isacharbraceright}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
-\ \ \isacommand{{\isacharbraceleft}}\isamarkupfalse%
+\ \ \isacommand{{\isaliteral{7B}{\isacharbraceleft}}}\isamarkupfalse%
\ \isacommand{assume}\isamarkupfalse%
-\ P\isactrlisub {\isadigit{3}}\isanewline
+\ P\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{3}}\isanewline
\ \ \ \ %
\isamarkupcmt{\dots%
}
\isanewline
\ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isacharquery}thesis\ \ %
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \ %
\isamarkupcmt{\dots%
}
-\ \isacommand{{\isacharbraceright}}\isamarkupfalse%
+\ \isacommand{{\isaliteral{7D}{\isacharbraceright}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{ultimately}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{by}\isamarkupfalse%
\ blast\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -1489,10 +1489,10 @@
If you want to remember intermediate fact(s) that cannot be
named directly, use \isakeyword{note}. For example the result of raw
proof block can be named by following it with
-\isakeyword{note}~\isa{some{\isacharunderscore}name\ {\isacharequal}\ this}. As a side effect,
+\isakeyword{note}~\isa{some{\isaliteral{5F}{\isacharunderscore}}name\ {\isaliteral{3D}{\isacharequal}}\ this}. As a side effect,
\isa{this} is set to the list of facts on the right-hand side. You
-can also say \isa{note\ some{\isacharunderscore}fact}, which simply sets \isa{this},
-i.e.\ recalls \isa{some{\isacharunderscore}fact}, e.g.\ in a \isakeyword{moreover} sequence.%
+can also say \isa{note\ some{\isaliteral{5F}{\isacharunderscore}}fact}, which simply sets \isa{this},
+i.e.\ recalls \isa{some{\isaliteral{5F}{\isacharunderscore}}fact}, e.g.\ in a \isakeyword{moreover} sequence.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -1504,11 +1504,11 @@
Sometimes it is necessary to decorate a proposition with type
constraints, as in Cantor's theorem above. These type constraints tend
to make the theorem less readable. The situation can be improved a
-little by combining the type constraint with an outer \isa{{\isasymAnd}}:%
+little by combining the type constraint with an outer \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymAnd}f\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ set{\isachardot}\ {\isasymexists}S{\isachardot}\ S\ {\isasymnotin}\ range\ f{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C416E643E}{\isasymAnd}}f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}S{\isaliteral{2E}{\isachardot}}\ S\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ range\ f{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -1529,7 +1529,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ \isakeyword{fixes}\ f\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ set{\isachardoublequoteclose}\ \isakeyword{shows}\ {\isachardoublequoteopen}{\isasymexists}S{\isachardot}\ S\ {\isasymnotin}\ range\ f{\isachardoublequoteclose}%
+\ \isakeyword{fixes}\ f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}S{\isaliteral{2E}{\isachardot}}\ S\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ range\ f{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -1549,12 +1549,12 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ comm{\isacharunderscore}mono{\isacharcolon}\isanewline
-\ \ \isakeyword{fixes}\ r\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{infix}\ {\isachardoublequoteopen}{\isachargreater}{\isachardoublequoteclose}\ {\isadigit{6}}{\isadigit{0}}{\isacharparenright}\ \isakeyword{and}\isanewline
-\ \ \ \ \ \ \ f\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isacharplus}{\isacharplus}{\isachardoublequoteclose}\ {\isadigit{7}}{\isadigit{0}}{\isacharparenright}\isanewline
-\ \ \isakeyword{assumes}\ comm{\isacharcolon}\ {\isachardoublequoteopen}{\isasymAnd}x\ y{\isacharcolon}{\isacharcolon}{\isacharprime}a{\isachardot}\ x\ {\isacharplus}{\isacharplus}\ y\ {\isacharequal}\ y\ {\isacharplus}{\isacharplus}\ x{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-\ \ \ \ \ \ \ \ \ \ mono{\isacharcolon}\ {\isachardoublequoteopen}{\isasymAnd}x\ y\ z{\isacharcolon}{\isacharcolon}{\isacharprime}a{\isachardot}\ x\ {\isachargreater}\ y\ {\isasymLongrightarrow}\ x\ {\isacharplus}{\isacharplus}\ z\ {\isachargreater}\ y\ {\isacharplus}{\isacharplus}\ z{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{shows}\ {\isachardoublequoteopen}x\ {\isachargreater}\ y\ {\isasymLongrightarrow}\ z\ {\isacharplus}{\isacharplus}\ x\ {\isachargreater}\ z\ {\isacharplus}{\isacharplus}\ y{\isachardoublequoteclose}\isanewline
+\ comm{\isaliteral{5F}{\isacharunderscore}}mono{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \isakeyword{fixes}\ r\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infix}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3E}{\isachargreater}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{6}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ \isakeyword{and}\isanewline
+\ \ \ \ \ \ \ f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{7}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \isakeyword{assumes}\ comm{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{2B}{\isacharplus}}{\isaliteral{2B}{\isacharplus}}\ y\ {\isaliteral{3D}{\isacharequal}}\ y\ {\isaliteral{2B}{\isacharplus}}{\isaliteral{2B}{\isacharplus}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+\ \ \ \ \ \ \ \ \ \ mono{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y\ z{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3E}{\isachargreater}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{2B}{\isacharplus}}{\isaliteral{2B}{\isacharplus}}\ z\ {\isaliteral{3E}{\isachargreater}}\ y\ {\isaliteral{2B}{\isacharplus}}{\isaliteral{2B}{\isacharplus}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3E}{\isachargreater}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ z\ {\isaliteral{2B}{\isacharplus}}{\isaliteral{2B}{\isacharplus}}\ x\ {\isaliteral{3E}{\isachargreater}}\ z\ {\isaliteral{2B}{\isacharplus}}{\isaliteral{2B}{\isacharplus}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1562,7 +1562,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-{\isacharparenleft}simp\ add{\isacharcolon}\ comm\ mono{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ comm\ mono{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1573,9 +1573,9 @@
\begin{isamarkuptext}%
\noindent The concrete syntax is dropped at the end of the proof and the
theorem becomes \begin{isabelle}%
-{\isasymlbrakk}{\isasymAnd}x\ y{\isachardot}\ {\isacharquery}f\ x\ y\ {\isacharequal}\ {\isacharquery}f\ y\ x{\isacharsemicolon}\isanewline
-\isaindent{\ }{\isasymAnd}x\ y\ z{\isachardot}\ {\isacharquery}r\ x\ y\ {\isasymLongrightarrow}\ {\isacharquery}r\ {\isacharparenleft}{\isacharquery}f\ x\ z{\isacharparenright}\ {\isacharparenleft}{\isacharquery}f\ y\ z{\isacharparenright}{\isacharsemicolon}\ {\isacharquery}r\ {\isacharquery}x\ {\isacharquery}y{\isasymrbrakk}\isanewline
-{\isasymLongrightarrow}\ {\isacharquery}r\ {\isacharparenleft}{\isacharquery}f\ {\isacharquery}z\ {\isacharquery}x{\isacharparenright}\ {\isacharparenleft}{\isacharquery}f\ {\isacharquery}z\ {\isacharquery}y{\isacharparenright}%
+{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}f\ x\ y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}f\ y\ x{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ }{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y\ z{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}r\ x\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}r\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}f\ x\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}f\ y\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{3F}{\isacharquery}}r\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{3F}{\isacharquery}}y{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}r\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}f\ {\isaliteral{3F}{\isacharquery}}z\ {\isaliteral{3F}{\isacharquery}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}f\ {\isaliteral{3F}{\isacharquery}}z\ {\isaliteral{3F}{\isacharquery}}y{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\tweakskip%
\end{isamarkuptext}%
@@ -1591,7 +1591,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ \isakeyword{assumes}\ A{\isacharcolon}\ {\isachardoublequoteopen}{\isasymexists}x\ y{\isachardot}\ P\ x\ y\ {\isasymand}\ Q\ x\ y{\isachardoublequoteclose}\ \isakeyword{shows}\ {\isachardoublequoteopen}R{\isachardoublequoteclose}\isanewline
+\ \isakeyword{assumes}\ A{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x\ y{\isaliteral{2E}{\isachardot}}\ P\ x\ y\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}R{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1599,10 +1599,10 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ A\ \isacommand{obtain}\isamarkupfalse%
-\ x\ y\ \isakeyword{where}\ P{\isacharcolon}\ {\isachardoublequoteopen}P\ x\ y{\isachardoublequoteclose}\ \isakeyword{and}\ Q{\isacharcolon}\ {\isachardoublequoteopen}Q\ x\ y{\isachardoublequoteclose}\ \ \isacommand{by}\isamarkupfalse%
+\ x\ y\ \isakeyword{where}\ P{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}P\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ Q{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}Q\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \ \isacommand{by}\isamarkupfalse%
\ blast%
\endisatagproof
{\isafoldproof}%
@@ -1613,7 +1613,7 @@
%
\begin{isamarkuptext}%
Remember also that one does not even need to start with a formula
-containing \isa{{\isasymexists}} as we saw in the proof of Cantor's theorem.%
+containing \isa{{\isaliteral{5C3C6578697374733E}{\isasymexists}}} as we saw in the proof of Cantor's theorem.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -1627,7 +1627,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymlongrightarrow}\ {\isacharparenleft}A\ {\isasymlongrightarrow}\ B{\isacharparenright}\ {\isasymlongrightarrow}\ B{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1637,15 +1637,15 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ a{\isacharcolon}\ {\isachardoublequoteopen}A{\isachardoublequoteclose}\isanewline
+\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}A\ {\isasymlongrightarrow}B{\isacharparenright}\ {\isasymlongrightarrow}\ B{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ impI{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule\ impI{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}erule\ impE{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}erule\ impE{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ a{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule\ a{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{apply}\isamarkupfalse%
\ assumption\isanewline
\ \ \ \ \isacommand{done}\isamarkupfalse%
--- a/doc-src/IsarRef/Thy/document/Document_Preparation.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarRef/Thy/document/Document_Preparation.tex Mon Nov 08 14:41:11 2010 +0100
@@ -1,6 +1,6 @@
%
\begin{isabellebody}%
-\def\isabellecontext{Document{\isacharunderscore}Preparation}%
+\def\isabellecontext{Document{\isaliteral{5F}{\isacharunderscore}}Preparation}%
%
\isadelimtheory
%
@@ -8,7 +8,7 @@
%
\isatagtheory
\isacommand{theory}\isamarkupfalse%
-\ Document{\isacharunderscore}Preparation\isanewline
+\ Document{\isaliteral{5F}{\isacharunderscore}}Preparation\isanewline
\isakeyword{imports}\ Main\isanewline
\isakeyword{begin}%
\endisatagtheory
@@ -77,25 +77,25 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{header}\hypertarget{command.header}{\hyperlink{command.header}{\mbox{\isa{\isacommand{header}}}}} & : & \isa{{\isachardoublequote}toplevel\ {\isasymrightarrow}\ toplevel{\isachardoublequote}} \\[0.5ex]
- \indexdef{}{command}{chapter}\hypertarget{command.chapter}{\hyperlink{command.chapter}{\mbox{\isa{\isacommand{chapter}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{section}\hypertarget{command.section}{\hyperlink{command.section}{\mbox{\isa{\isacommand{section}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{subsection}\hypertarget{command.subsection}{\hyperlink{command.subsection}{\mbox{\isa{\isacommand{subsection}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{subsubsection}\hypertarget{command.subsubsection}{\hyperlink{command.subsubsection}{\mbox{\isa{\isacommand{subsubsection}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{text}\hypertarget{command.text}{\hyperlink{command.text}{\mbox{\isa{\isacommand{text}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{text\_raw}\hypertarget{command.text-raw}{\hyperlink{command.text-raw}{\mbox{\isa{\isacommand{text{\isacharunderscore}raw}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\[0.5ex]
- \indexdef{}{command}{sect}\hypertarget{command.sect}{\hyperlink{command.sect}{\mbox{\isa{\isacommand{sect}}}}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}\ proof{\isachardoublequote}} \\
- \indexdef{}{command}{subsect}\hypertarget{command.subsect}{\hyperlink{command.subsect}{\mbox{\isa{\isacommand{subsect}}}}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}\ proof{\isachardoublequote}} \\
- \indexdef{}{command}{subsubsect}\hypertarget{command.subsubsect}{\hyperlink{command.subsubsect}{\mbox{\isa{\isacommand{subsubsect}}}}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}\ proof{\isachardoublequote}} \\
- \indexdef{}{command}{txt}\hypertarget{command.txt}{\hyperlink{command.txt}{\mbox{\isa{\isacommand{txt}}}}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}\ proof{\isachardoublequote}} \\
- \indexdef{}{command}{txt\_raw}\hypertarget{command.txt-raw}{\hyperlink{command.txt-raw}{\mbox{\isa{\isacommand{txt{\isacharunderscore}raw}}}}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}\ proof{\isachardoublequote}} \\
+ \indexdef{}{command}{header}\hypertarget{command.header}{\hyperlink{command.header}{\mbox{\isa{\isacommand{header}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}toplevel\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ toplevel{\isaliteral{22}{\isachardoublequote}}} \\[0.5ex]
+ \indexdef{}{command}{chapter}\hypertarget{command.chapter}{\hyperlink{command.chapter}{\mbox{\isa{\isacommand{chapter}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{section}\hypertarget{command.section}{\hyperlink{command.section}{\mbox{\isa{\isacommand{section}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{subsection}\hypertarget{command.subsection}{\hyperlink{command.subsection}{\mbox{\isa{\isacommand{subsection}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{subsubsection}\hypertarget{command.subsubsection}{\hyperlink{command.subsubsection}{\mbox{\isa{\isacommand{subsubsection}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{text}\hypertarget{command.text}{\hyperlink{command.text}{\mbox{\isa{\isacommand{text}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{text\_raw}\hypertarget{command.text-raw}{\hyperlink{command.text-raw}{\mbox{\isa{\isacommand{text{\isaliteral{5F}{\isacharunderscore}}raw}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\[0.5ex]
+ \indexdef{}{command}{sect}\hypertarget{command.sect}{\hyperlink{command.sect}{\mbox{\isa{\isacommand{sect}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{subsect}\hypertarget{command.subsect}{\hyperlink{command.subsect}{\mbox{\isa{\isacommand{subsect}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{subsubsect}\hypertarget{command.subsubsect}{\hyperlink{command.subsubsect}{\mbox{\isa{\isacommand{subsubsect}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{txt}\hypertarget{command.txt}{\hyperlink{command.txt}{\mbox{\isa{\isacommand{txt}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{txt\_raw}\hypertarget{command.txt-raw}{\hyperlink{command.txt-raw}{\mbox{\isa{\isacommand{txt{\isaliteral{5F}{\isacharunderscore}}raw}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
Markup commands provide a structured way to insert text into the
document generated from a theory. Each markup command takes a
single \hyperlink{syntax.text}{\mbox{\isa{text}}} argument, which is passed as argument to a
corresponding {\LaTeX} macro. The default macros provided by
- \hyperlink{file.~~/lib/texinputs/isabelle.sty}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}lib{\isacharslash}texinputs{\isacharslash}isabelle{\isachardot}sty}}}} can be redefined according
+ \hyperlink{file.~~/lib/texinputs/isabelle.sty}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}lib{\isaliteral{2F}{\isacharslash}}texinputs{\isaliteral{2F}{\isacharslash}}isabelle{\isaliteral{2E}{\isachardot}}sty}}}} can be redefined according
to the needs of the underlying document and {\LaTeX} styles.
Note that formal comments (\secref{sec:comments}) are similar to
@@ -126,20 +126,20 @@
macros are \verb|\isamarkupsect|, \verb|\isamarkupsubsect| etc.
\item \hyperlink{command.text}{\mbox{\isa{\isacommand{text}}}} and \hyperlink{command.txt}{\mbox{\isa{\isacommand{txt}}}} specify paragraphs of plain
- text. This corresponds to a {\LaTeX} environment \verb|\begin{isamarkuptext}| \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} \verb|\end{isamarkuptext}| etc.
+ text. This corresponds to a {\LaTeX} environment \verb|\begin{isamarkuptext}| \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \verb|\end{isamarkuptext}| etc.
- \item \hyperlink{command.text-raw}{\mbox{\isa{\isacommand{text{\isacharunderscore}raw}}}} and \hyperlink{command.txt-raw}{\mbox{\isa{\isacommand{txt{\isacharunderscore}raw}}}} insert {\LaTeX}
+ \item \hyperlink{command.text-raw}{\mbox{\isa{\isacommand{text{\isaliteral{5F}{\isacharunderscore}}raw}}}} and \hyperlink{command.txt-raw}{\mbox{\isa{\isacommand{txt{\isaliteral{5F}{\isacharunderscore}}raw}}}} insert {\LaTeX}
source into the output, without additional markup. Thus the full
range of document manipulations becomes available, at the risk of
messing up document output.
\end{description}
- Except for \hyperlink{command.text-raw}{\mbox{\isa{\isacommand{text{\isacharunderscore}raw}}}} and \hyperlink{command.txt-raw}{\mbox{\isa{\isacommand{txt{\isacharunderscore}raw}}}}, the text
+ Except for \hyperlink{command.text-raw}{\mbox{\isa{\isacommand{text{\isaliteral{5F}{\isacharunderscore}}raw}}}} and \hyperlink{command.txt-raw}{\mbox{\isa{\isacommand{txt{\isaliteral{5F}{\isacharunderscore}}raw}}}}, the text
passed to any of the above markup commands may refer to formal
entities via \emph{document antiquotations}, see also
\secref{sec:antiq}. These are interpreted in the present theory or
- proof context, or the named \isa{{\isachardoublequote}target{\isachardoublequote}}.
+ proof context, or the named \isa{{\isaliteral{22}{\isachardoublequote}}target{\isaliteral{22}{\isachardoublequote}}}.
\medskip The proof markup commands closely resemble those for theory
specifications, but have a different formal status and produce
@@ -159,7 +159,7 @@
\indexdef{}{antiquotation}{lemma}\hypertarget{antiquotation.lemma}{\hyperlink{antiquotation.lemma}{\mbox{\isa{lemma}}}} & : & \isa{antiquotation} \\
\indexdef{}{antiquotation}{prop}\hypertarget{antiquotation.prop}{\hyperlink{antiquotation.prop}{\mbox{\isa{prop}}}} & : & \isa{antiquotation} \\
\indexdef{}{antiquotation}{term}\hypertarget{antiquotation.term}{\hyperlink{antiquotation.term}{\mbox{\isa{term}}}} & : & \isa{antiquotation} \\
- \indexdef{}{antiquotation}{term\_type}\hypertarget{antiquotation.term-type}{\hyperlink{antiquotation.term-type}{\mbox{\isa{term{\isacharunderscore}type}}}} & : & \isa{antiquotation} \\
+ \indexdef{}{antiquotation}{term\_type}\hypertarget{antiquotation.term-type}{\hyperlink{antiquotation.term-type}{\mbox{\isa{term{\isaliteral{5F}{\isacharunderscore}}type}}}} & : & \isa{antiquotation} \\
\indexdef{}{antiquotation}{typeof}\hypertarget{antiquotation.typeof}{\hyperlink{antiquotation.typeof}{\mbox{\isa{typeof}}}} & : & \isa{antiquotation} \\
\indexdef{}{antiquotation}{const}\hypertarget{antiquotation.const}{\hyperlink{antiquotation.const}{\mbox{\isa{const}}}} & : & \isa{antiquotation} \\
\indexdef{}{antiquotation}{abbrev}\hypertarget{antiquotation.abbrev}{\hyperlink{antiquotation.abbrev}{\mbox{\isa{abbrev}}}} & : & \isa{antiquotation} \\
@@ -170,10 +170,10 @@
\indexdef{}{antiquotation}{goals}\hypertarget{antiquotation.goals}{\hyperlink{antiquotation.goals}{\mbox{\isa{goals}}}} & : & \isa{antiquotation} \\
\indexdef{}{antiquotation}{subgoals}\hypertarget{antiquotation.subgoals}{\hyperlink{antiquotation.subgoals}{\mbox{\isa{subgoals}}}} & : & \isa{antiquotation} \\
\indexdef{}{antiquotation}{prf}\hypertarget{antiquotation.prf}{\hyperlink{antiquotation.prf}{\mbox{\isa{prf}}}} & : & \isa{antiquotation} \\
- \indexdef{}{antiquotation}{full\_prf}\hypertarget{antiquotation.full-prf}{\hyperlink{antiquotation.full-prf}{\mbox{\isa{full{\isacharunderscore}prf}}}} & : & \isa{antiquotation} \\
+ \indexdef{}{antiquotation}{full\_prf}\hypertarget{antiquotation.full-prf}{\hyperlink{antiquotation.full-prf}{\mbox{\isa{full{\isaliteral{5F}{\isacharunderscore}}prf}}}} & : & \isa{antiquotation} \\
\indexdef{}{antiquotation}{ML}\hypertarget{antiquotation.ML}{\hyperlink{antiquotation.ML}{\mbox{\isa{ML}}}} & : & \isa{antiquotation} \\
- \indexdef{}{antiquotation}{ML\_type}\hypertarget{antiquotation.ML-type}{\hyperlink{antiquotation.ML-type}{\mbox{\isa{ML{\isacharunderscore}type}}}} & : & \isa{antiquotation} \\
- \indexdef{}{antiquotation}{ML\_struct}\hypertarget{antiquotation.ML-struct}{\hyperlink{antiquotation.ML-struct}{\mbox{\isa{ML{\isacharunderscore}struct}}}} & : & \isa{antiquotation} \\
+ \indexdef{}{antiquotation}{ML\_type}\hypertarget{antiquotation.ML-type}{\hyperlink{antiquotation.ML-type}{\mbox{\isa{ML{\isaliteral{5F}{\isacharunderscore}}type}}}} & : & \isa{antiquotation} \\
+ \indexdef{}{antiquotation}{ML\_struct}\hypertarget{antiquotation.ML-struct}{\hyperlink{antiquotation.ML-struct}{\mbox{\isa{ML{\isaliteral{5F}{\isacharunderscore}}struct}}}} & : & \isa{antiquotation} \\
\end{matharray}
The overall content of an Isabelle/Isar theory may alternate between
@@ -184,7 +184,7 @@
in the resulting document, but may again refer to formal entities
via \emph{document antiquotations}.
- For example, embedding of ``\isa{{\isacharat}{\isacharbraceleft}term\ {\isacharbrackleft}show{\isacharunderscore}types{\isacharbrackright}\ {\isachardoublequote}f\ x\ {\isacharequal}\ a\ {\isacharplus}\ x{\isachardoublequote}{\isacharbraceright}}''
+ For example, embedding of ``\isa{{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}term\ {\isaliteral{5B}{\isacharbrackleft}}show{\isaliteral{5F}{\isacharunderscore}}types{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{22}{\isachardoublequote}}f\ x\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{2B}{\isacharplus}}\ x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7D}{\isacharbraceright}}}''
within a text block makes
\isa{{\isacharparenleft}f{\isasymColon}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}\ {\isacharparenleft}x{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}a{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isacharplus}\ x} appear in the final {\LaTeX} document.
@@ -232,51 +232,51 @@
\end{rail}
Note that the syntax of antiquotations may \emph{not} include source
- comments \verb|(*|~\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}~\verb|*)| nor verbatim
- text \verb|{|\verb|*|~\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}~\verb|*|\verb|}|.
+ comments \verb|(*|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}~\verb|*)| nor verbatim
+ text \verb|{|\verb|*|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}~\verb|*|\verb|}|.
\begin{description}
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}theory\ A{\isacharbraceright}{\isachardoublequote}} prints the name \isa{{\isachardoublequote}A{\isachardoublequote}}, which is
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}theory\ A{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} prints the name \isa{{\isaliteral{22}{\isachardoublequote}}A{\isaliteral{22}{\isachardoublequote}}}, which is
guaranteed to refer to a valid ancestor theory in the current
context.
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}thm\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharbraceright}{\isachardoublequote}} prints theorems \isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}.
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}thm\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} prints theorems \isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}.
Full fact expressions are allowed here, including attributes
(\secref{sec:syn-att}).
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}prop\ {\isasymphi}{\isacharbraceright}{\isachardoublequote}} prints a well-typed proposition \isa{{\isachardoublequote}{\isasymphi}{\isachardoublequote}}.
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}prop\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} prints a well-typed proposition \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}}.
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}lemma\ {\isasymphi}\ by\ m{\isacharbraceright}{\isachardoublequote}} proves a well-typed proposition
- \isa{{\isachardoublequote}{\isasymphi}{\isachardoublequote}} by method \isa{m} and prints the original \isa{{\isachardoublequote}{\isasymphi}{\isachardoublequote}}.
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}lemma\ {\isaliteral{5C3C7068693E}{\isasymphi}}\ by\ m{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} proves a well-typed proposition
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} by method \isa{m} and prints the original \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}}.
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}term\ t{\isacharbraceright}{\isachardoublequote}} prints a well-typed term \isa{{\isachardoublequote}t{\isachardoublequote}}.
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}term\ t{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} prints a well-typed term \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{22}{\isachardoublequote}}}.
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}term{\isacharunderscore}type\ t{\isacharbraceright}{\isachardoublequote}} prints a well-typed term \isa{{\isachardoublequote}t{\isachardoublequote}}
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}term{\isaliteral{5F}{\isacharunderscore}}type\ t{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} prints a well-typed term \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{22}{\isachardoublequote}}}
annotated with its type.
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}typeof\ t{\isacharbraceright}{\isachardoublequote}} prints the type of a well-typed term
- \isa{{\isachardoublequote}t{\isachardoublequote}}.
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}typeof\ t{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} prints the type of a well-typed term
+ \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{22}{\isachardoublequote}}}.
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}const\ c{\isacharbraceright}{\isachardoublequote}} prints a logical or syntactic constant
- \isa{{\isachardoublequote}c{\isachardoublequote}}.
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}const\ c{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} prints a logical or syntactic constant
+ \isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{22}{\isachardoublequote}}}.
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}abbrev\ c\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n{\isacharbraceright}{\isachardoublequote}} prints a constant abbreviation
- \isa{{\isachardoublequote}c\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n\ {\isasymequiv}\ rhs{\isachardoublequote}} as defined in the current context.
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}abbrev\ c\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} prints a constant abbreviation
+ \isa{{\isaliteral{22}{\isachardoublequote}}c\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ rhs{\isaliteral{22}{\isachardoublequote}}} as defined in the current context.
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}typ\ {\isasymtau}{\isacharbraceright}{\isachardoublequote}} prints a well-formed type \isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}}.
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}typ\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} prints a well-formed type \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}}.
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}type\ {\isasymkappa}{\isacharbraceright}{\isachardoublequote}} prints a (logical or syntactic) type
- constructor \isa{{\isachardoublequote}{\isasymkappa}{\isachardoublequote}}.
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}type\ {\isaliteral{5C3C6B617070613E}{\isasymkappa}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} prints a (logical or syntactic) type
+ constructor \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6B617070613E}{\isasymkappa}}{\isaliteral{22}{\isachardoublequote}}}.
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}class\ c{\isacharbraceright}{\isachardoublequote}} prints a class \isa{c}.
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}class\ c{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} prints a class \isa{c}.
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}text\ s{\isacharbraceright}{\isachardoublequote}} prints uninterpreted source text \isa{s}. This is particularly useful to print portions of text according
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}text\ s{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} prints uninterpreted source text \isa{s}. This is particularly useful to print portions of text according
to the Isabelle document style, without demanding well-formedness,
e.g.\ small pieces of terms that should not be parsed or
type-checked yet.
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}goals{\isacharbraceright}{\isachardoublequote}} prints the current \emph{dynamic} goal
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}goals{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} prints the current \emph{dynamic} goal
state. This is mainly for support of tactic-emulation scripts
within Isar. Presentation of goal states does not conform to the
idea of human-readable proof documents!
@@ -285,19 +285,19 @@
the reasoning via proper Isar proof commands, instead of peeking at
the internal machine configuration.
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}subgoals{\isacharbraceright}{\isachardoublequote}} is similar to \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}goals{\isacharbraceright}{\isachardoublequote}}, but
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}subgoals{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} is similar to \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}goals{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}}, but
does not print the main goal.
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}prf\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharbraceright}{\isachardoublequote}} prints the (compact) proof terms
- corresponding to the theorems \isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}. Note that this
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}prf\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} prints the (compact) proof terms
+ corresponding to the theorems \isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}. Note that this
requires proof terms to be switched on for the current logic
session.
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}full{\isacharunderscore}prf\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharbraceright}{\isachardoublequote}} is like \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}prf\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharbraceright}{\isachardoublequote}}, but prints the full proof terms, i.e.\ also displays
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}full{\isaliteral{5F}{\isacharunderscore}}prf\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} is like \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}prf\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}}, but prints the full proof terms, i.e.\ also displays
information omitted in the compact proof term, which is denoted by
- ``\isa{{\isacharunderscore}}'' placeholders there.
+ ``\isa{{\isaliteral{5F}{\isacharunderscore}}}'' placeholders there.
- \item \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}ML\ s{\isacharbraceright}{\isachardoublequote}}, \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}ML{\isacharunderscore}type\ s{\isacharbraceright}{\isachardoublequote}}, and \isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}ML{\isacharunderscore}struct\ s{\isacharbraceright}{\isachardoublequote}} check text \isa{s} as ML value, type, and
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}ML\ s{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}ML{\isaliteral{5F}{\isacharunderscore}}type\ s{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}}, and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}ML{\isaliteral{5F}{\isacharunderscore}}struct\ s{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} check text \isa{s} as ML value, type, and
structure, respectively. The source is printed verbatim.
\end{description}%
@@ -323,12 +323,12 @@
\item \isa{rhs} is like \isa{lhs}, but extracts the second
argument.
- \item \isa{{\isachardoublequote}concl{\isachardoublequote}} extracts the conclusion \isa{C} from a rule
- in Horn-clause normal form \isa{{\isachardoublequote}A\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ A\isactrlsub n\ {\isasymLongrightarrow}\ C{\isachardoublequote}}.
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}concl{\isaliteral{22}{\isachardoublequote}}} extracts the conclusion \isa{C} from a rule
+ in Horn-clause normal form \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ A\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{22}{\isachardoublequote}}}.
- \item \isa{{\isachardoublequote}prem{\isachardoublequote}} \isa{n} extract premise number
- \isa{{\isachardoublequote}n{\isachardoublequote}} from from a rule in Horn-clause
- normal form \isa{{\isachardoublequote}A\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ A\isactrlsub n\ {\isasymLongrightarrow}\ C{\isachardoublequote}}
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}prem{\isaliteral{22}{\isachardoublequote}}} \isa{n} extract premise number
+ \isa{{\isaliteral{22}{\isachardoublequote}}n{\isaliteral{22}{\isachardoublequote}}} from from a rule in Horn-clause
+ normal form \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ A\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{22}{\isachardoublequote}}}
\end{description}%
\end{isamarkuptext}%
@@ -345,31 +345,31 @@
\begin{description}
- \item \indexdef{}{antiquotation option}{show\_types}\hypertarget{antiquotation option.show-types}{\hyperlink{antiquotation option.show-types}{\mbox{\isa{show{\isacharunderscore}types}}}}~\isa{{\isachardoublequote}{\isacharequal}\ bool{\isachardoublequote}} and
- \indexdef{}{antiquotation option}{show\_sorts}\hypertarget{antiquotation option.show-sorts}{\hyperlink{antiquotation option.show-sorts}{\mbox{\isa{show{\isacharunderscore}sorts}}}}~\isa{{\isachardoublequote}{\isacharequal}\ bool{\isachardoublequote}} control
+ \item \indexdef{}{antiquotation option}{show\_types}\hypertarget{antiquotation option.show-types}{\hyperlink{antiquotation option.show-types}{\mbox{\isa{show{\isaliteral{5F}{\isacharunderscore}}types}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}\ bool{\isaliteral{22}{\isachardoublequote}}} and
+ \indexdef{}{antiquotation option}{show\_sorts}\hypertarget{antiquotation option.show-sorts}{\hyperlink{antiquotation option.show-sorts}{\mbox{\isa{show{\isaliteral{5F}{\isacharunderscore}}sorts}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}\ bool{\isaliteral{22}{\isachardoublequote}}} control
printing of explicit type and sort constraints.
- \item \indexdef{}{antiquotation option}{show\_structs}\hypertarget{antiquotation option.show-structs}{\hyperlink{antiquotation option.show-structs}{\mbox{\isa{show{\isacharunderscore}structs}}}}~\isa{{\isachardoublequote}{\isacharequal}\ bool{\isachardoublequote}}
+ \item \indexdef{}{antiquotation option}{show\_structs}\hypertarget{antiquotation option.show-structs}{\hyperlink{antiquotation option.show-structs}{\mbox{\isa{show{\isaliteral{5F}{\isacharunderscore}}structs}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}\ bool{\isaliteral{22}{\isachardoublequote}}}
controls printing of implicit structures.
- \item \indexdef{}{antiquotation option}{long\_names}\hypertarget{antiquotation option.long-names}{\hyperlink{antiquotation option.long-names}{\mbox{\isa{long{\isacharunderscore}names}}}}~\isa{{\isachardoublequote}{\isacharequal}\ bool{\isachardoublequote}} forces
+ \item \indexdef{}{antiquotation option}{long\_names}\hypertarget{antiquotation option.long-names}{\hyperlink{antiquotation option.long-names}{\mbox{\isa{long{\isaliteral{5F}{\isacharunderscore}}names}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}\ bool{\isaliteral{22}{\isachardoublequote}}} forces
names of types and constants etc.\ to be printed in their fully
qualified internal form.
- \item \indexdef{}{antiquotation option}{short\_names}\hypertarget{antiquotation option.short-names}{\hyperlink{antiquotation option.short-names}{\mbox{\isa{short{\isacharunderscore}names}}}}~\isa{{\isachardoublequote}{\isacharequal}\ bool{\isachardoublequote}}
+ \item \indexdef{}{antiquotation option}{short\_names}\hypertarget{antiquotation option.short-names}{\hyperlink{antiquotation option.short-names}{\mbox{\isa{short{\isaliteral{5F}{\isacharunderscore}}names}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}\ bool{\isaliteral{22}{\isachardoublequote}}}
forces names of types and constants etc.\ to be printed unqualified.
Note that internalizing the output again in the current context may
well yield a different result.
- \item \indexdef{}{antiquotation option}{unique\_names}\hypertarget{antiquotation option.unique-names}{\hyperlink{antiquotation option.unique-names}{\mbox{\isa{unique{\isacharunderscore}names}}}}~\isa{{\isachardoublequote}{\isacharequal}\ bool{\isachardoublequote}}
+ \item \indexdef{}{antiquotation option}{unique\_names}\hypertarget{antiquotation option.unique-names}{\hyperlink{antiquotation option.unique-names}{\mbox{\isa{unique{\isaliteral{5F}{\isacharunderscore}}names}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}\ bool{\isaliteral{22}{\isachardoublequote}}}
determines whether the printed version of qualified names should be
made sufficiently long to avoid overlap with names declared further
back. Set to \isa{false} for more concise output.
- \item \indexdef{}{antiquotation option}{eta\_contract}\hypertarget{antiquotation option.eta-contract}{\hyperlink{antiquotation option.eta-contract}{\mbox{\isa{eta{\isacharunderscore}contract}}}}~\isa{{\isachardoublequote}{\isacharequal}\ bool{\isachardoublequote}}
- prints terms in \isa{{\isasymeta}}-contracted form.
+ \item \indexdef{}{antiquotation option}{eta\_contract}\hypertarget{antiquotation option.eta-contract}{\hyperlink{antiquotation option.eta-contract}{\mbox{\isa{eta{\isaliteral{5F}{\isacharunderscore}}contract}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}\ bool{\isaliteral{22}{\isachardoublequote}}}
+ prints terms in \isa{{\isaliteral{5C3C6574613E}{\isasymeta}}}-contracted form.
- \item \indexdef{}{antiquotation option}{display}\hypertarget{antiquotation option.display}{\hyperlink{antiquotation option.display}{\mbox{\isa{display}}}}~\isa{{\isachardoublequote}{\isacharequal}\ bool{\isachardoublequote}} indicates
+ \item \indexdef{}{antiquotation option}{display}\hypertarget{antiquotation option.display}{\hyperlink{antiquotation option.display}{\mbox{\isa{display}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}\ bool{\isaliteral{22}{\isachardoublequote}}} indicates
if the text is to be output as multi-line ``display material'',
rather than a small piece of text without line breaks (which is the
default).
@@ -377,45 +377,45 @@
In this mode the embedded entities are printed in the same style as
the main theory text.
- \item \indexdef{}{antiquotation option}{break}\hypertarget{antiquotation option.break}{\hyperlink{antiquotation option.break}{\mbox{\isa{break}}}}~\isa{{\isachardoublequote}{\isacharequal}\ bool{\isachardoublequote}} controls
+ \item \indexdef{}{antiquotation option}{break}\hypertarget{antiquotation option.break}{\hyperlink{antiquotation option.break}{\mbox{\isa{break}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}\ bool{\isaliteral{22}{\isachardoublequote}}} controls
line breaks in non-display material.
- \item \indexdef{}{antiquotation option}{quotes}\hypertarget{antiquotation option.quotes}{\hyperlink{antiquotation option.quotes}{\mbox{\isa{quotes}}}}~\isa{{\isachardoublequote}{\isacharequal}\ bool{\isachardoublequote}} indicates
+ \item \indexdef{}{antiquotation option}{quotes}\hypertarget{antiquotation option.quotes}{\hyperlink{antiquotation option.quotes}{\mbox{\isa{quotes}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}\ bool{\isaliteral{22}{\isachardoublequote}}} indicates
if the output should be enclosed in double quotes.
- \item \indexdef{}{antiquotation option}{mode}\hypertarget{antiquotation option.mode}{\hyperlink{antiquotation option.mode}{\mbox{\isa{mode}}}}~\isa{{\isachardoublequote}{\isacharequal}\ name{\isachardoublequote}} adds \isa{name} to the print mode to be used for presentation. Note that the
+ \item \indexdef{}{antiquotation option}{mode}\hypertarget{antiquotation option.mode}{\hyperlink{antiquotation option.mode}{\mbox{\isa{mode}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}\ name{\isaliteral{22}{\isachardoublequote}}} adds \isa{name} to the print mode to be used for presentation. Note that the
standard setup for {\LaTeX} output is already present by default,
including the modes \isa{latex} and \isa{xsymbols}.
- \item \indexdef{}{antiquotation option}{margin}\hypertarget{antiquotation option.margin}{\hyperlink{antiquotation option.margin}{\mbox{\isa{margin}}}}~\isa{{\isachardoublequote}{\isacharequal}\ nat{\isachardoublequote}} and
- \indexdef{}{antiquotation option}{indent}\hypertarget{antiquotation option.indent}{\hyperlink{antiquotation option.indent}{\mbox{\isa{indent}}}}~\isa{{\isachardoublequote}{\isacharequal}\ nat{\isachardoublequote}} change the margin
+ \item \indexdef{}{antiquotation option}{margin}\hypertarget{antiquotation option.margin}{\hyperlink{antiquotation option.margin}{\mbox{\isa{margin}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}\ nat{\isaliteral{22}{\isachardoublequote}}} and
+ \indexdef{}{antiquotation option}{indent}\hypertarget{antiquotation option.indent}{\hyperlink{antiquotation option.indent}{\mbox{\isa{indent}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}\ nat{\isaliteral{22}{\isachardoublequote}}} change the margin
or indentation for pretty printing of display material.
- \item \indexdef{}{antiquotation option}{goals\_limit}\hypertarget{antiquotation option.goals-limit}{\hyperlink{antiquotation option.goals-limit}{\mbox{\isa{goals{\isacharunderscore}limit}}}}~\isa{{\isachardoublequote}{\isacharequal}\ nat{\isachardoublequote}}
+ \item \indexdef{}{antiquotation option}{goals\_limit}\hypertarget{antiquotation option.goals-limit}{\hyperlink{antiquotation option.goals-limit}{\mbox{\isa{goals{\isaliteral{5F}{\isacharunderscore}}limit}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}\ nat{\isaliteral{22}{\isachardoublequote}}}
determines the maximum number of goals to be printed (for goal-based
antiquotation).
- \item \indexdef{}{antiquotation option}{source}\hypertarget{antiquotation option.source}{\hyperlink{antiquotation option.source}{\mbox{\isa{source}}}}~\isa{{\isachardoublequote}{\isacharequal}\ bool{\isachardoublequote}} prints the
+ \item \indexdef{}{antiquotation option}{source}\hypertarget{antiquotation option.source}{\hyperlink{antiquotation option.source}{\mbox{\isa{source}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}\ bool{\isaliteral{22}{\isachardoublequote}}} prints the
original source text of the antiquotation arguments, rather than its
internal representation. Note that formal checking of
\hyperlink{antiquotation.thm}{\mbox{\isa{thm}}}, \hyperlink{antiquotation.term}{\mbox{\isa{term}}}, etc. is still
enabled; use the \hyperlink{antiquotation.text}{\mbox{\isa{text}}} antiquotation for unchecked
output.
- Regular \isa{{\isachardoublequote}term{\isachardoublequote}} and \isa{{\isachardoublequote}typ{\isachardoublequote}} antiquotations with \isa{{\isachardoublequote}source\ {\isacharequal}\ false{\isachardoublequote}} involve a full round-trip from the original source
+ Regular \isa{{\isaliteral{22}{\isachardoublequote}}term{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}typ{\isaliteral{22}{\isachardoublequote}}} antiquotations with \isa{{\isaliteral{22}{\isachardoublequote}}source\ {\isaliteral{3D}{\isacharequal}}\ false{\isaliteral{22}{\isachardoublequote}}} involve a full round-trip from the original source
to an internalized logical entity back to a source form, according
to the syntax of the current context. Thus the printed output is
not under direct control of the author, it may even fluctuate a bit
as the underlying theory is changed later on.
- In contrast, \indexdef{}{antiquotation option}{source}\hypertarget{antiquotation option.source}{\hyperlink{antiquotation option.source}{\mbox{\isa{source}}}}~\isa{{\isachardoublequote}{\isacharequal}\ true{\isachardoublequote}}
+ In contrast, \indexdef{}{antiquotation option}{source}\hypertarget{antiquotation option.source}{\hyperlink{antiquotation option.source}{\mbox{\isa{source}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}\ true{\isaliteral{22}{\isachardoublequote}}}
admits direct printing of the given source text, with the desirable
well-formedness check in the background, but without modification of
the printed text.
\end{description}
- For boolean flags, ``\isa{{\isachardoublequote}name\ {\isacharequal}\ true{\isachardoublequote}}'' may be abbreviated as
+ For boolean flags, ``\isa{{\isaliteral{22}{\isachardoublequote}}name\ {\isaliteral{3D}{\isacharequal}}\ true{\isaliteral{22}{\isachardoublequote}}}'' may be abbreviated as
``\isa{name}''. All of the above flags are disabled by default,
unless changed from ML, say in the \verb|ROOT.ML| of the
logic session.%
@@ -443,9 +443,9 @@
\medskip
\begin{tabular}{ll}
- \isa{{\isachardoublequote}theory{\isachardoublequote}} & theory begin/end \\
- \isa{{\isachardoublequote}proof{\isachardoublequote}} & all proof commands \\
- \isa{{\isachardoublequote}ML{\isachardoublequote}} & all commands involving ML code \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}theory{\isaliteral{22}{\isachardoublequote}}} & theory begin/end \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{22}{\isachardoublequote}}} & all proof commands \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}ML{\isaliteral{22}{\isachardoublequote}}} & all commands involving ML code \\
\end{tabular}
\medskip The Isabelle document preparation system
@@ -453,20 +453,20 @@
specifically, e.g.\ to fold proof texts, or drop parts of the text
completely.
- For example ``\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isachardoublequote}{\isacharpercent}invisible\ auto{\isachardoublequote}}'' causes
+ For example ``\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{25}{\isacharpercent}}invisible\ auto{\isaliteral{22}{\isachardoublequote}}}'' causes
that piece of proof to be treated as \isa{invisible} instead of
- \isa{{\isachardoublequote}proof{\isachardoublequote}} (the default), which may be shown or hidden
- depending on the document setup. In contrast, ``\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isachardoublequote}{\isacharpercent}visible\ auto{\isachardoublequote}}'' forces this text to be shown
+ \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{22}{\isachardoublequote}}} (the default), which may be shown or hidden
+ depending on the document setup. In contrast, ``\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{25}{\isacharpercent}}visible\ auto{\isaliteral{22}{\isachardoublequote}}}'' forces this text to be shown
invariably.
Explicit tag specifications within a proof apply to all subsequent
- commands of the same level of nesting. For example, ``\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}{\isacharpercent}visible\ {\isasymdots}{\isachardoublequote}}~\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}'' forces the whole
+ commands of the same level of nesting. For example, ``\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{25}{\isacharpercent}}visible\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}'' forces the whole
sub-proof to be typeset as \isa{visible} (unless some of its parts
are tagged differently).
\medskip Command tags merely produce certain markup environments for
type-setting. The meaning of these is determined by {\LaTeX}
- macros, as defined in \hyperlink{file.~~/lib/texinputs/isabelle.sty}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}lib{\isacharslash}texinputs{\isacharslash}isabelle{\isachardot}sty}}}} or
+ macros, as defined in \hyperlink{file.~~/lib/texinputs/isabelle.sty}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}lib{\isaliteral{2F}{\isacharslash}}texinputs{\isaliteral{2F}{\isacharslash}}isabelle{\isaliteral{2E}{\isachardot}}sty}}}} or
by the document author. The Isabelle document preparation tools
also provide some high-level options to specify the meaning of
arbitrary tags to ``keep'', ``drop'', or ``fold'' the corresponding
@@ -482,8 +482,8 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{display\_drafts}\hypertarget{command.display-drafts}{\hyperlink{command.display-drafts}{\mbox{\isa{\isacommand{display{\isacharunderscore}drafts}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}any\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{print\_drafts}\hypertarget{command.print-drafts}{\hyperlink{command.print-drafts}{\mbox{\isa{\isacommand{print{\isacharunderscore}drafts}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}any\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{}{command}{display\_drafts}\hypertarget{command.display-drafts}{\hyperlink{command.display-drafts}{\mbox{\isa{\isacommand{display{\isaliteral{5F}{\isacharunderscore}}drafts}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}any\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_drafts}\hypertarget{command.print-drafts}{\hyperlink{command.print-drafts}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}drafts}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}any\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -493,7 +493,7 @@
\begin{description}
- \item \hyperlink{command.display-drafts}{\mbox{\isa{\isacommand{display{\isacharunderscore}drafts}}}}~\isa{paths} and \hyperlink{command.print-drafts}{\mbox{\isa{\isacommand{print{\isacharunderscore}drafts}}}}~\isa{paths} perform simple output of a given list
+ \item \hyperlink{command.display-drafts}{\mbox{\isa{\isacommand{display{\isaliteral{5F}{\isacharunderscore}}drafts}}}}~\isa{paths} and \hyperlink{command.print-drafts}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}drafts}}}}~\isa{paths} perform simple output of a given list
of raw source files. Only those symbols that do not require
additional {\LaTeX} packages are displayed properly, everything else
is left verbatim.
--- a/doc-src/IsarRef/Thy/document/First_Order_Logic.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarRef/Thy/document/First_Order_Logic.tex Mon Nov 08 14:41:11 2010 +0100
@@ -1,6 +1,6 @@
%
\begin{isabellebody}%
-\def\isabellecontext{First{\isacharunderscore}Order{\isacharunderscore}Logic}%
+\def\isabellecontext{First{\isaliteral{5F}{\isacharunderscore}}Order{\isaliteral{5F}{\isacharunderscore}}Logic}%
%
\isamarkupheader{Example: First-Order Logic%
}
@@ -12,7 +12,7 @@
%
\isatagvisible
\isacommand{theory}\isamarkupfalse%
-\ First{\isacharunderscore}Order{\isacharunderscore}Logic\isanewline
+\ First{\isaliteral{5F}{\isacharunderscore}}Order{\isaliteral{5F}{\isacharunderscore}}Logic\isanewline
\isakeyword{imports}\ Pure\isanewline
\isakeyword{begin}%
\endisatagvisible
@@ -24,8 +24,8 @@
%
\begin{isamarkuptext}%
\noindent In order to commence a new object-logic within
- Isabelle/Pure we introduce abstract syntactic categories \isa{{\isachardoublequote}i{\isachardoublequote}}
- for individuals and \isa{{\isachardoublequote}o{\isachardoublequote}} for object-propositions. The latter
+ Isabelle/Pure we introduce abstract syntactic categories \isa{{\isaliteral{22}{\isachardoublequote}}i{\isaliteral{22}{\isachardoublequote}}}
+ for individuals and \isa{{\isaliteral{22}{\isachardoublequote}}o{\isaliteral{22}{\isachardoublequote}}} for object-propositions. The latter
is embedded into the language of Pure propositions by means of a
separate judgment.%
\end{isamarkuptext}%
@@ -37,10 +37,10 @@
\isanewline
\isacommand{judgment}\isamarkupfalse%
\isanewline
-\ \ Trueprop\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}o\ {\isasymRightarrow}\ prop{\isachardoublequoteclose}\ \ \ \ {\isacharparenleft}{\isachardoublequoteopen}{\isacharunderscore}{\isachardoublequoteclose}\ {\isadigit{5}}{\isacharparenright}%
+\ \ Trueprop\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ prop{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{5}}{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptext}%
\noindent Note that the object-logic judgement is implicit in the
- syntax: writing \isa{A} produces \isa{{\isachardoublequote}Trueprop\ A{\isachardoublequote}} internally.
+ syntax: writing \isa{A} produces \isa{{\isaliteral{22}{\isachardoublequote}}Trueprop\ A{\isaliteral{22}{\isachardoublequote}}} internally.
From the Pure perspective this means ``\isa{A} is derivable in the
object-logic''.%
\end{isamarkuptext}%
@@ -55,16 +55,16 @@
reflexivity as introduction, and substitution as elimination
principle. Note that the latter is particularly convenient in a
framework like Isabelle, because syntactic congruences are
- implicitly produced by unification of \isa{{\isachardoublequote}B\ x{\isachardoublequote}} against
+ implicitly produced by unification of \isa{{\isaliteral{22}{\isachardoublequote}}B\ x{\isaliteral{22}{\isachardoublequote}}} against
expressions containing occurrences of \isa{x}.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{axiomatization}\isamarkupfalse%
\isanewline
-\ \ equal\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}i\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ o{\isachardoublequoteclose}\ \ {\isacharparenleft}\isakeyword{infix}\ {\isachardoublequoteopen}{\isacharequal}{\isachardoublequoteclose}\ {\isadigit{5}}{\isadigit{0}}{\isacharparenright}\isanewline
+\ \ equal\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infix}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{5}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isakeyword{where}\isanewline
-\ \ refl\ {\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isacharequal}\ x{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-\ \ subst\ {\isacharbrackleft}elim{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isacharequal}\ y\ {\isasymLongrightarrow}\ B\ x\ {\isasymLongrightarrow}\ B\ y{\isachardoublequoteclose}%
+\ \ refl\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+\ \ subst\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ y{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent Substitution is very powerful, but also hard to control in
full generality. We derive some common symmetry~/ transitivity
@@ -72,9 +72,9 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ sym\ {\isacharbrackleft}sym{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \isakeyword{assumes}\ {\isachardoublequoteopen}x\ {\isacharequal}\ y{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{shows}\ {\isachardoublequoteopen}y\ {\isacharequal}\ x{\isachardoublequoteclose}\isanewline
+\ sym\ {\isaliteral{5B}{\isacharbrackleft}}sym{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \isakeyword{assumes}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -82,13 +82,13 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isacharequal}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{with}\isamarkupfalse%
-\ {\isacharbackquoteopen}x\ {\isacharequal}\ y{\isacharbackquoteclose}\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isacharequal}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -101,9 +101,9 @@
\endisadelimproof
\isanewline
\isacommand{theorem}\isamarkupfalse%
-\ forw{\isacharunderscore}subst\ {\isacharbrackleft}trans{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \isakeyword{assumes}\ {\isachardoublequoteopen}y\ {\isacharequal}\ x{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}B\ x{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{shows}\ {\isachardoublequoteopen}B\ y{\isachardoublequoteclose}\isanewline
+\ forw{\isaliteral{5F}{\isacharunderscore}}subst\ {\isaliteral{5B}{\isacharbrackleft}}trans{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \isakeyword{assumes}\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -111,14 +111,14 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
-\ {\isacharbackquoteopen}y\ {\isacharequal}\ x{\isacharbackquoteclose}\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isacharequal}\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}y\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{have}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{from}\isamarkupfalse%
-\ this\ \isakeyword{and}\ {\isacharbackquoteopen}B\ x{\isacharbackquoteclose}\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}B\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ this\ \isakeyword{and}\ {\isaliteral{60}{\isacharbackquoteopen}}B\ x{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}B\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -131,9 +131,9 @@
\endisadelimproof
\isanewline
\isacommand{theorem}\isamarkupfalse%
-\ back{\isacharunderscore}subst\ {\isacharbrackleft}trans{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \isakeyword{assumes}\ {\isachardoublequoteopen}B\ x{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}x\ {\isacharequal}\ y{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{shows}\ {\isachardoublequoteopen}B\ y{\isachardoublequoteclose}\isanewline
+\ back{\isaliteral{5F}{\isacharunderscore}}subst\ {\isaliteral{5B}{\isacharbrackleft}}trans{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \isakeyword{assumes}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -141,11 +141,11 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
-\ {\isacharbackquoteopen}x\ {\isacharequal}\ y{\isacharbackquoteclose}\ \isakeyword{and}\ {\isacharbackquoteopen}B\ x{\isacharbackquoteclose}\isanewline
+\ {\isaliteral{60}{\isacharbackquoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{60}{\isacharbackquoteclose}}\ \isakeyword{and}\ {\isaliteral{60}{\isacharbackquoteopen}}B\ x{\isaliteral{60}{\isacharbackquoteclose}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}B\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}B\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -158,9 +158,9 @@
\endisadelimproof
\isanewline
\isacommand{theorem}\isamarkupfalse%
-\ trans\ {\isacharbrackleft}trans{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \isakeyword{assumes}\ {\isachardoublequoteopen}x\ {\isacharequal}\ y{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}y\ {\isacharequal}\ z{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{shows}\ {\isachardoublequoteopen}x\ {\isacharequal}\ z{\isachardoublequoteclose}\isanewline
+\ trans\ {\isaliteral{5B}{\isacharbrackleft}}trans{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \isakeyword{assumes}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{3D}{\isacharequal}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -168,11 +168,11 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
-\ {\isacharbackquoteopen}y\ {\isacharequal}\ z{\isacharbackquoteclose}\ \isakeyword{and}\ {\isacharbackquoteopen}x\ {\isacharequal}\ y{\isacharbackquoteclose}\isanewline
+\ {\isaliteral{60}{\isacharbackquoteopen}}y\ {\isaliteral{3D}{\isacharequal}}\ z{\isaliteral{60}{\isacharbackquoteclose}}\ \isakeyword{and}\ {\isaliteral{60}{\isacharbackquoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{60}{\isacharbackquoteclose}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isacharequal}\ z{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -195,17 +195,17 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{locale}\isamarkupfalse%
-\ group\ {\isacharequal}\isanewline
-\ \ \isakeyword{fixes}\ prod\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}i\ {\isasymRightarrow}\ i\ {\isasymRightarrow}\ i{\isachardoublequoteclose}\ \ {\isacharparenleft}\isakeyword{infix}\ {\isachardoublequoteopen}{\isasymcirc}{\isachardoublequoteclose}\ {\isadigit{7}}{\isadigit{0}}{\isacharparenright}\isanewline
-\ \ \ \ \isakeyword{and}\ inv\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}i\ {\isasymRightarrow}\ i{\isachardoublequoteclose}\ \ {\isacharparenleft}{\isachardoublequoteopen}{\isacharparenleft}{\isacharunderscore}{\isasyminverse}{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbrackleft}{\isadigit{1}}{\isadigit{0}}{\isadigit{0}}{\isadigit{0}}{\isacharbrackright}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isacharparenright}\isanewline
-\ \ \ \ \isakeyword{and}\ unit\ {\isacharcolon}{\isacharcolon}\ i\ \ {\isacharparenleft}{\isachardoublequoteopen}{\isadigit{1}}{\isachardoublequoteclose}{\isacharparenright}\isanewline
-\ \ \isakeyword{assumes}\ assoc{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}x\ {\isasymcirc}\ y{\isacharparenright}\ {\isasymcirc}\ z\ {\isacharequal}\ x\ {\isasymcirc}\ {\isacharparenleft}y\ {\isasymcirc}\ z{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ \ \ \isakeyword{and}\ left{\isacharunderscore}unit{\isacharcolon}\ \ {\isachardoublequoteopen}{\isadigit{1}}\ {\isasymcirc}\ x\ {\isacharequal}\ x{\isachardoublequoteclose}\isanewline
-\ \ \ \ \isakeyword{and}\ left{\isacharunderscore}inv{\isacharcolon}\ {\isachardoublequoteopen}x{\isasyminverse}\ {\isasymcirc}\ x\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequoteclose}\isanewline
+\ group\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \isakeyword{fixes}\ prod\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ i{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infix}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C636972633E}{\isasymcirc}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{7}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ \isakeyword{and}\ inv\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ i{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isadigit{0}}{\isadigit{0}}{\isadigit{0}}{\isaliteral{5D}{\isacharbrackright}}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ \isakeyword{and}\ unit\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ i\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \isakeyword{assumes}\ assoc{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ z\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \isakeyword{and}\ left{\isaliteral{5F}{\isacharunderscore}}unit{\isaliteral{3A}{\isacharcolon}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{1}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \isakeyword{and}\ left{\isaliteral{5F}{\isacharunderscore}}inv{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{theorem}\isamarkupfalse%
-\ right{\isacharunderscore}inv{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymcirc}\ x{\isasyminverse}\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequoteclose}\isanewline
+\ right{\isaliteral{5F}{\isacharunderscore}}inv{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -213,41 +213,41 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymcirc}\ x{\isasyminverse}\ {\isacharequal}\ {\isadigit{1}}\ {\isasymcirc}\ {\isacharparenleft}x\ {\isasymcirc}\ x{\isasyminverse}{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ left{\isacharunderscore}unit\ {\isacharbrackleft}symmetric{\isacharbrackright}{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ left{\isaliteral{5F}{\isacharunderscore}}unit\ {\isaliteral{5B}{\isacharbrackleft}}symmetric{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdots}\ {\isacharequal}\ {\isacharparenleft}{\isadigit{1}}\ {\isasymcirc}\ x{\isacharparenright}\ {\isasymcirc}\ x{\isasyminverse}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ assoc\ {\isacharbrackleft}symmetric{\isacharbrackright}{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ assoc\ {\isaliteral{5B}{\isacharbrackleft}}symmetric{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isadigit{1}}\ {\isacharequal}\ {\isacharparenleft}x{\isasyminverse}{\isacharparenright}{\isasyminverse}\ {\isasymcirc}\ x{\isasyminverse}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ left{\isacharunderscore}inv\ {\isacharbrackleft}symmetric{\isacharbrackright}{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ left{\isaliteral{5F}{\isacharunderscore}}inv\ {\isaliteral{5B}{\isacharbrackleft}}symmetric{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdots}\ {\isasymcirc}\ x\ {\isacharequal}\ {\isacharparenleft}x{\isasyminverse}{\isacharparenright}{\isasyminverse}\ {\isasymcirc}\ {\isacharparenleft}x{\isasyminverse}\ {\isasymcirc}\ x{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ assoc{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ assoc{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x{\isasyminverse}\ {\isasymcirc}\ x\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ left{\isacharunderscore}inv{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ left{\isaliteral{5F}{\isacharunderscore}}inv{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharparenleft}x{\isasyminverse}{\isacharparenright}{\isasyminverse}\ {\isasymcirc}\ {\isasymdots}{\isacharparenright}\ {\isasymcirc}\ x{\isasyminverse}\ {\isacharequal}\ {\isacharparenleft}x{\isasyminverse}{\isacharparenright}{\isasyminverse}\ {\isasymcirc}\ {\isacharparenleft}{\isadigit{1}}\ {\isasymcirc}\ x{\isasyminverse}{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ assoc{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ assoc{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isadigit{1}}\ {\isasymcirc}\ x{\isasyminverse}\ {\isacharequal}\ x{\isasyminverse}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ left{\isacharunderscore}unit{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{1}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ left{\isaliteral{5F}{\isacharunderscore}}unit{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}x{\isasyminverse}{\isacharparenright}{\isasyminverse}\ {\isasymcirc}\ {\isasymdots}\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ left{\isacharunderscore}inv{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ left{\isaliteral{5F}{\isacharunderscore}}inv{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymcirc}\ x{\isasyminverse}\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequoteclose}\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -260,7 +260,7 @@
\endisadelimproof
\isanewline
\isacommand{theorem}\isamarkupfalse%
-\ right{\isacharunderscore}unit{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymcirc}\ {\isadigit{1}}\ {\isacharequal}\ x{\isachardoublequoteclose}\isanewline
+\ right{\isaliteral{5F}{\isacharunderscore}}unit{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -268,25 +268,25 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isadigit{1}}\ {\isacharequal}\ x{\isasyminverse}\ {\isasymcirc}\ x{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ left{\isacharunderscore}inv\ {\isacharbrackleft}symmetric{\isacharbrackright}{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ left{\isaliteral{5F}{\isacharunderscore}}inv\ {\isaliteral{5B}{\isacharbrackleft}}symmetric{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymcirc}\ {\isasymdots}\ {\isacharequal}\ {\isacharparenleft}x\ {\isasymcirc}\ x{\isasyminverse}{\isacharparenright}\ {\isasymcirc}\ x{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ assoc\ {\isacharbrackleft}symmetric{\isacharbrackright}{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ assoc\ {\isaliteral{5B}{\isacharbrackleft}}symmetric{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymcirc}\ x{\isasyminverse}\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ right{\isacharunderscore}inv{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ right{\isaliteral{5F}{\isacharunderscore}}inv{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdots}\ {\isasymcirc}\ x\ {\isacharequal}\ x{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ left{\isacharunderscore}unit{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ left{\isaliteral{5F}{\isacharunderscore}}unit{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymcirc}\ {\isadigit{1}}\ {\isacharequal}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -300,12 +300,12 @@
\begin{isamarkuptext}%
\noindent Reasoning from basic axioms is often tedious. Our proofs
work by producing various instances of the given rules (potentially
- the symmetric form) using the pattern ``\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{eq}~\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isachardoublequote}{\isacharparenleft}rule\ r{\isacharparenright}{\isachardoublequote}}'' and composing the chain of
+ the symmetric form) using the pattern ``\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{eq}~\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}rule\ r{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' and composing the chain of
results via \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}/\hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}. These steps may
involve any of the transitivity rules declared in
\secref{sec:framework-ex-equal}, namely \isa{trans} in combining
- the first two results in \isa{right{\isacharunderscore}inv} and in the final steps of
- both proofs, \isa{forw{\isacharunderscore}subst} in the first combination of \isa{right{\isacharunderscore}unit}, and \isa{back{\isacharunderscore}subst} in all other calculational steps.
+ the first two results in \isa{right{\isaliteral{5F}{\isacharunderscore}}inv} and in the final steps of
+ both proofs, \isa{forw{\isaliteral{5F}{\isacharunderscore}}subst} in the first combination of \isa{right{\isaliteral{5F}{\isacharunderscore}}unit}, and \isa{back{\isaliteral{5F}{\isacharunderscore}}subst} in all other calculational steps.
Occasional substitutions in calculations are adequate, but should
not be over-emphasized. The other extreme is to compose a chain by
@@ -320,27 +320,27 @@
%
\isatagproof
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymcirc}\ {\isadigit{1}}\ {\isacharequal}\ x\ {\isasymcirc}\ {\isacharparenleft}x{\isasyminverse}\ {\isasymcirc}\ x{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{unfolding}\isamarkupfalse%
-\ left{\isacharunderscore}inv\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{unfolding}\isamarkupfalse%
+\ left{\isaliteral{5F}{\isacharunderscore}}inv\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdots}\ {\isacharequal}\ {\isacharparenleft}x\ {\isasymcirc}\ x{\isasyminverse}{\isacharparenright}\ {\isasymcirc}\ x{\isachardoublequoteclose}\ \isacommand{unfolding}\isamarkupfalse%
-\ assoc\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{unfolding}\isamarkupfalse%
+\ assoc\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdots}\ {\isacharequal}\ {\isadigit{1}}\ {\isasymcirc}\ x{\isachardoublequoteclose}\ \isacommand{unfolding}\isamarkupfalse%
-\ right{\isacharunderscore}inv\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{unfolding}\isamarkupfalse%
+\ right{\isaliteral{5F}{\isacharunderscore}}inv\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdots}\ {\isacharequal}\ x{\isachardoublequoteclose}\ \isacommand{unfolding}\isamarkupfalse%
-\ left{\isacharunderscore}unit\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{unfolding}\isamarkupfalse%
+\ left{\isaliteral{5F}{\isacharunderscore}}unit\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymcirc}\ {\isadigit{1}}\ {\isacharequal}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
@@ -354,7 +354,7 @@
definitions in order to normalize each equational problem. A more
realistic object-logic would include proper setup for the Simplifier
(\secref{sec:simplifier}), the main automated tool for equational
- reasoning in Isabelle. Then ``\hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}~\isa{left{\isacharunderscore}inv}~\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}}'' would become ``\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isachardoublequote}{\isacharparenleft}simp\ only{\isacharcolon}\ left{\isacharunderscore}inv{\isacharparenright}{\isachardoublequote}}'' etc.%
+ reasoning in Isabelle. Then ``\hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}~\isa{left{\isaliteral{5F}{\isacharunderscore}}inv}~\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}}'' would become ``\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}simp\ only{\isaliteral{3A}{\isacharcolon}}\ left{\isaliteral{5F}{\isacharunderscore}}inv{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' etc.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{end}\isamarkupfalse%
@@ -371,34 +371,34 @@
\isamarkuptrue%
\isacommand{axiomatization}\isamarkupfalse%
\isanewline
-\ \ imp\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}o\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ o{\isachardoublequoteclose}\ \ {\isacharparenleft}\isakeyword{infixr}\ {\isachardoublequoteopen}{\isasymlongrightarrow}{\isachardoublequoteclose}\ {\isadigit{2}}{\isadigit{5}}{\isacharparenright}\ \isakeyword{where}\isanewline
-\ \ impI\ {\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}A\ {\isasymLongrightarrow}\ B{\isacharparenright}\ {\isasymLongrightarrow}\ A\ {\isasymlongrightarrow}\ B{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-\ \ impD\ {\isacharbrackleft}dest{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}A\ {\isasymlongrightarrow}\ B{\isacharparenright}\ {\isasymLongrightarrow}\ A\ {\isasymLongrightarrow}\ B{\isachardoublequoteclose}\isanewline
+\ \ imp\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixr}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{2}}{\isadigit{5}}{\isaliteral{29}{\isacharparenright}}\ \isakeyword{where}\isanewline
+\ \ impI\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+\ \ impD\ {\isaliteral{5B}{\isacharbrackleft}}dest{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{axiomatization}\isamarkupfalse%
\isanewline
-\ \ disj\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}o\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ o{\isachardoublequoteclose}\ \ {\isacharparenleft}\isakeyword{infixr}\ {\isachardoublequoteopen}{\isasymor}{\isachardoublequoteclose}\ {\isadigit{3}}{\isadigit{0}}{\isacharparenright}\ \isakeyword{where}\isanewline
-\ \ disjI\isactrlisub {\isadigit{1}}\ {\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}A\ {\isasymLongrightarrow}\ A\ {\isasymor}\ B{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-\ \ disjI\isactrlisub {\isadigit{2}}\ {\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}B\ {\isasymLongrightarrow}\ A\ {\isasymor}\ B{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-\ \ disjE\ {\isacharbrackleft}elim{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}A\ {\isasymor}\ B\ {\isasymLongrightarrow}\ {\isacharparenleft}A\ {\isasymLongrightarrow}\ C{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}B\ {\isasymLongrightarrow}\ C{\isacharparenright}\ {\isasymLongrightarrow}\ C{\isachardoublequoteclose}\isanewline
+\ \ disj\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixr}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F723E}{\isasymor}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{3}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ \isakeyword{where}\isanewline
+\ \ disjI\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+\ \ disjI\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+\ \ disjE\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{axiomatization}\isamarkupfalse%
\isanewline
-\ \ conj\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}o\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ o{\isachardoublequoteclose}\ \ {\isacharparenleft}\isakeyword{infixr}\ {\isachardoublequoteopen}{\isasymand}{\isachardoublequoteclose}\ {\isadigit{3}}{\isadigit{5}}{\isacharparenright}\ \isakeyword{where}\isanewline
-\ \ conjI\ {\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}A\ {\isasymLongrightarrow}\ B\ {\isasymLongrightarrow}\ A\ {\isasymand}\ B{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-\ \ conjD\isactrlisub {\isadigit{1}}{\isacharcolon}\ {\isachardoublequoteopen}A\ {\isasymand}\ B\ {\isasymLongrightarrow}\ A{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-\ \ conjD\isactrlisub {\isadigit{2}}{\isacharcolon}\ {\isachardoublequoteopen}A\ {\isasymand}\ B\ {\isasymLongrightarrow}\ B{\isachardoublequoteclose}%
+\ \ conj\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixr}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C616E643E}{\isasymand}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{3}}{\isadigit{5}}{\isaliteral{29}{\isacharparenright}}\ \isakeyword{where}\isanewline
+\ \ conjI\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+\ \ conjD\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+\ \ conjD\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent The conjunctive destructions have the disadvantage that
- decomposing \isa{{\isachardoublequote}A\ {\isasymand}\ B{\isachardoublequote}} involves an immediate decision which
+ decomposing \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequote}}} involves an immediate decision which
component should be projected. The more convenient simultaneous
- elimination \isa{{\isachardoublequote}A\ {\isasymand}\ B\ {\isasymLongrightarrow}\ {\isacharparenleft}A\ {\isasymLongrightarrow}\ B\ {\isasymLongrightarrow}\ C{\isacharparenright}\ {\isasymLongrightarrow}\ C{\isachardoublequote}} can be derived as
+ elimination \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{22}{\isachardoublequote}}} can be derived as
follows:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ conjE\ {\isacharbrackleft}elim{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \isakeyword{assumes}\ {\isachardoublequoteopen}A\ {\isasymand}\ B{\isachardoublequoteclose}\isanewline
+\ conjE\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \isakeyword{assumes}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isakeyword{obtains}\ A\ \isakeyword{and}\ B\isanewline
%
\isadelimproof
@@ -409,13 +409,13 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{from}\isamarkupfalse%
-\ {\isacharbackquoteopen}A\ {\isasymand}\ B{\isacharbackquoteclose}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{show}\isamarkupfalse%
\ A\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ conjD\isactrlisub {\isadigit{1}}{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ conjD\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
-\ {\isacharbackquoteopen}A\ {\isasymand}\ B{\isacharbackquoteclose}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{show}\isamarkupfalse%
\ B\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ conjD\isactrlisub {\isadigit{2}}{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ conjD\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
@@ -437,14 +437,14 @@
%
\isatagproof
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymand}\ B{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{obtain}\isamarkupfalse%
-\ B\ \isakeyword{and}\ A\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ B\ \isakeyword{and}\ A\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}B\ {\isasymand}\ A{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
@@ -455,7 +455,7 @@
%
\begin{isamarkuptext}%
\noindent Note that the analogous elimination rule for disjunction
- ``\isa{{\isachardoublequote}{\isasymASSUMES}\ A\ {\isasymor}\ B\ {\isasymOBTAINS}\ A\ {\isasymBBAR}\ B{\isachardoublequote}}'' coincides with
+ ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B\ {\isaliteral{5C3C4F425441494E533E}{\isasymOBTAINS}}\ A\ {\isaliteral{5C3C424241523E}{\isasymBBAR}}\ B{\isaliteral{22}{\isachardoublequote}}}'' coincides with
the original axiomatization of \isa{disjE}.
\medskip We continue propositional logic by introducing absurdity
@@ -465,16 +465,16 @@
\isamarkuptrue%
\isacommand{axiomatization}\isamarkupfalse%
\isanewline
-\ \ false\ {\isacharcolon}{\isacharcolon}\ o\ \ {\isacharparenleft}{\isachardoublequoteopen}{\isasymbottom}{\isachardoublequoteclose}{\isacharparenright}\ \isakeyword{where}\isanewline
-\ \ falseE\ {\isacharbrackleft}elim{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymbottom}\ {\isasymLongrightarrow}\ A{\isachardoublequoteclose}\isanewline
+\ \ false\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ o\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\ \isakeyword{where}\isanewline
+\ \ falseE\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{definition}\isamarkupfalse%
\isanewline
-\ \ true\ {\isacharcolon}{\isacharcolon}\ o\ \ {\isacharparenleft}{\isachardoublequoteopen}{\isasymtop}{\isachardoublequoteclose}{\isacharparenright}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}{\isasymtop}\ {\isasymequiv}\ {\isasymbottom}\ {\isasymlongrightarrow}\ {\isasymbottom}{\isachardoublequoteclose}\isanewline
+\ \ true\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ o\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C746F703E}{\isasymtop}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C746F703E}{\isasymtop}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{theorem}\isamarkupfalse%
-\ trueI\ {\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\ {\isasymtop}\isanewline
+\ trueI\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C746F703E}{\isasymtop}}\isanewline
%
\isadelimproof
\ \ %
@@ -482,7 +482,7 @@
%
\isatagproof
\isacommand{unfolding}\isamarkupfalse%
-\ true{\isacharunderscore}def\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ true{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
@@ -498,13 +498,13 @@
\isamarkuptrue%
\isacommand{definition}\isamarkupfalse%
\isanewline
-\ \ not\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}o\ {\isasymRightarrow}\ o{\isachardoublequoteclose}\ \ {\isacharparenleft}{\isachardoublequoteopen}{\isasymnot}\ {\isacharunderscore}{\isachardoublequoteclose}\ {\isacharbrackleft}{\isadigit{4}}{\isadigit{0}}{\isacharbrackright}\ {\isadigit{4}}{\isadigit{0}}{\isacharparenright}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}{\isasymnot}\ A\ {\isasymequiv}\ A\ {\isasymlongrightarrow}\ {\isasymbottom}{\isachardoublequoteclose}\isanewline
+\ \ not\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{4}}{\isadigit{0}}{\isaliteral{5D}{\isacharbrackright}}\ {\isadigit{4}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{theorem}\isamarkupfalse%
-\ notI\ {\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \isakeyword{assumes}\ {\isachardoublequoteopen}A\ {\isasymLongrightarrow}\ {\isasymbottom}{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{shows}\ {\isachardoublequoteopen}{\isasymnot}\ A{\isachardoublequoteclose}\isanewline
+\ notI\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \isakeyword{assumes}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -512,15 +512,15 @@
%
\isatagproof
\isacommand{unfolding}\isamarkupfalse%
-\ not{\isacharunderscore}def\isanewline
+\ not{\isaliteral{5F}{\isacharunderscore}}def\isanewline
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
\ A\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isasymbottom}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ {\isacharbackquoteopen}A\ {\isasymLongrightarrow}\ {\isasymbottom}{\isacharbackquoteclose}{\isacharparenright}\isanewline
+\ {\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ {\isaliteral{60}{\isacharbackquoteopen}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}{\isaliteral{60}{\isacharbackquoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
@@ -532,8 +532,8 @@
\endisadelimproof
\isanewline
\isacommand{theorem}\isamarkupfalse%
-\ notE\ {\isacharbrackleft}elim{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \isakeyword{assumes}\ {\isachardoublequoteopen}{\isasymnot}\ A{\isachardoublequoteclose}\ \isakeyword{and}\ A\isanewline
+\ notE\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \isakeyword{assumes}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ A\isanewline
\ \ \isakeyword{shows}\ B\isanewline
%
\isadelimproof
@@ -542,19 +542,19 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
-\ {\isacharbackquoteopen}{\isasymnot}\ A{\isacharbackquoteclose}\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymlongrightarrow}\ {\isasymbottom}{\isachardoublequoteclose}\ \isacommand{unfolding}\isamarkupfalse%
-\ not{\isacharunderscore}def\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{have}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{unfolding}\isamarkupfalse%
+\ not{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{from}\isamarkupfalse%
-\ {\isacharbackquoteopen}A\ {\isasymlongrightarrow}\ {\isasymbottom}{\isacharbackquoteclose}\ \isakeyword{and}\ {\isacharbackquoteopen}A{\isacharbackquoteclose}\ \isacommand{have}\isamarkupfalse%
-\ {\isasymbottom}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}{\isaliteral{60}{\isacharbackquoteclose}}\ \isakeyword{and}\ {\isaliteral{60}{\isacharbackquoteopen}}A{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{have}\isamarkupfalse%
+\ {\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ B\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ B\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -577,13 +577,13 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{locale}\isamarkupfalse%
-\ classical\ {\isacharequal}\isanewline
-\ \ \isakeyword{assumes}\ classical{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isasymnot}\ C\ {\isasymLongrightarrow}\ C{\isacharparenright}\ {\isasymLongrightarrow}\ C{\isachardoublequoteclose}\isanewline
+\ classical\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \isakeyword{assumes}\ classical{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ C\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{theorem}\isamarkupfalse%
-\ double{\isacharunderscore}negation{\isacharcolon}\isanewline
-\ \ \isakeyword{assumes}\ {\isachardoublequoteopen}{\isasymnot}\ {\isasymnot}\ C{\isachardoublequoteclose}\isanewline
+\ double{\isaliteral{5F}{\isacharunderscore}}negation{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \isakeyword{assumes}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ C{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isakeyword{shows}\ C\isanewline
%
\isadelimproof
@@ -592,12 +592,12 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ classical{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ classical{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymnot}\ C{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ C{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{with}\isamarkupfalse%
-\ {\isacharbackquoteopen}{\isasymnot}\ {\isasymnot}\ C{\isacharbackquoteclose}\ \isacommand{show}\isamarkupfalse%
-\ C\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ C{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{show}\isamarkupfalse%
+\ C\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -610,7 +610,7 @@
\endisadelimproof
\isanewline
\isacommand{theorem}\isamarkupfalse%
-\ tertium{\isacharunderscore}non{\isacharunderscore}datur{\isacharcolon}\ {\isachardoublequoteopen}C\ {\isasymor}\ {\isasymnot}\ C{\isachardoublequoteclose}\isanewline
+\ tertium{\isaliteral{5F}{\isacharunderscore}}non{\isaliteral{5F}{\isacharunderscore}}datur{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}C\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ C{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -618,35 +618,35 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ double{\isacharunderscore}negation{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ double{\isaliteral{5F}{\isacharunderscore}}negation{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymnot}\ {\isasymnot}\ {\isacharparenleft}C\ {\isasymor}\ {\isasymnot}\ C{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{28}{\isacharparenleft}}C\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ C{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymnot}\ {\isacharparenleft}C\ {\isasymor}\ {\isasymnot}\ C{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{28}{\isacharparenleft}}C\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ C{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymnot}\ C{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ C{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{assume}\isamarkupfalse%
\ C\ \isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}C\ {\isasymor}\ {\isasymnot}\ C{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}C\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ C{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{with}\isamarkupfalse%
-\ {\isacharbackquoteopen}{\isasymnot}\ {\isacharparenleft}C\ {\isasymor}\ {\isasymnot}\ C{\isacharparenright}{\isacharbackquoteclose}\ \isacommand{show}\isamarkupfalse%
-\ {\isasymbottom}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{28}{\isacharparenleft}}C\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ C{\isaliteral{29}{\isacharparenright}}{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}C\ {\isasymor}\ {\isasymnot}\ C{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}C\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ C{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{with}\isamarkupfalse%
-\ {\isacharbackquoteopen}{\isasymnot}\ {\isacharparenleft}C\ {\isasymor}\ {\isasymnot}\ C{\isacharparenright}{\isacharbackquoteclose}\ \isacommand{show}\isamarkupfalse%
-\ {\isasymbottom}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{28}{\isacharparenleft}}C\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ C{\isaliteral{29}{\isacharparenright}}{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
@@ -664,9 +664,9 @@
non-trivial propositional proofs in general. All three rules
characterize classical logic independently, but the original rule is
already the most convenient to use, because it leaves the conclusion
- unchanged. Note that \isa{{\isachardoublequote}{\isacharparenleft}{\isasymnot}\ C\ {\isasymLongrightarrow}\ C{\isacharparenright}\ {\isasymLongrightarrow}\ C{\isachardoublequote}} fits again into our
+ unchanged. Note that \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ C\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{22}{\isachardoublequote}}} fits again into our
format for eliminations, despite the additional twist that the
- context refers to the main conclusion. So we may write \isa{classical} as the Isar statement ``\isa{{\isachardoublequote}{\isasymOBTAINS}\ {\isasymnot}\ thesis{\isachardoublequote}}''.
+ context refers to the main conclusion. So we may write \isa{classical} as the Isar statement ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4F425441494E533E}{\isasymOBTAINS}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ thesis{\isaliteral{22}{\isachardoublequote}}}''.
This also explains nicely how classical reasoning really works:
whatever the main \isa{thesis} might be, we may always assume its
negation!%
@@ -682,31 +682,31 @@
Representing quantifiers is easy, thanks to the higher-order nature
of the underlying framework. According to the well-known technique
introduced by Church \cite{church40}, quantifiers are operators on
- predicates, which are syntactically represented as \isa{{\isachardoublequote}{\isasymlambda}{\isachardoublequote}}-terms
- of type \isa{{\isachardoublequote}i\ {\isasymRightarrow}\ o{\isachardoublequote}}. Binder notation turns \isa{{\isachardoublequote}All\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ B\ x{\isacharparenright}{\isachardoublequote}} into \isa{{\isachardoublequote}{\isasymforall}x{\isachardot}\ B\ x{\isachardoublequote}} etc.%
+ predicates, which are syntactically represented as \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{22}{\isachardoublequote}}}-terms
+ of type \isa{{\isaliteral{22}{\isachardoublequote}}i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o{\isaliteral{22}{\isachardoublequote}}}. Binder notation turns \isa{{\isaliteral{22}{\isachardoublequote}}All\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} into \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{22}{\isachardoublequote}}} etc.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{axiomatization}\isamarkupfalse%
\isanewline
-\ \ All\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}i\ {\isasymRightarrow}\ o{\isacharparenright}\ {\isasymRightarrow}\ o{\isachardoublequoteclose}\ \ {\isacharparenleft}\isakeyword{binder}\ {\isachardoublequoteopen}{\isasymforall}{\isachardoublequoteclose}\ {\isadigit{1}}{\isadigit{0}}{\isacharparenright}\ \isakeyword{where}\isanewline
-\ \ allI\ {\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isasymAnd}x{\isachardot}\ B\ x{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymforall}x{\isachardot}\ B\ x{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-\ \ allD\ {\isacharbrackleft}dest{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isasymforall}x{\isachardot}\ B\ x{\isacharparenright}\ {\isasymLongrightarrow}\ B\ a{\isachardoublequoteclose}\isanewline
+\ \ All\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{binder}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{1}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ \isakeyword{where}\isanewline
+\ \ allI\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+\ \ allD\ {\isaliteral{5B}{\isacharbrackleft}}dest{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ a{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{axiomatization}\isamarkupfalse%
\isanewline
-\ \ Ex\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}i\ {\isasymRightarrow}\ o{\isacharparenright}\ {\isasymRightarrow}\ o{\isachardoublequoteclose}\ \ {\isacharparenleft}\isakeyword{binder}\ {\isachardoublequoteopen}{\isasymexists}{\isachardoublequoteclose}\ {\isadigit{1}}{\isadigit{0}}{\isacharparenright}\ \isakeyword{where}\isanewline
-\ \ exI\ {\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}B\ a\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymexists}x{\isachardot}\ B\ x{\isacharparenright}{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-\ \ exE\ {\isacharbrackleft}elim{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isasymexists}x{\isachardot}\ B\ x{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ B\ x\ {\isasymLongrightarrow}\ C{\isacharparenright}\ {\isasymLongrightarrow}\ C{\isachardoublequoteclose}%
+\ \ Ex\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{binder}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{1}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ \isakeyword{where}\isanewline
+\ \ exI\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ a\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+\ \ exE\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ B\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
-\noindent The statement of \isa{exE} corresponds to ``\isa{{\isachardoublequote}{\isasymASSUMES}\ {\isasymexists}x{\isachardot}\ B\ x\ {\isasymOBTAINS}\ x\ {\isasymWHERE}\ B\ x{\isachardoublequote}}'' in Isar. In the
+\noindent The statement of \isa{exE} corresponds to ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ B\ x\ {\isaliteral{5C3C4F425441494E533E}{\isasymOBTAINS}}\ x\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ B\ x{\isaliteral{22}{\isachardoublequote}}}'' in Isar. In the
subsequent example we illustrate quantifier reasoning involving all
four rules:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
\isanewline
-\ \ \isakeyword{assumes}\ {\isachardoublequoteopen}{\isasymexists}x{\isachardot}\ {\isasymforall}y{\isachardot}\ R\ x\ y{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{shows}\ {\isachardoublequoteopen}{\isasymforall}y{\isachardot}\ {\isasymexists}x{\isachardot}\ R\ x\ y{\isachardoublequoteclose}\isanewline
+\ \ \isakeyword{assumes}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}y{\isaliteral{2E}{\isachardot}}\ R\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}y{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ R\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -715,29 +715,29 @@
\isatagproof
\isacommand{proof}\isamarkupfalse%
\ \ \ \ %
-\isamarkupcmt{\isa{{\isachardoublequote}{\isasymforall}{\isachardoublequote}} introduction%
+\isamarkupcmt{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}{\isaliteral{22}{\isachardoublequote}}} introduction%
}
\isanewline
\ \ \isacommand{obtain}\isamarkupfalse%
-\ x\ \isakeyword{where}\ {\isachardoublequoteopen}{\isasymforall}y{\isachardot}\ R\ x\ y{\isachardoublequoteclose}\ \isacommand{using}\isamarkupfalse%
-\ {\isacharbackquoteopen}{\isasymexists}x{\isachardot}\ {\isasymforall}y{\isachardot}\ R\ x\ y{\isacharbackquoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ x\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}y{\isaliteral{2E}{\isachardot}}\ R\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{using}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}y{\isaliteral{2E}{\isachardot}}\ R\ x\ y{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\ \ \ \ %
-\isamarkupcmt{\isa{{\isachardoublequote}{\isasymexists}{\isachardoublequote}} elimination%
+\isamarkupcmt{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}{\isaliteral{22}{\isachardoublequote}}} elimination%
}
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
\ y\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}R\ x\ y{\isachardoublequoteclose}\ \isacommand{using}\isamarkupfalse%
-\ {\isacharbackquoteopen}{\isasymforall}y{\isachardot}\ R\ x\ y{\isacharbackquoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}R\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{using}\isamarkupfalse%
+\ {\isaliteral{60}{\isacharbackquoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}y{\isaliteral{2E}{\isachardot}}\ R\ x\ y{\isaliteral{60}{\isacharbackquoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\ \ \ \ %
-\isamarkupcmt{\isa{{\isachardoublequote}{\isasymforall}{\isachardoublequote}} destruction%
+\isamarkupcmt{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}{\isaliteral{22}{\isachardoublequote}}} destruction%
}
\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymexists}x{\isachardot}\ R\ x\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ R\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\ \ \ \ %
-\isamarkupcmt{\isa{{\isachardoublequote}{\isasymexists}{\isachardoublequote}} introduction%
+\isamarkupcmt{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}{\isaliteral{22}{\isachardoublequote}}} introduction%
}
\isanewline
\isacommand{qed}\isamarkupfalse%
@@ -761,27 +761,27 @@
\medskip
\begin{tabular}{l}
- \isa{{\isachardoublequote}impI{\isacharcolon}\ {\isasymASSUMES}\ A\ {\isasymLongrightarrow}\ B\ {\isasymSHOWS}\ A\ {\isasymlongrightarrow}\ B{\isachardoublequote}} \\
- \isa{{\isachardoublequote}impD{\isacharcolon}\ {\isasymASSUMES}\ A\ {\isasymlongrightarrow}\ B\ {\isasymAND}\ A\ {\isasymSHOWS}\ B{\isachardoublequote}} \\[1ex]
+ \isa{{\isaliteral{22}{\isachardoublequote}}impI{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{5C3C53484F57533E}{\isasymSHOWS}}\ A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}impD{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ A\ {\isaliteral{5C3C53484F57533E}{\isasymSHOWS}}\ B{\isaliteral{22}{\isachardoublequote}}} \\[1ex]
- \isa{{\isachardoublequote}disjI\isactrlisub {\isadigit{1}}{\isacharcolon}\ {\isasymASSUMES}\ A\ {\isasymSHOWS}\ A\ {\isasymor}\ B{\isachardoublequote}} \\
- \isa{{\isachardoublequote}disjI\isactrlisub {\isadigit{2}}{\isacharcolon}\ {\isasymASSUMES}\ B\ {\isasymSHOWS}\ A\ {\isasymor}\ B{\isachardoublequote}} \\
- \isa{{\isachardoublequote}disjE{\isacharcolon}\ {\isasymASSUMES}\ A\ {\isasymor}\ B\ {\isasymOBTAINS}\ A\ {\isasymBBAR}\ B{\isachardoublequote}} \\[1ex]
+ \isa{{\isaliteral{22}{\isachardoublequote}}disjI\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ A\ {\isaliteral{5C3C53484F57533E}{\isasymSHOWS}}\ A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}disjI\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ B\ {\isaliteral{5C3C53484F57533E}{\isasymSHOWS}}\ A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}disjE{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B\ {\isaliteral{5C3C4F425441494E533E}{\isasymOBTAINS}}\ A\ {\isaliteral{5C3C424241523E}{\isasymBBAR}}\ B{\isaliteral{22}{\isachardoublequote}}} \\[1ex]
- \isa{{\isachardoublequote}conjI{\isacharcolon}\ {\isasymASSUMES}\ A\ {\isasymAND}\ B\ {\isasymSHOWS}\ A\ {\isasymand}\ B{\isachardoublequote}} \\
- \isa{{\isachardoublequote}conjE{\isacharcolon}\ {\isasymASSUMES}\ A\ {\isasymand}\ B\ {\isasymOBTAINS}\ A\ {\isasymAND}\ B{\isachardoublequote}} \\[1ex]
+ \isa{{\isaliteral{22}{\isachardoublequote}}conjI{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ A\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ B\ {\isaliteral{5C3C53484F57533E}{\isasymSHOWS}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}conjE{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C4F425441494E533E}{\isasymOBTAINS}}\ A\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ B{\isaliteral{22}{\isachardoublequote}}} \\[1ex]
- \isa{{\isachardoublequote}falseE{\isacharcolon}\ {\isasymASSUMES}\ {\isasymbottom}\ {\isasymSHOWS}\ A{\isachardoublequote}} \\
- \isa{{\isachardoublequote}trueI{\isacharcolon}\ {\isasymSHOWS}\ {\isasymtop}{\isachardoublequote}} \\[1ex]
+ \isa{{\isaliteral{22}{\isachardoublequote}}falseE{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ {\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}\ {\isaliteral{5C3C53484F57533E}{\isasymSHOWS}}\ A{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}trueI{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C53484F57533E}{\isasymSHOWS}}\ {\isaliteral{5C3C746F703E}{\isasymtop}}{\isaliteral{22}{\isachardoublequote}}} \\[1ex]
- \isa{{\isachardoublequote}notI{\isacharcolon}\ {\isasymASSUMES}\ A\ {\isasymLongrightarrow}\ {\isasymbottom}\ {\isasymSHOWS}\ {\isasymnot}\ A{\isachardoublequote}} \\
- \isa{{\isachardoublequote}notE{\isacharcolon}\ {\isasymASSUMES}\ {\isasymnot}\ A\ {\isasymAND}\ A\ {\isasymSHOWS}\ B{\isachardoublequote}} \\[1ex]
+ \isa{{\isaliteral{22}{\isachardoublequote}}notI{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}\ {\isaliteral{5C3C53484F57533E}{\isasymSHOWS}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}notE{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ A\ {\isaliteral{5C3C53484F57533E}{\isasymSHOWS}}\ B{\isaliteral{22}{\isachardoublequote}}} \\[1ex]
- \isa{{\isachardoublequote}allI{\isacharcolon}\ {\isasymASSUMES}\ {\isasymAnd}x{\isachardot}\ B\ x\ {\isasymSHOWS}\ {\isasymforall}x{\isachardot}\ B\ x{\isachardoublequote}} \\
- \isa{{\isachardoublequote}allE{\isacharcolon}\ {\isasymASSUMES}\ {\isasymforall}x{\isachardot}\ B\ x\ {\isasymSHOWS}\ B\ a{\isachardoublequote}} \\[1ex]
+ \isa{{\isaliteral{22}{\isachardoublequote}}allI{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ B\ x\ {\isaliteral{5C3C53484F57533E}{\isasymSHOWS}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}allE{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ B\ x\ {\isaliteral{5C3C53484F57533E}{\isasymSHOWS}}\ B\ a{\isaliteral{22}{\isachardoublequote}}} \\[1ex]
- \isa{{\isachardoublequote}exI{\isacharcolon}\ {\isasymASSUMES}\ B\ a\ {\isasymSHOWS}\ {\isasymexists}x{\isachardot}\ B\ x{\isachardoublequote}} \\
- \isa{{\isachardoublequote}exE{\isacharcolon}\ {\isasymASSUMES}\ {\isasymexists}x{\isachardot}\ B\ x\ {\isasymOBTAINS}\ a\ {\isasymWHERE}\ B\ a{\isachardoublequote}}
+ \isa{{\isaliteral{22}{\isachardoublequote}}exI{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ B\ a\ {\isaliteral{5C3C53484F57533E}{\isasymSHOWS}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}exE{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ B\ x\ {\isaliteral{5C3C4F425441494E533E}{\isasymOBTAINS}}\ a\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ B\ a{\isaliteral{22}{\isachardoublequote}}}
\end{tabular}
\medskip
@@ -803,7 +803,7 @@
\begin{minipage}[t]{0.4\textwidth}
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymlongrightarrow}\ B{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
@@ -842,7 +842,7 @@
\end{minipage}\qquad\begin{minipage}[t]{0.4\textwidth}
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymlongrightarrow}\ B{\isachardoublequoteclose}\ \isakeyword{and}\ A%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ A%
\endisatagproof
{\isafoldproof}%
%
@@ -872,7 +872,7 @@
\isatagproof
\isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ B\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ B\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\end{minipage}\\[3ex]\begin{minipage}[t]{0.4\textwidth}
\isanewline
@@ -907,7 +907,7 @@
\isatagproof
\isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymor}\ B{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
@@ -941,12 +941,12 @@
\isatagproof
\isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymor}\ B{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\end{minipage}\qquad\begin{minipage}[t]{0.4\textwidth}
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymor}\ B{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ B{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1080,12 +1080,12 @@
\isatagproof
\isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymand}\ B{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\end{minipage}\qquad\begin{minipage}[t]{0.4\textwidth}
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymand}\ B{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1115,12 +1115,12 @@
\isatagproof
\isacommand{then}\isamarkupfalse%
\ \isacommand{obtain}\isamarkupfalse%
-\ A\ \isakeyword{and}\ B\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ A\ \isakeyword{and}\ B\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\end{minipage}\\[3ex]\begin{minipage}[t]{0.4\textwidth}
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymbottom}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1150,24 +1150,24 @@
\isatagproof
\isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ A\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ A\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\end{minipage}\qquad\begin{minipage}[t]{0.4\textwidth}
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymtop}{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C746F703E}{\isasymtop}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\end{minipage}\\[3ex]\begin{minipage}[t]{0.4\textwidth}
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymnot}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
\ A\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymbottom}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1200,7 +1200,7 @@
\end{minipage}\qquad\begin{minipage}[t]{0.4\textwidth}
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymnot}\ A{\isachardoublequoteclose}\ \isakeyword{and}\ A%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ A%
\endisatagproof
{\isafoldproof}%
%
@@ -1230,18 +1230,18 @@
\isatagproof
\isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ B\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ B\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\end{minipage}\\[3ex]\begin{minipage}[t]{0.4\textwidth}
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymforall}x{\isachardot}\ B\ x{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ x\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}B\ x{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}B\ x{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1274,7 +1274,7 @@
\end{minipage}\qquad\begin{minipage}[t]{0.4\textwidth}
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymforall}x{\isachardot}\ B\ x{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1304,16 +1304,16 @@
\isatagproof
\isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}B\ a{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}B\ a{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\end{minipage}\\[3ex]\begin{minipage}[t]{0.4\textwidth}
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymexists}x{\isachardot}\ B\ x{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}B\ a{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}B\ a{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1346,7 +1346,7 @@
\end{minipage}\qquad\begin{minipage}[t]{0.4\textwidth}
\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymexists}x{\isachardot}\ B\ x{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1376,7 +1376,7 @@
\isatagproof
\isacommand{then}\isamarkupfalse%
\ \isacommand{obtain}\isamarkupfalse%
-\ a\ \isakeyword{where}\ {\isachardoublequoteopen}B\ a{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ a\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ a{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\end{minipage}
%
--- a/doc-src/IsarRef/Thy/document/Framework.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarRef/Thy/document/Framework.tex Mon Nov 08 14:41:11 2010 +0100
@@ -45,7 +45,7 @@
So Isar challenges the traditional way of recording informal proofs
in mathematical prose, as well as the common tendency to see fully
formal proofs directly as objects of some logical calculus (e.g.\
- \isa{{\isachardoublequote}{\isasymlambda}{\isachardoublequote}}-terms in a version of type theory). In fact, Isar is
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{22}{\isachardoublequote}}}-terms in a version of type theory). In fact, Isar is
better understood as an interpreter of a simple block-structured
language for describing the data flow of local facts and goals,
interspersed with occasional invocations of proof methods.
@@ -75,10 +75,10 @@
includes common notions of predicate logic, naive set-theory etc.\
using fairly standard mathematical notation. From the perspective
of generic natural deduction there is nothing special about the
- logical connectives of HOL (\isa{{\isachardoublequote}{\isasymand}{\isachardoublequote}}, \isa{{\isachardoublequote}{\isasymor}{\isachardoublequote}}, \isa{{\isachardoublequote}{\isasymforall}{\isachardoublequote}},
- \isa{{\isachardoublequote}{\isasymexists}{\isachardoublequote}}, etc.), only the resulting reasoning principles are
+ logical connectives of HOL (\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616E643E}{\isasymand}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6F723E}{\isasymor}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}{\isaliteral{22}{\isachardoublequote}}},
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}{\isaliteral{22}{\isachardoublequote}}}, etc.), only the resulting reasoning principles are
relevant to the user. There are similar rules available for
- set-theory operators (\isa{{\isachardoublequote}{\isasyminter}{\isachardoublequote}}, \isa{{\isachardoublequote}{\isasymunion}{\isachardoublequote}}, \isa{{\isachardoublequote}{\isasymInter}{\isachardoublequote}}, \isa{{\isachardoublequote}{\isasymUnion}{\isachardoublequote}}, etc.), or any other theory developed in the library (lattice
+ set-theory operators (\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C696E7465723E}{\isasyminter}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C756E696F6E3E}{\isasymunion}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C496E7465723E}{\isasymInter}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C556E696F6E3E}{\isasymUnion}}{\isaliteral{22}{\isachardoublequote}}}, etc.), or any other theory developed in the library (lattice
theory, topology etc.).
Subsequently we briefly review fragments of Isar proof texts
@@ -86,7 +86,7 @@
examples shall refer to set-theory, to minimize the danger of
understanding connectives of predicate logic as something special.
- \medskip The following deduction performs \isa{{\isachardoublequote}{\isasyminter}{\isachardoublequote}}-introduction,
+ \medskip The following deduction performs \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C696E7465723E}{\isasyminter}}{\isaliteral{22}{\isachardoublequote}}}-introduction,
working forwards from assumptions towards the conclusion. We give
both the Isar text, and depict the primitive rule involved, as
determined by unification of the problem against rules that are
@@ -102,10 +102,10 @@
%
\isatagproof
\isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymin}\ A{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}x\ {\isasymin}\ B{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymin}\ A\ {\isasyminter}\ B{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
@@ -117,7 +117,7 @@
\end{minipage}\begin{minipage}{0.4\textwidth}
%
\begin{isamarkuptext}%
-\infer{\isa{{\isachardoublequote}x\ {\isasymin}\ A\ {\isasyminter}\ B{\isachardoublequote}}}{\isa{{\isachardoublequote}x\ {\isasymin}\ A{\isachardoublequote}} & \isa{{\isachardoublequote}x\ {\isasymin}\ B{\isachardoublequote}}}%
+\infer{\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ B{\isaliteral{22}{\isachardoublequote}}}}{\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ B{\isaliteral{22}{\isachardoublequote}}}}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -127,7 +127,7 @@
\medskip\noindent Note that \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}} augments the proof
context, \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}} indicates that the current fact shall be
used in the next step, and \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}} states an intermediate
- goal. The two dots ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}}'' refer to a complete proof of
+ goal. The two dots ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}}'' refer to a complete proof of
this claim, using the indicated facts and a canonical rule from the
context. We could have been more explicit here by spelling out the
final proof step via the \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}} command:%
@@ -140,11 +140,11 @@
%
\isatagproof
\isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymin}\ A{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}x\ {\isasymin}\ B{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymin}\ A\ {\isasyminter}\ B{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ IntI{\isacharparenright}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ IntI{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -153,11 +153,11 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-\noindent The format of the \isa{{\isachardoublequote}{\isasyminter}{\isachardoublequote}}-introduction rule represents
+\noindent The format of the \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C696E7465723E}{\isasyminter}}{\isaliteral{22}{\isachardoublequote}}}-introduction rule represents
the most basic inference, which proceeds from given premises to a
conclusion, without any nested proof context involved.
- The next example performs backwards introduction on \isa{{\isachardoublequote}{\isasymInter}{\isasymA}{\isachardoublequote}},
+ The next example performs backwards introduction on \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C496E7465723E}{\isasymInter}}{\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{22}{\isachardoublequote}}},
the intersection of all sets within a given set. This requires a
nested proof of set membership within a local context, where \isa{A} is an arbitrary-but-fixed member of the collection:%
\end{isamarkuptext}%
@@ -171,15 +171,15 @@
%
\isatagproof
\isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymin}\ {\isasymInter}{\isasymA}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C496E7465723E}{\isasymInter}}{\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{fix}\isamarkupfalse%
\ A\isanewline
\ \ \ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymin}\ {\isasymA}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymin}\ A{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -219,7 +219,7 @@
\end{minipage}\begin{minipage}{0.4\textwidth}
%
\begin{isamarkuptext}%
-\infer{\isa{{\isachardoublequote}x\ {\isasymin}\ {\isasymInter}{\isasymA}{\isachardoublequote}}}{\infer*{\isa{{\isachardoublequote}x\ {\isasymin}\ A{\isachardoublequote}}}{\isa{{\isachardoublequote}{\isacharbrackleft}A{\isacharbrackright}{\isacharbrackleft}A\ {\isasymin}\ {\isasymA}{\isacharbrackright}{\isachardoublequote}}}}%
+\infer{\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C496E7465723E}{\isasymInter}}{\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{22}{\isachardoublequote}}}}{\infer*{\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{22}{\isachardoublequote}}}}{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5B}{\isacharbrackleft}}A\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}}}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -229,9 +229,9 @@
\medskip\noindent This Isar reasoning pattern again refers to the
primitive rule depicted above. The system determines it in the
``\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}'' step, which could have been spelt out more
- explicitly as ``\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}{\isacharparenleft}rule\ InterI{\isacharparenright}{\isachardoublequote}}''. Note
- that the rule involves both a local parameter \isa{{\isachardoublequote}A{\isachardoublequote}} and an
- assumption \isa{{\isachardoublequote}A\ {\isasymin}\ {\isasymA}{\isachardoublequote}} in the nested reasoning. This kind of
+ explicitly as ``\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}rule\ InterI{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}''. Note
+ that the rule involves both a local parameter \isa{{\isaliteral{22}{\isachardoublequote}}A{\isaliteral{22}{\isachardoublequote}}} and an
+ assumption \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{22}{\isachardoublequote}}} in the nested reasoning. This kind of
compound rule typically demands a genuine sub-proof in Isar, working
backwards rather than forwards as seen before. In the proof body we
encounter the \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}-\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}-\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}
@@ -240,10 +240,10 @@
refinement of the enclosing claim, using the rule derived from the
proof body.
- \medskip The next example involves \isa{{\isachardoublequote}{\isasymUnion}{\isasymA}{\isachardoublequote}}, which can be
- characterized as the set of all \isa{{\isachardoublequote}x{\isachardoublequote}} such that \isa{{\isachardoublequote}{\isasymexists}A{\isachardot}\ x\ {\isasymin}\ A\ {\isasymand}\ A\ {\isasymin}\ {\isasymA}{\isachardoublequote}}. The elimination rule for \isa{{\isachardoublequote}x\ {\isasymin}\ {\isasymUnion}{\isasymA}{\isachardoublequote}} does
- not mention \isa{{\isachardoublequote}{\isasymexists}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isasymand}{\isachardoublequote}} at all, but admits to obtain
- directly a local \isa{{\isachardoublequote}A{\isachardoublequote}} such that \isa{{\isachardoublequote}x\ {\isasymin}\ A{\isachardoublequote}} and \isa{{\isachardoublequote}A\ {\isasymin}\ {\isasymA}{\isachardoublequote}} hold. This corresponds to the following Isar proof and
+ \medskip The next example involves \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C556E696F6E3E}{\isasymUnion}}{\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{22}{\isachardoublequote}}}, which can be
+ characterized as the set of all \isa{{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}} such that \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}A{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{22}{\isachardoublequote}}}. The elimination rule for \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C556E696F6E3E}{\isasymUnion}}{\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{22}{\isachardoublequote}}} does
+ not mention \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616E643E}{\isasymand}}{\isaliteral{22}{\isachardoublequote}}} at all, but admits to obtain
+ directly a local \isa{{\isaliteral{22}{\isachardoublequote}}A{\isaliteral{22}{\isachardoublequote}}} such that \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{22}{\isachardoublequote}}} hold. This corresponds to the following Isar proof and
inference rule, respectively:%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -256,7 +256,7 @@
%
\isatagproof
\isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymin}\ {\isasymUnion}{\isasymA}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C556E696F6E3E}{\isasymUnion}}{\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
\ C\isanewline
@@ -265,7 +265,7 @@
\ \ \ \ \ \ \isacommand{fix}\isamarkupfalse%
\ A\isanewline
\ \ \ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymin}\ A{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}A\ {\isasymin}\ {\isasymA}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ C%
\endisatagproof
@@ -307,7 +307,7 @@
\end{minipage}\begin{minipage}{0.4\textwidth}
%
\begin{isamarkuptext}%
-\infer{\isa{{\isachardoublequote}C{\isachardoublequote}}}{\isa{{\isachardoublequote}x\ {\isasymin}\ {\isasymUnion}{\isasymA}{\isachardoublequote}} & \infer*{\isa{{\isachardoublequote}C{\isachardoublequote}}~}{\isa{{\isachardoublequote}{\isacharbrackleft}A{\isacharbrackright}{\isacharbrackleft}x\ {\isasymin}\ A{\isacharcomma}\ A\ {\isasymin}\ {\isasymA}{\isacharbrackright}{\isachardoublequote}}}}%
+\infer{\isa{{\isaliteral{22}{\isachardoublequote}}C{\isaliteral{22}{\isachardoublequote}}}}{\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C556E696F6E3E}{\isasymUnion}}{\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{22}{\isachardoublequote}}} & \infer*{\isa{{\isaliteral{22}{\isachardoublequote}}C{\isaliteral{22}{\isachardoublequote}}}~}{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5B}{\isacharbrackleft}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{2C}{\isacharcomma}}\ A\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}}}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -317,7 +317,7 @@
\medskip\noindent Although the Isar proof follows the natural
deduction rule closely, the text reads not as natural as
anticipated. There is a double occurrence of an arbitrary
- conclusion \isa{{\isachardoublequote}C{\isachardoublequote}}, which represents the final result, but is
+ conclusion \isa{{\isaliteral{22}{\isachardoublequote}}C{\isaliteral{22}{\isachardoublequote}}}, which represents the final result, but is
irrelevant for now. This issue arises for any elimination rule
involving local parameters. Isar provides the derived language
element \hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}, which is able to perform the same
@@ -331,10 +331,10 @@
%
\isatagproof
\isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymin}\ {\isasymUnion}{\isasymA}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C556E696F6E3E}{\isasymUnion}}{\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{obtain}\isamarkupfalse%
-\ A\ \isakeyword{where}\ {\isachardoublequoteopen}x\ {\isasymin}\ A{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}A\ {\isasymin}\ {\isasymA}{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ A\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
@@ -344,9 +344,9 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-\noindent Here we avoid to mention the final conclusion \isa{{\isachardoublequote}C{\isachardoublequote}}
+\noindent Here we avoid to mention the final conclusion \isa{{\isaliteral{22}{\isachardoublequote}}C{\isaliteral{22}{\isachardoublequote}}}
and return to plain forward reasoning. The rule involved in the
- ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}}'' proof is the same as before.%
+ ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}}'' proof is the same as before.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -357,19 +357,19 @@
\begin{isamarkuptext}%
The Pure logic \cite{paulson-found,paulson700} is an intuitionistic
fragment of higher-order logic \cite{church40}. In type-theoretic
- parlance, there are three levels of \isa{{\isachardoublequote}{\isasymlambda}{\isachardoublequote}}-calculus with
- corresponding arrows \isa{{\isachardoublequote}{\isasymRightarrow}{\isachardoublequote}}/\isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}}/\isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}}:
+ parlance, there are three levels of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{22}{\isachardoublequote}}}-calculus with
+ corresponding arrows \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}{\isaliteral{22}{\isachardoublequote}}}/\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{22}{\isachardoublequote}}}/\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}}:
\medskip
\begin{tabular}{ll}
- \isa{{\isachardoublequote}{\isasymalpha}\ {\isasymRightarrow}\ {\isasymbeta}{\isachardoublequote}} & syntactic function space (terms depending on terms) \\
- \isa{{\isachardoublequote}{\isasymAnd}x{\isachardot}\ B{\isacharparenleft}x{\isacharparenright}{\isachardoublequote}} & universal quantification (proofs depending on terms) \\
- \isa{{\isachardoublequote}A\ {\isasymLongrightarrow}\ B{\isachardoublequote}} & implication (proofs depending on proofs) \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{22}{\isachardoublequote}}} & syntactic function space (terms depending on terms) \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ B{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & universal quantification (proofs depending on terms) \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{22}{\isachardoublequote}}} & implication (proofs depending on proofs) \\
\end{tabular}
\medskip
\noindent Here only the types of syntactic terms, and the
- propositions of proof terms have been shown. The \isa{{\isachardoublequote}{\isasymlambda}{\isachardoublequote}}-structure of proofs can be recorded as an optional feature of
+ propositions of proof terms have been shown. The \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{22}{\isachardoublequote}}}-structure of proofs can be recorded as an optional feature of
the Pure inference kernel \cite{Berghofer-Nipkow:2000:TPHOL}, but
the formal system can never depend on them due to \emph{proof
irrelevance}.
@@ -377,7 +377,7 @@
On top of this most primitive layer of proofs, Pure implements a
generic calculus for nested natural deduction rules, similar to
\cite{Schroeder-Heister:1984}. Here object-logic inferences are
- internalized as formulae over \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}}.
+ internalized as formulae over \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}}.
Combining such rule statements may involve higher-order unification
\cite{paulson-natural}.%
\end{isamarkuptext}%
@@ -388,43 +388,43 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-Term syntax provides explicit notation for abstraction \isa{{\isachardoublequote}{\isasymlambda}x\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}{\isachardot}\ b{\isacharparenleft}x{\isacharparenright}{\isachardoublequote}} and application \isa{{\isachardoublequote}b\ a{\isachardoublequote}}, while types are usually
- implicit thanks to type-inference; terms of type \isa{{\isachardoublequote}prop{\isachardoublequote}} are
- called propositions. Logical statements are composed via \isa{{\isachardoublequote}{\isasymAnd}x\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}{\isachardot}\ B{\isacharparenleft}x{\isacharparenright}{\isachardoublequote}} and \isa{{\isachardoublequote}A\ {\isasymLongrightarrow}\ B{\isachardoublequote}}. Primitive reasoning operates on
- judgments of the form \isa{{\isachardoublequote}{\isasymGamma}\ {\isasymturnstile}\ {\isasymphi}{\isachardoublequote}}, with standard introduction
- and elimination rules for \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}} that refer to
- fixed parameters \isa{{\isachardoublequote}x\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlisub m{\isachardoublequote}} and hypotheses
- \isa{{\isachardoublequote}A\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ A\isactrlisub n{\isachardoublequote}} from the context \isa{{\isachardoublequote}{\isasymGamma}{\isachardoublequote}};
+Term syntax provides explicit notation for abstraction \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{2E}{\isachardot}}\ b{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} and application \isa{{\isaliteral{22}{\isachardoublequote}}b\ a{\isaliteral{22}{\isachardoublequote}}}, while types are usually
+ implicit thanks to type-inference; terms of type \isa{{\isaliteral{22}{\isachardoublequote}}prop{\isaliteral{22}{\isachardoublequote}}} are
+ called propositions. Logical statements are composed via \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{2E}{\isachardot}}\ B{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{22}{\isachardoublequote}}}. Primitive reasoning operates on
+ judgments of the form \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}}, with standard introduction
+ and elimination rules for \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}} that refer to
+ fixed parameters \isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E697375623E}{}\isactrlisub m{\isaliteral{22}{\isachardoublequote}}} and hypotheses
+ \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ A\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{22}{\isachardoublequote}}} from the context \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{22}{\isachardoublequote}}};
the corresponding proof terms are left implicit. The subsequent
- inference rules define \isa{{\isachardoublequote}{\isasymGamma}\ {\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} inductively, relative to a
+ inference rules define \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} inductively, relative to a
collection of axioms:
\[
- \infer{\isa{{\isachardoublequote}{\isasymturnstile}\ A{\isachardoublequote}}}{(\isa{{\isachardoublequote}A{\isachardoublequote}} \text{~axiom})}
+ \infer{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A{\isaliteral{22}{\isachardoublequote}}}}{(\isa{{\isaliteral{22}{\isachardoublequote}}A{\isaliteral{22}{\isachardoublequote}}} \text{~axiom})}
\qquad
- \infer{\isa{{\isachardoublequote}A\ {\isasymturnstile}\ A{\isachardoublequote}}}{}
+ \infer{\isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A{\isaliteral{22}{\isachardoublequote}}}}{}
\]
\[
- \infer{\isa{{\isachardoublequote}{\isasymGamma}\ {\isasymturnstile}\ {\isasymAnd}x{\isachardot}\ B{\isacharparenleft}x{\isacharparenright}{\isachardoublequote}}}{\isa{{\isachardoublequote}{\isasymGamma}\ {\isasymturnstile}\ B{\isacharparenleft}x{\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}x\ {\isasymnotin}\ {\isasymGamma}{\isachardoublequote}}}
+ \infer{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ B{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}}{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ {\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{22}{\isachardoublequote}}}}
\qquad
- \infer{\isa{{\isachardoublequote}{\isasymGamma}\ {\isasymturnstile}\ B{\isacharparenleft}a{\isacharparenright}{\isachardoublequote}}}{\isa{{\isachardoublequote}{\isasymGamma}\ {\isasymturnstile}\ {\isasymAnd}x{\isachardot}\ B{\isacharparenleft}x{\isacharparenright}{\isachardoublequote}}}
+ \infer{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}}{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ B{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}}
\]
\[
- \infer{\isa{{\isachardoublequote}{\isasymGamma}\ {\isacharminus}\ A\ {\isasymturnstile}\ A\ {\isasymLongrightarrow}\ B{\isachardoublequote}}}{\isa{{\isachardoublequote}{\isasymGamma}\ {\isasymturnstile}\ B{\isachardoublequote}}}
+ \infer{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{2D}{\isacharminus}}\ A\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{22}{\isachardoublequote}}}}{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{22}{\isachardoublequote}}}}
\qquad
- \infer{\isa{{\isachardoublequote}{\isasymGamma}\isactrlsub {\isadigit{1}}\ {\isasymunion}\ {\isasymGamma}\isactrlsub {\isadigit{2}}\ {\isasymturnstile}\ B{\isachardoublequote}}}{\isa{{\isachardoublequote}{\isasymGamma}\isactrlsub {\isadigit{1}}\ {\isasymturnstile}\ A\ {\isasymLongrightarrow}\ B{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymGamma}\isactrlsub {\isadigit{2}}\ {\isasymturnstile}\ A{\isachardoublequote}}}
+ \infer{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ {\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{22}{\isachardoublequote}}}}{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A{\isaliteral{22}{\isachardoublequote}}}}
\]
- Furthermore, Pure provides a built-in equality \isa{{\isachardoublequote}{\isasymequiv}\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ {\isasymRightarrow}\ {\isasymalpha}\ {\isasymRightarrow}\ prop{\isachardoublequote}} with axioms for reflexivity, substitution, extensionality,
- and \isa{{\isachardoublequote}{\isasymalpha}{\isasymbeta}{\isasymeta}{\isachardoublequote}}-conversion on \isa{{\isachardoublequote}{\isasymlambda}{\isachardoublequote}}-terms.
+ Furthermore, Pure provides a built-in equality \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ prop{\isaliteral{22}{\isachardoublequote}}} with axioms for reflexivity, substitution, extensionality,
+ and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{5C3C6574613E}{\isasymeta}}{\isaliteral{22}{\isachardoublequote}}}-conversion on \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{22}{\isachardoublequote}}}-terms.
\medskip An object-logic introduces another layer on top of Pure,
- e.g.\ with types \isa{{\isachardoublequote}i{\isachardoublequote}} for individuals and \isa{{\isachardoublequote}o{\isachardoublequote}} for
- propositions, term constants \isa{{\isachardoublequote}Trueprop\ {\isacharcolon}{\isacharcolon}\ o\ {\isasymRightarrow}\ prop{\isachardoublequote}} as
- (implicit) derivability judgment and connectives like \isa{{\isachardoublequote}{\isasymand}\ {\isacharcolon}{\isacharcolon}\ o\ {\isasymRightarrow}\ o\ {\isasymRightarrow}\ o{\isachardoublequote}} or \isa{{\isachardoublequote}{\isasymforall}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}i\ {\isasymRightarrow}\ o{\isacharparenright}\ {\isasymRightarrow}\ o{\isachardoublequote}}, and axioms for object-level
- rules such as \isa{{\isachardoublequote}conjI{\isacharcolon}\ A\ {\isasymLongrightarrow}\ B\ {\isasymLongrightarrow}\ A\ {\isasymand}\ B{\isachardoublequote}} or \isa{{\isachardoublequote}allI{\isacharcolon}\ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ B\ x{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymforall}x{\isachardot}\ B\ x{\isachardoublequote}}. Derived object rules are represented as theorems of
+ e.g.\ with types \isa{{\isaliteral{22}{\isachardoublequote}}i{\isaliteral{22}{\isachardoublequote}}} for individuals and \isa{{\isaliteral{22}{\isachardoublequote}}o{\isaliteral{22}{\isachardoublequote}}} for
+ propositions, term constants \isa{{\isaliteral{22}{\isachardoublequote}}Trueprop\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ prop{\isaliteral{22}{\isachardoublequote}}} as
+ (implicit) derivability judgment and connectives like \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o{\isaliteral{22}{\isachardoublequote}}} or \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ o{\isaliteral{22}{\isachardoublequote}}}, and axioms for object-level
+ rules such as \isa{{\isaliteral{22}{\isachardoublequote}}conjI{\isaliteral{3A}{\isacharcolon}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequote}}} or \isa{{\isaliteral{22}{\isachardoublequote}}allI{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{22}{\isachardoublequote}}}. Derived object rules are represented as theorems of
Pure. After the initial object-logic setup, further axiomatizations
are usually avoided; plain definitions and derived principles are
used exclusively.%
@@ -438,45 +438,45 @@
\begin{isamarkuptext}%
Primitive inferences mostly serve foundational purposes. The main
reasoning mechanisms of Pure operate on nested natural deduction
- rules expressed as formulae, using \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}} to bind local
- parameters and \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}} to express entailment. Multiple
+ rules expressed as formulae, using \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{22}{\isachardoublequote}}} to bind local
+ parameters and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}} to express entailment. Multiple
parameters and premises are represented by repeating these
connectives in a right-associative manner.
- Since \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}} commute thanks to the theorem
- \isa{{\isachardoublequote}{\isacharparenleft}A\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ B\ x{\isacharparenright}{\isacharparenright}\ {\isasymequiv}\ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ A\ {\isasymLongrightarrow}\ B\ x{\isacharparenright}{\isachardoublequote}}, we may assume w.l.o.g.\
+ Since \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}} commute thanks to the theorem
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}, we may assume w.l.o.g.\
that rule statements always observe the normal form where
quantifiers are pulled in front of implications at each level of
nesting. This means that any Pure proposition may be presented as a
\emph{Hereditary Harrop Formula} \cite{Miller:1991} which is of the
- form \isa{{\isachardoublequote}{\isasymAnd}x\isactrlisub {\isadigit{1}}\ {\isasymdots}\ x\isactrlisub m{\isachardot}\ H\isactrlisub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ H\isactrlisub n\ {\isasymLongrightarrow}\ A{\isachardoublequote}} for \isa{{\isachardoublequote}m{\isacharcomma}\ n\ {\isasymge}\ {\isadigit{0}}{\isachardoublequote}}, and \isa{{\isachardoublequote}A{\isachardoublequote}} atomic, and \isa{{\isachardoublequote}H\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ H\isactrlisub n{\isachardoublequote}} being recursively of the same format.
+ form \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E697375623E}{}\isactrlisub m{\isaliteral{2E}{\isachardot}}\ H\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ H\isaliteral{5C3C5E697375623E}{}\isactrlisub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A{\isaliteral{22}{\isachardoublequote}}} for \isa{{\isaliteral{22}{\isachardoublequote}}m{\isaliteral{2C}{\isacharcomma}}\ n\ {\isaliteral{5C3C67653E}{\isasymge}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequote}}}, and \isa{{\isaliteral{22}{\isachardoublequote}}A{\isaliteral{22}{\isachardoublequote}}} atomic, and \isa{{\isaliteral{22}{\isachardoublequote}}H\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ H\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{22}{\isachardoublequote}}} being recursively of the same format.
Following the convention that outermost quantifiers are implicit,
- Horn clauses \isa{{\isachardoublequote}A\isactrlisub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ A\isactrlisub n\ {\isasymLongrightarrow}\ A{\isachardoublequote}} are a special
+ Horn clauses \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ A\isaliteral{5C3C5E697375623E}{}\isactrlisub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A{\isaliteral{22}{\isachardoublequote}}} are a special
case of this.
- For example, \isa{{\isachardoublequote}{\isasyminter}{\isachardoublequote}}-introduction rule encountered before is
+ For example, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C696E7465723E}{\isasyminter}}{\isaliteral{22}{\isachardoublequote}}}-introduction rule encountered before is
represented as a Pure theorem as follows:
\[
- \isa{{\isachardoublequote}IntI{\isacharcolon}{\isachardoublequote}}~\isa{{\isachardoublequote}x\ {\isasymin}\ A\ {\isasymLongrightarrow}\ x\ {\isasymin}\ B\ {\isasymLongrightarrow}\ x\ {\isasymin}\ A\ {\isasyminter}\ B{\isachardoublequote}}
+ \isa{{\isaliteral{22}{\isachardoublequote}}IntI{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ B{\isaliteral{22}{\isachardoublequote}}}
\]
\noindent This is a plain Horn clause, since no further nesting on
- the left is involved. The general \isa{{\isachardoublequote}{\isasymInter}{\isachardoublequote}}-introduction
+ the left is involved. The general \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C496E7465723E}{\isasymInter}}{\isaliteral{22}{\isachardoublequote}}}-introduction
corresponds to a Hereditary Harrop Formula with one additional level
of nesting:
\[
- \isa{{\isachardoublequote}InterI{\isacharcolon}{\isachardoublequote}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymAnd}A{\isachardot}\ A\ {\isasymin}\ {\isasymA}\ {\isasymLongrightarrow}\ x\ {\isasymin}\ A{\isacharparenright}\ {\isasymLongrightarrow}\ x\ {\isasymin}\ {\isasymInter}{\isasymA}{\isachardoublequote}}
+ \isa{{\isaliteral{22}{\isachardoublequote}}InterI{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}A{\isaliteral{2E}{\isachardot}}\ A\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C413E}{\isasymA}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{5C3C496E7465723E}{\isasymInter}}{\isaliteral{5C3C413E}{\isasymA}}{\isaliteral{22}{\isachardoublequote}}}
\]
- \medskip Goals are also represented as rules: \isa{{\isachardoublequote}A\isactrlisub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ A\isactrlisub n\ {\isasymLongrightarrow}\ C{\isachardoublequote}} states that the sub-goals \isa{{\isachardoublequote}A\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ A\isactrlisub n{\isachardoublequote}} entail the result \isa{{\isachardoublequote}C{\isachardoublequote}}; for \isa{{\isachardoublequote}n\ {\isacharequal}\ {\isadigit{0}}{\isachardoublequote}} the
- goal is finished. To allow \isa{{\isachardoublequote}C{\isachardoublequote}} being a rule statement
- itself, we introduce the protective marker \isa{{\isachardoublequote}{\isacharhash}\ {\isacharcolon}{\isacharcolon}\ prop\ {\isasymRightarrow}\ prop{\isachardoublequote}}, which is defined as identity and hidden from the user. We
+ \medskip Goals are also represented as rules: \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ A\isaliteral{5C3C5E697375623E}{}\isactrlisub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{22}{\isachardoublequote}}} states that the sub-goals \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ A\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{22}{\isachardoublequote}}} entail the result \isa{{\isaliteral{22}{\isachardoublequote}}C{\isaliteral{22}{\isachardoublequote}}}; for \isa{{\isaliteral{22}{\isachardoublequote}}n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequote}}} the
+ goal is finished. To allow \isa{{\isaliteral{22}{\isachardoublequote}}C{\isaliteral{22}{\isachardoublequote}}} being a rule statement
+ itself, we introduce the protective marker \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ prop\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ prop{\isaliteral{22}{\isachardoublequote}}}, which is defined as identity and hidden from the user. We
initialize and finish goal states as follows:
\[
\begin{array}{c@ {\qquad}c}
- \infer[(\indexdef{}{inference}{init}\hypertarget{inference.init}{\hyperlink{inference.init}{\mbox{\isa{init}}}})]{\isa{{\isachardoublequote}C\ {\isasymLongrightarrow}\ {\isacharhash}C{\isachardoublequote}}}{} &
- \infer[(\indexdef{}{inference}{finish}\hypertarget{inference.finish}{\hyperlink{inference.finish}{\mbox{\isa{finish}}}})]{\isa{C}}{\isa{{\isachardoublequote}{\isacharhash}C{\isachardoublequote}}}
+ \infer[(\indexdef{}{inference}{init}\hypertarget{inference.init}{\hyperlink{inference.init}{\mbox{\isa{init}}}})]{\isa{{\isaliteral{22}{\isachardoublequote}}C\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{23}{\isacharhash}}C{\isaliteral{22}{\isachardoublequote}}}}{} &
+ \infer[(\indexdef{}{inference}{finish}\hypertarget{inference.finish}{\hyperlink{inference.finish}{\mbox{\isa{finish}}}})]{\isa{C}}{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}C{\isaliteral{22}{\isachardoublequote}}}}
\end{array}
\]
@@ -484,29 +484,29 @@
a finished form is achieved. Here the two main reasoning principles
are \hyperlink{inference.resolution}{\mbox{\isa{resolution}}}, for back-chaining a rule against a
sub-goal (replacing it by zero or more sub-goals), and \hyperlink{inference.assumption}{\mbox{\isa{assumption}}}, for solving a sub-goal (finding a short-circuit with
- local assumptions). Below \isa{{\isachardoublequote}\isactrlvec x{\isachardoublequote}} stands for \isa{{\isachardoublequote}x\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlisub n{\isachardoublequote}} (\isa{{\isachardoublequote}n\ {\isasymge}\ {\isadigit{0}}{\isachardoublequote}}).
+ local assumptions). Below \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{22}{\isachardoublequote}}} stands for \isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{22}{\isachardoublequote}}} (\isa{{\isaliteral{22}{\isachardoublequote}}n\ {\isaliteral{5C3C67653E}{\isasymge}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequote}}}).
\[
\infer[(\indexdef{}{inference}{resolution}\hypertarget{inference.resolution}{\hyperlink{inference.resolution}{\mbox{\isa{resolution}}}})]
- {\isa{{\isachardoublequote}{\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec H\ \isactrlvec x\ {\isasymLongrightarrow}\ \isactrlvec A\ {\isacharparenleft}\isactrlvec a\ \isactrlvec x{\isacharparenright}{\isacharparenright}{\isasymvartheta}\ {\isasymLongrightarrow}\ C{\isasymvartheta}{\isachardoublequote}}}
+ {\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec H\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec A\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec a\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}{\isaliteral{22}{\isachardoublequote}}}}
{\begin{tabular}{rl}
- \isa{{\isachardoublequote}rule{\isacharcolon}{\isachardoublequote}} &
- \isa{{\isachardoublequote}\isactrlvec A\ \isactrlvec a\ {\isasymLongrightarrow}\ B\ \isactrlvec a{\isachardoublequote}} \\
- \isa{{\isachardoublequote}goal{\isacharcolon}{\isachardoublequote}} &
- \isa{{\isachardoublequote}{\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec H\ \isactrlvec x\ {\isasymLongrightarrow}\ B{\isacharprime}\ \isactrlvec x{\isacharparenright}\ {\isasymLongrightarrow}\ C{\isachardoublequote}} \\
- \isa{{\isachardoublequote}goal\ unifier{\isacharcolon}{\isachardoublequote}} &
- \isa{{\isachardoublequote}{\isacharparenleft}{\isasymlambda}\isactrlvec x{\isachardot}\ B\ {\isacharparenleft}\isactrlvec a\ \isactrlvec x{\isacharparenright}{\isacharparenright}{\isasymvartheta}\ {\isacharequal}\ B{\isacharprime}{\isasymvartheta}{\isachardoublequote}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}rule{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} &
+ \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7665633E}{}\isactrlvec A\ \isaliteral{5C3C5E7665633E}{}\isactrlvec a\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ \isaliteral{5C3C5E7665633E}{}\isactrlvec a{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}goal{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} &
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec H\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{27}{\isacharprime}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}goal\ unifier{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} &
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ B\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec a\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}\ {\isaliteral{3D}{\isacharequal}}\ B{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}}
\]
\medskip
\[
- \infer[(\indexdef{}{inference}{assumption}\hypertarget{inference.assumption}{\hyperlink{inference.assumption}{\mbox{\isa{assumption}}}})]{\isa{{\isachardoublequote}C{\isasymvartheta}{\isachardoublequote}}}
+ \infer[(\indexdef{}{inference}{assumption}\hypertarget{inference.assumption}{\hyperlink{inference.assumption}{\mbox{\isa{assumption}}}})]{\isa{{\isaliteral{22}{\isachardoublequote}}C{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}{\isaliteral{22}{\isachardoublequote}}}}
{\begin{tabular}{rl}
- \isa{{\isachardoublequote}goal{\isacharcolon}{\isachardoublequote}} &
- \isa{{\isachardoublequote}{\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec H\ \isactrlvec x\ {\isasymLongrightarrow}\ A\ \isactrlvec x{\isacharparenright}\ {\isasymLongrightarrow}\ C{\isachardoublequote}} \\
- \isa{{\isachardoublequote}assm\ unifier{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}A{\isasymvartheta}\ {\isacharequal}\ H\isactrlsub i{\isasymvartheta}{\isachardoublequote}}~~\text{(for some~\isa{{\isachardoublequote}H\isactrlsub i{\isachardoublequote}})} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}goal{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} &
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec H\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}assm\ unifier{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}A{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}\ {\isaliteral{3D}{\isacharequal}}\ H\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}{\isaliteral{22}{\isachardoublequote}}}~~\text{(for some~\isa{{\isaliteral{22}{\isachardoublequote}}H\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}})} \\
\end{tabular}}
\]
@@ -516,44 +516,44 @@
{\footnotesize
\medskip
\begin{tabular}{r@ {\quad}l}
- \isa{{\isachardoublequote}{\isacharparenleft}A\ {\isasymand}\ B\ {\isasymLongrightarrow}\ B\ {\isasymand}\ A{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharhash}{\isacharparenleft}A\ {\isasymand}\ B\ {\isasymLongrightarrow}\ B\ {\isasymand}\ A{\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}init{\isacharparenright}{\isachardoublequote}} \\
- \isa{{\isachardoublequote}{\isacharparenleft}A\ {\isasymand}\ B\ {\isasymLongrightarrow}\ B{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}A\ {\isasymand}\ B\ {\isasymLongrightarrow}\ A{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharhash}{\isasymdots}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}resolution\ B\ {\isasymLongrightarrow}\ A\ {\isasymLongrightarrow}\ B\ {\isasymand}\ A{\isacharparenright}{\isachardoublequote}} \\
- \isa{{\isachardoublequote}{\isacharparenleft}A\ {\isasymand}\ B\ {\isasymLongrightarrow}\ A\ {\isasymand}\ B{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}A\ {\isasymand}\ B\ {\isasymLongrightarrow}\ A{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharhash}{\isasymdots}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}resolution\ A\ {\isasymand}\ B\ {\isasymLongrightarrow}\ B{\isacharparenright}{\isachardoublequote}} \\
- \isa{{\isachardoublequote}{\isacharparenleft}A\ {\isasymand}\ B\ {\isasymLongrightarrow}\ A{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharhash}{\isasymdots}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}assumption{\isacharparenright}{\isachardoublequote}} \\
- \isa{{\isachardoublequote}{\isacharparenleft}A\ {\isasymand}\ B\ {\isasymLongrightarrow}\ B\ {\isasymand}\ A{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharhash}{\isasymdots}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}resolution\ A\ {\isasymand}\ B\ {\isasymLongrightarrow}\ A{\isacharparenright}{\isachardoublequote}} \\
- \isa{{\isachardoublequote}{\isacharhash}{\isasymdots}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}assumption{\isacharparenright}{\isachardoublequote}} \\
- \isa{{\isachardoublequote}A\ {\isasymand}\ B\ {\isasymLongrightarrow}\ B\ {\isasymand}\ A{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}finish{\isacharparenright}{\isachardoublequote}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{23}{\isacharhash}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}init{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{23}{\isacharhash}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}resolution\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{23}{\isacharhash}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}resolution\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{23}{\isacharhash}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}assumption{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{23}{\isacharhash}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}resolution\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}assumption{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}finish{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}
\medskip
}
Compositions of \hyperlink{inference.assumption}{\mbox{\isa{assumption}}} after \hyperlink{inference.resolution}{\mbox{\isa{resolution}}} occurs quite often, typically in elimination steps.
Traditional Isabelle tactics accommodate this by a combined
- \indexdef{}{inference}{elim\_resolution}\hypertarget{inference.elim-resolution}{\hyperlink{inference.elim-resolution}{\mbox{\isa{elim{\isacharunderscore}resolution}}}} principle. In contrast, Isar uses
+ \indexdef{}{inference}{elim\_resolution}\hypertarget{inference.elim-resolution}{\hyperlink{inference.elim-resolution}{\mbox{\isa{elim{\isaliteral{5F}{\isacharunderscore}}resolution}}}} principle. In contrast, Isar uses
a slightly more refined combination, where the assumptions to be
closed are marked explicitly, using again the protective marker
- \isa{{\isachardoublequote}{\isacharhash}{\isachardoublequote}}:
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}{\isaliteral{22}{\isachardoublequote}}}:
\[
\infer[(\hyperlink{inference.refinement}{\mbox{\isa{refinement}}})]
- {\isa{{\isachardoublequote}{\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec H\ \isactrlvec x\ {\isasymLongrightarrow}\ \isactrlvec G{\isacharprime}\ {\isacharparenleft}\isactrlvec a\ \isactrlvec x{\isacharparenright}{\isacharparenright}{\isasymvartheta}\ {\isasymLongrightarrow}\ C{\isasymvartheta}{\isachardoublequote}}}
+ {\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec H\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec G{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec a\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}{\isaliteral{22}{\isachardoublequote}}}}
{\begin{tabular}{rl}
- \isa{{\isachardoublequote}sub{\isasymdash}proof{\isacharcolon}{\isachardoublequote}} &
- \isa{{\isachardoublequote}\isactrlvec G\ \isactrlvec a\ {\isasymLongrightarrow}\ B\ \isactrlvec a{\isachardoublequote}} \\
- \isa{{\isachardoublequote}goal{\isacharcolon}{\isachardoublequote}} &
- \isa{{\isachardoublequote}{\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec H\ \isactrlvec x\ {\isasymLongrightarrow}\ B{\isacharprime}\ \isactrlvec x{\isacharparenright}\ {\isasymLongrightarrow}\ C{\isachardoublequote}} \\
- \isa{{\isachardoublequote}goal\ unifier{\isacharcolon}{\isachardoublequote}} &
- \isa{{\isachardoublequote}{\isacharparenleft}{\isasymlambda}\isactrlvec x{\isachardot}\ B\ {\isacharparenleft}\isactrlvec a\ \isactrlvec x{\isacharparenright}{\isacharparenright}{\isasymvartheta}\ {\isacharequal}\ B{\isacharprime}{\isasymvartheta}{\isachardoublequote}} \\
- \isa{{\isachardoublequote}assm\ unifiers{\isacharcolon}{\isachardoublequote}} &
- \isa{{\isachardoublequote}{\isacharparenleft}{\isasymlambda}\isactrlvec x{\isachardot}\ G\isactrlsub j\ {\isacharparenleft}\isactrlvec a\ \isactrlvec x{\isacharparenright}{\isacharparenright}{\isasymvartheta}\ {\isacharequal}\ {\isacharhash}H\isactrlsub i{\isasymvartheta}{\isachardoublequote}} \\
- & \quad (for each marked \isa{{\isachardoublequote}G\isactrlsub j{\isachardoublequote}} some \isa{{\isachardoublequote}{\isacharhash}H\isactrlsub i{\isachardoublequote}}) \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}sub{\isaliteral{5C3C646173683E}{\isasymdash}}proof{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} &
+ \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7665633E}{}\isactrlvec G\ \isaliteral{5C3C5E7665633E}{}\isactrlvec a\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ \isaliteral{5C3C5E7665633E}{}\isactrlvec a{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}goal{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} &
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec H\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{27}{\isacharprime}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}goal\ unifier{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} &
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ B\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec a\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}\ {\isaliteral{3D}{\isacharequal}}\ B{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}assm\ unifiers{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} &
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ G\isaliteral{5C3C5E7375623E}{}\isactrlsub j\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec a\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{23}{\isacharhash}}H\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{5C3C76617274686574613E}{\isasymvartheta}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \quad (for each marked \isa{{\isaliteral{22}{\isachardoublequote}}G\isaliteral{5C3C5E7375623E}{}\isactrlsub j{\isaliteral{22}{\isachardoublequote}}} some \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}H\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}}) \\
\end{tabular}}
\]
- \noindent Here the \isa{{\isachardoublequote}sub{\isasymdash}proof{\isachardoublequote}} rule stems from the
+ \noindent Here the \isa{{\isaliteral{22}{\isachardoublequote}}sub{\isaliteral{5C3C646173683E}{\isasymdash}}proof{\isaliteral{22}{\isachardoublequote}}} rule stems from the
main \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}-\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}-\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}} outline of
Isar (cf.\ \secref{sec:framework-subproof}): each assumption
- indicated in the text results in a marked premise \isa{{\isachardoublequote}G{\isachardoublequote}} above.
+ indicated in the text results in a marked premise \isa{{\isaliteral{22}{\isachardoublequote}}G{\isaliteral{22}{\isachardoublequote}}} above.
The marking enforces resolution against one of the sub-goal's
premises. Consequently, \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}-\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}-\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}} enables to fit the result of a sub-proof quite robustly into a
pending sub-goal, while maintaining a good measure of flexibility.%
@@ -574,46 +574,46 @@
Isar is an exercise in sound minimalism. Approximately half of the
language is introduced as primitive, the rest defined as derived
concepts. The following grammar describes the core language
- (category \isa{{\isachardoublequote}proof{\isachardoublequote}}), which is embedded into theory
+ (category \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{22}{\isachardoublequote}}}), which is embedded into theory
specification elements such as \hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}; see also
- \secref{sec:framework-stmt} for the separate category \isa{{\isachardoublequote}statement{\isachardoublequote}}.
+ \secref{sec:framework-stmt} for the separate category \isa{{\isaliteral{22}{\isachardoublequote}}statement{\isaliteral{22}{\isachardoublequote}}}.
\medskip
\begin{tabular}{rcl}
- \isa{{\isachardoublequote}theory{\isasymdash}stmt{\isachardoublequote}} & = & \hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}~\isa{{\isachardoublequote}statement\ proof\ \ {\isacharbar}{\isachardoublequote}}~~\hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}~\isa{{\isachardoublequote}{\isasymdots}\ \ {\isacharbar}\ \ {\isasymdots}{\isachardoublequote}} \\[1ex]
+ \isa{{\isaliteral{22}{\isachardoublequote}}theory{\isaliteral{5C3C646173683E}{\isasymdash}}stmt{\isaliteral{22}{\isachardoublequote}}} & = & \hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}statement\ proof\ \ {\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}}~~\hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\[1ex]
- \isa{{\isachardoublequote}proof{\isachardoublequote}} & = & \isa{{\isachardoublequote}prfx\isactrlsup {\isacharasterisk}{\isachardoublequote}}~\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}method\isactrlsup {\isacharquery}\ stmt\isactrlsup {\isacharasterisk}{\isachardoublequote}}~\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isachardoublequote}method\isactrlsup {\isacharquery}{\isachardoublequote}} \\[1ex]
+ \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{22}{\isachardoublequote}}} & = & \isa{{\isaliteral{22}{\isachardoublequote}}prfx\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}method\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{3F}{\isacharquery}}\ stmt\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}method\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}} \\[1ex]
- \isa{prfx} & = & \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{{\isachardoublequote}facts{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}~\isa{{\isachardoublequote}facts{\isachardoublequote}} \\
+ \isa{prfx} & = & \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}facts{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}facts{\isaliteral{22}{\isachardoublequote}}} \\
- \isa{stmt} & = & \hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isacharbraceleft}}}}}~\isa{{\isachardoublequote}stmt\isactrlsup {\isacharasterisk}{\isachardoublequote}}~\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isacharbraceright}}}}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.next}{\mbox{\isa{\isacommand{next}}}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isachardoublequote}name\ {\isacharequal}\ facts{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}~\isa{{\isachardoublequote}term\ {\isacharequal}\ term{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isachardoublequote}var\isactrlsup {\isacharplus}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}{\isasymguillemotleft}inference{\isasymguillemotright}\ name{\isacharcolon}\ props{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharquery}{\isachardoublequote}}~\isa{goal} \\
- \isa{goal} & = & \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}name{\isacharcolon}\ props\ proof{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{{\isachardoublequote}name{\isacharcolon}\ props\ proof{\isachardoublequote}} \\
+ \isa{stmt} & = & \hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isaliteral{7B}{\isacharbraceleft}}}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}stmt\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isaliteral{7D}{\isacharbraceright}}}}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.next}{\mbox{\isa{\isacommand{next}}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name\ {\isaliteral{3D}{\isacharequal}}\ facts{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}term\ {\isaliteral{3D}{\isacharequal}}\ term{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}var\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6775696C6C656D6F746C6566743E}{\isasymguillemotleft}}inference{\isaliteral{5C3C6775696C6C656D6F7472696768743E}{\isasymguillemotright}}\ name{\isaliteral{3A}{\isacharcolon}}\ props{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}~\isa{goal} \\
+ \isa{goal} & = & \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{3A}{\isacharcolon}}\ props\ proof{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{3A}{\isacharcolon}}\ props\ proof{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}
\medskip Simultaneous propositions or facts may be separated by the
\hyperlink{keyword.and}{\mbox{\isa{\isakeyword{and}}}} keyword.
\medskip The syntax for terms and propositions is inherited from
- Pure (and the object-logic). A \isa{{\isachardoublequote}pattern{\isachardoublequote}} is a \isa{{\isachardoublequote}term{\isachardoublequote}} with schematic variables, to be bound by higher-order
+ Pure (and the object-logic). A \isa{{\isaliteral{22}{\isachardoublequote}}pattern{\isaliteral{22}{\isachardoublequote}}} is a \isa{{\isaliteral{22}{\isachardoublequote}}term{\isaliteral{22}{\isachardoublequote}}} with schematic variables, to be bound by higher-order
matching.
\medskip Facts may be referenced by name or proposition. For
- example, the result of ``\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ A\ {\isasymlangle}proof{\isasymrangle}{\isachardoublequote}}''
- becomes available both as \isa{{\isachardoublequote}a{\isachardoublequote}} and
- \isacharbackquoteopen\isa{{\isachardoublequote}A{\isachardoublequote}}\isacharbackquoteclose. Moreover,
+ example, the result of ``\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ A\ {\isaliteral{5C3C6C616E676C653E}{\isasymlangle}}proof{\isaliteral{5C3C72616E676C653E}{\isasymrangle}}{\isaliteral{22}{\isachardoublequote}}}''
+ becomes available both as \isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{22}{\isachardoublequote}}} and
+ \isacharbackquoteopen\isa{{\isaliteral{22}{\isachardoublequote}}A{\isaliteral{22}{\isachardoublequote}}}\isacharbackquoteclose. Moreover,
fact expressions may involve attributes that modify either the
theorem or the background context. For example, the expression
- ``\isa{{\isachardoublequote}a\ {\isacharbrackleft}OF\ b{\isacharbrackright}{\isachardoublequote}}'' refers to the composition of two facts
+ ``\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{5B}{\isacharbrackleft}}OF\ b{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}'' refers to the composition of two facts
according to the \hyperlink{inference.resolution}{\mbox{\isa{resolution}}} inference of
- \secref{sec:framework-resolution}, while ``\isa{{\isachardoublequote}a\ {\isacharbrackleft}intro{\isacharbrackright}{\isachardoublequote}}''
+ \secref{sec:framework-resolution}, while ``\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}''
declares a fact as introduction rule in the context.
The special fact called ``\hyperlink{fact.this}{\mbox{\isa{this}}}'' always refers to the last
@@ -623,31 +623,31 @@
\medskip
\begin{tabular}{rcl}
- \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{a} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{a}~\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}} \\
- \hyperlink{command.with}{\mbox{\isa{\isacommand{with}}}}~\isa{a} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} & \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{{\isachardoublequote}a\ {\isasymAND}\ this{\isachardoublequote}} \\
+ \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{a} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{a}~\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}} \\
+ \hyperlink{command.with}{\mbox{\isa{\isacommand{with}}}}~\isa{a} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ this{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}
\medskip
- The \isa{{\isachardoublequote}method{\isachardoublequote}} category is essentially a parameter and may be
+ The \isa{{\isaliteral{22}{\isachardoublequote}}method{\isaliteral{22}{\isachardoublequote}}} category is essentially a parameter and may be
populated later. Methods use the facts indicated by \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}} or \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}, and then operate on the goal state.
- Some basic methods are predefined: ``\hyperlink{method.-}{\mbox{\isa{{\isacharminus}}}}'' leaves the goal
+ Some basic methods are predefined: ``\hyperlink{method.-}{\mbox{\isa{{\isaliteral{2D}{\isacharminus}}}}}'' leaves the goal
unchanged, ``\hyperlink{method.this}{\mbox{\isa{this}}}'' applies the facts as rules to the
goal, ``\hyperlink{method.rule}{\mbox{\isa{rule}}}'' applies the facts to another rule and the
result to the goal (both ``\hyperlink{method.this}{\mbox{\isa{this}}}'' and ``\hyperlink{method.rule}{\mbox{\isa{rule}}}''
refer to \hyperlink{inference.resolution}{\mbox{\isa{resolution}}} of
\secref{sec:framework-resolution}). The secondary arguments to
- ``\hyperlink{method.rule}{\mbox{\isa{rule}}}'' may be specified explicitly as in ``\isa{{\isachardoublequote}{\isacharparenleft}rule\ a{\isacharparenright}{\isachardoublequote}}'', or picked from the context. In the latter case, the system
+ ``\hyperlink{method.rule}{\mbox{\isa{rule}}}'' may be specified explicitly as in ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}rule\ a{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'', or picked from the context. In the latter case, the system
first tries rules declared as \hyperlink{attribute.Pure.elim}{\mbox{\isa{elim}}} or
\hyperlink{attribute.Pure.dest}{\mbox{\isa{dest}}}, followed by those declared as \hyperlink{attribute.Pure.intro}{\mbox{\isa{intro}}}.
The default method for \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}} is ``\hyperlink{method.rule}{\mbox{\isa{rule}}}''
(arguments picked from the context), for \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}} it is
- ``\hyperlink{method.-}{\mbox{\isa{{\isacharminus}}}}''. Further abbreviations for terminal proof steps
- are ``\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isachardoublequote}method\isactrlsub {\isadigit{1}}\ method\isactrlsub {\isadigit{2}}{\isachardoublequote}}'' for
- ``\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}method\isactrlsub {\isadigit{1}}{\isachardoublequote}}~\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isachardoublequote}method\isactrlsub {\isadigit{2}}{\isachardoublequote}}'', and ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}}'' for ``\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\hyperlink{method.rule}{\mbox{\isa{rule}}}, and ``\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isachardot}}}}}'' for ``\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\hyperlink{method.this}{\mbox{\isa{this}}}''. The \hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}} element operates
+ ``\hyperlink{method.-}{\mbox{\isa{{\isaliteral{2D}{\isacharminus}}}}}''. Further abbreviations for terminal proof steps
+ are ``\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}method\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ method\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}}'' for
+ ``\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}method\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}method\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}}'', and ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}}'' for ``\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\hyperlink{method.rule}{\mbox{\isa{rule}}}, and ``\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}}}}}'' for ``\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\hyperlink{method.this}{\mbox{\isa{this}}}''. The \hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}} element operates
directly on the current facts and goal by applying equalities.
- \medskip Block structure can be indicated explicitly by ``\hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isacharbraceleft}}}}}~\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}~\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isacharbraceright}}}}}'', although the body of a sub-proof
+ \medskip Block structure can be indicated explicitly by ``\hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isaliteral{7B}{\isacharbraceleft}}}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isaliteral{7D}{\isacharbraceright}}}}}}'', although the body of a sub-proof
already involves implicit nesting. In any case, \hyperlink{command.next}{\mbox{\isa{\isacommand{next}}}}
jumps into the next section of a block, i.e.\ it acts like closing
an implicit block scope and opening another one; there is no direct
@@ -667,18 +667,18 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-In judgments \isa{{\isachardoublequote}{\isasymGamma}\ {\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} of the primitive framework, \isa{{\isachardoublequote}{\isasymGamma}{\isachardoublequote}}
+In judgments \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} of the primitive framework, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}{\isaliteral{22}{\isachardoublequote}}}
essentially acts like a proof context. Isar elaborates this idea
towards a higher-level notion, with additional information for
type-inference, term abbreviations, local facts, hypotheses etc.
- The element \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isachardoublequote}x\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}{\isachardoublequote}} declares a local
+ The element \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{22}{\isachardoublequote}}} declares a local
parameter, i.e.\ an arbitrary-but-fixed entity of a given type; in
- results exported from the context, \isa{{\isachardoublequote}x{\isachardoublequote}} may become anything.
- The \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}{\isasymguillemotleft}inference{\isasymguillemotright}{\isachardoublequote}} element provides a
- general interface to hypotheses: ``\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}{\isasymguillemotleft}inference{\isasymguillemotright}\ A{\isachardoublequote}}'' produces \isa{{\isachardoublequote}A\ {\isasymturnstile}\ A{\isachardoublequote}} locally, while the
+ results exported from the context, \isa{{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}} may become anything.
+ The \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6775696C6C656D6F746C6566743E}{\isasymguillemotleft}}inference{\isaliteral{5C3C6775696C6C656D6F7472696768743E}{\isasymguillemotright}}{\isaliteral{22}{\isachardoublequote}}} element provides a
+ general interface to hypotheses: ``\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6775696C6C656D6F746C6566743E}{\isasymguillemotleft}}inference{\isaliteral{5C3C6775696C6C656D6F7472696768743E}{\isasymguillemotright}}\ A{\isaliteral{22}{\isachardoublequote}}}'' produces \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A{\isaliteral{22}{\isachardoublequote}}} locally, while the
included inference tells how to discharge \isa{A} from results
- \isa{{\isachardoublequote}A\ {\isasymturnstile}\ B{\isachardoublequote}} later on. There is no user-syntax for \isa{{\isachardoublequote}{\isasymguillemotleft}inference{\isasymguillemotright}{\isachardoublequote}}, i.e.\ it may only occur internally when derived
+ \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{22}{\isachardoublequote}}} later on. There is no user-syntax for \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6775696C6C656D6F746C6566743E}{\isasymguillemotleft}}inference{\isaliteral{5C3C6775696C6C656D6F7472696768743E}{\isasymguillemotright}}{\isaliteral{22}{\isachardoublequote}}}, i.e.\ it may only occur internally when derived
commands are defined in ML.
At the user-level, the default inference for \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}} is
@@ -687,62 +687,62 @@
\medskip
\begin{tabular}{rcl}
- \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}}~\isa{A} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} & \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}{\isasymguillemotleft}weak{\isasymdash}discharge{\isasymguillemotright}\ A{\isachardoublequote}} \\
- \hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isachardoublequote}x\ {\isasymequiv}\ a{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} & \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}{\isasymguillemotleft}expansion{\isasymguillemotright}\ x\ {\isasymequiv}\ a{\isachardoublequote}} \\
+ \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}}~\isa{A} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6775696C6C656D6F746C6566743E}{\isasymguillemotleft}}weak{\isaliteral{5C3C646173683E}{\isasymdash}}discharge{\isaliteral{5C3C6775696C6C656D6F7472696768743E}{\isasymguillemotright}}\ A{\isaliteral{22}{\isachardoublequote}}} \\
+ \hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ a{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6775696C6C656D6F746C6566743E}{\isasymguillemotleft}}expansion{\isaliteral{5C3C6775696C6C656D6F7472696768743E}{\isasymguillemotright}}\ x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ a{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}
\medskip
\[
- \infer[(\indexdef{}{inference}{discharge}\hypertarget{inference.discharge}{\hyperlink{inference.discharge}{\mbox{\isa{discharge}}}})]{\isa{{\isachardoublequote}{\isasymstrut}{\isasymGamma}\ {\isacharminus}\ A\ {\isasymturnstile}\ {\isacharhash}A\ {\isasymLongrightarrow}\ B{\isachardoublequote}}}{\isa{{\isachardoublequote}{\isasymstrut}{\isasymGamma}\ {\isasymturnstile}\ B{\isachardoublequote}}}
+ \infer[(\indexdef{}{inference}{discharge}\hypertarget{inference.discharge}{\hyperlink{inference.discharge}{\mbox{\isa{discharge}}}})]{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C73747275743E}{\isasymstrut}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{2D}{\isacharminus}}\ A\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{23}{\isacharhash}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{22}{\isachardoublequote}}}}{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C73747275743E}{\isasymstrut}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{22}{\isachardoublequote}}}}
\]
\[
- \infer[(\indexdef{}{inference}{weak-discharge}\hypertarget{inference.weak-discharge}{\hyperlink{inference.weak-discharge}{\mbox{\isa{weak{\isasymdash}discharge}}}})]{\isa{{\isachardoublequote}{\isasymstrut}{\isasymGamma}\ {\isacharminus}\ A\ {\isasymturnstile}\ A\ {\isasymLongrightarrow}\ B{\isachardoublequote}}}{\isa{{\isachardoublequote}{\isasymstrut}{\isasymGamma}\ {\isasymturnstile}\ B{\isachardoublequote}}}
+ \infer[(\indexdef{}{inference}{weak-discharge}\hypertarget{inference.weak-discharge}{\hyperlink{inference.weak-discharge}{\mbox{\isa{weak{\isaliteral{5C3C646173683E}{\isasymdash}}discharge}}}})]{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C73747275743E}{\isasymstrut}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{2D}{\isacharminus}}\ A\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{22}{\isachardoublequote}}}}{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C73747275743E}{\isasymstrut}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{22}{\isachardoublequote}}}}
\]
\[
- \infer[(\indexdef{}{inference}{expansion}\hypertarget{inference.expansion}{\hyperlink{inference.expansion}{\mbox{\isa{expansion}}}})]{\isa{{\isachardoublequote}{\isasymstrut}{\isasymGamma}\ {\isacharminus}\ {\isacharparenleft}x\ {\isasymequiv}\ a{\isacharparenright}\ {\isasymturnstile}\ B\ a{\isachardoublequote}}}{\isa{{\isachardoublequote}{\isasymstrut}{\isasymGamma}\ {\isasymturnstile}\ B\ x{\isachardoublequote}}}
+ \infer[(\indexdef{}{inference}{expansion}\hypertarget{inference.expansion}{\hyperlink{inference.expansion}{\mbox{\isa{expansion}}}})]{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C73747275743E}{\isasymstrut}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B\ a{\isaliteral{22}{\isachardoublequote}}}}{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C73747275743E}{\isasymstrut}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B\ x{\isaliteral{22}{\isachardoublequote}}}}
\]
- \medskip Note that \hyperlink{inference.discharge}{\mbox{\isa{discharge}}} and \hyperlink{inference.weak-discharge}{\mbox{\isa{weak{\isasymdash}discharge}}} differ in the marker for \isa{A}, which is
+ \medskip Note that \hyperlink{inference.discharge}{\mbox{\isa{discharge}}} and \hyperlink{inference.weak-discharge}{\mbox{\isa{weak{\isaliteral{5C3C646173683E}{\isasymdash}}discharge}}} differ in the marker for \isa{A}, which is
relevant when the result of a \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}-\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}-\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}} outline is composed with a pending goal,
cf.\ \secref{sec:framework-subproof}.
The most interesting derived context element in Isar is \hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}} \cite[\S5.3]{Wenzel-PhD}, which supports generalized
elimination steps in a purely forward manner. The \hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}
- command takes a specification of parameters \isa{{\isachardoublequote}\isactrlvec x{\isachardoublequote}} and
- assumptions \isa{{\isachardoublequote}\isactrlvec A{\isachardoublequote}} to be added to the context, together
+ command takes a specification of parameters \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{22}{\isachardoublequote}}} and
+ assumptions \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7665633E}{}\isactrlvec A{\isaliteral{22}{\isachardoublequote}}} to be added to the context, together
with a proof of a case rule stating that this extension is
conservative (i.e.\ may be removed from closed results later on):
\medskip
\begin{tabular}{l}
- \isa{{\isachardoublequote}{\isasymlangle}facts{\isasymrangle}{\isachardoublequote}}~~\hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}~\isa{{\isachardoublequote}\isactrlvec x\ {\isasymWHERE}\ \isactrlvec A\ \isactrlvec x\ \ {\isasymlangle}proof{\isasymrangle}\ {\isasymequiv}{\isachardoublequote}} \\[0.5ex]
- \quad \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}case{\isacharcolon}\ {\isasymAnd}thesis{\isachardot}\ {\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec A\ \isactrlvec x\ {\isasymLongrightarrow}\ thesis{\isacharparenright}\ {\isasymLongrightarrow}\ thesis{\isasymrangle}{\isachardoublequote}} \\
- \quad \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\hyperlink{method.-}{\mbox{\isa{{\isacharminus}}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616E676C653E}{\isasymlangle}}facts{\isaliteral{5C3C72616E676C653E}{\isasymrangle}}{\isaliteral{22}{\isachardoublequote}}}~~\hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec A\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ \ {\isaliteral{5C3C6C616E676C653E}{\isasymlangle}}proof{\isaliteral{5C3C72616E676C653E}{\isasymrangle}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} \\[0.5ex]
+ \quad \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}case{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}thesis{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec A\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ thesis{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ thesis{\isaliteral{5C3C72616E676C653E}{\isasymrangle}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \quad \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\hyperlink{method.-}{\mbox{\isa{{\isaliteral{2D}{\isacharminus}}}}} \\
\qquad \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{thesis} \\
- \qquad \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}{\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\ {\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec A\ \isactrlvec x\ {\isasymLongrightarrow}\ thesis{\isachardoublequote}} \\
- \qquad \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{thesis}~\hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{{\isachardoublequote}{\isasymlangle}facts{\isasymrangle}\ {\isasymlangle}proof{\isasymrangle}{\isachardoublequote}} \\
+ \qquad \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec A\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ thesis{\isaliteral{22}{\isachardoublequote}}} \\
+ \qquad \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{thesis}~\hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616E676C653E}{\isasymlangle}}facts{\isaliteral{5C3C72616E676C653E}{\isasymrangle}}\ {\isaliteral{5C3C6C616E676C653E}{\isasymlangle}}proof{\isaliteral{5C3C72616E676C653E}{\isasymrangle}}{\isaliteral{22}{\isachardoublequote}}} \\
\quad \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}} \\
- \quad \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isachardoublequote}\isactrlvec x{\isachardoublequote}}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}{\isasymguillemotleft}elimination\ case{\isasymguillemotright}\ \isactrlvec A\ \isactrlvec x{\isachardoublequote}} \\
+ \quad \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6775696C6C656D6F746C6566743E}{\isasymguillemotleft}}elimination\ case{\isaliteral{5C3C6775696C6C656D6F7472696768743E}{\isasymguillemotright}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec A\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}
\medskip
\[
- \infer[(\hyperlink{inference.elimination}{\mbox{\isa{elimination}}})]{\isa{{\isachardoublequote}{\isasymGamma}\ {\isasymturnstile}\ B{\isachardoublequote}}}{
+ \infer[(\hyperlink{inference.elimination}{\mbox{\isa{elimination}}})]{\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{22}{\isachardoublequote}}}}{
\begin{tabular}{rl}
- \isa{{\isachardoublequote}case{\isacharcolon}{\isachardoublequote}} &
- \isa{{\isachardoublequote}{\isasymGamma}\ {\isasymturnstile}\ {\isasymAnd}thesis{\isachardot}\ {\isacharparenleft}{\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec A\ \isactrlvec x\ {\isasymLongrightarrow}\ thesis{\isacharparenright}\ {\isasymLongrightarrow}\ thesis{\isachardoublequote}} \\[0.2ex]
- \isa{{\isachardoublequote}result{\isacharcolon}{\isachardoublequote}} &
- \isa{{\isachardoublequote}{\isasymGamma}\ {\isasymunion}\ \isactrlvec A\ \isactrlvec y\ {\isasymturnstile}\ B{\isachardoublequote}} \\[0.2ex]
+ \isa{{\isaliteral{22}{\isachardoublequote}}case{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} &
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}thesis{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec A\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ thesis{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ thesis{\isaliteral{22}{\isachardoublequote}}} \\[0.2ex]
+ \isa{{\isaliteral{22}{\isachardoublequote}}result{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} &
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C47616D6D613E}{\isasymGamma}}\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec A\ \isaliteral{5C3C5E7665633E}{}\isactrlvec y\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ B{\isaliteral{22}{\isachardoublequote}}} \\[0.2ex]
\end{tabular}}
\]
\noindent Here the name ``\isa{thesis}'' is a specific convention
for an arbitrary-but-fixed proposition; in the primitive natural
deduction rules shown before we have occasionally used \isa{C}.
- The whole statement of ``\hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}~\isa{x}~\hyperlink{keyword.where}{\mbox{\isa{\isakeyword{where}}}}~\isa{{\isachardoublequote}A\ x{\isachardoublequote}}'' may be read as a claim that \isa{{\isachardoublequote}A\ x{\isachardoublequote}}
- may be assumed for some arbitrary-but-fixed \isa{{\isachardoublequote}x{\isachardoublequote}}. Also note
- that ``\hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}~\isa{{\isachardoublequote}A\ {\isasymAND}\ B{\isachardoublequote}}'' without parameters
- is similar to ``\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}A\ {\isasymAND}\ B{\isachardoublequote}}'', but the
+ The whole statement of ``\hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}~\isa{x}~\hyperlink{keyword.where}{\mbox{\isa{\isakeyword{where}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}A\ x{\isaliteral{22}{\isachardoublequote}}}'' may be read as a claim that \isa{{\isaliteral{22}{\isachardoublequote}}A\ x{\isaliteral{22}{\isachardoublequote}}}
+ may be assumed for some arbitrary-but-fixed \isa{{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}}. Also note
+ that ``\hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ B{\isaliteral{22}{\isachardoublequote}}}'' without parameters
+ is similar to ``\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ B{\isaliteral{22}{\isachardoublequote}}}'', but the
latter involves multiple sub-goals.
\medskip The subsequent Isar proof texts explain all context
@@ -759,12 +759,12 @@
\isatagproof
%
\begin{minipage}[t]{0.4\textwidth}
-\ \ \isacommand{{\isacharbraceleft}}\isamarkupfalse%
+\ \ \isacommand{{\isaliteral{7B}{\isacharbraceleft}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ x\isanewline
\ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}B\ x{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}B\ x{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -792,12 +792,12 @@
\endisadelimproof
%
\isatagproof
-\isacommand{{\isacharbraceright}}\isamarkupfalse%
+\isacommand{{\isaliteral{7D}{\isacharbraceright}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{note}\isamarkupfalse%
-\ {\isacharbackquoteopen}{\isasymAnd}x{\isachardot}\ B\ x{\isacharbackquoteclose}%
+\ {\isaliteral{60}{\isacharbackquoteopen}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ B\ x{\isaliteral{60}{\isacharbackquoteclose}}%
\end{minipage}\quad\begin{minipage}[t]{0.4\textwidth}
-\ \ \isacommand{{\isacharbraceleft}}\isamarkupfalse%
+\ \ \isacommand{{\isaliteral{7B}{\isacharbraceleft}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
\ A\isanewline
@@ -830,17 +830,17 @@
\endisadelimproof
%
\isatagproof
-\isacommand{{\isacharbraceright}}\isamarkupfalse%
+\isacommand{{\isaliteral{7D}{\isacharbraceright}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{note}\isamarkupfalse%
-\ {\isacharbackquoteopen}A\ {\isasymLongrightarrow}\ B{\isacharbackquoteclose}%
+\ {\isaliteral{60}{\isacharbackquoteopen}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{60}{\isacharbackquoteclose}}%
\end{minipage}\\[3ex]\begin{minipage}[t]{0.4\textwidth}
-\ \ \isacommand{{\isacharbraceleft}}\isamarkupfalse%
+\ \ \isacommand{{\isaliteral{7B}{\isacharbraceleft}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{def}\isamarkupfalse%
-\ x\ {\isasymequiv}\ a\isanewline
+\ x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ a\isanewline
\ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}B\ x{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}B\ x{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -868,15 +868,15 @@
\endisadelimproof
%
\isatagproof
-\isacommand{{\isacharbraceright}}\isamarkupfalse%
+\isacommand{{\isaliteral{7D}{\isacharbraceright}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{note}\isamarkupfalse%
-\ {\isacharbackquoteopen}B\ a{\isacharbackquoteclose}%
+\ {\isaliteral{60}{\isacharbackquoteopen}}B\ a{\isaliteral{60}{\isacharbackquoteclose}}%
\end{minipage}\quad\begin{minipage}[t]{0.4\textwidth}
-\ \ \isacommand{{\isacharbraceleft}}\isamarkupfalse%
+\ \ \isacommand{{\isaliteral{7B}{\isacharbraceleft}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{obtain}\isamarkupfalse%
-\ x\ \isakeyword{where}\ {\isachardoublequoteopen}A\ x{\isachardoublequoteclose}%
+\ x\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ x{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -933,10 +933,10 @@
\endisadelimproof
%
\isatagproof
-\isacommand{{\isacharbraceright}}\isamarkupfalse%
+\isacommand{{\isaliteral{7D}{\isacharbraceright}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{note}\isamarkupfalse%
-\ {\isacharbackquoteopen}B{\isacharbackquoteclose}%
+\ {\isaliteral{60}{\isacharbackquoteopen}}B{\isaliteral{60}{\isacharbackquoteclose}}%
\end{minipage}
%
\endisatagproof
@@ -957,47 +957,47 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-The category \isa{{\isachardoublequote}statement{\isachardoublequote}} of top-level theorem specifications
+The category \isa{{\isaliteral{22}{\isachardoublequote}}statement{\isaliteral{22}{\isachardoublequote}}} of top-level theorem specifications
is defined as follows:
\medskip
\begin{tabular}{rcl}
- \isa{{\isachardoublequote}statement{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} & \isa{{\isachardoublequote}name{\isacharcolon}\ props\ {\isasymAND}\ {\isasymdots}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}context\isactrlsup {\isacharasterisk}\ conclusion{\isachardoublequote}} \\[0.5ex]
+ \isa{{\isaliteral{22}{\isachardoublequote}}statement{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{3A}{\isacharcolon}}\ props\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}context\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}\ conclusion{\isaliteral{22}{\isachardoublequote}}} \\[0.5ex]
- \isa{{\isachardoublequote}context{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymFIXES}\ vars\ {\isasymAND}\ {\isasymdots}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymASSUMES}\ name{\isacharcolon}\ props\ {\isasymAND}\ {\isasymdots}{\isachardoublequote}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}context{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C46495845533E}{\isasymFIXES}}\ vars\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ name{\isaliteral{3A}{\isacharcolon}}\ props\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\
- \isa{{\isachardoublequote}conclusion{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymSHOWS}\ name{\isacharcolon}\ props\ {\isasymAND}\ {\isasymdots}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymOBTAINS}\ vars\ {\isasymAND}\ {\isasymdots}\ {\isasymWHERE}\ name{\isacharcolon}\ props\ {\isasymAND}\ {\isasymdots}{\isachardoublequote}} \\
- & & \quad \isa{{\isachardoublequote}{\isasymBBAR}\ {\isasymdots}{\isachardoublequote}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}conclusion{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C53484F57533E}{\isasymSHOWS}}\ name{\isaliteral{3A}{\isacharcolon}}\ props\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4F425441494E533E}{\isasymOBTAINS}}\ vars\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ name{\isaliteral{3A}{\isacharcolon}}\ props\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & & \quad \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C424241523E}{\isasymBBAR}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}
- \medskip\noindent A simple \isa{{\isachardoublequote}statement{\isachardoublequote}} consists of named
+ \medskip\noindent A simple \isa{{\isaliteral{22}{\isachardoublequote}}statement{\isaliteral{22}{\isachardoublequote}}} consists of named
propositions. The full form admits local context elements followed
- by the actual conclusions, such as ``\hyperlink{keyword.fixes}{\mbox{\isa{\isakeyword{fixes}}}}~\isa{x}~\hyperlink{keyword.assumes}{\mbox{\isa{\isakeyword{assumes}}}}~\isa{{\isachardoublequote}A\ x{\isachardoublequote}}~\hyperlink{keyword.shows}{\mbox{\isa{\isakeyword{shows}}}}~\isa{{\isachardoublequote}B\ x{\isachardoublequote}}''. The final result emerges as a Pure rule after discharging
- the context: \isa{{\isachardoublequote}{\isasymAnd}x{\isachardot}\ A\ x\ {\isasymLongrightarrow}\ B\ x{\isachardoublequote}}.
+ by the actual conclusions, such as ``\hyperlink{keyword.fixes}{\mbox{\isa{\isakeyword{fixes}}}}~\isa{x}~\hyperlink{keyword.assumes}{\mbox{\isa{\isakeyword{assumes}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}A\ x{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{keyword.shows}{\mbox{\isa{\isakeyword{shows}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}B\ x{\isaliteral{22}{\isachardoublequote}}}''. The final result emerges as a Pure rule after discharging
+ the context: \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ A\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ x{\isaliteral{22}{\isachardoublequote}}}.
The \hyperlink{keyword.obtains}{\mbox{\isa{\isakeyword{obtains}}}} variant is another abbreviation defined
below; unlike \hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}} (cf.\
\secref{sec:framework-context}) there may be several ``cases''
- separated by ``\isa{{\isachardoublequote}{\isasymBBAR}{\isachardoublequote}}'', each consisting of several
- parameters (\isa{{\isachardoublequote}vars{\isachardoublequote}}) and several premises (\isa{{\isachardoublequote}props{\isachardoublequote}}).
+ separated by ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C424241523E}{\isasymBBAR}}{\isaliteral{22}{\isachardoublequote}}}'', each consisting of several
+ parameters (\isa{{\isaliteral{22}{\isachardoublequote}}vars{\isaliteral{22}{\isachardoublequote}}}) and several premises (\isa{{\isaliteral{22}{\isachardoublequote}}props{\isaliteral{22}{\isachardoublequote}}}).
This specifies multi-branch elimination rules.
\medskip
\begin{tabular}{l}
- \isa{{\isachardoublequote}{\isasymOBTAINS}\ \isactrlvec x\ {\isasymWHERE}\ \isactrlvec A\ \isactrlvec x\ \ \ {\isasymBBAR}\ \ \ {\isasymdots}\ \ \ {\isasymequiv}{\isachardoublequote}} \\[0.5ex]
- \quad \isa{{\isachardoublequote}{\isasymFIXES}\ thesis{\isachardoublequote}} \\
- \quad \isa{{\isachardoublequote}{\isasymASSUMES}\ {\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\ {\isasymAnd}\isactrlvec x{\isachardot}\ \isactrlvec A\ \isactrlvec x\ {\isasymLongrightarrow}\ thesis\ \ {\isasymAND}\ \ {\isasymdots}{\isachardoublequote}} \\
- \quad \isa{{\isachardoublequote}{\isasymSHOWS}\ thesis{\isachardoublequote}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4F425441494E533E}{\isasymOBTAINS}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec A\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ \ \ {\isaliteral{5C3C424241523E}{\isasymBBAR}}\ \ \ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ \ \ {\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} \\[0.5ex]
+ \quad \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C46495845533E}{\isasymFIXES}}\ thesis{\isaliteral{22}{\isachardoublequote}}} \\
+ \quad \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C415353554D45533E}{\isasymASSUMES}}\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}\isaliteral{5C3C5E7665633E}{}\isactrlvec x{\isaliteral{2E}{\isachardot}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec A\ \isaliteral{5C3C5E7665633E}{}\isactrlvec x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ thesis\ \ {\isaliteral{5C3C414E443E}{\isasymAND}}\ \ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \quad \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C53484F57533E}{\isasymSHOWS}}\ thesis{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}
\medskip
Presenting structured statements in such an ``open'' format usually
simplifies the subsequent proof, because the outer structure of the
problem is already laid out directly. E.g.\ consider the following
- canonical patterns for \isa{{\isachardoublequote}{\isasymSHOWS}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isasymOBTAINS}{\isachardoublequote}},
+ canonical patterns for \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C53484F57533E}{\isasymSHOWS}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4F425441494E533E}{\isasymOBTAINS}}{\isaliteral{22}{\isachardoublequote}}},
respectively:%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -1006,8 +1006,8 @@
\isacommand{theorem}\isamarkupfalse%
\isanewline
\ \ \isakeyword{fixes}\ x\ \isakeyword{and}\ y\isanewline
-\ \ \isakeyword{assumes}\ {\isachardoublequoteopen}A\ x{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}B\ y{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{shows}\ {\isachardoublequoteopen}C\ x\ y{\isachardoublequoteclose}\isanewline
+\ \ \isakeyword{assumes}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1015,11 +1015,11 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{from}\isamarkupfalse%
-\ {\isacharbackquoteopen}A\ x{\isacharbackquoteclose}\ \isakeyword{and}\ {\isacharbackquoteopen}B\ y{\isacharbackquoteclose}\isanewline
+\ {\isaliteral{60}{\isacharbackquoteopen}}A\ x{\isaliteral{60}{\isacharbackquoteclose}}\ \isakeyword{and}\ {\isaliteral{60}{\isacharbackquoteopen}}B\ y{\isaliteral{60}{\isacharbackquoteclose}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}C\ x\ y{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1060,7 +1060,7 @@
\isacommand{theorem}\isamarkupfalse%
\isanewline
\ \ \isakeyword{obtains}\ x\ \isakeyword{and}\ y\isanewline
-\ \ \isakeyword{where}\ {\isachardoublequoteopen}A\ x{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}B\ y{\isachardoublequoteclose}\isanewline
+\ \ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -1068,9 +1068,9 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ a{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}B\ b{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ a{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ b{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1100,7 +1100,7 @@
\isatagproof
\isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ thesis\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -1114,9 +1114,9 @@
\end{minipage}
%
\begin{isamarkuptext}%
-\medskip\noindent Here local facts \isacharbackquoteopen\isa{{\isachardoublequote}A\ x{\isachardoublequote}}\isacharbackquoteclose\ and \isacharbackquoteopen\isa{{\isachardoublequote}B\ y{\isachardoublequote}}\isacharbackquoteclose\ are referenced immediately; there is no
+\medskip\noindent Here local facts \isacharbackquoteopen\isa{{\isaliteral{22}{\isachardoublequote}}A\ x{\isaliteral{22}{\isachardoublequote}}}\isacharbackquoteclose\ and \isacharbackquoteopen\isa{{\isaliteral{22}{\isachardoublequote}}B\ y{\isaliteral{22}{\isachardoublequote}}}\isacharbackquoteclose\ are referenced immediately; there is no
need to decompose the logical rule structure again. In the second
- proof the final ``\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{thesis}~\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}}'' involves the local rule case \isa{{\isachardoublequote}{\isasymAnd}x\ y{\isachardot}\ A\ x\ {\isasymLongrightarrow}\ B\ y\ {\isasymLongrightarrow}\ thesis{\isachardoublequote}} for the particular instance of terms \isa{{\isachardoublequote}a{\isachardoublequote}} and \isa{{\isachardoublequote}b{\isachardoublequote}} produced in the body.%
+ proof the final ``\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{thesis}~\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}}'' involves the local rule case \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{2E}{\isachardot}}\ A\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ thesis{\isaliteral{22}{\isachardoublequote}}} for the particular instance of terms \isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}b{\isaliteral{22}{\isachardoublequote}}} produced in the body.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -1134,8 +1134,8 @@
configurations for debugging.
The basic idea is analogous to evaluating algebraic expressions on a
- stack machine: \isa{{\isachardoublequote}{\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ {\isasymcdot}\ c{\isachardoublequote}} then corresponds to a sequence
- of single transitions for each symbol \isa{{\isachardoublequote}{\isacharparenleft}{\isacharcomma}\ a{\isacharcomma}\ {\isacharplus}{\isacharcomma}\ b{\isacharcomma}\ {\isacharparenright}{\isacharcomma}\ {\isasymcdot}{\isacharcomma}\ c{\isachardoublequote}}.
+ stack machine: \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2B}{\isacharplus}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C63646F743E}{\isasymcdot}}\ c{\isaliteral{22}{\isachardoublequote}}} then corresponds to a sequence
+ of single transitions for each symbol \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2C}{\isacharcomma}}\ a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{2B}{\isacharplus}}{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C63646F743E}{\isasymcdot}}{\isaliteral{2C}{\isacharcomma}}\ c{\isaliteral{22}{\isachardoublequote}}}.
In Isar the algebraic values are facts or goals, and the operations
are inferences.
@@ -1153,13 +1153,13 @@
\caption{Isar/VM modes}\label{fig:isar-vm}
\end{figure}
- For example, in \isa{{\isachardoublequote}state{\isachardoublequote}} mode Isar acts like a mathematical
+ For example, in \isa{{\isaliteral{22}{\isachardoublequote}}state{\isaliteral{22}{\isachardoublequote}}} mode Isar acts like a mathematical
scratch-pad, accepting declarations like \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}, \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}, and claims like \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}, \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}. A goal
- statement changes the mode to \isa{{\isachardoublequote}prove{\isachardoublequote}}, which means that we
- may now refine the problem via \hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}} or \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}. Then we are again in \isa{{\isachardoublequote}state{\isachardoublequote}} mode of a proof body,
+ statement changes the mode to \isa{{\isaliteral{22}{\isachardoublequote}}prove{\isaliteral{22}{\isachardoublequote}}}, which means that we
+ may now refine the problem via \hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}} or \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}. Then we are again in \isa{{\isaliteral{22}{\isachardoublequote}}state{\isaliteral{22}{\isachardoublequote}}} mode of a proof body,
which may issue \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}} statements to solve pending
sub-goals. A concluding \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}} will return to the original
- \isa{{\isachardoublequote}state{\isachardoublequote}} mode one level upwards. The subsequent Isar/VM
+ \isa{{\isaliteral{22}{\isachardoublequote}}state{\isaliteral{22}{\isachardoublequote}}} mode one level upwards. The subsequent Isar/VM
trace indicates block structure, linguistic mode, goal state, and
inferences:%
\end{isamarkuptext}%
@@ -1175,7 +1175,7 @@
%
\begin{minipage}[t]{0.18\textwidth}
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymlongrightarrow}\ B{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
@@ -1214,34 +1214,34 @@
%
\end{minipage}\quad
\begin{minipage}[t]{0.06\textwidth}
-\isa{{\isachardoublequote}begin{\isachardoublequote}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}begin{\isaliteral{22}{\isachardoublequote}}} \\
\\
\\
-\isa{{\isachardoublequote}begin{\isachardoublequote}} \\
-\isa{{\isachardoublequote}end{\isachardoublequote}} \\
-\isa{{\isachardoublequote}end{\isachardoublequote}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}begin{\isaliteral{22}{\isachardoublequote}}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}end{\isaliteral{22}{\isachardoublequote}}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}end{\isaliteral{22}{\isachardoublequote}}} \\
\end{minipage}
\begin{minipage}[t]{0.08\textwidth}
-\isa{{\isachardoublequote}prove{\isachardoublequote}} \\
-\isa{{\isachardoublequote}state{\isachardoublequote}} \\
-\isa{{\isachardoublequote}state{\isachardoublequote}} \\
-\isa{{\isachardoublequote}prove{\isachardoublequote}} \\
-\isa{{\isachardoublequote}state{\isachardoublequote}} \\
-\isa{{\isachardoublequote}state{\isachardoublequote}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}prove{\isaliteral{22}{\isachardoublequote}}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}state{\isaliteral{22}{\isachardoublequote}}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}state{\isaliteral{22}{\isachardoublequote}}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}prove{\isaliteral{22}{\isachardoublequote}}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}state{\isaliteral{22}{\isachardoublequote}}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}state{\isaliteral{22}{\isachardoublequote}}} \\
\end{minipage}\begin{minipage}[t]{0.35\textwidth}
-\isa{{\isachardoublequote}{\isacharparenleft}A\ {\isasymlongrightarrow}\ B{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharhash}{\isacharparenleft}A\ {\isasymlongrightarrow}\ B{\isacharparenright}{\isachardoublequote}} \\
-\isa{{\isachardoublequote}{\isacharparenleft}A\ {\isasymLongrightarrow}\ B{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharhash}{\isacharparenleft}A\ {\isasymlongrightarrow}\ B{\isacharparenright}{\isachardoublequote}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{23}{\isacharhash}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{23}{\isacharhash}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\\
\\
-\isa{{\isachardoublequote}{\isacharhash}{\isacharparenleft}A\ {\isasymlongrightarrow}\ B{\isacharparenright}{\isachardoublequote}} \\
-\isa{{\isachardoublequote}A\ {\isasymlongrightarrow}\ B{\isachardoublequote}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B{\isaliteral{22}{\isachardoublequote}}} \\
\end{minipage}\begin{minipage}[t]{0.4\textwidth}
-\isa{{\isachardoublequote}{\isacharparenleft}init{\isacharparenright}{\isachardoublequote}} \\
-\isa{{\isachardoublequote}{\isacharparenleft}resolution\ impI{\isacharparenright}{\isachardoublequote}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}init{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}resolution\ impI{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\\
\\
-\isa{{\isachardoublequote}{\isacharparenleft}refinement\ {\isacharhash}A\ {\isasymLongrightarrow}\ B{\isacharparenright}{\isachardoublequote}} \\
-\isa{{\isachardoublequote}{\isacharparenleft}finish{\isacharparenright}{\isachardoublequote}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}refinement\ {\isaliteral{23}{\isacharhash}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}finish{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{minipage}
%
\endisatagproof
@@ -1273,15 +1273,15 @@
%
\isatagproof
\isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymAnd}x\ y{\isachardot}\ A\ x\ {\isasymLongrightarrow}\ B\ y\ {\isasymLongrightarrow}\ C\ x\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{2E}{\isachardot}}\ A\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ x\ \isakeyword{and}\ y\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ x{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}B\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}C\ x\ y{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1313,17 +1313,17 @@
%
\end{minipage}\begin{minipage}{0.5\textwidth}
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymAnd}x\ y{\isachardot}\ A\ x\ {\isasymLongrightarrow}\ B\ y\ {\isasymLongrightarrow}\ C\ x\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{2E}{\isachardot}}\ A\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ x\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ x{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ y\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}B\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}B\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}C\ x\ y{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagproof
{\isafoldproof}%
%
@@ -1355,32 +1355,32 @@
%
\end{minipage}\\[3ex]\begin{minipage}{0.5\textwidth}
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymAnd}x\ y{\isachardot}\ A\ x\ {\isasymLongrightarrow}\ B\ y\ {\isasymLongrightarrow}\ C\ x\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{2E}{\isachardot}}\ A\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ y\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}B\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}B\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ x\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ x{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}C\ x\ y{\isachardoublequoteclose}\ \isacommand{sorry}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{sorry}\isamarkupfalse%
\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
%
\end{minipage}\begin{minipage}{0.5\textwidth}
\ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymAnd}x\ y{\isachardot}\ A\ x\ {\isasymLongrightarrow}\ B\ y\ {\isasymLongrightarrow}\ C\ x\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{2E}{\isachardot}}\ A\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ y\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}B\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}B\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ x\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}C\ x\ y{\isachardoublequoteclose}\ \isacommand{sorry}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}C\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{sorry}\isamarkupfalse%
\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
%
@@ -1418,15 +1418,15 @@
concept. The generic proof elements introduced below depend on
rules declared as \hyperlink{attribute.trans}{\mbox{\isa{trans}}} in the context. It is left to
the object-logic to provide a suitable rule collection for mixed
- relations of \isa{{\isachardoublequote}{\isacharequal}{\isachardoublequote}}, \isa{{\isachardoublequote}{\isacharless}{\isachardoublequote}}, \isa{{\isachardoublequote}{\isasymle}{\isachardoublequote}}, \isa{{\isachardoublequote}{\isasymsubset}{\isachardoublequote}},
- \isa{{\isachardoublequote}{\isasymsubseteq}{\isachardoublequote}} etc. Due to the flexibility of rule composition
+ relations of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3C}{\isacharless}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C653E}{\isasymle}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7375627365743E}{\isasymsubset}}{\isaliteral{22}{\isachardoublequote}}},
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}{\isaliteral{22}{\isachardoublequote}}} etc. Due to the flexibility of rule composition
(\secref{sec:framework-resolution}), substitution of equals by
equals is covered as well, even substitution of inequalities
involving monotonicity conditions; see also \cite[\S6]{Wenzel-PhD}
and \cite{Bauer-Wenzel:2001}.
The generic calculational mechanism is based on the observation that
- rules such as \isa{{\isachardoublequote}trans{\isacharcolon}{\isachardoublequote}}~\isa{{\isachardoublequote}x\ {\isacharequal}\ y\ {\isasymLongrightarrow}\ y\ {\isacharequal}\ z\ {\isasymLongrightarrow}\ x\ {\isacharequal}\ z{\isachardoublequote}}
+ rules such as \isa{{\isaliteral{22}{\isachardoublequote}}trans{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3D}{\isacharequal}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ y\ {\isaliteral{3D}{\isacharequal}}\ z\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{3D}{\isacharequal}}\ z{\isaliteral{22}{\isachardoublequote}}}
proceed from the premises towards the conclusion in a deterministic
fashion. Thus we may reason in forward mode, feeding intermediate
results into rules selected from the context. The course of
@@ -1435,11 +1435,11 @@
already provided by the Isar primitives. In the definitions below,
\hyperlink{attribute.OF}{\mbox{\isa{OF}}} refers to \hyperlink{inference.resolution}{\mbox{\isa{resolution}}}
(\secref{sec:framework-resolution}) with multiple rule arguments,
- and \isa{{\isachardoublequote}trans{\isachardoublequote}} represents to a suitable rule from the context:
+ and \isa{{\isaliteral{22}{\isachardoublequote}}trans{\isaliteral{22}{\isachardoublequote}}} represents to a suitable rule from the context:
\begin{matharray}{rcl}
- \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isachardoublequote}\isactrlsub {\isadigit{0}}{\isachardoublequote}} & \equiv & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ this{\isachardoublequote}} \\
- \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isachardoublequote}\isactrlsub n\isactrlsub {\isacharplus}\isactrlsub {\isadigit{1}}{\isachardoublequote}} & \equiv & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ trans\ {\isacharbrackleft}OF\ calculation\ this{\isacharbrackright}{\isachardoublequote}} \\[0.5ex]
+ \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{0}}{\isaliteral{22}{\isachardoublequote}}} & \equiv & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}calculation\ {\isaliteral{3D}{\isacharequal}}\ this{\isaliteral{22}{\isachardoublequote}}} \\
+ \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{2B}{\isacharplus}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & \equiv & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}calculation\ {\isaliteral{3D}{\isacharequal}}\ trans\ {\isaliteral{5B}{\isacharbrackleft}}OF\ calculation\ this{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} \\[0.5ex]
\hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}} & \equiv & \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}~\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{calculation} \\
\end{matharray}
@@ -1461,19 +1461,19 @@
%
\isatagproof
\isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}a\ {\isacharequal}\ b{\isachardoublequoteclose}\ \isacommand{sorry}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}a\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{sorry}\isamarkupfalse%
\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdots}\ {\isacharequal}\ c{\isachardoublequoteclose}\ \isacommand{sorry}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{sorry}\isamarkupfalse%
\isanewline
\ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdots}\ {\isacharequal}\ d{\isachardoublequoteclose}\ \isacommand{sorry}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ d{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{sorry}\isamarkupfalse%
\isanewline
\ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}a\ {\isacharequal}\ d{\isachardoublequoteclose}\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}a\ {\isaliteral{3D}{\isacharequal}}\ d{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
@@ -1483,18 +1483,18 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-\noindent The term ``\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}'' above is a special abbreviation
+\noindent The term ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}'' above is a special abbreviation
provided by the Isabelle/Isar syntax layer: it statically refers to
the right-hand side argument of the previous statement given in the
text. Thus it happens to coincide with relevant sub-expressions in
the calculational chain, but the exact correspondence is dependent
on the transitivity rules being involved.
- \medskip Symmetry rules such as \isa{{\isachardoublequote}x\ {\isacharequal}\ y\ {\isasymLongrightarrow}\ y\ {\isacharequal}\ x{\isachardoublequote}} are like
+ \medskip Symmetry rules such as \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3D}{\isacharequal}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ y\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequote}}} are like
transitivities with only one premise. Isar maintains a separate
rule collection declared via the \hyperlink{attribute.sym}{\mbox{\isa{sym}}} attribute, to be
- used in fact expressions ``\isa{{\isachardoublequote}a\ {\isacharbrackleft}symmetric{\isacharbrackright}{\isachardoublequote}}'', or single-step
- proofs ``\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}x\ {\isacharequal}\ y{\isachardoublequote}}~\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}y\ {\isacharequal}\ x{\isachardoublequote}}~\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}}''.%
+ used in fact expressions ``\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{5B}{\isacharbrackleft}}symmetric{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}'', or single-step
+ proofs ``\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}y\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}}''.%
\end{isamarkuptext}%
\isamarkuptrue%
%
--- a/doc-src/IsarRef/Thy/document/Generic.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarRef/Thy/document/Generic.tex Mon Nov 08 14:41:11 2010 +0100
@@ -42,7 +42,7 @@
``global'', which may not be changed within a local context.
\begin{matharray}{rcll}
- \indexdef{}{command}{print\_configs}\hypertarget{command.print-configs}{\hyperlink{command.print-configs}{\mbox{\isa{\isacommand{print{\isacharunderscore}configs}}}}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{}{command}{print\_configs}\hypertarget{command.print-configs}{\hyperlink{command.print-configs}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}configs}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -51,10 +51,10 @@
\begin{description}
- \item \hyperlink{command.print-configs}{\mbox{\isa{\isacommand{print{\isacharunderscore}configs}}}} prints the available configuration
+ \item \hyperlink{command.print-configs}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}configs}}}} prints the available configuration
options, with names, types, and current values.
- \item \isa{{\isachardoublequote}name\ {\isacharequal}\ value{\isachardoublequote}} as an attribute expression modifies the
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}name\ {\isaliteral{3D}{\isacharequal}}\ value{\isaliteral{22}{\isachardoublequote}}} as an attribute expression modifies the
named option, with the syntax of the value depending on the option's
type. For \verb|bool| the default value is \isa{true}. Any
attempt to change a global option in a local context is ignored.
@@ -76,9 +76,9 @@
\indexdef{}{method}{unfold}\hypertarget{method.unfold}{\hyperlink{method.unfold}{\mbox{\isa{unfold}}}} & : & \isa{method} \\
\indexdef{}{method}{fold}\hypertarget{method.fold}{\hyperlink{method.fold}{\mbox{\isa{fold}}}} & : & \isa{method} \\
\indexdef{}{method}{insert}\hypertarget{method.insert}{\hyperlink{method.insert}{\mbox{\isa{insert}}}} & : & \isa{method} \\[0.5ex]
- \indexdef{}{method}{erule}\hypertarget{method.erule}{\hyperlink{method.erule}{\mbox{\isa{erule}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{}{method}{drule}\hypertarget{method.drule}{\hyperlink{method.drule}{\mbox{\isa{drule}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{}{method}{frule}\hypertarget{method.frule}{\hyperlink{method.frule}{\mbox{\isa{frule}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
+ \indexdef{}{method}{erule}\hypertarget{method.erule}{\hyperlink{method.erule}{\mbox{\isa{erule}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{}{method}{drule}\hypertarget{method.drule}{\hyperlink{method.drule}{\mbox{\isa{drule}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{}{method}{frule}\hypertarget{method.frule}{\hyperlink{method.frule}{\mbox{\isa{frule}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
\indexdef{}{method}{succeed}\hypertarget{method.succeed}{\hyperlink{method.succeed}{\mbox{\isa{succeed}}}} & : & \isa{method} \\
\indexdef{}{method}{fail}\hypertarget{method.fail}{\hyperlink{method.fail}{\mbox{\isa{fail}}}} & : & \isa{method} \\
\end{matharray}
@@ -92,15 +92,15 @@
\begin{description}
- \item \hyperlink{method.unfold}{\mbox{\isa{unfold}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} and \hyperlink{method.fold}{\mbox{\isa{fold}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} expand (or fold back) the given definitions throughout
+ \item \hyperlink{method.unfold}{\mbox{\isa{unfold}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} and \hyperlink{method.fold}{\mbox{\isa{fold}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} expand (or fold back) the given definitions throughout
all goals; any chained facts provided are inserted into the goal and
subject to rewriting as well.
- \item \hyperlink{method.insert}{\mbox{\isa{insert}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} inserts theorems as facts
+ \item \hyperlink{method.insert}{\mbox{\isa{insert}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} inserts theorems as facts
into all goals of the proof state. Note that current facts
indicated for forward chaining are ignored.
- \item \hyperlink{method.erule}{\mbox{\isa{erule}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}, \hyperlink{method.drule}{\mbox{\isa{drule}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}, and \hyperlink{method.frule}{\mbox{\isa{frule}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} are similar to the basic \hyperlink{method.rule}{\mbox{\isa{rule}}}
+ \item \hyperlink{method.erule}{\mbox{\isa{erule}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}, \hyperlink{method.drule}{\mbox{\isa{drule}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}, and \hyperlink{method.frule}{\mbox{\isa{frule}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} are similar to the basic \hyperlink{method.rule}{\mbox{\isa{rule}}}
method (see \secref{sec:pure-meth-att}), but apply rules by
elim-resolution, destruct-resolution, and forward-resolution,
respectively \cite{isabelle-implementation}. The optional natural
@@ -116,11 +116,11 @@
facts.
\item \hyperlink{method.succeed}{\mbox{\isa{succeed}}} yields a single (unchanged) result; it is
- the identity of the ``\isa{{\isachardoublequote}{\isacharcomma}{\isachardoublequote}}'' method combinator (cf.\
+ the identity of the ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}}'' method combinator (cf.\
\secref{sec:proof-meth}).
\item \hyperlink{method.fail}{\mbox{\isa{fail}}} yields an empty result sequence; it is the
- identity of the ``\isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}}'' method combinator (cf.\
+ identity of the ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}}'' method combinator (cf.\
\secref{sec:proof-meth}).
\end{description}
@@ -133,9 +133,9 @@
\indexdef{}{attribute}{unfolded}\hypertarget{attribute.unfolded}{\hyperlink{attribute.unfolded}{\mbox{\isa{unfolded}}}} & : & \isa{attribute} \\
\indexdef{}{attribute}{folded}\hypertarget{attribute.folded}{\hyperlink{attribute.folded}{\mbox{\isa{folded}}}} & : & \isa{attribute} \\[0.5ex]
\indexdef{}{attribute}{rotated}\hypertarget{attribute.rotated}{\hyperlink{attribute.rotated}{\mbox{\isa{rotated}}}} & : & \isa{attribute} \\
- \indexdef{Pure}{attribute}{elim\_format}\hypertarget{attribute.Pure.elim-format}{\hyperlink{attribute.Pure.elim-format}{\mbox{\isa{elim{\isacharunderscore}format}}}} & : & \isa{attribute} \\
- \indexdef{}{attribute}{standard}\hypertarget{attribute.standard}{\hyperlink{attribute.standard}{\mbox{\isa{standard}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{attribute} \\
- \indexdef{}{attribute}{no\_vars}\hypertarget{attribute.no-vars}{\hyperlink{attribute.no-vars}{\mbox{\isa{no{\isacharunderscore}vars}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{attribute} \\
+ \indexdef{Pure}{attribute}{elim\_format}\hypertarget{attribute.Pure.elim-format}{\hyperlink{attribute.Pure.elim-format}{\mbox{\isa{elim{\isaliteral{5F}{\isacharunderscore}}format}}}} & : & \isa{attribute} \\
+ \indexdef{}{attribute}{standard}\hypertarget{attribute.standard}{\hyperlink{attribute.standard}{\mbox{\isa{standard}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{attribute} \\
+ \indexdef{}{attribute}{no\_vars}\hypertarget{attribute.no-vars}{\hyperlink{attribute.no-vars}{\mbox{\isa{no{\isaliteral{5F}{\isacharunderscore}}vars}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{attribute} \\
\end{matharray}
\begin{rail}
@@ -152,7 +152,7 @@
\begin{description}
- \item \hyperlink{attribute.tagged}{\mbox{\isa{tagged}}}~\isa{{\isachardoublequote}name\ value{\isachardoublequote}} and \hyperlink{attribute.untagged}{\mbox{\isa{untagged}}}~\isa{name} add and remove \emph{tags} of some theorem.
+ \item \hyperlink{attribute.tagged}{\mbox{\isa{tagged}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name\ value{\isaliteral{22}{\isachardoublequote}}} and \hyperlink{attribute.untagged}{\mbox{\isa{untagged}}}~\isa{name} add and remove \emph{tags} of some theorem.
Tags may be any list of string pairs that serve as formal comment.
The first string is considered the tag name, the second its value.
Note that \hyperlink{attribute.untagged}{\mbox{\isa{untagged}}} removes any tags of the same name.
@@ -164,14 +164,14 @@
lifting process that is normally intended (cf.\ \verb|op RS| and
\verb|op COMP| in \cite{isabelle-implementation}).
- \item \hyperlink{attribute.unfolded}{\mbox{\isa{unfolded}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} and \hyperlink{attribute.folded}{\mbox{\isa{folded}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} expand and fold back again the given
+ \item \hyperlink{attribute.unfolded}{\mbox{\isa{unfolded}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} and \hyperlink{attribute.folded}{\mbox{\isa{folded}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} expand and fold back again the given
definitions throughout a rule.
\item \hyperlink{attribute.rotated}{\mbox{\isa{rotated}}}~\isa{n} rotate the premises of a
theorem by \isa{n} (default 1).
- \item \hyperlink{attribute.Pure.elim-format}{\mbox{\isa{elim{\isacharunderscore}format}}} turns a destruction rule into
- elimination rule format, by resolving with the rule \isa{{\isachardoublequote}PROP\ A\ {\isasymLongrightarrow}\ {\isacharparenleft}PROP\ A\ {\isasymLongrightarrow}\ PROP\ B{\isacharparenright}\ {\isasymLongrightarrow}\ PROP\ B{\isachardoublequote}}.
+ \item \hyperlink{attribute.Pure.elim-format}{\mbox{\isa{elim{\isaliteral{5F}{\isacharunderscore}}format}}} turns a destruction rule into
+ elimination rule format, by resolving with the rule \isa{{\isaliteral{22}{\isachardoublequote}}PROP\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}PROP\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ PROP\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ PROP\ B{\isaliteral{22}{\isachardoublequote}}}.
Note that the Classical Reasoner (\secref{sec:classical}) provides
its own version of this operation.
@@ -181,7 +181,7 @@
operation violates the local proof context (including active
locales).
- \item \hyperlink{attribute.no-vars}{\mbox{\isa{no{\isacharunderscore}vars}}} replaces schematic variables by free
+ \item \hyperlink{attribute.no-vars}{\mbox{\isa{no{\isaliteral{5F}{\isacharunderscore}}vars}}} replaces schematic variables by free
ones; this is mainly for tuning output of pretty printed theorems.
\end{description}%
@@ -219,34 +219,34 @@
using rule \isa{eq}, which may be either a meta or object
equality.
- \item \hyperlink{method.subst}{\mbox{\isa{subst}}}~\isa{{\isachardoublequote}{\isacharparenleft}asm{\isacharparenright}\ eq{\isachardoublequote}} substitutes in an
+ \item \hyperlink{method.subst}{\mbox{\isa{subst}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}asm{\isaliteral{29}{\isacharparenright}}\ eq{\isaliteral{22}{\isachardoublequote}}} substitutes in an
assumption.
- \item \hyperlink{method.subst}{\mbox{\isa{subst}}}~\isa{{\isachardoublequote}{\isacharparenleft}i\ {\isasymdots}\ j{\isacharparenright}\ eq{\isachardoublequote}} performs several
+ \item \hyperlink{method.subst}{\mbox{\isa{subst}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ j{\isaliteral{29}{\isacharparenright}}\ eq{\isaliteral{22}{\isachardoublequote}}} performs several
substitutions in the conclusion. The numbers \isa{i} to \isa{j}
indicate the positions to substitute at. Positions are ordered from
the top of the term tree moving down from left to right. For
- example, in \isa{{\isachardoublequote}{\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ {\isacharplus}\ {\isacharparenleft}c\ {\isacharplus}\ d{\isacharparenright}{\isachardoublequote}} there are three positions
- where commutativity of \isa{{\isachardoublequote}{\isacharplus}{\isachardoublequote}} is applicable: 1 refers to \isa{{\isachardoublequote}a\ {\isacharplus}\ b{\isachardoublequote}}, 2 to the whole term, and 3 to \isa{{\isachardoublequote}c\ {\isacharplus}\ d{\isachardoublequote}}.
+ example, in \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2B}{\isacharplus}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}c\ {\isaliteral{2B}{\isacharplus}}\ d{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} there are three positions
+ where commutativity of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequote}}} is applicable: 1 refers to \isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{2B}{\isacharplus}}\ b{\isaliteral{22}{\isachardoublequote}}}, 2 to the whole term, and 3 to \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{2B}{\isacharplus}}\ d{\isaliteral{22}{\isachardoublequote}}}.
- If the positions in the list \isa{{\isachardoublequote}{\isacharparenleft}i\ {\isasymdots}\ j{\isacharparenright}{\isachardoublequote}} are non-overlapping
- (e.g.\ \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{2}}\ {\isadigit{3}}{\isacharparenright}{\isachardoublequote}} in \isa{{\isachardoublequote}{\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ {\isacharplus}\ {\isacharparenleft}c\ {\isacharplus}\ d{\isacharparenright}{\isachardoublequote}}) you may
+ If the positions in the list \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ j{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} are non-overlapping
+ (e.g.\ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}\ {\isadigit{3}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} in \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2B}{\isacharplus}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}c\ {\isaliteral{2B}{\isacharplus}}\ d{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}) you may
assume all substitutions are performed simultaneously. Otherwise
the behaviour of \isa{subst} is not specified.
- \item \hyperlink{method.subst}{\mbox{\isa{subst}}}~\isa{{\isachardoublequote}{\isacharparenleft}asm{\isacharparenright}\ {\isacharparenleft}i\ {\isasymdots}\ j{\isacharparenright}\ eq{\isachardoublequote}} performs the
+ \item \hyperlink{method.subst}{\mbox{\isa{subst}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}asm{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ j{\isaliteral{29}{\isacharparenright}}\ eq{\isaliteral{22}{\isachardoublequote}}} performs the
substitutions in the assumptions. The positions refer to the
assumptions in order from left to right. For example, given in a
- goal of the form \isa{{\isachardoublequote}P\ {\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}c\ {\isacharplus}\ d{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymdots}{\isachardoublequote}}, position 1 of
- commutativity of \isa{{\isachardoublequote}{\isacharplus}{\isachardoublequote}} is the subterm \isa{{\isachardoublequote}a\ {\isacharplus}\ b{\isachardoublequote}} and
- position 2 is the subterm \isa{{\isachardoublequote}c\ {\isacharplus}\ d{\isachardoublequote}}.
+ goal of the form \isa{{\isaliteral{22}{\isachardoublequote}}P\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2B}{\isacharplus}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ {\isaliteral{28}{\isacharparenleft}}c\ {\isaliteral{2B}{\isacharplus}}\ d{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}, position 1 of
+ commutativity of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequote}}} is the subterm \isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{2B}{\isacharplus}}\ b{\isaliteral{22}{\isachardoublequote}}} and
+ position 2 is the subterm \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{2B}{\isacharplus}}\ d{\isaliteral{22}{\isachardoublequote}}}.
\item \hyperlink{method.hypsubst}{\mbox{\isa{hypsubst}}} performs substitution using some
- assumption; this only works for equations of the form \isa{{\isachardoublequote}x\ {\isacharequal}\ t{\isachardoublequote}} where \isa{x} is a free or bound variable.
+ assumption; this only works for equations of the form \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{22}{\isachardoublequote}}} where \isa{x} is a free or bound variable.
- \item \hyperlink{method.split}{\mbox{\isa{split}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} performs single-step case
+ \item \hyperlink{method.split}{\mbox{\isa{split}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} performs single-step case
splitting using the given rules. By default, splitting is performed
- in the conclusion of a goal; the \isa{{\isachardoublequote}{\isacharparenleft}asm{\isacharparenright}{\isachardoublequote}} option indicates to
+ in the conclusion of a goal; the \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}asm{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option indicates to
operate on assumptions instead.
Note that the \hyperlink{method.simp}{\mbox{\isa{simp}}} method already involves repeated
@@ -282,24 +282,24 @@
to be solved by unification with certain parts of the subgoal.
Note that the tactic emulation proof methods in Isabelle/Isar are
- consistently named \isa{foo{\isacharunderscore}tac}. Note also that variable names
+ consistently named \isa{foo{\isaliteral{5F}{\isacharunderscore}}tac}. Note also that variable names
occurring on left hand sides of instantiations must be preceded by a
question mark if they coincide with a keyword or contain dots. This
is consistent with the attribute \hyperlink{attribute.where}{\mbox{\isa{where}}} (see
\secref{sec:pure-meth-att}).
\begin{matharray}{rcl}
- \indexdef{}{method}{rule\_tac}\hypertarget{method.rule-tac}{\hyperlink{method.rule-tac}{\mbox{\isa{rule{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{}{method}{erule\_tac}\hypertarget{method.erule-tac}{\hyperlink{method.erule-tac}{\mbox{\isa{erule{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{}{method}{drule\_tac}\hypertarget{method.drule-tac}{\hyperlink{method.drule-tac}{\mbox{\isa{drule{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{}{method}{frule\_tac}\hypertarget{method.frule-tac}{\hyperlink{method.frule-tac}{\mbox{\isa{frule{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{}{method}{cut\_tac}\hypertarget{method.cut-tac}{\hyperlink{method.cut-tac}{\mbox{\isa{cut{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{}{method}{thin\_tac}\hypertarget{method.thin-tac}{\hyperlink{method.thin-tac}{\mbox{\isa{thin{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{}{method}{subgoal\_tac}\hypertarget{method.subgoal-tac}{\hyperlink{method.subgoal-tac}{\mbox{\isa{subgoal{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{}{method}{rename\_tac}\hypertarget{method.rename-tac}{\hyperlink{method.rename-tac}{\mbox{\isa{rename{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{}{method}{rotate\_tac}\hypertarget{method.rotate-tac}{\hyperlink{method.rotate-tac}{\mbox{\isa{rotate{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{}{method}{tactic}\hypertarget{method.tactic}{\hyperlink{method.tactic}{\mbox{\isa{tactic}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{}{method}{raw\_tactic}\hypertarget{method.raw-tactic}{\hyperlink{method.raw-tactic}{\mbox{\isa{raw{\isacharunderscore}tactic}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
+ \indexdef{}{method}{rule\_tac}\hypertarget{method.rule-tac}{\hyperlink{method.rule-tac}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{}{method}{erule\_tac}\hypertarget{method.erule-tac}{\hyperlink{method.erule-tac}{\mbox{\isa{erule{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{}{method}{drule\_tac}\hypertarget{method.drule-tac}{\hyperlink{method.drule-tac}{\mbox{\isa{drule{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{}{method}{frule\_tac}\hypertarget{method.frule-tac}{\hyperlink{method.frule-tac}{\mbox{\isa{frule{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{}{method}{cut\_tac}\hypertarget{method.cut-tac}{\hyperlink{method.cut-tac}{\mbox{\isa{cut{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{}{method}{thin\_tac}\hypertarget{method.thin-tac}{\hyperlink{method.thin-tac}{\mbox{\isa{thin{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{}{method}{subgoal\_tac}\hypertarget{method.subgoal-tac}{\hyperlink{method.subgoal-tac}{\mbox{\isa{subgoal{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{}{method}{rename\_tac}\hypertarget{method.rename-tac}{\hyperlink{method.rename-tac}{\mbox{\isa{rename{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{}{method}{rotate\_tac}\hypertarget{method.rotate-tac}{\hyperlink{method.rotate-tac}{\mbox{\isa{rotate{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{}{method}{tactic}\hypertarget{method.tactic}{\hyperlink{method.tactic}{\mbox{\isa{tactic}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{}{method}{raw\_tactic}\hypertarget{method.raw-tactic}{\hyperlink{method.raw-tactic}{\mbox{\isa{raw{\isaliteral{5F}{\isacharunderscore}}tactic}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
\end{matharray}
\begin{rail}
@@ -321,44 +321,44 @@
\begin{description}
- \item \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isacharunderscore}tac}}} etc. do resolution of rules with explicit
+ \item \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}tac}}} etc. do resolution of rules with explicit
instantiation. This works the same way as the ML tactics \verb|res_inst_tac| etc. (see \cite{isabelle-implementation})
Multiple rules may be only given if there is no instantiation; then
- \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isacharunderscore}tac}}} is the same as \verb|resolve_tac| in ML (see
+ \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}tac}}} is the same as \verb|resolve_tac| in ML (see
\cite{isabelle-implementation}).
- \item \hyperlink{method.cut-tac}{\mbox{\isa{cut{\isacharunderscore}tac}}} inserts facts into the proof state as
+ \item \hyperlink{method.cut-tac}{\mbox{\isa{cut{\isaliteral{5F}{\isacharunderscore}}tac}}} inserts facts into the proof state as
assumption of a subgoal, see also \verb|Tactic.cut_facts_tac| in
\cite{isabelle-implementation}. Note that the scope of schematic
variables is spread over the main goal statement. Instantiations
may be given as well, see also ML tactic \verb|cut_inst_tac| in
\cite{isabelle-implementation}.
- \item \hyperlink{method.thin-tac}{\mbox{\isa{thin{\isacharunderscore}tac}}}~\isa{{\isasymphi}} deletes the specified assumption
- from a subgoal; note that \isa{{\isasymphi}} may contain schematic variables.
+ \item \hyperlink{method.thin-tac}{\mbox{\isa{thin{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} deletes the specified assumption
+ from a subgoal; note that \isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} may contain schematic variables.
See also \verb|thin_tac| in \cite{isabelle-implementation}.
- \item \hyperlink{method.subgoal-tac}{\mbox{\isa{subgoal{\isacharunderscore}tac}}}~\isa{{\isasymphi}} adds \isa{{\isasymphi}} as an
+ \item \hyperlink{method.subgoal-tac}{\mbox{\isa{subgoal{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} adds \isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} as an
assumption to a subgoal. See also \verb|subgoal_tac| and \verb|subgoals_tac| in \cite{isabelle-implementation}.
- \item \hyperlink{method.rename-tac}{\mbox{\isa{rename{\isacharunderscore}tac}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n{\isachardoublequote}} renames parameters of a
- goal according to the list \isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub n{\isachardoublequote}}, which refers to the
+ \item \hyperlink{method.rename-tac}{\mbox{\isa{rename{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} renames parameters of a
+ goal according to the list \isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}, which refers to the
\emph{suffix} of variables.
- \item \hyperlink{method.rotate-tac}{\mbox{\isa{rotate{\isacharunderscore}tac}}}~\isa{n} rotates the assumptions of a
+ \item \hyperlink{method.rotate-tac}{\mbox{\isa{rotate{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{n} rotates the assumptions of a
goal by \isa{n} positions: from right to left if \isa{n} is
positive, and from left to right if \isa{n} is negative; the
default value is 1. See also \verb|rotate_tac| in
\cite{isabelle-implementation}.
- \item \hyperlink{method.tactic}{\mbox{\isa{tactic}}}~\isa{{\isachardoublequote}text{\isachardoublequote}} produces a proof method from
+ \item \hyperlink{method.tactic}{\mbox{\isa{tactic}}}~\isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}} produces a proof method from
any ML text of type \verb|tactic|. Apart from the usual ML
environment and the current proof context, the ML code may refer to
the locally bound values \verb|facts|, which indicates any
current facts used for forward-chaining.
- \item \hyperlink{method.raw-tactic}{\mbox{\isa{raw{\isacharunderscore}tactic}}} is similar to \hyperlink{method.tactic}{\mbox{\isa{tactic}}}, but
+ \item \hyperlink{method.raw-tactic}{\mbox{\isa{raw{\isaliteral{5F}{\isacharunderscore}}tactic}}} is similar to \hyperlink{method.tactic}{\mbox{\isa{tactic}}}, but
presents the goal state in its raw internal form, where simultaneous
subgoals appear as conjunction of the logical framework instead of
the usual split into several subgoals. While feature this is useful
@@ -380,7 +380,7 @@
\begin{isamarkuptext}%
\begin{matharray}{rcl}
\indexdef{}{method}{simp}\hypertarget{method.simp}{\hyperlink{method.simp}{\mbox{\isa{simp}}}} & : & \isa{method} \\
- \indexdef{}{method}{simp\_all}\hypertarget{method.simp-all}{\hyperlink{method.simp-all}{\mbox{\isa{simp{\isacharunderscore}all}}}} & : & \isa{method} \\
+ \indexdef{}{method}{simp\_all}\hypertarget{method.simp-all}{\hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}}} & : & \isa{method} \\
\end{matharray}
\indexouternonterm{simpmod}
@@ -413,7 +413,7 @@
include the Splitter (all major object logics such HOL, HOLCF, FOL,
ZF do this already).
- \item \hyperlink{method.simp-all}{\mbox{\isa{simp{\isacharunderscore}all}}} is similar to \hyperlink{method.simp}{\mbox{\isa{simp}}}, but acts on
+ \item \hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}} is similar to \hyperlink{method.simp}{\mbox{\isa{simp}}}, but acts on
all goals (backwards from the last to the first one).
\end{description}
@@ -429,20 +429,20 @@
Additional Simplifier options may be specified to tune the behavior
further (mostly for unstructured scripts with many accidental local
- facts): ``\isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharparenright}{\isachardoublequote}}'' means assumptions are ignored
- completely (cf.\ \verb|simp_tac|), ``\isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharunderscore}simp{\isacharparenright}{\isachardoublequote}}'' means
+ facts): ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' means assumptions are ignored
+ completely (cf.\ \verb|simp_tac|), ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' means
assumptions are used in the simplification of the conclusion but are
- not themselves simplified (cf.\ \verb|asm_simp_tac|), and ``\isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharunderscore}use{\isacharparenright}{\isachardoublequote}}'' means assumptions are simplified but are not used
+ not themselves simplified (cf.\ \verb|asm_simp_tac|), and ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{5F}{\isacharunderscore}}use{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' means assumptions are simplified but are not used
in the simplification of each other or the conclusion (cf.\ \verb|full_simp_tac|). For compatibility reasons, there is also an option
- ``\isa{{\isachardoublequote}{\isacharparenleft}asm{\isacharunderscore}lr{\isacharparenright}{\isachardoublequote}}'', which means that an assumption is only used
+ ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}asm{\isaliteral{5F}{\isacharunderscore}}lr{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'', which means that an assumption is only used
for simplifying assumptions which are to the right of it (cf.\ \verb|asm_lr_simp_tac|).
- The configuration option \isa{{\isachardoublequote}depth{\isacharunderscore}limit{\isachardoublequote}} limits the number of
+ The configuration option \isa{{\isaliteral{22}{\isachardoublequote}}depth{\isaliteral{5F}{\isacharunderscore}}limit{\isaliteral{22}{\isachardoublequote}}} limits the number of
recursive invocations of the simplifier during conditional
rewriting.
\medskip The Splitter package is usually configured to work as part
- of the Simplifier. The effect of repeatedly applying \verb|split_tac| can be simulated by ``\isa{{\isachardoublequote}{\isacharparenleft}simp\ only{\isacharcolon}\ split{\isacharcolon}\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharparenright}{\isachardoublequote}}''. There is also a separate \isa{split}
+ of the Simplifier. The effect of repeatedly applying \verb|split_tac| can be simulated by ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}simp\ only{\isaliteral{3A}{\isacharcolon}}\ split{\isaliteral{3A}{\isacharcolon}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}''. There is also a separate \isa{split}
method available for single-step case splitting.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -453,7 +453,7 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{print\_simpset}\hypertarget{command.print-simpset}{\hyperlink{command.print-simpset}{\mbox{\isa{\isacommand{print{\isacharunderscore}simpset}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{}{command}{print\_simpset}\hypertarget{command.print-simpset}{\hyperlink{command.print-simpset}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}simpset}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
\indexdef{}{attribute}{simp}\hypertarget{attribute.simp}{\hyperlink{attribute.simp}{\mbox{\isa{simp}}}} & : & \isa{attribute} \\
\indexdef{}{attribute}{cong}\hypertarget{attribute.cong}{\hyperlink{attribute.cong}{\mbox{\isa{cong}}}} & : & \isa{attribute} \\
\indexdef{}{attribute}{split}\hypertarget{attribute.split}{\hyperlink{attribute.split}{\mbox{\isa{split}}}} & : & \isa{attribute} \\
@@ -466,7 +466,7 @@
\begin{description}
- \item \hyperlink{command.print-simpset}{\mbox{\isa{\isacommand{print{\isacharunderscore}simpset}}}} prints the collection of rules
+ \item \hyperlink{command.print-simpset}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}simpset}}}} prints the collection of rules
declared to the Simplifier, which is also known as ``simpset''
internally \cite{isabelle-ref}.
@@ -486,7 +486,7 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{simproc\_setup}\hypertarget{command.simproc-setup}{\hyperlink{command.simproc-setup}{\mbox{\isa{\isacommand{simproc{\isacharunderscore}setup}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
+ \indexdef{}{command}{simproc\_setup}\hypertarget{command.simproc-setup}{\hyperlink{command.simproc-setup}{\mbox{\isa{\isacommand{simproc{\isaliteral{5F}{\isacharunderscore}}setup}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
simproc & : & \isa{attribute} \\
\end{matharray}
@@ -500,11 +500,11 @@
\begin{description}
- \item \hyperlink{command.simproc-setup}{\mbox{\isa{\isacommand{simproc{\isacharunderscore}setup}}}} defines a named simplification
+ \item \hyperlink{command.simproc-setup}{\mbox{\isa{\isacommand{simproc{\isaliteral{5F}{\isacharunderscore}}setup}}}} defines a named simplification
procedure that is invoked by the Simplifier whenever any of the
given term patterns match the current redex. The implementation,
which is provided as ML source text, needs to be of type \verb|morphism -> simpset -> cterm -> thm option|, where the \verb|cterm| represents the current redex \isa{r} and the result is
- supposed to be some proven rewrite rule \isa{{\isachardoublequote}r\ {\isasymequiv}\ r{\isacharprime}{\isachardoublequote}} (or a
+ supposed to be some proven rewrite rule \isa{{\isaliteral{22}{\isachardoublequote}}r\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ r{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequote}}} (or a
generalized version), or \verb|NONE| to indicate failure. The
\verb|simpset| argument holds the full context of the current
Simplifier invocation, including the actual Isar proof context. The
@@ -517,9 +517,9 @@
Morphisms and identifiers are only relevant for simprocs that are
defined within a local target context, e.g.\ in a locale.
- \item \isa{{\isachardoublequote}simproc\ add{\isacharcolon}\ name{\isachardoublequote}} and \isa{{\isachardoublequote}simproc\ del{\isacharcolon}\ name{\isachardoublequote}}
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}simproc\ add{\isaliteral{3A}{\isacharcolon}}\ name{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}simproc\ del{\isaliteral{3A}{\isacharcolon}}\ name{\isaliteral{22}{\isachardoublequote}}}
add or delete named simprocs to the current Simplifier context. The
- default is to add a simproc. Note that \hyperlink{command.simproc-setup}{\mbox{\isa{\isacommand{simproc{\isacharunderscore}setup}}}}
+ default is to add a simproc. Note that \hyperlink{command.simproc-setup}{\mbox{\isa{\isacommand{simproc{\isaliteral{5F}{\isacharunderscore}}setup}}}}
already adds the new simproc to the subsequent context.
\end{description}%
@@ -545,10 +545,10 @@
\begin{description}
- \item \hyperlink{attribute.simplified}{\mbox{\isa{simplified}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} causes a theorem to
- be simplified, either by exactly the specified rules \isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n{\isachardoublequote}}, or the implicit Simplifier context if no arguments are given.
+ \item \hyperlink{attribute.simplified}{\mbox{\isa{simplified}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} causes a theorem to
+ be simplified, either by exactly the specified rules \isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}, or the implicit Simplifier context if no arguments are given.
The result is fully simplified by default, including assumptions and
- conclusion; the options \isa{no{\isacharunderscore}asm} etc.\ tune the Simplifier in
+ conclusion; the options \isa{no{\isaliteral{5F}{\isacharunderscore}}asm} etc.\ tune the Simplifier in
the same way as the for the \isa{simp} method.
Note that forward simplification restricts the simplifier to its
@@ -595,7 +595,7 @@
Isabelle/Pure (\secref{sec:pure-meth-att}).
\item \hyperlink{method.contradiction}{\mbox{\isa{contradiction}}} solves some goal by contradiction,
- deriving any result from both \isa{{\isachardoublequote}{\isasymnot}\ A{\isachardoublequote}} and \isa{A}. Chained
+ deriving any result from both \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A{\isaliteral{22}{\isachardoublequote}}} and \isa{A}. Chained
facts, which are guaranteed to participate, may appear in either
order.
@@ -704,7 +704,7 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{print\_claset}\hypertarget{command.print-claset}{\hyperlink{command.print-claset}{\mbox{\isa{\isacommand{print{\isacharunderscore}claset}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{}{command}{print\_claset}\hypertarget{command.print-claset}{\hyperlink{command.print-claset}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}claset}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
\indexdef{}{attribute}{intro}\hypertarget{attribute.intro}{\hyperlink{attribute.intro}{\mbox{\isa{intro}}}} & : & \isa{attribute} \\
\indexdef{}{attribute}{elim}\hypertarget{attribute.elim}{\hyperlink{attribute.elim}{\mbox{\isa{elim}}}} & : & \isa{attribute} \\
\indexdef{}{attribute}{dest}\hypertarget{attribute.dest}{\hyperlink{attribute.dest}{\mbox{\isa{dest}}}} & : & \isa{attribute} \\
@@ -723,15 +723,15 @@
\begin{description}
- \item \hyperlink{command.print-claset}{\mbox{\isa{\isacommand{print{\isacharunderscore}claset}}}} prints the collection of rules
+ \item \hyperlink{command.print-claset}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}claset}}}} prints the collection of rules
declared to the Classical Reasoner, which is also known as
``claset'' internally \cite{isabelle-ref}.
\item \hyperlink{attribute.intro}{\mbox{\isa{intro}}}, \hyperlink{attribute.elim}{\mbox{\isa{elim}}}, and \hyperlink{attribute.dest}{\mbox{\isa{dest}}}
declare introduction, elimination, and destruction rules,
respectively. By default, rules are considered as \emph{unsafe}
- (i.e.\ not applied blindly without backtracking), while ``\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}'' classifies as \emph{safe}. Rule declarations marked by
- ``\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}'' coincide with those of Isabelle/Pure, cf.\
+ (i.e.\ not applied blindly without backtracking), while ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}}'' classifies as \emph{safe}. Rule declarations marked by
+ ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}'' coincide with those of Isabelle/Pure, cf.\
\secref{sec:pure-meth-att} (i.e.\ are only applied in single steps
of the \hyperlink{method.rule}{\mbox{\isa{rule}}} method). The optional natural number
specifies an explicit weight argument, which is ignored by automated
@@ -744,9 +744,9 @@
Simplifier and the Classical reasoner at the same time.
Non-conditional rules result in a ``safe'' introduction and
elimination pair; conditional ones are considered ``unsafe''. Rules
- with negative conclusion are automatically inverted (using \isa{{\isachardoublequote}{\isasymnot}{\isachardoublequote}}-elimination internally).
+ with negative conclusion are automatically inverted (using \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}{\isaliteral{22}{\isachardoublequote}}}-elimination internally).
- The ``\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}'' version of \hyperlink{attribute.iff}{\mbox{\isa{iff}}} declares rules to
+ The ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}'' version of \hyperlink{attribute.iff}{\mbox{\isa{iff}}} declares rules to
the Isabelle/Pure context only, and omits the Simplifier
declaration.
@@ -766,7 +766,7 @@
\begin{description}
\item \hyperlink{attribute.swapped}{\mbox{\isa{swapped}}} turns an introduction rule into an
- elimination, by resolving with the classical swap principle \isa{{\isachardoublequote}{\isacharparenleft}{\isasymnot}\ B\ {\isasymLongrightarrow}\ A{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymnot}\ A\ {\isasymLongrightarrow}\ B{\isacharparenright}{\isachardoublequote}}.
+ elimination, by resolving with the classical swap principle \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}.
\end{description}%
\end{isamarkuptext}%
@@ -778,26 +778,26 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{judgment}\hypertarget{command.judgment}{\hyperlink{command.judgment}{\mbox{\isa{\isacommand{judgment}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
+ \indexdef{}{command}{judgment}\hypertarget{command.judgment}{\hyperlink{command.judgment}{\mbox{\isa{\isacommand{judgment}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\indexdef{}{method}{atomize}\hypertarget{method.atomize}{\hyperlink{method.atomize}{\mbox{\isa{atomize}}}} & : & \isa{method} \\
\indexdef{}{attribute}{atomize}\hypertarget{attribute.atomize}{\hyperlink{attribute.atomize}{\mbox{\isa{atomize}}}} & : & \isa{attribute} \\
- \indexdef{}{attribute}{rule\_format}\hypertarget{attribute.rule-format}{\hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isacharunderscore}format}}}} & : & \isa{attribute} \\
+ \indexdef{}{attribute}{rule\_format}\hypertarget{attribute.rule-format}{\hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}format}}}} & : & \isa{attribute} \\
\indexdef{}{attribute}{rulify}\hypertarget{attribute.rulify}{\hyperlink{attribute.rulify}{\mbox{\isa{rulify}}}} & : & \isa{attribute} \\
\end{matharray}
The very starting point for any Isabelle object-logic is a ``truth
judgment'' that links object-level statements to the meta-logic
(with its minimal language of \isa{prop} that covers universal
- quantification \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}} and implication \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}}).
+ quantification \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{22}{\isachardoublequote}}} and implication \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}}).
Common object-logics are sufficiently expressive to internalize rule
- statements over \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}} within their own
+ statements over \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}} within their own
language. This is useful in certain situations where a rule needs
to be viewed as an atomic statement from the meta-level perspective,
- e.g.\ \isa{{\isachardoublequote}{\isasymAnd}x{\isachardot}\ x\ {\isasymin}\ A\ {\isasymLongrightarrow}\ P\ x{\isachardoublequote}} versus \isa{{\isachardoublequote}{\isasymforall}x\ {\isasymin}\ A{\isachardot}\ P\ x{\isachardoublequote}}.
+ e.g.\ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ x{\isaliteral{22}{\isachardoublequote}}} versus \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{22}{\isachardoublequote}}}.
From the following language elements, only the \hyperlink{method.atomize}{\mbox{\isa{atomize}}}
- method and \hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isacharunderscore}format}}} attribute are occasionally
+ method and \hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}format}}} attribute are occasionally
required by end-users, the rest is for those who need to setup their
own object-logic. In the latter case existing formulations of
Isabelle/FOL or Isabelle/HOL may be taken as realistic examples.
@@ -816,11 +816,11 @@
\begin{description}
- \item \hyperlink{command.judgment}{\mbox{\isa{\isacommand{judgment}}}}~\isa{{\isachardoublequote}c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\ {\isacharparenleft}mx{\isacharparenright}{\isachardoublequote}} declares constant
+ \item \hyperlink{command.judgment}{\mbox{\isa{\isacommand{judgment}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\ {\isaliteral{28}{\isacharparenleft}}mx{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} declares constant
\isa{c} as the truth judgment of the current object-logic. Its
- type \isa{{\isasymsigma}} should specify a coercion of the category of
+ type \isa{{\isaliteral{5C3C7369676D613E}{\isasymsigma}}} should specify a coercion of the category of
object-level propositions to \isa{prop} of the Pure meta-logic;
- the mixfix annotation \isa{{\isachardoublequote}{\isacharparenleft}mx{\isacharparenright}{\isachardoublequote}} would typically just link the
+ the mixfix annotation \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}mx{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} would typically just link the
object language (internally of syntactic category \isa{logic})
with that of \isa{prop}. Only one \hyperlink{command.judgment}{\mbox{\isa{\isacommand{judgment}}}}
declaration may be given in any theory development.
@@ -829,25 +829,25 @@
premises of a sub-goal, using the meta-level equations declared via
\hyperlink{attribute.atomize}{\mbox{\isa{atomize}}} (as an attribute) beforehand. As a result,
heavily nested goals become amenable to fundamental operations such
- as resolution (cf.\ the \hyperlink{method.rule}{\mbox{\isa{rule}}} method). Giving the ``\isa{{\isachardoublequote}{\isacharparenleft}full{\isacharparenright}{\isachardoublequote}}'' option here means to turn the whole subgoal into an
+ as resolution (cf.\ the \hyperlink{method.rule}{\mbox{\isa{rule}}} method). Giving the ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}full{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' option here means to turn the whole subgoal into an
object-statement (if possible), including the outermost parameters
and assumptions as well.
A typical collection of \hyperlink{attribute.atomize}{\mbox{\isa{atomize}}} rules for a particular
object-logic would provide an internalization for each of the
- connectives of \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}}, \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}}, and \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}}.
+ connectives of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}}, and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}}.
Meta-level conjunction should be covered as well (this is
particularly important for locales, see \secref{sec:locale}).
- \item \hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isacharunderscore}format}}} rewrites a theorem by the equalities
+ \item \hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}format}}} rewrites a theorem by the equalities
declared as \hyperlink{attribute.rulify}{\mbox{\isa{rulify}}} rules in the current object-logic.
By default, the result is fully normalized, including assumptions
- and conclusions at any depth. The \isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharparenright}{\isachardoublequote}} option
+ and conclusions at any depth. The \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option
restricts the transformation to the conclusion of a rule.
- In common object-logics (HOL, FOL, ZF), the effect of \hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isacharunderscore}format}}} is to replace (bounded) universal quantification
- (\isa{{\isachardoublequote}{\isasymforall}{\isachardoublequote}}) and implication (\isa{{\isachardoublequote}{\isasymlongrightarrow}{\isachardoublequote}}) by the corresponding
- rule statements over \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}}.
+ In common object-logics (HOL, FOL, ZF), the effect of \hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}format}}} is to replace (bounded) universal quantification
+ (\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}{\isaliteral{22}{\isachardoublequote}}}) and implication (\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}{\isaliteral{22}{\isachardoublequote}}}) by the corresponding
+ rule statements over \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}}.
\end{description}%
\end{isamarkuptext}%
--- a/doc-src/IsarRef/Thy/document/HOLCF_Specific.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarRef/Thy/document/HOLCF_Specific.tex Mon Nov 08 14:41:11 2010 +0100
@@ -1,6 +1,6 @@
%
\begin{isabellebody}%
-\def\isabellecontext{HOLCF{\isacharunderscore}Specific}%
+\def\isabellecontext{HOLCF{\isaliteral{5F}{\isacharunderscore}}Specific}%
%
\isadelimtheory
%
@@ -8,7 +8,7 @@
%
\isatagtheory
\isacommand{theory}\isamarkupfalse%
-\ HOLCF{\isacharunderscore}Specific\isanewline
+\ HOLCF{\isaliteral{5F}{\isacharunderscore}}Specific\isanewline
\isakeyword{imports}\ HOLCF\isanewline
\isakeyword{begin}%
\endisatagtheory
@@ -28,12 +28,12 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{HOLCF}{command}{consts}\hypertarget{command.HOLCF.consts}{\hyperlink{command.HOLCF.consts}{\mbox{\isa{\isacommand{consts}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
+ \indexdef{HOLCF}{command}{consts}\hypertarget{command.HOLCF.consts}{\hyperlink{command.HOLCF.consts}{\mbox{\isa{\isacommand{consts}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
- HOLCF provides a separate type for continuous functions \isa{{\isachardoublequote}{\isasymalpha}\ {\isasymrightarrow}\ {\isasymbeta}{\isachardoublequote}}, with an explicit application operator \isa{{\isachardoublequote}f\ {\isasymcdot}\ x{\isachardoublequote}}.
+ HOLCF provides a separate type for continuous functions \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{22}{\isachardoublequote}}}, with an explicit application operator \isa{{\isaliteral{22}{\isachardoublequote}}f\ {\isaliteral{5C3C63646F743E}{\isasymcdot}}\ x{\isaliteral{22}{\isachardoublequote}}}.
Isabelle mixfix syntax normally refers directly to the pure
- meta-level function type \isa{{\isachardoublequote}{\isasymalpha}\ {\isasymRightarrow}\ {\isasymbeta}{\isachardoublequote}}, with application \isa{{\isachardoublequote}f\ x{\isachardoublequote}}.
+ meta-level function type \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{22}{\isachardoublequote}}}, with application \isa{{\isaliteral{22}{\isachardoublequote}}f\ x{\isaliteral{22}{\isachardoublequote}}}.
The HOLCF variant of \hyperlink{command.HOLCF.consts}{\mbox{\isa{\isacommand{consts}}}} modifies that of
Pure Isabelle (cf.\ \secref{sec:consts}) such that declarations
@@ -51,7 +51,7 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{HOLCF}{command}{domain}\hypertarget{command.HOLCF.domain}{\hyperlink{command.HOLCF.domain}{\mbox{\isa{\isacommand{domain}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
+ \indexdef{HOLCF}{command}{domain}\hypertarget{command.HOLCF.domain}{\hyperlink{command.HOLCF.domain}{\mbox{\isa{\isacommand{domain}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
--- a/doc-src/IsarRef/Thy/document/HOL_Specific.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarRef/Thy/document/HOL_Specific.tex Mon Nov 08 14:41:11 2010 +0100
@@ -1,6 +1,6 @@
%
\begin{isabellebody}%
-\def\isabellecontext{HOL{\isacharunderscore}Specific}%
+\def\isabellecontext{HOL{\isaliteral{5F}{\isacharunderscore}}Specific}%
%
\isadelimtheory
%
@@ -8,7 +8,7 @@
%
\isatagtheory
\isacommand{theory}\isamarkupfalse%
-\ HOL{\isacharunderscore}Specific\isanewline
+\ HOL{\isaliteral{5F}{\isacharunderscore}}Specific\isanewline
\isakeyword{imports}\ Main\isanewline
\isakeyword{begin}%
\endisatagtheory
@@ -28,7 +28,7 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{typedef}\hypertarget{command.HOL.typedef}{\hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
+ \indexdef{HOL}{command}{typedef}\hypertarget{command.HOL.typedef}{\hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -45,7 +45,7 @@
\begin{description}
- \item \hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t\ {\isacharequal}\ A{\isachardoublequote}}
+ \item \hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}\ t\ {\isaliteral{3D}{\isacharequal}}\ A{\isaliteral{22}{\isachardoublequote}}}
axiomatizes a Gordon/HOL-style type definition in the background
theory of the current context, depending on a non-emptiness result
of the set \isa{A} (which needs to be proven interactively).
@@ -59,19 +59,19 @@
By default, \hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}} defines both a type \isa{t}
and a set (term constant) of the same name, unless an alternative
- base name is given in parentheses, or the ``\isa{{\isachardoublequote}{\isacharparenleft}open{\isacharparenright}{\isachardoublequote}}''
+ base name is given in parentheses, or the ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}open{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}''
declaration is used to suppress a separate constant definition
- altogether. The injection from type to set is called \isa{Rep{\isacharunderscore}t},
- its inverse \isa{Abs{\isacharunderscore}t} --- this may be changed via an explicit
+ altogether. The injection from type to set is called \isa{Rep{\isaliteral{5F}{\isacharunderscore}}t},
+ its inverse \isa{Abs{\isaliteral{5F}{\isacharunderscore}}t} --- this may be changed via an explicit
\hyperlink{keyword.HOL.morphisms}{\mbox{\isa{\isakeyword{morphisms}}}} declaration.
- Theorems \isa{Rep{\isacharunderscore}t}, \isa{Rep{\isacharunderscore}t{\isacharunderscore}inverse}, and \isa{Abs{\isacharunderscore}t{\isacharunderscore}inverse} provide the most basic characterization as a
+ Theorems \isa{Rep{\isaliteral{5F}{\isacharunderscore}}t}, \isa{Rep{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{5F}{\isacharunderscore}}inverse}, and \isa{Abs{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{5F}{\isacharunderscore}}inverse} provide the most basic characterization as a
corresponding injection/surjection pair (in both directions). Rules
- \isa{Rep{\isacharunderscore}t{\isacharunderscore}inject} and \isa{Abs{\isacharunderscore}t{\isacharunderscore}inject} provide a slightly
+ \isa{Rep{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{5F}{\isacharunderscore}}inject} and \isa{Abs{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{5F}{\isacharunderscore}}inject} provide a slightly
more convenient view on the injectivity part, suitable for automated
proof tools (e.g.\ in \hyperlink{attribute.simp}{\mbox{\isa{simp}}} or \hyperlink{attribute.iff}{\mbox{\isa{iff}}}
- declarations). Rules \isa{Rep{\isacharunderscore}t{\isacharunderscore}cases}/\isa{Rep{\isacharunderscore}t{\isacharunderscore}induct}, and
- \isa{Abs{\isacharunderscore}t{\isacharunderscore}cases}/\isa{Abs{\isacharunderscore}t{\isacharunderscore}induct} provide alternative views
+ declarations). Rules \isa{Rep{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{5F}{\isacharunderscore}}cases}/\isa{Rep{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{5F}{\isacharunderscore}}induct}, and
+ \isa{Abs{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{5F}{\isacharunderscore}}cases}/\isa{Abs{\isaliteral{5F}{\isacharunderscore}}t{\isaliteral{5F}{\isacharunderscore}}induct} provide alternative views
on surjectivity; these are already declared as set or type rules for
the generic \hyperlink{method.cases}{\mbox{\isa{cases}}} and \hyperlink{method.induct}{\mbox{\isa{induct}}} methods.
@@ -89,7 +89,7 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \hyperlink{attribute.HOL.split-format}{\mbox{\isa{split{\isacharunderscore}format}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{attribute} \\
+ \hyperlink{attribute.HOL.split-format}{\mbox{\isa{split{\isaliteral{5F}{\isacharunderscore}}format}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{attribute} \\
\end{matharray}
\begin{rail}
@@ -99,7 +99,7 @@
\begin{description}
- \item \hyperlink{attribute.HOL.split-format}{\mbox{\isa{split{\isacharunderscore}format}}}\ \isa{{\isachardoublequote}{\isacharparenleft}complete{\isacharparenright}{\isachardoublequote}} causes
+ \item \hyperlink{attribute.HOL.split-format}{\mbox{\isa{split{\isaliteral{5F}{\isacharunderscore}}format}}}\ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}complete{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} causes
arguments in function applications to be represented canonically
according to their tuple type structure.
@@ -137,32 +137,32 @@
\begin{center}
\begin{tabular}{l|l|l}
& record terms & record types \\ \hline
- fixed & \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isasymrparr}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharcolon}{\isacharcolon}\ A{\isacharcomma}\ y\ {\isacharcolon}{\isacharcolon}\ B{\isasymrparr}{\isachardoublequote}} \\
- schematic & \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ m{\isasymrparr}{\isachardoublequote}} &
- \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharcolon}{\isacharcolon}\ A{\isacharcomma}\ y\ {\isacharcolon}{\isacharcolon}\ B{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ M{\isasymrparr}{\isachardoublequote}} \\
+ fixed & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ B{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
+ schematic & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ m{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} &
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ B{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ M{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}
\end{center}
- \noindent The ASCII representation of \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isasymrparr}{\isachardoublequote}} is \isa{{\isachardoublequote}{\isacharparenleft}{\isacharbar}\ x\ {\isacharequal}\ a\ {\isacharbar}{\isacharparenright}{\isachardoublequote}}.
+ \noindent The ASCII representation of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} is \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{7C}{\isacharbar}}\ x\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}.
- A fixed record \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isasymrparr}{\isachardoublequote}} has field \isa{x} of value
+ A fixed record \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} has field \isa{x} of value
\isa{a} and field \isa{y} of value \isa{b}. The corresponding
- type is \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharcolon}{\isacharcolon}\ A{\isacharcomma}\ y\ {\isacharcolon}{\isacharcolon}\ B{\isasymrparr}{\isachardoublequote}}, assuming that \isa{{\isachardoublequote}a\ {\isacharcolon}{\isacharcolon}\ A{\isachardoublequote}}
- and \isa{{\isachardoublequote}b\ {\isacharcolon}{\isacharcolon}\ B{\isachardoublequote}}.
+ type is \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ B{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}, assuming that \isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{22}{\isachardoublequote}}}
+ and \isa{{\isaliteral{22}{\isachardoublequote}}b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ B{\isaliteral{22}{\isachardoublequote}}}.
- A record scheme like \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ m{\isasymrparr}{\isachardoublequote}} contains fields
+ A record scheme like \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ m{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} contains fields
\isa{x} and \isa{y} as before, but also possibly further fields
- as indicated by the ``\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}'' notation (which is actually part
- of the syntax). The improper field ``\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}'' of a record
+ as indicated by the ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}'' notation (which is actually part
+ of the syntax). The improper field ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}'' of a record
scheme is called the \emph{more part}. Logically it is just a free
variable, which is occasionally referred to as ``row variable'' in
the literature. The more part of a record scheme may be
instantiated by zero or more further components. For example, the
- previous scheme may get instantiated to \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isacharcomma}\ z\ {\isacharequal}\ c{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ m{\isacharprime}{\isasymrparr}{\isachardoublequote}}, where \isa{m{\isacharprime}} refers to a different more part.
+ previous scheme may get instantiated to \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ z\ {\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ m{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}, where \isa{m{\isaliteral{27}{\isacharprime}}} refers to a different more part.
Fixed records are special instances of record schemes, where
- ``\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}'' is properly terminated by the \isa{{\isachardoublequote}{\isacharparenleft}{\isacharparenright}\ {\isacharcolon}{\isacharcolon}\ unit{\isachardoublequote}}
- element. In fact, \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isasymrparr}{\isachardoublequote}} is just an abbreviation
- for \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharequal}\ a{\isacharcomma}\ y\ {\isacharequal}\ b{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ {\isacharparenleft}{\isacharparenright}{\isasymrparr}{\isachardoublequote}}.
+ ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}'' is properly terminated by the \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ unit{\isaliteral{22}{\isachardoublequote}}}
+ element. In fact, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} is just an abbreviation
+ for \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}.
\medskip Two key observations make extensible records in a simply
typed language like HOL work out:
@@ -195,7 +195,7 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{record}\hypertarget{command.HOL.record}{\hyperlink{command.HOL.record}{\mbox{\isa{\isacommand{record}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
+ \indexdef{HOL}{command}{record}\hypertarget{command.HOL.record}{\hyperlink{command.HOL.record}{\mbox{\isa{\isacommand{record}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -205,26 +205,26 @@
\begin{description}
- \item \hyperlink{command.HOL.record}{\mbox{\isa{\isacommand{record}}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharparenright}\ t\ {\isacharequal}\ {\isasymtau}\ {\isacharplus}\ c\isactrlsub {\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ c\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub n{\isachardoublequote}} defines extensible record type \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharparenright}\ t{\isachardoublequote}},
- derived from the optional parent record \isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}} by adding new
- field components \isa{{\isachardoublequote}c\isactrlsub i\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub i{\isachardoublequote}} etc.
+ \item \hyperlink{command.HOL.record}{\mbox{\isa{\isacommand{record}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}\ t\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\ {\isaliteral{2B}{\isacharplus}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} defines extensible record type \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}},
+ derived from the optional parent record \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}} by adding new
+ field components \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} etc.
- The type variables of \isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isasymsigma}\isactrlsub i{\isachardoublequote}} need to be
- covered by the (distinct) parameters \isa{{\isachardoublequote}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isachardoublequote}}. Type constructor \isa{t} has to be new, while \isa{{\isasymtau}} needs to specify an instance of an existing record type. At
- least one new field \isa{{\isachardoublequote}c\isactrlsub i{\isachardoublequote}} has to be specified.
+ The type variables of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} need to be
+ covered by the (distinct) parameters \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}}. Type constructor \isa{t} has to be new, while \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} needs to specify an instance of an existing record type. At
+ least one new field \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} has to be specified.
Basically, field names need to belong to a unique record. This is
not a real restriction in practice, since fields are qualified by
the record name internally.
- The parent record specification \isa{{\isasymtau}} is optional; if omitted
+ The parent record specification \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} is optional; if omitted
\isa{t} becomes a root record. The hierarchy of all records
declared within a theory context forms a forest structure, i.e.\ a
set of trees starting with a root record each. There is no way to
merge multiple parent records!
- For convenience, \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharparenright}\ t{\isachardoublequote}} is made a
- type abbreviation for the fixed record type \isa{{\isachardoublequote}{\isasymlparr}c\isactrlsub {\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub n{\isasymrparr}{\isachardoublequote}}, likewise is \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharcomma}\ {\isasymzeta}{\isacharparenright}\ t{\isacharunderscore}scheme{\isachardoublequote}} made an abbreviation for
- \isa{{\isachardoublequote}{\isasymlparr}c\isactrlsub {\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub n{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}{\isachardoublequote}}.
+ For convenience, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}} is made a
+ type abbreviation for the fixed record type \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}, likewise is \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{5F}{\isacharunderscore}}scheme{\isaliteral{22}{\isachardoublequote}}} made an abbreviation for
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}.
\end{description}%
\end{isamarkuptext}%
@@ -239,21 +239,21 @@
standard operations. Selectors and updates are provided for any
field, including the improper one ``\isa{more}''. There are also
cumulative record constructor functions. To simplify the
- presentation below, we assume for now that \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharparenright}\ t{\isachardoublequote}} is a root record with fields \isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\isactrlsub n{\isachardoublequote}}.
+ presentation below, we assume for now that \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}} is a root record with fields \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}.
\medskip \textbf{Selectors} and \textbf{updates} are available for
any field (including ``\isa{more}''):
\begin{matharray}{lll}
- \isa{{\isachardoublequote}c\isactrlsub i{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymlparr}\isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}\ {\isasymRightarrow}\ {\isasymsigma}\isactrlsub i{\isachardoublequote}} \\
- \isa{{\isachardoublequote}c\isactrlsub i{\isacharunderscore}update{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymsigma}\isactrlsub i\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}{\isachardoublequote}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{5F}{\isacharunderscore}}update{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
- There is special syntax for application of updates: \isa{{\isachardoublequote}r{\isasymlparr}x\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}{\isachardoublequote}} abbreviates term \isa{{\isachardoublequote}x{\isacharunderscore}update\ a\ r{\isachardoublequote}}. Further notation for
- repeated updates is also available: \isa{{\isachardoublequote}r{\isasymlparr}x\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}{\isasymlparr}y\ {\isacharcolon}{\isacharequal}\ b{\isasymrparr}{\isasymlparr}z\ {\isacharcolon}{\isacharequal}\ c{\isasymrparr}{\isachardoublequote}} may be written \isa{{\isachardoublequote}r{\isasymlparr}x\ {\isacharcolon}{\isacharequal}\ a{\isacharcomma}\ y\ {\isacharcolon}{\isacharequal}\ b{\isacharcomma}\ z\ {\isacharcolon}{\isacharequal}\ c{\isasymrparr}{\isachardoublequote}}. Note that
+ There is special syntax for application of updates: \isa{{\isaliteral{22}{\isachardoublequote}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} abbreviates term \isa{{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{5F}{\isacharunderscore}}update\ a\ r{\isaliteral{22}{\isachardoublequote}}}. Further notation for
+ repeated updates is also available: \isa{{\isaliteral{22}{\isachardoublequote}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}z\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} may be written \isa{{\isaliteral{22}{\isachardoublequote}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ z\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}. Note that
because of postfix notation the order of fields shown here is
reverse than in the actual term. Since repeated updates are just
- function applications, fields may be freely permuted in \isa{{\isachardoublequote}{\isasymlparr}x\ {\isacharcolon}{\isacharequal}\ a{\isacharcomma}\ y\ {\isacharcolon}{\isacharequal}\ b{\isacharcomma}\ z\ {\isacharcolon}{\isacharequal}\ c{\isasymrparr}{\isachardoublequote}}, as far as logical equality is concerned.
+ function applications, fields may be freely permuted in \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ z\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}}, as far as logical equality is concerned.
Thus commutativity of independent updates can be proven within the
logic for any two fields, but not as a general theorem.
@@ -261,7 +261,7 @@
constructor function:
\begin{matharray}{lll}
- \isa{{\isachardoublequote}t{\isachardot}make{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymsigma}\isactrlsub {\isadigit{1}}\ {\isasymRightarrow}\ {\isasymdots}\ {\isasymsigma}\isactrlsub n\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isasymrparr}{\isachardoublequote}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}make{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\medskip We now reconsider the case of non-root records, which are
@@ -270,33 +270,33 @@
records}. Appending the lists of fields of all ancestors results in
a certain field prefix. The record package automatically takes care
of this by lifting operations over this context of ancestor fields.
- Assuming that \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub m{\isacharparenright}\ t{\isachardoublequote}} has ancestor
- fields \isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isasymrho}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ b\isactrlsub k\ {\isacharcolon}{\isacharcolon}\ {\isasymrho}\isactrlsub k{\isachardoublequote}},
+ Assuming that \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}} has ancestor
+ fields \isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C72686F3E}{\isasymrho}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub k\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C72686F3E}{\isasymrho}}\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{22}{\isachardoublequote}}},
the above record operations will get the following types:
\medskip
\begin{tabular}{lll}
- \isa{{\isachardoublequote}c\isactrlsub i{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymlparr}\isactrlvec b\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymrho}{\isacharcomma}\ \isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}\ {\isasymRightarrow}\ {\isasymsigma}\isactrlsub i{\isachardoublequote}} \\
- \isa{{\isachardoublequote}c\isactrlsub i{\isacharunderscore}update{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymsigma}\isactrlsub i\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec b\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymrho}{\isacharcomma}\ \isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec b\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymrho}{\isacharcomma}\ \isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}{\isachardoublequote}} \\
- \isa{{\isachardoublequote}t{\isachardot}make{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymrho}\isactrlsub {\isadigit{1}}\ {\isasymRightarrow}\ {\isasymdots}\ {\isasymrho}\isactrlsub k\ {\isasymRightarrow}\ {\isasymsigma}\isactrlsub {\isadigit{1}}\ {\isasymRightarrow}\ {\isasymdots}\ {\isasymsigma}\isactrlsub n\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec b\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymrho}{\isacharcomma}\ \isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isasymrparr}{\isachardoublequote}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{5F}{\isacharunderscore}}update{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}make{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C72686F3E}{\isasymrho}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C72686F3E}{\isasymrho}}\isaliteral{5C3C5E7375623E}{}\isactrlsub k\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}
\medskip
\noindent Some further operations address the extension aspect of a
- derived record scheme specifically: \isa{{\isachardoublequote}t{\isachardot}fields{\isachardoublequote}} produces a
+ derived record scheme specifically: \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}fields{\isaliteral{22}{\isachardoublequote}}} produces a
record fragment consisting of exactly the new fields introduced here
- (the result may serve as a more part elsewhere); \isa{{\isachardoublequote}t{\isachardot}extend{\isachardoublequote}}
- takes a fixed record and adds a given more part; \isa{{\isachardoublequote}t{\isachardot}truncate{\isachardoublequote}} restricts a record scheme to a fixed record.
+ (the result may serve as a more part elsewhere); \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}extend{\isaliteral{22}{\isachardoublequote}}}
+ takes a fixed record and adds a given more part; \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}truncate{\isaliteral{22}{\isachardoublequote}}} restricts a record scheme to a fixed record.
\medskip
\begin{tabular}{lll}
- \isa{{\isachardoublequote}t{\isachardot}fields{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymsigma}\isactrlsub {\isadigit{1}}\ {\isasymRightarrow}\ {\isasymdots}\ {\isasymsigma}\isactrlsub n\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isasymrparr}{\isachardoublequote}} \\
- \isa{{\isachardoublequote}t{\isachardot}extend{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymlparr}\isactrlvec b\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymrho}{\isacharcomma}\ \isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isasymrparr}\ {\isasymRightarrow}\ {\isasymzeta}\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec b\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymrho}{\isacharcomma}\ \isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}{\isachardoublequote}} \\
- \isa{{\isachardoublequote}t{\isachardot}truncate{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharcolon}{\isacharcolon}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymlparr}\isactrlvec b\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymrho}{\isacharcomma}\ \isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isasymzeta}{\isasymrparr}\ {\isasymRightarrow}\ {\isasymlparr}\isactrlvec b\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymrho}{\isacharcomma}\ \isactrlvec c\ {\isacharcolon}{\isacharcolon}\ \isactrlvec {\isasymsigma}{\isasymrparr}{\isachardoublequote}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}fields{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}extend{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}truncate{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7A6574613E}{\isasymzeta}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}\isaliteral{5C3C5E7665633E}{}\isactrlvec b\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C72686F3E}{\isasymrho}}{\isaliteral{2C}{\isacharcomma}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}
\medskip
- \noindent Note that \isa{{\isachardoublequote}t{\isachardot}make{\isachardoublequote}} and \isa{{\isachardoublequote}t{\isachardot}fields{\isachardoublequote}} coincide
+ \noindent Note that \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}make{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}fields{\isaliteral{22}{\isachardoublequote}}} coincide
for root records.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -317,19 +317,19 @@
record constructor terms are made part of the default Simplifier
context; thus proofs by reduction of basic operations merely require
the \hyperlink{method.simp}{\mbox{\isa{simp}}} method without further arguments. These rules
- are available as \isa{{\isachardoublequote}t{\isachardot}simps{\isachardoublequote}}, too.
+ are available as \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}simps{\isaliteral{22}{\isachardoublequote}}}, too.
\item Selectors applied to updated records are automatically reduced
by an internal simplification procedure, which is also part of the
standard Simplifier setup.
- \item Inject equations of a form analogous to \isa{{\isachardoublequote}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}x{\isacharprime}{\isacharcomma}\ y{\isacharprime}{\isacharparenright}\ {\isasymequiv}\ x\ {\isacharequal}\ x{\isacharprime}\ {\isasymand}\ y\ {\isacharequal}\ y{\isacharprime}{\isachardoublequote}} are declared to the Simplifier and Classical
+ \item Inject equations of a form analogous to \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ x\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ y\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequote}}} are declared to the Simplifier and Classical
Reasoner as \hyperlink{attribute.iff}{\mbox{\isa{iff}}} rules. These rules are available as
- \isa{{\isachardoublequote}t{\isachardot}iffs{\isachardoublequote}}.
+ \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}iffs{\isaliteral{22}{\isachardoublequote}}}.
- \item The introduction rule for record equality analogous to \isa{{\isachardoublequote}x\ r\ {\isacharequal}\ x\ r{\isacharprime}\ {\isasymLongrightarrow}\ y\ r\ {\isacharequal}\ y\ r{\isacharprime}\ {\isasymdots}\ {\isasymLongrightarrow}\ r\ {\isacharequal}\ r{\isacharprime}{\isachardoublequote}} is declared to the Simplifier,
- and as the basic rule context as ``\hyperlink{attribute.intro}{\mbox{\isa{intro}}}\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}''.
- The rule is called \isa{{\isachardoublequote}t{\isachardot}equality{\isachardoublequote}}.
+ \item The introduction rule for record equality analogous to \isa{{\isaliteral{22}{\isachardoublequote}}x\ r\ {\isaliteral{3D}{\isacharequal}}\ x\ r{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ y\ r\ {\isaliteral{3D}{\isacharequal}}\ y\ r{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ r\ {\isaliteral{3D}{\isacharequal}}\ r{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequote}}} is declared to the Simplifier,
+ and as the basic rule context as ``\hyperlink{attribute.intro}{\mbox{\isa{intro}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}''.
+ The rule is called \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}equality{\isaliteral{22}{\isachardoublequote}}}.
\item Representations of arbitrary record expressions as canonical
constructor terms are provided both in \hyperlink{method.cases}{\mbox{\isa{cases}}} and \hyperlink{method.induct}{\mbox{\isa{induct}}} format (cf.\ the generic proof methods of the same name,
@@ -338,11 +338,11 @@
The generic proof methods are sufficiently smart to pick the most
sensible rule according to the type of the indicated record
- expression: users just need to apply something like ``\isa{{\isachardoublequote}{\isacharparenleft}cases\ r{\isacharparenright}{\isachardoublequote}}'' to a certain proof problem.
+ expression: users just need to apply something like ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}cases\ r{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' to a certain proof problem.
- \item The derived record operations \isa{{\isachardoublequote}t{\isachardot}make{\isachardoublequote}}, \isa{{\isachardoublequote}t{\isachardot}fields{\isachardoublequote}}, \isa{{\isachardoublequote}t{\isachardot}extend{\isachardoublequote}}, \isa{{\isachardoublequote}t{\isachardot}truncate{\isachardoublequote}} are \emph{not}
+ \item The derived record operations \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}make{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}fields{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}extend{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}truncate{\isaliteral{22}{\isachardoublequote}}} are \emph{not}
treated automatically, but usually need to be expanded by hand,
- using the collective fact \isa{{\isachardoublequote}t{\isachardot}defs{\isachardoublequote}}.
+ using the collective fact \isa{{\isaliteral{22}{\isachardoublequote}}t{\isaliteral{2E}{\isachardot}}defs{\isaliteral{22}{\isachardoublequote}}}.
\end{enumerate}%
\end{isamarkuptext}%
@@ -354,8 +354,8 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{datatype}\hypertarget{command.HOL.datatype}{\hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{rep\_datatype}\hypertarget{command.HOL.rep-datatype}{\hyperlink{command.HOL.rep-datatype}{\mbox{\isa{\isacommand{rep{\isacharunderscore}datatype}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
+ \indexdef{HOL}{command}{datatype}\hypertarget{command.HOL.datatype}{\hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{rep\_datatype}\hypertarget{command.HOL.rep-datatype}{\hyperlink{command.HOL.rep-datatype}{\mbox{\isa{\isacommand{rep{\isaliteral{5F}{\isacharunderscore}}datatype}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -374,7 +374,7 @@
\item \hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}} defines inductive datatypes in
HOL.
- \item \hyperlink{command.HOL.rep-datatype}{\mbox{\isa{\isacommand{rep{\isacharunderscore}datatype}}}} represents existing types as
+ \item \hyperlink{command.HOL.rep-datatype}{\mbox{\isa{\isacommand{rep{\isaliteral{5F}{\isacharunderscore}}datatype}}}} represents existing types as
inductive ones, generating the standard infrastructure of derived
concepts (primitive recursion etc.).
@@ -387,7 +387,7 @@
See \cite{isabelle-HOL} for more details on datatypes, but beware of
the old-style theory syntax being used there! Apart from proper
proof methods for case-analysis and induction, there are also
- emulations of ML tactics \hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isacharunderscore}tac}}} and \hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isacharunderscore}tac}}} available, see \secref{sec:hol-induct-tac}; these admit
+ emulations of ML tactics \hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}tac}}} and \hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}tac}}} available, see \secref{sec:hol-induct-tac}; these admit
to refer directly to the internal structure of subgoals (including
internally bound parameters).%
\end{isamarkuptext}%
@@ -399,10 +399,10 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{primrec}\hypertarget{command.HOL.primrec}{\hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{fun}\hypertarget{command.HOL.fun}{\hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{function}\hypertarget{command.HOL.function}{\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{HOL}{command}{termination}\hypertarget{command.HOL.termination}{\hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
+ \indexdef{HOL}{command}{primrec}\hypertarget{command.HOL.primrec}{\hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{fun}\hypertarget{command.HOL.fun}{\hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{function}\hypertarget{command.HOL.function}{\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{termination}\hypertarget{command.HOL.termination}{\hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -430,12 +430,12 @@
completeness and the compatibility of patterns.
The defined function is considered partial, and the resulting
- simplification rules (named \isa{{\isachardoublequote}f{\isachardot}psimps{\isachardoublequote}}) and induction rule
- (named \isa{{\isachardoublequote}f{\isachardot}pinduct{\isachardoublequote}}) are guarded by a generated domain
- predicate \isa{{\isachardoublequote}f{\isacharunderscore}dom{\isachardoublequote}}. The \hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}
+ simplification rules (named \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{2E}{\isachardot}}psimps{\isaliteral{22}{\isachardoublequote}}}) and induction rule
+ (named \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{2E}{\isachardot}}pinduct{\isaliteral{22}{\isachardoublequote}}}) are guarded by a generated domain
+ predicate \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{5F}{\isacharunderscore}}dom{\isaliteral{22}{\isachardoublequote}}}. The \hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}
command can then be used to establish that the function is total.
- \item \hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}} is a shorthand notation for ``\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}~\isa{{\isachardoublequote}{\isacharparenleft}sequential{\isacharparenright}{\isachardoublequote}}, followed by automated
+ \item \hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}} is a shorthand notation for ``\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}sequential{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}, followed by automated
proof attempts regarding pattern matching and termination. See
\cite{isabelle-function} for further details.
@@ -449,7 +449,7 @@
Recursive definitions introduced by the \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}
command accommodate
- reasoning by induction (cf.\ \secref{sec:cases-induct}): rule \isa{{\isachardoublequote}c{\isachardot}induct{\isachardoublequote}} (where \isa{c} is the name of the function definition)
+ reasoning by induction (cf.\ \secref{sec:cases-induct}): rule \isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{2E}{\isachardot}}induct{\isaliteral{22}{\isachardoublequote}}} (where \isa{c} is the name of the function definition)
refers to a specific induction rule, with parameters named according
to the user-specified equations. Cases are numbered (starting from 1).
@@ -458,7 +458,7 @@
out.
The equations provided by these packages may be referred later as
- theorem list \isa{{\isachardoublequote}f{\isachardot}simps{\isachardoublequote}}, where \isa{f} is the (collective)
+ theorem list \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{2E}{\isachardot}}simps{\isaliteral{22}{\isachardoublequote}}}, where \isa{f} is the (collective)
name of the functions defined. Individual equations may be named
explicitly as well.
@@ -485,9 +485,9 @@
equations even without a termination proof, provided that the
function is tail-recursive. This currently only works
- \item \isa{{\isachardoublequote}default\ d{\isachardoublequote}} allows to specify a default value for a
- (partial) function, which will ensure that \isa{{\isachardoublequote}f\ x\ {\isacharequal}\ d\ x{\isachardoublequote}}
- whenever \isa{{\isachardoublequote}x\ {\isasymnotin}\ f{\isacharunderscore}dom{\isachardoublequote}}.
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}default\ d{\isaliteral{22}{\isachardoublequote}}} allows to specify a default value for a
+ (partial) function, which will ensure that \isa{{\isaliteral{22}{\isachardoublequote}}f\ x\ {\isaliteral{3D}{\isacharequal}}\ d\ x{\isaliteral{22}{\isachardoublequote}}}
+ whenever \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ f{\isaliteral{5F}{\isacharunderscore}}dom{\isaliteral{22}{\isachardoublequote}}}.
\end{description}%
\end{isamarkuptext}%
@@ -499,10 +499,10 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{HOL}{method}{pat\_completeness}\hypertarget{method.HOL.pat-completeness}{\hyperlink{method.HOL.pat-completeness}{\mbox{\isa{pat{\isacharunderscore}completeness}}}} & : & \isa{method} \\
+ \indexdef{HOL}{method}{pat\_completeness}\hypertarget{method.HOL.pat-completeness}{\hyperlink{method.HOL.pat-completeness}{\mbox{\isa{pat{\isaliteral{5F}{\isacharunderscore}}completeness}}}} & : & \isa{method} \\
\indexdef{HOL}{method}{relation}\hypertarget{method.HOL.relation}{\hyperlink{method.HOL.relation}{\mbox{\isa{relation}}}} & : & \isa{method} \\
- \indexdef{HOL}{method}{lexicographic\_order}\hypertarget{method.HOL.lexicographic-order}{\hyperlink{method.HOL.lexicographic-order}{\mbox{\isa{lexicographic{\isacharunderscore}order}}}} & : & \isa{method} \\
- \indexdef{HOL}{method}{size\_change}\hypertarget{method.HOL.size-change}{\hyperlink{method.HOL.size-change}{\mbox{\isa{size{\isacharunderscore}change}}}} & : & \isa{method} \\
+ \indexdef{HOL}{method}{lexicographic\_order}\hypertarget{method.HOL.lexicographic-order}{\hyperlink{method.HOL.lexicographic-order}{\mbox{\isa{lexicographic{\isaliteral{5F}{\isacharunderscore}}order}}}} & : & \isa{method} \\
+ \indexdef{HOL}{method}{size\_change}\hypertarget{method.HOL.size-change}{\hyperlink{method.HOL.size-change}{\mbox{\isa{size{\isaliteral{5F}{\isacharunderscore}}change}}}} & : & \isa{method} \\
\end{matharray}
\begin{rail}
@@ -517,7 +517,7 @@
\begin{description}
- \item \hyperlink{method.HOL.pat-completeness}{\mbox{\isa{pat{\isacharunderscore}completeness}}} is a specialized method to
+ \item \hyperlink{method.HOL.pat-completeness}{\mbox{\isa{pat{\isaliteral{5F}{\isacharunderscore}}completeness}}} is a specialized method to
solve goals regarding the completeness of pattern matching, as
required by the \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} package (cf.\
\cite{isabelle-function}).
@@ -529,7 +529,7 @@
Usually, this method is used as the initial proof step of manual
termination proofs.
- \item \hyperlink{method.HOL.lexicographic-order}{\mbox{\isa{lexicographic{\isacharunderscore}order}}} attempts a fully
+ \item \hyperlink{method.HOL.lexicographic-order}{\mbox{\isa{lexicographic{\isaliteral{5F}{\isacharunderscore}}order}}} attempts a fully
automated termination proof by searching for a lexicographic
combination of size measures on the arguments of the function. The
method accepts the same arguments as the \hyperlink{method.auto}{\mbox{\isa{auto}}} method,
@@ -540,7 +540,7 @@
In case of failure, extensive information is printed, which can help
to analyse the situation (cf.\ \cite{isabelle-function}).
- \item \hyperlink{method.HOL.size-change}{\mbox{\isa{size{\isacharunderscore}change}}} also works on termination goals,
+ \item \hyperlink{method.HOL.size-change}{\mbox{\isa{size{\isaliteral{5F}{\isacharunderscore}}change}}} also works on termination goals,
using a variation of the size-change principle, together with a
graph decomposition technique (see \cite{krauss_phd} for details).
Three kinds of orders are used internally: \isa{max}, \isa{min},
@@ -561,8 +561,8 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{partial\_function}\hypertarget{command.HOL.partial-function}{\hyperlink{command.HOL.partial-function}{\mbox{\isa{\isacommand{partial{\isacharunderscore}function}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{HOL}{attribute}{partial\_function\_mono}\hypertarget{attribute.HOL.partial-function-mono}{\hyperlink{attribute.HOL.partial-function-mono}{\mbox{\isa{partial{\isacharunderscore}function{\isacharunderscore}mono}}}} & : & \isa{attribute} \\
+ \indexdef{HOL}{command}{partial\_function}\hypertarget{command.HOL.partial-function}{\hyperlink{command.HOL.partial-function}{\mbox{\isa{\isacommand{partial{\isaliteral{5F}{\isacharunderscore}}function}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{attribute}{partial\_function\_mono}\hypertarget{attribute.HOL.partial-function-mono}{\hyperlink{attribute.HOL.partial-function-mono}{\mbox{\isa{partial{\isaliteral{5F}{\isacharunderscore}}function{\isaliteral{5F}{\isacharunderscore}}mono}}}} & : & \isa{attribute} \\
\end{matharray}
\begin{rail}
@@ -571,7 +571,7 @@
\begin{description}
- \item \hyperlink{command.HOL.partial-function}{\mbox{\isa{\isacommand{partial{\isacharunderscore}function}}}} defines recursive
+ \item \hyperlink{command.HOL.partial-function}{\mbox{\isa{\isacommand{partial{\isaliteral{5F}{\isacharunderscore}}function}}}} defines recursive
functions based on fixpoints in complete partial orders. No
termination proof is required from the user or constructed
internally. Instead, the possibility of non-termination is modelled
@@ -587,7 +587,7 @@
wrt.\ the underlying order. The monotonicitity proof is performed
internally, and the definition is rejected when it fails. The proof
can be influenced by declaring hints using the
- \hyperlink{attribute.HOL.partial-function-mono}{\mbox{\isa{partial{\isacharunderscore}function{\isacharunderscore}mono}}} attribute.
+ \hyperlink{attribute.HOL.partial-function-mono}{\mbox{\isa{partial{\isaliteral{5F}{\isacharunderscore}}function{\isaliteral{5F}{\isacharunderscore}}mono}}} attribute.
The mandatory \isa{mode} argument specifies the mode of operation
of the command, which directly corresponds to a complete partial
@@ -598,10 +598,10 @@
\item \isa{option} defines functions that map into the \isa{option} type. Here, the value \isa{None} is used to model a
non-terminating computation. Monotonicity requires that if \isa{None} is returned by a recursive call, then the overall result
must also be \isa{None}. This is best achieved through the use of
- the monadic operator \isa{{\isachardoublequote}Option{\isachardot}bind{\isachardoublequote}}.
+ the monadic operator \isa{{\isaliteral{22}{\isachardoublequote}}Option{\isaliteral{2E}{\isachardot}}bind{\isaliteral{22}{\isachardoublequote}}}.
\item \isa{tailrec} defines functions with an arbitrary result
- type and uses the slightly degenerated partial order where \isa{{\isachardoublequote}undefined{\isachardoublequote}} is the bottom element. Now, monotonicity requires that
+ type and uses the slightly degenerated partial order where \isa{{\isaliteral{22}{\isachardoublequote}}undefined{\isaliteral{22}{\isachardoublequote}}} is the bottom element. Now, monotonicity requires that
if \isa{undefined} is returned by a recursive call, then the
overall result must also be \isa{undefined}. In practice, this is
only satisfied when each recursive call is a tail call, whose result
@@ -610,9 +610,9 @@
\end{description}
Experienced users may define new modes by instantiating the locale
- \isa{{\isachardoublequote}partial{\isacharunderscore}function{\isacharunderscore}definitions{\isachardoublequote}} appropriately.
+ \isa{{\isaliteral{22}{\isachardoublequote}}partial{\isaliteral{5F}{\isacharunderscore}}function{\isaliteral{5F}{\isacharunderscore}}definitions{\isaliteral{22}{\isachardoublequote}}} appropriately.
- \item \hyperlink{attribute.HOL.partial-function-mono}{\mbox{\isa{partial{\isacharunderscore}function{\isacharunderscore}mono}}} declares rules for
+ \item \hyperlink{attribute.HOL.partial-function-mono}{\mbox{\isa{partial{\isaliteral{5F}{\isacharunderscore}}function{\isaliteral{5F}{\isacharunderscore}}mono}}} declares rules for
use in the internal monononicity proofs of partial function
definitions.
@@ -625,11 +625,11 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-The old TFL commands \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} and \hyperlink{command.HOL.recdef-tc}{\mbox{\isa{\isacommand{recdef{\isacharunderscore}tc}}}} for defining recursive are mostly obsolete; \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} or \hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}} should be used instead.
+The old TFL commands \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} and \hyperlink{command.HOL.recdef-tc}{\mbox{\isa{\isacommand{recdef{\isaliteral{5F}{\isacharunderscore}}tc}}}} for defining recursive are mostly obsolete; \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} or \hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}} should be used instead.
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{recdef}\hypertarget{command.HOL.recdef}{\hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{HOL}{command}{recdef\_tc}\hypertarget{command.HOL.recdef-tc}{\hyperlink{command.HOL.recdef-tc}{\mbox{\isa{\isacommand{recdef{\isacharunderscore}tc}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
+ \indexdef{HOL}{command}{recdef}\hypertarget{command.HOL.recdef}{\hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{recdef\_tc}\hypertarget{command.HOL.recdef-tc}{\hyperlink{command.HOL.recdef-tc}{\mbox{\isa{\isacommand{recdef{\isaliteral{5F}{\isacharunderscore}}tc}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -649,15 +649,15 @@
\item \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} defines general well-founded
recursive functions (using the TFL package), see also
- \cite{isabelle-HOL}. The ``\isa{{\isachardoublequote}{\isacharparenleft}permissive{\isacharparenright}{\isachardoublequote}}'' option tells
+ \cite{isabelle-HOL}. The ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}permissive{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' option tells
TFL to recover from failed proof attempts, returning unfinished
- results. The \isa{recdef{\isacharunderscore}simp}, \isa{recdef{\isacharunderscore}cong}, and \isa{recdef{\isacharunderscore}wf} hints refer to auxiliary rules to be used in the internal
+ results. The \isa{recdef{\isaliteral{5F}{\isacharunderscore}}simp}, \isa{recdef{\isaliteral{5F}{\isacharunderscore}}cong}, and \isa{recdef{\isaliteral{5F}{\isacharunderscore}}wf} hints refer to auxiliary rules to be used in the internal
automated proof process of TFL. Additional \hyperlink{syntax.clasimpmod}{\mbox{\isa{clasimpmod}}}
declarations (cf.\ \secref{sec:clasimp}) may be given to tune the
context of the Simplifier (cf.\ \secref{sec:simplifier}) and
Classical reasoner (cf.\ \secref{sec:classical}).
- \item \hyperlink{command.HOL.recdef-tc}{\mbox{\isa{\isacommand{recdef{\isacharunderscore}tc}}}}~\isa{{\isachardoublequote}c\ {\isacharparenleft}i{\isacharparenright}{\isachardoublequote}} recommences the
+ \item \hyperlink{command.HOL.recdef-tc}{\mbox{\isa{\isacommand{recdef{\isaliteral{5F}{\isacharunderscore}}tc}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{28}{\isacharparenleft}}i{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} recommences the
proof for leftover termination condition number \isa{i} (default
1) as generated by a \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} definition of
constant \isa{c}.
@@ -671,9 +671,9 @@
globally, using the following attributes.
\begin{matharray}{rcl}
- \indexdef{HOL}{attribute}{recdef\_simp}\hypertarget{attribute.HOL.recdef-simp}{\hyperlink{attribute.HOL.recdef-simp}{\mbox{\isa{recdef{\isacharunderscore}simp}}}} & : & \isa{attribute} \\
- \indexdef{HOL}{attribute}{recdef\_cong}\hypertarget{attribute.HOL.recdef-cong}{\hyperlink{attribute.HOL.recdef-cong}{\mbox{\isa{recdef{\isacharunderscore}cong}}}} & : & \isa{attribute} \\
- \indexdef{HOL}{attribute}{recdef\_wf}\hypertarget{attribute.HOL.recdef-wf}{\hyperlink{attribute.HOL.recdef-wf}{\mbox{\isa{recdef{\isacharunderscore}wf}}}} & : & \isa{attribute} \\
+ \indexdef{HOL}{attribute}{recdef\_simp}\hypertarget{attribute.HOL.recdef-simp}{\hyperlink{attribute.HOL.recdef-simp}{\mbox{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}simp}}}} & : & \isa{attribute} \\
+ \indexdef{HOL}{attribute}{recdef\_cong}\hypertarget{attribute.HOL.recdef-cong}{\hyperlink{attribute.HOL.recdef-cong}{\mbox{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}cong}}}} & : & \isa{attribute} \\
+ \indexdef{HOL}{attribute}{recdef\_wf}\hypertarget{attribute.HOL.recdef-wf}{\hyperlink{attribute.HOL.recdef-wf}{\mbox{\isa{recdef{\isaliteral{5F}{\isacharunderscore}}wf}}}} & : & \isa{attribute} \\
\end{matharray}
\begin{rail}
@@ -711,10 +711,10 @@
to use inference rules for type-checking.
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{inductive}\hypertarget{command.HOL.inductive}{\hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{inductive\_set}\hypertarget{command.HOL.inductive-set}{\hyperlink{command.HOL.inductive-set}{\mbox{\isa{\isacommand{inductive{\isacharunderscore}set}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{coinductive}\hypertarget{command.HOL.coinductive}{\hyperlink{command.HOL.coinductive}{\mbox{\isa{\isacommand{coinductive}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{coinductive\_set}\hypertarget{command.HOL.coinductive-set}{\hyperlink{command.HOL.coinductive-set}{\mbox{\isa{\isacommand{coinductive{\isacharunderscore}set}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
+ \indexdef{HOL}{command}{inductive}\hypertarget{command.HOL.inductive}{\hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{inductive\_set}\hypertarget{command.HOL.inductive-set}{\hyperlink{command.HOL.inductive-set}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{coinductive}\hypertarget{command.HOL.coinductive}{\hyperlink{command.HOL.coinductive}{\mbox{\isa{\isacommand{coinductive}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{coinductive\_set}\hypertarget{command.HOL.coinductive-set}{\hyperlink{command.HOL.coinductive-set}{\mbox{\isa{\isacommand{coinductive{\isaliteral{5F}{\isacharunderscore}}set}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
\indexdef{HOL}{attribute}{mono}\hypertarget{attribute.HOL.mono}{\hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}}} & : & \isa{attribute} \\
\end{matharray}
@@ -737,10 +737,10 @@
definition. The optional \hyperlink{keyword.monos}{\mbox{\isa{\isakeyword{monos}}}} section contains
\emph{monotonicity theorems}, which are required for each operator
applied to a recursive set in the introduction rules. There
- \emph{must} be a theorem of the form \isa{{\isachardoublequote}A\ {\isasymle}\ B\ {\isasymLongrightarrow}\ M\ A\ {\isasymle}\ M\ B{\isachardoublequote}},
- for each premise \isa{{\isachardoublequote}M\ R\isactrlsub i\ t{\isachardoublequote}} in an introduction rule!
+ \emph{must} be a theorem of the form \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C6C653E}{\isasymle}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ M\ A\ {\isaliteral{5C3C6C653E}{\isasymle}}\ M\ B{\isaliteral{22}{\isachardoublequote}}},
+ for each premise \isa{{\isaliteral{22}{\isachardoublequote}}M\ R\isaliteral{5C3C5E7375623E}{}\isactrlsub i\ t{\isaliteral{22}{\isachardoublequote}}} in an introduction rule!
- \item \hyperlink{command.HOL.inductive-set}{\mbox{\isa{\isacommand{inductive{\isacharunderscore}set}}}} and \hyperlink{command.HOL.coinductive-set}{\mbox{\isa{\isacommand{coinductive{\isacharunderscore}set}}}} are wrappers for to the previous commands,
+ \item \hyperlink{command.HOL.inductive-set}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}}}} and \hyperlink{command.HOL.coinductive-set}{\mbox{\isa{\isacommand{coinductive{\isaliteral{5F}{\isacharunderscore}}set}}}} are wrappers for to the previous commands,
allowing the definition of (co)inductive sets.
\item \hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}} declares monotonicity rules. These
@@ -760,23 +760,23 @@
\begin{description}
- \item \isa{R{\isachardot}intros} is the list of introduction rules as proven
+ \item \isa{R{\isaliteral{2E}{\isachardot}}intros} is the list of introduction rules as proven
theorems, for the recursive predicates (or sets). The rules are
also available individually, using the names given them in the
theory file;
- \item \isa{R{\isachardot}cases} is the case analysis (or elimination) rule;
+ \item \isa{R{\isaliteral{2E}{\isachardot}}cases} is the case analysis (or elimination) rule;
- \item \isa{R{\isachardot}induct} or \isa{R{\isachardot}coinduct} is the (co)induction
+ \item \isa{R{\isaliteral{2E}{\isachardot}}induct} or \isa{R{\isaliteral{2E}{\isachardot}}coinduct} is the (co)induction
rule.
\end{description}
- When several predicates \isa{{\isachardoublequote}R\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ R\isactrlsub n{\isachardoublequote}} are
+ When several predicates \isa{{\isaliteral{22}{\isachardoublequote}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ R\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} are
defined simultaneously, the list of introduction rules is called
- \isa{{\isachardoublequote}R\isactrlsub {\isadigit{1}}{\isacharunderscore}{\isasymdots}{\isacharunderscore}R\isactrlsub n{\isachardot}intros{\isachardoublequote}}, the case analysis rules are
- called \isa{{\isachardoublequote}R\isactrlsub {\isadigit{1}}{\isachardot}cases{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ R\isactrlsub n{\isachardot}cases{\isachardoublequote}}, and the list
- of mutual induction rules is called \isa{{\isachardoublequote}R\isactrlsub {\isadigit{1}}{\isacharunderscore}{\isasymdots}{\isacharunderscore}R\isactrlsub n{\isachardot}inducts{\isachardoublequote}}.%
+ \isa{{\isaliteral{22}{\isachardoublequote}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5F}{\isacharunderscore}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{2E}{\isachardot}}intros{\isaliteral{22}{\isachardoublequote}}}, the case analysis rules are
+ called \isa{{\isaliteral{22}{\isachardoublequote}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2E}{\isachardot}}cases{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ R\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{2E}{\isachardot}}cases{\isaliteral{22}{\isachardoublequote}}}, and the list
+ of mutual induction rules is called \isa{{\isaliteral{22}{\isachardoublequote}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5F}{\isacharunderscore}}R\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{2E}{\isachardot}}inducts{\isaliteral{22}{\isachardoublequote}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -793,29 +793,29 @@
\begin{itemize}
- \item Theorems of the form \isa{{\isachardoublequote}A\ {\isasymle}\ B\ {\isasymLongrightarrow}\ M\ A\ {\isasymle}\ M\ B{\isachardoublequote}}, for proving
+ \item Theorems of the form \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C6C653E}{\isasymle}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ M\ A\ {\isaliteral{5C3C6C653E}{\isasymle}}\ M\ B{\isaliteral{22}{\isachardoublequote}}}, for proving
monotonicity of inductive definitions whose introduction rules have
- premises involving terms such as \isa{{\isachardoublequote}M\ R\isactrlsub i\ t{\isachardoublequote}}.
+ premises involving terms such as \isa{{\isaliteral{22}{\isachardoublequote}}M\ R\isaliteral{5C3C5E7375623E}{}\isactrlsub i\ t{\isaliteral{22}{\isachardoublequote}}}.
\item Monotonicity theorems for logical operators, which are of the
- general form \isa{{\isachardoublequote}{\isacharparenleft}{\isasymdots}\ {\isasymlongrightarrow}\ {\isasymdots}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isacharparenleft}{\isasymdots}\ {\isasymlongrightarrow}\ {\isasymdots}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymlongrightarrow}\ {\isasymdots}{\isachardoublequote}}. For example, in
- the case of the operator \isa{{\isachardoublequote}{\isasymor}{\isachardoublequote}}, the corresponding theorem is
+ general form \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}. For example, in
+ the case of the operator \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6F723E}{\isasymor}}{\isaliteral{22}{\isachardoublequote}}}, the corresponding theorem is
\[
- \infer{\isa{{\isachardoublequote}P\isactrlsub {\isadigit{1}}\ {\isasymor}\ P\isactrlsub {\isadigit{2}}\ {\isasymlongrightarrow}\ Q\isactrlsub {\isadigit{1}}\ {\isasymor}\ Q\isactrlsub {\isadigit{2}}{\isachardoublequote}}}{\isa{{\isachardoublequote}P\isactrlsub {\isadigit{1}}\ {\isasymlongrightarrow}\ Q\isactrlsub {\isadigit{1}}{\isachardoublequote}} & \isa{{\isachardoublequote}P\isactrlsub {\isadigit{2}}\ {\isasymlongrightarrow}\ Q\isactrlsub {\isadigit{2}}{\isachardoublequote}}}
+ \infer{\isa{{\isaliteral{22}{\isachardoublequote}}P\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ P\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ Q\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}}}{\isa{{\isaliteral{22}{\isachardoublequote}}P\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}P\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}}}
\]
\item De Morgan style equations for reasoning about the ``polarity''
of expressions, e.g.
\[
- \isa{{\isachardoublequote}{\isasymnot}\ {\isasymnot}\ P\ {\isasymlongleftrightarrow}\ P{\isachardoublequote}} \qquad\qquad
- \isa{{\isachardoublequote}{\isasymnot}\ {\isacharparenleft}P\ {\isasymand}\ Q{\isacharparenright}\ {\isasymlongleftrightarrow}\ {\isasymnot}\ P\ {\isasymor}\ {\isasymnot}\ Q{\isachardoublequote}}
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ P\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ P{\isaliteral{22}{\isachardoublequote}}} \qquad\qquad
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{28}{\isacharparenleft}}P\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ P\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ Q{\isaliteral{22}{\isachardoublequote}}}
\]
\item Equations for reducing complex operators to more primitive
ones whose monotonicity can easily be proved, e.g.
\[
- \isa{{\isachardoublequote}{\isacharparenleft}P\ {\isasymlongrightarrow}\ Q{\isacharparenright}\ {\isasymlongleftrightarrow}\ {\isasymnot}\ P\ {\isasymor}\ Q{\isachardoublequote}} \qquad\qquad
- \isa{{\isachardoublequote}Ball\ A\ P\ {\isasymequiv}\ {\isasymforall}x{\isachardot}\ x\ {\isasymin}\ A\ {\isasymlongrightarrow}\ P\ x{\isachardoublequote}}
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}P\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ P\ {\isaliteral{5C3C6F723E}{\isasymor}}\ Q{\isaliteral{22}{\isachardoublequote}}} \qquad\qquad
+ \isa{{\isaliteral{22}{\isachardoublequote}}Ball\ A\ P\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ P\ x{\isaliteral{22}{\isachardoublequote}}}
\]
\end{itemize}
@@ -832,7 +832,7 @@
\begin{matharray}{rcl}
\indexdef{HOL}{method}{arith}\hypertarget{method.HOL.arith}{\hyperlink{method.HOL.arith}{\mbox{\isa{arith}}}} & : & \isa{method} \\
\indexdef{HOL}{attribute}{arith}\hypertarget{attribute.HOL.arith}{\hyperlink{attribute.HOL.arith}{\mbox{\isa{arith}}}} & : & \isa{attribute} \\
- \indexdef{HOL}{attribute}{arith\_split}\hypertarget{attribute.HOL.arith-split}{\hyperlink{attribute.HOL.arith-split}{\mbox{\isa{arith{\isacharunderscore}split}}}} & : & \isa{attribute} \\
+ \indexdef{HOL}{attribute}{arith\_split}\hypertarget{attribute.HOL.arith-split}{\hyperlink{attribute.HOL.arith-split}{\mbox{\isa{arith{\isaliteral{5F}{\isacharunderscore}}split}}}} & : & \isa{attribute} \\
\end{matharray}
The \hyperlink{method.HOL.arith}{\mbox{\isa{arith}}} method decides linear arithmetic problems
@@ -842,7 +842,7 @@
The \hyperlink{attribute.HOL.arith}{\mbox{\isa{arith}}} attribute declares facts that are
always supplied to the arithmetic provers implicitly.
- The \hyperlink{attribute.HOL.arith-split}{\mbox{\isa{arith{\isacharunderscore}split}}} attribute declares case split
+ The \hyperlink{attribute.HOL.arith-split}{\mbox{\isa{arith{\isaliteral{5F}{\isacharunderscore}}split}}} attribute declares case split
rules to be expanded before \hyperlink{method.HOL.arith}{\mbox{\isa{arith}}} is invoked.
Note that a simpler (but faster) arithmetic prover is
@@ -871,9 +871,9 @@
Rules need to be classified as \hyperlink{attribute.Pure.intro}{\mbox{\isa{intro}}},
\hyperlink{attribute.Pure.elim}{\mbox{\isa{elim}}}, or \hyperlink{attribute.Pure.dest}{\mbox{\isa{dest}}}; here the
- ``\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}'' indicator refers to ``safe'' rules, which may be
+ ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}}'' indicator refers to ``safe'' rules, which may be
applied aggressively (without considering back-tracking later).
- Rules declared with ``\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}'' are ignored in proof search (the
+ Rules declared with ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}'' are ignored in proof search (the
single-step \hyperlink{method.rule}{\mbox{\isa{rule}}} method still observes these). An
explicit weight annotation may be given as well; otherwise the
number of rule premises will be taken into account here.%
@@ -897,7 +897,7 @@
The \hyperlink{method.HOL.coherent}{\mbox{\isa{coherent}}} method solves problems of
\emph{Coherent Logic} \cite{Bezem-Coquand:2005}, which covers
applications in confluence theory, lattice theory and projective
- geometry. See \hyperlink{file.~~/src/HOL/ex/Coherent.thy}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}HOL{\isacharslash}ex{\isacharslash}Coherent{\isachardot}thy}}}} for some
+ geometry. See \hyperlink{file.~~/src/HOL/ex/Coherent.thy}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}HOL{\isaliteral{2F}{\isacharslash}}ex{\isaliteral{2F}{\isacharslash}}Coherent{\isaliteral{2E}{\isachardot}}thy}}}} for some
examples.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -912,9 +912,9 @@
is supported by the following commands.
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{value}\hypertarget{command.HOL.value}{\hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{HOL}{command}{quickcheck}\hypertarget{command.HOL.quickcheck}{\hyperlink{command.HOL.quickcheck}{\mbox{\isa{\isacommand{quickcheck}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{HOL}{command}{quickcheck\_params}\hypertarget{command.HOL.quickcheck-params}{\hyperlink{command.HOL.quickcheck-params}{\mbox{\isa{\isacommand{quickcheck{\isacharunderscore}params}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}}
+ \indexdef{HOL}{command}{value}\hypertarget{command.HOL.value}{\hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{quickcheck}\hypertarget{command.HOL.quickcheck}{\hyperlink{command.HOL.quickcheck}{\mbox{\isa{\isacommand{quickcheck}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{quickcheck\_params}\hypertarget{command.HOL.quickcheck-params}{\hyperlink{command.HOL.quickcheck-params}{\mbox{\isa{\isacommand{quickcheck{\isaliteral{5F}{\isacharunderscore}}params}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}}
\end{matharray}
\begin{rail}
@@ -962,12 +962,12 @@
\item[\isa{iterations}] sets how many sets of assignments are
generated for each particular size.
- \item[\isa{no{\isacharunderscore}assms}] specifies whether assumptions in
+ \item[\isa{no{\isaliteral{5F}{\isacharunderscore}}assms}] specifies whether assumptions in
structured proofs should be ignored.
\item[\isa{timeout}] sets the time limit in seconds.
- \item[\isa{default{\isacharunderscore}type}] sets the type(s) generally used to
+ \item[\isa{default{\isaliteral{5F}{\isacharunderscore}}type}] sets the type(s) generally used to
instantiate type variables.
\item[\isa{report}] if set quickcheck reports how many tests
@@ -977,13 +977,13 @@
current size for assignment values.
\item[\isa{expect}] can be used to check if the user's
- expectation was met (\isa{no{\isacharunderscore}expectation}, \isa{no{\isacharunderscore}counterexample}, or \isa{counterexample}).
+ expectation was met (\isa{no{\isaliteral{5F}{\isacharunderscore}}expectation}, \isa{no{\isaliteral{5F}{\isacharunderscore}}counterexample}, or \isa{counterexample}).
\end{description}
These option can be given within square brackets.
- \item \hyperlink{command.HOL.quickcheck-params}{\mbox{\isa{\isacommand{quickcheck{\isacharunderscore}params}}}} changes quickcheck
+ \item \hyperlink{command.HOL.quickcheck-params}{\mbox{\isa{\isacommand{quickcheck{\isaliteral{5F}{\isacharunderscore}}params}}}} changes quickcheck
configuration options persitently.
\end{description}%
@@ -1000,10 +1000,10 @@
\secref{sec:cases-induct} for proper Isar versions of similar ideas.
\begin{matharray}{rcl}
- \indexdef{HOL}{method}{case\_tac}\hypertarget{method.HOL.case-tac}{\hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{HOL}{method}{induct\_tac}\hypertarget{method.HOL.induct-tac}{\hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{HOL}{method}{ind\_cases}\hypertarget{method.HOL.ind-cases}{\hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isacharunderscore}cases}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{HOL}{command}{inductive\_cases}\hypertarget{command.HOL.inductive-cases}{\hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isacharunderscore}cases}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
+ \indexdef{HOL}{method}{case\_tac}\hypertarget{method.HOL.case-tac}{\hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{HOL}{method}{induct\_tac}\hypertarget{method.HOL.induct-tac}{\hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{HOL}{method}{ind\_cases}\hypertarget{method.HOL.ind-cases}{\hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{HOL}{command}{inductive\_cases}\hypertarget{command.HOL.inductive-cases}{\hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}cases}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -1022,7 +1022,7 @@
\begin{description}
- \item \hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isacharunderscore}tac}}} and \hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isacharunderscore}tac}}} admit
+ \item \hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}tac}}} and \hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}tac}}} admit
to reason about inductive types. Rules are selected according to
the declarations by the \hyperlink{attribute.cases}{\mbox{\isa{cases}}} and \hyperlink{attribute.induct}{\mbox{\isa{induct}}}
attributes, cf.\ \secref{sec:cases-induct}. The \hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}} package already takes care of this.
@@ -1030,16 +1030,16 @@
These unstructured tactics feature both goal addressing and dynamic
instantiation. Note that named rule cases are \emph{not} provided
as would be by the proper \hyperlink{method.cases}{\mbox{\isa{cases}}} and \hyperlink{method.induct}{\mbox{\isa{induct}}} proof
- methods (see \secref{sec:cases-induct}). Unlike the \hyperlink{method.induct}{\mbox{\isa{induct}}} method, \hyperlink{method.induct-tac}{\mbox{\isa{induct{\isacharunderscore}tac}}} does not handle structured rule
+ methods (see \secref{sec:cases-induct}). Unlike the \hyperlink{method.induct}{\mbox{\isa{induct}}} method, \hyperlink{method.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}tac}}} does not handle structured rule
statements, only the compact object-logic conclusion of the subgoal
being addressed.
- \item \hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isacharunderscore}cases}}} and \hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isacharunderscore}cases}}}} provide an interface to the internal \verb|mk_cases| operation. Rules are simplified in an unrestricted
+ \item \hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}} and \hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}cases}}}} provide an interface to the internal \verb|mk_cases| operation. Rules are simplified in an unrestricted
forward manner.
- While \hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isacharunderscore}cases}}} is a proof method to apply the
- result immediately as elimination rules, \hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isacharunderscore}cases}}}} provides case split theorems at the theory level
- for later use. The \hyperlink{keyword.for}{\mbox{\isa{\isakeyword{for}}}} argument of the \hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isacharunderscore}cases}}} method allows to specify a list of variables that should
+ While \hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}} is a proof method to apply the
+ result immediately as elimination rules, \hyperlink{command.HOL.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}cases}}}} provides case split theorems at the theory level
+ for later use. The \hyperlink{keyword.for}{\mbox{\isa{\isakeyword{for}}}} argument of the \hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}} method allows to specify a list of variables that should
be generalized before applying the resulting rule.
\end{description}%
@@ -1068,25 +1068,25 @@
See \cite{isabelle-codegen} for an introduction.
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{export\_code}\hypertarget{command.HOL.export-code}{\hyperlink{command.HOL.export-code}{\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{HOL}{command}{export\_code}\hypertarget{command.HOL.export-code}{\hyperlink{command.HOL.export-code}{\mbox{\isa{\isacommand{export{\isaliteral{5F}{\isacharunderscore}}code}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
\indexdef{HOL}{attribute}{code}\hypertarget{attribute.HOL.code}{\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}} & : & \isa{attribute} \\
- \indexdef{HOL}{command}{code\_abort}\hypertarget{command.HOL.code-abort}{\hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isacharunderscore}abort}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{code\_datatype}\hypertarget{command.HOL.code-datatype}{\hyperlink{command.HOL.code-datatype}{\mbox{\isa{\isacommand{code{\isacharunderscore}datatype}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{print\_codesetup}\hypertarget{command.HOL.print-codesetup}{\hyperlink{command.HOL.print-codesetup}{\mbox{\isa{\isacommand{print{\isacharunderscore}codesetup}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{HOL}{attribute}{code\_inline}\hypertarget{attribute.HOL.code-inline}{\hyperlink{attribute.HOL.code-inline}{\mbox{\isa{code{\isacharunderscore}inline}}}} & : & \isa{attribute} \\
- \indexdef{HOL}{attribute}{code\_post}\hypertarget{attribute.HOL.code-post}{\hyperlink{attribute.HOL.code-post}{\mbox{\isa{code{\isacharunderscore}post}}}} & : & \isa{attribute} \\
- \indexdef{HOL}{command}{print\_codeproc}\hypertarget{command.HOL.print-codeproc}{\hyperlink{command.HOL.print-codeproc}{\mbox{\isa{\isacommand{print{\isacharunderscore}codeproc}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{HOL}{command}{code\_thms}\hypertarget{command.HOL.code-thms}{\hyperlink{command.HOL.code-thms}{\mbox{\isa{\isacommand{code{\isacharunderscore}thms}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{HOL}{command}{code\_deps}\hypertarget{command.HOL.code-deps}{\hyperlink{command.HOL.code-deps}{\mbox{\isa{\isacommand{code{\isacharunderscore}deps}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{HOL}{command}{code\_const}\hypertarget{command.HOL.code-const}{\hyperlink{command.HOL.code-const}{\mbox{\isa{\isacommand{code{\isacharunderscore}const}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{code\_type}\hypertarget{command.HOL.code-type}{\hyperlink{command.HOL.code-type}{\mbox{\isa{\isacommand{code{\isacharunderscore}type}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{code\_class}\hypertarget{command.HOL.code-class}{\hyperlink{command.HOL.code-class}{\mbox{\isa{\isacommand{code{\isacharunderscore}class}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{code\_instance}\hypertarget{command.HOL.code-instance}{\hyperlink{command.HOL.code-instance}{\mbox{\isa{\isacommand{code{\isacharunderscore}instance}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{code\_reserved}\hypertarget{command.HOL.code-reserved}{\hyperlink{command.HOL.code-reserved}{\mbox{\isa{\isacommand{code{\isacharunderscore}reserved}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{code\_monad}\hypertarget{command.HOL.code-monad}{\hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isacharunderscore}monad}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{code\_include}\hypertarget{command.HOL.code-include}{\hyperlink{command.HOL.code-include}{\mbox{\isa{\isacommand{code{\isacharunderscore}include}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{code\_modulename}\hypertarget{command.HOL.code-modulename}{\hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isacharunderscore}modulename}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{code\_reflect}\hypertarget{command.HOL.code-reflect}{\hyperlink{command.HOL.code-reflect}{\mbox{\isa{\isacommand{code{\isacharunderscore}reflect}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}}
+ \indexdef{HOL}{command}{code\_abort}\hypertarget{command.HOL.code-abort}{\hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}abort}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{code\_datatype}\hypertarget{command.HOL.code-datatype}{\hyperlink{command.HOL.code-datatype}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}datatype}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{print\_codesetup}\hypertarget{command.HOL.print-codesetup}{\hyperlink{command.HOL.print-codesetup}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}codesetup}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{attribute}{code\_inline}\hypertarget{attribute.HOL.code-inline}{\hyperlink{attribute.HOL.code-inline}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}inline}}}} & : & \isa{attribute} \\
+ \indexdef{HOL}{attribute}{code\_post}\hypertarget{attribute.HOL.code-post}{\hyperlink{attribute.HOL.code-post}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}post}}}} & : & \isa{attribute} \\
+ \indexdef{HOL}{command}{print\_codeproc}\hypertarget{command.HOL.print-codeproc}{\hyperlink{command.HOL.print-codeproc}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}codeproc}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{code\_thms}\hypertarget{command.HOL.code-thms}{\hyperlink{command.HOL.code-thms}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}thms}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{code\_deps}\hypertarget{command.HOL.code-deps}{\hyperlink{command.HOL.code-deps}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}deps}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{code\_const}\hypertarget{command.HOL.code-const}{\hyperlink{command.HOL.code-const}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}const}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{code\_type}\hypertarget{command.HOL.code-type}{\hyperlink{command.HOL.code-type}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}type}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{code\_class}\hypertarget{command.HOL.code-class}{\hyperlink{command.HOL.code-class}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}class}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{code\_instance}\hypertarget{command.HOL.code-instance}{\hyperlink{command.HOL.code-instance}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}instance}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{code\_reserved}\hypertarget{command.HOL.code-reserved}{\hyperlink{command.HOL.code-reserved}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reserved}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{code\_monad}\hypertarget{command.HOL.code-monad}{\hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}monad}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{code\_include}\hypertarget{command.HOL.code-include}{\hyperlink{command.HOL.code-include}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}include}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{code\_modulename}\hypertarget{command.HOL.code-modulename}{\hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}modulename}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{code\_reflect}\hypertarget{command.HOL.code-reflect}{\hyperlink{command.HOL.code-reflect}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reflect}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}}
\end{matharray}
\begin{rail}
@@ -1170,18 +1170,18 @@
\begin{description}
- \item \hyperlink{command.HOL.export-code}{\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}} generates code for a given list
+ \item \hyperlink{command.HOL.export-code}{\mbox{\isa{\isacommand{export{\isaliteral{5F}{\isacharunderscore}}code}}}} generates code for a given list
of constants in the specified target language(s). If no
serialization instruction is given, only abstract code is generated
internally.
Constants may be specified by giving them literally, referring to
- all executable contants within a certain theory by giving \isa{{\isachardoublequote}name{\isachardot}{\isacharasterisk}{\isachardoublequote}}, or referring to \emph{all} executable constants currently
- available by giving \isa{{\isachardoublequote}{\isacharasterisk}{\isachardoublequote}}.
+ all executable contants within a certain theory by giving \isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{2E}{\isachardot}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}, or referring to \emph{all} executable constants currently
+ available by giving \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}.
By default, for each involved theory one corresponding name space
module is generated. Alternativly, a module name may be specified
- after the \hyperlink{keyword.module-name}{\mbox{\isa{\isakeyword{module{\isacharunderscore}name}}}} keyword; then \emph{all} code is
+ after the \hyperlink{keyword.module-name}{\mbox{\isa{\isakeyword{module{\isaliteral{5F}{\isacharunderscore}}name}}}} keyword; then \emph{all} code is
placed in this module.
For \emph{SML}, \emph{OCaml} and \emph{Scala} the file specification
@@ -1191,86 +1191,86 @@
output.
Serializers take an optional list of arguments in parentheses. For
- \emph{SML} and \emph{OCaml}, ``\isa{no{\isacharunderscore}signatures}`` omits
+ \emph{SML} and \emph{OCaml}, ``\isa{no{\isaliteral{5F}{\isacharunderscore}}signatures}`` omits
explicit module signatures.
For \emph{Haskell} a module name prefix may be given using the
- ``\isa{{\isachardoublequote}root{\isacharcolon}{\isachardoublequote}}'' argument; ``\isa{string{\isacharunderscore}classes}'' adds a
+ ``\isa{{\isaliteral{22}{\isachardoublequote}}root{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}}'' argument; ``\isa{string{\isaliteral{5F}{\isacharunderscore}}classes}'' adds a
``\verb|deriving (Read, Show)|'' clause to each appropriate
datatype declaration.
\item \hyperlink{attribute.HOL.code}{\mbox{\isa{code}}} explicitly selects (or with option
- ``\isa{{\isachardoublequote}del{\isachardoublequote}}'' deselects) a code equation for code generation.
+ ``\isa{{\isaliteral{22}{\isachardoublequote}}del{\isaliteral{22}{\isachardoublequote}}}'' deselects) a code equation for code generation.
Usually packages introducing code equations provide a reasonable
- default setup for selection. Variants \isa{{\isachardoublequote}code\ abstype{\isachardoublequote}} and
- \isa{{\isachardoublequote}code\ abstract{\isachardoublequote}} declare abstract datatype certificates or
+ default setup for selection. Variants \isa{{\isaliteral{22}{\isachardoublequote}}code\ abstype{\isaliteral{22}{\isachardoublequote}}} and
+ \isa{{\isaliteral{22}{\isachardoublequote}}code\ abstract{\isaliteral{22}{\isachardoublequote}}} declare abstract datatype certificates or
code equations on abstract datatype representations respectively.
- \item \hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isacharunderscore}abort}}}} declares constants which are not
+ \item \hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}abort}}}} declares constants which are not
required to have a definition by means of code equations; if needed
these are implemented by program abort instead.
- \item \hyperlink{command.HOL.code-datatype}{\mbox{\isa{\isacommand{code{\isacharunderscore}datatype}}}} specifies a constructor set
+ \item \hyperlink{command.HOL.code-datatype}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}datatype}}}} specifies a constructor set
for a logical type.
- \item \hyperlink{command.HOL.print-codesetup}{\mbox{\isa{\isacommand{print{\isacharunderscore}codesetup}}}} gives an overview on
+ \item \hyperlink{command.HOL.print-codesetup}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}codesetup}}}} gives an overview on
selected code equations and code generator datatypes.
- \item \hyperlink{attribute.HOL.code-inline}{\mbox{\isa{code{\isacharunderscore}inline}}} declares (or with option
- ``\isa{{\isachardoublequote}del{\isachardoublequote}}'' removes) inlining theorems which are applied as
+ \item \hyperlink{attribute.HOL.code-inline}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}inline}}} declares (or with option
+ ``\isa{{\isaliteral{22}{\isachardoublequote}}del{\isaliteral{22}{\isachardoublequote}}}'' removes) inlining theorems which are applied as
rewrite rules to any code equation during preprocessing.
- \item \hyperlink{attribute.HOL.code-post}{\mbox{\isa{code{\isacharunderscore}post}}} declares (or with option ``\isa{{\isachardoublequote}del{\isachardoublequote}}'' removes) theorems which are applied as rewrite rules to any
+ \item \hyperlink{attribute.HOL.code-post}{\mbox{\isa{code{\isaliteral{5F}{\isacharunderscore}}post}}} declares (or with option ``\isa{{\isaliteral{22}{\isachardoublequote}}del{\isaliteral{22}{\isachardoublequote}}}'' removes) theorems which are applied as rewrite rules to any
result of an evaluation.
- \item \hyperlink{command.HOL.print-codeproc}{\mbox{\isa{\isacommand{print{\isacharunderscore}codeproc}}}} prints the setup of the code
+ \item \hyperlink{command.HOL.print-codeproc}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}codeproc}}}} prints the setup of the code
generator preprocessor.
- \item \hyperlink{command.HOL.code-thms}{\mbox{\isa{\isacommand{code{\isacharunderscore}thms}}}} prints a list of theorems
+ \item \hyperlink{command.HOL.code-thms}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}thms}}}} prints a list of theorems
representing the corresponding program containing all given
constants after preprocessing.
- \item \hyperlink{command.HOL.code-deps}{\mbox{\isa{\isacommand{code{\isacharunderscore}deps}}}} visualizes dependencies of
+ \item \hyperlink{command.HOL.code-deps}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}deps}}}} visualizes dependencies of
theorems representing the corresponding program containing all given
constants after preprocessing.
- \item \hyperlink{command.HOL.code-const}{\mbox{\isa{\isacommand{code{\isacharunderscore}const}}}} associates a list of constants
+ \item \hyperlink{command.HOL.code-const}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}const}}}} associates a list of constants
with target-specific serializations; omitting a serialization
deletes an existing serialization.
- \item \hyperlink{command.HOL.code-type}{\mbox{\isa{\isacommand{code{\isacharunderscore}type}}}} associates a list of type
+ \item \hyperlink{command.HOL.code-type}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}type}}}} associates a list of type
constructors with target-specific serializations; omitting a
serialization deletes an existing serialization.
- \item \hyperlink{command.HOL.code-class}{\mbox{\isa{\isacommand{code{\isacharunderscore}class}}}} associates a list of classes
+ \item \hyperlink{command.HOL.code-class}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}class}}}} associates a list of classes
with target-specific class names; omitting a serialization deletes
an existing serialization. This applies only to \emph{Haskell}.
- \item \hyperlink{command.HOL.code-instance}{\mbox{\isa{\isacommand{code{\isacharunderscore}instance}}}} declares a list of type
+ \item \hyperlink{command.HOL.code-instance}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}instance}}}} declares a list of type
constructor / class instance relations as ``already present'' for a
- given target. Omitting a ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' deletes an existing
+ given target. Omitting a ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{22}{\isachardoublequote}}}'' deletes an existing
``already present'' declaration. This applies only to
\emph{Haskell}.
- \item \hyperlink{command.HOL.code-reserved}{\mbox{\isa{\isacommand{code{\isacharunderscore}reserved}}}} declares a list of names as
+ \item \hyperlink{command.HOL.code-reserved}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reserved}}}} declares a list of names as
reserved for a given target, preventing it to be shadowed by any
generated code.
- \item \hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isacharunderscore}monad}}}} provides an auxiliary mechanism
+ \item \hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}monad}}}} provides an auxiliary mechanism
to generate monadic code for Haskell.
- \item \hyperlink{command.HOL.code-include}{\mbox{\isa{\isacommand{code{\isacharunderscore}include}}}} adds arbitrary named content
- (``include'') to generated code. A ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' as last argument
+ \item \hyperlink{command.HOL.code-include}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}include}}}} adds arbitrary named content
+ (``include'') to generated code. A ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{22}{\isachardoublequote}}}'' as last argument
will remove an already added ``include''.
- \item \hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isacharunderscore}modulename}}}} declares aliasings from one
+ \item \hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}modulename}}}} declares aliasings from one
module name onto another.
- \item \hyperlink{command.HOL.code-reflect}{\mbox{\isa{\isacommand{code{\isacharunderscore}reflect}}}} without a ``\isa{{\isachardoublequote}file{\isachardoublequote}}''
+ \item \hyperlink{command.HOL.code-reflect}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}reflect}}}} without a ``\isa{{\isaliteral{22}{\isachardoublequote}}file{\isaliteral{22}{\isachardoublequote}}}''
argument compiles code into the system runtime environment and
modifies the code generator setup that future invocations of system
- runtime code generation referring to one of the ``\isa{{\isachardoublequote}datatypes{\isachardoublequote}}'' or ``\isa{{\isachardoublequote}functions{\isachardoublequote}}'' entities use these precompiled
- entities. With a ``\isa{{\isachardoublequote}file{\isachardoublequote}}'' argument, the corresponding code
+ runtime code generation referring to one of the ``\isa{{\isaliteral{22}{\isachardoublequote}}datatypes{\isaliteral{22}{\isachardoublequote}}}'' or ``\isa{{\isaliteral{22}{\isachardoublequote}}functions{\isaliteral{22}{\isachardoublequote}}}'' entities use these precompiled
+ entities. With a ``\isa{{\isaliteral{22}{\isachardoublequote}}file{\isaliteral{22}{\isachardoublequote}}}'' argument, the corresponding code
is generated into that specified file without modifying the code
generator setup.
@@ -1282,10 +1282,10 @@
well).
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{code\_module}\hypertarget{command.HOL.code-module}{\hyperlink{command.HOL.code-module}{\mbox{\isa{\isacommand{code{\isacharunderscore}module}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{code\_library}\hypertarget{command.HOL.code-library}{\hyperlink{command.HOL.code-library}{\mbox{\isa{\isacommand{code{\isacharunderscore}library}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{consts\_code}\hypertarget{command.HOL.consts-code}{\hyperlink{command.HOL.consts-code}{\mbox{\isa{\isacommand{consts{\isacharunderscore}code}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{HOL}{command}{types\_code}\hypertarget{command.HOL.types-code}{\hyperlink{command.HOL.types-code}{\mbox{\isa{\isacommand{types{\isacharunderscore}code}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
+ \indexdef{HOL}{command}{code\_module}\hypertarget{command.HOL.code-module}{\hyperlink{command.HOL.code-module}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}module}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{code\_library}\hypertarget{command.HOL.code-library}{\hyperlink{command.HOL.code-library}{\mbox{\isa{\isacommand{code{\isaliteral{5F}{\isacharunderscore}}library}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{consts\_code}\hypertarget{command.HOL.consts-code}{\hyperlink{command.HOL.consts-code}{\mbox{\isa{\isacommand{consts{\isaliteral{5F}{\isacharunderscore}}code}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{types\_code}\hypertarget{command.HOL.types-code}{\hyperlink{command.HOL.types-code}{\mbox{\isa{\isacommand{types{\isaliteral{5F}{\isacharunderscore}}code}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\indexdef{HOL}{attribute}{code}\hypertarget{attribute.HOL.code}{\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}} & : & \isa{attribute} \\
\end{matharray}
@@ -1331,8 +1331,8 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{specification}\hypertarget{command.HOL.specification}{\hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{HOL}{command}{ax\_specification}\hypertarget{command.HOL.ax-specification}{\hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
+ \indexdef{HOL}{command}{specification}\hypertarget{command.HOL.specification}{\hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{HOL}{command}{ax\_specification}\hypertarget{command.HOL.ax-specification}{\hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -1343,14 +1343,14 @@
\begin{description}
- \item \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}~\isa{{\isachardoublequote}decls\ {\isasymphi}{\isachardoublequote}} sets up a
+ \item \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}decls\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} sets up a
goal stating the existence of terms with the properties specified to
hold for the constants given in \isa{decls}. After finishing the
proof, the theory will be augmented with definitions for the given
constants, as well as with theorems stating the properties for these
constants.
- \item \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}}~\isa{{\isachardoublequote}decls\ {\isasymphi}{\isachardoublequote}} sets up
+ \item \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}decls\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} sets up
a goal stating the existence of terms with the properties specified
to hold for the constants given in \isa{decls}. After finishing
the proof, the theory will be augmented with axioms expressing the
@@ -1358,18 +1358,18 @@
\item \isa{decl} declares a constant to be defined by the
specification given. The definition for the constant \isa{c} is
- bound to the name \isa{c{\isacharunderscore}def} unless a theorem name is given in
+ bound to the name \isa{c{\isaliteral{5F}{\isacharunderscore}}def} unless a theorem name is given in
the declaration. Overloaded constants should be declared as such.
\end{description}
- Whether to use \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}} or \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}} is to some extent a matter of style. \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}} introduces no new axioms, and so by
- construction cannot introduce inconsistencies, whereas \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}} does introduce axioms, but only after the
+ Whether to use \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}} or \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}} is to some extent a matter of style. \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}} introduces no new axioms, and so by
+ construction cannot introduce inconsistencies, whereas \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}} does introduce axioms, but only after the
user has explicitly proven it to be safe. A practical issue must be
considered, though: After introducing two constants with the same
properties using \hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}, one can prove
that the two constants are, in fact, equal. If this might be a
- problem, one should use \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}}.%
+ problem, one should use \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isaliteral{5F}{\isacharunderscore}}specification}}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
--- a/doc-src/IsarRef/Thy/document/Inner_Syntax.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarRef/Thy/document/Inner_Syntax.tex Mon Nov 08 14:41:11 2010 +0100
@@ -1,6 +1,6 @@
%
\begin{isabellebody}%
-\def\isabellecontext{Inner{\isacharunderscore}Syntax}%
+\def\isabellecontext{Inner{\isaliteral{5F}{\isacharunderscore}}Syntax}%
%
\isadelimtheory
%
@@ -8,7 +8,7 @@
%
\isatagtheory
\isacommand{theory}\isamarkupfalse%
-\ Inner{\isacharunderscore}Syntax\isanewline
+\ Inner{\isaliteral{5F}{\isacharunderscore}}Syntax\isanewline
\isakeyword{imports}\ Main\isanewline
\isakeyword{begin}%
\endisatagtheory
@@ -32,13 +32,13 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{typ}\hypertarget{command.typ}{\hyperlink{command.typ}{\mbox{\isa{\isacommand{typ}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{term}\hypertarget{command.term}{\hyperlink{command.term}{\mbox{\isa{\isacommand{term}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{prop}\hypertarget{command.prop}{\hyperlink{command.prop}{\mbox{\isa{\isacommand{prop}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{thm}\hypertarget{command.thm}{\hyperlink{command.thm}{\mbox{\isa{\isacommand{thm}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{prf}\hypertarget{command.prf}{\hyperlink{command.prf}{\mbox{\isa{\isacommand{prf}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{full\_prf}\hypertarget{command.full-prf}{\hyperlink{command.full-prf}{\mbox{\isa{\isacommand{full{\isacharunderscore}prf}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{pr}\hypertarget{command.pr}{\hyperlink{command.pr}{\mbox{\isa{\isacommand{pr}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}any\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{}{command}{typ}\hypertarget{command.typ}{\hyperlink{command.typ}{\mbox{\isa{\isacommand{typ}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{term}\hypertarget{command.term}{\hyperlink{command.term}{\mbox{\isa{\isacommand{term}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{prop}\hypertarget{command.prop}{\hyperlink{command.prop}{\mbox{\isa{\isacommand{prop}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{thm}\hypertarget{command.thm}{\hyperlink{command.thm}{\mbox{\isa{\isacommand{thm}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{prf}\hypertarget{command.prf}{\hyperlink{command.prf}{\mbox{\isa{\isacommand{prf}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{full\_prf}\hypertarget{command.full-prf}{\hyperlink{command.full-prf}{\mbox{\isa{\isacommand{full{\isaliteral{5F}{\isacharunderscore}}prf}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{pr}\hypertarget{command.pr}{\hyperlink{command.pr}{\mbox{\isa{\isacommand{pr}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}any\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
These diagnostic commands assist interactive development by printing
@@ -64,20 +64,20 @@
\begin{description}
- \item \hyperlink{command.typ}{\mbox{\isa{\isacommand{typ}}}}~\isa{{\isasymtau}} reads and prints types of the
+ \item \hyperlink{command.typ}{\mbox{\isa{\isacommand{typ}}}}~\isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} reads and prints types of the
meta-logic according to the current theory or proof context.
- \item \hyperlink{command.term}{\mbox{\isa{\isacommand{term}}}}~\isa{t} and \hyperlink{command.prop}{\mbox{\isa{\isacommand{prop}}}}~\isa{{\isasymphi}}
+ \item \hyperlink{command.term}{\mbox{\isa{\isacommand{term}}}}~\isa{t} and \hyperlink{command.prop}{\mbox{\isa{\isacommand{prop}}}}~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}}
read, type-check and print terms or propositions according to the
current theory or proof context; the inferred type of \isa{t} is
output as well. Note that these commands are also useful in
inspecting the current environment of term abbreviations.
- \item \hyperlink{command.thm}{\mbox{\isa{\isacommand{thm}}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} retrieves
+ \item \hyperlink{command.thm}{\mbox{\isa{\isacommand{thm}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} retrieves
theorems from the current theory or proof context. Note that any
attributes included in the theorem specifications are applied to a
temporary context derived from the current theory or proof; the
- result is discarded, i.e.\ attributes involved in \isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n{\isachardoublequote}} do not have any permanent effect.
+ result is discarded, i.e.\ attributes involved in \isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} do not have any permanent effect.
\item \hyperlink{command.prf}{\mbox{\isa{\isacommand{prf}}}} displays the (compact) proof term of the
current proof state (if present), or of the given theorems. Note
@@ -85,12 +85,12 @@
object logic (see the ``Proof terms'' section of the Isabelle
reference manual for information on how to do this).
- \item \hyperlink{command.full-prf}{\mbox{\isa{\isacommand{full{\isacharunderscore}prf}}}} is like \hyperlink{command.prf}{\mbox{\isa{\isacommand{prf}}}}, but displays
+ \item \hyperlink{command.full-prf}{\mbox{\isa{\isacommand{full{\isaliteral{5F}{\isacharunderscore}}prf}}}} is like \hyperlink{command.prf}{\mbox{\isa{\isacommand{prf}}}}, but displays
the full proof term, i.e.\ also displays information omitted in the
- compact proof term, which is denoted by ``\isa{{\isacharunderscore}}'' placeholders
+ compact proof term, which is denoted by ``\isa{{\isaliteral{5F}{\isacharunderscore}}}'' placeholders
there.
- \item \hyperlink{command.pr}{\mbox{\isa{\isacommand{pr}}}}~\isa{{\isachardoublequote}goals{\isachardoublequote}} prints the current proof state
+ \item \hyperlink{command.pr}{\mbox{\isa{\isacommand{pr}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}goals{\isaliteral{22}{\isachardoublequote}}} prints the current proof state
(if present), including current facts and goals. The optional limit
arguments affect the number of goals to be displayed, which is
initially 10. Omitting limit value leaves the current setting
@@ -101,7 +101,7 @@
All of the diagnostic commands above admit a list of \isa{modes}
to be specified, which is appended to the current print mode (see
also \cite{isabelle-ref}). Thus the output behavior may be modified
- according particular print mode features. For example, \hyperlink{command.pr}{\mbox{\isa{\isacommand{pr}}}}~\isa{{\isachardoublequote}{\isacharparenleft}latex\ xsymbols{\isacharparenright}{\isachardoublequote}} would print the current proof state
+ according particular print mode features. For example, \hyperlink{command.pr}{\mbox{\isa{\isacommand{pr}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}latex\ xsymbols{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} would print the current proof state
with mathematical symbols and special characters represented in
{\LaTeX} source, according to the Isabelle style
\cite{isabelle-sys}.
@@ -139,7 +139,7 @@
In interactive sessions, the user interface usually manages these
global parameters of the Isabelle process, even with some concept of
persistence. Nonetheless it is occasionally useful to manipulate ML
- variables directly, e.g.\ using \hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isacharunderscore}val}}}} or \hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isacharunderscore}command}}}}.
+ variables directly, e.g.\ using \hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}}}} or \hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}command}}}}.
Batch-mode logic sessions may be configured by putting appropriate
ML text directly into the \verb|ROOT.ML| file.
@@ -174,20 +174,20 @@
pretty printed entities may occasionally help to diagnose problems
with operator priorities, for example.
- \item \verb|eta_contract| controls \isa{{\isachardoublequote}{\isasymeta}{\isachardoublequote}}-contracted printing of
+ \item \verb|eta_contract| controls \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6574613E}{\isasymeta}}{\isaliteral{22}{\isachardoublequote}}}-contracted printing of
terms.
- The \isa{{\isasymeta}}-contraction law asserts \isa{{\isachardoublequote}{\isacharparenleft}{\isasymlambda}x{\isachardot}\ f\ x{\isacharparenright}\ {\isasymequiv}\ f{\isachardoublequote}},
+ The \isa{{\isaliteral{5C3C6574613E}{\isasymeta}}}-contraction law asserts \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ f\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ f{\isaliteral{22}{\isachardoublequote}}},
provided \isa{x} is not free in \isa{f}. It asserts
- \emph{extensionality} of functions: \isa{{\isachardoublequote}f\ {\isasymequiv}\ g{\isachardoublequote}} if \isa{{\isachardoublequote}f\ x\ {\isasymequiv}\ g\ x{\isachardoublequote}} for all \isa{x}. Higher-order unification frequently puts
- terms into a fully \isa{{\isasymeta}}-expanded form. For example, if \isa{F} has type \isa{{\isachardoublequote}{\isacharparenleft}{\isasymtau}\ {\isasymRightarrow}\ {\isasymtau}{\isacharparenright}\ {\isasymRightarrow}\ {\isasymtau}{\isachardoublequote}} then its expanded form is \isa{{\isachardoublequote}{\isasymlambda}h{\isachardot}\ F\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ h\ x{\isacharparenright}{\isachardoublequote}}.
+ \emph{extensionality} of functions: \isa{{\isaliteral{22}{\isachardoublequote}}f\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ g{\isaliteral{22}{\isachardoublequote}}} if \isa{{\isaliteral{22}{\isachardoublequote}}f\ x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ g\ x{\isaliteral{22}{\isachardoublequote}}} for all \isa{x}. Higher-order unification frequently puts
+ terms into a fully \isa{{\isaliteral{5C3C6574613E}{\isasymeta}}}-expanded form. For example, if \isa{F} has type \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C7461753E}{\isasymtau}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}} then its expanded form is \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}h{\isaliteral{2E}{\isachardot}}\ F\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ h\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}.
- Setting \verb|eta_contract| makes Isabelle perform \isa{{\isasymeta}}-contractions before printing, so that \isa{{\isachardoublequote}{\isasymlambda}h{\isachardot}\ F\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ h\ x{\isacharparenright}{\isachardoublequote}}
+ Setting \verb|eta_contract| makes Isabelle perform \isa{{\isaliteral{5C3C6574613E}{\isasymeta}}}-contractions before printing, so that \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}h{\isaliteral{2E}{\isachardot}}\ F\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ h\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}
appears simply as \isa{F}.
- Note that the distinction between a term and its \isa{{\isasymeta}}-expanded
+ Note that the distinction between a term and its \isa{{\isaliteral{5C3C6574613E}{\isasymeta}}}-expanded
form occasionally matters. While higher-order resolution and
- rewriting operate modulo \isa{{\isachardoublequote}{\isasymalpha}{\isasymbeta}{\isasymeta}{\isachardoublequote}}-conversion, some other tools
+ rewriting operate modulo \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{5C3C6574613E}{\isasymeta}}{\isaliteral{22}{\isachardoublequote}}}-conversion, some other tools
might look at terms more discretely.
\item \verb|Goal_Display.goals_limit| controls the maximum number of
@@ -209,14 +209,14 @@
\item \verb|show_tags| controls printing of extra annotations within
theorems, such as internal position information, or the case names
- being attached by the attribute \hyperlink{attribute.case-names}{\mbox{\isa{case{\isacharunderscore}names}}}.
+ being attached by the attribute \hyperlink{attribute.case-names}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}names}}}.
Note that the \hyperlink{attribute.tagged}{\mbox{\isa{tagged}}} and \hyperlink{attribute.untagged}{\mbox{\isa{untagged}}}
attributes provide low-level access to the collection of tags
associated with a theorem.
\item \verb|show_question_marks| controls printing of question marks
- for schematic variables, such as \isa{{\isacharquery}x}. Only the leading
+ for schematic variables, such as \isa{{\isaliteral{3F}{\isacharquery}}x}. Only the leading
question mark is affected, the remaining text is unchanged
(including proper markup for schematic variables that might be
relevant for user interfaces).
@@ -280,8 +280,8 @@
Here the \railtok{string} specifications refer to the actual mixfix
template, which may include literal text, spacing, blocks, and
- arguments (denoted by ``\isa{{\isacharunderscore}}''); the special symbol
- ``\verb|\<index>|'' (printed as ``\isa{{\isachardoublequote}{\isasymindex}{\isachardoublequote}}'') represents an index
+ arguments (denoted by ``\isa{{\isaliteral{5F}{\isacharunderscore}}}''); the special symbol
+ ``\verb|\<index>|'' (printed as ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C696E6465783E}{\isasymindex}}{\isaliteral{22}{\isachardoublequote}}}'') represents an index
argument that specifies an implicit structure reference (see also
\secref{sec:locale}). Infix and binder declarations provide common
abbreviations for particular mixfix declarations. So in practice,
@@ -289,23 +289,23 @@
syntax, such as ``\verb|++|'' for an infix symbol.
\medskip In full generality, mixfix declarations work as follows.
- Suppose a constant \isa{{\isachardoublequote}c\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}\isactrlsub {\isadigit{1}}\ {\isasymRightarrow}\ {\isasymdots}\ {\isasymtau}\isactrlsub n\ {\isasymRightarrow}\ {\isasymtau}{\isachardoublequote}} is
- annotated by \isa{{\isachardoublequote}{\isacharparenleft}mixfix\ {\isacharbrackleft}p\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ p\isactrlsub n{\isacharbrackright}\ p{\isacharparenright}{\isachardoublequote}}, where \isa{{\isachardoublequote}mixfix{\isachardoublequote}} is a string \isa{{\isachardoublequote}d\isactrlsub {\isadigit{0}}\ {\isacharunderscore}\ d\isactrlsub {\isadigit{1}}\ {\isacharunderscore}\ {\isasymdots}\ {\isacharunderscore}\ d\isactrlsub n{\isachardoublequote}} consisting of
+ Suppose a constant \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}} is
+ annotated by \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}mixfix\ {\isaliteral{5B}{\isacharbrackleft}}p\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{5D}{\isacharbrackright}}\ p{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}, where \isa{{\isaliteral{22}{\isachardoublequote}}mixfix{\isaliteral{22}{\isachardoublequote}}} is a string \isa{{\isaliteral{22}{\isachardoublequote}}d\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{0}}\ {\isaliteral{5F}{\isacharunderscore}}\ d\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5F}{\isacharunderscore}}\ d\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} consisting of
delimiters that surround argument positions as indicated by
underscores.
Altogether this determines a production for a context-free priority
- grammar, where for each argument \isa{{\isachardoublequote}i{\isachardoublequote}} the syntactic category
- is determined by \isa{{\isachardoublequote}{\isasymtau}\isactrlsub i{\isachardoublequote}} (with priority \isa{{\isachardoublequote}p\isactrlsub i{\isachardoublequote}}), and
- the result category is determined from \isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}} (with
- priority \isa{{\isachardoublequote}p{\isachardoublequote}}). Priority specifications are optional, with
+ grammar, where for each argument \isa{{\isaliteral{22}{\isachardoublequote}}i{\isaliteral{22}{\isachardoublequote}}} the syntactic category
+ is determined by \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} (with priority \isa{{\isaliteral{22}{\isachardoublequote}}p\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}}), and
+ the result category is determined from \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}} (with
+ priority \isa{{\isaliteral{22}{\isachardoublequote}}p{\isaliteral{22}{\isachardoublequote}}}). Priority specifications are optional, with
default 0 for arguments and 1000 for the result.
- Since \isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}} may be again a function type, the constant
+ Since \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}} may be again a function type, the constant
type scheme may have more argument positions than the mixfix
- pattern. Printing a nested application \isa{{\isachardoublequote}c\ t\isactrlsub {\isadigit{1}}\ {\isasymdots}\ t\isactrlsub m{\isachardoublequote}} for
- \isa{{\isachardoublequote}m\ {\isachargreater}\ n{\isachardoublequote}} works by attaching concrete notation only to the
- innermost part, essentially by printing \isa{{\isachardoublequote}{\isacharparenleft}c\ t\isactrlsub {\isadigit{1}}\ {\isasymdots}\ t\isactrlsub n{\isacharparenright}\ {\isasymdots}\ t\isactrlsub m{\isachardoublequote}}
+ pattern. Printing a nested application \isa{{\isaliteral{22}{\isachardoublequote}}c\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}} for
+ \isa{{\isaliteral{22}{\isachardoublequote}}m\ {\isaliteral{3E}{\isachargreater}}\ n{\isaliteral{22}{\isachardoublequote}}} works by attaching concrete notation only to the
+ innermost part, essentially by printing \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}c\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}}
instead. If a term has fewer arguments than specified in the mixfix
template, the concrete syntax is ignored.
@@ -316,14 +316,14 @@
\begin{description}
- \item \isa{{\isachardoublequote}d{\isachardoublequote}} is a delimiter, namely a non-empty sequence of
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}d{\isaliteral{22}{\isachardoublequote}}} is a delimiter, namely a non-empty sequence of
characters other than the following special characters:
\smallskip
\begin{tabular}{ll}
\verb|'| & single quote \\
\verb|_| & underscore \\
- \isa{{\isachardoublequote}{\isasymindex}{\isachardoublequote}} & index symbol \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C696E6465783E}{\isasymindex}}{\isaliteral{22}{\isachardoublequote}}} & index symbol \\
\verb|(| & open parenthesis \\
\verb|)| & close parenthesis \\
\verb|/| & slash \\
@@ -341,10 +341,10 @@
\item \verb|_| is an argument position, which stands for a
certain syntactic category in the underlying grammar.
- \item \isa{{\isachardoublequote}{\isasymindex}{\isachardoublequote}} is an indexed argument position; this is the place
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C696E6465783E}{\isasymindex}}{\isaliteral{22}{\isachardoublequote}}} is an indexed argument position; this is the place
where implicit structure arguments can be attached.
- \item \isa{{\isachardoublequote}s{\isachardoublequote}} is a non-empty sequence of spaces for printing.
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}s{\isaliteral{22}{\isachardoublequote}}} is a non-empty sequence of spaces for printing.
This and the following specifications do not affect parsing at all.
\item \verb|(|\isa{n} opens a pretty printing block. The
@@ -379,11 +379,11 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcll}
- \indexdef{}{command}{type\_notation}\hypertarget{command.type-notation}{\hyperlink{command.type-notation}{\mbox{\isa{\isacommand{type{\isacharunderscore}notation}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{no\_type\_notation}\hypertarget{command.no-type-notation}{\hyperlink{command.no-type-notation}{\mbox{\isa{\isacommand{no{\isacharunderscore}type{\isacharunderscore}notation}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{notation}\hypertarget{command.notation}{\hyperlink{command.notation}{\mbox{\isa{\isacommand{notation}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{no\_notation}\hypertarget{command.no-notation}{\hyperlink{command.no-notation}{\mbox{\isa{\isacommand{no{\isacharunderscore}notation}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{write}\hypertarget{command.write}{\hyperlink{command.write}{\mbox{\isa{\isacommand{write}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
+ \indexdef{}{command}{type\_notation}\hypertarget{command.type-notation}{\hyperlink{command.type-notation}{\mbox{\isa{\isacommand{type{\isaliteral{5F}{\isacharunderscore}}notation}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{no\_type\_notation}\hypertarget{command.no-type-notation}{\hyperlink{command.no-type-notation}{\mbox{\isa{\isacommand{no{\isaliteral{5F}{\isacharunderscore}}type{\isaliteral{5F}{\isacharunderscore}}notation}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{notation}\hypertarget{command.notation}{\hyperlink{command.notation}{\mbox{\isa{\isacommand{notation}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{no\_notation}\hypertarget{command.no-notation}{\hyperlink{command.no-notation}{\mbox{\isa{\isacommand{no{\isaliteral{5F}{\isacharunderscore}}notation}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{write}\hypertarget{command.write}{\hyperlink{command.write}{\mbox{\isa{\isacommand{write}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -397,18 +397,18 @@
\begin{description}
- \item \hyperlink{command.type-notation}{\mbox{\isa{\isacommand{type{\isacharunderscore}notation}}}}~\isa{{\isachardoublequote}c\ {\isacharparenleft}mx{\isacharparenright}{\isachardoublequote}} associates mixfix
+ \item \hyperlink{command.type-notation}{\mbox{\isa{\isacommand{type{\isaliteral{5F}{\isacharunderscore}}notation}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{28}{\isacharparenleft}}mx{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} associates mixfix
syntax with an existing type constructor. The arity of the
constructor is retrieved from the context.
- \item \hyperlink{command.no-type-notation}{\mbox{\isa{\isacommand{no{\isacharunderscore}type{\isacharunderscore}notation}}}} is similar to \hyperlink{command.type-notation}{\mbox{\isa{\isacommand{type{\isacharunderscore}notation}}}}, but removes the specified syntax annotation from
+ \item \hyperlink{command.no-type-notation}{\mbox{\isa{\isacommand{no{\isaliteral{5F}{\isacharunderscore}}type{\isaliteral{5F}{\isacharunderscore}}notation}}}} is similar to \hyperlink{command.type-notation}{\mbox{\isa{\isacommand{type{\isaliteral{5F}{\isacharunderscore}}notation}}}}, but removes the specified syntax annotation from
the present context.
- \item \hyperlink{command.notation}{\mbox{\isa{\isacommand{notation}}}}~\isa{{\isachardoublequote}c\ {\isacharparenleft}mx{\isacharparenright}{\isachardoublequote}} associates mixfix
+ \item \hyperlink{command.notation}{\mbox{\isa{\isacommand{notation}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{28}{\isacharparenleft}}mx{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} associates mixfix
syntax with an existing constant or fixed variable. The type
declaration of the given entity is retrieved from the context.
- \item \hyperlink{command.no-notation}{\mbox{\isa{\isacommand{no{\isacharunderscore}notation}}}} is similar to \hyperlink{command.notation}{\mbox{\isa{\isacommand{notation}}}},
+ \item \hyperlink{command.no-notation}{\mbox{\isa{\isacommand{no{\isaliteral{5F}{\isacharunderscore}}notation}}}} is similar to \hyperlink{command.notation}{\mbox{\isa{\isacommand{notation}}}},
but removes the specified syntax annotation from the present
context.
@@ -418,7 +418,7 @@
\end{description}
Note that the more primitive commands \hyperlink{command.syntax}{\mbox{\isa{\isacommand{syntax}}}} and
- \hyperlink{command.no-syntax}{\mbox{\isa{\isacommand{no{\isacharunderscore}syntax}}}} (\secref{sec:syn-trans}) provide raw access
+ \hyperlink{command.no-syntax}{\mbox{\isa{\isacommand{no{\isaliteral{5F}{\isacharunderscore}}syntax}}}} (\secref{sec:syn-trans}) provide raw access
to the syntax tables of a global theory.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -434,8 +434,8 @@
\begin{isamarkuptext}%
A context-free grammar consists of a set of \emph{terminal
symbols}, a set of \emph{nonterminal symbols} and a set of
- \emph{productions}. Productions have the form \isa{{\isachardoublequote}A\ {\isacharequal}\ {\isasymgamma}{\isachardoublequote}},
- where \isa{A} is a nonterminal and \isa{{\isasymgamma}} is a string of
+ \emph{productions}. Productions have the form \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C67616D6D613E}{\isasymgamma}}{\isaliteral{22}{\isachardoublequote}}},
+ where \isa{A} is a nonterminal and \isa{{\isaliteral{5C3C67616D6D613E}{\isasymgamma}}} is a string of
terminals and nonterminals. One designated nonterminal is called
the \emph{root symbol}. The language defined by the grammar
consists of all strings of terminals that can be derived from the
@@ -443,15 +443,15 @@
The standard Isabelle parser for inner syntax uses a \emph{priority
grammar}. Each nonterminal is decorated by an integer priority:
- \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup p\isactrlsup {\isacharparenright}{\isachardoublequote}}. In a derivation, \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup p\isactrlsup {\isacharparenright}{\isachardoublequote}} may be rewritten
- using a production \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup q\isactrlsup {\isacharparenright}\ {\isacharequal}\ {\isasymgamma}{\isachardoublequote}} only if \isa{{\isachardoublequote}p\ {\isasymle}\ q{\isachardoublequote}}. Any
+ \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup p\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}. In a derivation, \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup p\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} may be rewritten
+ using a production \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup q\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C67616D6D613E}{\isasymgamma}}{\isaliteral{22}{\isachardoublequote}}} only if \isa{{\isaliteral{22}{\isachardoublequote}}p\ {\isaliteral{5C3C6C653E}{\isasymle}}\ q{\isaliteral{22}{\isachardoublequote}}}. Any
priority grammar can be translated into a normal context-free
grammar by introducing new nonterminals and productions.
\medskip Formally, a set of context free productions \isa{G}
- induces a derivation relation \isa{{\isachardoublequote}{\isasymlongrightarrow}\isactrlsub G{\isachardoublequote}} as follows. Let \isa{{\isasymalpha}} and \isa{{\isasymbeta}} denote strings of terminal or nonterminal symbols.
- Then \isa{{\isachardoublequote}{\isasymalpha}\ A\isactrlsup {\isacharparenleft}\isactrlsup p\isactrlsup {\isacharparenright}\ {\isasymbeta}\ {\isasymlongrightarrow}\isactrlsub G\ {\isasymalpha}\ {\isasymgamma}\ {\isasymbeta}{\isachardoublequote}} holds if and only if \isa{G}
- contains some production \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup q\isactrlsup {\isacharparenright}\ {\isacharequal}\ {\isasymgamma}{\isachardoublequote}} for \isa{{\isachardoublequote}p\ {\isasymle}\ q{\isachardoublequote}}.
+ induces a derivation relation \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\isaliteral{5C3C5E7375623E}{}\isactrlsub G{\isaliteral{22}{\isachardoublequote}}} as follows. Let \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}} and \isa{{\isaliteral{5C3C626574613E}{\isasymbeta}}} denote strings of terminal or nonterminal symbols.
+ Then \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup p\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\isaliteral{5C3C5E7375623E}{}\isactrlsub G\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C67616D6D613E}{\isasymgamma}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{22}{\isachardoublequote}}} holds if and only if \isa{G}
+ contains some production \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup q\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C67616D6D613E}{\isasymgamma}}{\isaliteral{22}{\isachardoublequote}}} for \isa{{\isaliteral{22}{\isachardoublequote}}p\ {\isaliteral{5C3C6C653E}{\isasymle}}\ q{\isaliteral{22}{\isachardoublequote}}}.
\medskip The following grammar for arithmetic expressions
demonstrates how binding power and associativity of operators can be
@@ -459,11 +459,11 @@
\begin{center}
\begin{tabular}{rclr}
- \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharequal}{\isachardoublequote}} & \verb|(| \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{0}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \verb|)| \\
- \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharequal}{\isachardoublequote}} & \verb|0| \\
- \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{0}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharequal}{\isachardoublequote}} & \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{0}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \verb|+| \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \\
- \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{2}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharequal}{\isachardoublequote}} & \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{3}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \verb|*| \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{2}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \\
- \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{3}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharequal}{\isachardoublequote}} & \verb|-| \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{3}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}} & \verb|(| \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \verb|)| \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}} & \verb|0| \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \verb|+| \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{2}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{3}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \verb|*| \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{2}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{3}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}} & \verb|-| \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{3}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}
\end{center}
The choice of priorities determines that \verb|-| binds
@@ -478,12 +478,12 @@
\item Priority 0 on the right-hand side and priority 1000 on the
left-hand side may be omitted.
- \item The production \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup p\isactrlsup {\isacharparenright}\ {\isacharequal}\ {\isasymalpha}{\isachardoublequote}} is written as \isa{{\isachardoublequote}A\ {\isacharequal}\ {\isasymalpha}\ {\isacharparenleft}p{\isacharparenright}{\isachardoublequote}}, i.e.\ the priority of the left-hand side actually appears in
+ \item The production \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup p\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{22}{\isachardoublequote}}} is written as \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}, i.e.\ the priority of the left-hand side actually appears in
a column on the far right.
- \item Alternatives are separated by \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}}.
+ \item Alternatives are separated by \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}}.
- \item Repetition is indicated by dots \isa{{\isachardoublequote}{\isacharparenleft}{\isasymdots}{\isacharparenright}{\isachardoublequote}} in an informal
+ \item Repetition is indicated by dots \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} in an informal
but obvious way.
\end{itemize}
@@ -492,11 +492,11 @@
takes the form:
\begin{center}
\begin{tabular}{rclc}
- \isa{A} & \isa{{\isachardoublequote}{\isacharequal}{\isachardoublequote}} & \verb|(| \isa{A} \verb|)| \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|0| & \qquad\qquad \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{A} \verb|+| \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{0}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{3}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \verb|*| \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{2}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{2}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|-| \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{3}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{3}}{\isacharparenright}{\isachardoublequote}} \\
+ \isa{A} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}} & \verb|(| \isa{A} \verb|)| \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|0| & \qquad\qquad \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{A} \verb|+| \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{3}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \verb|*| \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{2}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|-| \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{3}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}
\end{center}%
\end{isamarkuptext}%
@@ -507,7 +507,7 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-The priority grammar of the \isa{{\isachardoublequote}Pure{\isachardoublequote}} theory is defined as follows:
+The priority grammar of the \isa{{\isaliteral{22}{\isachardoublequote}}Pure{\isaliteral{22}{\isachardoublequote}}} theory is defined as follows:
%FIXME syntax for "index" (?)
%FIXME "op" versions of ==> etc. (?)
@@ -515,62 +515,62 @@
\begin{center}
\begin{supertabular}{rclr}
- \indexdef{inner}{syntax}{any}\hypertarget{syntax.inner.any}{\hyperlink{syntax.inner.any}{\mbox{\isa{any}}}} & = & \isa{{\isachardoublequote}prop\ \ {\isacharbar}\ \ logic{\isachardoublequote}} \\\\
+ \indexdef{inner}{syntax}{any}\hypertarget{syntax.inner.any}{\hyperlink{syntax.inner.any}{\mbox{\isa{any}}}} & = & \isa{{\isaliteral{22}{\isachardoublequote}}prop\ \ {\isaliteral{7C}{\isacharbar}}\ \ logic{\isaliteral{22}{\isachardoublequote}}} \\\\
\indexdef{inner}{syntax}{prop}\hypertarget{syntax.inner.prop}{\hyperlink{syntax.inner.prop}{\mbox{\isa{prop}}}} & = & \verb|(| \isa{prop} \verb|)| \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}prop\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{4}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \verb|::| \isa{type} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{3}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}any\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{3}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \verb|=?=| \isa{{\isachardoublequote}any\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{2}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{2}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}any\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{3}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \verb|==| \isa{{\isachardoublequote}any\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{2}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{2}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}any\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{3}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} \isa{{\isachardoublequote}any\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{2}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{2}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}prop\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{3}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \verb|&&&| \isa{{\isachardoublequote}prop\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{2}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{2}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}prop\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{2}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \verb|==>| \isa{{\isachardoublequote}prop\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{1}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}prop\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{2}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}} \isa{{\isachardoublequote}prop\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{1}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|[|\verb,|,\verb|| \isa{prop} \verb|;| \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} \verb|;| \isa{prop} \verb||\verb,|,\verb|]| \verb|==>| \isa{{\isachardoublequote}prop\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{1}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymlbrakk}{\isachardoublequote}} \isa{prop} \verb|;| \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} \verb|;| \isa{prop} \isa{{\isachardoublequote}{\isasymrbrakk}{\isachardoublequote}} \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}} \isa{{\isachardoublequote}prop\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{1}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|!!| \isa{idts} \verb|.| \isa{prop} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{0}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}} \isa{idts} \verb|.| \isa{prop} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{0}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|OFCLASS| \verb|(| \isa{type} \verb|,| \isa{logic} \verb|)| \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|SORT_CONSTRAINT| \verb|(| \isa{type} \verb|)| \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|TERM| \isa{logic} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|PROP| \isa{aprop} \\\\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}prop\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{4}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \verb|::| \isa{type} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}any\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{3}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \verb|=?=| \isa{{\isaliteral{22}{\isachardoublequote}}any\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{2}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}any\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{3}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \verb|==| \isa{{\isaliteral{22}{\isachardoublequote}}any\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{2}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}any\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{3}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} \isa{{\isaliteral{22}{\isachardoublequote}}any\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{2}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}prop\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{3}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \verb|&&&| \isa{{\isaliteral{22}{\isachardoublequote}}prop\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{2}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}prop\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{2}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \verb|==>| \isa{{\isaliteral{22}{\isachardoublequote}}prop\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}prop\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{2}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \isa{{\isaliteral{22}{\isachardoublequote}}prop\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|[|\verb,|,\verb|| \isa{prop} \verb|;| \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \verb|;| \isa{prop} \verb||\verb,|,\verb|]| \verb|==>| \isa{{\isaliteral{22}{\isachardoublequote}}prop\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{22}{\isachardoublequote}}} \isa{prop} \verb|;| \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \verb|;| \isa{prop} \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}{\isaliteral{22}{\isachardoublequote}}} \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \isa{{\isaliteral{22}{\isachardoublequote}}prop\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|!!| \isa{idts} \verb|.| \isa{prop} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{22}{\isachardoublequote}}} \isa{idts} \verb|.| \isa{prop} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|OFCLASS| \verb|(| \isa{type} \verb|,| \isa{logic} \verb|)| \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|SORT_CONSTRAINT| \verb|(| \isa{type} \verb|)| \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|TERM| \isa{logic} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|PROP| \isa{aprop} \\\\
\indexdef{inner}{syntax}{aprop}\hypertarget{syntax.inner.aprop}{\hyperlink{syntax.inner.aprop}{\mbox{\isa{aprop}}}} & = & \verb|(| \isa{aprop} \verb|)| \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}id\ \ {\isacharbar}\ \ longid\ \ {\isacharbar}\ \ var\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|_|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|...| \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|CONST| \isa{{\isachardoublequote}id\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|CONST| \isa{{\isachardoublequote}longid{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}logic\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isacharparenright}\ \ any\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isacharparenright}\ {\isasymdots}\ any\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isacharparenright}{\isachardoublequote}} \\\\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}id\ \ {\isaliteral{7C}{\isacharbar}}\ \ longid\ \ {\isaliteral{7C}{\isacharbar}}\ \ var\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|_|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|...| \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|CONST| \isa{{\isaliteral{22}{\isachardoublequote}}id\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|CONST| \isa{{\isaliteral{22}{\isachardoublequote}}longid{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}logic\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}\ \ any\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ any\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\\\
\indexdef{inner}{syntax}{logic}\hypertarget{syntax.inner.logic}{\hyperlink{syntax.inner.logic}{\mbox{\isa{logic}}}} & = & \verb|(| \isa{logic} \verb|)| \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}logic\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{4}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \verb|::| \isa{type} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{3}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}id\ \ {\isacharbar}\ \ longid\ \ {\isacharbar}\ \ var\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|_|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|...| \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|CONST| \isa{{\isachardoublequote}id\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|CONST| \isa{{\isachardoublequote}longid{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}logic\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isacharparenright}\ \ any\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isacharparenright}\ {\isasymdots}\ any\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|%| \isa{pttrns} \verb|.| \isa{{\isachardoublequote}any\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{3}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{3}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isasymlambda}} \isa{pttrns} \verb|.| \isa{{\isachardoublequote}any\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{3}}\isactrlsup {\isacharparenright}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{3}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|TYPE| \verb|(| \isa{type} \verb|)| \\\\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}logic\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{4}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \verb|::| \isa{type} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}id\ \ {\isaliteral{7C}{\isacharbar}}\ \ longid\ \ {\isaliteral{7C}{\isacharbar}}\ \ var\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|_|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|...| \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|CONST| \isa{{\isaliteral{22}{\isachardoublequote}}id\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|CONST| \isa{{\isaliteral{22}{\isachardoublequote}}longid{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}logic\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}\ \ any\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ any\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|%| \isa{pttrns} \verb|.| \isa{{\isaliteral{22}{\isachardoublequote}}any\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{3}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}} \isa{pttrns} \verb|.| \isa{{\isaliteral{22}{\isachardoublequote}}any\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{3}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|TYPE| \verb|(| \isa{type} \verb|)| \\\\
- \indexdef{inner}{syntax}{idt}\hypertarget{syntax.inner.idt}{\hyperlink{syntax.inner.idt}{\mbox{\isa{idt}}}} & = & \verb|(| \isa{idt} \verb|)|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ id\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|_| \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{id} \verb|::| \isa{type} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{0}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|_| \verb|::| \isa{type} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{0}}{\isacharparenright}{\isachardoublequote}} \\\\
+ \indexdef{inner}{syntax}{idt}\hypertarget{syntax.inner.idt}{\hyperlink{syntax.inner.idt}{\mbox{\isa{idt}}}} & = & \verb|(| \isa{idt} \verb|)|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ id\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|_| \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{id} \verb|::| \isa{type} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|_| \verb|::| \isa{type} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\\\
- \indexdef{inner}{syntax}{idts}\hypertarget{syntax.inner.idts}{\hyperlink{syntax.inner.idts}{\mbox{\isa{idts}}}} & = & \isa{{\isachardoublequote}idt\ \ {\isacharbar}\ \ idt\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isacharparenright}\ idts{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{0}}{\isacharparenright}{\isachardoublequote}} \\\\
+ \indexdef{inner}{syntax}{idts}\hypertarget{syntax.inner.idts}{\hyperlink{syntax.inner.idts}{\mbox{\isa{idts}}}} & = & \isa{{\isaliteral{22}{\isachardoublequote}}idt\ \ {\isaliteral{7C}{\isacharbar}}\ \ idt\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}\ idts{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\\\
\indexdef{inner}{syntax}{pttrn}\hypertarget{syntax.inner.pttrn}{\hyperlink{syntax.inner.pttrn}{\mbox{\isa{pttrn}}}} & = & \isa{idt} \\\\
- \indexdef{inner}{syntax}{pttrns}\hypertarget{syntax.inner.pttrns}{\hyperlink{syntax.inner.pttrns}{\mbox{\isa{pttrns}}}} & = & \isa{{\isachardoublequote}pttrn\ \ {\isacharbar}\ \ pttrn\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isacharparenright}\ pttrns{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{0}}{\isacharparenright}{\isachardoublequote}} \\\\
+ \indexdef{inner}{syntax}{pttrns}\hypertarget{syntax.inner.pttrns}{\hyperlink{syntax.inner.pttrns}{\mbox{\isa{pttrns}}}} & = & \isa{{\isaliteral{22}{\isachardoublequote}}pttrn\ \ {\isaliteral{7C}{\isacharbar}}\ \ pttrn\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}\ pttrns{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\\\
\indexdef{inner}{syntax}{type}\hypertarget{syntax.inner.type}{\hyperlink{syntax.inner.type}{\mbox{\isa{type}}}} & = & \verb|(| \isa{type} \verb|)| \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}tid\ \ {\isacharbar}\ \ tvar\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|_| \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}tid{\isachardoublequote}} \verb|::| \isa{{\isachardoublequote}sort\ \ {\isacharbar}\ \ tvar\ \ {\isachardoublequote}}\verb|::| \isa{{\isachardoublequote}sort\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|_| \verb|::| \isa{{\isachardoublequote}sort{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}id\ \ {\isacharbar}\ \ type\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isacharparenright}\ id\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|(| \isa{type} \verb|,| \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} \verb|,| \isa{type} \verb|)| \isa{id} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}longid\ \ {\isacharbar}\ \ type\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isadigit{0}}\isactrlsup {\isacharparenright}\ longid{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|(| \isa{type} \verb|,| \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} \verb|,| \isa{type} \verb|)| \isa{longid} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}type\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \verb|=>| \isa{type} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{0}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}type\isactrlsup {\isacharparenleft}\isactrlsup {\isadigit{1}}\isactrlsup {\isacharparenright}{\isachardoublequote}} \isa{{\isachardoublequote}{\isasymRightarrow}{\isachardoublequote}} \isa{type} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{0}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|[| \isa{type} \verb|,| \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} \verb|,| \isa{type} \verb|]| \verb|=>| \isa{type} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{0}}{\isacharparenright}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|[| \isa{type} \verb|,| \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} \verb|,| \isa{type} \verb|]| \isa{{\isachardoublequote}{\isasymRightarrow}{\isachardoublequote}} \isa{type} & \isa{{\isachardoublequote}{\isacharparenleft}{\isadigit{0}}{\isacharparenright}{\isachardoublequote}} \\\\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}tid\ \ {\isaliteral{7C}{\isacharbar}}\ \ tvar\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|_| \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}tid{\isaliteral{22}{\isachardoublequote}}} \verb|::| \isa{{\isaliteral{22}{\isachardoublequote}}sort\ \ {\isaliteral{7C}{\isacharbar}}\ \ tvar\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|::| \isa{{\isaliteral{22}{\isachardoublequote}}sort\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|_| \verb|::| \isa{{\isaliteral{22}{\isachardoublequote}}sort{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}id\ \ {\isaliteral{7C}{\isacharbar}}\ \ type\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}\ id\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|(| \isa{type} \verb|,| \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \verb|,| \isa{type} \verb|)| \isa{id} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}longid\ \ {\isaliteral{7C}{\isacharbar}}\ \ type\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{0}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}\ longid{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|(| \isa{type} \verb|,| \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \verb|,| \isa{type} \verb|)| \isa{longid} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}type\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \verb|=>| \isa{type} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}type\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isadigit{1}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}{\isaliteral{22}{\isachardoublequote}}} \isa{type} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|[| \isa{type} \verb|,| \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \verb|,| \isa{type} \verb|]| \verb|=>| \isa{type} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|[| \isa{type} \verb|,| \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \verb|,| \isa{type} \verb|]| \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}{\isaliteral{22}{\isachardoublequote}}} \isa{type} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\\\
- \indexdef{inner}{syntax}{sort}\hypertarget{syntax.inner.sort}{\hyperlink{syntax.inner.sort}{\mbox{\isa{sort}}}} & = & \isa{{\isachardoublequote}id\ \ {\isacharbar}\ \ longid\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|{}| \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \verb|{| \isa{{\isachardoublequote}{\isacharparenleft}id\ {\isacharbar}\ longid{\isacharparenright}{\isachardoublequote}} \verb|,| \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} \verb|,| \isa{{\isachardoublequote}{\isacharparenleft}id\ {\isacharbar}\ longid{\isacharparenright}{\isachardoublequote}} \verb|}| \\
+ \indexdef{inner}{syntax}{sort}\hypertarget{syntax.inner.sort}{\hyperlink{syntax.inner.sort}{\mbox{\isa{sort}}}} & = & \isa{{\isaliteral{22}{\isachardoublequote}}id\ \ {\isaliteral{7C}{\isacharbar}}\ \ longid\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|{}| \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \verb|{| \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}id\ {\isaliteral{7C}{\isacharbar}}\ longid{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \verb|,| \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \verb|,| \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}id\ {\isaliteral{7C}{\isacharbar}}\ longid{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \verb|}| \\
\end{supertabular}
\end{center}
@@ -586,7 +586,7 @@
\item \indexref{inner}{syntax}{prop}\hyperlink{syntax.inner.prop}{\mbox{\isa{prop}}} denotes meta-level propositions,
which are terms of type \isa{prop}. The syntax of such formulae of
the meta-logic is carefully distinguished from usual conventions for
- object-logics. In particular, plain \isa{{\isachardoublequote}{\isasymlambda}{\isachardoublequote}}-term notation is
+ object-logics. In particular, plain \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{22}{\isachardoublequote}}}-term notation is
\emph{not} recognized as \hyperlink{syntax.inner.prop}{\mbox{\isa{prop}}}.
\item \indexref{inner}{syntax}{aprop}\hyperlink{syntax.inner.aprop}{\mbox{\isa{aprop}}} denotes atomic propositions, which
@@ -600,7 +600,7 @@
\item \indexref{inner}{syntax}{logic}\hyperlink{syntax.inner.logic}{\mbox{\isa{logic}}} denotes arbitrary terms of a
logical type, excluding type \isa{prop}. This is the main
- syntactic category of object-logic entities, covering plain \isa{{\isasymlambda}}-term notation (variables, abstraction, application), plus
+ syntactic category of object-logic entities, covering plain \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}}-term notation (variables, abstraction, application), plus
anything defined by the user.
When specifying notation for logical entities, all logical types
@@ -611,7 +611,7 @@
constrained by types.
\item \indexref{inner}{syntax}{idts}\hyperlink{syntax.inner.idts}{\mbox{\isa{idts}}} denotes a sequence of \indexref{inner}{syntax}{idt}\hyperlink{syntax.inner.idt}{\mbox{\isa{idt}}}. This is the most basic category for variables in
- iterated binders, such as \isa{{\isachardoublequote}{\isasymlambda}{\isachardoublequote}} or \isa{{\isachardoublequote}{\isasymAnd}{\isachardoublequote}}.
+ iterated binders, such as \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{22}{\isachardoublequote}}} or \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}{\isaliteral{22}{\isachardoublequote}}}.
\item \indexref{inner}{syntax}{pttrn}\hyperlink{syntax.inner.pttrn}{\mbox{\isa{pttrn}}} and \indexref{inner}{syntax}{pttrns}\hyperlink{syntax.inner.pttrns}{\mbox{\isa{pttrns}}}
denote patterns for abstraction, cases bindings etc. In Pure, these
@@ -629,17 +629,17 @@
\begin{itemize}
- \item In \hyperlink{syntax.inner.idts}{\mbox{\isa{idts}}}, note that \isa{{\isachardoublequote}x\ {\isacharcolon}{\isacharcolon}\ nat\ y{\isachardoublequote}} is
- parsed as \isa{{\isachardoublequote}x\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}nat\ y{\isacharparenright}{\isachardoublequote}}, treating \isa{y} like a type
+ \item In \hyperlink{syntax.inner.idts}{\mbox{\isa{idts}}}, note that \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat\ y{\isaliteral{22}{\isachardoublequote}}} is
+ parsed as \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}nat\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}, treating \isa{y} like a type
constructor applied to \isa{nat}. To avoid this interpretation,
- write \isa{{\isachardoublequote}{\isacharparenleft}x\ {\isacharcolon}{\isacharcolon}\ nat{\isacharparenright}\ y{\isachardoublequote}} with explicit parentheses.
+ write \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{29}{\isacharparenright}}\ y{\isaliteral{22}{\isachardoublequote}}} with explicit parentheses.
- \item Similarly, \isa{{\isachardoublequote}x\ {\isacharcolon}{\isacharcolon}\ nat\ y\ {\isacharcolon}{\isacharcolon}\ nat{\isachardoublequote}} is parsed as \isa{{\isachardoublequote}x\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}nat\ y\ {\isacharcolon}{\isacharcolon}\ nat{\isacharparenright}{\isachardoublequote}}. The correct form is \isa{{\isachardoublequote}{\isacharparenleft}x\ {\isacharcolon}{\isacharcolon}\ nat{\isacharparenright}\ {\isacharparenleft}y\ {\isacharcolon}{\isacharcolon}\ nat{\isacharparenright}{\isachardoublequote}}, or \isa{{\isachardoublequote}{\isacharparenleft}x\ {\isacharcolon}{\isacharcolon}\ nat{\isacharparenright}\ y\ {\isacharcolon}{\isacharcolon}\ nat{\isachardoublequote}} if \isa{y} is last in the
+ \item Similarly, \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{22}{\isachardoublequote}}} is parsed as \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}nat\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}. The correct form is \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}, or \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{29}{\isacharparenright}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{22}{\isachardoublequote}}} if \isa{y} is last in the
sequence of identifiers.
\item Type constraints for terms bind very weakly. For example,
- \isa{{\isachardoublequote}x\ {\isacharless}\ y\ {\isacharcolon}{\isacharcolon}\ nat{\isachardoublequote}} is normally parsed as \isa{{\isachardoublequote}{\isacharparenleft}x\ {\isacharless}\ y{\isacharparenright}\ {\isacharcolon}{\isacharcolon}\ nat{\isachardoublequote}}, unless \isa{{\isachardoublequote}{\isacharless}{\isachardoublequote}} has a very low priority, in which case the
- input is likely to be ambiguous. The correct form is \isa{{\isachardoublequote}x\ {\isacharless}\ {\isacharparenleft}y\ {\isacharcolon}{\isacharcolon}\ nat{\isacharparenright}{\isachardoublequote}}.
+ \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3C}{\isacharless}}\ y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{22}{\isachardoublequote}}} is normally parsed as \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3C}{\isacharless}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{22}{\isachardoublequote}}}, unless \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3C}{\isacharless}}{\isaliteral{22}{\isachardoublequote}}} has a very low priority, in which case the
+ input is likely to be ambiguous. The correct form is \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3C}{\isacharless}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}.
\item Constraints may be either written with two literal colons
``\verb|::|'' or the double-colon symbol \verb|\<Colon>|,
@@ -650,21 +650,21 @@
\begin{description}
- \item A type ``\isa{{\isachardoublequote}{\isacharunderscore}{\isachardoublequote}}'' or ``\isa{{\isachardoublequote}{\isacharunderscore}\ {\isacharcolon}{\isacharcolon}\ sort{\isachardoublequote}}'' acts like an
+ \item A type ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequote}}}'' or ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ sort{\isaliteral{22}{\isachardoublequote}}}'' acts like an
anonymous inference parameter, which is filled-in according to the
most general type produced by the type-checking phase.
- \item A bound ``\isa{{\isachardoublequote}{\isacharunderscore}{\isachardoublequote}}'' refers to a vacuous abstraction, where
+ \item A bound ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequote}}}'' refers to a vacuous abstraction, where
the body does not refer to the binding introduced here. As in the
- term \isa{{\isachardoublequote}{\isasymlambda}x\ {\isacharunderscore}{\isachardot}\ x{\isachardoublequote}}, which is \isa{{\isachardoublequote}{\isasymalpha}{\isachardoublequote}}-equivalent to \isa{{\isachardoublequote}{\isasymlambda}x\ y{\isachardot}\ x{\isachardoublequote}}.
+ term \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{22}{\isachardoublequote}}}, which is \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{22}{\isachardoublequote}}}-equivalent to \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x\ y{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{22}{\isachardoublequote}}}.
- \item A free ``\isa{{\isachardoublequote}{\isacharunderscore}{\isachardoublequote}}'' refers to an implicit outer binding.
- Higher definitional packages usually allow forms like \isa{{\isachardoublequote}f\ x\ {\isacharunderscore}\ {\isacharequal}\ x{\isachardoublequote}}.
+ \item A free ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequote}}}'' refers to an implicit outer binding.
+ Higher definitional packages usually allow forms like \isa{{\isaliteral{22}{\isachardoublequote}}f\ x\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequote}}}.
- \item A schematic ``\isa{{\isachardoublequote}{\isacharunderscore}{\isachardoublequote}}'' (within a term pattern, see
+ \item A schematic ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequote}}}'' (within a term pattern, see
\secref{sec:term-decls}) refers to an anonymous variable that is
implicitly abstracted over its context of locally bound variables.
- For example, this allows pattern matching of \isa{{\isachardoublequote}{\isacharbraceleft}x{\isachardot}\ f\ x\ {\isacharequal}\ g\ x{\isacharbraceright}{\isachardoublequote}} against \isa{{\isachardoublequote}{\isacharbraceleft}x{\isachardot}\ {\isacharunderscore}\ {\isacharequal}\ {\isacharunderscore}{\isacharbraceright}{\isachardoublequote}}, or even \isa{{\isachardoublequote}{\isacharbraceleft}{\isacharunderscore}{\isachardot}\ {\isacharunderscore}\ {\isacharequal}\ {\isacharunderscore}{\isacharbraceright}{\isachardoublequote}} by
+ For example, this allows pattern matching of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7B}{\isacharbraceleft}}x{\isaliteral{2E}{\isachardot}}\ f\ x\ {\isaliteral{3D}{\isacharequal}}\ g\ x{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} against \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7B}{\isacharbraceleft}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}}, or even \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} by
using both bound and schematic dummies.
\end{description}
@@ -714,21 +714,21 @@
\indexdef{inner}{syntax}{var}\hypertarget{syntax.inner.var}{\hyperlink{syntax.inner.var}{\mbox{\isa{var}}}} & = & \indexref{}{syntax}{var}\hyperlink{syntax.var}{\mbox{\isa{var}}} \\
\indexdef{inner}{syntax}{tid}\hypertarget{syntax.inner.tid}{\hyperlink{syntax.inner.tid}{\mbox{\isa{tid}}}} & = & \indexref{}{syntax}{typefree}\hyperlink{syntax.typefree}{\mbox{\isa{typefree}}} \\
\indexdef{inner}{syntax}{tvar}\hypertarget{syntax.inner.tvar}{\hyperlink{syntax.inner.tvar}{\mbox{\isa{tvar}}}} & = & \indexref{}{syntax}{typevar}\hyperlink{syntax.typevar}{\mbox{\isa{typevar}}} \\
- \indexdef{inner}{syntax}{num}\hypertarget{syntax.inner.num}{\hyperlink{syntax.inner.num}{\mbox{\isa{num}}}} & = & \indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}}\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|-|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}} \\
- \indexdef{inner}{syntax}{float\_token}\hypertarget{syntax.inner.float-token}{\hyperlink{syntax.inner.float-token}{\mbox{\isa{float{\isacharunderscore}token}}}} & = & \indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}}\verb|.|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}}\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|-|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}}\verb|.|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}} \\
- \indexdef{inner}{syntax}{xnum}\hypertarget{syntax.inner.xnum}{\hyperlink{syntax.inner.xnum}{\mbox{\isa{xnum}}}} & = & \verb|#|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}}\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|#-|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}} \\
+ \indexdef{inner}{syntax}{num}\hypertarget{syntax.inner.num}{\hyperlink{syntax.inner.num}{\mbox{\isa{num}}}} & = & \indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}}\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|-|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}} \\
+ \indexdef{inner}{syntax}{float\_token}\hypertarget{syntax.inner.float-token}{\hyperlink{syntax.inner.float-token}{\mbox{\isa{float{\isaliteral{5F}{\isacharunderscore}}token}}}} & = & \indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}}\verb|.|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}}\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|-|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}}\verb|.|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}} \\
+ \indexdef{inner}{syntax}{xnum}\hypertarget{syntax.inner.xnum}{\hyperlink{syntax.inner.xnum}{\mbox{\isa{xnum}}}} & = & \verb|#|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}}\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|#-|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}} \\
- \indexdef{inner}{syntax}{xstr}\hypertarget{syntax.inner.xstr}{\hyperlink{syntax.inner.xstr}{\mbox{\isa{xstr}}}} & = & \verb|''| \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} \verb|''| \\
+ \indexdef{inner}{syntax}{xstr}\hypertarget{syntax.inner.xstr}{\hyperlink{syntax.inner.xstr}{\mbox{\isa{xstr}}}} & = & \verb|''| \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \verb|''| \\
\end{supertabular}
\end{center}
- The token categories \hyperlink{syntax.inner.num}{\mbox{\isa{num}}}, \hyperlink{syntax.inner.float-token}{\mbox{\isa{float{\isacharunderscore}token}}}, \hyperlink{syntax.inner.xnum}{\mbox{\isa{xnum}}}, and \hyperlink{syntax.inner.xstr}{\mbox{\isa{xstr}}} are
+ The token categories \hyperlink{syntax.inner.num}{\mbox{\isa{num}}}, \hyperlink{syntax.inner.float-token}{\mbox{\isa{float{\isaliteral{5F}{\isacharunderscore}}token}}}, \hyperlink{syntax.inner.xnum}{\mbox{\isa{xnum}}}, and \hyperlink{syntax.inner.xstr}{\mbox{\isa{xstr}}} are
not used in Pure. Object-logics may implement numerals and string
constants by adding appropriate syntax declarations, together with
some translation functions (e.g.\ see Isabelle/HOL).
- The derived categories \indexdef{inner}{syntax}{num\_const}\hypertarget{syntax.inner.num-const}{\hyperlink{syntax.inner.num-const}{\mbox{\isa{num{\isacharunderscore}const}}}} and
- \indexdef{inner}{syntax}{float\_const}\hypertarget{syntax.inner.float-const}{\hyperlink{syntax.inner.float-const}{\mbox{\isa{float{\isacharunderscore}const}}}} provide robust access to \hyperlink{syntax.inner.num}{\mbox{\isa{num}}}, and \hyperlink{syntax.inner.float-token}{\mbox{\isa{float{\isacharunderscore}token}}}, respectively: the
+ The derived categories \indexdef{inner}{syntax}{num\_const}\hypertarget{syntax.inner.num-const}{\hyperlink{syntax.inner.num-const}{\mbox{\isa{num{\isaliteral{5F}{\isacharunderscore}}const}}}} and
+ \indexdef{inner}{syntax}{float\_const}\hypertarget{syntax.inner.float-const}{\hyperlink{syntax.inner.float-const}{\mbox{\isa{float{\isaliteral{5F}{\isacharunderscore}}const}}}} provide robust access to \hyperlink{syntax.inner.num}{\mbox{\isa{num}}}, and \hyperlink{syntax.inner.float-token}{\mbox{\isa{float{\isaliteral{5F}{\isacharunderscore}}token}}}, respectively: the
syntax tree holds a syntactic constant instead of a free variable.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -739,11 +739,11 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{nonterminals}\hypertarget{command.nonterminals}{\hyperlink{command.nonterminals}{\mbox{\isa{\isacommand{nonterminals}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{syntax}\hypertarget{command.syntax}{\hyperlink{command.syntax}{\mbox{\isa{\isacommand{syntax}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{no\_syntax}\hypertarget{command.no-syntax}{\hyperlink{command.no-syntax}{\mbox{\isa{\isacommand{no{\isacharunderscore}syntax}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{translations}\hypertarget{command.translations}{\hyperlink{command.translations}{\mbox{\isa{\isacommand{translations}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{no\_translations}\hypertarget{command.no-translations}{\hyperlink{command.no-translations}{\mbox{\isa{\isacommand{no{\isacharunderscore}translations}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
+ \indexdef{}{command}{nonterminals}\hypertarget{command.nonterminals}{\hyperlink{command.nonterminals}{\mbox{\isa{\isacommand{nonterminals}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{syntax}\hypertarget{command.syntax}{\hyperlink{command.syntax}{\mbox{\isa{\isacommand{syntax}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{no\_syntax}\hypertarget{command.no-syntax}{\hyperlink{command.no-syntax}{\mbox{\isa{\isacommand{no{\isaliteral{5F}{\isacharunderscore}}syntax}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{translations}\hypertarget{command.translations}{\hyperlink{command.translations}{\mbox{\isa{\isacommand{translations}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{no\_translations}\hypertarget{command.no-translations}{\hyperlink{command.no-translations}{\mbox{\isa{\isacommand{no{\isaliteral{5F}{\isacharunderscore}}translations}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -766,7 +766,7 @@
constructor \isa{c} (without arguments) to act as purely syntactic
type: a nonterminal symbol of the inner syntax.
- \item \hyperlink{command.syntax}{\mbox{\isa{\isacommand{syntax}}}}~\isa{{\isachardoublequote}{\isacharparenleft}mode{\isacharparenright}\ decls{\isachardoublequote}} is similar to
+ \item \hyperlink{command.syntax}{\mbox{\isa{\isacommand{syntax}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}mode{\isaliteral{29}{\isacharparenright}}\ decls{\isaliteral{22}{\isachardoublequote}}} is similar to
\hyperlink{command.consts}{\mbox{\isa{\isacommand{consts}}}}~\isa{decls}, except that the actual logical
signature extension is omitted. Thus the context free grammar of
Isabelle's inner syntax may be augmented in arbitrary ways,
@@ -774,17 +774,17 @@
print mode that the grammar rules belong; unless the \indexref{}{keyword}{output}\hyperlink{keyword.output}{\mbox{\isa{\isakeyword{output}}}} indicator is given, all productions are added both to the
input and output grammar.
- \item \hyperlink{command.no-syntax}{\mbox{\isa{\isacommand{no{\isacharunderscore}syntax}}}}~\isa{{\isachardoublequote}{\isacharparenleft}mode{\isacharparenright}\ decls{\isachardoublequote}} removes grammar
+ \item \hyperlink{command.no-syntax}{\mbox{\isa{\isacommand{no{\isaliteral{5F}{\isacharunderscore}}syntax}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}mode{\isaliteral{29}{\isacharparenright}}\ decls{\isaliteral{22}{\isachardoublequote}}} removes grammar
declarations (and translations) resulting from \isa{decls}, which
are interpreted in the same manner as for \hyperlink{command.syntax}{\mbox{\isa{\isacommand{syntax}}}} above.
\item \hyperlink{command.translations}{\mbox{\isa{\isacommand{translations}}}}~\isa{rules} specifies syntactic
- translation rules (i.e.\ macros): parse~/ print rules (\isa{{\isachardoublequote}{\isasymrightleftharpoons}{\isachardoublequote}}),
- parse rules (\isa{{\isachardoublequote}{\isasymrightharpoonup}{\isachardoublequote}}), or print rules (\isa{{\isachardoublequote}{\isasymleftharpoondown}{\isachardoublequote}}).
+ translation rules (i.e.\ macros): parse~/ print rules (\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C72696768746C656674686172706F6F6E733E}{\isasymrightleftharpoons}}{\isaliteral{22}{\isachardoublequote}}}),
+ parse rules (\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7269676874686172706F6F6E75703E}{\isasymrightharpoonup}}{\isaliteral{22}{\isachardoublequote}}}), or print rules (\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C656674686172706F6F6E646F776E3E}{\isasymleftharpoondown}}{\isaliteral{22}{\isachardoublequote}}}).
Translation patterns may be prefixed by the syntactic category to be
used for parsing; the default is \isa{logic}.
- \item \hyperlink{command.no-translations}{\mbox{\isa{\isacommand{no{\isacharunderscore}translations}}}}~\isa{rules} removes syntactic
+ \item \hyperlink{command.no-translations}{\mbox{\isa{\isacommand{no{\isaliteral{5F}{\isacharunderscore}}translations}}}}~\isa{rules} removes syntactic
translation rules, which are interpreted in the same manner as for
\hyperlink{command.translations}{\mbox{\isa{\isacommand{translations}}}} above.
@@ -798,11 +798,11 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{parse\_ast\_translation}\hypertarget{command.parse-ast-translation}{\hyperlink{command.parse-ast-translation}{\mbox{\isa{\isacommand{parse{\isacharunderscore}ast{\isacharunderscore}translation}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{parse\_translation}\hypertarget{command.parse-translation}{\hyperlink{command.parse-translation}{\mbox{\isa{\isacommand{parse{\isacharunderscore}translation}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{print\_translation}\hypertarget{command.print-translation}{\hyperlink{command.print-translation}{\mbox{\isa{\isacommand{print{\isacharunderscore}translation}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{typed\_print\_translation}\hypertarget{command.typed-print-translation}{\hyperlink{command.typed-print-translation}{\mbox{\isa{\isacommand{typed{\isacharunderscore}print{\isacharunderscore}translation}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{print\_ast\_translation}\hypertarget{command.print-ast-translation}{\hyperlink{command.print-ast-translation}{\mbox{\isa{\isacommand{print{\isacharunderscore}ast{\isacharunderscore}translation}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
+ \indexdef{}{command}{parse\_ast\_translation}\hypertarget{command.parse-ast-translation}{\hyperlink{command.parse-ast-translation}{\mbox{\isa{\isacommand{parse{\isaliteral{5F}{\isacharunderscore}}ast{\isaliteral{5F}{\isacharunderscore}}translation}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{parse\_translation}\hypertarget{command.parse-translation}{\hyperlink{command.parse-translation}{\mbox{\isa{\isacommand{parse{\isaliteral{5F}{\isacharunderscore}}translation}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_translation}\hypertarget{command.print-translation}{\hyperlink{command.print-translation}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}translation}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{typed\_print\_translation}\hypertarget{command.typed-print-translation}{\hyperlink{command.typed-print-translation}{\mbox{\isa{\isacommand{typed{\isaliteral{5F}{\isacharunderscore}}print{\isaliteral{5F}{\isacharunderscore}}translation}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_ast\_translation}\hypertarget{command.print-ast-translation}{\hyperlink{command.print-ast-translation}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}ast{\isaliteral{5F}{\isacharunderscore}}translation}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -826,7 +826,7 @@
val print_ast_translation : (string * (ast list -> ast)) list
\end{ttbox}
- If the \isa{{\isachardoublequote}{\isacharparenleft}advanced{\isacharparenright}{\isachardoublequote}} option is given, the corresponding
+ If the \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}advanced{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option is given, the corresponding
translation functions may depend on the current theory or proof
context. This allows to implement advanced syntax mechanisms, as
translations functions may refer to specific theory declarations or
@@ -857,25 +857,25 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{print\_syntax}\hypertarget{command.print-syntax}{\hyperlink{command.print-syntax}{\mbox{\isa{\isacommand{print{\isacharunderscore}syntax}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{}{command}{print\_syntax}\hypertarget{command.print-syntax}{\hyperlink{command.print-syntax}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}syntax}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{description}
- \item \hyperlink{command.print-syntax}{\mbox{\isa{\isacommand{print{\isacharunderscore}syntax}}}} prints the inner syntax of the
+ \item \hyperlink{command.print-syntax}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}syntax}}}} prints the inner syntax of the
current context. The output can be quite large; the most important
sections are explained below.
\begin{description}
- \item \isa{{\isachardoublequote}lexicon{\isachardoublequote}} lists the delimiters of the inner token
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}lexicon{\isaliteral{22}{\isachardoublequote}}} lists the delimiters of the inner token
language; see \secref{sec:inner-lex}.
- \item \isa{{\isachardoublequote}prods{\isachardoublequote}} lists the productions of the underlying
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}prods{\isaliteral{22}{\isachardoublequote}}} lists the productions of the underlying
priority grammar; see \secref{sec:priority-grammar}.
- The nonterminal \isa{{\isachardoublequote}A\isactrlsup {\isacharparenleft}\isactrlsup p\isactrlsup {\isacharparenright}{\isachardoublequote}} is rendered in plain text as \isa{{\isachardoublequote}A{\isacharbrackleft}p{\isacharbrackright}{\isachardoublequote}}; delimiters are quoted. Many productions have an extra
- \isa{{\isachardoublequote}{\isasymdots}\ {\isacharequal}{\isachargreater}\ name{\isachardoublequote}}. These names later become the heads of parse
+ The nonterminal \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7375703E}{}\isactrlsup p\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} is rendered in plain text as \isa{{\isaliteral{22}{\isachardoublequote}}A{\isaliteral{5B}{\isacharbrackleft}}p{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}; delimiters are quoted. Many productions have an extra
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ name{\isaliteral{22}{\isachardoublequote}}}. These names later become the heads of parse
trees; they also guide the pretty printer.
Productions without such parse tree names are called \emph{copy
@@ -889,19 +889,19 @@
production}. Chain productions act as abbreviations: conceptually,
they are removed from the grammar by adding new productions.
Priority information attached to chain productions is ignored; only
- the dummy value \isa{{\isachardoublequote}{\isacharminus}{\isadigit{1}}{\isachardoublequote}} is displayed.
+ the dummy value \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} is displayed.
- \item \isa{{\isachardoublequote}print\ modes{\isachardoublequote}} lists the alternative print modes
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}print\ modes{\isaliteral{22}{\isachardoublequote}}} lists the alternative print modes
provided by this grammar; see \secref{sec:print-modes}.
- \item \isa{{\isachardoublequote}parse{\isacharunderscore}rules{\isachardoublequote}} and \isa{{\isachardoublequote}print{\isacharunderscore}rules{\isachardoublequote}} relate to
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}parse{\isaliteral{5F}{\isacharunderscore}}rules{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}print{\isaliteral{5F}{\isacharunderscore}}rules{\isaliteral{22}{\isachardoublequote}}} relate to
syntax translations (macros); see \secref{sec:syn-trans}.
- \item \isa{{\isachardoublequote}parse{\isacharunderscore}ast{\isacharunderscore}translation{\isachardoublequote}} and \isa{{\isachardoublequote}print{\isacharunderscore}ast{\isacharunderscore}translation{\isachardoublequote}} list sets of constants that invoke
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}parse{\isaliteral{5F}{\isacharunderscore}}ast{\isaliteral{5F}{\isacharunderscore}}translation{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}print{\isaliteral{5F}{\isacharunderscore}}ast{\isaliteral{5F}{\isacharunderscore}}translation{\isaliteral{22}{\isachardoublequote}}} list sets of constants that invoke
translation functions for abstract syntax trees, which are only
required in very special situations; see \secref{sec:tr-funs}.
- \item \isa{{\isachardoublequote}parse{\isacharunderscore}translation{\isachardoublequote}} and \isa{{\isachardoublequote}print{\isacharunderscore}translation{\isachardoublequote}}
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}parse{\isaliteral{5F}{\isacharunderscore}}translation{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}print{\isaliteral{5F}{\isacharunderscore}}translation{\isaliteral{22}{\isachardoublequote}}}
list the sets of constants that invoke regular translation
functions; see \secref{sec:tr-funs}.
--- a/doc-src/IsarRef/Thy/document/Introduction.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarRef/Thy/document/Introduction.tex Mon Nov 08 14:41:11 2010 +0100
@@ -82,7 +82,7 @@
\medskip Isar commands may be either \emph{proper} document
constructors, or \emph{improper commands}. Some proof methods and
attributes introduced later are classified as improper as well.
- Improper Isar language elements, which are marked by ``\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}}'' in the subsequent chapters; they are often helpful
+ Improper Isar language elements, which are marked by ``\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}'' in the subsequent chapters; they are often helpful
when developing proof documents, but their use is discouraged for
the final human-readable outcome. Typical examples are diagnostic
commands that print terms or theorems according to the current
--- a/doc-src/IsarRef/Thy/document/ML_Tactic.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarRef/Thy/document/ML_Tactic.tex Mon Nov 08 14:41:11 2010 +0100
@@ -1,6 +1,6 @@
%
\begin{isabellebody}%
-\def\isabellecontext{ML{\isacharunderscore}Tactic}%
+\def\isabellecontext{ML{\isaliteral{5F}{\isacharunderscore}}Tactic}%
%
\isadelimtheory
%
@@ -8,7 +8,7 @@
%
\isatagtheory
\isacommand{theory}\isamarkupfalse%
-\ ML{\isacharunderscore}Tactic\isanewline
+\ ML{\isaliteral{5F}{\isacharunderscore}}Tactic\isanewline
\isakeyword{imports}\ Main\isanewline
\isakeyword{begin}%
\endisatagtheory
@@ -65,8 +65,8 @@
\end{enumerate}
- Basically, the set of Isar tactic emulations \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isacharunderscore}tac}}},
- \hyperlink{method.erule-tac}{\mbox{\isa{erule{\isacharunderscore}tac}}}, \hyperlink{method.drule-tac}{\mbox{\isa{drule{\isacharunderscore}tac}}}, \hyperlink{method.frule-tac}{\mbox{\isa{frule{\isacharunderscore}tac}}} (see
+ Basically, the set of Isar tactic emulations \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}tac}}},
+ \hyperlink{method.erule-tac}{\mbox{\isa{erule{\isaliteral{5F}{\isacharunderscore}}tac}}}, \hyperlink{method.drule-tac}{\mbox{\isa{drule{\isaliteral{5F}{\isacharunderscore}}tac}}}, \hyperlink{method.frule-tac}{\mbox{\isa{frule{\isaliteral{5F}{\isacharunderscore}}tac}}} (see
\secref{sec:tactics}) would be sufficient to cover the four modes,
either with or without instantiation, and either with single or
multiple arguments. Although it is more convenient in most cases to
@@ -74,21 +74,21 @@
\secref{sec:pure-meth-att}), or any of its ``improper'' variants
\hyperlink{method.erule}{\mbox{\isa{erule}}}, \hyperlink{method.drule}{\mbox{\isa{drule}}}, \hyperlink{method.frule}{\mbox{\isa{frule}}} (see
\secref{sec:misc-meth-att}). Note that explicit goal addressing is
- only supported by the actual \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isacharunderscore}tac}}} version.
+ only supported by the actual \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}tac}}} version.
With this in mind, plain resolution tactics correspond to Isar
methods as follows.
\medskip
\begin{tabular}{lll}
- \verb|rtac|~\isa{{\isachardoublequote}a\ {\isadigit{1}}{\isachardoublequote}} & & \isa{{\isachardoublequote}rule\ a{\isachardoublequote}} \\
- \verb|resolve_tac|~\isa{{\isachardoublequote}{\isacharbrackleft}a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}\ {\isadigit{1}}{\isachardoublequote}} & & \isa{{\isachardoublequote}rule\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}{\isachardoublequote}} \\
- \verb|res_inst_tac|~\isa{{\isachardoublequote}ctxt\ {\isacharbrackleft}{\isacharparenleft}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ t\isactrlsub {\isadigit{1}}{\isacharparenright}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}\ a\ {\isadigit{1}}{\isachardoublequote}} & &
- \isa{{\isachardoublequote}rule{\isacharunderscore}tac\ x\isactrlsub {\isadigit{1}}\ {\isacharequal}\ t\isactrlsub {\isadigit{1}}\ {\isasymAND}\ {\isasymdots}\ {\isasymIN}\ a{\isachardoublequote}} \\[0.5ex]
- \verb|rtac|~\isa{{\isachardoublequote}a\ i{\isachardoublequote}} & & \isa{{\isachardoublequote}rule{\isacharunderscore}tac\ {\isacharbrackleft}i{\isacharbrackright}\ a{\isachardoublequote}} \\
- \verb|resolve_tac|~\isa{{\isachardoublequote}{\isacharbrackleft}a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}\ i{\isachardoublequote}} & & \isa{{\isachardoublequote}rule{\isacharunderscore}tac\ {\isacharbrackleft}i{\isacharbrackright}\ a\isactrlsub {\isadigit{1}}\ {\isasymdots}{\isachardoublequote}} \\
- \verb|res_inst_tac|~\isa{{\isachardoublequote}ctxt\ {\isacharbrackleft}{\isacharparenleft}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ t\isactrlsub {\isadigit{1}}{\isacharparenright}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}\ a\ i{\isachardoublequote}} & &
- \isa{{\isachardoublequote}rule{\isacharunderscore}tac\ {\isacharbrackleft}i{\isacharbrackright}\ x\isactrlsub {\isadigit{1}}\ {\isacharequal}\ t\isactrlsub {\isadigit{1}}\ {\isasymAND}\ {\isasymdots}\ {\isasymIN}\ a{\isachardoublequote}} \\
+ \verb|rtac|~\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}rule\ a{\isaliteral{22}{\isachardoublequote}}} \\
+ \verb|resolve_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5D}{\isacharbrackright}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}rule\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \verb|res_inst_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}ctxt\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5D}{\isacharbrackright}}\ a\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & &
+ \isa{{\isaliteral{22}{\isachardoublequote}}rule{\isaliteral{5F}{\isacharunderscore}}tac\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C494E3E}{\isasymIN}}\ a{\isaliteral{22}{\isachardoublequote}}} \\[0.5ex]
+ \verb|rtac|~\isa{{\isaliteral{22}{\isachardoublequote}}a\ i{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}rule{\isaliteral{5F}{\isacharunderscore}}tac\ {\isaliteral{5B}{\isacharbrackleft}}i{\isaliteral{5D}{\isacharbrackright}}\ a{\isaliteral{22}{\isachardoublequote}}} \\
+ \verb|resolve_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5D}{\isacharbrackright}}\ i{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}rule{\isaliteral{5F}{\isacharunderscore}}tac\ {\isaliteral{5B}{\isacharbrackleft}}i{\isaliteral{5D}{\isacharbrackright}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \verb|res_inst_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}ctxt\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5D}{\isacharbrackright}}\ a\ i{\isaliteral{22}{\isachardoublequote}}} & &
+ \isa{{\isaliteral{22}{\isachardoublequote}}rule{\isaliteral{5F}{\isacharunderscore}}tac\ {\isaliteral{5B}{\isacharbrackleft}}i{\isaliteral{5D}{\isacharbrackright}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C494E3E}{\isasymIN}}\ a{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}
\medskip
@@ -104,19 +104,19 @@
\begin{isamarkuptext}%
The main Simplifier tactics \verb|simp_tac| and variants (cf.\
\cite{isabelle-ref}) are all covered by the \hyperlink{method.simp}{\mbox{\isa{simp}}} and
- \hyperlink{method.simp-all}{\mbox{\isa{simp{\isacharunderscore}all}}} methods (see \secref{sec:simplifier}). Note that
+ \hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}} methods (see \secref{sec:simplifier}). Note that
there is no individual goal addressing available, simplification
acts either on the first goal (\hyperlink{method.simp}{\mbox{\isa{simp}}}) or all goals
- (\hyperlink{method.simp-all}{\mbox{\isa{simp{\isacharunderscore}all}}}).
+ (\hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}}).
\medskip
\begin{tabular}{lll}
- \verb|asm_full_simp_tac|~\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}simpset{\isacharbraceright}\ {\isadigit{1}}{\isachardoublequote}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}} \\
- \verb|ALLGOALS|~(\verb|asm_full_simp_tac|~\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}simpset{\isacharbraceright}{\isachardoublequote}}) & & \hyperlink{method.simp-all}{\mbox{\isa{simp{\isacharunderscore}all}}} \\[0.5ex]
- \verb|simp_tac|~\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}simpset{\isacharbraceright}\ {\isadigit{1}}{\isachardoublequote}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}}~\isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharparenright}{\isachardoublequote}} \\
- \verb|asm_simp_tac|~\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}simpset{\isacharbraceright}\ {\isadigit{1}}{\isachardoublequote}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}}~\isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharunderscore}simp{\isacharparenright}{\isachardoublequote}} \\
- \verb|full_simp_tac|~\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}simpset{\isacharbraceright}\ {\isadigit{1}}{\isachardoublequote}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}}~\isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}asm{\isacharunderscore}use{\isacharparenright}{\isachardoublequote}} \\
- \verb|asm_lr_simp_tac|~\isa{{\isachardoublequote}{\isacharat}{\isacharbraceleft}simpset{\isacharbraceright}\ {\isadigit{1}}{\isachardoublequote}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}}~\isa{{\isachardoublequote}{\isacharparenleft}asm{\isacharunderscore}lr{\isacharparenright}{\isachardoublequote}} \\
+ \verb|asm_full_simp_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}simpset{\isaliteral{7D}{\isacharbraceright}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}} \\
+ \verb|ALLGOALS|~(\verb|asm_full_simp_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}simpset{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}}) & & \hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}} \\[0.5ex]
+ \verb|simp_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}simpset{\isaliteral{7D}{\isacharbraceright}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \verb|asm_simp_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}simpset{\isaliteral{7D}{\isacharbraceright}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \verb|full_simp_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}simpset{\isaliteral{7D}{\isacharbraceright}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{5F}{\isacharunderscore}}use{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \verb|asm_lr_simp_tac|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{40}{\isacharat}}{\isaliteral{7B}{\isacharbraceleft}}simpset{\isaliteral{7D}{\isacharbraceright}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & & \hyperlink{method.simp}{\mbox{\isa{simp}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}asm{\isaliteral{5F}{\isacharunderscore}}lr{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}
\medskip%
\end{isamarkuptext}%
@@ -145,12 +145,12 @@
\medskip
\begin{tabular}{lll}
- \verb|stac|~\isa{{\isachardoublequote}a\ {\isadigit{1}}{\isachardoublequote}} & & \isa{{\isachardoublequote}subst\ a{\isachardoublequote}} \\
+ \verb|stac|~\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}subst\ a{\isaliteral{22}{\isachardoublequote}}} \\
\verb|hyp_subst_tac|~\isa{{\isadigit{1}}} & & \isa{hypsubst} \\
- \verb|strip_tac|~\isa{{\isadigit{1}}} & \isa{{\isachardoublequote}{\isasymapprox}{\isachardoublequote}} & \isa{{\isachardoublequote}intro\ strip{\isachardoublequote}} \\
- \verb|split_all_tac|~\isa{{\isadigit{1}}} & & \isa{{\isachardoublequote}simp\ {\isacharparenleft}no{\isacharunderscore}asm{\isacharunderscore}simp{\isacharparenright}\ only{\isacharcolon}\ split{\isacharunderscore}tupled{\isacharunderscore}all{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isasymapprox}{\isachardoublequote}} & \isa{{\isachardoublequote}simp\ only{\isacharcolon}\ split{\isacharunderscore}tupled{\isacharunderscore}all{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isasymlless}{\isachardoublequote}} & \isa{{\isachardoublequote}clarify{\isachardoublequote}} \\
+ \verb|strip_tac|~\isa{{\isadigit{1}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}intro\ strip{\isaliteral{22}{\isachardoublequote}}} \\
+ \verb|split_all_tac|~\isa{{\isadigit{1}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}simp\ {\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{29}{\isacharparenright}}\ only{\isaliteral{3A}{\isacharcolon}}\ split{\isaliteral{5F}{\isacharunderscore}}tupled{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}simp\ only{\isaliteral{3A}{\isacharcolon}}\ split{\isaliteral{5F}{\isacharunderscore}}tupled{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C6C6573733E}{\isasymlless}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}clarify{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -162,8 +162,8 @@
\begin{isamarkuptext}%
Classic Isabelle provides a huge amount of tacticals for combination
and modification of existing tactics. This has been greatly reduced
- in Isar, providing the bare minimum of combinators only: ``\isa{{\isachardoublequote}{\isacharcomma}{\isachardoublequote}}'' (sequential composition), ``\isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}}'' (alternative
- choices), ``\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}'' (try), ``\isa{{\isachardoublequote}{\isacharplus}{\isachardoublequote}}'' (repeat at least
+ in Isar, providing the bare minimum of combinators only: ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}}'' (sequential composition), ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}}'' (alternative
+ choices), ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}'' (try), ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequote}}}'' (repeat at least
once). These are usually sufficient in practice; if all fails,
arbitrary ML tactic code may be invoked via the \hyperlink{method.tactic}{\mbox{\isa{tactic}}}
method (see \secref{sec:tactics}).
@@ -173,27 +173,27 @@
\medskip
\begin{tabular}{lll}
- \isa{{\isachardoublequote}tac\isactrlsub {\isadigit{1}}{\isachardoublequote}}~\verb|THEN|~\isa{{\isachardoublequote}tac\isactrlsub {\isadigit{2}}{\isachardoublequote}} & & \isa{{\isachardoublequote}meth\isactrlsub {\isadigit{1}}{\isacharcomma}\ meth\isactrlsub {\isadigit{2}}{\isachardoublequote}} \\
- \isa{{\isachardoublequote}tac\isactrlsub {\isadigit{1}}{\isachardoublequote}}~\verb|ORELSE|~\isa{{\isachardoublequote}tac\isactrlsub {\isadigit{2}}{\isachardoublequote}} & & \isa{{\isachardoublequote}meth\isactrlsub {\isadigit{1}}\ {\isacharbar}\ meth\isactrlsub {\isadigit{2}}{\isachardoublequote}} \\
- \verb|TRY|~\isa{tac} & & \isa{{\isachardoublequote}meth{\isacharquery}{\isachardoublequote}} \\
- \verb|REPEAT1|~\isa{tac} & & \isa{{\isachardoublequote}meth{\isacharplus}{\isachardoublequote}} \\
- \verb|REPEAT|~\isa{tac} & & \isa{{\isachardoublequote}{\isacharparenleft}meth{\isacharplus}{\isacharparenright}{\isacharquery}{\isachardoublequote}} \\
- \verb|EVERY|~\isa{{\isachardoublequote}{\isacharbrackleft}tac\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}{\isachardoublequote}} & & \isa{{\isachardoublequote}meth\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isachardoublequote}} \\
- \verb|FIRST|~\isa{{\isachardoublequote}{\isacharbrackleft}tac\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharbrackright}{\isachardoublequote}} & & \isa{{\isachardoublequote}meth\isactrlsub {\isadigit{1}}\ {\isacharbar}\ {\isasymdots}{\isachardoublequote}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}tac\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}~\verb|THEN|~\isa{{\isaliteral{22}{\isachardoublequote}}tac\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}meth\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ meth\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}tac\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}~\verb|ORELSE|~\isa{{\isaliteral{22}{\isachardoublequote}}tac\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}meth\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{7C}{\isacharbar}}\ meth\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \verb|TRY|~\isa{tac} & & \isa{{\isaliteral{22}{\isachardoublequote}}meth{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \verb|REPEAT1|~\isa{tac} & & \isa{{\isaliteral{22}{\isachardoublequote}}meth{\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \verb|REPEAT|~\isa{tac} & & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}meth{\isaliteral{2B}{\isacharplus}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \verb|EVERY|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}tac\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}meth\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \verb|FIRST|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}tac\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}meth\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}
\medskip
\medskip \verb|CHANGED| (see \cite{isabelle-ref}) is usually not
required in Isar, since most basic proof methods already fail unless
- there is an actual change in the goal state. Nevertheless, ``\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}'' (try) may be used to accept \emph{unchanged} results as
+ there is an actual change in the goal state. Nevertheless, ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}'' (try) may be used to accept \emph{unchanged} results as
well.
\medskip \verb|ALLGOALS|, \verb|SOMEGOAL| etc.\ (see
\cite{isabelle-ref}) are not available in Isar, since there is no
direct goal addressing. Nevertheless, some basic methods address
- all goals internally, notably \hyperlink{method.simp-all}{\mbox{\isa{simp{\isacharunderscore}all}}} (see
+ all goals internally, notably \hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}} (see
\secref{sec:simplifier}). Also note that \verb|ALLGOALS| can be
- often replaced by ``\isa{{\isachardoublequote}{\isacharplus}{\isachardoublequote}}'' (repeat at least once), although
+ often replaced by ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequote}}}'' (repeat at least once), although
this usually has a different operational behavior, such as solving
goals in a different order.
--- a/doc-src/IsarRef/Thy/document/Misc.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarRef/Thy/document/Misc.tex Mon Nov 08 14:41:11 2010 +0100
@@ -28,16 +28,16 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{print\_commands}\hypertarget{command.print-commands}{\hyperlink{command.print-commands}{\mbox{\isa{\isacommand{print{\isacharunderscore}commands}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}any\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{print\_theory}\hypertarget{command.print-theory}{\hyperlink{command.print-theory}{\mbox{\isa{\isacommand{print{\isacharunderscore}theory}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{print\_methods}\hypertarget{command.print-methods}{\hyperlink{command.print-methods}{\mbox{\isa{\isacommand{print{\isacharunderscore}methods}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{print\_attributes}\hypertarget{command.print-attributes}{\hyperlink{command.print-attributes}{\mbox{\isa{\isacommand{print{\isacharunderscore}attributes}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{print\_theorems}\hypertarget{command.print-theorems}{\hyperlink{command.print-theorems}{\mbox{\isa{\isacommand{print{\isacharunderscore}theorems}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{find\_theorems}\hypertarget{command.find-theorems}{\hyperlink{command.find-theorems}{\mbox{\isa{\isacommand{find{\isacharunderscore}theorems}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{find\_consts}\hypertarget{command.find-consts}{\hyperlink{command.find-consts}{\mbox{\isa{\isacommand{find{\isacharunderscore}consts}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{thm\_deps}\hypertarget{command.thm-deps}{\hyperlink{command.thm-deps}{\mbox{\isa{\isacommand{thm{\isacharunderscore}deps}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{print\_facts}\hypertarget{command.print-facts}{\hyperlink{command.print-facts}{\mbox{\isa{\isacommand{print{\isacharunderscore}facts}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{print\_binds}\hypertarget{command.print-binds}{\hyperlink{command.print-binds}{\mbox{\isa{\isacommand{print{\isacharunderscore}binds}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{}{command}{print\_commands}\hypertarget{command.print-commands}{\hyperlink{command.print-commands}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}commands}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}any\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_theory}\hypertarget{command.print-theory}{\hyperlink{command.print-theory}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}theory}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_methods}\hypertarget{command.print-methods}{\hyperlink{command.print-methods}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}methods}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_attributes}\hypertarget{command.print-attributes}{\hyperlink{command.print-attributes}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}attributes}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_theorems}\hypertarget{command.print-theorems}{\hyperlink{command.print-theorems}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}theorems}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{find\_theorems}\hypertarget{command.find-theorems}{\hyperlink{command.find-theorems}{\mbox{\isa{\isacommand{find{\isaliteral{5F}{\isacharunderscore}}theorems}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{find\_consts}\hypertarget{command.find-consts}{\hyperlink{command.find-consts}{\mbox{\isa{\isacommand{find{\isaliteral{5F}{\isacharunderscore}}consts}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{thm\_deps}\hypertarget{command.thm-deps}{\hyperlink{command.thm-deps}{\mbox{\isa{\isacommand{thm{\isaliteral{5F}{\isacharunderscore}}deps}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_facts}\hypertarget{command.print-facts}{\hyperlink{command.print-facts}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}facts}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_binds}\hypertarget{command.print-binds}{\hyperlink{command.print-binds}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}binds}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -63,59 +63,59 @@
\begin{description}
- \item \hyperlink{command.print-commands}{\mbox{\isa{\isacommand{print{\isacharunderscore}commands}}}} prints Isabelle's outer theory
+ \item \hyperlink{command.print-commands}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}commands}}}} prints Isabelle's outer theory
syntax, including keywords and command.
- \item \hyperlink{command.print-theory}{\mbox{\isa{\isacommand{print{\isacharunderscore}theory}}}} prints the main logical content of
- the theory context; the ``\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}'' option indicates extra
+ \item \hyperlink{command.print-theory}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}theory}}}} prints the main logical content of
+ the theory context; the ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}}'' option indicates extra
verbosity.
- \item \hyperlink{command.print-methods}{\mbox{\isa{\isacommand{print{\isacharunderscore}methods}}}} prints all proof methods
+ \item \hyperlink{command.print-methods}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}methods}}}} prints all proof methods
available in the current theory context.
- \item \hyperlink{command.print-attributes}{\mbox{\isa{\isacommand{print{\isacharunderscore}attributes}}}} prints all attributes
+ \item \hyperlink{command.print-attributes}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}attributes}}}} prints all attributes
available in the current theory context.
- \item \hyperlink{command.print-theorems}{\mbox{\isa{\isacommand{print{\isacharunderscore}theorems}}}} prints theorems resulting from the
- last command; the ``\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}'' option indicates extra verbosity.
+ \item \hyperlink{command.print-theorems}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}theorems}}}} prints theorems resulting from the
+ last command; the ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}}'' option indicates extra verbosity.
- \item \hyperlink{command.find-theorems}{\mbox{\isa{\isacommand{find{\isacharunderscore}theorems}}}}~\isa{criteria} retrieves facts
+ \item \hyperlink{command.find-theorems}{\mbox{\isa{\isacommand{find{\isaliteral{5F}{\isacharunderscore}}theorems}}}}~\isa{criteria} retrieves facts
from the theory or proof context matching all of given search
- criteria. The criterion \isa{{\isachardoublequote}name{\isacharcolon}\ p{\isachardoublequote}} selects all theorems
+ criteria. The criterion \isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{3A}{\isacharcolon}}\ p{\isaliteral{22}{\isachardoublequote}}} selects all theorems
whose fully qualified name matches pattern \isa{p}, which may
- contain ``\isa{{\isachardoublequote}{\isacharasterisk}{\isachardoublequote}}'' wildcards. The criteria \isa{intro},
+ contain ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}'' wildcards. The criteria \isa{intro},
\isa{elim}, and \isa{dest} select theorems that match the
current goal as introduction, elimination or destruction rules,
- respectively. The criterion \isa{{\isachardoublequote}solves{\isachardoublequote}} returns all rules
+ respectively. The criterion \isa{{\isaliteral{22}{\isachardoublequote}}solves{\isaliteral{22}{\isachardoublequote}}} returns all rules
that would directly solve the current goal. The criterion
- \isa{{\isachardoublequote}simp{\isacharcolon}\ t{\isachardoublequote}} selects all rewrite rules whose left-hand side
+ \isa{{\isaliteral{22}{\isachardoublequote}}simp{\isaliteral{3A}{\isacharcolon}}\ t{\isaliteral{22}{\isachardoublequote}}} selects all rewrite rules whose left-hand side
matches the given term. The criterion term \isa{t} selects all
theorems that contain the pattern \isa{t} -- as usual, patterns
- may contain occurrences of the dummy ``\isa{{\isacharunderscore}}'', schematic
+ may contain occurrences of the dummy ``\isa{{\isaliteral{5F}{\isacharunderscore}}}'', schematic
variables, and type constraints.
- Criteria can be preceded by ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' to select theorems that
+ Criteria can be preceded by ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{22}{\isachardoublequote}}}'' to select theorems that
do \emph{not} match. Note that giving the empty list of criteria
yields \emph{all} currently known facts. An optional limit for the
number of printed facts may be given; the default is 40. By
default, duplicates are removed from the search result. Use
- \isa{with{\isacharunderscore}dups} to display duplicates.
+ \isa{with{\isaliteral{5F}{\isacharunderscore}}dups} to display duplicates.
- \item \hyperlink{command.find-consts}{\mbox{\isa{\isacommand{find{\isacharunderscore}consts}}}}~\isa{criteria} prints all constants
- whose type meets all of the given criteria. The criterion \isa{{\isachardoublequote}strict{\isacharcolon}\ ty{\isachardoublequote}} is met by any type that matches the type pattern
- \isa{ty}. Patterns may contain both the dummy type ``\isa{{\isacharunderscore}}''
+ \item \hyperlink{command.find-consts}{\mbox{\isa{\isacommand{find{\isaliteral{5F}{\isacharunderscore}}consts}}}}~\isa{criteria} prints all constants
+ whose type meets all of the given criteria. The criterion \isa{{\isaliteral{22}{\isachardoublequote}}strict{\isaliteral{3A}{\isacharcolon}}\ ty{\isaliteral{22}{\isachardoublequote}}} is met by any type that matches the type pattern
+ \isa{ty}. Patterns may contain both the dummy type ``\isa{{\isaliteral{5F}{\isacharunderscore}}}''
and sort constraints. The criterion \isa{ty} is similar, but it
- also matches against subtypes. The criterion \isa{{\isachardoublequote}name{\isacharcolon}\ p{\isachardoublequote}} and
- the prefix ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' function as described for \hyperlink{command.find-theorems}{\mbox{\isa{\isacommand{find{\isacharunderscore}theorems}}}}.
+ also matches against subtypes. The criterion \isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{3A}{\isacharcolon}}\ p{\isaliteral{22}{\isachardoublequote}}} and
+ the prefix ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{22}{\isachardoublequote}}}'' function as described for \hyperlink{command.find-theorems}{\mbox{\isa{\isacommand{find{\isaliteral{5F}{\isacharunderscore}}theorems}}}}.
- \item \hyperlink{command.thm-deps}{\mbox{\isa{\isacommand{thm{\isacharunderscore}deps}}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}}
+ \item \hyperlink{command.thm-deps}{\mbox{\isa{\isacommand{thm{\isaliteral{5F}{\isacharunderscore}}deps}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}
visualizes dependencies of facts, using Isabelle's graph browser
tool (see also \cite{isabelle-sys}).
- \item \hyperlink{command.print-facts}{\mbox{\isa{\isacommand{print{\isacharunderscore}facts}}}} prints all local facts of the
+ \item \hyperlink{command.print-facts}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}facts}}}} prints all local facts of the
current context, both named and unnamed ones.
- \item \hyperlink{command.print-binds}{\mbox{\isa{\isacommand{print{\isacharunderscore}binds}}}} prints all term abbreviations
+ \item \hyperlink{command.print-binds}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}binds}}}} prints all term abbreviations
present in the context.
\end{description}%
@@ -128,9 +128,9 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{undo}\hypertarget{command.undo}{\hyperlink{command.undo}{\mbox{\isa{\isacommand{undo}}}}}^{{ * }{ * }} & : & \isa{{\isachardoublequote}any\ {\isasymrightarrow}\ any{\isachardoublequote}} \\
- \indexdef{}{command}{linear\_undo}\hypertarget{command.linear-undo}{\hyperlink{command.linear-undo}{\mbox{\isa{\isacommand{linear{\isacharunderscore}undo}}}}}^{{ * }{ * }} & : & \isa{{\isachardoublequote}any\ {\isasymrightarrow}\ any{\isachardoublequote}} \\
- \indexdef{}{command}{kill}\hypertarget{command.kill}{\hyperlink{command.kill}{\mbox{\isa{\isacommand{kill}}}}}^{{ * }{ * }} & : & \isa{{\isachardoublequote}any\ {\isasymrightarrow}\ any{\isachardoublequote}} \\
+ \indexdef{}{command}{undo}\hypertarget{command.undo}{\hyperlink{command.undo}{\mbox{\isa{\isacommand{undo}}}}}^{{ * }{ * }} & : & \isa{{\isaliteral{22}{\isachardoublequote}}any\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ any{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{linear\_undo}\hypertarget{command.linear-undo}{\hyperlink{command.linear-undo}{\mbox{\isa{\isacommand{linear{\isaliteral{5F}{\isacharunderscore}}undo}}}}}^{{ * }{ * }} & : & \isa{{\isaliteral{22}{\isachardoublequote}}any\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ any{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{kill}\hypertarget{command.kill}{\hyperlink{command.kill}{\mbox{\isa{\isacommand{kill}}}}}^{{ * }{ * }} & : & \isa{{\isaliteral{22}{\isachardoublequote}}any\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ any{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
The Isabelle/Isar top-level maintains a two-stage history, for
@@ -138,7 +138,7 @@
be undone using \hyperlink{command.undo}{\mbox{\isa{\isacommand{undo}}}}, excluding mere diagnostic
elements. Note that a theorem statement with a \emph{finished}
proof is treated as a single unit by \hyperlink{command.undo}{\mbox{\isa{\isacommand{undo}}}}. In
- contrast, the variant \hyperlink{command.linear-undo}{\mbox{\isa{\isacommand{linear{\isacharunderscore}undo}}}} admits to step back
+ contrast, the variant \hyperlink{command.linear-undo}{\mbox{\isa{\isacommand{linear{\isaliteral{5F}{\isacharunderscore}}undo}}}} admits to step back
into the middle of a proof. The \hyperlink{command.kill}{\mbox{\isa{\isacommand{kill}}}} command aborts
the current history node altogether, discontinuing a proof or even
the whole theory. This operation is \emph{not} undo-able.
@@ -147,7 +147,7 @@
History commands should never be used with user interfaces such as
Proof~General \cite{proofgeneral,Aspinall:TACAS:2000}, which takes
care of stepping forth and back itself. Interfering by manual
- \hyperlink{command.undo}{\mbox{\isa{\isacommand{undo}}}}, \hyperlink{command.linear-undo}{\mbox{\isa{\isacommand{linear{\isacharunderscore}undo}}}}, or even \hyperlink{command.kill}{\mbox{\isa{\isacommand{kill}}}} commands would quickly result in utter confusion.
+ \hyperlink{command.undo}{\mbox{\isa{\isacommand{undo}}}}, \hyperlink{command.linear-undo}{\mbox{\isa{\isacommand{linear{\isaliteral{5F}{\isacharunderscore}}undo}}}}, or even \hyperlink{command.kill}{\mbox{\isa{\isacommand{kill}}}} commands would quickly result in utter confusion.
\end{warn}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -158,9 +158,9 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{cd}\hypertarget{command.cd}{\hyperlink{command.cd}{\mbox{\isa{\isacommand{cd}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}any\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{pwd}\hypertarget{command.pwd}{\hyperlink{command.pwd}{\mbox{\isa{\isacommand{pwd}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}any\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{use\_thy}\hypertarget{command.use-thy}{\hyperlink{command.use-thy}{\mbox{\isa{\isacommand{use{\isacharunderscore}thy}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}any\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{}{command}{cd}\hypertarget{command.cd}{\hyperlink{command.cd}{\mbox{\isa{\isacommand{cd}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}any\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{pwd}\hypertarget{command.pwd}{\hyperlink{command.pwd}{\mbox{\isa{\isacommand{pwd}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}any\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{use\_thy}\hypertarget{command.use-thy}{\hyperlink{command.use-thy}{\mbox{\isa{\isacommand{use{\isaliteral{5F}{\isacharunderscore}}thy}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}any\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -175,7 +175,7 @@
\item \hyperlink{command.pwd}{\mbox{\isa{\isacommand{pwd}}}} prints the current working directory.
- \item \hyperlink{command.use-thy}{\mbox{\isa{\isacommand{use{\isacharunderscore}thy}}}}~\isa{A} preload theory \isa{A}.
+ \item \hyperlink{command.use-thy}{\mbox{\isa{\isacommand{use{\isaliteral{5F}{\isacharunderscore}}thy}}}}~\isa{A} preload theory \isa{A}.
These system commands are scarcely used when working interactively,
since loading of theories is done automatically as required.
--- a/doc-src/IsarRef/Thy/document/Outer_Syntax.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarRef/Thy/document/Outer_Syntax.tex Mon Nov 08 14:41:11 2010 +0100
@@ -1,6 +1,6 @@
%
\begin{isabellebody}%
-\def\isabellecontext{Outer{\isacharunderscore}Syntax}%
+\def\isabellecontext{Outer{\isaliteral{5F}{\isacharunderscore}}Syntax}%
%
\isadelimtheory
%
@@ -8,7 +8,7 @@
%
\isatagtheory
\isacommand{theory}\isamarkupfalse%
-\ Outer{\isacharunderscore}Syntax\isanewline
+\ Outer{\isaliteral{5F}{\isacharunderscore}}Syntax\isanewline
\isakeyword{imports}\ Main\isanewline
\isakeyword{begin}%
\endisatagtheory
@@ -123,42 +123,42 @@
\begin{center}
\begin{supertabular}{rcl}
- \indexdef{}{syntax}{ident}\hypertarget{syntax.ident}{\hyperlink{syntax.ident}{\mbox{\isa{ident}}}} & = & \isa{{\isachardoublequote}letter\ quasiletter\isactrlsup {\isacharasterisk}{\isachardoublequote}} \\
- \indexdef{}{syntax}{longident}\hypertarget{syntax.longident}{\hyperlink{syntax.longident}{\mbox{\isa{longident}}}} & = & \isa{{\isachardoublequote}ident{\isacharparenleft}{\isachardoublequote}}\verb|.|\isa{{\isachardoublequote}ident{\isacharparenright}\isactrlsup {\isacharplus}{\isachardoublequote}} \\
- \indexdef{}{syntax}{symident}\hypertarget{syntax.symident}{\hyperlink{syntax.symident}{\mbox{\isa{symident}}}} & = & \isa{{\isachardoublequote}sym\isactrlsup {\isacharplus}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\|\verb|<|\isa{ident}\verb|>| \\
- \indexdef{}{syntax}{nat}\hypertarget{syntax.nat}{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}} & = & \isa{{\isachardoublequote}digit\isactrlsup {\isacharplus}{\isachardoublequote}} \\
- \indexdef{}{syntax}{float}\hypertarget{syntax.float}{\hyperlink{syntax.float}{\mbox{\isa{float}}}} & = & \indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}}\verb|.|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}}\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|-|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}}\verb|.|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}} \\
- \indexdef{}{syntax}{var}\hypertarget{syntax.var}{\hyperlink{syntax.var}{\mbox{\isa{var}}}} & = & \verb|?|\isa{{\isachardoublequote}ident\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|?|\isa{ident}\verb|.|\isa{nat} \\
+ \indexdef{}{syntax}{ident}\hypertarget{syntax.ident}{\hyperlink{syntax.ident}{\mbox{\isa{ident}}}} & = & \isa{{\isaliteral{22}{\isachardoublequote}}letter\ quasiletter\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{syntax}{longident}\hypertarget{syntax.longident}{\hyperlink{syntax.longident}{\mbox{\isa{longident}}}} & = & \isa{{\isaliteral{22}{\isachardoublequote}}ident{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}}\verb|.|\isa{{\isaliteral{22}{\isachardoublequote}}ident{\isaliteral{29}{\isacharparenright}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{syntax}{symident}\hypertarget{syntax.symident}{\hyperlink{syntax.symident}{\mbox{\isa{symident}}}} & = & \isa{{\isaliteral{22}{\isachardoublequote}}sym\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2B}{\isacharplus}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\|\verb|<|\isa{ident}\verb|>| \\
+ \indexdef{}{syntax}{nat}\hypertarget{syntax.nat}{\hyperlink{syntax.nat}{\mbox{\isa{nat}}}} & = & \isa{{\isaliteral{22}{\isachardoublequote}}digit\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{syntax}{float}\hypertarget{syntax.float}{\hyperlink{syntax.float}{\mbox{\isa{float}}}} & = & \indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}}\verb|.|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}}\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|-|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}}\verb|.|\indexref{}{syntax}{nat}\hyperlink{syntax.nat}{\mbox{\isa{nat}}} \\
+ \indexdef{}{syntax}{var}\hypertarget{syntax.var}{\hyperlink{syntax.var}{\mbox{\isa{var}}}} & = & \verb|?|\isa{{\isaliteral{22}{\isachardoublequote}}ident\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|?|\isa{ident}\verb|.|\isa{nat} \\
\indexdef{}{syntax}{typefree}\hypertarget{syntax.typefree}{\hyperlink{syntax.typefree}{\mbox{\isa{typefree}}}} & = & \verb|'|\isa{ident} \\
- \indexdef{}{syntax}{typevar}\hypertarget{syntax.typevar}{\hyperlink{syntax.typevar}{\mbox{\isa{typevar}}}} & = & \verb|?|\isa{{\isachardoublequote}typefree\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|?|\isa{typefree}\verb|.|\isa{nat} \\
- \indexdef{}{syntax}{string}\hypertarget{syntax.string}{\hyperlink{syntax.string}{\mbox{\isa{string}}}} & = & \verb|"| \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} \verb|"| \\
- \indexdef{}{syntax}{altstring}\hypertarget{syntax.altstring}{\hyperlink{syntax.altstring}{\mbox{\isa{altstring}}}} & = & \verb|`| \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} \verb|`| \\
- \indexdef{}{syntax}{verbatim}\hypertarget{syntax.verbatim}{\hyperlink{syntax.verbatim}{\mbox{\isa{verbatim}}}} & = & \verb|{*| \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} \verb|*|\verb|}| \\[1ex]
+ \indexdef{}{syntax}{typevar}\hypertarget{syntax.typevar}{\hyperlink{syntax.typevar}{\mbox{\isa{typevar}}}} & = & \verb|?|\isa{{\isaliteral{22}{\isachardoublequote}}typefree\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|?|\isa{typefree}\verb|.|\isa{nat} \\
+ \indexdef{}{syntax}{string}\hypertarget{syntax.string}{\hyperlink{syntax.string}{\mbox{\isa{string}}}} & = & \verb|"| \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \verb|"| \\
+ \indexdef{}{syntax}{altstring}\hypertarget{syntax.altstring}{\hyperlink{syntax.altstring}{\mbox{\isa{altstring}}}} & = & \verb|`| \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \verb|`| \\
+ \indexdef{}{syntax}{verbatim}\hypertarget{syntax.verbatim}{\hyperlink{syntax.verbatim}{\mbox{\isa{verbatim}}}} & = & \verb|{*| \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \verb|*|\verb|}| \\[1ex]
- \isa{letter} & = & \isa{{\isachardoublequote}latin\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\|\verb|<|\isa{latin}\verb|>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\|\verb|<|\isa{{\isachardoublequote}latin\ latin{\isachardoublequote}}\verb|>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ greek\ \ {\isacharbar}{\isachardoublequote}} \\
- & & \verb|\<^isub>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<^isup>| \\
- \isa{quasiletter} & = & \isa{{\isachardoublequote}letter\ \ {\isacharbar}\ \ digit\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|_|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|'| \\
- \isa{latin} & = & \verb|a|\isa{{\isachardoublequote}\ \ {\isacharbar}\ {\isasymdots}\ {\isacharbar}\ \ {\isachardoublequote}}\verb|z|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|A|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isasymdots}\ {\isacharbar}\ \ {\isachardoublequote}}\verb|Z| \\
- \isa{digit} & = & \verb|0|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isasymdots}\ {\isacharbar}\ \ {\isachardoublequote}}\verb|9| \\
- \isa{sym} & = & \verb|!|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|#|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|$|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|%|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|&|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|*|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|+|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|-|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|/|\isa{{\isachardoublequote}\ \ {\isacharbar}{\isachardoublequote}} \\
- & & \verb|<|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|=|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|?|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|@|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|^|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|_|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb||\verb,|,\verb||\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|~| \\
- \isa{greek} & = & \verb|\<alpha>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<beta>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<gamma>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<delta>|\isa{{\isachardoublequote}\ \ {\isacharbar}{\isachardoublequote}} \\
- & & \verb|\<epsilon>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<zeta>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<eta>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<theta>|\isa{{\isachardoublequote}\ \ {\isacharbar}{\isachardoublequote}} \\
- & & \verb|\<iota>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<kappa>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<mu>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<nu>|\isa{{\isachardoublequote}\ \ {\isacharbar}{\isachardoublequote}} \\
- & & \verb|\<xi>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<pi>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<rho>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<sigma>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<tau>|\isa{{\isachardoublequote}\ \ {\isacharbar}{\isachardoublequote}} \\
- & & \verb|\<upsilon>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<phi>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<chi>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<psi>|\isa{{\isachardoublequote}\ \ {\isacharbar}{\isachardoublequote}} \\
- & & \verb|\<omega>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<Gamma>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<Delta>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<Theta>|\isa{{\isachardoublequote}\ \ {\isacharbar}{\isachardoublequote}} \\
- & & \verb|\<Lambda>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<Xi>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<Pi>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<Sigma>|\isa{{\isachardoublequote}\ \ {\isacharbar}{\isachardoublequote}} \\
- & & \verb|\<Upsilon>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<Phi>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<Psi>|\isa{{\isachardoublequote}\ \ {\isacharbar}\ \ {\isachardoublequote}}\verb|\<Omega>| \\
+ \isa{letter} & = & \isa{{\isaliteral{22}{\isachardoublequote}}latin\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\|\verb|<|\isa{latin}\verb|>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\|\verb|<|\isa{{\isaliteral{22}{\isachardoublequote}}latin\ latin{\isaliteral{22}{\isachardoublequote}}}\verb|>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ greek\ \ {\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & & \verb|\<^isub>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<^isup>| \\
+ \isa{quasiletter} & = & \isa{{\isaliteral{22}{\isachardoublequote}}letter\ \ {\isaliteral{7C}{\isacharbar}}\ \ digit\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|_|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|'| \\
+ \isa{latin} & = & \verb|a|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|z|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|A|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|Z| \\
+ \isa{digit} & = & \verb|0|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|9| \\
+ \isa{sym} & = & \verb|!|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|#|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|$|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|%|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|&|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|*|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|+|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|-|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|/|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & & \verb|<|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|=|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|?|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|@|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|^|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|_|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb||\verb,|,\verb||\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|~| \\
+ \isa{greek} & = & \verb|\<alpha>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<beta>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<gamma>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<delta>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & & \verb|\<epsilon>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<zeta>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<eta>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<theta>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & & \verb|\<iota>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<kappa>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<mu>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<nu>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & & \verb|\<xi>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<pi>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<rho>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<sigma>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<tau>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & & \verb|\<upsilon>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<phi>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<chi>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<psi>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & & \verb|\<omega>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<Gamma>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<Delta>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<Theta>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & & \verb|\<Lambda>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<Xi>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<Pi>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<Sigma>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & & \verb|\<Upsilon>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<Phi>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<Psi>|\isa{{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{22}{\isachardoublequote}}}\verb|\<Omega>| \\
\end{supertabular}
\end{center}
A \indexref{}{syntax}{var}\hyperlink{syntax.var}{\mbox{\isa{var}}} or \indexref{}{syntax}{typevar}\hyperlink{syntax.typevar}{\mbox{\isa{typevar}}} describes an unknown,
which is internally a pair of base name and index (ML type \verb|indexname|). These components are either separated by a dot as in
- \isa{{\isachardoublequote}{\isacharquery}x{\isachardot}{\isadigit{1}}{\isachardoublequote}} or \isa{{\isachardoublequote}{\isacharquery}x{\isadigit{7}}{\isachardot}{\isadigit{3}}{\isachardoublequote}} or run together as in \isa{{\isachardoublequote}{\isacharquery}x{\isadigit{1}}{\isachardoublequote}}. The latter form is possible if the base name does not end
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{2E}{\isachardot}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} or \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}x{\isadigit{7}}{\isaliteral{2E}{\isachardot}}{\isadigit{3}}{\isaliteral{22}{\isachardoublequote}}} or run together as in \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}x{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}. The latter form is possible if the base name does not end
with digits. If the index is 0, it may be dropped altogether:
- \isa{{\isachardoublequote}{\isacharquery}x{\isachardoublequote}} and \isa{{\isachardoublequote}{\isacharquery}x{\isadigit{0}}{\isachardoublequote}} and \isa{{\isachardoublequote}{\isacharquery}x{\isachardot}{\isadigit{0}}{\isachardoublequote}} all refer to the
- same unknown, with basename \isa{{\isachardoublequote}x{\isachardoublequote}} and index 0.
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}x{\isadigit{0}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{2E}{\isachardot}}{\isadigit{0}}{\isaliteral{22}{\isachardoublequote}}} all refer to the
+ same unknown, with basename \isa{{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}} and index 0.
The syntax of \indexref{}{syntax}{string}\hyperlink{syntax.string}{\mbox{\isa{string}}} admits any characters, including
newlines; ``\verb|"|'' (double-quote) and ``\verb|\|'' (backslash) need to be escaped by a backslash; arbitrary
@@ -174,13 +174,13 @@
text is {\LaTeX} source, one may usually add some blank or comment
to avoid the critical character sequence.
- Source comments take the form \verb|(*|~\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}~\verb|*)| and may be nested, although the user-interface
+ Source comments take the form \verb|(*|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}~\verb|*)| and may be nested, although the user-interface
might prevent this. Note that this form indicates source comments
only, which are stripped after lexical analysis of the input. The
Isar syntax also provides proper \emph{document comments} that are
considered as part of the text (see \secref{sec:comments}).
- Common mathematical symbols such as \isa{{\isasymforall}} are represented in
+ Common mathematical symbols such as \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}} are represented in
Isabelle as \verb|\<forall>|. There are infinitely many Isabelle
symbols like this, although proper presentation is left to front-end
tools such as {\LaTeX} or Proof~General with the X-Symbol package.
@@ -255,7 +255,7 @@
%
\begin{isamarkuptext}%
Large chunks of plain \railqtok{text} are usually given
- \railtok{verbatim}, i.e.\ enclosed in \verb|{|\verb|*|~\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}~\verb|*|\verb|}|. For convenience,
+ \railtok{verbatim}, i.e.\ enclosed in \verb|{|\verb|*|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}~\verb|*|\verb|}|. For convenience,
any of the smaller text units conforming to \railqtok{nameref} are
admitted as well. A marginal \railnonterm{comment} is of the form
\verb|--| \railqtok{text}. Any number of these may occur
@@ -278,7 +278,7 @@
\begin{isamarkuptext}%
Classes are specified by plain names. Sorts have a very simple
inner syntax, which is either a single class name \isa{c} or a
- list \isa{{\isachardoublequote}{\isacharbraceleft}c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n{\isacharbraceright}{\isachardoublequote}} referring to the
+ list \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7B}{\isacharbraceleft}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}} referring to the
intersection of these classes. The syntax of type arities is given
directly at the outer level.
@@ -308,7 +308,7 @@
liberal convention is adopted: quotes may be omitted for any type or
term that is already atomic at the outer level. For example, one
may just write \verb|x| instead of quoted \verb|"x"|.
- Note that symbolic identifiers (e.g.\ \verb|++| or \isa{{\isachardoublequote}{\isasymforall}{\isachardoublequote}} are available as well, provided these have not been superseded
+ Note that symbolic identifiers (e.g.\ \verb|++| or \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}{\isaliteral{22}{\isachardoublequote}}} are available as well, provided these have not been superseded
by commands or other keywords already (such as \verb|=| or
\verb|+|).
@@ -323,7 +323,7 @@
\end{rail}
Positional instantiations are indicated by giving a sequence of
- terms, or the placeholder ``\isa{{\isacharunderscore}}'' (underscore), which means to
+ terms, or the placeholder ``\isa{{\isaliteral{5F}{\isacharunderscore}}}'' (underscore), which means to
skip a position.
\indexoutertoken{inst}\indexoutertoken{insts}
@@ -358,7 +358,7 @@
\begin{isamarkuptext}%
Wherever explicit propositions (or term fragments) occur in a proof
text, casual binding of schematic term variables may be given
- specified via patterns of the form ``\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIS}\ p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub n{\isacharparenright}{\isachardoublequote}}''. This works both for \railqtok{term} and \railqtok{prop}.
+ specified via patterns of the form ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C49533E}{\isasymIS}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}''. This works both for \railqtok{term} and \railqtok{prop}.
\indexouternonterm{termpat}\indexouternonterm{proppat}
\begin{rail}
@@ -368,8 +368,8 @@
;
\end{rail}
- \medskip Declarations of local variables \isa{{\isachardoublequote}x\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}{\isachardoublequote}} and
- logical propositions \isa{{\isachardoublequote}a\ {\isacharcolon}\ {\isasymphi}{\isachardoublequote}} represent different views on
+ \medskip Declarations of local variables \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}} and
+ logical propositions \isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} represent different views on
the same principle of introducing a local scope. In practice, one
may usually omit the typing of \railnonterm{vars} (due to
type-inference), and the naming of propositions (due to implicit
@@ -386,8 +386,8 @@
The treatment of multiple declarations corresponds to the
complementary focus of \railnonterm{vars} versus
- \railnonterm{props}. In ``\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}{\isachardoublequote}}''
- the typing refers to all variables, while in \isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}} the naming refers to all propositions collectively.
+ \railnonterm{props}. In ``\isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}}''
+ the typing refers to all variables, while in \isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} the naming refers to all propositions collectively.
Isar language elements that refer to \railnonterm{vars} or
\railnonterm{props} typically admit separate typings or namings via
another level of iteration, with explicit \indexref{}{keyword}{and}\hyperlink{keyword.and}{\mbox{\isa{\isakeyword{and}}}}
@@ -432,12 +432,12 @@
There are three forms of theorem references:
\begin{enumerate}
- \item named facts \isa{{\isachardoublequote}a{\isachardoublequote}},
+ \item named facts \isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{22}{\isachardoublequote}}},
- \item selections from named facts \isa{{\isachardoublequote}a{\isacharparenleft}i{\isacharparenright}{\isachardoublequote}} or \isa{{\isachardoublequote}a{\isacharparenleft}j\ {\isacharminus}\ k{\isacharparenright}{\isachardoublequote}},
+ \item selections from named facts \isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{28}{\isacharparenleft}}i{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} or \isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{28}{\isacharparenleft}}j\ {\isaliteral{2D}{\isacharminus}}\ k{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}},
\item literal fact propositions using \indexref{}{syntax}{altstring}\hyperlink{syntax.altstring}{\mbox{\isa{altstring}}} syntax
- \verb|`|\isa{{\isachardoublequote}{\isasymphi}{\isachardoublequote}}\verb|`| (see also method
+ \verb|`|\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}}\verb|`| (see also method
\indexref{}{method}{fact}\hyperlink{method.fact}{\mbox{\isa{fact}}}).
\end{enumerate}
@@ -448,7 +448,7 @@
not stored within the theorem database of the theory or proof
context, but any given attributes are applied nonetheless.
- An extra pair of brackets around attributes (like ``\isa{{\isachardoublequote}{\isacharbrackleft}{\isacharbrackleft}simproc\ a{\isacharbrackright}{\isacharbrackright}{\isachardoublequote}}'') abbreviates a theorem reference involving an
+ An extra pair of brackets around attributes (like ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5B}{\isacharbrackleft}}simproc\ a{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}'') abbreviates a theorem reference involving an
internal dummy fact, which will be ignored later on. So only the
effect of the attribute on the background context will persist.
This form of in-place declarations is particularly useful with
--- a/doc-src/IsarRef/Thy/document/Proof.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarRef/Thy/document/Proof.tex Mon Nov 08 14:41:11 2010 +0100
@@ -31,16 +31,16 @@
\begin{description}
- \item \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} means that a new goal has just been
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} means that a new goal has just been
stated that is now to be \emph{proven}; the next command may refine
it by some proof method, and enter a sub-proof to establish the
actual result.
- \item \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} is like a nested theory mode: the
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} is like a nested theory mode: the
context may be augmented by \emph{stating} additional assumptions,
intermediate results etc.
- \item \isa{{\isachardoublequote}proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} is intermediate between \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} and \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}}: existing facts (i.e.\
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} is intermediate between \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}: existing facts (i.e.\
the contents of the special ``\indexref{}{fact}{this}\hyperlink{fact.this}{\mbox{\isa{this}}}'' register) have been
just picked up in order to be used when refining the goal claimed
next.
@@ -71,17 +71,17 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{example\_proof}\hypertarget{command.example-proof}{\hyperlink{command.example-proof}{\mbox{\isa{\isacommand{example{\isacharunderscore}proof}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
+ \indexdef{}{command}{example\_proof}\hypertarget{command.example-proof}{\hyperlink{command.example-proof}{\mbox{\isa{\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{description}
- \item \hyperlink{command.example-proof}{\mbox{\isa{\isacommand{example{\isacharunderscore}proof}}}} opens an empty proof body. This
+ \item \hyperlink{command.example-proof}{\mbox{\isa{\isacommand{example{\isaliteral{5F}{\isacharunderscore}}proof}}}} opens an empty proof body. This
allows to experiment with Isar, without producing any persistent
result.
Structurally, this is like a vacous \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}} statement
- followed by ``\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'', which means the
+ followed by ``\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{22}{\isachardoublequote}}}'', which means the
example proof may be closed by a regular \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}, or
discontinued by \hyperlink{command.oops}{\mbox{\isa{\isacommand{oops}}}}.
@@ -95,9 +95,9 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{next}\hypertarget{command.next}{\hyperlink{command.next}{\mbox{\isa{\isacommand{next}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{\{}\hypertarget{command.braceleft}{\hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isacharbraceleft}}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{\}}\hypertarget{command.braceright}{\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isacharbraceright}}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
+ \indexdef{}{command}{next}\hypertarget{command.next}{\hyperlink{command.next}{\mbox{\isa{\isacommand{next}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{\{}\hypertarget{command.braceleft}{\hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isaliteral{7B}{\isacharbraceleft}}}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{\}}\hypertarget{command.braceright}{\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isaliteral{7D}{\isacharbraceright}}}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
While Isar is inherently block-structured, opening and closing
@@ -119,9 +119,9 @@
\item \hyperlink{command.next}{\mbox{\isa{\isacommand{next}}}} switches to a fresh block within a
sub-proof, resetting the local context to the initial one.
- \item \hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isacharbraceleft}}}}} and \hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isacharbraceright}}}}} explicitly open and close
- blocks. Any current facts pass through ``\hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isacharbraceleft}}}}}''
- unchanged, while ``\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isacharbraceright}}}}}'' causes any result to be
+ \item \hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isaliteral{7B}{\isacharbraceleft}}}}}} and \hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isaliteral{7D}{\isacharbraceright}}}}}} explicitly open and close
+ blocks. Any current facts pass through ``\hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isaliteral{7B}{\isacharbraceleft}}}}}}''
+ unchanged, while ``\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isaliteral{7D}{\isacharbraceright}}}}}}'' causes any result to be
\emph{exported} into the enclosing context. Thus fixed variables
are generalized, assumptions discharged, and local definitions
unfolded (cf.\ \secref{sec:proof-context}). There is no difference
@@ -139,7 +139,7 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{oops}\hypertarget{command.oops}{\hyperlink{command.oops}{\mbox{\isa{\isacommand{oops}}}}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}\ local{\isacharunderscore}theory\ {\isacharbar}\ theory{\isachardoublequote}} \\
+ \indexdef{}{command}{oops}\hypertarget{command.oops}{\hyperlink{command.oops}{\mbox{\isa{\isacommand{oops}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{7C}{\isacharbar}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
The \hyperlink{command.oops}{\mbox{\isa{\isacommand{oops}}}} command discontinues the current proof
@@ -157,7 +157,7 @@
preparation tools of Isabelle described in \chref{ch:document-prep}.
Thus partial or even wrong proof attempts can be discussed in a
logically sound manner. Note that the Isabelle {\LaTeX} macros can
- be easily adapted to print something like ``\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}'' instead of
+ be easily adapted to print something like ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}'' instead of
the keyword ``\hyperlink{command.oops}{\mbox{\isa{\isacommand{oops}}}}''.
\medskip The \hyperlink{command.oops}{\mbox{\isa{\isacommand{oops}}}} command is undo-able, unlike
@@ -176,10 +176,10 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{fix}\hypertarget{command.fix}{\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{assume}\hypertarget{command.assume}{\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{presume}\hypertarget{command.presume}{\hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{def}\hypertarget{command.def}{\hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
+ \indexdef{}{command}{fix}\hypertarget{command.fix}{\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{assume}\hypertarget{command.assume}{\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{presume}\hypertarget{command.presume}{\hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{def}\hypertarget{command.def}{\hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
The logical proof context consists of fixed variables and
@@ -188,16 +188,16 @@
logical framework. Introducing some \emph{arbitrary, but fixed}
variable via ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}'' results in a local value
that may be used in the subsequent proof as any other variable or
- constant. Furthermore, any result \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymphi}{\isacharbrackleft}x{\isacharbrackright}{\isachardoublequote}} exported from
+ constant. Furthermore, any result \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} exported from
the context will be universally closed wrt.\ \isa{x} at the
- outermost level: \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymAnd}x{\isachardot}\ {\isasymphi}{\isacharbrackleft}x{\isacharbrackright}{\isachardoublequote}} (this is expressed in normal
+ outermost level: \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} (this is expressed in normal
form using Isabelle's meta-variables).
- Similarly, introducing some assumption \isa{{\isasymchi}} has two effects.
+ Similarly, introducing some assumption \isa{{\isaliteral{5C3C6368693E}{\isasymchi}}} has two effects.
On the one hand, a local theorem is created that may be used as a
fact in subsequent proof steps. On the other hand, any result
- \isa{{\isachardoublequote}{\isasymchi}\ {\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} exported from the context becomes conditional wrt.\
- the assumption: \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymchi}\ {\isasymLongrightarrow}\ {\isasymphi}{\isachardoublequote}}. Thus, solving an enclosing goal
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6368693E}{\isasymchi}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} exported from the context becomes conditional wrt.\
+ the assumption: \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C6368693E}{\isasymchi}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}}. Thus, solving an enclosing goal
using such a result would basically introduce a new subgoal stemming
from the assumption. How this situation is handled depends on the
version of assumption command used: while \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}
@@ -205,10 +205,10 @@
the goal, \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}} leaves the subgoal unchanged in order
to be proved later by the user.
- Local definitions, introduced by ``\hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}}'', are achieved by combining ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}'' with
+ Local definitions, introduced by ``\hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}'', are achieved by combining ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}'' with
another version of assumption that causes any hypothetical equation
- \isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}} to be eliminated by the reflexivity rule. Thus,
- exporting some result \isa{{\isachardoublequote}x\ {\isasymequiv}\ t\ {\isasymturnstile}\ {\isasymphi}{\isacharbrackleft}x{\isacharbrackright}{\isachardoublequote}} yields \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymphi}{\isacharbrackleft}t{\isacharbrackright}{\isachardoublequote}}.
+ \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}} to be eliminated by the reflexivity rule. Thus,
+ exporting some result \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} yields \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{5B}{\isacharbrackleft}}t{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}.
\begin{rail}
'fix' (vars + 'and')
@@ -225,21 +225,21 @@
\item \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x} introduces a local variable \isa{x} that is \emph{arbitrary, but fixed.}
- \item \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} and \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} introduce a local fact \isa{{\isachardoublequote}{\isasymphi}\ {\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} by
+ \item \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} and \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} introduce a local fact \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ {\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} by
assumption. Subsequent results applied to an enclosing goal (e.g.\
by \indexref{}{command}{show}\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}) are handled as follows: \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}} expects to be able to unify with existing premises in the
- goal, while \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}} leaves \isa{{\isasymphi}} as new subgoals.
+ goal, while \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}} leaves \isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} as new subgoals.
Several lists of assumptions may be given (separated by
\indexref{}{keyword}{and}\hyperlink{keyword.and}{\mbox{\isa{\isakeyword{and}}}}; the resulting list of current facts consists
of all of these concatenated.
- \item \hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}} introduces a local
+ \item \hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}} introduces a local
(non-polymorphic) definition. In results exported from the context,
- \isa{x} is replaced by \isa{t}. Basically, ``\hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}}'' abbreviates ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}}'', with the resulting
+ \isa{x} is replaced by \isa{t}. Basically, ``\hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}'' abbreviates ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}'', with the resulting
hypothetical equation solved by reflexivity.
- The default name for the definitional equation is \isa{x{\isacharunderscore}def}.
+ The default name for the definitional equation is \isa{x{\isaliteral{5F}{\isacharunderscore}}def}.
Several simultaneous definitions may be given at the same time.
\end{description}
@@ -256,15 +256,15 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{let}\hypertarget{command.let}{\hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
+ \indexdef{}{command}{let}\hypertarget{command.let}{\hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\indexdef{}{keyword}{is}\hypertarget{keyword.is}{\hyperlink{keyword.is}{\mbox{\isa{\isakeyword{is}}}}} & : & syntax \\
\end{matharray}
- Abbreviations may be either bound by explicit \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}~\isa{{\isachardoublequote}p\ {\isasymequiv}\ t{\isachardoublequote}} statements, or by annotating assumptions or
- goal statements with a list of patterns ``\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIS}\ p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub n{\isacharparenright}{\isachardoublequote}}''. In both cases, higher-order matching is invoked to
+ Abbreviations may be either bound by explicit \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}p\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}} statements, or by annotating assumptions or
+ goal statements with a list of patterns ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C49533E}{\isasymIS}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}''. In both cases, higher-order matching is invoked to
bind extra-logical term variables, which may be either named
- schematic variables of the form \isa{{\isacharquery}x}, or nameless dummies
- ``\hyperlink{variable.underscore}{\mbox{\isa{{\isacharunderscore}}}}'' (underscore). Note that in the \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}
+ schematic variables of the form \isa{{\isaliteral{3F}{\isacharquery}}x}, or nameless dummies
+ ``\hyperlink{variable.underscore}{\mbox{\isa{{\isaliteral{5F}{\isacharunderscore}}}}}'' (underscore). Note that in the \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}
form the patterns occur on the left-hand side, while the \hyperlink{keyword.is}{\mbox{\isa{\isakeyword{is}}}} patterns are in postfix position.
Polymorphism of term bindings is handled in Hindley-Milner style,
@@ -292,12 +292,12 @@
\begin{description}
- \item \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}~\isa{{\isachardoublequote}p\isactrlsub {\isadigit{1}}\ {\isacharequal}\ t\isactrlsub {\isadigit{1}}\ {\isasymAND}\ {\isasymdots}\ p\isactrlsub n\ {\isacharequal}\ t\isactrlsub n{\isachardoublequote}} binds any
- text variables in patterns \isa{{\isachardoublequote}p\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ p\isactrlsub n{\isachardoublequote}} by simultaneous
- higher-order matching against terms \isa{{\isachardoublequote}t\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ t\isactrlsub n{\isachardoublequote}}.
+ \item \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}p\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3D}{\isacharequal}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} binds any
+ text variables in patterns \isa{{\isaliteral{22}{\isachardoublequote}}p\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} by simultaneous
+ higher-order matching against terms \isa{{\isaliteral{22}{\isachardoublequote}}t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}.
- \item \isa{{\isachardoublequote}{\isacharparenleft}{\isasymIS}\ p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub n{\isacharparenright}{\isachardoublequote}} resembles \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}, but
- matches \isa{{\isachardoublequote}p\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ p\isactrlsub n{\isachardoublequote}} against the preceding statement. Also
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C49533E}{\isasymIS}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} resembles \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}, but
+ matches \isa{{\isaliteral{22}{\isachardoublequote}}p\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} against the preceding statement. Also
note that \hyperlink{keyword.is}{\mbox{\isa{\isakeyword{is}}}} is not a separate command, but part of
others (such as \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}, \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}} etc.).
@@ -309,8 +309,8 @@
abstracted over any meta-level parameters (if present). Likewise,
\indexref{}{variable}{this}\hyperlink{variable.this}{\mbox{\isa{this}}} is bound for fact statements resulting from
assumptions or finished goals. In case \hyperlink{variable.this}{\mbox{\isa{this}}} refers to
- an object-logic statement that is an application \isa{{\isachardoublequote}f\ t{\isachardoublequote}}, then
- \isa{t} is bound to the special text variable ``\hyperlink{variable.dots}{\mbox{\isa{{\isasymdots}}}}''
+ an object-logic statement that is an application \isa{{\isaliteral{22}{\isachardoublequote}}f\ t{\isaliteral{22}{\isachardoublequote}}}, then
+ \isa{t} is bound to the special text variable ``\hyperlink{variable.dots}{\mbox{\isa{{\isaliteral{5C3C646F74733E}{\isasymdots}}}}}''
(three dots). The canonical application of this convenience are
calculational proofs (see \secref{sec:calculation}).%
\end{isamarkuptext}%
@@ -322,12 +322,12 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{note}\hypertarget{command.note}{\hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{then}\hypertarget{command.then}{\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{from}\hypertarget{command.from}{\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{with}\hypertarget{command.with}{\hyperlink{command.with}{\mbox{\isa{\isacommand{with}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{using}\hypertarget{command.using}{\hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{unfolding}\hypertarget{command.unfolding}{\hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
+ \indexdef{}{command}{note}\hypertarget{command.note}{\hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{then}\hypertarget{command.then}{\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{from}\hypertarget{command.from}{\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{with}\hypertarget{command.with}{\hyperlink{command.with}{\mbox{\isa{\isacommand{with}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{using}\hypertarget{command.using}{\hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{unfolding}\hypertarget{command.unfolding}{\hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
New facts are established either by assumption or proof of local
@@ -350,8 +350,8 @@
\begin{description}
- \item \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isachardoublequote}a\ {\isacharequal}\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}} recalls existing facts
- \isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ b\isactrlsub n{\isachardoublequote}}, binding the result as \isa{a}. Note that
+ \item \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{3D}{\isacharequal}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} recalls existing facts
+ \isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}, binding the result as \isa{a}. Note that
attributes may be involved as well, both on the left and right hand
sides.
@@ -368,30 +368,30 @@
\item \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{b} abbreviates ``\hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{b}~\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}''; thus \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}} is
equivalent to ``\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{this}''.
- \item \hyperlink{command.with}{\mbox{\isa{\isacommand{with}}}}~\isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}} abbreviates ``\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n\ {\isasymAND}\ this{\isachardoublequote}}''; thus the forward chaining
+ \item \hyperlink{command.with}{\mbox{\isa{\isacommand{with}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} abbreviates ``\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ this{\isaliteral{22}{\isachardoublequote}}}''; thus the forward chaining
is from earlier facts together with the current ones.
- \item \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}} augments the facts being
+ \item \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} augments the facts being
currently indicated for use by a subsequent refinement step (such as
\indexref{}{command}{apply}\hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}} or \indexref{}{command}{proof}\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}).
- \item \hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}~\isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}} is structurally
+ \item \hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} is structurally
similar to \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}, but unfolds definitional equations
- \isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}} throughout the goal state and facts.
+ \isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} throughout the goal state and facts.
\end{description}
Forward chaining with an empty list of theorems is the same as not
chaining at all. Thus ``\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{nothing}'' has no
- effect apart from entering \isa{{\isachardoublequote}prove{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} mode, since
+ effect apart from entering \isa{{\isaliteral{22}{\isachardoublequote}}prove{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} mode, since
\indexref{}{fact}{nothing}\hyperlink{fact.nothing}{\mbox{\isa{nothing}}} is bound to the empty list of theorems.
Basic proof methods (such as \indexref{}{method}{rule}\hyperlink{method.rule}{\mbox{\isa{rule}}}) expect multiple
facts to be given in their proper order, corresponding to a prefix
of the premises of the rule involved. Note that positions may be
- easily skipped using something like \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{{\isachardoublequote}{\isacharunderscore}\ {\isasymAND}\ a\ {\isasymAND}\ b{\isachardoublequote}}, for example. This involves the trivial rule
- \isa{{\isachardoublequote}PROP\ {\isasympsi}\ {\isasymLongrightarrow}\ PROP\ {\isasympsi}{\isachardoublequote}}, which is bound in Isabelle/Pure as
- ``\indexref{}{fact}{\_}\hyperlink{fact.underscore}{\mbox{\isa{{\isacharunderscore}}}}'' (underscore).
+ easily skipped using something like \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ a\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ b{\isaliteral{22}{\isachardoublequote}}}, for example. This involves the trivial rule
+ \isa{{\isaliteral{22}{\isachardoublequote}}PROP\ {\isaliteral{5C3C7073693E}{\isasympsi}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ PROP\ {\isaliteral{5C3C7073693E}{\isasympsi}}{\isaliteral{22}{\isachardoublequote}}}, which is bound in Isabelle/Pure as
+ ``\indexref{}{fact}{\_}\hyperlink{fact.underscore}{\mbox{\isa{{\isaliteral{5F}{\isacharunderscore}}}}}'' (underscore).
Automated methods (such as \hyperlink{method.simp}{\mbox{\isa{simp}}} or \hyperlink{method.auto}{\mbox{\isa{auto}}}) just
insert any given facts before their usual operation. Depending on
@@ -406,17 +406,17 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{lemma}\hypertarget{command.lemma}{\hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{theorem}\hypertarget{command.theorem}{\hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{corollary}\hypertarget{command.corollary}{\hyperlink{command.corollary}{\mbox{\isa{\isacommand{corollary}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{schematic\_lemma}\hypertarget{command.schematic-lemma}{\hyperlink{command.schematic-lemma}{\mbox{\isa{\isacommand{schematic{\isacharunderscore}lemma}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{schematic\_theorem}\hypertarget{command.schematic-theorem}{\hyperlink{command.schematic-theorem}{\mbox{\isa{\isacommand{schematic{\isacharunderscore}theorem}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{schematic\_corollary}\hypertarget{command.schematic-corollary}{\hyperlink{command.schematic-corollary}{\mbox{\isa{\isacommand{schematic{\isacharunderscore}corollary}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{have}\hypertarget{command.have}{\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ proof{\isacharparenleft}chain{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{show}\hypertarget{command.show}{\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ proof{\isacharparenleft}chain{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{hence}\hypertarget{command.hence}{\hyperlink{command.hence}{\mbox{\isa{\isacommand{hence}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{thus}\hypertarget{command.thus}{\hyperlink{command.thus}{\mbox{\isa{\isacommand{thus}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{print\_statement}\hypertarget{command.print-statement}{\hyperlink{command.print-statement}{\mbox{\isa{\isacommand{print{\isacharunderscore}statement}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{}{command}{lemma}\hypertarget{command.lemma}{\hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{theorem}\hypertarget{command.theorem}{\hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{corollary}\hypertarget{command.corollary}{\hyperlink{command.corollary}{\mbox{\isa{\isacommand{corollary}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{schematic\_lemma}\hypertarget{command.schematic-lemma}{\hyperlink{command.schematic-lemma}{\mbox{\isa{\isacommand{schematic{\isaliteral{5F}{\isacharunderscore}}lemma}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{schematic\_theorem}\hypertarget{command.schematic-theorem}{\hyperlink{command.schematic-theorem}{\mbox{\isa{\isacommand{schematic{\isaliteral{5F}{\isacharunderscore}}theorem}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{schematic\_corollary}\hypertarget{command.schematic-corollary}{\hyperlink{command.schematic-corollary}{\mbox{\isa{\isacommand{schematic{\isaliteral{5F}{\isacharunderscore}}corollary}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{have}\hypertarget{command.have}{\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{show}\hypertarget{command.show}{\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{hence}\hypertarget{command.hence}{\hyperlink{command.hence}{\mbox{\isa{\isacommand{hence}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{thus}\hypertarget{command.thus}{\hyperlink{command.thus}{\mbox{\isa{\isacommand{thus}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_statement}\hypertarget{command.print-statement}{\hyperlink{command.print-statement}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}statement}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
From a theory context, proof mode is entered by an initial goal
@@ -429,7 +429,7 @@
Goals may consist of multiple statements, resulting in a list of
facts eventually. A pending multi-goal is internally represented as
- a meta-level conjunction (\isa{{\isachardoublequote}{\isacharampersand}{\isacharampersand}{\isacharampersand}{\isachardoublequote}}), which is usually
+ a meta-level conjunction (\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}{\isaliteral{26}{\isacharampersand}}{\isaliteral{22}{\isachardoublequote}}}), which is usually
split into the corresponding number of sub-goals prior to an initial
method application, via \indexref{}{command}{proof}\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}
(\secref{sec:proof-steps}) or \indexref{}{command}{apply}\hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}
@@ -472,19 +472,19 @@
\begin{description}
- \item \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} enters proof mode with
- \isa{{\isasymphi}} as main goal, eventually resulting in some fact \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} to be put back into the target context. An additional
+ \item \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} enters proof mode with
+ \isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} as main goal, eventually resulting in some fact \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} to be put back into the target context. An additional
\railnonterm{context} specification may build up an initial proof
context for the subsequent claim; this includes local definitions
and syntax as well, see the definition of \hyperlink{syntax.contextelem}{\mbox{\isa{contextelem}}} in
\secref{sec:locale}.
- \item \hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} and \hyperlink{command.corollary}{\mbox{\isa{\isacommand{corollary}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} are essentially the same as \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}}, but the facts are internally marked as
+ \item \hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} and \hyperlink{command.corollary}{\mbox{\isa{\isacommand{corollary}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} are essentially the same as \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}}, but the facts are internally marked as
being of a different kind. This discrimination acts like a formal
comment.
- \item \hyperlink{command.schematic-lemma}{\mbox{\isa{\isacommand{schematic{\isacharunderscore}lemma}}}}, \hyperlink{command.schematic-theorem}{\mbox{\isa{\isacommand{schematic{\isacharunderscore}theorem}}}},
- \hyperlink{command.schematic-corollary}{\mbox{\isa{\isacommand{schematic{\isacharunderscore}corollary}}}} are similar to \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}},
+ \item \hyperlink{command.schematic-lemma}{\mbox{\isa{\isacommand{schematic{\isaliteral{5F}{\isacharunderscore}}lemma}}}}, \hyperlink{command.schematic-theorem}{\mbox{\isa{\isacommand{schematic{\isaliteral{5F}{\isacharunderscore}}theorem}}}},
+ \hyperlink{command.schematic-corollary}{\mbox{\isa{\isacommand{schematic{\isaliteral{5F}{\isacharunderscore}}corollary}}}} are similar to \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}},
\hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}, \hyperlink{command.corollary}{\mbox{\isa{\isacommand{corollary}}}}, respectively but allow
the statement to contain unbound schematic variables.
@@ -495,14 +495,14 @@
proofs is lost, which also impacts performance, because proof
checking is forced into sequential mode.
- \item \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} claims a local goal,
+ \item \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} claims a local goal,
eventually resulting in a fact within the current logical context.
This operation is completely independent of any pending sub-goals of
an enclosing goal statements, so \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}} may be freely
used for experimental exploration of potential results within a
proof body.
- \item \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} is like \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} plus a second stage to refine some pending
+ \item \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} is like \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} plus a second stage to refine some pending
sub-goal for each one of the finished result, after having been
exported into the corresponding context (at the head of the
sub-proof of this \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}} command).
@@ -525,14 +525,14 @@
\item \hyperlink{command.thus}{\mbox{\isa{\isacommand{thus}}}} abbreviates ``\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}''. Note that \hyperlink{command.thus}{\mbox{\isa{\isacommand{thus}}}} is also equivalent to
``\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{this}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}''.
- \item \hyperlink{command.print-statement}{\mbox{\isa{\isacommand{print{\isacharunderscore}statement}}}}~\isa{a} prints facts from the
+ \item \hyperlink{command.print-statement}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}statement}}}}~\isa{a} prints facts from the
current theory or proof context in long statement form, according to
the syntax for \hyperlink{command.lemma}{\mbox{\isa{\isacommand{lemma}}}} given above.
\end{description}
Any goal statement causes some term abbreviations (such as
- \indexref{}{variable}{?thesis}\hyperlink{variable.?thesis}{\mbox{\isa{{\isacharquery}thesis}}}) to be bound automatically, see also
+ \indexref{}{variable}{?thesis}\hyperlink{variable.?thesis}{\mbox{\isa{{\isaliteral{3F}{\isacharquery}}thesis}}}) to be bound automatically, see also
\secref{sec:term-abbrev}.
The optional case names of \indexref{}{element}{obtains}\hyperlink{element.obtains}{\mbox{\isa{\isakeyword{obtains}}}} have a twofold
@@ -556,7 +556,7 @@
methods via ``\verb|,|'' (sequential composition),
``\verb||\verb,|,\verb||'' (alternative choices), ``\verb|?|''
(try), ``\verb|+|'' (repeat at least once), ``\verb|[|\isa{n}\verb|]|'' (restriction to first \isa{n}
- sub-goals, with default \isa{{\isachardoublequote}n\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequote}}). In practice, proof
+ sub-goals, with default \isa{{\isaliteral{22}{\isachardoublequote}}n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}). In practice, proof
methods are usually just a comma separated list of
\railqtok{nameref}~\railnonterm{args} specifications. Note that
parentheses may be dropped for single method specifications (with no
@@ -572,18 +572,18 @@
Proper Isar proof methods do \emph{not} admit arbitrary goal
addressing, but refer either to the first sub-goal or all sub-goals
- uniformly. The goal restriction operator ``\isa{{\isachardoublequote}{\isacharbrackleft}n{\isacharbrackright}{\isachardoublequote}}''
+ uniformly. The goal restriction operator ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}''
evaluates a method expression within a sandbox consisting of the
first \isa{n} sub-goals (which need to exist). For example, the
- method ``\isa{{\isachardoublequote}simp{\isacharunderscore}all{\isacharbrackleft}{\isadigit{3}}{\isacharbrackright}{\isachardoublequote}}'' simplifies the first three
- sub-goals, while ``\isa{{\isachardoublequote}{\isacharparenleft}rule\ foo{\isacharcomma}\ simp{\isacharunderscore}all{\isacharparenright}{\isacharbrackleft}{\isacharbrackright}{\isachardoublequote}}'' simplifies all
- new goals that emerge from applying rule \isa{{\isachardoublequote}foo{\isachardoublequote}} to the
+ method ``\isa{{\isaliteral{22}{\isachardoublequote}}simp{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{3}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}'' simplifies the first three
+ sub-goals, while ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}rule\ foo{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{29}{\isacharparenright}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}'' simplifies all
+ new goals that emerge from applying rule \isa{{\isaliteral{22}{\isachardoublequote}}foo{\isaliteral{22}{\isachardoublequote}}} to the
originally first one.
Improper methods, notably tactic emulations, offer a separate
low-level goal addressing scheme as explicit argument to the
- individual tactic being involved. Here ``\isa{{\isachardoublequote}{\isacharbrackleft}{\isacharbang}{\isacharbrackright}{\isachardoublequote}}'' refers to
- all goals, and ``\isa{{\isachardoublequote}{\isacharbrackleft}n{\isacharminus}{\isacharbrackright}{\isachardoublequote}}'' to all goals starting from \isa{{\isachardoublequote}n{\isachardoublequote}}.
+ individual tactic being involved. Here ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}'' refers to
+ all goals, and ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}n{\isaliteral{2D}{\isacharminus}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}'' to all goals starting from \isa{{\isaliteral{22}{\isachardoublequote}}n{\isaliteral{22}{\isachardoublequote}}}.
\indexouternonterm{goalspec}
\begin{rail}
@@ -599,12 +599,12 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{proof}\hypertarget{command.proof}{\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{qed}\hypertarget{command.qed}{\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ local{\isacharunderscore}theory\ {\isacharbar}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{by}\hypertarget{command.by}{\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ local{\isacharunderscore}theory\ {\isacharbar}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{..}\hypertarget{command.ddot}{\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ local{\isacharunderscore}theory\ {\isacharbar}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{.}\hypertarget{command.dot}{\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isachardot}}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ local{\isacharunderscore}theory\ {\isacharbar}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{sorry}\hypertarget{command.sorry}{\hyperlink{command.sorry}{\mbox{\isa{\isacommand{sorry}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ local{\isacharunderscore}theory\ {\isacharbar}\ theory{\isachardoublequote}} \\
+ \indexdef{}{command}{proof}\hypertarget{command.proof}{\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{qed}\hypertarget{command.qed}{\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{7C}{\isacharbar}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{by}\hypertarget{command.by}{\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{7C}{\isacharbar}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{..}\hypertarget{command.ddot}{\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{7C}{\isacharbar}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{.}\hypertarget{command.dot}{\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{7C}{\isacharbar}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{sorry}\hypertarget{command.sorry}{\hyperlink{command.sorry}{\mbox{\isa{\isacommand{sorry}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{7C}{\isacharbar}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
Arbitrary goal refinement via tactics is considered harmful.
@@ -613,12 +613,12 @@
\begin{enumerate}
- \item An \emph{initial} refinement step \indexref{}{command}{proof}\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}} reduces a newly stated goal to a number
+ \item An \emph{initial} refinement step \indexref{}{command}{proof}\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} reduces a newly stated goal to a number
of sub-goals that are to be solved later. Facts are passed to
- \isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}} for forward chaining, if so indicated by \isa{{\isachardoublequote}proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} mode.
+ \isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} for forward chaining, if so indicated by \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} mode.
- \item A \emph{terminal} conclusion step \indexref{}{command}{qed}\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}} is intended to solve remaining goals. No facts are
- passed to \isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}}.
+ \item A \emph{terminal} conclusion step \indexref{}{command}{qed}\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} is intended to solve remaining goals. No facts are
+ passed to \isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}}.
\end{enumerate}
@@ -654,15 +654,15 @@
\begin{description}
- \item \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}} refines the goal by proof
- method \isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}}; facts for forward chaining are passed if so
- indicated by \isa{{\isachardoublequote}proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} mode.
+ \item \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} refines the goal by proof
+ method \isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}; facts for forward chaining are passed if so
+ indicated by \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} mode.
- \item \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}} refines any remaining goals by
- proof method \isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}} and concludes the sub-proof by assumption.
- If the goal had been \isa{{\isachardoublequote}show{\isachardoublequote}} (or \isa{{\isachardoublequote}thus{\isachardoublequote}}), some
+ \item \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} refines any remaining goals by
+ proof method \isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} and concludes the sub-proof by assumption.
+ If the goal had been \isa{{\isaliteral{22}{\isachardoublequote}}show{\isaliteral{22}{\isachardoublequote}}} (or \isa{{\isaliteral{22}{\isachardoublequote}}thus{\isaliteral{22}{\isachardoublequote}}}), some
pending sub-goal is solved as well by the rule resulting from the
- result \emph{exported} into the enclosing goal context. Thus \isa{{\isachardoublequote}qed{\isachardoublequote}} may fail for two reasons: either \isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}} fails, or the
+ result \emph{exported} into the enclosing goal context. Thus \isa{{\isaliteral{22}{\isachardoublequote}}qed{\isaliteral{22}{\isachardoublequote}}} may fail for two reasons: either \isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} fails, or the
resulting rule does not fit to any pending goal\footnote{This
includes any additional ``strong'' assumptions as introduced by
\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}.} of the enclosing context. Debugging such a
@@ -670,25 +670,25 @@
\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}, or weakening the local context by replacing
occurrences of \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}} by \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}}.
- \item \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}\ m\isactrlsub {\isadigit{2}}{\isachardoublequote}} is a \emph{terminal
- proof}\index{proof!terminal}; it abbreviates \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}}~\isa{{\isachardoublequote}qed{\isachardoublequote}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}}, but with
+ \item \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} is a \emph{terminal
+ proof}\index{proof!terminal}; it abbreviates \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}~\isa{{\isaliteral{22}{\isachardoublequote}}qed{\isaliteral{22}{\isachardoublequote}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}}, but with
backtracking across both methods. Debugging an unsuccessful
- \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}\ m\isactrlsub {\isadigit{2}}{\isachardoublequote}} command can be done by expanding its
- definition; in many cases \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}} (or even
- \isa{{\isachardoublequote}apply{\isachardoublequote}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}}) is already sufficient to see the
+ \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} command can be done by expanding its
+ definition; in many cases \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} (or even
+ \isa{{\isaliteral{22}{\isachardoublequote}}apply{\isaliteral{22}{\isachardoublequote}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}) is already sufficient to see the
problem.
- \item ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}}'' is a \emph{default
- proof}\index{proof!default}; it abbreviates \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isachardoublequote}rule{\isachardoublequote}}.
+ \item ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}}'' is a \emph{default
+ proof}\index{proof!default}; it abbreviates \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}rule{\isaliteral{22}{\isachardoublequote}}}.
- \item ``\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isachardot}}}}}'' is a \emph{trivial
- proof}\index{proof!trivial}; it abbreviates \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isachardoublequote}this{\isachardoublequote}}.
+ \item ``\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}}}}}'' is a \emph{trivial
+ proof}\index{proof!trivial}; it abbreviates \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}this{\isaliteral{22}{\isachardoublequote}}}.
\item \hyperlink{command.sorry}{\mbox{\isa{\isacommand{sorry}}}} is a \emph{fake proof}\index{proof!fake}
pretending to solve the pending claim without further ado. This
only works in interactive development, or if the \verb|quick_and_dirty| flag is enabled (in ML). Facts emerging from fake
proofs are not the real thing. Internally, each theorem container
- is tainted by an oracle invocation, which is indicated as ``\isa{{\isachardoublequote}{\isacharbrackleft}{\isacharbang}{\isacharbrackright}{\isachardoublequote}}'' in the printed result.
+ is tainted by an oracle invocation, which is indicated as ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}'' in the printed result.
The most important application of \hyperlink{command.sorry}{\mbox{\isa{\isacommand{sorry}}}} is to support
experimentation and top-down proof development.
@@ -708,7 +708,7 @@
\chref{ch:gen-tools} and \chref{ch:hol}).
\begin{matharray}{rcl}
- \indexdef{}{method}{-}\hypertarget{method.-}{\hyperlink{method.-}{\mbox{\isa{{\isacharminus}}}}} & : & \isa{method} \\
+ \indexdef{}{method}{-}\hypertarget{method.-}{\hyperlink{method.-}{\mbox{\isa{{\isaliteral{2D}{\isacharminus}}}}}} & : & \isa{method} \\
\indexdef{}{method}{fact}\hypertarget{method.fact}{\hyperlink{method.fact}{\mbox{\isa{fact}}}} & : & \isa{method} \\
\indexdef{}{method}{assumption}\hypertarget{method.assumption}{\hyperlink{method.assumption}{\mbox{\isa{assumption}}}} & : & \isa{method} \\
\indexdef{}{method}{this}\hypertarget{method.this}{\hyperlink{method.this}{\mbox{\isa{this}}}} & : & \isa{method} \\
@@ -743,19 +743,19 @@
\begin{description}
- \item ``\hyperlink{method.-}{\mbox{\isa{{\isacharminus}}}}'' (minus) does nothing but insert the forward
+ \item ``\hyperlink{method.-}{\mbox{\isa{{\isaliteral{2D}{\isacharminus}}}}}'' (minus) does nothing but insert the forward
chaining facts as premises into the goal. Note that command
\indexref{}{command}{proof}\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}} without any method actually performs a single
reduction step using the \indexref{}{method}{rule}\hyperlink{method.rule}{\mbox{\isa{rule}}} method; thus a plain
- \emph{do-nothing} proof step would be ``\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' rather than \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}} alone.
+ \emph{do-nothing} proof step would be ``\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{22}{\isachardoublequote}}}'' rather than \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}} alone.
- \item \hyperlink{method.fact}{\mbox{\isa{fact}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} composes some fact from
- \isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n{\isachardoublequote}} (or implicitly from the current proof context)
+ \item \hyperlink{method.fact}{\mbox{\isa{fact}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} composes some fact from
+ \isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} (or implicitly from the current proof context)
modulo unification of schematic type and term variables. The rule
structure is not taken into account, i.e.\ meta-level implication is
considered atomic. This is the same principle underlying literal
- facts (cf.\ \secref{sec:syn-att}): ``\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}{\isasymphi}{\isachardoublequote}}~\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{fact}'' is equivalent to ``\hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\verb|`|\isa{{\isasymphi}}\verb|`|'' provided that
- \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} is an instance of some known \isa{{\isachardoublequote}{\isasymturnstile}\ {\isasymphi}{\isachardoublequote}} in the
+ facts (cf.\ \secref{sec:syn-att}): ``\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{fact}'' is equivalent to ``\hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\verb|`|\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}}\verb|`|'' provided that
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} is an instance of some known \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} in the
proof context.
\item \hyperlink{method.assumption}{\mbox{\isa{assumption}}} solves some goal by a single assumption
@@ -767,9 +767,9 @@
all.
\item \hyperlink{method.this}{\mbox{\isa{this}}} applies all of the current facts directly as
- rules. Recall that ``\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isachardot}}}}}'' (dot) abbreviates ``\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{this}''.
+ rules. Recall that ``\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}}}}}'' (dot) abbreviates ``\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{this}''.
- \item \hyperlink{method.rule}{\mbox{\isa{rule}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} applies some rule given as
+ \item \hyperlink{method.rule}{\mbox{\isa{rule}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} applies some rule given as
argument in backward manner; facts are used to reduce the rule
before applying it to the goal. Thus \hyperlink{method.rule}{\mbox{\isa{rule}}} without facts
is plain introduction, while with facts it becomes elimination.
@@ -778,39 +778,39 @@
appropriate rules automatically, as declared in the current context
using the \hyperlink{attribute.Pure.intro}{\mbox{\isa{intro}}}, \hyperlink{attribute.Pure.elim}{\mbox{\isa{elim}}},
\hyperlink{attribute.Pure.dest}{\mbox{\isa{dest}}} attributes (see below). This is the
- default behavior of \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}} and ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}}''
+ default behavior of \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}} and ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}}''
(double-dot) steps (see \secref{sec:proof-steps}).
\item \hyperlink{attribute.Pure.intro}{\mbox{\isa{intro}}}, \hyperlink{attribute.Pure.elim}{\mbox{\isa{elim}}}, and
\hyperlink{attribute.Pure.dest}{\mbox{\isa{dest}}} declare introduction, elimination, and
destruct rules, to be used with method \hyperlink{method.rule}{\mbox{\isa{rule}}}, and similar
tools. Note that the latter will ignore rules declared with
- ``\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}'', while ``\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}'' are used most aggressively.
+ ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}'', while ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}}'' are used most aggressively.
The classical reasoner (see \secref{sec:classical}) introduces its
own variants of these attributes; use qualified names to access the
- present versions of Isabelle/Pure, i.e.\ \hyperlink{attribute.Pure.Pure.intro}{\mbox{\isa{Pure{\isachardot}intro}}}.
+ present versions of Isabelle/Pure, i.e.\ \hyperlink{attribute.Pure.Pure.intro}{\mbox{\isa{Pure{\isaliteral{2E}{\isachardot}}intro}}}.
\item \hyperlink{attribute.rule}{\mbox{\isa{rule}}}~\isa{del} undeclares introduction,
elimination, or destruct rules.
- \item \hyperlink{attribute.OF}{\mbox{\isa{OF}}}~\isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isachardoublequote}} applies some
- theorem to all of the given rules \isa{{\isachardoublequote}a\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ a\isactrlsub n{\isachardoublequote}}
+ \item \hyperlink{attribute.OF}{\mbox{\isa{OF}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} applies some
+ theorem to all of the given rules \isa{{\isaliteral{22}{\isachardoublequote}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}
(in parallel). This corresponds to the \verb|op MRS| operation in
ML, but note the reversed order. Positions may be effectively
- skipped by including ``\isa{{\isacharunderscore}}'' (underscore) as argument.
+ skipped by including ``\isa{{\isaliteral{5F}{\isacharunderscore}}}'' (underscore) as argument.
- \item \hyperlink{attribute.of}{\mbox{\isa{of}}}~\isa{{\isachardoublequote}t\isactrlsub {\isadigit{1}}\ {\isasymdots}\ t\isactrlsub n{\isachardoublequote}} performs positional
- instantiation of term variables. The terms \isa{{\isachardoublequote}t\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ t\isactrlsub n{\isachardoublequote}} are
+ \item \hyperlink{attribute.of}{\mbox{\isa{of}}}~\isa{{\isaliteral{22}{\isachardoublequote}}t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} performs positional
+ instantiation of term variables. The terms \isa{{\isaliteral{22}{\isachardoublequote}}t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} are
substituted for any schematic variables occurring in a theorem from
- left to right; ``\isa{{\isacharunderscore}}'' (underscore) indicates to skip a
- position. Arguments following a ``\isa{{\isachardoublequote}concl{\isacharcolon}{\isachardoublequote}}'' specification
+ left to right; ``\isa{{\isaliteral{5F}{\isacharunderscore}}}'' (underscore) indicates to skip a
+ position. Arguments following a ``\isa{{\isaliteral{22}{\isachardoublequote}}concl{\isaliteral{3A}{\isacharcolon}}{\isaliteral{22}{\isachardoublequote}}}'' specification
refer to positions of the conclusion of a rule.
- \item \hyperlink{attribute.where}{\mbox{\isa{where}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isacharequal}\ t\isactrlsub {\isadigit{1}}\ {\isasymAND}\ {\isasymdots}\ x\isactrlsub n\ {\isacharequal}\ t\isactrlsub n{\isachardoublequote}}
+ \item \hyperlink{attribute.where}{\mbox{\isa{where}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3D}{\isacharequal}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}
performs named instantiation of schematic type and term variables
occurring in a theorem. Schematic variables have to be specified on
- the left-hand side (e.g.\ \isa{{\isachardoublequote}{\isacharquery}x{\isadigit{1}}{\isachardot}{\isadigit{3}}{\isachardoublequote}}). The question mark may
+ the left-hand side (e.g.\ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}x{\isadigit{1}}{\isaliteral{2E}{\isachardot}}{\isadigit{3}}{\isaliteral{22}{\isachardoublequote}}}). The question mark may
be omitted if the variable name is a plain identifier without index.
As type instantiations are inferred from term instantiations,
explicit type instantiations are seldom necessary.
@@ -834,12 +834,12 @@
be used in scripts, too.
\begin{matharray}{rcl}
- \indexdef{}{command}{apply}\hypertarget{command.apply}{\hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{apply\_end}\hypertarget{command.apply-end}{\hyperlink{command.apply-end}{\mbox{\isa{\isacommand{apply{\isacharunderscore}end}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{done}\hypertarget{command.done}{\hyperlink{command.done}{\mbox{\isa{\isacommand{done}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ local{\isacharunderscore}theory\ {\isacharbar}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{defer}\hypertarget{command.defer}{\hyperlink{command.defer}{\mbox{\isa{\isacommand{defer}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}\ proof{\isachardoublequote}} \\
- \indexdef{}{command}{prefer}\hypertarget{command.prefer}{\hyperlink{command.prefer}{\mbox{\isa{\isacommand{prefer}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}\ proof{\isachardoublequote}} \\
- \indexdef{}{command}{back}\hypertarget{command.back}{\hyperlink{command.back}{\mbox{\isa{\isacommand{back}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}\ proof{\isachardoublequote}} \\
+ \indexdef{}{command}{apply}\hypertarget{command.apply}{\hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{apply\_end}\hypertarget{command.apply-end}{\hyperlink{command.apply-end}{\mbox{\isa{\isacommand{apply{\isaliteral{5F}{\isacharunderscore}}end}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{done}\hypertarget{command.done}{\hyperlink{command.done}{\mbox{\isa{\isacommand{done}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{7C}{\isacharbar}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{defer}\hypertarget{command.defer}{\hyperlink{command.defer}{\mbox{\isa{\isacommand{defer}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{prefer}\hypertarget{command.prefer}{\hyperlink{command.prefer}{\mbox{\isa{\isacommand{prefer}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{back}\hypertarget{command.back}{\hyperlink{command.back}{\mbox{\isa{\isacommand{back}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -854,7 +854,7 @@
\begin{description}
\item \hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}~\isa{m} applies proof method \isa{m} in
- initial position, but unlike \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}} it retains ``\isa{{\isachardoublequote}proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}}'' mode. Thus consecutive method applications may be
+ initial position, but unlike \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}} it retains ``\isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' mode. Thus consecutive method applications may be
given just as in tactic scripts.
Facts are passed to \isa{m} as indicated by the goal's
@@ -862,7 +862,7 @@
further \hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}} command would always work in a purely
backward manner.
- \item \hyperlink{command.apply-end}{\mbox{\isa{\isacommand{apply{\isacharunderscore}end}}}}~\isa{{\isachardoublequote}m{\isachardoublequote}} applies proof method \isa{m} as if in terminal position. Basically, this simulates a
+ \item \hyperlink{command.apply-end}{\mbox{\isa{\isacommand{apply{\isaliteral{5F}{\isacharunderscore}}end}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m{\isaliteral{22}{\isachardoublequote}}} applies proof method \isa{m} as if in terminal position. Basically, this simulates a
multi-step tactic script for \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}, but may be given
anywhere within the proof body.
@@ -872,11 +872,11 @@
\item \hyperlink{command.done}{\mbox{\isa{\isacommand{done}}}} completes a proof script, provided that the
current goal state is solved completely. Note that actual
- structured proof commands (e.g.\ ``\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isachardot}}}}}'' or \hyperlink{command.sorry}{\mbox{\isa{\isacommand{sorry}}}}) may be used to conclude proof scripts as well.
+ structured proof commands (e.g.\ ``\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}}}}}'' or \hyperlink{command.sorry}{\mbox{\isa{\isacommand{sorry}}}}) may be used to conclude proof scripts as well.
\item \hyperlink{command.defer}{\mbox{\isa{\isacommand{defer}}}}~\isa{n} and \hyperlink{command.prefer}{\mbox{\isa{\isacommand{prefer}}}}~\isa{n}
shuffle the list of pending goals: \hyperlink{command.defer}{\mbox{\isa{\isacommand{defer}}}} puts off
- sub-goal \isa{n} to the end of the list (\isa{{\isachardoublequote}n\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequote}} by
+ sub-goal \isa{n} to the end of the list (\isa{{\isaliteral{22}{\isachardoublequote}}n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} by
default), while \hyperlink{command.prefer}{\mbox{\isa{\isacommand{prefer}}}} brings sub-goal \isa{n} to the
front.
@@ -899,7 +899,7 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{method\_setup}\hypertarget{command.method-setup}{\hyperlink{command.method-setup}{\mbox{\isa{\isacommand{method{\isacharunderscore}setup}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
+ \indexdef{}{command}{method\_setup}\hypertarget{command.method-setup}{\hyperlink{command.method-setup}{\mbox{\isa{\isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -909,8 +909,8 @@
\begin{description}
- \item \hyperlink{command.method-setup}{\mbox{\isa{\isacommand{method{\isacharunderscore}setup}}}}~\isa{{\isachardoublequote}name\ {\isacharequal}\ text\ description{\isachardoublequote}}
- defines a proof method in the current theory. The given \isa{{\isachardoublequote}text{\isachardoublequote}} has to be an ML expression of type
+ \item \hyperlink{command.method-setup}{\mbox{\isa{\isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name\ {\isaliteral{3D}{\isacharequal}}\ text\ description{\isaliteral{22}{\isachardoublequote}}}
+ defines a proof method in the current theory. The given \isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}} has to be an ML expression of type
\verb|(Proof.context -> Proof.method) context_parser|, cf.\
basic parsers defined in structure \verb|Args| and \verb|Attrib|. There are also combinators like \verb|METHOD| and \verb|SIMPLE_METHOD| to turn certain tactic forms into official proof
methods; the primed versions refer to tactics with explicit goal
@@ -927,22 +927,22 @@
\endisadelimML
%
\isatagML
-\isacommand{method{\isacharunderscore}setup}\isamarkupfalse%
-\ my{\isacharunderscore}method{\isadigit{1}}\ {\isacharequal}\ {\isacharverbatimopen}\isanewline
-\ \ \ \ \ \ Scan{\isachardot}succeed\ {\isacharparenleft}K\ {\isacharparenleft}SIMPLE{\isacharunderscore}METHOD{\isacharprime}\ {\isacharparenleft}fn\ i{\isacharcolon}\ int\ {\isacharequal}{\isachargreater}\ no{\isacharunderscore}tac{\isacharparenright}{\isacharparenright}{\isacharparenright}\isanewline
-\ \ \ \ {\isacharverbatimclose}\ \ {\isachardoublequoteopen}my\ first\ method\ {\isacharparenleft}without\ any\ arguments{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}\isamarkupfalse%
+\ my{\isaliteral{5F}{\isacharunderscore}}method{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ \ \ \ \ Scan{\isaliteral{2E}{\isachardot}}succeed\ {\isaliteral{28}{\isacharparenleft}}K\ {\isaliteral{28}{\isacharparenleft}}SIMPLE{\isaliteral{5F}{\isacharunderscore}}METHOD{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}fn\ i{\isaliteral{3A}{\isacharcolon}}\ int\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ no{\isaliteral{5F}{\isacharunderscore}}tac{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ {\isaliteral{2A7D}{\isacharverbatimclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}my\ first\ method\ {\isaliteral{28}{\isacharparenleft}}without\ any\ arguments{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
-\ \ \ \ \isacommand{method{\isacharunderscore}setup}\isamarkupfalse%
-\ my{\isacharunderscore}method{\isadigit{2}}\ {\isacharequal}\ {\isacharverbatimopen}\isanewline
-\ \ \ \ \ \ Scan{\isachardot}succeed\ {\isacharparenleft}fn\ ctxt{\isacharcolon}\ Proof{\isachardot}context\ {\isacharequal}{\isachargreater}\isanewline
-\ \ \ \ \ \ \ \ SIMPLE{\isacharunderscore}METHOD{\isacharprime}\ {\isacharparenleft}fn\ i{\isacharcolon}\ int\ {\isacharequal}{\isachargreater}\ no{\isacharunderscore}tac{\isacharparenright}{\isacharparenright}\isanewline
-\ \ \ \ {\isacharverbatimclose}\ \ {\isachardoublequoteopen}my\ second\ method\ {\isacharparenleft}with\ context{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ \ \ \isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}\isamarkupfalse%
+\ my{\isaliteral{5F}{\isacharunderscore}}method{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ \ \ \ \ Scan{\isaliteral{2E}{\isachardot}}succeed\ {\isaliteral{28}{\isacharparenleft}}fn\ ctxt{\isaliteral{3A}{\isacharcolon}}\ Proof{\isaliteral{2E}{\isachardot}}context\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline
+\ \ \ \ \ \ \ \ SIMPLE{\isaliteral{5F}{\isacharunderscore}}METHOD{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}fn\ i{\isaliteral{3A}{\isacharcolon}}\ int\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ no{\isaliteral{5F}{\isacharunderscore}}tac{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ {\isaliteral{2A7D}{\isacharverbatimclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}my\ second\ method\ {\isaliteral{28}{\isacharparenleft}}with\ context{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
-\ \ \ \ \isacommand{method{\isacharunderscore}setup}\isamarkupfalse%
-\ my{\isacharunderscore}method{\isadigit{3}}\ {\isacharequal}\ {\isacharverbatimopen}\isanewline
-\ \ \ \ \ \ Attrib{\isachardot}thms\ {\isachargreater}{\isachargreater}\ {\isacharparenleft}fn\ thms{\isacharcolon}\ thm\ list\ {\isacharequal}{\isachargreater}\ fn\ ctxt{\isacharcolon}\ Proof{\isachardot}context\ {\isacharequal}{\isachargreater}\isanewline
-\ \ \ \ \ \ \ \ SIMPLE{\isacharunderscore}METHOD{\isacharprime}\ {\isacharparenleft}fn\ i{\isacharcolon}\ int\ {\isacharequal}{\isachargreater}\ no{\isacharunderscore}tac{\isacharparenright}{\isacharparenright}\isanewline
-\ \ \ \ {\isacharverbatimclose}\ \ {\isachardoublequoteopen}my\ third\ method\ {\isacharparenleft}with\ theorem\ arguments\ and\ context{\isacharparenright}{\isachardoublequoteclose}%
+\ \ \ \ \isacommand{method{\isaliteral{5F}{\isacharunderscore}}setup}\isamarkupfalse%
+\ my{\isaliteral{5F}{\isacharunderscore}}method{\isadigit{3}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ \ \ \ \ Attrib{\isaliteral{2E}{\isachardot}}thms\ {\isaliteral{3E}{\isachargreater}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}fn\ thms{\isaliteral{3A}{\isacharcolon}}\ thm\ list\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ fn\ ctxt{\isaliteral{3A}{\isacharcolon}}\ Proof{\isaliteral{2E}{\isachardot}}context\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline
+\ \ \ \ \ \ \ \ SIMPLE{\isaliteral{5F}{\isacharunderscore}}METHOD{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}fn\ i{\isaliteral{3A}{\isacharcolon}}\ int\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ no{\isaliteral{5F}{\isacharunderscore}}tac{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ {\isaliteral{2A7D}{\isacharverbatimclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}my\ third\ method\ {\isaliteral{28}{\isacharparenleft}}with\ theorem\ arguments\ and\ context{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagML
{\isafoldML}%
%
@@ -956,8 +956,8 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{obtain}\hypertarget{command.obtain}{\hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ proof{\isacharparenleft}chain{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{guess}\hypertarget{command.guess}{\hyperlink{command.guess}{\mbox{\isa{\isacommand{guess}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ proof{\isacharparenleft}chain{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
+ \indexdef{}{command}{obtain}\hypertarget{command.obtain}{\hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{guess}\hypertarget{command.guess}{\hyperlink{command.guess}{\mbox{\isa{\isacommand{guess}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
Generalized elimination means that additional elements with certain
@@ -979,19 +979,19 @@
\end{rail}
The derived Isar command \hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}} is defined as follows
- (where \isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ b\isactrlsub k{\isachardoublequote}} shall refer to (optional)
+ (where \isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{22}{\isachardoublequote}}} shall refer to (optional)
facts indicated for forward chaining).
\begin{matharray}{l}
- \isa{{\isachardoublequote}{\isasymlangle}using\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub k{\isasymrangle}{\isachardoublequote}}~~\hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m\ {\isasymWHERE}\ a{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ \ {\isasymlangle}proof{\isasymrangle}\ {\isasymequiv}{\isachardoublequote}} \\[1ex]
- \quad \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}{\isasymAnd}thesis{\isachardot}\ {\isacharparenleft}{\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ {\isasymLongrightarrow}\ thesis{\isacharparenright}\ {\isasymLongrightarrow}\ thesis{\isachardoublequote}} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C616E676C653E}{\isasymlangle}}using\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{5C3C72616E676C653E}{\isasymrangle}}{\isaliteral{22}{\isachardoublequote}}}~~\hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ \ {\isaliteral{5C3C6C616E676C653E}{\isasymlangle}}proof{\isaliteral{5C3C72616E676C653E}{\isasymrangle}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} \\[1ex]
+ \quad \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}thesis{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ thesis{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ thesis{\isaliteral{22}{\isachardoublequote}}} \\
\quad \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\hyperlink{method.succeed}{\mbox{\isa{succeed}}} \\
\qquad \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{thesis} \\
- \qquad \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}that\ {\isacharbrackleft}Pure{\isachardot}intro{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ {\isasymLongrightarrow}\ thesis{\isachardoublequote}} \\
+ \qquad \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}that\ {\isaliteral{5B}{\isacharbrackleft}}Pure{\isaliteral{2E}{\isachardot}}intro{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ thesis{\isaliteral{22}{\isachardoublequote}}} \\
\qquad \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{thesis} \\
- \quad\qquad \hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}~\isa{{\isacharminus}} \\
- \quad\qquad \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{{\isachardoublequote}b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub k\ \ {\isasymlangle}proof{\isasymrangle}{\isachardoublequote}} \\
+ \quad\qquad \hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}~\isa{{\isaliteral{2D}{\isacharminus}}} \\
+ \quad\qquad \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub k\ \ {\isaliteral{5C3C6C616E676C653E}{\isasymlangle}}proof{\isaliteral{5C3C72616E676C653E}{\isasymrangle}}{\isaliteral{22}{\isachardoublequote}}} \\
\quad \hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}} \\
- \quad \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardoublequote}}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}\ a{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}} \\
+ \quad \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
Typically, the soundness proof is relatively straight-forward, often
@@ -1015,9 +1015,9 @@
\medskip The improper variant \hyperlink{command.guess}{\mbox{\isa{\isacommand{guess}}}} is similar to
\hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}, but derives the obtained statement from the
course of reasoning! The proof starts with a fixed goal \isa{thesis}. The subsequent proof may refine this to anything of the
- form like \isa{{\isachardoublequote}{\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ {\isasymLongrightarrow}\ thesis{\isachardoublequote}}, but must not introduce new subgoals. The
+ form like \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ thesis{\isaliteral{22}{\isachardoublequote}}}, but must not introduce new subgoals. The
final goal state is then used as reduction rule for the obtain
- scheme described above. Obtained parameters \isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isachardoublequote}} are marked as internal by default, which prevents the
+ scheme described above. Obtained parameters \isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}} are marked as internal by default, which prevents the
proof context from being polluted by ad-hoc variables. The variable
names and type constraints given as arguments for \hyperlink{command.guess}{\mbox{\isa{\isacommand{guess}}}}
specify a prefix of obtained parameters explicitly in the text.
@@ -1033,19 +1033,19 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{also}\hypertarget{command.also}{\hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{finally}\hypertarget{command.finally}{\hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{moreover}\hypertarget{command.moreover}{\hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{ultimately}\hypertarget{command.ultimately}{\hyperlink{command.ultimately}{\mbox{\isa{\isacommand{ultimately}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}chain{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{print\_trans\_rules}\hypertarget{command.print-trans-rules}{\hyperlink{command.print-trans-rules}{\mbox{\isa{\isacommand{print{\isacharunderscore}trans{\isacharunderscore}rules}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{}{command}{also}\hypertarget{command.also}{\hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{finally}\hypertarget{command.finally}{\hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{moreover}\hypertarget{command.moreover}{\hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{ultimately}\hypertarget{command.ultimately}{\hyperlink{command.ultimately}{\mbox{\isa{\isacommand{ultimately}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_trans\_rules}\hypertarget{command.print-trans-rules}{\hyperlink{command.print-trans-rules}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}trans{\isaliteral{5F}{\isacharunderscore}}rules}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
\hyperlink{attribute.trans}{\mbox{\isa{trans}}} & : & \isa{attribute} \\
\hyperlink{attribute.sym}{\mbox{\isa{sym}}} & : & \isa{attribute} \\
\hyperlink{attribute.symmetric}{\mbox{\isa{symmetric}}} & : & \isa{attribute} \\
\end{matharray}
Calculational proof is forward reasoning with implicit application
- of transitivity rules (such those of \isa{{\isachardoublequote}{\isacharequal}{\isachardoublequote}}, \isa{{\isachardoublequote}{\isasymle}{\isachardoublequote}},
- \isa{{\isachardoublequote}{\isacharless}{\isachardoublequote}}). Isabelle/Isar maintains an auxiliary fact register
+ of transitivity rules (such those of \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}}, \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C653E}{\isasymle}}{\isaliteral{22}{\isachardoublequote}}},
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3C}{\isacharless}}{\isaliteral{22}{\isachardoublequote}}}). Isabelle/Isar maintains an auxiliary fact register
\indexref{}{fact}{calculation}\hyperlink{fact.calculation}{\mbox{\isa{calculation}}} for accumulating results obtained by
transitivity composed with the current result. Command \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}} updates \hyperlink{fact.calculation}{\mbox{\isa{calculation}}} involving \hyperlink{fact.this}{\mbox{\isa{this}}}, while
\hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}} exhibits the final \hyperlink{fact.calculation}{\mbox{\isa{calculation}}} by
@@ -1056,7 +1056,7 @@
but only collect further results in \hyperlink{fact.calculation}{\mbox{\isa{calculation}}} without
applying any rules yet.
- Also note that the implicit term abbreviation ``\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}'' has
+ Also note that the implicit term abbreviation ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}'' has
its canonical application with calculational proofs. It refers to
the argument of the preceding statement. (The argument of a curried
infix expression happens to be its right-hand side.)
@@ -1073,10 +1073,10 @@
handling of block-structure.}
\begin{matharray}{rcl}
- \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isachardoublequote}\isactrlsub {\isadigit{0}}{\isachardoublequote}} & \equiv & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ this{\isachardoublequote}} \\
- \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isachardoublequote}\isactrlsub n{\isacharplus}{\isadigit{1}}{\isachardoublequote}} & \equiv & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ trans\ {\isacharbrackleft}OF\ calculation\ this{\isacharbrackright}{\isachardoublequote}} \\[0.5ex]
+ \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{0}}{\isaliteral{22}{\isachardoublequote}}} & \equiv & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}calculation\ {\isaliteral{3D}{\isacharequal}}\ this{\isaliteral{22}{\isachardoublequote}}} \\
+ \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{2B}{\isacharplus}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & \equiv & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}calculation\ {\isaliteral{3D}{\isacharequal}}\ trans\ {\isaliteral{5B}{\isacharbrackleft}}OF\ calculation\ this{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} \\[0.5ex]
\hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}} & \equiv & \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}~\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{calculation} \\[0.5ex]
- \hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}} & \equiv & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ calculation\ this{\isachardoublequote}} \\
+ \hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}} & \equiv & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}calculation\ {\isaliteral{3D}{\isacharequal}}\ calculation\ this{\isaliteral{22}{\isachardoublequote}}} \\
\hyperlink{command.ultimately}{\mbox{\isa{\isacommand{ultimately}}}} & \equiv & \hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}}~\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{calculation} \\
\end{matharray}
@@ -1089,7 +1089,7 @@
\begin{description}
- \item \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}~\isa{{\isachardoublequote}{\isacharparenleft}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharparenright}{\isachardoublequote}} maintains the auxiliary
+ \item \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} maintains the auxiliary
\hyperlink{fact.calculation}{\mbox{\isa{calculation}}} register as follows. The first occurrence of
\hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}} in some calculational thread initializes \hyperlink{fact.calculation}{\mbox{\isa{calculation}}} by \hyperlink{fact.this}{\mbox{\isa{this}}}. Any subsequent \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}} on
the same level of block-structure updates \hyperlink{fact.calculation}{\mbox{\isa{calculation}}} by
@@ -1097,16 +1097,16 @@
current context, unless alternative rules are given as explicit
arguments.
- \item \hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}~\isa{{\isachardoublequote}{\isacharparenleft}a\isactrlsub {\isadigit{1}}\ {\isasymdots}\ a\isactrlsub n{\isacharparenright}{\isachardoublequote}} maintaining \hyperlink{fact.calculation}{\mbox{\isa{calculation}}} in the same way as \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}, and concludes the
+ \item \hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}a\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ a\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} maintaining \hyperlink{fact.calculation}{\mbox{\isa{calculation}}} in the same way as \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}, and concludes the
current calculational thread. The final result is exhibited as fact
for forward chaining towards the next goal. Basically, \hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}} just abbreviates \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}~\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\hyperlink{fact.calculation}{\mbox{\isa{calculation}}}. Typical idioms for concluding
- calculational proofs are ``\hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{{\isacharquery}thesis}~\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isachardot}}}}}'' and ``\hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isasymphi}}~\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isachardot}}}}}''.
+ calculational proofs are ``\hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{{\isaliteral{3F}{\isacharquery}}thesis}~\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}}}}}'' and ``\hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}}~\hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}}}}}''.
\item \hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}} and \hyperlink{command.ultimately}{\mbox{\isa{\isacommand{ultimately}}}} are
analogous to \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}} and \hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}, but collect
results only, without applying rules.
- \item \hyperlink{command.print-trans-rules}{\mbox{\isa{\isacommand{print{\isacharunderscore}trans{\isacharunderscore}rules}}}} prints the list of transitivity
+ \item \hyperlink{command.print-trans-rules}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}trans{\isaliteral{5F}{\isacharunderscore}}rules}}}} prints the list of transitivity
rules (for calculational commands \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}} and \hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}}) and symmetry rules (for the \hyperlink{attribute.symmetric}{\mbox{\isa{symmetric}}}
operation and single step elimination patters) of the current
context.
@@ -1114,15 +1114,15 @@
\item \hyperlink{attribute.trans}{\mbox{\isa{trans}}} declares theorems as transitivity rules.
\item \hyperlink{attribute.sym}{\mbox{\isa{sym}}} declares symmetry rules, as well as
- \hyperlink{attribute.Pure.elim}{\mbox{\isa{Pure{\isachardot}elim}}}\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}} rules.
+ \hyperlink{attribute.Pure.elim}{\mbox{\isa{Pure{\isaliteral{2E}{\isachardot}}elim}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}} rules.
\item \hyperlink{attribute.symmetric}{\mbox{\isa{symmetric}}} resolves a theorem with some rule
declared as \hyperlink{attribute.sym}{\mbox{\isa{sym}}} in the current context. For example,
- ``\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}{\isacharbrackleft}symmetric{\isacharbrackright}{\isacharcolon}\ x\ {\isacharequal}\ y{\isachardoublequote}}'' produces a
+ ``\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}symmetric{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequote}}}'' produces a
swapped fact derived from that assumption.
In structured proof texts it is often more appropriate to use an
- explicit single-step elimination proof, such as ``\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}x\ {\isacharequal}\ y{\isachardoublequote}}~\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}y\ {\isacharequal}\ x{\isachardoublequote}}~\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}}''.
+ explicit single-step elimination proof, such as ``\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}y\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}}''.
\end{description}%
\end{isamarkuptext}%
@@ -1138,10 +1138,10 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{case}\hypertarget{command.case}{\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}state{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{print\_cases}\hypertarget{command.print-cases}{\hyperlink{command.print-cases}{\mbox{\isa{\isacommand{print{\isacharunderscore}cases}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{attribute}{case\_names}\hypertarget{attribute.case-names}{\hyperlink{attribute.case-names}{\mbox{\isa{case{\isacharunderscore}names}}}} & : & \isa{attribute} \\
- \indexdef{}{attribute}{case\_conclusion}\hypertarget{attribute.case-conclusion}{\hyperlink{attribute.case-conclusion}{\mbox{\isa{case{\isacharunderscore}conclusion}}}} & : & \isa{attribute} \\
+ \indexdef{}{command}{case}\hypertarget{command.case}{\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_cases}\hypertarget{command.print-cases}{\hyperlink{command.print-cases}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}cases}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{attribute}{case\_names}\hypertarget{attribute.case-names}{\hyperlink{attribute.case-names}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}names}}}} & : & \isa{attribute} \\
+ \indexdef{}{attribute}{case\_conclusion}\hypertarget{attribute.case-conclusion}{\hyperlink{attribute.case-conclusion}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}conclusion}}}} & : & \isa{attribute} \\
\indexdef{}{attribute}{params}\hypertarget{attribute.params}{\hyperlink{attribute.params}{\mbox{\isa{params}}}} & : & \isa{attribute} \\
\indexdef{}{attribute}{consumes}\hypertarget{attribute.consumes}{\hyperlink{attribute.consumes}{\mbox{\isa{consumes}}}} & : & \isa{attribute} \\
\end{matharray}
@@ -1155,20 +1155,20 @@
The \hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}} command provides a shorthand to refer to a
local context symbolically: certain proof methods provide an
- environment of named ``cases'' of the form \isa{{\isachardoublequote}c{\isacharcolon}\ x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isacharcomma}\ {\isasymphi}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymphi}\isactrlsub n{\isachardoublequote}}; the effect of ``\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{c}'' is then equivalent to ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardoublequote}}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}c{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}}''. Term bindings may be covered as well, notably
- \hyperlink{variable.?case}{\mbox{\isa{{\isacharquery}case}}} for the main conclusion.
+ environment of named ``cases'' of the form \isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{3A}{\isacharcolon}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}; the effect of ``\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{c}'' is then equivalent to ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}''. Term bindings may be covered as well, notably
+ \hyperlink{variable.?case}{\mbox{\isa{{\isaliteral{3F}{\isacharquery}}case}}} for the main conclusion.
- By default, the ``terminology'' \isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isachardoublequote}} of
+ By default, the ``terminology'' \isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}} of
a case value is marked as hidden, i.e.\ there is no way to refer to
such parameters in the subsequent proof text. After all, original
rule parameters stem from somewhere outside of the current proof
- text. By using the explicit form ``\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{{\isachardoublequote}{\isacharparenleft}c\ y\isactrlsub {\isadigit{1}}\ {\isasymdots}\ y\isactrlsub m{\isacharparenright}{\isachardoublequote}}'' instead, the proof author is able to
+ text. By using the explicit form ``\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}c\ y\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ y\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' instead, the proof author is able to
chose local names that fit nicely into the current context.
\medskip It is important to note that proper use of \hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}} does not provide means to peek at the current goal state,
which is not directly observable in Isar! Nonetheless, goal
- refinement commands do provide named cases \isa{{\isachardoublequote}goal\isactrlsub i{\isachardoublequote}}
- for each subgoal \isa{{\isachardoublequote}i\ {\isacharequal}\ {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ n{\isachardoublequote}} of the resulting goal state.
+ refinement commands do provide named cases \isa{{\isaliteral{22}{\isachardoublequote}}goal\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}}
+ for each subgoal \isa{{\isaliteral{22}{\isachardoublequote}}i\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ n{\isaliteral{22}{\isachardoublequote}}} of the resulting goal state.
Using this extra feature requires great care, because some bits of
the internal tactical machinery intrude the proof text. In
particular, parameter names stemming from the left-over of automated
@@ -1204,28 +1204,28 @@
\begin{description}
- \item \hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{{\isachardoublequote}{\isacharparenleft}c\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isacharparenright}{\isachardoublequote}} invokes a named local
- context \isa{{\isachardoublequote}c{\isacharcolon}\ x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isacharcomma}\ {\isasymphi}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymphi}\isactrlsub m{\isachardoublequote}}, as provided by an
+ \item \hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}c\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} invokes a named local
+ context \isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{3A}{\isacharcolon}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}}, as provided by an
appropriate proof method (such as \indexref{}{method}{cases}\hyperlink{method.cases}{\mbox{\isa{cases}}} and
- \indexref{}{method}{induct}\hyperlink{method.induct}{\mbox{\isa{induct}}}). The command ``\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{{\isachardoublequote}{\isacharparenleft}c\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isacharparenright}{\isachardoublequote}}'' abbreviates ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardoublequote}}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}c{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}}''.
+ \indexref{}{method}{induct}\hyperlink{method.induct}{\mbox{\isa{induct}}}). The command ``\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}c\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' abbreviates ``\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}''.
- \item \hyperlink{command.print-cases}{\mbox{\isa{\isacommand{print{\isacharunderscore}cases}}}} prints all local contexts of the
+ \item \hyperlink{command.print-cases}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}cases}}}} prints all local contexts of the
current state, using Isar proof language notation.
- \item \hyperlink{attribute.case-names}{\mbox{\isa{case{\isacharunderscore}names}}}~\isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}\ {\isasymdots}\ c\isactrlsub k{\isachardoublequote}} declares names for
- the local contexts of premises of a theorem; \isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub k{\isachardoublequote}}
+ \item \hyperlink{attribute.case-names}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}names}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{22}{\isachardoublequote}}} declares names for
+ the local contexts of premises of a theorem; \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{22}{\isachardoublequote}}}
refers to the \emph{suffix} of the list of premises.
- \item \hyperlink{attribute.case-conclusion}{\mbox{\isa{case{\isacharunderscore}conclusion}}}~\isa{{\isachardoublequote}c\ d\isactrlsub {\isadigit{1}}\ {\isasymdots}\ d\isactrlsub k{\isachardoublequote}} declares
- names for the conclusions of a named premise \isa{c}; here \isa{{\isachardoublequote}d\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ d\isactrlsub k{\isachardoublequote}} refers to the prefix of arguments of a logical formula
- built by nesting a binary connective (e.g.\ \isa{{\isachardoublequote}{\isasymor}{\isachardoublequote}}).
+ \item \hyperlink{attribute.case-conclusion}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}conclusion}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ d\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ d\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{22}{\isachardoublequote}}} declares
+ names for the conclusions of a named premise \isa{c}; here \isa{{\isaliteral{22}{\isachardoublequote}}d\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ d\isaliteral{5C3C5E7375623E}{}\isactrlsub k{\isaliteral{22}{\isachardoublequote}}} refers to the prefix of arguments of a logical formula
+ built by nesting a binary connective (e.g.\ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6F723E}{\isasymor}}{\isaliteral{22}{\isachardoublequote}}}).
Note that proof methods such as \hyperlink{method.induct}{\mbox{\isa{induct}}} and \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}} already provide a default name for the conclusion as a
whole. The need to name subformulas only arises with cases that
split into several sub-cases, as in common co-induction rules.
- \item \hyperlink{attribute.params}{\mbox{\isa{params}}}~\isa{{\isachardoublequote}p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub m\ {\isasymAND}\ {\isasymdots}\ q\isactrlsub {\isadigit{1}}\ {\isasymdots}\ q\isactrlsub n{\isachardoublequote}} renames
- the innermost parameters of premises \isa{{\isachardoublequote}{\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ n{\isachardoublequote}} of some
+ \item \hyperlink{attribute.params}{\mbox{\isa{params}}}~\isa{{\isaliteral{22}{\isachardoublequote}}p\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub m\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ q\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ q\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} renames
+ the innermost parameters of premises \isa{{\isaliteral{22}{\isachardoublequote}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ n{\isaliteral{22}{\isachardoublequote}}} of some
theorem. An empty list of names may be given to skip positions,
leaving the present parameters unchanged.
@@ -1235,7 +1235,7 @@
\item \hyperlink{attribute.consumes}{\mbox{\isa{consumes}}}~\isa{n} declares the number of ``major
premises'' of a rule, i.e.\ the number of facts to be consumed when
it is applied by an appropriate proof method. The default value of
- \hyperlink{attribute.consumes}{\mbox{\isa{consumes}}} is \isa{{\isachardoublequote}n\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequote}}, which is appropriate for
+ \hyperlink{attribute.consumes}{\mbox{\isa{consumes}}} is \isa{{\isaliteral{22}{\isachardoublequote}}n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}, which is appropriate for
the usual kind of cases and induction rules for inductive sets (cf.\
\secref{sec:hol-inductive}). Rules without any \hyperlink{attribute.consumes}{\mbox{\isa{consumes}}} declaration given are treated as if \hyperlink{attribute.consumes}{\mbox{\isa{consumes}}}~\isa{{\isadigit{0}}} had been specified.
@@ -1296,7 +1296,7 @@
\begin{description}
- \item \hyperlink{method.cases}{\mbox{\isa{cases}}}~\isa{{\isachardoublequote}insts\ R{\isachardoublequote}} applies method \hyperlink{method.rule}{\mbox{\isa{rule}}} with an appropriate case distinction theorem, instantiated to
+ \item \hyperlink{method.cases}{\mbox{\isa{cases}}}~\isa{{\isaliteral{22}{\isachardoublequote}}insts\ R{\isaliteral{22}{\isachardoublequote}}} applies method \hyperlink{method.rule}{\mbox{\isa{rule}}} with an appropriate case distinction theorem, instantiated to
the subjects \isa{insts}. Symbolic case names are bound according
to the rule's local contexts.
@@ -1308,8 +1308,8 @@
facts & & arguments & rule \\\hline
& \hyperlink{method.cases}{\mbox{\isa{cases}}} & & classical case split \\
& \hyperlink{method.cases}{\mbox{\isa{cases}}} & \isa{t} & datatype exhaustion (type of \isa{t}) \\
- \isa{{\isachardoublequote}{\isasymturnstile}\ A\ t{\isachardoublequote}} & \hyperlink{method.cases}{\mbox{\isa{cases}}} & \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & inductive predicate/set elimination (of \isa{A}) \\
- \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & \hyperlink{method.cases}{\mbox{\isa{cases}}} & \isa{{\isachardoublequote}{\isasymdots}\ rule{\isacharcolon}\ R{\isachardoublequote}} & explicit rule \isa{R} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A\ t{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{method.cases}{\mbox{\isa{cases}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & inductive predicate/set elimination (of \isa{A}) \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{method.cases}{\mbox{\isa{cases}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ rule{\isaliteral{3A}{\isacharcolon}}\ R{\isaliteral{22}{\isachardoublequote}}} & explicit rule \isa{R} \\
\end{tabular}
\medskip
@@ -1317,31 +1317,31 @@
of premises of the case rule; within each premise, the \emph{prefix}
of variables is instantiated. In most situations, only a single
term needs to be specified; this refers to the first variable of the
- last premise (it is usually the same for all cases). The \isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}simp{\isacharparenright}{\isachardoublequote}} option can be used to disable pre-simplification of
+ last premise (it is usually the same for all cases). The \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option can be used to disable pre-simplification of
cases (see the description of \hyperlink{method.induct}{\mbox{\isa{induct}}} below for details).
- \item \hyperlink{method.induct}{\mbox{\isa{induct}}}~\isa{{\isachardoublequote}insts\ R{\isachardoublequote}} is analogous to the
+ \item \hyperlink{method.induct}{\mbox{\isa{induct}}}~\isa{{\isaliteral{22}{\isachardoublequote}}insts\ R{\isaliteral{22}{\isachardoublequote}}} is analogous to the
\hyperlink{method.cases}{\mbox{\isa{cases}}} method, but refers to induction rules, which are
determined as follows:
\medskip
\begin{tabular}{llll}
facts & & arguments & rule \\\hline
- & \hyperlink{method.induct}{\mbox{\isa{induct}}} & \isa{{\isachardoublequote}P\ x{\isachardoublequote}} & datatype induction (type of \isa{x}) \\
- \isa{{\isachardoublequote}{\isasymturnstile}\ A\ x{\isachardoublequote}} & \hyperlink{method.induct}{\mbox{\isa{induct}}} & \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & predicate/set induction (of \isa{A}) \\
- \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & \hyperlink{method.induct}{\mbox{\isa{induct}}} & \isa{{\isachardoublequote}{\isasymdots}\ rule{\isacharcolon}\ R{\isachardoublequote}} & explicit rule \isa{R} \\
+ & \hyperlink{method.induct}{\mbox{\isa{induct}}} & \isa{{\isaliteral{22}{\isachardoublequote}}P\ x{\isaliteral{22}{\isachardoublequote}}} & datatype induction (type of \isa{x}) \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7475726E7374696C653E}{\isasymturnstile}}\ A\ x{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{method.induct}{\mbox{\isa{induct}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & predicate/set induction (of \isa{A}) \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{method.induct}{\mbox{\isa{induct}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ rule{\isaliteral{3A}{\isacharcolon}}\ R{\isaliteral{22}{\isachardoublequote}}} & explicit rule \isa{R} \\
\end{tabular}
\medskip
Several instantiations may be given, each referring to some part of
a mutual inductive definition or datatype --- only related partial
induction rules may be used together, though. Any of the lists of
- terms \isa{{\isachardoublequote}P{\isacharcomma}\ x{\isacharcomma}\ {\isasymdots}{\isachardoublequote}} refers to the \emph{suffix} of variables
+ terms \isa{{\isaliteral{22}{\isachardoublequote}}P{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} refers to the \emph{suffix} of variables
present in the induction rule. This enables the writer to specify
only induction variables, or both predicates and variables, for
example.
- Instantiations may be definitional: equations \isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}}
+ Instantiations may be definitional: equations \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}
introduce local definitions, which are inserted into the claim and
discharged after applying the induction rule. Equalities reappear
in the inductive cases, but have been transformed according to the
@@ -1349,7 +1349,7 @@
practically useful induction hypotheses, some variables occurring in
\isa{t} need to be fixed (see below). Instantiations of the form
\isa{t}, where \isa{t} is not a variable, are taken as a
- shorthand for \mbox{\isa{{\isachardoublequote}x\ {\isasymequiv}\ t{\isachardoublequote}}}, where \isa{x} is a fresh
+ shorthand for \mbox{\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}}, where \isa{x} is a fresh
variable. If this is not intended, \isa{t} has to be enclosed in
parentheses. By default, the equalities generated by definitional
instantiations are pre-simplified using a specific set of rules,
@@ -1357,23 +1357,23 @@
datatypes. This pre-simplification may cause some of the parameters
of an inductive case to disappear, or may even completely delete
some of the inductive cases, if one of the equalities occurring in
- their premises can be simplified to \isa{False}. The \isa{{\isachardoublequote}{\isacharparenleft}no{\isacharunderscore}simp{\isacharparenright}{\isachardoublequote}} option can be used to disable pre-simplification.
+ their premises can be simplified to \isa{False}. The \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option can be used to disable pre-simplification.
Additional rules to be used in pre-simplification can be declared
- using the \indexdef{}{attribute}{induct\_simp}\hypertarget{attribute.induct-simp}{\hyperlink{attribute.induct-simp}{\mbox{\isa{induct{\isacharunderscore}simp}}}} attribute.
+ using the \indexdef{}{attribute}{induct\_simp}\hypertarget{attribute.induct-simp}{\hyperlink{attribute.induct-simp}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}simp}}}} attribute.
- The optional ``\isa{{\isachardoublequote}arbitrary{\isacharcolon}\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardoublequote}}''
- specification generalizes variables \isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ x\isactrlsub m{\isachardoublequote}} of the original goal before applying induction. Thus
+ The optional ``\isa{{\isaliteral{22}{\isachardoublequote}}arbitrary{\isaliteral{3A}{\isacharcolon}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}}''
+ specification generalizes variables \isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}} of the original goal before applying induction. Thus
induction hypotheses may become sufficiently general to get the
proof through. Together with definitional instantiations, one may
effectively perform induction over expressions of a certain
structure.
- The optional ``\isa{{\isachardoublequote}taking{\isacharcolon}\ t\isactrlsub {\isadigit{1}}\ {\isasymdots}\ t\isactrlsub n{\isachardoublequote}}''
+ The optional ``\isa{{\isaliteral{22}{\isachardoublequote}}taking{\isaliteral{3A}{\isacharcolon}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}''
specification provides additional instantiations of a prefix of
pending variables in the rule. Such schematic induction rules
rarely occur in practice, though.
- \item \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}}~\isa{{\isachardoublequote}inst\ R{\isachardoublequote}} is analogous to the
+ \item \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}}~\isa{{\isaliteral{22}{\isachardoublequote}}inst\ R{\isaliteral{22}{\isachardoublequote}}} is analogous to the
\hyperlink{method.induct}{\mbox{\isa{induct}}} method, but refers to coinduction rules, which are
determined as follows:
@@ -1381,20 +1381,20 @@
\begin{tabular}{llll}
goal & & arguments & rule \\\hline
& \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}} & \isa{x} & type coinduction (type of \isa{x}) \\
- \isa{{\isachardoublequote}A\ x{\isachardoublequote}} & \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}} & \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & predicate/set coinduction (of \isa{A}) \\
- \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}} & \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}} & \isa{{\isachardoublequote}{\isasymdots}\ rule{\isacharcolon}\ R{\isachardoublequote}} & explicit rule \isa{R} \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}A\ x{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & predicate/set coinduction (of \isa{A}) \\
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ rule{\isaliteral{3A}{\isacharcolon}}\ R{\isaliteral{22}{\isachardoublequote}}} & explicit rule \isa{R} \\
\end{tabular}
Coinduction is the dual of induction. Induction essentially
- eliminates \isa{{\isachardoublequote}A\ x{\isachardoublequote}} towards a generic result \isa{{\isachardoublequote}P\ x{\isachardoublequote}},
- while coinduction introduces \isa{{\isachardoublequote}A\ x{\isachardoublequote}} starting with \isa{{\isachardoublequote}B\ x{\isachardoublequote}}, for a suitable ``bisimulation'' \isa{B}. The cases of a
+ eliminates \isa{{\isaliteral{22}{\isachardoublequote}}A\ x{\isaliteral{22}{\isachardoublequote}}} towards a generic result \isa{{\isaliteral{22}{\isachardoublequote}}P\ x{\isaliteral{22}{\isachardoublequote}}},
+ while coinduction introduces \isa{{\isaliteral{22}{\isachardoublequote}}A\ x{\isaliteral{22}{\isachardoublequote}}} starting with \isa{{\isaliteral{22}{\isachardoublequote}}B\ x{\isaliteral{22}{\isachardoublequote}}}, for a suitable ``bisimulation'' \isa{B}. The cases of a
coinduct rule are typically named after the predicates or sets being
covered, while the conclusions consist of several alternatives being
named after the individual destructor patterns.
The given instantiation refers to the \emph{suffix} of variables
occurring in the rule's major premise, or conclusion if unavailable.
- An additional ``\isa{{\isachardoublequote}taking{\isacharcolon}\ t\isactrlsub {\isadigit{1}}\ {\isasymdots}\ t\isactrlsub n{\isachardoublequote}}''
+ An additional ``\isa{{\isaliteral{22}{\isachardoublequote}}taking{\isaliteral{3A}{\isacharcolon}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}''
specification may be required in order to specify the bisimulation
to be used in the coinduction step.
@@ -1404,17 +1404,17 @@
instantiated rule as given in the text. Beyond that, the \hyperlink{method.induct}{\mbox{\isa{induct}}} and \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}} methods guess further instantiations
from the goal specification itself. Any persisting unresolved
schematic variables of the resulting rule will render the the
- corresponding case invalid. The term binding \hyperlink{variable.?case}{\mbox{\isa{{\isacharquery}case}}} for
+ corresponding case invalid. The term binding \hyperlink{variable.?case}{\mbox{\isa{{\isaliteral{3F}{\isacharquery}}case}}} for
the conclusion will be provided with each case, provided that term
is fully specified.
- The \hyperlink{command.print-cases}{\mbox{\isa{\isacommand{print{\isacharunderscore}cases}}}} command prints all named cases present
+ The \hyperlink{command.print-cases}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}cases}}}} command prints all named cases present
in the current proof state.
\medskip Despite the additional infrastructure, both \hyperlink{method.cases}{\mbox{\isa{cases}}}
and \hyperlink{method.coinduct}{\mbox{\isa{coinduct}}} merely apply a certain rule, after
instantiation, while conforming due to the usual way of monotonic
- natural deduction: the context of a structured statement \isa{{\isachardoublequote}{\isasymAnd}x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub m{\isachardot}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ {\isasymdots}\ {\isasymphi}\isactrlsub n\ {\isasymLongrightarrow}\ {\isasymdots}{\isachardoublequote}}
+ natural deduction: the context of a structured statement \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}
reappears unchanged after the case split.
The \hyperlink{method.induct}{\mbox{\isa{induct}}} method is fundamentally different in this
@@ -1429,7 +1429,7 @@
In induction proofs, local assumptions introduced by cases are split
into two different kinds: \isa{hyps} stemming from the rule and
\isa{prems} from the goal statement. This is reflected in the
- extracted cases accordingly, so invoking ``\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{c}'' will provide separate facts \isa{c{\isachardot}hyps} and \isa{c{\isachardot}prems},
+ extracted cases accordingly, so invoking ``\hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{c}'' will provide separate facts \isa{c{\isaliteral{2E}{\isachardot}}hyps} and \isa{c{\isaliteral{2E}{\isachardot}}prems},
as well as fact \isa{c} to hold the all-inclusive list.
\medskip Facts presented to either method are consumed according to
@@ -1448,7 +1448,7 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{print\_induct\_rules}\hypertarget{command.print-induct-rules}{\hyperlink{command.print-induct-rules}{\mbox{\isa{\isacommand{print{\isacharunderscore}induct{\isacharunderscore}rules}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{}{command}{print\_induct\_rules}\hypertarget{command.print-induct-rules}{\hyperlink{command.print-induct-rules}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}induct{\isaliteral{5F}{\isacharunderscore}}rules}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
\indexdef{}{attribute}{cases}\hypertarget{attribute.cases}{\hyperlink{attribute.cases}{\mbox{\isa{cases}}}} & : & \isa{attribute} \\
\indexdef{}{attribute}{induct}\hypertarget{attribute.induct}{\hyperlink{attribute.induct}{\mbox{\isa{induct}}}} & : & \isa{attribute} \\
\indexdef{}{attribute}{coinduct}\hypertarget{attribute.coinduct}{\hyperlink{attribute.coinduct}{\mbox{\isa{coinduct}}}} & : & \isa{attribute} \\
@@ -1468,7 +1468,7 @@
\begin{description}
- \item \hyperlink{command.print-induct-rules}{\mbox{\isa{\isacommand{print{\isacharunderscore}induct{\isacharunderscore}rules}}}} prints cases and induct rules
+ \item \hyperlink{command.print-induct-rules}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}induct{\isaliteral{5F}{\isacharunderscore}}rules}}}} prints cases and induct rules
for predicates (or sets) and types of the current context.
\item \hyperlink{attribute.cases}{\mbox{\isa{cases}}}, \hyperlink{attribute.induct}{\mbox{\isa{induct}}}, and \hyperlink{attribute.coinduct}{\mbox{\isa{coinduct}}} (as attributes) declare rules for reasoning about
@@ -1477,12 +1477,12 @@
packages of object-logics usually declare emerging cases and
induction rules as expected, so users rarely need to intervene.
- Rules may be deleted via the \isa{{\isachardoublequote}del{\isachardoublequote}} specification, which
- covers all of the \isa{{\isachardoublequote}type{\isachardoublequote}}/\isa{{\isachardoublequote}pred{\isachardoublequote}}/\isa{{\isachardoublequote}set{\isachardoublequote}}
+ Rules may be deleted via the \isa{{\isaliteral{22}{\isachardoublequote}}del{\isaliteral{22}{\isachardoublequote}}} specification, which
+ covers all of the \isa{{\isaliteral{22}{\isachardoublequote}}type{\isaliteral{22}{\isachardoublequote}}}/\isa{{\isaliteral{22}{\isachardoublequote}}pred{\isaliteral{22}{\isachardoublequote}}}/\isa{{\isaliteral{22}{\isachardoublequote}}set{\isaliteral{22}{\isachardoublequote}}}
sub-categories simultaneously. For example, \hyperlink{attribute.cases}{\mbox{\isa{cases}}}~\isa{del} removes any \hyperlink{attribute.cases}{\mbox{\isa{cases}}} rules declared for
some type, predicate, or set.
- Manual rule declarations usually refer to the \hyperlink{attribute.case-names}{\mbox{\isa{case{\isacharunderscore}names}}} and \hyperlink{attribute.params}{\mbox{\isa{params}}} attributes to adjust names of
+ Manual rule declarations usually refer to the \hyperlink{attribute.case-names}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}names}}} and \hyperlink{attribute.params}{\mbox{\isa{params}}} attributes to adjust names of
cases and parameters of a rule; the \hyperlink{attribute.consumes}{\mbox{\isa{consumes}}}
declaration is taken care of automatically: \hyperlink{attribute.consumes}{\mbox{\isa{consumes}}}~\isa{{\isadigit{0}}} is specified for ``type'' rules and \hyperlink{attribute.consumes}{\mbox{\isa{consumes}}}~\isa{{\isadigit{1}}} for ``predicate'' / ``set'' rules.
--- a/doc-src/IsarRef/Thy/document/Quick_Reference.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarRef/Thy/document/Quick_Reference.tex Mon Nov 08 14:41:11 2010 +0100
@@ -1,6 +1,6 @@
%
\begin{isabellebody}%
-\def\isabellecontext{Quick{\isacharunderscore}Reference}%
+\def\isabellecontext{Quick{\isaliteral{5F}{\isacharunderscore}}Reference}%
%
\isadelimtheory
%
@@ -8,7 +8,7 @@
%
\isatagtheory
\isacommand{theory}\isamarkupfalse%
-\ Quick{\isacharunderscore}Reference\isanewline
+\ Quick{\isaliteral{5F}{\isacharunderscore}}Reference\isanewline
\isakeyword{imports}\ Main\isanewline
\isakeyword{begin}%
\endisatagtheory
@@ -32,38 +32,38 @@
%
\begin{isamarkuptext}%
\begin{tabular}{ll}
- \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x} & augment context by \isa{{\isachardoublequote}{\isasymAnd}x{\isachardot}\ {\isasymbox}{\isachardoublequote}} \\
- \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} & augment context by \isa{{\isachardoublequote}{\isasymphi}\ {\isasymLongrightarrow}\ {\isasymbox}{\isachardoublequote}} \\
+ \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x} & augment context by \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C626F783E}{\isasymbox}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} & augment context by \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C626F783E}{\isasymbox}}{\isaliteral{22}{\isachardoublequote}}} \\
\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}} & indicate forward chaining of facts \\
- \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} & prove local result \\
- \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} & prove local result, refining some goal \\
+ \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} & prove local result \\
+ \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} & prove local result, refining some goal \\
\hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{a} & indicate use of additional facts \\
\hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}~\isa{a} & unfold definitional equations \\
- \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}}~\dots~\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}} & indicate proof structure and refinements \\
- \hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isacharbraceleft}}}}}~\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}~\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isacharbraceright}}}}} & indicate explicit blocks \\
+ \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}~\dots~\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} & indicate proof structure and refinements \\
+ \hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isaliteral{7B}{\isacharbraceleft}}}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isaliteral{7D}{\isacharbraceright}}}}}} & indicate explicit blocks \\
\hyperlink{command.next}{\mbox{\isa{\isacommand{next}}}} & switch blocks \\
- \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isachardoublequote}a\ {\isacharequal}\ b{\isachardoublequote}} & reconsider facts \\
- \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}~\isa{{\isachardoublequote}p\ {\isacharequal}\ t{\isachardoublequote}} & abbreviate terms by higher-order matching \\
+ \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{22}{\isachardoublequote}}} & reconsider facts \\
+ \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}p\ {\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{22}{\isachardoublequote}}} & abbreviate terms by higher-order matching \\
\end{tabular}
\medskip
\begin{tabular}{rcl}
- \isa{{\isachardoublequote}theory{\isasymdash}stmt{\isachardoublequote}} & = & \hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}~\isa{{\isachardoublequote}name{\isacharcolon}\ props\ proof\ \ {\isacharbar}{\isachardoublequote}}~~\hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}~\isa{{\isachardoublequote}{\isasymdots}\ \ {\isacharbar}\ \ {\isasymdots}{\isachardoublequote}} \\[1ex]
- \isa{{\isachardoublequote}proof{\isachardoublequote}} & = & \isa{{\isachardoublequote}prfx\isactrlsup {\isacharasterisk}{\isachardoublequote}}~\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}method\isactrlsup {\isacharquery}\ stmt\isactrlsup {\isacharasterisk}{\isachardoublequote}}~\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isachardoublequote}method\isactrlsup {\isacharquery}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \isa{{\isachardoublequote}prfx\isactrlsup {\isacharasterisk}{\isachardoublequote}}~\hyperlink{command.done}{\mbox{\isa{\isacommand{done}}}} \\[1ex]
+ \isa{{\isaliteral{22}{\isachardoublequote}}theory{\isaliteral{5C3C646173683E}{\isasymdash}}stmt{\isaliteral{22}{\isachardoublequote}}} & = & \hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{3A}{\isacharcolon}}\ props\ proof\ \ {\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}}~~\hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ \ {\isaliteral{7C}{\isacharbar}}\ \ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}} \\[1ex]
+ \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{22}{\isachardoublequote}}} & = & \isa{{\isaliteral{22}{\isachardoublequote}}prfx\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}method\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{3F}{\isacharquery}}\ stmt\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}method\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}prfx\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.done}{\mbox{\isa{\isacommand{done}}}} \\[1ex]
\isa{prfx} & = & \hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}~\isa{method} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{{\isachardoublequote}facts{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}~\isa{{\isachardoublequote}facts{\isachardoublequote}} \\
- \isa{stmt} & = & \hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isacharbraceleft}}}}}~\isa{{\isachardoublequote}stmt\isactrlsup {\isacharasterisk}{\isachardoublequote}}~\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isacharbraceright}}}}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.next}{\mbox{\isa{\isacommand{next}}}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isachardoublequote}name\ {\isacharequal}\ facts{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}~\isa{{\isachardoublequote}term\ {\isacharequal}\ term{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isachardoublequote}var\isactrlsup {\isacharplus}{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}name{\isacharcolon}\ props{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharquery}{\isachardoublequote}}~\isa{goal} \\
- \isa{goal} & = & \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isachardoublequote}name{\isacharcolon}\ props\ proof{\isachardoublequote}} \\
- & \isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}} & \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{{\isachardoublequote}name{\isacharcolon}\ props\ proof{\isachardoublequote}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.using}{\mbox{\isa{\isacommand{using}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}facts{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.unfolding}{\mbox{\isa{\isacommand{unfolding}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}facts{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{stmt} & = & \hyperlink{command.braceleft}{\mbox{\isa{\isacommand{{\isaliteral{7B}{\isacharbraceleft}}}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}stmt\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.braceright}{\mbox{\isa{\isacommand{{\isaliteral{7D}{\isacharbraceright}}}}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.next}{\mbox{\isa{\isacommand{next}}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name\ {\isaliteral{3D}{\isacharequal}}\ facts{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.let}{\mbox{\isa{\isacommand{let}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}term\ {\isaliteral{3D}{\isacharequal}}\ term{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}var\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{3A}{\isacharcolon}}\ props{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}~\isa{goal} \\
+ \isa{goal} & = & \hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{3A}{\isacharcolon}}\ props\ proof{\isaliteral{22}{\isachardoublequote}}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{3A}{\isacharcolon}}\ props\ proof{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -74,17 +74,17 @@
%
\begin{isamarkuptext}%
\begin{tabular}{rcl}
- \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}\ m\isactrlsub {\isadigit{2}}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} &
- \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{1}}{\isachardoublequote}}~\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isachardoublequote}m\isactrlsub {\isadigit{2}}{\isachardoublequote}} \\
- \hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} & \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{rule} \\
- \hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isachardot}}}}} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} & \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{this} \\
- \hyperlink{command.hence}{\mbox{\isa{\isacommand{hence}}}} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} & \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}} \\
- \hyperlink{command.thus}{\mbox{\isa{\isacommand{thus}}}} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} & \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}} \\
- \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{a} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{a}~\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}} \\
- \hyperlink{command.with}{\mbox{\isa{\isacommand{with}}}}~\isa{a} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} & \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{{\isachardoublequote}a\ {\isasymAND}\ this{\isachardoublequote}} \\[1ex]
- \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{this} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} & \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}} \\
- \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{this}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} & \hyperlink{command.hence}{\mbox{\isa{\isacommand{hence}}}} \\
- \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{this}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}} & \isa{{\isachardoublequote}{\isasymequiv}{\isachardoublequote}} & \hyperlink{command.thus}{\mbox{\isa{\isacommand{thus}}}} \\
+ \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} &
+ \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.qed}{\mbox{\isa{\isacommand{qed}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}m\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{rule} \\
+ \hyperlink{command.dot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{this} \\
+ \hyperlink{command.hence}{\mbox{\isa{\isacommand{hence}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}} \\
+ \hyperlink{command.thus}{\mbox{\isa{\isacommand{thus}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}} \\
+ \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{a} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{a}~\hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}} \\
+ \hyperlink{command.with}{\mbox{\isa{\isacommand{with}}}}~\isa{a} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ this{\isaliteral{22}{\isachardoublequote}}} \\[1ex]
+ \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{this} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.then}{\mbox{\isa{\isacommand{then}}}} \\
+ \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{this}~\hyperlink{command.have}{\mbox{\isa{\isacommand{have}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.hence}{\mbox{\isa{\isacommand{hence}}}} \\
+ \hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{this}~\hyperlink{command.show}{\mbox{\isa{\isacommand{show}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C65717569763E}{\isasymequiv}}{\isaliteral{22}{\isachardoublequote}}} & \hyperlink{command.thus}{\mbox{\isa{\isacommand{thus}}}} \\
\end{tabular}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -95,25 +95,25 @@
%
\begin{isamarkuptext}%
\begin{tabular}{rcl}
- \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isachardoublequote}\isactrlsub {\isadigit{0}}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymapprox}{\isachardoublequote}} &
- \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ this{\isachardoublequote}} \\
- \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isachardoublequote}\isactrlsub n\isactrlsub {\isacharplus}\isactrlsub {\isadigit{1}}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymapprox}{\isachardoublequote}} &
- \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ trans\ {\isacharbrackleft}OF\ calculation\ this{\isacharbrackright}{\isachardoublequote}} \\
- \hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}} & \isa{{\isachardoublequote}{\isasymapprox}{\isachardoublequote}} &
+ \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{0}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
+ \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}calculation\ {\isaliteral{3D}{\isacharequal}}\ this{\isaliteral{22}{\isachardoublequote}}} \\
+ \hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isaliteral{2B}{\isacharplus}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
+ \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}calculation\ {\isaliteral{3D}{\isacharequal}}\ trans\ {\isaliteral{5B}{\isacharbrackleft}}OF\ calculation\ this{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \hyperlink{command.finally}{\mbox{\isa{\isacommand{finally}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
\hyperlink{command.also}{\mbox{\isa{\isacommand{also}}}}~\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{calculation} \\[0.5ex]
- \hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}} & \isa{{\isachardoublequote}{\isasymapprox}{\isachardoublequote}} &
- \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isachardoublequote}calculation\ {\isacharequal}\ calculation\ this{\isachardoublequote}} \\
- \hyperlink{command.ultimately}{\mbox{\isa{\isacommand{ultimately}}}} & \isa{{\isachardoublequote}{\isasymapprox}{\isachardoublequote}} &
+ \hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
+ \hyperlink{command.note}{\mbox{\isa{\isacommand{note}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}calculation\ {\isaliteral{3D}{\isacharequal}}\ calculation\ this{\isaliteral{22}{\isachardoublequote}}} \\
+ \hyperlink{command.ultimately}{\mbox{\isa{\isacommand{ultimately}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
\hyperlink{command.moreover}{\mbox{\isa{\isacommand{moreover}}}}~\hyperlink{command.from}{\mbox{\isa{\isacommand{from}}}}~\isa{calculation} \\[0.5ex]
- \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymapprox}{\isachardoublequote}} &
- \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} \\
- \hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ x\ {\isasymequiv}\ t{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymapprox}{\isachardoublequote}} &
- \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ x\ {\isasymequiv}\ t{\isachardoublequote}} \\
- \hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}~\isa{{\isachardoublequote}x\ {\isasymWHERE}\ a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymapprox}{\isachardoublequote}} &
- \isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}~\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} \\
- \hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{c} & \isa{{\isachardoublequote}{\isasymapprox}{\isachardoublequote}} &
- \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isachardoublequote}c{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} \\
- \hyperlink{command.sorry}{\mbox{\isa{\isacommand{sorry}}}} & \isa{{\isachardoublequote}{\isasymapprox}{\isachardoublequote}} &
+ \hyperlink{command.presume}{\mbox{\isa{\isacommand{presume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
+ \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
+ \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}} \\
+ \hyperlink{command.obtain}{\mbox{\isa{\isacommand{obtain}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}~\hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \hyperlink{command.case}{\mbox{\isa{\isacommand{case}}}}~\isa{c} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
+ \hyperlink{command.fix}{\mbox{\isa{\isacommand{fix}}}}~\isa{x}~\hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \hyperlink{command.sorry}{\mbox{\isa{\isacommand{sorry}}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequote}}} &
\hyperlink{command.by}{\mbox{\isa{\isacommand{by}}}}~\isa{cheating} \\
\end{tabular}%
\end{isamarkuptext}%
@@ -128,8 +128,8 @@
\hyperlink{command.pr}{\mbox{\isa{\isacommand{pr}}}} & print current state \\
\hyperlink{command.thm}{\mbox{\isa{\isacommand{thm}}}}~\isa{a} & print fact \\
\hyperlink{command.term}{\mbox{\isa{\isacommand{term}}}}~\isa{t} & print term \\
- \hyperlink{command.prop}{\mbox{\isa{\isacommand{prop}}}}~\isa{{\isasymphi}} & print meta-level proposition \\
- \hyperlink{command.typ}{\mbox{\isa{\isacommand{typ}}}}~\isa{{\isasymtau}} & print meta-level type \\
+ \hyperlink{command.prop}{\mbox{\isa{\isacommand{prop}}}}~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} & print meta-level proposition \\
+ \hyperlink{command.typ}{\mbox{\isa{\isacommand{typ}}}}~\isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} & print meta-level type \\
\end{tabular}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -145,21 +145,21 @@
\hyperlink{method.this}{\mbox{\isa{this}}} & apply current facts \\
\hyperlink{method.rule}{\mbox{\isa{rule}}}~\isa{a} & apply some rule \\
\hyperlink{method.rule}{\mbox{\isa{rule}}} & apply standard rule (default for \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}) \\
- \hyperlink{method.contradiction}{\mbox{\isa{contradiction}}} & apply \isa{{\isachardoublequote}{\isasymnot}{\isachardoublequote}} elimination rule (any order) \\
+ \hyperlink{method.contradiction}{\mbox{\isa{contradiction}}} & apply \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}{\isaliteral{22}{\isachardoublequote}}} elimination rule (any order) \\
\hyperlink{method.cases}{\mbox{\isa{cases}}}~\isa{t} & case analysis (provides cases) \\
\hyperlink{method.induct}{\mbox{\isa{induct}}}~\isa{x} & proof by induction (provides cases) \\[2ex]
\multicolumn{2}{l}{\textbf{Repeated steps (inserting facts)}} \\[0.5ex]
- \hyperlink{method.-}{\mbox{\isa{{\isacharminus}}}} & no rules \\
+ \hyperlink{method.-}{\mbox{\isa{{\isaliteral{2D}{\isacharminus}}}}} & no rules \\
\hyperlink{method.intro}{\mbox{\isa{intro}}}~\isa{a} & introduction rules \\
- \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isacharunderscore}classes}}} & class introduction rules \\
+ \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}classes}}} & class introduction rules \\
\hyperlink{method.elim}{\mbox{\isa{elim}}}~\isa{a} & elimination rules \\
\hyperlink{method.unfold}{\mbox{\isa{unfold}}}~\isa{a} & definitional rewrite rules \\[2ex]
\multicolumn{2}{l}{\textbf{Automated proof tools (inserting facts)}} \\[0.5ex]
\hyperlink{method.iprover}{\mbox{\isa{iprover}}} & intuitionistic proof search \\
\hyperlink{method.blast}{\mbox{\isa{blast}}}, \hyperlink{method.fast}{\mbox{\isa{fast}}} & Classical Reasoner \\
- \hyperlink{method.simp}{\mbox{\isa{simp}}}, \hyperlink{method.simp-all}{\mbox{\isa{simp{\isacharunderscore}all}}} & Simplifier (+ Splitter) \\
+ \hyperlink{method.simp}{\mbox{\isa{simp}}}, \hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}} & Simplifier (+ Splitter) \\
\hyperlink{method.auto}{\mbox{\isa{auto}}}, \hyperlink{method.force}{\mbox{\isa{force}}} & Simplifier + Classical Reasoner \\
\hyperlink{method.arith}{\mbox{\isa{arith}}} & Arithmetic procedures \\
\end{tabular}%
@@ -173,13 +173,13 @@
\begin{isamarkuptext}%
\begin{tabular}{ll}
\multicolumn{2}{l}{\textbf{Operations}} \\[0.5ex]
- \hyperlink{attribute.OF}{\mbox{\isa{OF}}}~\isa{a} & rule resolved with facts (skipping ``\isa{{\isacharunderscore}}'') \\
- \hyperlink{attribute.of}{\mbox{\isa{of}}}~\isa{t} & rule instantiated with terms (skipping ``\isa{{\isacharunderscore}}'') \\
- \hyperlink{attribute.where}{\mbox{\isa{where}}}~\isa{{\isachardoublequote}x\ {\isacharequal}\ t{\isachardoublequote}} & rule instantiated with terms, by variable name \\
+ \hyperlink{attribute.OF}{\mbox{\isa{OF}}}~\isa{a} & rule resolved with facts (skipping ``\isa{{\isaliteral{5F}{\isacharunderscore}}}'') \\
+ \hyperlink{attribute.of}{\mbox{\isa{of}}}~\isa{t} & rule instantiated with terms (skipping ``\isa{{\isaliteral{5F}{\isacharunderscore}}}'') \\
+ \hyperlink{attribute.where}{\mbox{\isa{where}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{22}{\isachardoublequote}}} & rule instantiated with terms, by variable name \\
\hyperlink{attribute.symmetric}{\mbox{\isa{symmetric}}} & resolution with symmetry rule \\
\hyperlink{attribute.THEN}{\mbox{\isa{THEN}}}~\isa{b} & resolution with another rule \\
- \hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isacharunderscore}format}}} & result put into standard rule format \\
- \hyperlink{attribute.elim-format}{\mbox{\isa{elim{\isacharunderscore}format}}} & destruct rule turned into elimination rule format \\[1ex]
+ \hyperlink{attribute.rule-format}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}format}}} & result put into standard rule format \\
+ \hyperlink{attribute.elim-format}{\mbox{\isa{elim{\isaliteral{5F}{\isacharunderscore}}format}}} & destruct rule turned into elimination rule format \\[1ex]
\multicolumn{2}{l}{\textbf{Declarations}} \\[0.5ex]
\hyperlink{attribute.simp}{\mbox{\isa{simp}}} & Simplifier rule \\
@@ -199,28 +199,28 @@
\begin{isamarkuptext}%
\begin{tabular}{l|lllll}
& \hyperlink{method.rule}{\mbox{\isa{rule}}} & \hyperlink{method.iprover}{\mbox{\isa{iprover}}} & \hyperlink{method.blast}{\mbox{\isa{blast}}} & \hyperlink{method.simp}{\mbox{\isa{simp}}} & \hyperlink{method.auto}{\mbox{\isa{auto}}} \\
- & & & \hyperlink{method.fast}{\mbox{\isa{fast}}} & \hyperlink{method.simp-all}{\mbox{\isa{simp{\isacharunderscore}all}}} & \hyperlink{method.force}{\mbox{\isa{force}}} \\
+ & & & \hyperlink{method.fast}{\mbox{\isa{fast}}} & \hyperlink{method.simp-all}{\mbox{\isa{simp{\isaliteral{5F}{\isacharunderscore}}all}}} & \hyperlink{method.force}{\mbox{\isa{force}}} \\
\hline
- \hyperlink{attribute.Pure.elim}{\mbox{\isa{Pure{\isachardot}elim}}}\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}} \hyperlink{attribute.Pure.intro}{\mbox{\isa{Pure{\isachardot}intro}}}\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}
- & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\
- \hyperlink{attribute.Pure.elim}{\mbox{\isa{Pure{\isachardot}elim}}} \hyperlink{attribute.Pure.intro}{\mbox{\isa{Pure{\isachardot}intro}}}
- & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\
- \hyperlink{attribute.elim}{\mbox{\isa{elim}}}\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}} \hyperlink{attribute.intro}{\mbox{\isa{intro}}}\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}}
- & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\
+ \hyperlink{attribute.Pure.elim}{\mbox{\isa{Pure{\isaliteral{2E}{\isachardot}}elim}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}} \hyperlink{attribute.Pure.intro}{\mbox{\isa{Pure{\isaliteral{2E}{\isachardot}}intro}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}}
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \hyperlink{attribute.Pure.elim}{\mbox{\isa{Pure{\isaliteral{2E}{\isachardot}}elim}}} \hyperlink{attribute.Pure.intro}{\mbox{\isa{Pure{\isaliteral{2E}{\isachardot}}intro}}}
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \hyperlink{attribute.elim}{\mbox{\isa{elim}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}} \hyperlink{attribute.intro}{\mbox{\isa{intro}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}}
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
\hyperlink{attribute.elim}{\mbox{\isa{elim}}} \hyperlink{attribute.intro}{\mbox{\isa{intro}}}
- & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
\hyperlink{attribute.iff}{\mbox{\isa{iff}}}
- & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\
- \hyperlink{attribute.iff}{\mbox{\isa{iff}}}\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}
- & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\
- \hyperlink{attribute.elim}{\mbox{\isa{elim}}}\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}} \hyperlink{attribute.intro}{\mbox{\isa{intro}}}\isa{{\isachardoublequote}{\isacharquery}{\isachardoublequote}}
- & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} & & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \hyperlink{attribute.iff}{\mbox{\isa{iff}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \hyperlink{attribute.elim}{\mbox{\isa{elim}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}} \hyperlink{attribute.intro}{\mbox{\isa{intro}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}
+ & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
\hyperlink{attribute.simp}{\mbox{\isa{simp}}}
- & & & & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\
+ & & & & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
\hyperlink{attribute.cong}{\mbox{\isa{cong}}}
- & & & & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\
+ & & & & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
\hyperlink{attribute.split}{\mbox{\isa{split}}}
- & & & & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isasymtimes}{\isachardoublequote}} \\
+ & & & & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C74696D65733E}{\isasymtimes}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -236,7 +236,7 @@
\begin{isamarkuptext}%
\begin{tabular}{ll}
\hyperlink{command.apply}{\mbox{\isa{\isacommand{apply}}}}~\isa{m} & apply proof method at initial position \\
- \hyperlink{command.apply-end}{\mbox{\isa{\isacommand{apply{\isacharunderscore}end}}}}~\isa{m} & apply proof method near terminal position \\
+ \hyperlink{command.apply-end}{\mbox{\isa{\isacommand{apply{\isaliteral{5F}{\isacharunderscore}}end}}}}~\isa{m} & apply proof method near terminal position \\
\hyperlink{command.done}{\mbox{\isa{\isacommand{done}}}} & complete proof \\
\hyperlink{command.defer}{\mbox{\isa{\isacommand{defer}}}}~\isa{n} & move subgoal to end \\
\hyperlink{command.prefer}{\mbox{\isa{\isacommand{prefer}}}}~\isa{n} & move subgoal to beginning \\
@@ -251,19 +251,19 @@
%
\begin{isamarkuptext}%
\begin{tabular}{ll}
- \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isacharunderscore}tac}}}~\isa{insts} & resolution (with instantiation) \\
- \hyperlink{method.erule-tac}{\mbox{\isa{erule{\isacharunderscore}tac}}}~\isa{insts} & elim-resolution (with instantiation) \\
- \hyperlink{method.drule-tac}{\mbox{\isa{drule{\isacharunderscore}tac}}}~\isa{insts} & destruct-resolution (with instantiation) \\
- \hyperlink{method.frule-tac}{\mbox{\isa{frule{\isacharunderscore}tac}}}~\isa{insts} & forward-resolution (with instantiation) \\
- \hyperlink{method.cut-tac}{\mbox{\isa{cut{\isacharunderscore}tac}}}~\isa{insts} & insert facts (with instantiation) \\
- \hyperlink{method.thin-tac}{\mbox{\isa{thin{\isacharunderscore}tac}}}~\isa{{\isasymphi}} & delete assumptions \\
- \hyperlink{method.subgoal-tac}{\mbox{\isa{subgoal{\isacharunderscore}tac}}}~\isa{{\isasymphi}} & new claims \\
- \hyperlink{method.rename-tac}{\mbox{\isa{rename{\isacharunderscore}tac}}}~\isa{x} & rename innermost goal parameters \\
- \hyperlink{method.rotate-tac}{\mbox{\isa{rotate{\isacharunderscore}tac}}}~\isa{n} & rotate assumptions of goal \\
- \hyperlink{method.tactic}{\mbox{\isa{tactic}}}~\isa{{\isachardoublequote}text{\isachardoublequote}} & arbitrary ML tactic \\
- \hyperlink{method.case-tac}{\mbox{\isa{case{\isacharunderscore}tac}}}~\isa{t} & exhaustion (datatypes) \\
- \hyperlink{method.induct-tac}{\mbox{\isa{induct{\isacharunderscore}tac}}}~\isa{x} & induction (datatypes) \\
- \hyperlink{method.ind-cases}{\mbox{\isa{ind{\isacharunderscore}cases}}}~\isa{t} & exhaustion + simplification (inductive predicates) \\
+ \hyperlink{method.rule-tac}{\mbox{\isa{rule{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{insts} & resolution (with instantiation) \\
+ \hyperlink{method.erule-tac}{\mbox{\isa{erule{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{insts} & elim-resolution (with instantiation) \\
+ \hyperlink{method.drule-tac}{\mbox{\isa{drule{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{insts} & destruct-resolution (with instantiation) \\
+ \hyperlink{method.frule-tac}{\mbox{\isa{frule{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{insts} & forward-resolution (with instantiation) \\
+ \hyperlink{method.cut-tac}{\mbox{\isa{cut{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{insts} & insert facts (with instantiation) \\
+ \hyperlink{method.thin-tac}{\mbox{\isa{thin{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} & delete assumptions \\
+ \hyperlink{method.subgoal-tac}{\mbox{\isa{subgoal{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} & new claims \\
+ \hyperlink{method.rename-tac}{\mbox{\isa{rename{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{x} & rename innermost goal parameters \\
+ \hyperlink{method.rotate-tac}{\mbox{\isa{rotate{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{n} & rotate assumptions of goal \\
+ \hyperlink{method.tactic}{\mbox{\isa{tactic}}}~\isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}} & arbitrary ML tactic \\
+ \hyperlink{method.case-tac}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{t} & exhaustion (datatypes) \\
+ \hyperlink{method.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}tac}}}~\isa{x} & induction (datatypes) \\
+ \hyperlink{method.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}}~\isa{t} & exhaustion + simplification (inductive predicates) \\
\end{tabular}%
\end{isamarkuptext}%
\isamarkuptrue%
--- a/doc-src/IsarRef/Thy/document/Spec.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarRef/Thy/document/Spec.tex Mon Nov 08 14:41:11 2010 +0100
@@ -45,8 +45,8 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{theory}\hypertarget{command.theory}{\hyperlink{command.theory}{\mbox{\isa{\isacommand{theory}}}}} & : & \isa{{\isachardoublequote}toplevel\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{global}{command}{end}\hypertarget{command.global.end}{\hyperlink{command.global.end}{\mbox{\isa{\isacommand{end}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ toplevel{\isachardoublequote}} \\
+ \indexdef{}{command}{theory}\hypertarget{command.theory}{\hyperlink{command.theory}{\mbox{\isa{\isacommand{theory}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}toplevel\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{global}{command}{end}\hypertarget{command.global.end}{\hyperlink{command.global.end}{\mbox{\isa{\isacommand{end}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ toplevel{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
Isabelle/Isar theories are defined via theory files, which may
@@ -77,9 +77,9 @@
\begin{description}
- \item \hyperlink{command.theory}{\mbox{\isa{\isacommand{theory}}}}~\isa{{\isachardoublequote}A\ {\isasymIMPORTS}\ B\isactrlsub {\isadigit{1}}\ {\isasymdots}\ B\isactrlsub n\ {\isasymBEGIN}{\isachardoublequote}}
+ \item \hyperlink{command.theory}{\mbox{\isa{\isacommand{theory}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C494D504F5254533E}{\isasymIMPORTS}}\ B\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ B\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C424547494E3E}{\isasymBEGIN}}{\isaliteral{22}{\isachardoublequote}}}
starts a new theory \isa{A} based on the merge of existing
- theories \isa{{\isachardoublequote}B\isactrlsub {\isadigit{1}}\ {\isasymdots}\ B\isactrlsub n{\isachardoublequote}}.
+ theories \isa{{\isaliteral{22}{\isachardoublequote}}B\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ B\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}.
Due to the possibility to import more than one ancestor, the
resulting theory structure of an Isabelle session forms a directed
@@ -114,12 +114,12 @@
variables) and assumptions (hypotheses). Definitions and theorems
depending on the context may be added incrementally later on. Named
contexts refer to locales (cf.\ \secref{sec:locale}) or type classes
- (cf.\ \secref{sec:class}); the name ``\isa{{\isachardoublequote}{\isacharminus}{\isachardoublequote}}'' signifies the
+ (cf.\ \secref{sec:class}); the name ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{22}{\isachardoublequote}}}'' signifies the
global theory context.
\begin{matharray}{rcll}
- \indexdef{}{command}{context}\hypertarget{command.context}{\hyperlink{command.context}{\mbox{\isa{\isacommand{context}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{local}{command}{end}\hypertarget{command.local.end}{\hyperlink{command.local.end}{\mbox{\isa{\isacommand{end}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
+ \indexdef{}{command}{context}\hypertarget{command.context}{\hyperlink{command.context}{\mbox{\isa{\isacommand{context}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{local}{command}{end}\hypertarget{command.local.end}{\hyperlink{command.local.end}{\mbox{\isa{\isacommand{end}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\indexouternonterm{target}
@@ -133,7 +133,7 @@
\begin{description}
- \item \hyperlink{command.context}{\mbox{\isa{\isacommand{context}}}}~\isa{{\isachardoublequote}c\ {\isasymBEGIN}{\isachardoublequote}} recommences an
+ \item \hyperlink{command.context}{\mbox{\isa{\isacommand{context}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{5C3C424547494E3E}{\isasymBEGIN}}{\isaliteral{22}{\isachardoublequote}}} recommences an
existing locale or class context \isa{c}. Note that locale and
class definitions allow to include the \hyperlink{keyword.begin}{\mbox{\isa{\isakeyword{begin}}}} keyword as
well, in order to continue the local theory immediately after the
@@ -144,11 +144,11 @@
\hyperlink{command.global.end}{\mbox{\isa{\isacommand{end}}}} has a different meaning: it concludes the
theory itself (\secref{sec:begin-thy}).
- \item \isa{{\isachardoublequote}{\isacharparenleft}{\isachardoublequote}}\indexdef{}{keyword}{in}\hypertarget{keyword.in}{\hyperlink{keyword.in}{\mbox{\isa{\isakeyword{in}}}}}~\isa{{\isachardoublequote}c{\isacharparenright}{\isachardoublequote}} given after any
+ \item \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}}\indexdef{}{keyword}{in}\hypertarget{keyword.in}{\hyperlink{keyword.in}{\mbox{\isa{\isakeyword{in}}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} given after any
local theory command specifies an immediate target, e.g.\
- ``\hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIN}\ c{\isacharparenright}\ {\isasymdots}{\isachardoublequote}}'' or ``\hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIN}\ c{\isacharparenright}\ {\isasymdots}{\isachardoublequote}}''. This works both in a local or
+ ``\hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C494E3E}{\isasymIN}}\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}'' or ``\hyperlink{command.theorem}{\mbox{\isa{\isacommand{theorem}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C494E3E}{\isasymIN}}\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}''. This works both in a local or
global theory context; the current target context will be suspended
- for this command only. Note that ``\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIN}\ {\isacharminus}{\isacharparenright}{\isachardoublequote}}'' will
+ for this command only. Note that ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C494E3E}{\isasymIN}}\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' will
always produce a global result independently of the current target
context.
@@ -157,19 +157,19 @@
The exact meaning of results produced within a local theory context
depends on the underlying target infrastructure (locale, type class
etc.). The general idea is as follows, considering a context named
- \isa{c} with parameter \isa{x} and assumption \isa{{\isachardoublequote}A{\isacharbrackleft}x{\isacharbrackright}{\isachardoublequote}}.
+ \isa{c} with parameter \isa{x} and assumption \isa{{\isaliteral{22}{\isachardoublequote}}A{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}.
Definitions are exported by introducing a global version with
additional arguments; a syntactic abbreviation links the long form
with the abstract version of the target context. For example,
- \isa{{\isachardoublequote}a\ {\isasymequiv}\ t{\isacharbrackleft}x{\isacharbrackright}{\isachardoublequote}} becomes \isa{{\isachardoublequote}c{\isachardot}a\ {\isacharquery}x\ {\isasymequiv}\ t{\isacharbrackleft}{\isacharquery}x{\isacharbrackright}{\isachardoublequote}} at the theory
- level (for arbitrary \isa{{\isachardoublequote}{\isacharquery}x{\isachardoublequote}}), together with a local
- abbreviation \isa{{\isachardoublequote}c\ {\isasymequiv}\ c{\isachardot}a\ x{\isachardoublequote}} in the target context (for the
+ \isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} becomes \isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{2E}{\isachardot}}a\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} at the theory
+ level (for arbitrary \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{22}{\isachardoublequote}}}), together with a local
+ abbreviation \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ c{\isaliteral{2E}{\isachardot}}a\ x{\isaliteral{22}{\isachardoublequote}}} in the target context (for the
fixed parameter \isa{x}).
Theorems are exported by discharging the assumptions and
- generalizing the parameters of the context. For example, \isa{{\isachardoublequote}a{\isacharcolon}\ B{\isacharbrackleft}x{\isacharbrackright}{\isachardoublequote}} becomes \isa{{\isachardoublequote}c{\isachardot}a{\isacharcolon}\ A{\isacharbrackleft}{\isacharquery}x{\isacharbrackright}\ {\isasymLongrightarrow}\ B{\isacharbrackleft}{\isacharquery}x{\isacharbrackright}{\isachardoublequote}}, again for arbitrary
- \isa{{\isachardoublequote}{\isacharquery}x{\isachardoublequote}}.%
+ generalizing the parameters of the context. For example, \isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ B{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} becomes \isa{{\isaliteral{22}{\isachardoublequote}}c{\isaliteral{2E}{\isachardot}}a{\isaliteral{3A}{\isacharcolon}}\ A{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ B{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}, again for arbitrary
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}x{\isaliteral{22}{\isachardoublequote}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -179,11 +179,11 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcll}
- \indexdef{}{command}{axiomatization}\hypertarget{command.axiomatization}{\hyperlink{command.axiomatization}{\mbox{\isa{\isacommand{axiomatization}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} & (axiomatic!) \\
- \indexdef{}{command}{definition}\hypertarget{command.definition}{\hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
+ \indexdef{}{command}{axiomatization}\hypertarget{command.axiomatization}{\hyperlink{command.axiomatization}{\mbox{\isa{\isacommand{axiomatization}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} & (axiomatic!) \\
+ \indexdef{}{command}{definition}\hypertarget{command.definition}{\hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
\indexdef{}{attribute}{defn}\hypertarget{attribute.defn}{\hyperlink{attribute.defn}{\mbox{\isa{defn}}}} & : & \isa{attribute} \\
- \indexdef{}{command}{abbreviation}\hypertarget{command.abbreviation}{\hyperlink{command.abbreviation}{\mbox{\isa{\isacommand{abbreviation}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{print\_abbrevs}\hypertarget{command.print-abbrevs}{\hyperlink{command.print-abbrevs}{\mbox{\isa{\isacommand{print{\isacharunderscore}abbrevs}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}\ {\isachardoublequote}} \\
+ \indexdef{}{command}{abbreviation}\hypertarget{command.abbreviation}{\hyperlink{command.abbreviation}{\mbox{\isa{\isacommand{abbreviation}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_abbrevs}\hypertarget{command.print-abbrevs}{\hyperlink{command.print-abbrevs}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}abbrevs}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ {\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
These specification mechanisms provide a slightly more abstract view
@@ -209,7 +209,7 @@
\begin{description}
- \item \hyperlink{command.axiomatization}{\mbox{\isa{\isacommand{axiomatization}}}}~\isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}\ {\isasymdots}\ c\isactrlsub m\ {\isasymWHERE}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}}
+ \item \hyperlink{command.axiomatization}{\mbox{\isa{\isacommand{axiomatization}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub m\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}
introduces several constants simultaneously and states axiomatic
properties for these. The constants are marked as being specified
once and for all, which prevents additional specifications being
@@ -220,20 +220,20 @@
restricted to global theory contexts. Normal applications should
only use definitional mechanisms!
- \item \hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}~\isa{{\isachardoublequote}c\ {\isasymWHERE}\ eq{\isachardoublequote}} produces an
- internal definition \isa{{\isachardoublequote}c\ {\isasymequiv}\ t{\isachardoublequote}} according to the specification
+ \item \hyperlink{command.definition}{\mbox{\isa{\isacommand{definition}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ eq{\isaliteral{22}{\isachardoublequote}}} produces an
+ internal definition \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}} according to the specification
given as \isa{eq}, which is then turned into a proven fact. The
given proposition may deviate from internal meta-level equality
according to the rewrite rules declared as \hyperlink{attribute.defn}{\mbox{\isa{defn}}} by the
- object-logic. This usually covers object-level equality \isa{{\isachardoublequote}x\ {\isacharequal}\ y{\isachardoublequote}} and equivalence \isa{{\isachardoublequote}A\ {\isasymleftrightarrow}\ B{\isachardoublequote}}. End-users normally need not
+ object-logic. This usually covers object-level equality \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequote}}} and equivalence \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C6C65667472696768746172726F773E}{\isasymleftrightarrow}}\ B{\isaliteral{22}{\isachardoublequote}}}. End-users normally need not
change the \hyperlink{attribute.defn}{\mbox{\isa{defn}}} setup.
Definitions may be presented with explicit arguments on the LHS, as
- well as additional conditions, e.g.\ \isa{{\isachardoublequote}f\ x\ y\ {\isacharequal}\ t{\isachardoublequote}} instead of
- \isa{{\isachardoublequote}f\ {\isasymequiv}\ {\isasymlambda}x\ y{\isachardot}\ t{\isachardoublequote}} and \isa{{\isachardoublequote}y\ {\isasymnoteq}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ g\ x\ y\ {\isacharequal}\ u{\isachardoublequote}} instead of an
- unrestricted \isa{{\isachardoublequote}g\ {\isasymequiv}\ {\isasymlambda}x\ y{\isachardot}\ u{\isachardoublequote}}.
+ well as additional conditions, e.g.\ \isa{{\isaliteral{22}{\isachardoublequote}}f\ x\ y\ {\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{22}{\isachardoublequote}}} instead of
+ \isa{{\isaliteral{22}{\isachardoublequote}}f\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x\ y{\isaliteral{2E}{\isachardot}}\ t{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}y\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ g\ x\ y\ {\isaliteral{3D}{\isacharequal}}\ u{\isaliteral{22}{\isachardoublequote}}} instead of an
+ unrestricted \isa{{\isaliteral{22}{\isachardoublequote}}g\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x\ y{\isaliteral{2E}{\isachardot}}\ u{\isaliteral{22}{\isachardoublequote}}}.
- \item \hyperlink{command.abbreviation}{\mbox{\isa{\isacommand{abbreviation}}}}~\isa{{\isachardoublequote}c\ {\isasymWHERE}\ eq{\isachardoublequote}} introduces a
+ \item \hyperlink{command.abbreviation}{\mbox{\isa{\isacommand{abbreviation}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ eq{\isaliteral{22}{\isachardoublequote}}} introduces a
syntactic constant which is associated with a certain term according
to the meta-level equality \isa{eq}.
@@ -250,7 +250,7 @@
declared for abbreviations, cf.\ \hyperlink{command.syntax}{\mbox{\isa{\isacommand{syntax}}}} in
\secref{sec:syn-trans}.
- \item \hyperlink{command.print-abbrevs}{\mbox{\isa{\isacommand{print{\isacharunderscore}abbrevs}}}} prints all constant abbreviations
+ \item \hyperlink{command.print-abbrevs}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}abbrevs}}}} prints all constant abbreviations
of the current context.
\end{description}%
@@ -272,8 +272,8 @@
means of an attribute.
\begin{matharray}{rcl}
- \indexdef{}{command}{declaration}\hypertarget{command.declaration}{\hyperlink{command.declaration}{\mbox{\isa{\isacommand{declaration}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{declare}\hypertarget{command.declare}{\hyperlink{command.declare}{\mbox{\isa{\isacommand{declare}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
+ \indexdef{}{command}{declaration}\hypertarget{command.declaration}{\hyperlink{command.declaration}{\mbox{\isa{\isacommand{declaration}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{declare}\hypertarget{command.declare}{\hyperlink{command.declare}{\mbox{\isa{\isacommand{declare}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -291,7 +291,7 @@
function is transformed according to the morphisms being involved in
the interpretation hierarchy.
- If the \isa{{\isachardoublequote}{\isacharparenleft}pervasive{\isacharparenright}{\isachardoublequote}} option is given, the corresponding
+ If the \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}pervasive{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option is given, the corresponding
declaration is applied to all possible contexts involved, including
the global background theory.
@@ -346,7 +346,7 @@
A locale instance consists of a reference to a locale and either
positional or named parameter instantiations. Identical
instantiations (that is, those that instante a parameter by itself)
- may be omitted. The notation `\isa{{\isachardoublequote}{\isacharunderscore}{\isachardoublequote}}' enables to omit the
+ may be omitted. The notation `\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequote}}}' enables to omit the
instantiation for a parameter inside a positional instantiation.
Terms in instantiations are from the context the locale expressions
@@ -372,11 +372,11 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{locale}\hypertarget{command.locale}{\hyperlink{command.locale}{\mbox{\isa{\isacommand{locale}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{print\_locale}\hypertarget{command.print-locale}{\hyperlink{command.print-locale}{\mbox{\isa{\isacommand{print{\isacharunderscore}locale}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{print\_locales}\hypertarget{command.print-locales}{\hyperlink{command.print-locales}{\mbox{\isa{\isacommand{print{\isacharunderscore}locales}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{method}{intro\_locales}\hypertarget{method.intro-locales}{\hyperlink{method.intro-locales}{\mbox{\isa{intro{\isacharunderscore}locales}}}} & : & \isa{method} \\
- \indexdef{}{method}{unfold\_locales}\hypertarget{method.unfold-locales}{\hyperlink{method.unfold-locales}{\mbox{\isa{unfold{\isacharunderscore}locales}}}} & : & \isa{method} \\
+ \indexdef{}{command}{locale}\hypertarget{command.locale}{\hyperlink{command.locale}{\mbox{\isa{\isacommand{locale}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_locale}\hypertarget{command.print-locale}{\hyperlink{command.print-locale}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}locale}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_locales}\hypertarget{command.print-locales}{\hyperlink{command.print-locales}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}locales}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{method}{intro\_locales}\hypertarget{method.intro-locales}{\hyperlink{method.intro-locales}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}locales}}}} & : & \isa{method} \\
+ \indexdef{}{method}{unfold\_locales}\hypertarget{method.unfold-locales}{\hyperlink{method.unfold-locales}{\mbox{\isa{unfold{\isaliteral{5F}{\isacharunderscore}}locales}}}} & : & \isa{method} \\
\end{matharray}
\indexouternonterm{contextelem}
@@ -400,7 +400,7 @@
\begin{description}
- \item \hyperlink{command.locale}{\mbox{\isa{\isacommand{locale}}}}~\isa{{\isachardoublequote}loc\ {\isacharequal}\ import\ {\isacharplus}\ body{\isachardoublequote}} defines a
+ \item \hyperlink{command.locale}{\mbox{\isa{\isacommand{locale}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}loc\ {\isaliteral{3D}{\isacharequal}}\ import\ {\isaliteral{2B}{\isacharplus}}\ body{\isaliteral{22}{\isachardoublequote}}} defines a
new locale \isa{loc} as a context consisting of a certain view of
existing locales (\isa{import}) plus some additional elements
(\isa{body}). Both \isa{import} and \isa{body} are optional;
@@ -424,28 +424,28 @@
\begin{description}
- \item \hyperlink{element.fixes}{\mbox{\isa{\isakeyword{fixes}}}}~\isa{{\isachardoublequote}x\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}\ {\isacharparenleft}mx{\isacharparenright}{\isachardoublequote}} declares a local
- parameter of type \isa{{\isasymtau}} and mixfix annotation \isa{mx} (both
- are optional). The special syntax declaration ``\isa{{\isachardoublequote}{\isacharparenleft}{\isasymSTRUCTURE}{\isacharparenright}{\isachardoublequote}}'' means that \isa{x} may be referenced
+ \item \hyperlink{element.fixes}{\mbox{\isa{\isakeyword{fixes}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\ {\isaliteral{28}{\isacharparenleft}}mx{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} declares a local
+ parameter of type \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} and mixfix annotation \isa{mx} (both
+ are optional). The special syntax declaration ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C5354525543545552453E}{\isasymSTRUCTURE}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' means that \isa{x} may be referenced
implicitly in this context.
- \item \hyperlink{element.constrains}{\mbox{\isa{\isakeyword{constrains}}}}~\isa{{\isachardoublequote}x\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}{\isachardoublequote}} introduces a type
- constraint \isa{{\isasymtau}} on the local parameter \isa{x}. This
+ \item \hyperlink{element.constrains}{\mbox{\isa{\isakeyword{constrains}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}} introduces a type
+ constraint \isa{{\isaliteral{5C3C7461753E}{\isasymtau}}} on the local parameter \isa{x}. This
element is deprecated. The type constraint should be introduced in
the for clause or the relevant \hyperlink{element.fixes}{\mbox{\isa{\isakeyword{fixes}}}} element.
- \item \hyperlink{element.assumes}{\mbox{\isa{\isakeyword{assumes}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}\isactrlsub {\isadigit{1}}\ {\isasymdots}\ {\isasymphi}\isactrlsub n{\isachardoublequote}}
+ \item \hyperlink{element.assumes}{\mbox{\isa{\isakeyword{assumes}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}
introduces local premises, similar to \hyperlink{command.assume}{\mbox{\isa{\isacommand{assume}}}} within a
proof (cf.\ \secref{sec:proof-context}).
- \item \hyperlink{element.defines}{\mbox{\isa{\isakeyword{defines}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ x\ {\isasymequiv}\ t{\isachardoublequote}} defines a previously
+ \item \hyperlink{element.defines}{\mbox{\isa{\isakeyword{defines}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ x\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}} defines a previously
declared parameter. This is similar to \hyperlink{command.def}{\mbox{\isa{\isacommand{def}}}} within a
proof (cf.\ \secref{sec:proof-context}), but \hyperlink{element.defines}{\mbox{\isa{\isakeyword{defines}}}}
takes an equational proposition instead of variable-term pair. The
left-hand side of the equation may have additional arguments, e.g.\
- ``\hyperlink{element.defines}{\mbox{\isa{\isakeyword{defines}}}}~\isa{{\isachardoublequote}f\ x\isactrlsub {\isadigit{1}}\ {\isasymdots}\ x\isactrlsub n\ {\isasymequiv}\ t{\isachardoublequote}}''.
+ ``\hyperlink{element.defines}{\mbox{\isa{\isakeyword{defines}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}f\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}''.
- \item \hyperlink{element.notes}{\mbox{\isa{\isakeyword{notes}}}}~\isa{{\isachardoublequote}a\ {\isacharequal}\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}}
+ \item \hyperlink{element.notes}{\mbox{\isa{\isakeyword{notes}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{3D}{\isacharequal}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}
reconsiders facts within a local context. Most notably, this may
include arbitrary declarations in any attribute specifications
included here, e.g.\ a local \hyperlink{attribute.simp}{\mbox{\isa{simp}}} rule.
@@ -456,14 +456,14 @@
\end{description}
- Note that ``\isa{{\isachardoublequote}{\isacharparenleft}{\isasymIS}\ p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub n{\isacharparenright}{\isachardoublequote}}'' patterns given
+ Note that ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C49533E}{\isasymIS}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ p\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}'' patterns given
in the syntax of \hyperlink{element.assumes}{\mbox{\isa{\isakeyword{assumes}}}} and \hyperlink{element.defines}{\mbox{\isa{\isakeyword{defines}}}} above
are illegal in locale definitions. In the long goal format of
\secref{sec:goals}, term bindings may be included as expected,
though.
\medskip Locale specifications are ``closed up'' by
- turning the given text into a predicate definition \isa{loc{\isacharunderscore}axioms} and deriving the original assumptions as local lemmas
+ turning the given text into a predicate definition \isa{loc{\isaliteral{5F}{\isacharunderscore}}axioms} and deriving the original assumptions as local lemmas
(modulo local definitions). The predicate statement covers only the
newly specified assumptions, omitting the content of included locale
expressions. The full cumulative view is only provided on export,
@@ -474,23 +474,23 @@
that actually occur in the respective piece of text. Also note that
these predicates operate at the meta-level in theory, but the locale
packages attempts to internalize statements according to the
- object-logic setup (e.g.\ replacing \isa{{\isasymAnd}} by \isa{{\isasymforall}}, and
- \isa{{\isachardoublequote}{\isasymLongrightarrow}{\isachardoublequote}} by \isa{{\isachardoublequote}{\isasymlongrightarrow}{\isachardoublequote}} in HOL; see also
- \secref{sec:object-logic}). Separate introduction rules \isa{loc{\isacharunderscore}axioms{\isachardot}intro} and \isa{loc{\isachardot}intro} are provided as well.
+ object-logic setup (e.g.\ replacing \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}} by \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}}, and
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}{\isaliteral{22}{\isachardoublequote}}} by \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}{\isaliteral{22}{\isachardoublequote}}} in HOL; see also
+ \secref{sec:object-logic}). Separate introduction rules \isa{loc{\isaliteral{5F}{\isacharunderscore}}axioms{\isaliteral{2E}{\isachardot}}intro} and \isa{loc{\isaliteral{2E}{\isachardot}}intro} are provided as well.
- \item \hyperlink{command.print-locale}{\mbox{\isa{\isacommand{print{\isacharunderscore}locale}}}}~\isa{{\isachardoublequote}locale{\isachardoublequote}} prints the
+ \item \hyperlink{command.print-locale}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}locale}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}locale{\isaliteral{22}{\isachardoublequote}}} prints the
contents of the named locale. The command omits \hyperlink{element.notes}{\mbox{\isa{\isakeyword{notes}}}}
- elements by default. Use \hyperlink{command.print-locale}{\mbox{\isa{\isacommand{print{\isacharunderscore}locale}}}}\isa{{\isachardoublequote}{\isacharbang}{\isachardoublequote}} to
+ elements by default. Use \hyperlink{command.print-locale}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}locale}}}}\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{21}{\isacharbang}}{\isaliteral{22}{\isachardoublequote}}} to
have them included.
- \item \hyperlink{command.print-locales}{\mbox{\isa{\isacommand{print{\isacharunderscore}locales}}}} prints the names of all locales
+ \item \hyperlink{command.print-locales}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}locales}}}} prints the names of all locales
of the current theory.
- \item \hyperlink{method.intro-locales}{\mbox{\isa{intro{\isacharunderscore}locales}}} and \hyperlink{method.unfold-locales}{\mbox{\isa{unfold{\isacharunderscore}locales}}}
+ \item \hyperlink{method.intro-locales}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}locales}}} and \hyperlink{method.unfold-locales}{\mbox{\isa{unfold{\isaliteral{5F}{\isacharunderscore}}locales}}}
repeatedly expand all introduction rules of locale predicates of the
- theory. While \hyperlink{method.intro-locales}{\mbox{\isa{intro{\isacharunderscore}locales}}} only applies the \isa{loc{\isachardot}intro} introduction rules and therefore does not decend to
- assumptions, \hyperlink{method.unfold-locales}{\mbox{\isa{unfold{\isacharunderscore}locales}}} is more aggressive and applies
- \isa{loc{\isacharunderscore}axioms{\isachardot}intro} as well. Both methods are aware of locale
+ theory. While \hyperlink{method.intro-locales}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}locales}}} only applies the \isa{loc{\isaliteral{2E}{\isachardot}}intro} introduction rules and therefore does not decend to
+ assumptions, \hyperlink{method.unfold-locales}{\mbox{\isa{unfold{\isaliteral{5F}{\isacharunderscore}}locales}}} is more aggressive and applies
+ \isa{loc{\isaliteral{5F}{\isacharunderscore}}axioms{\isaliteral{2E}{\isachardot}}intro} as well. Both methods are aware of locale
specifications entailed by the context, both from target statements,
and from interpretations (see below). New goals that are entailed
by the current context are discharged automatically.
@@ -511,10 +511,10 @@
also within a proof body (command \hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}}).
\begin{matharray}{rcl}
- \indexdef{}{command}{sublocale}\hypertarget{command.sublocale}{\hyperlink{command.sublocale}{\mbox{\isa{\isacommand{sublocale}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{interpretation}\hypertarget{command.interpretation}{\hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{interpret}\hypertarget{command.interpret}{\hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}}} & : & \isa{{\isachardoublequote}proof{\isacharparenleft}state{\isacharparenright}\ {\isacharbar}\ proof{\isacharparenleft}chain{\isacharparenright}\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{print\_interps}\hypertarget{command.print-interps}{\hyperlink{command.print-interps}{\mbox{\isa{\isacommand{print{\isacharunderscore}interps}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{}{command}{sublocale}\hypertarget{command.sublocale}{\hyperlink{command.sublocale}{\mbox{\isa{\isacommand{sublocale}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{interpretation}\hypertarget{command.interpretation}{\hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{interpret}\hypertarget{command.interpret}{\hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof{\isaliteral{28}{\isacharparenleft}}state{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7C}{\isacharbar}}\ proof{\isaliteral{28}{\isacharparenleft}}chain{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_interps}\hypertarget{command.print-interps}{\hyperlink{command.print-interps}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}interps}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\indexouternonterm{interp}
@@ -533,7 +533,7 @@
\begin{description}
- \item \hyperlink{command.sublocale}{\mbox{\isa{\isacommand{sublocale}}}}~\isa{{\isachardoublequote}name\ {\isasymsubseteq}\ expr{\isachardoublequote}}
+ \item \hyperlink{command.sublocale}{\mbox{\isa{\isacommand{sublocale}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ expr{\isaliteral{22}{\isachardoublequote}}}
interprets \isa{expr} in the locale \isa{name}. A proof that
the specification of \isa{name} implies the specification of
\isa{expr} is required. As in the localized version of the
@@ -556,7 +556,7 @@
qualifier, although only for fragments of \isa{expr} that are not
interpreted in the theory already.
- \item \hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}}~\isa{{\isachardoublequote}expr\ {\isasymWHERE}\ eqns{\isachardoublequote}}
+ \item \hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}expr\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ eqns{\isaliteral{22}{\isachardoublequote}}}
interprets \isa{expr} in the theory. The command generates proof
obligations for the instantiated specifications (assumes and defines
elements). Once these are discharged by the user, instantiated
@@ -569,8 +569,8 @@
The command is aware of interpretations already active in the
theory, but does not simplify the goal automatically. In order to
- simplify the proof obligations use methods \hyperlink{method.intro-locales}{\mbox{\isa{intro{\isacharunderscore}locales}}}
- or \hyperlink{method.unfold-locales}{\mbox{\isa{unfold{\isacharunderscore}locales}}}. Post-processing is not applied to
+ simplify the proof obligations use methods \hyperlink{method.intro-locales}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}locales}}}
+ or \hyperlink{method.unfold-locales}{\mbox{\isa{unfold{\isaliteral{5F}{\isacharunderscore}}locales}}}. Post-processing is not applied to
facts of interpretations that are already active. This avoids
duplication of interpreted facts, in particular. Note that, in the
case of a locale with import, parts of the interpretation may
@@ -582,13 +582,13 @@
interpretations dynamically participate in any facts added to
locales.
- \item \hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}}~\isa{{\isachardoublequote}expr\ {\isasymWHERE}\ eqns{\isachardoublequote}} interprets
+ \item \hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}expr\ {\isaliteral{5C3C57484552453E}{\isasymWHERE}}\ eqns{\isaliteral{22}{\isachardoublequote}}} interprets
\isa{expr} in the proof context and is otherwise similar to
interpretation in theories. Note that rewrite rules given to
\hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}} should be explicitly universally quantified.
- \item \hyperlink{command.print-interps}{\mbox{\isa{\isacommand{print{\isacharunderscore}interps}}}}~\isa{{\isachardoublequote}locale{\isachardoublequote}} lists all
- interpretations of \isa{{\isachardoublequote}locale{\isachardoublequote}} in the current theory or proof
+ \item \hyperlink{command.print-interps}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}interps}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}locale{\isaliteral{22}{\isachardoublequote}}} lists all
+ interpretations of \isa{{\isaliteral{22}{\isachardoublequote}}locale{\isaliteral{22}{\isachardoublequote}}} in the current theory or proof
context, including those due to a combination of a \hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}} or \hyperlink{command.interpret}{\mbox{\isa{\isacommand{interpret}}}} and one or several
\hyperlink{command.sublocale}{\mbox{\isa{\isacommand{sublocale}}}} declarations.
@@ -620,7 +620,7 @@
%
\begin{isamarkuptext}%
A class is a particular locale with \emph{exactly one} type variable
- \isa{{\isasymalpha}}. Beyond the underlying locale, a corresponding type class
+ \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}}. Beyond the underlying locale, a corresponding type class
is established which is interpreted logically as axiomatic type
class \cite{Wenzel:1997:TPHOL} whose logical content are the
assumptions of the locale. Thus, classes provide the full
@@ -629,14 +629,14 @@
tutorial.
\begin{matharray}{rcl}
- \indexdef{}{command}{class}\hypertarget{command.class}{\hyperlink{command.class}{\mbox{\isa{\isacommand{class}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{instantiation}\hypertarget{command.instantiation}{\hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{instance}\hypertarget{command.instance}{\hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{instance}\hypertarget{command.instance}{\hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
- \indexdef{}{command}{subclass}\hypertarget{command.subclass}{\hyperlink{command.subclass}{\mbox{\isa{\isacommand{subclass}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{print\_classes}\hypertarget{command.print-classes}{\hyperlink{command.print-classes}{\mbox{\isa{\isacommand{print{\isacharunderscore}classes}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{class\_deps}\hypertarget{command.class-deps}{\hyperlink{command.class-deps}{\mbox{\isa{\isacommand{class{\isacharunderscore}deps}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{method}{intro\_classes}\hypertarget{method.intro-classes}{\hyperlink{method.intro-classes}{\mbox{\isa{intro{\isacharunderscore}classes}}}} & : & \isa{method} \\
+ \indexdef{}{command}{class}\hypertarget{command.class}{\hyperlink{command.class}{\mbox{\isa{\isacommand{class}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{instantiation}\hypertarget{command.instantiation}{\hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{instance}\hypertarget{command.instance}{\hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{instance}\hypertarget{command.instance}{\hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{28}{\isacharparenleft}}prove{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{subclass}\hypertarget{command.subclass}{\hyperlink{command.subclass}{\mbox{\isa{\isacommand{subclass}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{print\_classes}\hypertarget{command.print-classes}{\hyperlink{command.print-classes}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}classes}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{class\_deps}\hypertarget{command.class-deps}{\hyperlink{command.class-deps}{\mbox{\isa{\isacommand{class{\isaliteral{5F}{\isacharunderscore}}deps}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{method}{intro\_classes}\hypertarget{method.intro-classes}{\hyperlink{method.intro-classes}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}classes}}}} & : & \isa{method} \\
\end{matharray}
\begin{rail}
@@ -664,24 +664,24 @@
\begin{description}
- \item \hyperlink{command.class}{\mbox{\isa{\isacommand{class}}}}~\isa{{\isachardoublequote}c\ {\isacharequal}\ superclasses\ {\isacharplus}\ body{\isachardoublequote}} defines
+ \item \hyperlink{command.class}{\mbox{\isa{\isacommand{class}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{3D}{\isacharequal}}\ superclasses\ {\isaliteral{2B}{\isacharplus}}\ body{\isaliteral{22}{\isachardoublequote}}} defines
a new class \isa{c}, inheriting from \isa{superclasses}. This
introduces a locale \isa{c} with import of all locales \isa{superclasses}.
Any \hyperlink{element.fixes}{\mbox{\isa{\isakeyword{fixes}}}} in \isa{body} are lifted to the global
- theory level (\emph{class operations} \isa{{\isachardoublequote}f\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ f\isactrlsub n{\isachardoublequote}} of class \isa{c}), mapping the local type parameter
- \isa{{\isasymalpha}} to a schematic type variable \isa{{\isachardoublequote}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isachardoublequote}}.
+ theory level (\emph{class operations} \isa{{\isaliteral{22}{\isachardoublequote}}f\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ f\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} of class \isa{c}), mapping the local type parameter
+ \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}} to a schematic type variable \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ c{\isaliteral{22}{\isachardoublequote}}}.
Likewise, \hyperlink{element.assumes}{\mbox{\isa{\isakeyword{assumes}}}} in \isa{body} are also lifted,
- mapping each local parameter \isa{{\isachardoublequote}f\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}{\isachardoublequote}} to its
- corresponding global constant \isa{{\isachardoublequote}f\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}{\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isacharbrackright}{\isachardoublequote}}. The
- corresponding introduction rule is provided as \isa{c{\isacharunderscore}class{\isacharunderscore}axioms{\isachardot}intro}. This rule should be rarely needed directly
- --- the \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isacharunderscore}classes}}} method takes care of the details of
+ mapping each local parameter \isa{{\isaliteral{22}{\isachardoublequote}}f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} to its
+ corresponding global constant \isa{{\isaliteral{22}{\isachardoublequote}}f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ c{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}. The
+ corresponding introduction rule is provided as \isa{c{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{5F}{\isacharunderscore}}axioms{\isaliteral{2E}{\isachardot}}intro}. This rule should be rarely needed directly
+ --- the \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}classes}}} method takes care of the details of
class membership proofs.
- \item \hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}}~\isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}s\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s\isactrlsub n{\isacharparenright}s\ {\isasymBEGIN}{\isachardoublequote}} opens a theory target (cf.\ \secref{sec:target}) which
- allows to specify class operations \isa{{\isachardoublequote}f\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ f\isactrlsub n{\isachardoublequote}} corresponding
- to sort \isa{s} at the particular type instance \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ s\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ s\isactrlsub n{\isacharparenright}\ t{\isachardoublequote}}. A plain \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}} command in the
+ \item \hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ s\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}s\ {\isaliteral{5C3C424547494E3E}{\isasymBEGIN}}{\isaliteral{22}{\isachardoublequote}}} opens a theory target (cf.\ \secref{sec:target}) which
+ allows to specify class operations \isa{{\isaliteral{22}{\isachardoublequote}}f\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ f\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} corresponding
+ to sort \isa{s} at the particular type instance \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ s\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}}. A plain \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}} command in the
target body poses a goal stating these type arities. The target is
concluded by an \indexref{local}{command}{end}\hyperlink{command.local.end}{\mbox{\isa{\isacommand{end}}}} command.
@@ -690,11 +690,11 @@
in Isabelle/HOL.
\item \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}} in an instantiation target body sets
- up a goal stating the type arities claimed at the opening \hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}}. The proof would usually proceed by \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isacharunderscore}classes}}}, and then establish the characteristic theorems of
+ up a goal stating the type arities claimed at the opening \hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}}. The proof would usually proceed by \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}classes}}}, and then establish the characteristic theorems of
the type classes involved. After finishing the proof, the
background theory will be augmented by the proven type arities.
- On the theory level, \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}~\isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}s\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s\isactrlsub n{\isacharparenright}s{\isachardoublequote}} provides a convenient way to instantiate a type class with no
+ On the theory level, \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ s\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}s{\isaliteral{22}{\isachardoublequote}}} provides a convenient way to instantiate a type class with no
need to specify operations: one can continue with the
instantiation proof immediately.
@@ -704,24 +704,24 @@
\isa{d} is proven to be subclass \isa{c} and the locale \isa{c} is interpreted into \isa{d} simultaneously.
A weakend form of this is available through a further variant of
- \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}: \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}~\isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{2}}{\isachardoublequote}} opens
- a proof that class \isa{{\isachardoublequote}c\isactrlisub {\isadigit{2}}{\isachardoublequote}} implies \isa{{\isachardoublequote}c\isactrlisub {\isadigit{1}}{\isachardoublequote}} without reference
+ \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}: \hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} opens
+ a proof that class \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} implies \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} without reference
to the underlying locales; this is useful if the properties to prove
the logical connection are not sufficent on the locale level but on
the theory level.
- \item \hyperlink{command.print-classes}{\mbox{\isa{\isacommand{print{\isacharunderscore}classes}}}} prints all classes in the current
+ \item \hyperlink{command.print-classes}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}classes}}}} prints all classes in the current
theory.
- \item \hyperlink{command.class-deps}{\mbox{\isa{\isacommand{class{\isacharunderscore}deps}}}} visualizes all classes and their
+ \item \hyperlink{command.class-deps}{\mbox{\isa{\isacommand{class{\isaliteral{5F}{\isacharunderscore}}deps}}}} visualizes all classes and their
subclass relations as a Hasse diagram.
- \item \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isacharunderscore}classes}}} repeatedly expands all class
+ \item \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}classes}}} repeatedly expands all class
introduction rules of this theory. Note that this method usually
needs not be named explicitly, as it is already included in the
default proof step (e.g.\ of \hyperlink{command.proof}{\mbox{\isa{\isacommand{proof}}}}). In particular,
instantiation of trivial (syntactic) classes may be performed by a
- single ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isachardot}{\isachardot}}}}}'' proof step.
+ single ``\hyperlink{command.ddot}{\mbox{\isa{\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}}}}'' proof step.
\end{description}%
\end{isamarkuptext}%
@@ -740,15 +740,15 @@
\begin{itemize}
- \item Local constant declarations \isa{{\isachardoublequote}g{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}{\isachardoublequote}} referring to the
- local type parameter \isa{{\isasymalpha}} and local parameters \isa{{\isachardoublequote}f{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}{\isachardoublequote}}
- are accompanied by theory-level constants \isa{{\isachardoublequote}g{\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isacharbrackright}{\isachardoublequote}}
- referring to theory-level class operations \isa{{\isachardoublequote}f{\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isacharbrackright}{\isachardoublequote}}.
+ \item Local constant declarations \isa{{\isaliteral{22}{\isachardoublequote}}g{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} referring to the
+ local type parameter \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}} and local parameters \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}
+ are accompanied by theory-level constants \isa{{\isaliteral{22}{\isachardoublequote}}g{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ c{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}
+ referring to theory-level class operations \isa{{\isaliteral{22}{\isachardoublequote}}f{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ c{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}}.
\item Local theorem bindings are lifted as are assumptions.
- \item Local syntax refers to local operations \isa{{\isachardoublequote}g{\isacharbrackleft}{\isasymalpha}{\isacharbrackright}{\isachardoublequote}} and
- global operations \isa{{\isachardoublequote}g{\isacharbrackleft}{\isacharquery}{\isasymalpha}\ {\isacharcolon}{\isacharcolon}\ c{\isacharbrackright}{\isachardoublequote}} uniformly. Type inference
+ \item Local syntax refers to local operations \isa{{\isaliteral{22}{\isachardoublequote}}g{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} and
+ global operations \isa{{\isaliteral{22}{\isachardoublequote}}g{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ c{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} uniformly. Type inference
resolves ambiguities. In rare cases, manual type annotations are
needed.
@@ -767,15 +767,15 @@
\medskip For the subsequent formulation of co-regularity we assume
that the class relation is closed by transitivity and reflexivity.
- Moreover the collection of arities \isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s{\isacharparenright}c{\isachardoublequote}} is
- completed such that \isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s{\isacharparenright}c{\isachardoublequote}} and \isa{{\isachardoublequote}c\ {\isasymsubseteq}\ c{\isacharprime}{\isachardoublequote}}
- implies \isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s{\isacharparenright}c{\isacharprime}{\isachardoublequote}} for all such declarations.
+ Moreover the collection of arities \isa{{\isaliteral{22}{\isachardoublequote}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec s{\isaliteral{29}{\isacharparenright}}c{\isaliteral{22}{\isachardoublequote}}} is
+ completed such that \isa{{\isaliteral{22}{\isachardoublequote}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec s{\isaliteral{29}{\isacharparenright}}c{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequote}}}
+ implies \isa{{\isaliteral{22}{\isachardoublequote}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec s{\isaliteral{29}{\isacharparenright}}c{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequote}}} for all such declarations.
Treating sorts as finite sets of classes (meaning the intersection),
- the class relation \isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{2}}{\isachardoublequote}} is extended to sorts as
+ the class relation \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} is extended to sorts as
follows:
\[
- \isa{{\isachardoublequote}s\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ s\isactrlsub {\isadigit{2}}\ {\isasymequiv}\ {\isasymforall}c\isactrlsub {\isadigit{2}}\ {\isasymin}\ s\isactrlsub {\isadigit{2}}{\isachardot}\ {\isasymexists}c\isactrlsub {\isadigit{1}}\ {\isasymin}\ s\isactrlsub {\isadigit{1}}{\isachardot}\ c\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{2}}{\isachardoublequote}}
+ \isa{{\isaliteral{22}{\isachardoublequote}}s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}}
\]
This relation on sorts is further extended to tuples of sorts (of
@@ -784,7 +784,7 @@
\smallskip Co-regularity of the class relation together with the
arities relation means:
\[
- \isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s\isactrlsub {\isadigit{1}}{\isacharparenright}c\isactrlsub {\isadigit{1}}\ {\isasymLongrightarrow}\ t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}\isactrlvec s\isactrlsub {\isadigit{2}}{\isacharparenright}c\isactrlsub {\isadigit{2}}\ {\isasymLongrightarrow}\ c\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{2}}\ {\isasymLongrightarrow}\ \isactrlvec s\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ \isactrlvec s\isactrlsub {\isadigit{2}}{\isachardoublequote}}
+ \isa{{\isaliteral{22}{\isachardoublequote}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}\isaliteral{5C3C5E7665633E}{}\isactrlvec s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ \isaliteral{5C3C5E7665633E}{}\isactrlvec s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}}
\]
\noindent for all such arities. In other words, whenever the result
classes of some type-constructor arities are related, then the
@@ -803,9 +803,9 @@
\begin{isamarkuptext}%
Isabelle/Pure's definitional schemes support certain forms of
overloading (see \secref{sec:consts}). Overloading means that a
- constant being declared as \isa{{\isachardoublequote}c\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ decl{\isachardoublequote}} may be
+ constant being declared as \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ decl{\isaliteral{22}{\isachardoublequote}}} may be
defined separately on type instances
- \isa{{\isachardoublequote}c\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}{\isasymbeta}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymbeta}\isactrlsub n{\isacharparenright}\ t\ decl{\isachardoublequote}}
+ \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}\ t\ decl{\isaliteral{22}{\isachardoublequote}}}
for each type constructor \isa{t}. At most occassions
overloading will be used in a Haskell-like fashion together with
type classes by means of \hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}} (see
@@ -814,7 +814,7 @@
end-users.
\begin{matharray}{rcl}
- \indexdef{}{command}{overloading}\hypertarget{command.overloading}{\hyperlink{command.overloading}{\mbox{\isa{\isacommand{overloading}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
+ \indexdef{}{command}{overloading}\hypertarget{command.overloading}{\hyperlink{command.overloading}{\mbox{\isa{\isacommand{overloading}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -824,16 +824,16 @@
\begin{description}
- \item \hyperlink{command.overloading}{\mbox{\isa{\isacommand{overloading}}}}~\isa{{\isachardoublequote}x\isactrlsub {\isadigit{1}}\ {\isasymequiv}\ c\isactrlsub {\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}\isactrlsub {\isadigit{1}}\ {\isasymAND}\ {\isasymdots}\ x\isactrlsub n\ {\isasymequiv}\ c\isactrlsub n\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}\isactrlsub n\ {\isasymBEGIN}{\isachardoublequote}}
+ \item \hyperlink{command.overloading}{\mbox{\isa{\isacommand{overloading}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C414E443E}{\isasymAND}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n\ {\isaliteral{5C3C424547494E3E}{\isasymBEGIN}}{\isaliteral{22}{\isachardoublequote}}}
opens a theory target (cf.\ \secref{sec:target}) which allows to
specify constants with overloaded definitions. These are identified
- by an explicitly given mapping from variable names \isa{{\isachardoublequote}x\isactrlsub i{\isachardoublequote}} to
- constants \isa{{\isachardoublequote}c\isactrlsub i{\isachardoublequote}} at particular type instances. The
+ by an explicitly given mapping from variable names \isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} to
+ constants \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} at particular type instances. The
definitions themselves are established using common specification
- tools, using the names \isa{{\isachardoublequote}x\isactrlsub i{\isachardoublequote}} as reference to the
+ tools, using the names \isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub i{\isaliteral{22}{\isachardoublequote}}} as reference to the
corresponding constants. The target is concluded by \hyperlink{command.local.end}{\mbox{\isa{\isacommand{end}}}}.
- A \isa{{\isachardoublequote}{\isacharparenleft}unchecked{\isacharparenright}{\isachardoublequote}} option disables global dependency checks for
+ A \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}unchecked{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option disables global dependency checks for
the corresponding definition, which is occasionally useful for
exotic overloading (see \secref{sec:consts} for a precise description).
It is at the discretion of the user to avoid
@@ -849,14 +849,14 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{use}\hypertarget{command.use}{\hyperlink{command.use}{\mbox{\isa{\isacommand{use}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{ML}\hypertarget{command.ML}{\hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{ML\_prf}\hypertarget{command.ML-prf}{\hyperlink{command.ML-prf}{\mbox{\isa{\isacommand{ML{\isacharunderscore}prf}}}}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}\ proof{\isachardoublequote}} \\
- \indexdef{}{command}{ML\_val}\hypertarget{command.ML-val}{\hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isacharunderscore}val}}}}} & : & \isa{{\isachardoublequote}any\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{ML\_command}\hypertarget{command.ML-command}{\hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isacharunderscore}command}}}}} & : & \isa{{\isachardoublequote}any\ {\isasymrightarrow}{\isachardoublequote}} \\
- \indexdef{}{command}{setup}\hypertarget{command.setup}{\hyperlink{command.setup}{\mbox{\isa{\isacommand{setup}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{local\_setup}\hypertarget{command.local-setup}{\hyperlink{command.local-setup}{\mbox{\isa{\isacommand{local{\isacharunderscore}setup}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{attribute\_setup}\hypertarget{command.attribute-setup}{\hyperlink{command.attribute-setup}{\mbox{\isa{\isacommand{attribute{\isacharunderscore}setup}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
+ \indexdef{}{command}{use}\hypertarget{command.use}{\hyperlink{command.use}{\mbox{\isa{\isacommand{use}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{ML}\hypertarget{command.ML}{\hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{ML\_prf}\hypertarget{command.ML-prf}{\hyperlink{command.ML-prf}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}prf}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}proof\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ proof{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{ML\_val}\hypertarget{command.ML-val}{\hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}any\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{ML\_command}\hypertarget{command.ML-command}{\hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}command}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}any\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{setup}\hypertarget{command.setup}{\hyperlink{command.setup}{\mbox{\isa{\isacommand{setup}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{local\_setup}\hypertarget{command.local-setup}{\hyperlink{command.local-setup}{\mbox{\isa{\isacommand{local{\isaliteral{5F}{\isacharunderscore}}setup}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{attribute\_setup}\hypertarget{command.attribute-setup}{\hyperlink{command.attribute-setup}{\mbox{\isa{\isacommand{attribute{\isaliteral{5F}{\isacharunderscore}}setup}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -870,8 +870,8 @@
\begin{description}
- \item \hyperlink{command.use}{\mbox{\isa{\isacommand{use}}}}~\isa{{\isachardoublequote}file{\isachardoublequote}} reads and executes ML
- commands from \isa{{\isachardoublequote}file{\isachardoublequote}}. The current theory context is passed
+ \item \hyperlink{command.use}{\mbox{\isa{\isacommand{use}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}file{\isaliteral{22}{\isachardoublequote}}} reads and executes ML
+ commands from \isa{{\isaliteral{22}{\isachardoublequote}}file{\isaliteral{22}{\isachardoublequote}}}. The current theory context is passed
down to the ML toplevel and may be modified, using \verb|Context.>>| or derived ML commands. The file name is checked with
the \indexref{}{keyword}{uses}\hyperlink{keyword.uses}{\mbox{\isa{\isakeyword{uses}}}} dependency declaration given in the theory
header (see also \secref{sec:begin-thy}).
@@ -879,37 +879,37 @@
Top-level ML bindings are stored within the (global or local) theory
context.
- \item \hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}}~\isa{{\isachardoublequote}text{\isachardoublequote}} is similar to \hyperlink{command.use}{\mbox{\isa{\isacommand{use}}}},
- but executes ML commands directly from the given \isa{{\isachardoublequote}text{\isachardoublequote}}.
+ \item \hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}} is similar to \hyperlink{command.use}{\mbox{\isa{\isacommand{use}}}},
+ but executes ML commands directly from the given \isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}}.
Top-level ML bindings are stored within the (global or local) theory
context.
- \item \hyperlink{command.ML-prf}{\mbox{\isa{\isacommand{ML{\isacharunderscore}prf}}}} is analogous to \hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}} but works
+ \item \hyperlink{command.ML-prf}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}prf}}}} is analogous to \hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}} but works
within a proof context.
Top-level ML bindings are stored within the proof context in a
purely sequential fashion, disregarding the nested proof structure.
- ML bindings introduced by \hyperlink{command.ML-prf}{\mbox{\isa{\isacommand{ML{\isacharunderscore}prf}}}} are discarded at the
+ ML bindings introduced by \hyperlink{command.ML-prf}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}prf}}}} are discarded at the
end of the proof.
- \item \hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isacharunderscore}val}}}} and \hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isacharunderscore}command}}}} are diagnostic
+ \item \hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}}}} and \hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}command}}}} are diagnostic
versions of \hyperlink{command.ML}{\mbox{\isa{\isacommand{ML}}}}, which means that the context may not be
- updated. \hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isacharunderscore}val}}}} echos the bindings produced at the ML
- toplevel, but \hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isacharunderscore}command}}}} is silent.
+ updated. \hyperlink{command.ML-val}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}val}}}} echos the bindings produced at the ML
+ toplevel, but \hyperlink{command.ML-command}{\mbox{\isa{\isacommand{ML{\isaliteral{5F}{\isacharunderscore}}command}}}} is silent.
- \item \hyperlink{command.setup}{\mbox{\isa{\isacommand{setup}}}}~\isa{{\isachardoublequote}text{\isachardoublequote}} changes the current theory
- context by applying \isa{{\isachardoublequote}text{\isachardoublequote}}, which refers to an ML expression
+ \item \hyperlink{command.setup}{\mbox{\isa{\isacommand{setup}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}} changes the current theory
+ context by applying \isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}}, which refers to an ML expression
of type \verb|theory -> theory|. This enables to initialize
any object-logic specific tools and packages written in ML, for
example.
- \item \hyperlink{command.local-setup}{\mbox{\isa{\isacommand{local{\isacharunderscore}setup}}}} is similar to \hyperlink{command.setup}{\mbox{\isa{\isacommand{setup}}}} for
+ \item \hyperlink{command.local-setup}{\mbox{\isa{\isacommand{local{\isaliteral{5F}{\isacharunderscore}}setup}}}} is similar to \hyperlink{command.setup}{\mbox{\isa{\isacommand{setup}}}} for
a local theory context, and an ML expression of type \verb|local_theory -> local_theory|. This allows to
invoke local theory specification packages without going through
concrete outer syntax, for example.
- \item \hyperlink{command.attribute-setup}{\mbox{\isa{\isacommand{attribute{\isacharunderscore}setup}}}}~\isa{{\isachardoublequote}name\ {\isacharequal}\ text\ description{\isachardoublequote}}
- defines an attribute in the current theory. The given \isa{{\isachardoublequote}text{\isachardoublequote}} has to be an ML expression of type
+ \item \hyperlink{command.attribute-setup}{\mbox{\isa{\isacommand{attribute{\isaliteral{5F}{\isacharunderscore}}setup}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name\ {\isaliteral{3D}{\isacharequal}}\ text\ description{\isaliteral{22}{\isachardoublequote}}}
+ defines an attribute in the current theory. The given \isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}} has to be an ML expression of type
\verb|attribute context_parser|, cf.\ basic parsers defined in
structure \verb|Args| and \verb|Attrib|.
@@ -926,19 +926,19 @@
\endisadelimML
%
\isatagML
-\isacommand{attribute{\isacharunderscore}setup}\isamarkupfalse%
-\ my{\isacharunderscore}rule\ {\isacharequal}\ {\isacharverbatimopen}\isanewline
-\ \ \ \ \ \ Attrib{\isachardot}thms\ {\isachargreater}{\isachargreater}\ {\isacharparenleft}fn\ ths\ {\isacharequal}{\isachargreater}\isanewline
-\ \ \ \ \ \ \ \ Thm{\isachardot}rule{\isacharunderscore}attribute\ {\isacharparenleft}fn\ context{\isacharcolon}\ Context{\isachardot}generic\ {\isacharequal}{\isachargreater}\ fn\ th{\isacharcolon}\ thm\ {\isacharequal}{\isachargreater}\isanewline
-\ \ \ \ \ \ \ \ \ \ let\ val\ th{\isacharprime}\ {\isacharequal}\ th\ OF\ ths\isanewline
-\ \ \ \ \ \ \ \ \ \ in\ th{\isacharprime}\ end{\isacharparenright}{\isacharparenright}\ {\isacharverbatimclose}\ \ {\isachardoublequoteopen}my\ rule{\isachardoublequoteclose}\isanewline
+\isacommand{attribute{\isaliteral{5F}{\isacharunderscore}}setup}\isamarkupfalse%
+\ my{\isaliteral{5F}{\isacharunderscore}}rule\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ \ \ \ \ Attrib{\isaliteral{2E}{\isachardot}}thms\ {\isaliteral{3E}{\isachargreater}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}fn\ ths\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline
+\ \ \ \ \ \ \ \ Thm{\isaliteral{2E}{\isachardot}}rule{\isaliteral{5F}{\isacharunderscore}}attribute\ {\isaliteral{28}{\isacharparenleft}}fn\ context{\isaliteral{3A}{\isacharcolon}}\ Context{\isaliteral{2E}{\isachardot}}generic\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ fn\ th{\isaliteral{3A}{\isacharcolon}}\ thm\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline
+\ \ \ \ \ \ \ \ \ \ let\ val\ th{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ th\ OF\ ths\isanewline
+\ \ \ \ \ \ \ \ \ \ in\ th{\isaliteral{27}{\isacharprime}}\ end{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}my\ rule{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
-\ \ \ \ \isacommand{attribute{\isacharunderscore}setup}\isamarkupfalse%
-\ my{\isacharunderscore}declaration\ {\isacharequal}\ {\isacharverbatimopen}\isanewline
-\ \ \ \ \ \ Attrib{\isachardot}thms\ {\isachargreater}{\isachargreater}\ {\isacharparenleft}fn\ ths\ {\isacharequal}{\isachargreater}\isanewline
-\ \ \ \ \ \ \ \ Thm{\isachardot}declaration{\isacharunderscore}attribute\ {\isacharparenleft}fn\ th{\isacharcolon}\ thm\ {\isacharequal}{\isachargreater}\ fn\ context{\isacharcolon}\ Context{\isachardot}generic\ {\isacharequal}{\isachargreater}\isanewline
-\ \ \ \ \ \ \ \ \ \ let\ val\ context{\isacharprime}\ {\isacharequal}\ context\isanewline
-\ \ \ \ \ \ \ \ \ \ in\ context{\isacharprime}\ end{\isacharparenright}{\isacharparenright}\ {\isacharverbatimclose}\ \ {\isachardoublequoteopen}my\ declaration{\isachardoublequoteclose}%
+\ \ \ \ \isacommand{attribute{\isaliteral{5F}{\isacharunderscore}}setup}\isamarkupfalse%
+\ my{\isaliteral{5F}{\isacharunderscore}}declaration\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
+\ \ \ \ \ \ Attrib{\isaliteral{2E}{\isachardot}}thms\ {\isaliteral{3E}{\isachargreater}}{\isaliteral{3E}{\isachargreater}}\ {\isaliteral{28}{\isacharparenleft}}fn\ ths\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline
+\ \ \ \ \ \ \ \ Thm{\isaliteral{2E}{\isachardot}}declaration{\isaliteral{5F}{\isacharunderscore}}attribute\ {\isaliteral{28}{\isacharparenleft}}fn\ th{\isaliteral{3A}{\isacharcolon}}\ thm\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ fn\ context{\isaliteral{3A}{\isacharcolon}}\ Context{\isaliteral{2E}{\isachardot}}generic\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\isanewline
+\ \ \ \ \ \ \ \ \ \ let\ val\ context{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ context\isanewline
+\ \ \ \ \ \ \ \ \ \ in\ context{\isaliteral{27}{\isacharprime}}\ end{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}my\ declaration{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagML
{\isafoldML}%
%
@@ -956,9 +956,9 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcll}
- \indexdef{}{command}{classes}\hypertarget{command.classes}{\hyperlink{command.classes}{\mbox{\isa{\isacommand{classes}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{classrel}\hypertarget{command.classrel}{\hyperlink{command.classrel}{\mbox{\isa{\isacommand{classrel}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} & (axiomatic!) \\
- \indexdef{}{command}{default\_sort}\hypertarget{command.default-sort}{\hyperlink{command.default-sort}{\mbox{\isa{\isacommand{default{\isacharunderscore}sort}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}}
+ \indexdef{}{command}{classes}\hypertarget{command.classes}{\hyperlink{command.classes}{\mbox{\isa{\isacommand{classes}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{classrel}\hypertarget{command.classrel}{\hyperlink{command.classrel}{\mbox{\isa{\isacommand{classrel}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} & (axiomatic!) \\
+ \indexdef{}{command}{default\_sort}\hypertarget{command.default-sort}{\hyperlink{command.default-sort}{\mbox{\isa{\isacommand{default{\isaliteral{5F}{\isacharunderscore}}sort}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}}
\end{matharray}
\begin{rail}
@@ -972,18 +972,18 @@
\begin{description}
- \item \hyperlink{command.classes}{\mbox{\isa{\isacommand{classes}}}}~\isa{{\isachardoublequote}c\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n{\isachardoublequote}} declares class
- \isa{c} to be a subclass of existing classes \isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ c\isactrlsub n{\isachardoublequote}}.
+ \item \hyperlink{command.classes}{\mbox{\isa{\isacommand{classes}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} declares class
+ \isa{c} to be a subclass of existing classes \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}.
Isabelle implicitly maintains the transitive closure of the class
hierarchy. Cyclic class structures are not permitted.
- \item \hyperlink{command.classrel}{\mbox{\isa{\isacommand{classrel}}}}~\isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}\ {\isasymsubseteq}\ c\isactrlsub {\isadigit{2}}{\isachardoublequote}} states subclass
- relations between existing classes \isa{{\isachardoublequote}c\isactrlsub {\isadigit{1}}{\isachardoublequote}} and \isa{{\isachardoublequote}c\isactrlsub {\isadigit{2}}{\isachardoublequote}}.
+ \item \hyperlink{command.classrel}{\mbox{\isa{\isacommand{classrel}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}} states subclass
+ relations between existing classes \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}c\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}}.
This is done axiomatically! The \indexref{}{command}{subclass}\hyperlink{command.subclass}{\mbox{\isa{\isacommand{subclass}}}} and
\indexref{}{command}{instance}\hyperlink{command.instance}{\mbox{\isa{\isacommand{instance}}}} commands (see \secref{sec:class}) provide
a way to introduce proven class relations.
- \item \hyperlink{command.default-sort}{\mbox{\isa{\isacommand{default{\isacharunderscore}sort}}}}~\isa{s} makes sort \isa{s} the
+ \item \hyperlink{command.default-sort}{\mbox{\isa{\isacommand{default{\isaliteral{5F}{\isacharunderscore}}sort}}}}~\isa{s} makes sort \isa{s} the
new default sort for any type variable that is given explicitly in
the text, but lacks a sort constraint (wrt.\ the current context).
Type variables generated by type inference are not affected.
@@ -1006,9 +1006,9 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcll}
- \indexdef{}{command}{types}\hypertarget{command.types}{\hyperlink{command.types}{\mbox{\isa{\isacommand{types}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{typedecl}\hypertarget{command.typedecl}{\hyperlink{command.typedecl}{\mbox{\isa{\isacommand{typedecl}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{arities}\hypertarget{command.arities}{\hyperlink{command.arities}{\mbox{\isa{\isacommand{arities}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} & (axiomatic!) \\
+ \indexdef{}{command}{types}\hypertarget{command.types}{\hyperlink{command.types}{\mbox{\isa{\isacommand{types}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{typedecl}\hypertarget{command.typedecl}{\hyperlink{command.typedecl}{\mbox{\isa{\isacommand{typedecl}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{arities}\hypertarget{command.arities}{\hyperlink{command.arities}{\mbox{\isa{\isacommand{arities}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} & (axiomatic!) \\
\end{matharray}
\begin{rail}
@@ -1022,19 +1022,19 @@
\begin{description}
- \item \hyperlink{command.types}{\mbox{\isa{\isacommand{types}}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t\ {\isacharequal}\ {\isasymtau}{\isachardoublequote}} introduces a
- \emph{type synonym} \isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t{\isachardoublequote}} for the existing type
- \isa{{\isachardoublequote}{\isasymtau}{\isachardoublequote}}. Unlike actual type definitions, as are available in
+ \item \hyperlink{command.types}{\mbox{\isa{\isacommand{types}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}\ t\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}} introduces a
+ \emph{type synonym} \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}} for the existing type
+ \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7461753E}{\isasymtau}}{\isaliteral{22}{\isachardoublequote}}}. Unlike actual type definitions, as are available in
Isabelle/HOL for example, type synonyms are merely syntactic
abbreviations without any logical significance. Internally, type
synonyms are fully expanded.
- \item \hyperlink{command.typedecl}{\mbox{\isa{\isacommand{typedecl}}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t{\isachardoublequote}} declares a new
+ \item \hyperlink{command.typedecl}{\mbox{\isa{\isacommand{typedecl}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{22}{\isachardoublequote}}} declares a new
type constructor \isa{t}. If the object-logic defines a base sort
\isa{s}, then the constructor is declared to operate on that, via
- the axiomatic specification \hyperlink{command.arities}{\mbox{\isa{\isacommand{arities}}}}~\isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}s{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s{\isacharparenright}s{\isachardoublequote}}.
+ the axiomatic specification \hyperlink{command.arities}{\mbox{\isa{\isacommand{arities}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ s{\isaliteral{29}{\isacharparenright}}s{\isaliteral{22}{\isachardoublequote}}}.
- \item \hyperlink{command.arities}{\mbox{\isa{\isacommand{arities}}}}~\isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}s\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ s\isactrlsub n{\isacharparenright}s{\isachardoublequote}} augments
+ \item \hyperlink{command.arities}{\mbox{\isa{\isacommand{arities}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}s\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ s\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{29}{\isacharparenright}}s{\isaliteral{22}{\isachardoublequote}}} augments
Isabelle's order-sorted signature of types by new type constructor
arities. This is done axiomatically! The \indexref{}{command}{instantiation}\hyperlink{command.instantiation}{\mbox{\isa{\isacommand{instantiation}}}}
target (see \secref{sec:class}) provides a way to introduce
@@ -1050,12 +1050,12 @@
%
\begin{isamarkuptext}%
Definitions essentially express abbreviations within the logic. The
- simplest form of a definition is \isa{{\isachardoublequote}c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}\ {\isasymequiv}\ t{\isachardoublequote}}, where \isa{c} is a newly declared constant. Isabelle also allows derived forms
+ simplest form of a definition is \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}, where \isa{c} is a newly declared constant. Isabelle also allows derived forms
where the arguments of \isa{c} appear on the left, abbreviating a
- prefix of \isa{{\isasymlambda}}-abstractions, e.g.\ \isa{{\isachardoublequote}c\ {\isasymequiv}\ {\isasymlambda}x\ y{\isachardot}\ t{\isachardoublequote}} may be
- written more conveniently as \isa{{\isachardoublequote}c\ x\ y\ {\isasymequiv}\ t{\isachardoublequote}}. Moreover,
+ prefix of \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}}-abstractions, e.g.\ \isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x\ y{\isaliteral{2E}{\isachardot}}\ t{\isaliteral{22}{\isachardoublequote}}} may be
+ written more conveniently as \isa{{\isaliteral{22}{\isachardoublequote}}c\ x\ y\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}. Moreover,
definitions may be weakened by adding arbitrary pre-conditions:
- \isa{{\isachardoublequote}A\ {\isasymLongrightarrow}\ c\ x\ y\ {\isasymequiv}\ t{\isachardoublequote}}.
+ \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ c\ x\ y\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ t{\isaliteral{22}{\isachardoublequote}}}.
\medskip The built-in well-formedness conditions for definitional
specifications are:
@@ -1068,7 +1068,7 @@
left-hand side.
\item All type variables on the right-hand side must also appear on
- the left-hand side; this prohibits \isa{{\isachardoublequote}{\isadigit{0}}\ {\isacharcolon}{\isacharcolon}\ nat\ {\isasymequiv}\ length\ {\isacharparenleft}{\isacharbrackleft}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ list{\isacharparenright}{\isachardoublequote}} for example.
+ the left-hand side; this prohibits \isa{{\isaliteral{22}{\isachardoublequote}}{\isadigit{0}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ length\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ list{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} for example.
\item The definition must not be recursive. Most object-logics
provide definitional principles that can be used to express
@@ -1078,15 +1078,15 @@
The right-hand side of overloaded definitions may mention overloaded constants
recursively at type instances corresponding to the immediate
- argument types \isa{{\isachardoublequote}{\isasymbeta}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymbeta}\isactrlsub n{\isachardoublequote}}. Incomplete
+ argument types \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}. Incomplete
specification patterns impose global constraints on all occurrences,
- e.g.\ \isa{{\isachardoublequote}d\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ {\isasymtimes}\ {\isasymalpha}{\isachardoublequote}} on the left-hand side means that all
+ e.g.\ \isa{{\isaliteral{22}{\isachardoublequote}}d\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{22}{\isachardoublequote}}} on the left-hand side means that all
corresponding occurrences on some right-hand side need to be an
- instance of this, general \isa{{\isachardoublequote}d\ {\isacharcolon}{\isacharcolon}\ {\isasymalpha}\ {\isasymtimes}\ {\isasymbeta}{\isachardoublequote}} will be disallowed.
+ instance of this, general \isa{{\isaliteral{22}{\isachardoublequote}}d\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{5C3C626574613E}{\isasymbeta}}{\isaliteral{22}{\isachardoublequote}}} will be disallowed.
\begin{matharray}{rcl}
- \indexdef{}{command}{consts}\hypertarget{command.consts}{\hyperlink{command.consts}{\mbox{\isa{\isacommand{consts}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{defs}\hypertarget{command.defs}{\hyperlink{command.defs}{\mbox{\isa{\isacommand{defs}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
+ \indexdef{}{command}{consts}\hypertarget{command.consts}{\hyperlink{command.consts}{\mbox{\isa{\isacommand{consts}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{defs}\hypertarget{command.defs}{\hyperlink{command.defs}{\mbox{\isa{\isacommand{defs}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -1098,19 +1098,19 @@
\begin{description}
- \item \hyperlink{command.consts}{\mbox{\isa{\isacommand{consts}}}}~\isa{{\isachardoublequote}c\ {\isacharcolon}{\isacharcolon}\ {\isasymsigma}{\isachardoublequote}} declares constant \isa{c} to have any instance of type scheme \isa{{\isasymsigma}}. The optional
+ \item \hyperlink{command.consts}{\mbox{\isa{\isacommand{consts}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}c\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7369676D613E}{\isasymsigma}}{\isaliteral{22}{\isachardoublequote}}} declares constant \isa{c} to have any instance of type scheme \isa{{\isaliteral{5C3C7369676D613E}{\isasymsigma}}}. The optional
mixfix annotations may attach concrete syntax to the constants
declared.
- \item \hyperlink{command.defs}{\mbox{\isa{\isacommand{defs}}}}~\isa{{\isachardoublequote}name{\isacharcolon}\ eqn{\isachardoublequote}} introduces \isa{eqn}
+ \item \hyperlink{command.defs}{\mbox{\isa{\isacommand{defs}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name{\isaliteral{3A}{\isacharcolon}}\ eqn{\isaliteral{22}{\isachardoublequote}}} introduces \isa{eqn}
as a definitional axiom for some existing constant.
- The \isa{{\isachardoublequote}{\isacharparenleft}unchecked{\isacharparenright}{\isachardoublequote}} option disables global dependency checks
+ The \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}unchecked{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option disables global dependency checks
for this definition, which is occasionally useful for exotic
overloading. It is at the discretion of the user to avoid malformed
theory specifications!
- The \isa{{\isachardoublequote}{\isacharparenleft}overloaded{\isacharparenright}{\isachardoublequote}} option declares definitions to be
+ The \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}overloaded{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} option declares definitions to be
potentially overloaded. Unless this option is given, a warning
message would be issued for any definitional equation with a more
special type than that of the corresponding constant declaration.
@@ -1125,9 +1125,9 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcll}
- \indexdef{}{command}{axioms}\hypertarget{command.axioms}{\hyperlink{command.axioms}{\mbox{\isa{\isacommand{axioms}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} & (axiomatic!) \\
- \indexdef{}{command}{lemmas}\hypertarget{command.lemmas}{\hyperlink{command.lemmas}{\mbox{\isa{\isacommand{lemmas}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
- \indexdef{}{command}{theorems}\hypertarget{command.theorems}{\hyperlink{command.theorems}{\mbox{\isa{\isacommand{theorems}}}}} & : & \isa{{\isachardoublequote}local{\isacharunderscore}theory\ {\isasymrightarrow}\ local{\isacharunderscore}theory{\isachardoublequote}} \\
+ \indexdef{}{command}{axioms}\hypertarget{command.axioms}{\hyperlink{command.axioms}{\mbox{\isa{\isacommand{axioms}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} & (axiomatic!) \\
+ \indexdef{}{command}{lemmas}\hypertarget{command.lemmas}{\hyperlink{command.lemmas}{\mbox{\isa{\isacommand{lemmas}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{theorems}\hypertarget{command.theorems}{\hyperlink{command.theorems}{\mbox{\isa{\isacommand{theorems}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}local{\isaliteral{5F}{\isacharunderscore}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ local{\isaliteral{5F}{\isacharunderscore}}theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -1139,7 +1139,7 @@
\begin{description}
- \item \hyperlink{command.axioms}{\mbox{\isa{\isacommand{axioms}}}}~\isa{{\isachardoublequote}a{\isacharcolon}\ {\isasymphi}{\isachardoublequote}} introduces arbitrary
+ \item \hyperlink{command.axioms}{\mbox{\isa{\isacommand{axioms}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{22}{\isachardoublequote}}} introduces arbitrary
statements as axioms of the meta-logic. In fact, axioms are
``axiomatic theorems'', and may be referred later just as any other
theorem.
@@ -1148,7 +1148,7 @@
systems. Everyday work is typically done the hard way, with proper
definitions and proven theorems.
- \item \hyperlink{command.lemmas}{\mbox{\isa{\isacommand{lemmas}}}}~\isa{{\isachardoublequote}a\ {\isacharequal}\ b\isactrlsub {\isadigit{1}}\ {\isasymdots}\ b\isactrlsub n{\isachardoublequote}} retrieves and stores
+ \item \hyperlink{command.lemmas}{\mbox{\isa{\isacommand{lemmas}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}a\ {\isaliteral{3D}{\isacharequal}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ b\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}} retrieves and stores
existing facts in the theory context, or the specified target
context (see also \secref{sec:target}). Typical applications would
also involve attributes, to declare Simplifier rules, for example.
@@ -1180,7 +1180,7 @@
presumed theorems depend on unproven suppositions.
\begin{matharray}{rcll}
- \indexdef{}{command}{oracle}\hypertarget{command.oracle}{\hyperlink{command.oracle}{\mbox{\isa{\isacommand{oracle}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} & (axiomatic!) \\
+ \indexdef{}{command}{oracle}\hypertarget{command.oracle}{\hyperlink{command.oracle}{\mbox{\isa{\isacommand{oracle}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} & (axiomatic!) \\
\end{matharray}
\begin{rail}
@@ -1190,8 +1190,8 @@
\begin{description}
- \item \hyperlink{command.oracle}{\mbox{\isa{\isacommand{oracle}}}}~\isa{{\isachardoublequote}name\ {\isacharequal}\ text{\isachardoublequote}} turns the given ML
- expression \isa{{\isachardoublequote}text{\isachardoublequote}} of type \verb|'a -> cterm| into an
+ \item \hyperlink{command.oracle}{\mbox{\isa{\isacommand{oracle}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}name\ {\isaliteral{3D}{\isacharequal}}\ text{\isaliteral{22}{\isachardoublequote}}} turns the given ML
+ expression \isa{{\isaliteral{22}{\isachardoublequote}}text{\isaliteral{22}{\isachardoublequote}}} of type \verb|'a -> cterm| into an
ML function of type \verb|'a -> thm|, which is bound to the
global identifier \verb|name|. This acts like an infinitary
specification of axioms! Invoking the oracle only works within the
@@ -1199,7 +1199,7 @@
\end{description}
- See \hyperlink{file.~~/src/HOL/ex/Iff-Oracle.thy}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}HOL{\isacharslash}ex{\isacharslash}Iff{\isacharunderscore}Oracle{\isachardot}thy}}}} for a worked example of
+ See \hyperlink{file.~~/src/HOL/ex/Iff-Oracle.thy}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}HOL{\isaliteral{2F}{\isacharslash}}ex{\isaliteral{2F}{\isacharslash}}Iff{\isaliteral{5F}{\isacharunderscore}}Oracle{\isaliteral{2E}{\isachardot}}thy}}}} for a worked example of
defining a new primitive rule as oracle, and turning it into a proof
method.%
\end{isamarkuptext}%
@@ -1211,10 +1211,10 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{}{command}{hide\_class}\hypertarget{command.hide-class}{\hyperlink{command.hide-class}{\mbox{\isa{\isacommand{hide{\isacharunderscore}class}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{hide\_type}\hypertarget{command.hide-type}{\hyperlink{command.hide-type}{\mbox{\isa{\isacommand{hide{\isacharunderscore}type}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{hide\_const}\hypertarget{command.hide-const}{\hyperlink{command.hide-const}{\mbox{\isa{\isacommand{hide{\isacharunderscore}const}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{}{command}{hide\_fact}\hypertarget{command.hide-fact}{\hyperlink{command.hide-fact}{\mbox{\isa{\isacommand{hide{\isacharunderscore}fact}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
+ \indexdef{}{command}{hide\_class}\hypertarget{command.hide-class}{\hyperlink{command.hide-class}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}class}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{hide\_type}\hypertarget{command.hide-type}{\hyperlink{command.hide-type}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}type}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{hide\_const}\hypertarget{command.hide-const}{\hyperlink{command.hide-const}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}const}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{}{command}{hide\_fact}\hypertarget{command.hide-fact}{\hyperlink{command.hide-fact}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}fact}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -1230,16 +1230,16 @@
\begin{description}
- \item \hyperlink{command.hide-class}{\mbox{\isa{\isacommand{hide{\isacharunderscore}class}}}}~\isa{names} fully removes class
- declarations from a given name space; with the \isa{{\isachardoublequote}{\isacharparenleft}open{\isacharparenright}{\isachardoublequote}}
+ \item \hyperlink{command.hide-class}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}class}}}}~\isa{names} fully removes class
+ declarations from a given name space; with the \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}open{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}
option, only the base name is hidden.
Note that hiding name space accesses has no impact on logical
declarations --- they remain valid internally. Entities that are no
longer accessible to the user are printed with the special qualifier
- ``\isa{{\isachardoublequote}{\isacharquery}{\isacharquery}{\isachardoublequote}}'' prefixed to the full internal name.
+ ``\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}}'' prefixed to the full internal name.
- \item \hyperlink{command.hide-type}{\mbox{\isa{\isacommand{hide{\isacharunderscore}type}}}}, \hyperlink{command.hide-const}{\mbox{\isa{\isacommand{hide{\isacharunderscore}const}}}}, and \hyperlink{command.hide-fact}{\mbox{\isa{\isacommand{hide{\isacharunderscore}fact}}}} are similar to \hyperlink{command.hide-class}{\mbox{\isa{\isacommand{hide{\isacharunderscore}class}}}}, but hide types,
+ \item \hyperlink{command.hide-type}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}type}}}}, \hyperlink{command.hide-const}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}const}}}}, and \hyperlink{command.hide-fact}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}fact}}}} are similar to \hyperlink{command.hide-class}{\mbox{\isa{\isacommand{hide{\isaliteral{5F}{\isacharunderscore}}class}}}}, but hide types,
constants, and facts, respectively.
\end{description}%
--- a/doc-src/IsarRef/Thy/document/Symbols.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarRef/Thy/document/Symbols.tex Mon Nov 08 14:41:11 2010 +0100
@@ -33,13 +33,13 @@
package.
Moreover, any single symbol (or ASCII character) may be prefixed by
- \verb|\|\verb|<^sup>|, for superscript and \verb|\|\verb|<^sub>|, for subscript, such as \verb|A\|\verb|<^sup>\<star>|, for \isa{{\isachardoublequote}A\isactrlsup {\isasymstar}{\isachardoublequote}} the alternative
+ \verb|\|\verb|<^sup>|, for superscript and \verb|\|\verb|<^sub>|, for subscript, such as \verb|A\|\verb|<^sup>\<star>|, for \isa{{\isaliteral{22}{\isachardoublequote}}A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{5C3C737461723E}{\isasymstar}}{\isaliteral{22}{\isachardoublequote}}} the alternative
versions \verb|\|\verb|<^isub>| and \verb|\|\verb|<^isup>| are considered as quasi letters and may
be used within identifiers. Sub- and superscripts that span a
- region of text are marked up with \verb|\|\verb|<^bsub>|\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}\verb|\|\verb|<^esub>|, and
- \verb|\|\verb|<^bsup>|\isa{{\isachardoublequote}{\isasymdots}{\isachardoublequote}}\verb|\|\verb|<^esup>| respectively. Furthermore, all ASCII
+ region of text are marked up with \verb|\|\verb|<^bsub>|\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}\verb|\|\verb|<^esub>|, and
+ \verb|\|\verb|<^bsup>|\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}\verb|\|\verb|<^esup>| respectively. Furthermore, all ASCII
characters and most other symbols may be printed in bold by
- prefixing \verb|\|\verb|<^bold>| such as \verb|\|\verb|<^bold>\|\verb|<alpha>| for \isa{{\isachardoublequote}\isactrlbold {\isasymalpha}{\isachardoublequote}}. Note that \verb|\|\verb|<^bold>|, may
+ prefixing \verb|\|\verb|<^bold>| such as \verb|\|\verb|<^bold>\|\verb|<alpha>| for \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E626F6C643E}{}\isactrlbold {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{22}{\isachardoublequote}}}. Note that \verb|\|\verb|<^bold>|, may
\emph{not} be combined with sub- or superscripts for single symbols.
Further details of Isabelle document preparation are covered in
--- a/doc-src/IsarRef/Thy/document/ZF_Specific.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/IsarRef/Thy/document/ZF_Specific.tex Mon Nov 08 14:41:11 2010 +0100
@@ -1,6 +1,6 @@
%
\begin{isabellebody}%
-\def\isabellecontext{ZF{\isacharunderscore}Specific}%
+\def\isabellecontext{ZF{\isaliteral{5F}{\isacharunderscore}}Specific}%
%
\isadelimtheory
%
@@ -8,7 +8,7 @@
%
\isatagtheory
\isacommand{theory}\isamarkupfalse%
-\ ZF{\isacharunderscore}Specific\isanewline
+\ ZF{\isaliteral{5F}{\isacharunderscore}}Specific\isanewline
\isakeyword{imports}\ Main\isanewline
\isakeyword{begin}%
\endisatagtheory
@@ -34,7 +34,7 @@
Simplifier setup.
\begin{matharray}{rcl}
- \indexdef{ZF}{command}{print\_tcset}\hypertarget{command.ZF.print-tcset}{\hyperlink{command.ZF.print-tcset}{\mbox{\isa{\isacommand{print{\isacharunderscore}tcset}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{ZF}{command}{print\_tcset}\hypertarget{command.ZF.print-tcset}{\hyperlink{command.ZF.print-tcset}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}tcset}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}context\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}{\isaliteral{22}{\isachardoublequote}}} \\
\indexdef{ZF}{method}{typecheck}\hypertarget{method.ZF.typecheck}{\hyperlink{method.ZF.typecheck}{\mbox{\isa{typecheck}}}} & : & \isa{method} \\
\indexdef{ZF}{attribute}{TC}\hypertarget{attribute.ZF.TC}{\hyperlink{attribute.ZF.TC}{\mbox{\isa{TC}}}} & : & \isa{attribute} \\
\end{matharray}
@@ -46,7 +46,7 @@
\begin{description}
- \item \hyperlink{command.ZF.print-tcset}{\mbox{\isa{\isacommand{print{\isacharunderscore}tcset}}}} prints the collection of
+ \item \hyperlink{command.ZF.print-tcset}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}tcset}}}} prints the collection of
typechecking rules of the current context.
\item \hyperlink{method.ZF.typecheck}{\mbox{\isa{typecheck}}} attempts to solve any pending
@@ -73,10 +73,10 @@
Coinductive definitions are available in both cases, too.
\begin{matharray}{rcl}
- \indexdef{ZF}{command}{inductive}\hypertarget{command.ZF.inductive}{\hyperlink{command.ZF.inductive}{\mbox{\isa{\isacommand{inductive}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{ZF}{command}{coinductive}\hypertarget{command.ZF.coinductive}{\hyperlink{command.ZF.coinductive}{\mbox{\isa{\isacommand{coinductive}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{ZF}{command}{datatype}\hypertarget{command.ZF.datatype}{\hyperlink{command.ZF.datatype}{\mbox{\isa{\isacommand{datatype}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
- \indexdef{ZF}{command}{codatatype}\hypertarget{command.ZF.codatatype}{\hyperlink{command.ZF.codatatype}{\mbox{\isa{\isacommand{codatatype}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
+ \indexdef{ZF}{command}{inductive}\hypertarget{command.ZF.inductive}{\hyperlink{command.ZF.inductive}{\mbox{\isa{\isacommand{inductive}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{ZF}{command}{coinductive}\hypertarget{command.ZF.coinductive}{\hyperlink{command.ZF.coinductive}{\mbox{\isa{\isacommand{coinductive}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{ZF}{command}{datatype}\hypertarget{command.ZF.datatype}{\hyperlink{command.ZF.datatype}{\mbox{\isa{\isacommand{datatype}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
+ \indexdef{ZF}{command}{codatatype}\hypertarget{command.ZF.codatatype}{\hyperlink{command.ZF.codatatype}{\mbox{\isa{\isacommand{codatatype}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -99,7 +99,7 @@
;
\end{rail}
- In the following syntax specification \isa{{\isachardoublequote}monos{\isachardoublequote}}, \isa{typeintros}, and \isa{typeelims} are the same as above.
+ In the following syntax specification \isa{{\isaliteral{22}{\isachardoublequote}}monos{\isaliteral{22}{\isachardoublequote}}}, \isa{typeintros}, and \isa{typeelims} are the same as above.
\begin{rail}
('datatype' | 'codatatype') domain? (dtspec + 'and') hints
@@ -127,7 +127,7 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{ZF}{command}{primrec}\hypertarget{command.ZF.primrec}{\hyperlink{command.ZF.primrec}{\mbox{\isa{\isacommand{primrec}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
+ \indexdef{ZF}{command}{primrec}\hypertarget{command.ZF.primrec}{\hyperlink{command.ZF.primrec}{\mbox{\isa{\isacommand{primrec}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
@@ -146,10 +146,10 @@
ported to Isar. These should not be used in proper proof texts.
\begin{matharray}{rcl}
- \indexdef{ZF}{method}{case\_tac}\hypertarget{method.ZF.case-tac}{\hyperlink{method.ZF.case-tac}{\mbox{\isa{case{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{ZF}{method}{induct\_tac}\hypertarget{method.ZF.induct-tac}{\hyperlink{method.ZF.induct-tac}{\mbox{\isa{induct{\isacharunderscore}tac}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{ZF}{method}{ind\_cases}\hypertarget{method.ZF.ind-cases}{\hyperlink{method.ZF.ind-cases}{\mbox{\isa{ind{\isacharunderscore}cases}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{method} \\
- \indexdef{ZF}{command}{inductive\_cases}\hypertarget{command.ZF.inductive-cases}{\hyperlink{command.ZF.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isacharunderscore}cases}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
+ \indexdef{ZF}{method}{case\_tac}\hypertarget{method.ZF.case-tac}{\hyperlink{method.ZF.case-tac}{\mbox{\isa{case{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{ZF}{method}{induct\_tac}\hypertarget{method.ZF.induct-tac}{\hyperlink{method.ZF.induct-tac}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}tac}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{ZF}{method}{ind\_cases}\hypertarget{method.ZF.ind-cases}{\hyperlink{method.ZF.ind-cases}{\mbox{\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}} & : & \isa{method} \\
+ \indexdef{ZF}{command}{inductive\_cases}\hypertarget{command.ZF.inductive-cases}{\hyperlink{command.ZF.inductive-cases}{\mbox{\isa{\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}cases}}}}} & : & \isa{{\isaliteral{22}{\isachardoublequote}}theory\ {\isaliteral{5C3C72696768746172726F773E}{\isasymrightarrow}}\ theory{\isaliteral{22}{\isachardoublequote}}} \\
\end{matharray}
\begin{rail}
--- a/doc-src/LaTeXsugar/Sugar/document/Sugar.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/LaTeXsugar/Sugar/document/Sugar.tex Mon Nov 08 14:41:11 2010 +0100
@@ -26,7 +26,7 @@
bliss of writing \verb!@!\verb!{thm[display]setsum_cartesian_product[no_vars]}!
and seeing Isabelle typeset it for them:
\begin{isabelle}%
-{\isacharparenleft}{\isasymSum}x{\isasymin}A{\isachardot}\ {\isasymSum}y{\isasymin}B{\isachardot}\ f\ x\ y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isasymSum}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isasymin}A\ {\isasymtimes}\ B{\isachardot}\ f\ x\ y{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C53756D3E}{\isasymSum}}x{\isaliteral{5C3C696E3E}{\isasymin}}A{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C53756D3E}{\isasymSum}}y{\isaliteral{5C3C696E3E}{\isasymin}}B{\isaliteral{2E}{\isachardot}}\ f\ x\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C53756D3E}{\isasymSum}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C696E3E}{\isasymin}}A\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ B{\isaliteral{2E}{\isachardot}}\ f\ x\ y{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
No typos, no omissions, no sweat.
If you have not experienced that joy, read Chapter 4, \emph{Presenting
@@ -39,8 +39,8 @@
awe at the beauty unfolding in front of their eyes. Until one day you
come across that very critical of readers known as the ``common referee''.
He has the nasty habit of refusing to understand unfamiliar notation
-like Isabelle's infamous \isa{{\isasymlbrakk}\ {\isasymrbrakk}\ {\isasymLongrightarrow}} no matter how many times you
-explain it in your paper. Even worse, he thinks that using \isa{{\isasymlbrakk}\ {\isasymrbrakk}} for anything other than denotational semantics is a cardinal sin
+like Isabelle's infamous \isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}} no matter how many times you
+explain it in your paper. Even worse, he thinks that using \isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}} for anything other than denotational semantics is a cardinal sin
that must be punished by instant rejection.
@@ -57,8 +57,8 @@
you so), you include them at the beginning of your \LaTeX\ document,
typically in \texttt{root.tex}. For a start, you should
\verb!\usepackage{amssymb}! --- otherwise typesetting
-\isa{{\isachardoublequote}{\isasymnot}{\isacharparenleft}{\isasymexists}x{\isachardot}\ P\ x{\isacharparenright}{\isachardoublequote}} will fail because the AMS symbol
-\isa{{\isasymnexists}} is missing.
+\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} will fail because the AMS symbol
+\isa{{\isaliteral{5C3C6E6578697374733E}{\isasymnexists}}} is missing.
\end{itemize}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -72,16 +72,16 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-The formula \isa{{\isachardoublequote}{\isasymnot}{\isacharparenleft}{\isasymexists}x{\isachardot}\ P\ x{\isacharparenright}{\isachardoublequote}} is typeset as \isa{{\isasymnexists}x{\isachardot}\ P\ x}.
+The formula \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} is typeset as \isa{{\isaliteral{5C3C6E6578697374733E}{\isasymnexists}}x{\isaliteral{2E}{\isachardot}}\ P\ x}.
The predefined constructs \isa{if}, \isa{let} and
\isa{case} are set in sans serif font to distinguish them from
other functions. This improves readability:
\begin{itemize}
-\item \isa{\textsf{if}\ b\ \textsf{then}\ e\isactrlisub {\isadigit{1}}\ \textsf{else}\ e\isactrlisub {\isadigit{2}}} instead of \isa{if\ b\ then\ e\isactrlisub {\isadigit{1}}\ else\ e\isactrlisub {\isadigit{2}}}.
-\item \isa{\textsf{let}\ x\ {\isacharequal}\ e\isactrlisub {\isadigit{1}}\ \textsf{in}\ e\isactrlisub {\isadigit{2}}} instead of \isa{let\ x\ {\isacharequal}\ e\isactrlisub {\isadigit{1}}\ in\ e\isactrlisub {\isadigit{2}}}.
-\item \isa{\textsf{case}\ x\ \textsf{of}\ True\ {\isasymRightarrow}\ e\isactrlisub {\isadigit{1}}\ {\isacharbar}\ False\ {\isasymRightarrow}\ e\isactrlisub {\isadigit{2}}} instead of\\
- \isa{case\ x\ of\ True\ {\isasymRightarrow}\ e\isactrlisub {\isadigit{1}}\ {\isacharbar}\ False\ {\isasymRightarrow}\ e\isactrlisub {\isadigit{2}}}.
+\item \isa{\textsf{if}\ b\ \textsf{then}\ e\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ \textsf{else}\ e\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}} instead of \isa{if\ b\ then\ e\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ else\ e\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}.
+\item \isa{\textsf{let}\ x\ {\isaliteral{3D}{\isacharequal}}\ e\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ \textsf{in}\ e\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}} instead of \isa{let\ x\ {\isaliteral{3D}{\isacharequal}}\ e\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ in\ e\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}.
+\item \isa{\textsf{case}\ x\ \textsf{of}\ True\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ e\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{7C}{\isacharbar}}\ False\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ e\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}} instead of\\
+ \isa{case\ x\ of\ True\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ e\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{7C}{\isacharbar}}\ False\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ e\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}}.
\end{itemize}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -94,10 +94,10 @@
Although set syntax in HOL is already close to
standard, we provide a few further improvements:
\begin{itemize}
-\item \isa{{\isacharbraceleft}x\ {\isacharbar}\ P{\isacharbraceright}} instead of \isa{{\isacharbraceleft}x{\isachardot}\ P{\isacharbraceright}}.
-\item \isa{{\isasymemptyset}} instead of \isa{{\isacharbraceleft}{\isacharbraceright}}, where
- \isa{{\isasymemptyset}} is also input syntax.
-\item \isa{{\isacharbraceleft}a{\isacharcomma}\ b{\isacharcomma}\ c{\isacharbraceright}\ {\isasymunion}\ M} instead of \isa{insert\ a\ {\isacharparenleft}insert\ b\ {\isacharparenleft}insert\ c\ M{\isacharparenright}{\isacharparenright}}.
+\item \isa{{\isaliteral{7B}{\isacharbraceleft}}x\ {\isaliteral{7C}{\isacharbar}}\ P{\isaliteral{7D}{\isacharbraceright}}} instead of \isa{{\isaliteral{7B}{\isacharbraceleft}}x{\isaliteral{2E}{\isachardot}}\ P{\isaliteral{7D}{\isacharbraceright}}}.
+\item \isa{{\isaliteral{5C3C656D7074797365743E}{\isasymemptyset}}} instead of \isa{{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{7D}{\isacharbraceright}}}, where
+ \isa{{\isaliteral{5C3C656D7074797365743E}{\isasymemptyset}}} is also input syntax.
+\item \isa{{\isaliteral{7B}{\isacharbraceleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{2C}{\isacharcomma}}\ c{\isaliteral{7D}{\isacharbraceright}}\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ M} instead of \isa{insert\ a\ {\isaliteral{28}{\isacharparenleft}}insert\ b\ {\isaliteral{28}{\isacharparenleft}}insert\ c\ M{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}}.
\end{itemize}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -109,28 +109,28 @@
\begin{isamarkuptext}%
If lists are used heavily, the following notations increase readability:
\begin{itemize}
-\item \isa{x{\isasymcdot}xs} instead of \isa{x\ {\isacharhash}\ xs},
- where \isa{x{\isasymcdot}xs} is also input syntax.
+\item \isa{x{\isaliteral{5C3C63646F743E}{\isasymcdot}}xs} instead of \isa{x\ {\isaliteral{23}{\isacharhash}}\ xs},
+ where \isa{x{\isaliteral{5C3C63646F743E}{\isasymcdot}}xs} is also input syntax.
If you prefer more space around the $\cdot$ you have to redefine
\verb!\isasymcdot! in \LaTeX:
\verb!\renewcommand{\isasymcdot}{\isamath{\,\cdot\,}}!
-\item \isa{{\isacharbar}xs{\isacharbar}} instead of \isa{length\ xs}.
+\item \isa{{\isaliteral{7C}{\isacharbar}}xs{\isaliteral{7C}{\isacharbar}}} instead of \isa{length\ xs}.
\item \isa{xs\ensuremath{_{[\mathit{n}]}}} instead of \isa{nth\ xs\ n},
the $n$th element of \isa{xs}.
\item Human readers are good at converting automatically from lists to
sets. Hence \texttt{OptionalSugar} contains syntax for suppressing the
-conversion function \isa{set}: for example, \isa{{\isachardoublequote}x\ {\isasymin}\ set\ xs{\isachardoublequote}}
-becomes \isa{x\ {\isasymin}\ xs}.
+conversion function \isa{set}: for example, \isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ set\ xs{\isaliteral{22}{\isachardoublequote}}}
+becomes \isa{x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ xs}.
-\item The \isa{{\isacharat}} operation associates implicitly to the right,
+\item The \isa{{\isaliteral{40}{\isacharat}}} operation associates implicitly to the right,
which leads to unpleasant line breaks if the term is too long for one
line. To avoid this, \texttt{OptionalSugar} contains syntax to group
-\isa{{\isacharat}}-terms to the left before printing, which leads to better
+\isa{{\isaliteral{40}{\isacharat}}}-terms to the left before printing, which leads to better
line breaking behaviour:
\begin{isabelle}%
-term\isactrlisub {\isadigit{0}}\ \isacharat\ term\isactrlisub {\isadigit{1}}\ \isacharat\ term\isactrlisub {\isadigit{2}}\ \isacharat\ term\isactrlisub {\isadigit{3}}\ \isacharat\ term\isactrlisub {\isadigit{4}}\ \isacharat\ term\isactrlisub {\isadigit{5}}\ \isacharat\ term\isactrlisub {\isadigit{6}}\ \isacharat\ term\isactrlisub {\isadigit{7}}\ \isacharat\ term\isactrlisub {\isadigit{8}}\ \isacharat\ term\isactrlisub {\isadigit{9}}\ \isacharat\ term\isactrlisub {\isadigit{1}}\isactrlisub {\isadigit{0}}%
+term\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{0}}\ \isacharat\ term\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ \isacharat\ term\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}\ \isacharat\ term\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{3}}\ \isacharat\ term\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{4}}\ \isacharat\ term\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{5}}\ \isacharat\ term\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{6}}\ \isacharat\ term\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{7}}\ \isacharat\ term\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{8}}\ \isacharat\ term\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{9}}\ \isacharat\ term\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{0}}%
\end{isabelle}
\end{itemize}%
@@ -145,10 +145,10 @@
Coercions between numeric types are alien to mathematicians who
consider, for example, \isa{nat} as a subset of \isa{int}.
\texttt{OptionalSugar} contains syntax for suppressing numeric coercions such
-as \isa{int} \isa{{\isacharcolon}{\isacharcolon}} \isa{nat\ {\isasymRightarrow}\ int}. For example,
-\isa{{\isachardoublequote}int\ {\isadigit{5}}{\isachardoublequote}} is printed as \isa{{\isadigit{5}}}. Embeddings of types
+as \isa{int} \isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}} \isa{nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int}. For example,
+\isa{{\isaliteral{22}{\isachardoublequote}}int\ {\isadigit{5}}{\isaliteral{22}{\isachardoublequote}}} is printed as \isa{{\isadigit{5}}}. Embeddings of types
\isa{nat}, \isa{int}, \isa{real} are covered; non-injective coercions such
-as \isa{nat} \isa{{\isacharcolon}{\isacharcolon}} \isa{int\ {\isasymRightarrow}\ nat} are not and should not be
+as \isa{nat} \isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}} \isa{int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat} are not and should not be
hidden.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -164,11 +164,11 @@
\begin{isamarkuptext}%
If you print anything, especially theorems, containing
schematic variables they are prefixed with a question mark:
-\verb!@!\verb!{thm conjI}! results in \isa{{\isasymlbrakk}{\isacharquery}P{\isacharsemicolon}\ {\isacharquery}Q{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}P\ {\isasymand}\ {\isacharquery}Q}. Most of the time
+\verb!@!\verb!{thm conjI}! results in \isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{3F}{\isacharquery}}P{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{3F}{\isacharquery}}Q{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{3F}{\isacharquery}}Q}. Most of the time
you would rather not see the question marks. There is an attribute
\verb!no_vars! that you can attach to the theorem that turns its
schematic into ordinary free variables: \verb!@!\verb!{thm conjI[no_vars]}!
-results in \isa{{\isasymlbrakk}P{\isacharsemicolon}\ Q{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isasymand}\ Q}.
+results in \isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}P{\isaliteral{3B}{\isacharsemicolon}}\ Q{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q}.
This \verb!no_vars! business can become a bit tedious.
If you would rather never see question marks, simply put
@@ -180,10 +180,10 @@
Hint: Setting \verb!show_question_marks_default! to \texttt{false} only
suppresses question marks; variables that end in digits,
-e.g. \isa{x{\isadigit{1}}}, are still printed with a trailing \isa{{\isachardot}{\isadigit{0}}},
-e.g. \isa{x{\isadigit{1}}{\isachardot}{\isadigit{0}}}, their internal index. This can be avoided by
+e.g. \isa{x{\isadigit{1}}}, are still printed with a trailing \isa{{\isaliteral{2E}{\isachardot}}{\isadigit{0}}},
+e.g. \isa{x{\isadigit{1}}{\isaliteral{2E}{\isachardot}}{\isadigit{0}}}, their internal index. This can be avoided by
turning the last digit into a subscript: write \verb!x\<^isub>1! and
-obtain the much nicer \isa{x\isactrlisub {\isadigit{1}}}.%
+obtain the much nicer \isa{x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -193,8 +193,8 @@
%
\begin{isamarkuptext}%
If there are multiple declarations of the same name, Isabelle prints
-the qualified name, for example \isa{T{\isachardot}length}, where \isa{T} is the
-theory it is defined in, to distinguish it from the predefined \isa{{\isachardoublequote}List{\isachardot}length{\isachardoublequote}}. In case there is no danger of confusion, you can insist on
+the qualified name, for example \isa{T{\isaliteral{2E}{\isachardot}}length}, where \isa{T} is the
+theory it is defined in, to distinguish it from the predefined \isa{{\isaliteral{22}{\isachardoublequote}}List{\isaliteral{2E}{\isachardot}}length{\isaliteral{22}{\isachardoublequote}}}. In case there is no danger of confusion, you can insist on
short names (no qualifiers) by setting \verb!short_names!, typically
in \texttt{ROOT.ML}:
\begin{quote}
@@ -211,13 +211,13 @@
It sometimes happens that you want to change the name of a
variable in a theorem before printing it. This can easily be achieved
with the help of Isabelle's instantiation attribute \texttt{where}:
-\isa{{\isasymlbrakk}{\isasymphi}{\isacharsemicolon}\ {\isasympsi}{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isasymphi}\ {\isasymand}\ {\isasympsi}} is the result of
+\isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C7068693E}{\isasymphi}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C7073693E}{\isasympsi}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{5C3C7073693E}{\isasympsi}}} is the result of
\begin{quote}
\verb!@!\verb!{thm conjI[where P = \<phi> and Q = \<psi>]}!
\end{quote}
To support the ``\_''-notation for irrelevant variables
the constant \texttt{DUMMY} has been introduced:
-\isa{fst\ {\isacharparenleft}a{\isacharcomma}\ \_{\isacharparenright}\ {\isacharequal}\ a} is produced by
+\isa{fst\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ \_{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ a} is produced by
\begin{quote}
\verb!@!\verb!{thm fst_conv[where b = DUMMY]}!
\end{quote}
@@ -228,7 +228,7 @@
\begin{quote}
\verb!@!\verb!{thm split_paired_All[rename_abs _ l r]}!
\end{quote}
-produces \isa{{\isacharparenleft}{\isasymforall}x{\isachardot}\ P\ x{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isasymforall}l\ r{\isachardot}\ P\ {\isacharparenleft}l{\isacharcomma}\ r{\isacharparenright}{\isacharparenright}}.%
+produces \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}l\ r{\isaliteral{2E}{\isachardot}}\ P\ {\isaliteral{28}{\isacharparenleft}}l{\isaliteral{2C}{\isacharcomma}}\ r{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -242,10 +242,10 @@
for typesetting inference rules in your \LaTeX\ file.
Writing \verb!@!\verb!{thm[mode=Rule] conjI}! produces
-\isa{\mbox{}\inferrule{\mbox{P}\\\ \mbox{Q}}{\mbox{P\ {\isasymand}\ Q}}}, even in the middle of a sentence.
+\isa{\mbox{}\inferrule{\mbox{P}\\\ \mbox{Q}}{\mbox{P\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q}}}, even in the middle of a sentence.
If you prefer your inference rule on a separate line, maybe with a name,
\begin{center}
-\isa{\mbox{}\inferrule{\mbox{P}\\\ \mbox{Q}}{\mbox{P\ {\isasymand}\ Q}}} {\sc conjI}
+\isa{\mbox{}\inferrule{\mbox{P}\\\ \mbox{Q}}{\mbox{P\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q}}} {\sc conjI}
\end{center}
is produced by
\begin{quote}
@@ -268,19 +268,19 @@
\end{quote}
yields
\begin{center}\small
-\isa{\mbox{}\inferrule{\mbox{P}\\\ \mbox{Q}}{\mbox{P\ {\isasymand}\ Q}}} {\sc conjI} \\[1ex]
-\isa{\mbox{}\inferrule{\mbox{P}}{\mbox{P\ {\isasymor}\ Q}}} {\sc disjI$_1$} \qquad
-\isa{\mbox{}\inferrule{\mbox{Q}}{\mbox{P\ {\isasymor}\ Q}}} {\sc disjI$_2$}
+\isa{\mbox{}\inferrule{\mbox{P}\\\ \mbox{Q}}{\mbox{P\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q}}} {\sc conjI} \\[1ex]
+\isa{\mbox{}\inferrule{\mbox{P}}{\mbox{P\ {\isaliteral{5C3C6F723E}{\isasymor}}\ Q}}} {\sc disjI$_1$} \qquad
+\isa{\mbox{}\inferrule{\mbox{Q}}{\mbox{P\ {\isaliteral{5C3C6F723E}{\isasymor}}\ Q}}} {\sc disjI$_2$}
\end{center}
The \texttt{mathpartir} package copes well if there are too many
premises for one line:
\begin{center}
-\isa{\mbox{}\inferrule{\mbox{A\ {\isasymlongrightarrow}\ B}\\\ \mbox{B\ {\isasymlongrightarrow}\ C}\\\ \mbox{C\ {\isasymlongrightarrow}\ D}\\\ \mbox{D\ {\isasymlongrightarrow}\ E}\\\ \mbox{E\ {\isasymlongrightarrow}\ F}\\\ \mbox{F\ {\isasymlongrightarrow}\ G}\\\ \mbox{G\ {\isasymlongrightarrow}\ H}\\\ \mbox{H\ {\isasymlongrightarrow}\ I}\\\ \mbox{I\ {\isasymlongrightarrow}\ J}\\\ \mbox{J\ {\isasymlongrightarrow}\ K}}{\mbox{A\ {\isasymlongrightarrow}\ K}}}
+\isa{\mbox{}\inferrule{\mbox{A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ B}\\\ \mbox{B\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ C}\\\ \mbox{C\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ D}\\\ \mbox{D\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ E}\\\ \mbox{E\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ F}\\\ \mbox{F\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ G}\\\ \mbox{G\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ H}\\\ \mbox{H\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ I}\\\ \mbox{I\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ J}\\\ \mbox{J\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ K}}{\mbox{A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ K}}}
\end{center}
Limitations: 1. Premises and conclusion must each not be longer than
-the line. 2. Premises that are \isa{{\isasymLongrightarrow}}-implications are again
+the line. 2. Premises that are \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}}-implications are again
displayed with a horizontal line, which looks at least unusual.
@@ -293,7 +293,7 @@
\end{quote}
yields
\begin{center}
-\isa{\mbox{}\inferrule{\mbox{}}{\mbox{t\ {\isacharequal}\ t}}} {\sc refl}
+\isa{\mbox{}\inferrule{\mbox{}}{\mbox{t\ {\isaliteral{3D}{\isacharequal}}\ t}}} {\sc refl}
\end{center}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -305,14 +305,14 @@
\begin{isamarkuptext}%
When displaying theorems with the \texttt{display} option, e.g.
\verb!@!\verb!{thm[display] refl}! \begin{isabelle}%
-t\ {\isacharequal}\ t%
+t\ {\isaliteral{3D}{\isacharequal}}\ t%
\end{isabelle} the theorem is
set in small font. It uses the \LaTeX-macro \verb!\isastyle!,
which is also the style that regular theory text is set in, e.g.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}t\ {\isacharequal}\ t{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}t\ {\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -342,8 +342,8 @@
list of theorems in one go. For example,
\verb!@!\verb!{thm[display] foldl.simps}!
generates \begin{isabelle}%
-foldl\ f\ a\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ a\isasep\isanewline%
-foldl\ f\ a\ {\isacharparenleft}x{\isasymcdot}xs{\isacharparenright}\ {\isacharequal}\ foldl\ f\ {\isacharparenleft}f\ a\ x{\isacharparenright}\ xs%
+foldl\ f\ a\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ a\isasep\isanewline%
+foldl\ f\ a\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{5C3C63646F743E}{\isasymcdot}}xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ foldl\ f\ {\isaliteral{28}{\isacharparenleft}}f\ a\ x{\isaliteral{29}{\isacharparenright}}\ xs%
\end{isabelle}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -357,7 +357,7 @@
the body of
\newtheorem{theorem}{Theorem}
\begin{theorem}
-\isa{{\normalsize{}If\,}\ \mbox{i\ {\isasymle}\ j}\ {\normalsize \,and\,}\ \mbox{j\ {\isasymle}\ k}\ {\normalsize \,then\,}\ i\ {\isasymle}\ k{\isachardot}}
+\isa{{\normalsize{}If\,}\ \mbox{i\ {\isaliteral{5C3C6C653E}{\isasymle}}\ j}\ {\normalsize \,and\,}\ \mbox{j\ {\isaliteral{5C3C6C653E}{\isasymle}}\ k}\ {\normalsize \,then\,}\ i\ {\isaliteral{5C3C6C653E}{\isasymle}}\ k{\isaliteral{2E}{\isachardot}}}
\end{theorem}
by typing
\begin{quote}
@@ -367,12 +367,12 @@
In order to prevent odd line breaks, the premises are put into boxes.
At times this is too drastic:
\begin{theorem}
-\isa{{\normalsize{}If\,}\ \mbox{longpremise}\ {\normalsize \,and\,}\ \mbox{longerpremise}\ {\normalsize \,and\,}\ \mbox{P\ {\isacharparenleft}f\ {\isacharparenleft}f\ {\isacharparenleft}f\ {\isacharparenleft}f\ {\isacharparenleft}f\ {\isacharparenleft}f\ {\isacharparenleft}f\ {\isacharparenleft}f\ {\isacharparenleft}f\ x{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}}\ {\normalsize \,and\,}\ \mbox{longestpremise}\ {\normalsize \,then\,}\ conclusion{\isachardot}}
+\isa{{\normalsize{}If\,}\ \mbox{longpremise}\ {\normalsize \,and\,}\ \mbox{longerpremise}\ {\normalsize \,and\,}\ \mbox{P\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}f\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}}\ {\normalsize \,and\,}\ \mbox{longestpremise}\ {\normalsize \,then\,}\ conclusion{\isaliteral{2E}{\isachardot}}}
\end{theorem}
In which case you should use \texttt{IfThenNoBox} instead of
\texttt{IfThen}:
\begin{theorem}
-\isa{{\normalsize{}If\,}\ longpremise\ {\normalsize \,and\,}\ longerpremise\ {\normalsize \,and\,}\ P\ {\isacharparenleft}f\ {\isacharparenleft}f\ {\isacharparenleft}f\ {\isacharparenleft}f\ {\isacharparenleft}f\ {\isacharparenleft}f\ {\isacharparenleft}f\ {\isacharparenleft}f\ {\isacharparenleft}f\ x{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\normalsize \,and\,}\ longestpremise\ {\normalsize \,then\,}\ conclusion{\isachardot}}
+\isa{{\normalsize{}If\,}\ longpremise\ {\normalsize \,and\,}\ longerpremise\ {\normalsize \,and\,}\ P\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}f\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\normalsize \,and\,}\ longestpremise\ {\normalsize \,then\,}\ conclusion{\isaliteral{2E}{\isachardot}}}
\end{theorem}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -392,7 +392,7 @@
prints the conclusion of $thm$.
\end{itemize}
For example, ``from \isa{Q} and
-\isa{P} we conclude \isa{P\ {\isasymand}\ Q}''
+\isa{P} we conclude \isa{P\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q}''
is produced by
\begin{quote}
\verb!from !\verb!@!\verb!{thm (prem 2) conjI}! \verb!and !\verb!@!\verb!{thm (prem 1) conjI}!\\
@@ -418,11 +418,11 @@
\begin{center}
\begin{tabular}{l@ {~~produced by~~}l}
- \isa{\textsf{let}\ {\isacharparenleft}x{\isacharcomma}\ \_{\isacharparenright}\ {\isacharequal}\ p\ \textsf{in}\ t} & \verb!@!\verb!{term "let x = fst p in t"}!\\
- \isa{\textsf{let}\ {\isacharparenleft}\_{\isacharcomma}\ x{\isacharparenright}\ {\isacharequal}\ p\ \textsf{in}\ t} & \verb!@!\verb!{term "let x = snd p in t"}!\\
- \isa{\textsf{let}\ x{\isasymcdot}\_\ {\isacharequal}\ xs\ \textsf{in}\ t} & \verb!@!\verb!{term "let x = hd xs in t"}!\\
- \isa{\textsf{let}\ \_{\isasymcdot}x\ {\isacharequal}\ xs\ \textsf{in}\ t} & \verb!@!\verb!{term "let x = tl xs in t"}!\\
- \isa{\textsf{let}\ Some\ x\ {\isacharequal}\ y\ \textsf{in}\ t} & \verb!@!\verb!{term "let x = the y in t"}!\\
+ \isa{\textsf{let}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ \_{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ p\ \textsf{in}\ t} & \verb!@!\verb!{term "let x = fst p in t"}!\\
+ \isa{\textsf{let}\ {\isaliteral{28}{\isacharparenleft}}\_{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ p\ \textsf{in}\ t} & \verb!@!\verb!{term "let x = snd p in t"}!\\
+ \isa{\textsf{let}\ x{\isaliteral{5C3C63646F743E}{\isasymcdot}}\_\ {\isaliteral{3D}{\isacharequal}}\ xs\ \textsf{in}\ t} & \verb!@!\verb!{term "let x = hd xs in t"}!\\
+ \isa{\textsf{let}\ \_{\isaliteral{5C3C63646F743E}{\isasymcdot}}x\ {\isaliteral{3D}{\isacharequal}}\ xs\ \textsf{in}\ t} & \verb!@!\verb!{term "let x = tl xs in t"}!\\
+ \isa{\textsf{let}\ Some\ x\ {\isaliteral{3D}{\isacharequal}}\ y\ \textsf{in}\ t} & \verb!@!\verb!{term "let x = the y in t"}!\\
\end{tabular}
\end{center}%
\end{isamarkuptext}%
@@ -453,7 +453,7 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ %
\isamarkupcmt{pretty trivial%
}
@@ -505,7 +505,7 @@
\begin{isamarkuptext}%
The \verb!thm! antiquotation works nicely for single theorems, but
sets of equations as used in definitions are more difficult to
- typeset nicely: people tend to prefer aligned \isa{{\isacharequal}} signs.
+ typeset nicely: people tend to prefer aligned \isa{{\isaliteral{3D}{\isacharequal}}} signs.
To deal with such cases where it is desirable to dive into the structure
of terms and theorems, Isabelle offers antiquotations featuring
@@ -524,9 +524,9 @@
For example,
the output
\begin{center}
- \begin{tabular}{l@ {~~\isa{{\isacharequal}}~~}l}
- \isa{foldl\ f\ a\ {\isacharbrackleft}{\isacharbrackright}} & \isa{a}\\
- \isa{foldl\ f\ a\ {\isacharparenleft}x{\isasymcdot}xs{\isacharparenright}} & \isa{foldl\ f\ {\isacharparenleft}f\ a\ x{\isacharparenright}\ xs}
+ \begin{tabular}{l@ {~~\isa{{\isaliteral{3D}{\isacharequal}}}~~}l}
+ \isa{foldl\ f\ a\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}} & \isa{a}\\
+ \isa{foldl\ f\ a\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{5C3C63646F743E}{\isasymcdot}}xs{\isaliteral{29}{\isacharparenright}}} & \isa{foldl\ f\ {\isaliteral{28}{\isacharparenleft}}f\ a\ x{\isaliteral{29}{\isacharparenright}}\ xs}
\end{tabular}
\end{center}
is produced by the following code:
@@ -543,16 +543,16 @@
as an antiquotation. The styles \verb!lhs! and \verb!rhs!
extract the left hand side (or right hand side respectively) from the
conclusion of propositions consisting of a binary operator
- (e.~g.~\isa{{\isacharequal}}, \isa{{\isasymequiv}}, \isa{{\isacharless}}).
+ (e.~g.~\isa{{\isaliteral{3D}{\isacharequal}}}, \isa{{\isaliteral{5C3C65717569763E}{\isasymequiv}}}, \isa{{\isaliteral{3C}{\isacharless}}}).
Likewise, \verb!concl! may be used as a style to show just the
conclusion of a proposition. For example, take \verb!hd_Cons_tl!:
\begin{center}
- \isa{xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymLongrightarrow}\ hd\ xs{\isasymcdot}tl\ xs\ {\isacharequal}\ xs}
+ \isa{xs\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ hd\ xs{\isaliteral{5C3C63646F743E}{\isasymcdot}}tl\ xs\ {\isaliteral{3D}{\isacharequal}}\ xs}
\end{center}
To print just the conclusion,
\begin{center}
- \isa{hd\ xs{\isasymcdot}tl\ xs\ {\isacharequal}\ xs}
+ \isa{hd\ xs{\isaliteral{5C3C63646F743E}{\isasymcdot}}tl\ xs\ {\isaliteral{3D}{\isacharequal}}\ xs}
\end{center}
type
\begin{quote}
--- a/doc-src/Locales/Locales/document/Examples.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/Locales/Locales/document/Examples.tex Mon Nov 08 14:41:11 2010 +0100
@@ -25,7 +25,7 @@
\endisadeliminvisible
%
\isataginvisible
-\isacommand{pretty{\isacharunderscore}setmargin}\isamarkupfalse%
+\isacommand{pretty{\isaliteral{5F}{\isacharunderscore}}setmargin}\isamarkupfalse%
\ {\isadigit{6}}{\isadigit{5}}%
\endisataginvisible
{\isafoldinvisible}%
@@ -42,13 +42,13 @@
Locales are based on contexts. A \emph{context} can be seen as a
formula schema
\[
- \isa{{\isasymAnd}x\isactrlsub {\isadigit{1}}{\isasymdots}x\isactrlsub n{\isachardot}\ {\isasymlbrakk}\ A\isactrlsub {\isadigit{1}}{\isacharsemicolon}\ {\isasymdots}\ {\isacharsemicolon}A\isactrlsub m\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isasymdots}}
+ \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{5C3C646F74733E}{\isasymdots}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ A\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3B}{\isacharsemicolon}}A\isaliteral{5C3C5E7375623E}{}\isactrlsub m\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}}
\]
- where the variables~\isa{x\isactrlsub {\isadigit{1}}}, \ldots,~\isa{x\isactrlsub n} are called
- \emph{parameters} and the premises $\isa{A\isactrlsub {\isadigit{1}}}, \ldots,~\isa{A\isactrlsub m}$ \emph{assumptions}. A formula~\isa{C}
+ where the variables~\isa{x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}}, \ldots,~\isa{x\isaliteral{5C3C5E7375623E}{}\isactrlsub n} are called
+ \emph{parameters} and the premises $\isa{A\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}}, \ldots,~\isa{A\isaliteral{5C3C5E7375623E}{}\isactrlsub m}$ \emph{assumptions}. A formula~\isa{C}
is a \emph{theorem} in the context if it is a conclusion
\[
- \isa{{\isasymAnd}x\isactrlsub {\isadigit{1}}{\isasymdots}x\isactrlsub n{\isachardot}\ {\isasymlbrakk}\ A\isactrlsub {\isadigit{1}}{\isacharsemicolon}\ {\isasymdots}\ {\isacharsemicolon}A\isactrlsub m\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ C}.
+ \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{5C3C646F74733E}{\isasymdots}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ A\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3B}{\isacharsemicolon}}A\isaliteral{5C3C5E7375623E}{}\isactrlsub m\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C}.
\]
Isabelle/Isar's notion of context goes beyond this logical view.
Its contexts record, in a consecutive order, proved
@@ -70,25 +70,25 @@
\emph{locale declaration} consists of a sequence of context elements
declaring parameters (keyword \isakeyword{fixes}) and assumptions
(keyword \isakeyword{assumes}). The following is the specification of
- partial orders, as locale \isa{partial{\isacharunderscore}order}.%
+ partial orders, as locale \isa{partial{\isaliteral{5F}{\isacharunderscore}}order}.%
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{locale}\isamarkupfalse%
-\ partial{\isacharunderscore}order\ {\isacharequal}\isanewline
-\ \ \ \ \isakeyword{fixes}\ le\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasymsqsubseteq}{\isachardoublequoteclose}\ {\isadigit{5}}{\isadigit{0}}{\isacharparenright}\isanewline
-\ \ \ \ \isakeyword{assumes}\ refl\ {\isacharbrackleft}intro{\isacharcomma}\ simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\isanewline
-\ \ \ \ \ \ \isakeyword{and}\ anti{\isacharunderscore}sym\ {\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymlbrakk}\ x\ {\isasymsqsubseteq}\ y{\isacharsemicolon}\ y\ {\isasymsqsubseteq}\ x\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ x\ {\isacharequal}\ y{\isachardoublequoteclose}\isanewline
-\ \ \ \ \ \ \isakeyword{and}\ trans\ {\isacharbrackleft}trans{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymlbrakk}\ x\ {\isasymsqsubseteq}\ y{\isacharsemicolon}\ y\ {\isasymsqsubseteq}\ z\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ x\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}%
+\ partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \isakeyword{fixes}\ le\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{5}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ \isakeyword{assumes}\ refl\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \ \ \isakeyword{and}\ anti{\isaliteral{5F}{\isacharunderscore}}sym\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{3B}{\isacharsemicolon}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \ \ \isakeyword{and}\ trans\ {\isaliteral{5B}{\isacharbrackleft}}trans{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{3B}{\isacharsemicolon}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
The parameter of this locale is~\isa{le},
- which is a binary predicate with infix syntax~\isa{{\isasymsqsubseteq}}. The
+ which is a binary predicate with infix syntax~\isa{{\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}}. The
parameter syntax is available in the subsequent
assumptions, which are the familiar partial order axioms.
Isabelle recognises unbound names as free variables. In locale
assumptions, these are implicitly universally quantified. That is,
- \isa{{\isasymlbrakk}x\ {\isasymsqsubseteq}\ y{\isacharsemicolon}\ y\ {\isasymsqsubseteq}\ z{\isasymrbrakk}\ {\isasymLongrightarrow}\ x\ {\isasymsqsubseteq}\ z} in fact means
- \isa{{\isasymAnd}x\ y\ z{\isachardot}\ {\isasymlbrakk}x\ {\isasymsqsubseteq}\ y{\isacharsemicolon}\ y\ {\isasymsqsubseteq}\ z{\isasymrbrakk}\ {\isasymLongrightarrow}\ x\ {\isasymsqsubseteq}\ z}.
+ \isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{3B}{\isacharsemicolon}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z} in fact means
+ \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y\ z{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{3B}{\isacharsemicolon}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z}.
Two commands are provided to inspect locales:
\isakeyword{print\_locales} lists the names of all locales of the
@@ -96,7 +96,7 @@
and assumptions of locale $n$; the variation \isakeyword{print\_locale!}~$n$
additionally outputs the conclusions that are stored in the locale.
We may inspect the new locale
- by issuing \isakeyword{print\_locale!} \isa{partial{\isacharunderscore}order}. The output
+ by issuing \isakeyword{print\_locale!} \isa{partial{\isaliteral{5F}{\isacharunderscore}}order}. The output
is the following list of context elements.
\begin{small}
\begin{alltt}
@@ -112,15 +112,15 @@
\end{small}
The keyword \isakeyword{notes} denotes a conclusion element. There
is one conclusion, which was added automatically. Instead, there is
- only one assumption, namely \isa{partial{\isacharunderscore}order\ op\ {\isasymsqsubseteq}}. The locale
- declaration has introduced the predicate \isa{partial{\isacharunderscore}order} to the theory. This predicate is the
+ only one assumption, namely \isa{partial{\isaliteral{5F}{\isacharunderscore}}order\ op\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}}. The locale
+ declaration has introduced the predicate \isa{partial{\isaliteral{5F}{\isacharunderscore}}order} to the theory. This predicate is the
\emph{locale predicate}. Its definition may be inspected by
- issuing \isakeyword{thm} \isa{partial{\isacharunderscore}order{\isacharunderscore}def}.
+ issuing \isakeyword{thm} \isa{partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{5F}{\isacharunderscore}}def}.
\begin{isabelle}%
-\ \ partial{\isacharunderscore}order\ {\isacharquery}le\ {\isasymequiv}\isanewline
-\isaindent{\ \ }{\isacharparenleft}{\isasymforall}x{\isachardot}\ {\isacharquery}le\ x\ x{\isacharparenright}\ {\isasymand}\isanewline
-\isaindent{\ \ }{\isacharparenleft}{\isasymforall}x\ y{\isachardot}\ {\isacharquery}le\ x\ y\ {\isasymlongrightarrow}\ {\isacharquery}le\ y\ x\ {\isasymlongrightarrow}\ x\ {\isacharequal}\ y{\isacharparenright}\ {\isasymand}\isanewline
-\isaindent{\ \ }{\isacharparenleft}{\isasymforall}x\ y\ z{\isachardot}\ {\isacharquery}le\ x\ y\ {\isasymlongrightarrow}\ {\isacharquery}le\ y\ z\ {\isasymlongrightarrow}\ {\isacharquery}le\ x\ z{\isacharparenright}%
+\ \ partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{3F}{\isacharquery}}le\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\isanewline
+\isaindent{\ \ }{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}le\ x\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\isanewline
+\isaindent{\ \ }{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x\ y{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}le\ x\ y\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}le\ y\ x\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\isanewline
+\isaindent{\ \ }{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x\ y\ z{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}le\ x\ y\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}le\ y\ z\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}le\ x\ z{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
In our example, this is a unary predicate over the parameter of the
locale. It is equivalent to the original assumptions, which have
@@ -132,9 +132,9 @@
Each conclusion has a \emph{foundational theorem} as counterpart
in the theory. Technically, this is simply the theorem composed
of context and conclusion. For the transitivity theorem, this is
- \isa{partial{\isacharunderscore}order{\isachardot}trans}:
+ \isa{partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}trans}:
\begin{isabelle}%
-\ \ {\isasymlbrakk}partial{\isacharunderscore}order\ {\isacharquery}le{\isacharsemicolon}\ {\isacharquery}le\ {\isacharquery}x\ {\isacharquery}y{\isacharsemicolon}\ {\isacharquery}le\ {\isacharquery}y\ {\isacharquery}z{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}le\ {\isacharquery}x\ {\isacharquery}z%
+\ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{3F}{\isacharquery}}le{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{3F}{\isacharquery}}le\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{3F}{\isacharquery}}y{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{3F}{\isacharquery}}le\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{3F}{\isacharquery}}z{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}le\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{3F}{\isacharquery}}z%
\end{isabelle}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -175,27 +175,27 @@
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{definition}\isamarkupfalse%
-\ {\isacharparenleft}\isakeyword{in}\ partial{\isacharunderscore}order{\isacharparenright}\isanewline
-\ \ \ \ less\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasymsqsubset}{\isachardoublequoteclose}\ {\isadigit{5}}{\isadigit{0}}{\isacharparenright}\isanewline
-\ \ \ \ \isakeyword{where}\ {\isachardoublequoteopen}{\isacharparenleft}x\ {\isasymsqsubset}\ y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}x\ {\isasymsqsubseteq}\ y\ {\isasymand}\ x\ {\isasymnoteq}\ y{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{in}\ partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ less\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C73717375627365743E}{\isasymsqsubset}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{5}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C73717375627365743E}{\isasymsqsubset}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C616E643E}{\isasymand}}\ x\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
The strict order \isa{less} with infix
- syntax~\isa{{\isasymsqsubset}} is
+ syntax~\isa{{\isaliteral{5C3C73717375627365743E}{\isasymsqsubset}}} is
defined in terms of the locale parameter~\isa{le} and the general
equality of the object logic we work in. The definition generates a
\emph{foundational constant}
- \isa{partial{\isacharunderscore}order{\isachardot}less} with definition \isa{partial{\isacharunderscore}order{\isachardot}less{\isacharunderscore}def}:
+ \isa{partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less} with definition \isa{partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less{\isaliteral{5F}{\isacharunderscore}}def}:
\begin{isabelle}%
-\ \ partial{\isacharunderscore}order\ {\isacharquery}le\ {\isasymLongrightarrow}\isanewline
-\isaindent{\ \ }partial{\isacharunderscore}order{\isachardot}less\ {\isacharquery}le\ {\isacharquery}x\ {\isacharquery}y\ {\isacharequal}\ {\isacharparenleft}{\isacharquery}le\ {\isacharquery}x\ {\isacharquery}y\ {\isasymand}\ {\isacharquery}x\ {\isasymnoteq}\ {\isacharquery}y{\isacharparenright}%
+\ \ partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{3F}{\isacharquery}}le\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\isanewline
+\isaindent{\ \ }partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ {\isaliteral{3F}{\isacharquery}}le\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}le\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{3F}{\isacharquery}}y{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
At the same time, the locale is extended by syntax transformations
hiding this construction in the context of the locale. Here, the
abbreviation \isa{less} is available for
- \isa{partial{\isacharunderscore}order{\isachardot}less\ le}, and it is printed
- and parsed as infix~\isa{{\isasymsqsubset}}. Finally, the conclusion \isa{less{\isacharunderscore}def} is added to the locale:
+ \isa{partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ le}, and it is printed
+ and parsed as infix~\isa{{\isaliteral{5C3C73717375627365743E}{\isasymsqsubset}}}. Finally, the conclusion \isa{less{\isaliteral{5F}{\isacharunderscore}}def} is added to the locale:
\begin{isabelle}%
-\ \ {\isacharparenleft}{\isacharquery}x\ {\isasymsqsubset}\ {\isacharquery}y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isacharquery}x\ {\isasymsqsubseteq}\ {\isacharquery}y\ {\isasymand}\ {\isacharquery}x\ {\isasymnoteq}\ {\isacharquery}y{\isacharparenright}%
+\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C73717375627365743E}{\isasymsqsubset}}\ {\isaliteral{3F}{\isacharquery}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{3F}{\isacharquery}}y{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -207,8 +207,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{lemma}\isamarkupfalse%
-\ {\isacharparenleft}\isakeyword{in}\ partial{\isacharunderscore}order{\isacharparenright}\ less{\isacharunderscore}le{\isacharunderscore}trans\ {\isacharbrackleft}trans{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ {\isachardoublequoteopen}{\isasymlbrakk}\ x\ {\isasymsqsubset}\ y{\isacharsemicolon}\ y\ {\isasymsqsubseteq}\ z\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ x\ {\isasymsqsubset}\ z{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{in}\ partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{29}{\isacharparenright}}\ less{\isaliteral{5F}{\isacharunderscore}}le{\isaliteral{5F}{\isacharunderscore}}trans\ {\isaliteral{5B}{\isacharbrackleft}}trans{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ x\ {\isaliteral{5C3C73717375627365743E}{\isasymsqsubset}}\ y{\isaliteral{3B}{\isacharsemicolon}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C73717375627365743E}{\isasymsqsubset}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimvisible
\ \ \ \ %
@@ -216,8 +216,8 @@
%
\isatagvisible
\isacommand{unfolding}\isamarkupfalse%
-\ less{\isacharunderscore}def\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}blast\ intro{\isacharcolon}\ trans{\isacharparenright}%
+\ less{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}blast\ intro{\isaliteral{3A}{\isacharcolon}}\ trans{\isaliteral{29}{\isacharparenright}}%
\endisatagvisible
{\isafoldvisible}%
%
@@ -227,7 +227,7 @@
%
\begin{isamarkuptext}%
In the context of the proof, conclusions of the
- locale may be used like theorems. Attributes are effective: \isa{anti{\isacharunderscore}sym} was
+ locale may be used like theorems. Attributes are effective: \isa{anti{\isaliteral{5F}{\isacharunderscore}}sym} was
declared as introduction rule, hence it is in the context's set of
rules used by the classical reasoner by default.%
\end{isamarkuptext}%
@@ -253,17 +253,17 @@
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{context}\isamarkupfalse%
-\ partial{\isacharunderscore}order\ \isakeyword{begin}\isanewline
+\ partial{\isaliteral{5F}{\isacharunderscore}}order\ \isakeyword{begin}\isanewline
\isanewline
\ \ \isacommand{definition}\isamarkupfalse%
\isanewline
-\ \ \ \ is{\isacharunderscore}inf\ \isakeyword{where}\ {\isachardoublequoteopen}is{\isacharunderscore}inf\ x\ y\ i\ {\isacharequal}\isanewline
-\ \ \ \ \ \ {\isacharparenleft}i\ {\isasymsqsubseteq}\ x\ {\isasymand}\ i\ {\isasymsqsubseteq}\ y\ {\isasymand}\ {\isacharparenleft}{\isasymforall}z{\isachardot}\ z\ {\isasymsqsubseteq}\ x\ {\isasymand}\ z\ {\isasymsqsubseteq}\ y\ {\isasymlongrightarrow}\ z\ {\isasymsqsubseteq}\ i{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ \ \ is{\isaliteral{5F}{\isacharunderscore}}inf\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ i\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C616E643E}{\isasymand}}\ i\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}z{\isaliteral{2E}{\isachardot}}\ z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C616E643E}{\isasymand}}\ z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\ \ \isacommand{definition}\isamarkupfalse%
\isanewline
-\ \ \ \ is{\isacharunderscore}sup\ \isakeyword{where}\ {\isachardoublequoteopen}is{\isacharunderscore}sup\ x\ y\ s\ {\isacharequal}\isanewline
-\ \ \ \ \ \ {\isacharparenleft}x\ {\isasymsqsubseteq}\ s\ {\isasymand}\ y\ {\isasymsqsubseteq}\ s\ {\isasymand}\ {\isacharparenleft}{\isasymforall}z{\isachardot}\ x\ {\isasymsqsubseteq}\ z\ {\isasymand}\ y\ {\isasymsqsubseteq}\ z\ {\isasymlongrightarrow}\ s\ {\isasymsqsubseteq}\ z{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ \ \ is{\isaliteral{5F}{\isacharunderscore}}sup\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ s\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ s\ {\isaliteral{5C3C616E643E}{\isasymand}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ s\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}z{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z\ {\isaliteral{5C3C616E643E}{\isasymand}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ s\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadeliminvisible
\isanewline
@@ -272,22 +272,22 @@
%
\isataginvisible
\isacommand{lemma}\isamarkupfalse%
-\ is{\isacharunderscore}infI\ {\isacharbrackleft}intro{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}i\ {\isasymsqsubseteq}\ x\ {\isasymLongrightarrow}\ i\ {\isasymsqsubseteq}\ y\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ \ {\isacharparenleft}{\isasymAnd}z{\isachardot}\ z\ {\isasymsqsubseteq}\ x\ {\isasymLongrightarrow}\ z\ {\isasymsqsubseteq}\ y\ {\isasymLongrightarrow}\ z\ {\isasymsqsubseteq}\ i{\isacharparenright}\ {\isasymLongrightarrow}\ is{\isacharunderscore}inf\ x\ y\ i{\isachardoublequoteclose}\isanewline
+\ is{\isaliteral{5F}{\isacharunderscore}}infI\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}i\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ i\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\isanewline
+\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}z{\isaliteral{2E}{\isachardot}}\ z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ i{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ i{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}unfold\ is{\isacharunderscore}inf{\isacharunderscore}def{\isacharparenright}\ blast\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}unfold\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\ blast\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ is{\isacharunderscore}inf{\isacharunderscore}lower\ {\isacharbrackleft}elim{\isacharquery}{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ {\isachardoublequoteopen}is{\isacharunderscore}inf\ x\ y\ i\ {\isasymLongrightarrow}\ {\isacharparenleft}i\ {\isasymsqsubseteq}\ x\ {\isasymLongrightarrow}\ i\ {\isasymsqsubseteq}\ y\ {\isasymLongrightarrow}\ C{\isacharparenright}\ {\isasymLongrightarrow}\ C{\isachardoublequoteclose}\isanewline
+\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}lower\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ i\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ i\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}unfold\ is{\isacharunderscore}inf{\isacharunderscore}def{\isacharparenright}\ blast\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}unfold\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\ blast\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ is{\isacharunderscore}inf{\isacharunderscore}greatest\ {\isacharbrackleft}elim{\isacharquery}{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ \ \ {\isachardoublequoteopen}is{\isacharunderscore}inf\ x\ y\ i\ {\isasymLongrightarrow}\ z\ {\isasymsqsubseteq}\ x\ {\isasymLongrightarrow}\ z\ {\isasymsqsubseteq}\ y\ {\isasymLongrightarrow}\ z\ {\isasymsqsubseteq}\ i{\isachardoublequoteclose}\isanewline
+\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}greatest\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ i\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ i{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}unfold\ is{\isacharunderscore}inf{\isacharunderscore}def{\isacharparenright}\ blast%
+\ {\isaliteral{28}{\isacharparenleft}}unfold\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\ blast%
\endisataginvisible
{\isafoldinvisible}%
%
@@ -297,7 +297,7 @@
\endisadeliminvisible
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ is{\isacharunderscore}inf{\isacharunderscore}uniq{\isacharcolon}\ {\isachardoublequoteopen}{\isasymlbrakk}is{\isacharunderscore}inf\ x\ y\ i{\isacharsemicolon}\ is{\isacharunderscore}inf\ x\ y\ i{\isacharprime}{\isasymrbrakk}\ {\isasymLongrightarrow}\ i\ {\isacharequal}\ i{\isacharprime}{\isachardoublequoteclose}\isanewline
+\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}uniq{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ i{\isaliteral{3B}{\isacharsemicolon}}\ is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ i{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ i\ {\isaliteral{3D}{\isacharequal}}\ i{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ \ \ %
@@ -305,42 +305,42 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ inf{\isacharcolon}\ {\isachardoublequoteopen}is{\isacharunderscore}inf\ x\ y\ i{\isachardoublequoteclose}\isanewline
+\ inf{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ i{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ inf{\isacharprime}{\isacharcolon}\ {\isachardoublequoteopen}is{\isacharunderscore}inf\ x\ y\ i{\isacharprime}{\isachardoublequoteclose}\isanewline
+\ inf{\isaliteral{27}{\isacharprime}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ i{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\isanewline
+\ {\isaliteral{3F}{\isacharquery}}thesis\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ anti{\isacharunderscore}sym{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ anti{\isaliteral{5F}{\isacharunderscore}}sym{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \ \ \isacommand{from}\isamarkupfalse%
-\ inf{\isacharprime}\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}i\ {\isasymsqsubseteq}\ i{\isacharprime}{\isachardoublequoteclose}\isanewline
+\ inf{\isaliteral{27}{\isacharprime}}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}i\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ i{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ is{\isacharunderscore}inf{\isacharunderscore}greatest{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}greatest{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{from}\isamarkupfalse%
\ inf\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}i\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}i\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{from}\isamarkupfalse%
\ inf\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}i\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}i\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{from}\isamarkupfalse%
\ inf\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}i{\isacharprime}\ {\isasymsqsubseteq}\ i{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}i{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ i{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ is{\isacharunderscore}inf{\isacharunderscore}greatest{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}greatest{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{from}\isamarkupfalse%
-\ inf{\isacharprime}\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}i{\isacharprime}\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ inf{\isaliteral{27}{\isacharprime}}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}i{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{from}\isamarkupfalse%
-\ inf{\isacharprime}\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}i{\isacharprime}\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ inf{\isaliteral{27}{\isacharprime}}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}i{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
@@ -363,25 +363,25 @@
%
\isataginvisible
\isacommand{theorem}\isamarkupfalse%
-\ is{\isacharunderscore}inf{\isacharunderscore}related\ {\isacharbrackleft}elim{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y\ {\isasymLongrightarrow}\ is{\isacharunderscore}inf\ x\ y\ x{\isachardoublequoteclose}\isanewline
+\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}related\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\isanewline
+\ {\isaliteral{3F}{\isacharquery}}thesis\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ fact\isanewline
\ \ \ \ \ \ \isacommand{fix}\isamarkupfalse%
\ z\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ fact\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
@@ -389,22 +389,22 @@
\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ is{\isacharunderscore}supI\ {\isacharbrackleft}intro{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ s\ {\isasymLongrightarrow}\ y\ {\isasymsqsubseteq}\ s\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ \ {\isacharparenleft}{\isasymAnd}z{\isachardot}\ x\ {\isasymsqsubseteq}\ z\ {\isasymLongrightarrow}\ y\ {\isasymsqsubseteq}\ z\ {\isasymLongrightarrow}\ s\ {\isasymsqsubseteq}\ z{\isacharparenright}\ {\isasymLongrightarrow}\ is{\isacharunderscore}sup\ x\ y\ s{\isachardoublequoteclose}\isanewline
+\ is{\isaliteral{5F}{\isacharunderscore}}supI\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ s\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ s\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\isanewline
+\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}z{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ s\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ s{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}unfold\ is{\isacharunderscore}sup{\isacharunderscore}def{\isacharparenright}\ blast\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}unfold\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\ blast\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ is{\isacharunderscore}sup{\isacharunderscore}least\ {\isacharbrackleft}elim{\isacharquery}{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ \ \ {\isachardoublequoteopen}is{\isacharunderscore}sup\ x\ y\ s\ {\isasymLongrightarrow}\ x\ {\isasymsqsubseteq}\ z\ {\isasymLongrightarrow}\ y\ {\isasymsqsubseteq}\ z\ {\isasymLongrightarrow}\ s\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\isanewline
+\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}least\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ s\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ s\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}unfold\ is{\isacharunderscore}sup{\isacharunderscore}def{\isacharparenright}\ blast\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}unfold\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\ blast\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ is{\isacharunderscore}sup{\isacharunderscore}upper\ {\isacharbrackleft}elim{\isacharquery}{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ \ \ {\isachardoublequoteopen}is{\isacharunderscore}sup\ x\ y\ s\ {\isasymLongrightarrow}\ {\isacharparenleft}x\ {\isasymsqsubseteq}\ s\ {\isasymLongrightarrow}\ y\ {\isasymsqsubseteq}\ s\ {\isasymLongrightarrow}\ C{\isacharparenright}\ {\isasymLongrightarrow}\ C{\isachardoublequoteclose}\isanewline
+\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}upper\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ s\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ s\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ s\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ C{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}unfold\ is{\isacharunderscore}sup{\isacharunderscore}def{\isacharparenright}\ blast%
+\ {\isaliteral{28}{\isacharparenleft}}unfold\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\ blast%
\endisataginvisible
{\isafoldinvisible}%
%
@@ -414,7 +414,7 @@
\endisadeliminvisible
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ is{\isacharunderscore}sup{\isacharunderscore}uniq{\isacharcolon}\ {\isachardoublequoteopen}{\isasymlbrakk}is{\isacharunderscore}sup\ x\ y\ s{\isacharsemicolon}\ is{\isacharunderscore}sup\ x\ y\ s{\isacharprime}{\isasymrbrakk}\ {\isasymLongrightarrow}\ s\ {\isacharequal}\ s{\isacharprime}{\isachardoublequoteclose}\isanewline
+\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}uniq{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ s{\isaliteral{3B}{\isacharsemicolon}}\ is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ s{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ s\ {\isaliteral{3D}{\isacharequal}}\ s{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ \ \ %
@@ -422,42 +422,42 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ sup{\isacharcolon}\ {\isachardoublequoteopen}is{\isacharunderscore}sup\ x\ y\ s{\isachardoublequoteclose}\isanewline
+\ sup{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ s{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ sup{\isacharprime}{\isacharcolon}\ {\isachardoublequoteopen}is{\isacharunderscore}sup\ x\ y\ s{\isacharprime}{\isachardoublequoteclose}\isanewline
+\ sup{\isaliteral{27}{\isacharprime}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ s{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\isanewline
+\ {\isaliteral{3F}{\isacharquery}}thesis\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ anti{\isacharunderscore}sym{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ anti{\isaliteral{5F}{\isacharunderscore}}sym{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \ \ \isacommand{from}\isamarkupfalse%
\ sup\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}s\ {\isasymsqsubseteq}\ s{\isacharprime}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}s\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ s{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ is{\isacharunderscore}sup{\isacharunderscore}least{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}least{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{from}\isamarkupfalse%
-\ sup{\isacharprime}\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ s{\isacharprime}{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ sup{\isaliteral{27}{\isacharprime}}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ s{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{from}\isamarkupfalse%
-\ sup{\isacharprime}\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ s{\isacharprime}{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ sup{\isaliteral{27}{\isacharprime}}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ s{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{from}\isamarkupfalse%
-\ sup{\isacharprime}\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}s{\isacharprime}\ {\isasymsqsubseteq}\ s{\isachardoublequoteclose}\isanewline
+\ sup{\isaliteral{27}{\isacharprime}}\ \isacommand{show}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}s{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ s{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ is{\isacharunderscore}sup{\isacharunderscore}least{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}least{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{from}\isamarkupfalse%
\ sup\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ s{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ s{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{from}\isamarkupfalse%
\ sup\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ s{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ s{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
@@ -480,26 +480,26 @@
%
\isataginvisible
\isacommand{theorem}\isamarkupfalse%
-\ is{\isacharunderscore}sup{\isacharunderscore}related\ {\isacharbrackleft}elim{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y\ {\isasymLongrightarrow}\ is{\isacharunderscore}sup\ x\ y\ y{\isachardoublequoteclose}\isanewline
+\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}related\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\isanewline
+\ {\isaliteral{3F}{\isacharquery}}thesis\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ fact\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{fix}\isamarkupfalse%
\ z\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ fact\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
@@ -545,22 +545,22 @@
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{locale}\isamarkupfalse%
-\ lattice\ {\isacharequal}\ partial{\isacharunderscore}order\ {\isacharplus}\isanewline
-\ \ \ \ \isakeyword{assumes}\ ex{\isacharunderscore}inf{\isacharcolon}\ {\isachardoublequoteopen}{\isasymexists}inf{\isachardot}\ is{\isacharunderscore}inf\ x\ y\ inf{\isachardoublequoteclose}\isanewline
-\ \ \ \ \ \ \isakeyword{and}\ ex{\isacharunderscore}sup{\isacharcolon}\ {\isachardoublequoteopen}{\isasymexists}sup{\isachardot}\ is{\isacharunderscore}sup\ x\ y\ sup{\isachardoublequoteclose}\isanewline
+\ lattice\ {\isaliteral{3D}{\isacharequal}}\ partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{2B}{\isacharplus}}\isanewline
+\ \ \ \ \isakeyword{assumes}\ ex{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}inf{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ inf{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \ \ \isakeyword{and}\ ex{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}sup{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ sup{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isakeyword{begin}%
\begin{isamarkuptext}%
These assumptions refer to the predicates for infimum
- and supremum defined for \isa{partial{\isacharunderscore}order} in the previous
+ and supremum defined for \isa{partial{\isaliteral{5F}{\isacharunderscore}}order} in the previous
section. We now introduce the notions of meet and join.%
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{definition}\isamarkupfalse%
\isanewline
-\ \ \ \ meet\ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasymsqinter}{\isachardoublequoteclose}\ {\isadigit{7}}{\isadigit{0}}{\isacharparenright}\ \isakeyword{where}\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ y\ {\isacharequal}\ {\isacharparenleft}THE\ inf{\isachardot}\ is{\isacharunderscore}inf\ x\ y\ inf{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ \ \ meet\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{7}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}THE\ inf{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ inf{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{definition}\isamarkupfalse%
\isanewline
-\ \ \ \ join\ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasymsqunion}{\isachardoublequoteclose}\ {\isadigit{6}}{\isadigit{5}}{\isacharparenright}\ \isakeyword{where}\ {\isachardoublequoteopen}x\ {\isasymsqunion}\ y\ {\isacharequal}\ {\isacharparenleft}THE\ sup{\isachardot}\ is{\isacharunderscore}sup\ x\ y\ sup{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ \ \ join\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{6}}{\isadigit{5}}{\isaliteral{29}{\isacharparenright}}\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}THE\ sup{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ sup{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadeliminvisible
\isanewline
@@ -569,207 +569,207 @@
%
\isataginvisible
\isacommand{lemma}\isamarkupfalse%
-\ meet{\isacharunderscore}equality\ {\isacharbrackleft}elim{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}is{\isacharunderscore}inf\ x\ y\ i\ {\isasymLongrightarrow}\ x\ {\isasymsqinter}\ y\ {\isacharequal}\ i{\isachardoublequoteclose}\isanewline
+\ meet{\isaliteral{5F}{\isacharunderscore}}equality\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ i\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y\ {\isaliteral{3D}{\isacharequal}}\ i{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}unfold\ meet{\isacharunderscore}def{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}unfold\ meet{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}is{\isacharunderscore}inf\ x\ y\ i{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ i{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}THE\ i{\isachardot}\ is{\isacharunderscore}inf\ x\ y\ i{\isacharparenright}\ {\isacharequal}\ i{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}THE\ i{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ i{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ i{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ the{\isacharunderscore}equality{\isacharparenright}\ {\isacharparenleft}rule\ is{\isacharunderscore}inf{\isacharunderscore}uniq\ {\isacharbrackleft}OF\ {\isacharunderscore}\ {\isacharbackquoteopen}is{\isacharunderscore}inf\ x\ y\ i{\isacharbackquoteclose}{\isacharbrackright}{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ the{\isaliteral{5F}{\isacharunderscore}}equality{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}uniq\ {\isaliteral{5B}{\isacharbrackleft}}OF\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{60}{\isacharbackquoteopen}}is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ i{\isaliteral{60}{\isacharbackquoteclose}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ meetI\ {\isacharbrackleft}intro{\isacharquery}{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ \ \ {\isachardoublequoteopen}i\ {\isasymsqsubseteq}\ x\ {\isasymLongrightarrow}\ i\ {\isasymsqsubseteq}\ y\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymAnd}z{\isachardot}\ z\ {\isasymsqsubseteq}\ x\ {\isasymLongrightarrow}\ z\ {\isasymsqsubseteq}\ y\ {\isasymLongrightarrow}\ z\ {\isasymsqsubseteq}\ i{\isacharparenright}\ {\isasymLongrightarrow}\ x\ {\isasymsqinter}\ y\ {\isacharequal}\ i{\isachardoublequoteclose}\isanewline
+\ meetI\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}i\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ i\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}z{\isaliteral{2E}{\isachardot}}\ z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ i{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y\ {\isaliteral{3D}{\isacharequal}}\ i{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ meet{\isacharunderscore}equality{\isacharcomma}\ rule\ is{\isacharunderscore}infI{\isacharparenright}\ blast{\isacharplus}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ meet{\isaliteral{5F}{\isacharunderscore}}equality{\isaliteral{2C}{\isacharcomma}}\ rule\ is{\isaliteral{5F}{\isacharunderscore}}infI{\isaliteral{29}{\isacharparenright}}\ blast{\isaliteral{2B}{\isacharplus}}\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ is{\isacharunderscore}inf{\isacharunderscore}meet\ {\isacharbrackleft}intro{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}is{\isacharunderscore}inf\ x\ y\ {\isacharparenleft}x\ {\isasymsqinter}\ y{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}meet\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}unfold\ meet{\isacharunderscore}def{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}unfold\ meet{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{from}\isamarkupfalse%
-\ ex{\isacharunderscore}inf\ \isacommand{obtain}\isamarkupfalse%
-\ i\ \isakeyword{where}\ {\isachardoublequoteopen}is{\isacharunderscore}inf\ x\ y\ i{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ ex{\isaliteral{5F}{\isacharunderscore}}inf\ \isacommand{obtain}\isamarkupfalse%
+\ i\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ i{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}is{\isacharunderscore}inf\ x\ y\ {\isacharparenleft}THE\ i{\isachardot}\ is{\isacharunderscore}inf\ x\ y\ i{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ {\isaliteral{28}{\isacharparenleft}}THE\ i{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ theI{\isacharparenright}\ {\isacharparenleft}rule\ is{\isacharunderscore}inf{\isacharunderscore}uniq\ {\isacharbrackleft}OF\ {\isacharunderscore}\ {\isacharbackquoteopen}is{\isacharunderscore}inf\ x\ y\ i{\isacharbackquoteclose}{\isacharbrackright}{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ theI{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}uniq\ {\isaliteral{5B}{\isacharbrackleft}}OF\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{60}{\isacharbackquoteopen}}is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ i{\isaliteral{60}{\isacharbackquoteclose}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ meet{\isacharunderscore}left\ {\isacharbrackleft}intro{\isacharquery}{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ {\isachardoublequoteopen}x\ {\isasymsqinter}\ y\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\isanewline
+\ meet{\isaliteral{5F}{\isacharunderscore}}left\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ is{\isacharunderscore}inf{\isacharunderscore}lower{\isacharparenright}\ {\isacharparenleft}rule\ is{\isacharunderscore}inf{\isacharunderscore}meet{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}lower{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}meet{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ meet{\isacharunderscore}right\ {\isacharbrackleft}intro{\isacharquery}{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ {\isachardoublequoteopen}x\ {\isasymsqinter}\ y\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\isanewline
+\ meet{\isaliteral{5F}{\isacharunderscore}}right\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ is{\isacharunderscore}inf{\isacharunderscore}lower{\isacharparenright}\ {\isacharparenleft}rule\ is{\isacharunderscore}inf{\isacharunderscore}meet{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}lower{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}meet{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ meet{\isacharunderscore}le\ {\isacharbrackleft}intro{\isacharquery}{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ {\isachardoublequoteopen}{\isasymlbrakk}\ z\ {\isasymsqsubseteq}\ x{\isacharsemicolon}\ z\ {\isasymsqsubseteq}\ y\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ z\ {\isasymsqsubseteq}\ x\ {\isasymsqinter}\ y{\isachardoublequoteclose}\isanewline
+\ meet{\isaliteral{5F}{\isacharunderscore}}le\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{3B}{\isacharsemicolon}}\ z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ is{\isacharunderscore}inf{\isacharunderscore}greatest{\isacharparenright}\ {\isacharparenleft}rule\ is{\isacharunderscore}inf{\isacharunderscore}meet{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}greatest{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}meet{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ join{\isacharunderscore}equality\ {\isacharbrackleft}elim{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}is{\isacharunderscore}sup\ x\ y\ s\ {\isasymLongrightarrow}\ x\ {\isasymsqunion}\ y\ {\isacharequal}\ s{\isachardoublequoteclose}\isanewline
+\ join{\isaliteral{5F}{\isacharunderscore}}equality\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ s\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y\ {\isaliteral{3D}{\isacharequal}}\ s{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}unfold\ join{\isacharunderscore}def{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}unfold\ join{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}is{\isacharunderscore}sup\ x\ y\ s{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ s{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}THE\ s{\isachardot}\ is{\isacharunderscore}sup\ x\ y\ s{\isacharparenright}\ {\isacharequal}\ s{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}THE\ s{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ s{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ s{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ the{\isacharunderscore}equality{\isacharparenright}\ {\isacharparenleft}rule\ is{\isacharunderscore}sup{\isacharunderscore}uniq\ {\isacharbrackleft}OF\ {\isacharunderscore}\ {\isacharbackquoteopen}is{\isacharunderscore}sup\ x\ y\ s{\isacharbackquoteclose}{\isacharbrackright}{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ the{\isaliteral{5F}{\isacharunderscore}}equality{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}uniq\ {\isaliteral{5B}{\isacharbrackleft}}OF\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{60}{\isacharbackquoteopen}}is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ s{\isaliteral{60}{\isacharbackquoteclose}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ joinI\ {\isacharbrackleft}intro{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ s\ {\isasymLongrightarrow}\ y\ {\isasymsqsubseteq}\ s\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ \ {\isacharparenleft}{\isasymAnd}z{\isachardot}\ x\ {\isasymsqsubseteq}\ z\ {\isasymLongrightarrow}\ y\ {\isasymsqsubseteq}\ z\ {\isasymLongrightarrow}\ s\ {\isasymsqsubseteq}\ z{\isacharparenright}\ {\isasymLongrightarrow}\ x\ {\isasymsqunion}\ y\ {\isacharequal}\ s{\isachardoublequoteclose}\isanewline
+\ joinI\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ s\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ s\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\isanewline
+\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}z{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ s\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y\ {\isaliteral{3D}{\isacharequal}}\ s{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ join{\isacharunderscore}equality{\isacharcomma}\ rule\ is{\isacharunderscore}supI{\isacharparenright}\ blast{\isacharplus}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ join{\isaliteral{5F}{\isacharunderscore}}equality{\isaliteral{2C}{\isacharcomma}}\ rule\ is{\isaliteral{5F}{\isacharunderscore}}supI{\isaliteral{29}{\isacharparenright}}\ blast{\isaliteral{2B}{\isacharplus}}\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ is{\isacharunderscore}sup{\isacharunderscore}join\ {\isacharbrackleft}intro{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}is{\isacharunderscore}sup\ x\ y\ {\isacharparenleft}x\ {\isasymsqunion}\ y{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}join\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}unfold\ join{\isacharunderscore}def{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}unfold\ join{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{from}\isamarkupfalse%
-\ ex{\isacharunderscore}sup\ \isacommand{obtain}\isamarkupfalse%
-\ s\ \isakeyword{where}\ {\isachardoublequoteopen}is{\isacharunderscore}sup\ x\ y\ s{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ ex{\isaliteral{5F}{\isacharunderscore}}sup\ \isacommand{obtain}\isamarkupfalse%
+\ s\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ s{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}is{\isacharunderscore}sup\ x\ y\ {\isacharparenleft}THE\ s{\isachardot}\ is{\isacharunderscore}sup\ x\ y\ s{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ {\isaliteral{28}{\isacharparenleft}}THE\ s{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ s{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ theI{\isacharparenright}\ {\isacharparenleft}rule\ is{\isacharunderscore}sup{\isacharunderscore}uniq\ {\isacharbrackleft}OF\ {\isacharunderscore}\ {\isacharbackquoteopen}is{\isacharunderscore}sup\ x\ y\ s{\isacharbackquoteclose}{\isacharbrackright}{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ theI{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}uniq\ {\isaliteral{5B}{\isacharbrackleft}}OF\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{60}{\isacharbackquoteopen}}is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ s{\isaliteral{60}{\isacharbackquoteclose}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ join{\isacharunderscore}left\ {\isacharbrackleft}intro{\isacharquery}{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ x\ {\isasymsqunion}\ y{\isachardoublequoteclose}\isanewline
+\ join{\isaliteral{5F}{\isacharunderscore}}left\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ is{\isacharunderscore}sup{\isacharunderscore}upper{\isacharparenright}\ {\isacharparenleft}rule\ is{\isacharunderscore}sup{\isacharunderscore}join{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}upper{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}join{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ join{\isacharunderscore}right\ {\isacharbrackleft}intro{\isacharquery}{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ x\ {\isasymsqunion}\ y{\isachardoublequoteclose}\isanewline
+\ join{\isaliteral{5F}{\isacharunderscore}}right\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ is{\isacharunderscore}sup{\isacharunderscore}upper{\isacharparenright}\ {\isacharparenleft}rule\ is{\isacharunderscore}sup{\isacharunderscore}join{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}upper{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}join{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ join{\isacharunderscore}le\ {\isacharbrackleft}intro{\isacharquery}{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ {\isachardoublequoteopen}{\isasymlbrakk}\ x\ {\isasymsqsubseteq}\ z{\isacharsemicolon}\ y\ {\isasymsqsubseteq}\ z\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ x\ {\isasymsqunion}\ y\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\isanewline
+\ join{\isaliteral{5F}{\isacharunderscore}}le\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{3B}{\isacharsemicolon}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ is{\isacharunderscore}sup{\isacharunderscore}least{\isacharparenright}\ {\isacharparenleft}rule\ is{\isacharunderscore}sup{\isacharunderscore}join{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}least{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}join{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ meet{\isacharunderscore}assoc{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}x\ {\isasymsqinter}\ y{\isacharparenright}\ {\isasymsqinter}\ z\ {\isacharequal}\ x\ {\isasymsqinter}\ {\isacharparenleft}y\ {\isasymsqinter}\ z{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ meet{\isaliteral{5F}{\isacharunderscore}}assoc{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ meetI{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ meetI{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ {\isacharparenleft}y\ {\isasymsqinter}\ z{\isacharparenright}\ {\isasymsqsubseteq}\ x\ {\isasymsqinter}\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ {\isacharparenleft}y\ {\isasymsqinter}\ z{\isacharparenright}\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ {\isacharparenleft}y\ {\isasymsqinter}\ z{\isacharparenright}\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ {\isacharparenleft}y\ {\isasymsqinter}\ z{\isacharparenright}\ {\isasymsqsubseteq}\ y\ {\isasymsqinter}\ z{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdots}\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ {\isacharparenleft}y\ {\isasymsqinter}\ z{\isacharparenright}\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ {\isacharparenleft}y\ {\isasymsqinter}\ z{\isacharparenright}\ {\isasymsqsubseteq}\ y\ {\isasymsqinter}\ z{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdots}\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ w\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}w\ {\isasymsqsubseteq}\ x\ {\isasymsqinter}\ y{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}w\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}w\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}w\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}w\ {\isasymsqsubseteq}\ x\ {\isasymsqinter}\ {\isacharparenleft}y\ {\isasymsqinter}\ z{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}w\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}w\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}w\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}w\ {\isasymsqsubseteq}\ x\ {\isasymsqinter}\ y{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}w\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ fact\isanewline
\ \ \ \ \ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdots}\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}w\ {\isasymsqsubseteq}\ y\ {\isasymsqinter}\ z{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}w\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}w\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}w\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}w\ {\isasymsqsubseteq}\ x\ {\isasymsqinter}\ y{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}w\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ fact\isanewline
\ \ \ \ \ \ \ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdots}\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}w\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}w\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ fact\isanewline
\ \ \ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
@@ -779,138 +779,138 @@
\isanewline
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ meet{\isacharunderscore}commute{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ y\ {\isacharequal}\ y\ {\isasymsqinter}\ x{\isachardoublequoteclose}\isanewline
+\ meet{\isaliteral{5F}{\isacharunderscore}}commute{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y\ {\isaliteral{3D}{\isacharequal}}\ y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ meetI{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ meetI{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymsqinter}\ x\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymsqinter}\ x\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ z\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ y\ {\isasymsqinter}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ meet{\isacharunderscore}join{\isacharunderscore}absorb{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ {\isacharparenleft}x\ {\isasymsqunion}\ y{\isacharparenright}\ {\isacharequal}\ x{\isachardoublequoteclose}\isanewline
+\ meet{\isaliteral{5F}{\isacharunderscore}}join{\isaliteral{5F}{\isacharunderscore}}absorb{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ meetI{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ meetI{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ x\ {\isasymsqunion}\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ z\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ x\ {\isasymsqunion}\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ fact\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ join{\isacharunderscore}assoc{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}x\ {\isasymsqunion}\ y{\isacharparenright}\ {\isasymsqunion}\ z\ {\isacharequal}\ x\ {\isasymsqunion}\ {\isacharparenleft}y\ {\isasymsqunion}\ z{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ join{\isaliteral{5F}{\isacharunderscore}}assoc{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ joinI{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ joinI{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqunion}\ y\ {\isasymsqsubseteq}\ x\ {\isasymsqunion}\ {\isacharparenleft}y\ {\isasymsqunion}\ z{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ x\ {\isasymsqunion}\ {\isacharparenleft}y\ {\isasymsqunion}\ z{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ x\ {\isasymsqunion}\ {\isacharparenleft}y\ {\isasymsqunion}\ z{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ y\ {\isasymsqunion}\ z{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isachardot}{\isachardot}{\isachardot}\ {\isasymsqsubseteq}\ x\ {\isasymsqunion}\ {\isacharparenleft}y\ {\isasymsqunion}\ z{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ x\ {\isasymsqunion}\ {\isacharparenleft}y\ {\isasymsqunion}\ z{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ y\ {\isasymsqunion}\ z{\isachardoublequoteclose}\ \ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isachardot}{\isachardot}{\isachardot}\ {\isasymsqsubseteq}\ x\ {\isasymsqunion}\ {\isacharparenleft}y\ {\isasymsqunion}\ z{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ w\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqunion}\ y\ {\isasymsqsubseteq}\ w{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ w{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ w{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ w{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqunion}\ {\isacharparenleft}y\ {\isasymsqunion}\ z{\isacharparenright}\ {\isasymsqsubseteq}\ w{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ w{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ w{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ w{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ x\ {\isasymsqunion}\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdots}\ {\isasymsqsubseteq}\ w{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ w{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ fact\isanewline
\ \ \ \ \ \ \ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymsqunion}\ z\ {\isasymsqsubseteq}\ w{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ w{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ w{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ w{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ x\ {\isasymsqunion}\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isachardot}{\isachardot}{\isachardot}\ {\isasymsqsubseteq}\ w{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ w{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ fact\isanewline
\ \ \ \ \ \ \ \ \ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ w{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ w{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ fact\isanewline
\ \ \ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
@@ -920,194 +920,194 @@
\isanewline
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ join{\isacharunderscore}commute{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqunion}\ y\ {\isacharequal}\ y\ {\isasymsqunion}\ x{\isachardoublequoteclose}\isanewline
+\ join{\isaliteral{5F}{\isacharunderscore}}commute{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y\ {\isaliteral{3D}{\isacharequal}}\ y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ joinI{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ joinI{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y\ {\isasymsqunion}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ y\ {\isasymsqunion}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ z\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymsqunion}\ x\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ join{\isacharunderscore}meet{\isacharunderscore}absorb{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqunion}\ {\isacharparenleft}x\ {\isasymsqinter}\ y{\isacharparenright}\ {\isacharequal}\ x{\isachardoublequoteclose}\isanewline
+\ join{\isaliteral{5F}{\isacharunderscore}}meet{\isaliteral{5F}{\isacharunderscore}}absorb{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ joinI{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ joinI{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ y\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ z\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ y\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ fact\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ meet{\isacharunderscore}idem{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ x\ {\isacharequal}\ x{\isachardoublequoteclose}\isanewline
+\ meet{\isaliteral{5F}{\isacharunderscore}}idem{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ x\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ {\isacharparenleft}x\ {\isasymsqunion}\ {\isacharparenleft}x\ {\isasymsqinter}\ x{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ x{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ meet{\isacharunderscore}join{\isacharunderscore}absorb{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ meet{\isaliteral{5F}{\isacharunderscore}}join{\isaliteral{5F}{\isacharunderscore}}absorb{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqunion}\ {\isacharparenleft}x\ {\isasymsqinter}\ x{\isacharparenright}\ {\isacharequal}\ x{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ join{\isacharunderscore}meet{\isacharunderscore}absorb{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ join{\isaliteral{5F}{\isacharunderscore}}meet{\isaliteral{5F}{\isacharunderscore}}absorb{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ meet{\isacharunderscore}related\ {\isacharbrackleft}elim{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y\ {\isasymLongrightarrow}\ x\ {\isasymsqinter}\ y\ {\isacharequal}\ x{\isachardoublequoteclose}\isanewline
+\ meet{\isaliteral{5F}{\isacharunderscore}}related\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ meetI{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ meetI{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ fact\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ z\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ fact\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ meet{\isacharunderscore}related{\isadigit{2}}\ {\isacharbrackleft}elim{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ x\ {\isasymLongrightarrow}\ x\ {\isasymsqinter}\ y\ {\isacharequal}\ y{\isachardoublequoteclose}\isanewline
+\ meet{\isaliteral{5F}{\isacharunderscore}}related{\isadigit{2}}\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}drule\ meet{\isacharunderscore}related{\isacharparenright}\ {\isacharparenleft}simp\ add{\isacharcolon}\ meet{\isacharunderscore}commute{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}drule\ meet{\isaliteral{5F}{\isacharunderscore}}related{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ meet{\isaliteral{5F}{\isacharunderscore}}commute{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ join{\isacharunderscore}related\ {\isacharbrackleft}elim{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y\ {\isasymLongrightarrow}\ x\ {\isasymsqunion}\ y\ {\isacharequal}\ y{\isachardoublequoteclose}\isanewline
+\ join{\isaliteral{5F}{\isacharunderscore}}related\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}rule\ joinI{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}rule\ joinI{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ fact\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ z\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ fact\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ join{\isacharunderscore}related{\isadigit{2}}\ {\isacharbrackleft}elim{\isacharquery}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ x\ {\isasymLongrightarrow}\ x\ {\isasymsqunion}\ y\ {\isacharequal}\ x{\isachardoublequoteclose}\isanewline
+\ join{\isaliteral{5F}{\isacharunderscore}}related{\isadigit{2}}\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{3F}{\isacharquery}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}drule\ join{\isacharunderscore}related{\isacharparenright}\ {\isacharparenleft}simp\ add{\isacharcolon}\ join{\isacharunderscore}commute{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}drule\ join{\isaliteral{5F}{\isacharunderscore}}related{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ join{\isaliteral{5F}{\isacharunderscore}}commute{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ meet{\isacharunderscore}connection{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}x\ {\isasymsqsubseteq}\ y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}x\ {\isasymsqinter}\ y\ {\isacharequal}\ x{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ meet{\isaliteral{5F}{\isacharunderscore}}connection{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}is{\isacharunderscore}inf\ x\ y\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ y\ {\isacharequal}\ x{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ y\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ y\ {\isacharequal}\ x{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ join{\isacharunderscore}connection{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}x\ {\isasymsqsubseteq}\ y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}x\ {\isasymsqunion}\ y\ {\isacharequal}\ y{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ join{\isaliteral{5F}{\isacharunderscore}}connection{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}is{\isacharunderscore}sup\ x\ y\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqunion}\ y\ {\isacharequal}\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ x\ {\isasymsqunion}\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqunion}\ y\ {\isacharequal}\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ meet{\isacharunderscore}connection{\isadigit{2}}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}x\ {\isasymsqsubseteq}\ y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}y\ {\isasymsqinter}\ x\ {\isacharequal}\ x{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ meet{\isaliteral{5F}{\isacharunderscore}}connection{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ x\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{using}\isamarkupfalse%
-\ meet{\isacharunderscore}commute\ meet{\isacharunderscore}connection\ \isacommand{by}\isamarkupfalse%
+\ meet{\isaliteral{5F}{\isacharunderscore}}commute\ meet{\isaliteral{5F}{\isacharunderscore}}connection\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isanewline
\ \ \isacommand{theorem}\isamarkupfalse%
-\ join{\isacharunderscore}connection{\isadigit{2}}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}x\ {\isasymsqsubseteq}\ y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}x\ {\isasymsqunion}\ y\ {\isacharequal}\ y{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ join{\isaliteral{5F}{\isacharunderscore}}connection{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{using}\isamarkupfalse%
-\ join{\isacharunderscore}commute\ join{\isacharunderscore}connection\ \isacommand{by}\isamarkupfalse%
+\ join{\isaliteral{5F}{\isacharunderscore}}commute\ join{\isaliteral{5F}{\isacharunderscore}}connection\ \isacommand{by}\isamarkupfalse%
\ simp%
\begin{isamarkuptext}%
Naming according to Jacobson I, p.\ 459.%
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{lemmas}\isamarkupfalse%
-\ L{\isadigit{1}}\ {\isacharequal}\ join{\isacharunderscore}commute\ meet{\isacharunderscore}commute\isanewline
+\ L{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ join{\isaliteral{5F}{\isacharunderscore}}commute\ meet{\isaliteral{5F}{\isacharunderscore}}commute\isanewline
\ \ \isacommand{lemmas}\isamarkupfalse%
-\ L{\isadigit{2}}\ {\isacharequal}\ join{\isacharunderscore}assoc\ meet{\isacharunderscore}assoc\isanewline
+\ L{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ join{\isaliteral{5F}{\isacharunderscore}}assoc\ meet{\isaliteral{5F}{\isacharunderscore}}assoc\isanewline
\ \ \isanewline
\ \ \isacommand{lemmas}\isamarkupfalse%
-\ L{\isadigit{4}}\ {\isacharequal}\ join{\isacharunderscore}meet{\isacharunderscore}absorb\ meet{\isacharunderscore}join{\isacharunderscore}absorb%
+\ L{\isadigit{4}}\ {\isaliteral{3D}{\isacharequal}}\ join{\isaliteral{5F}{\isacharunderscore}}meet{\isaliteral{5F}{\isacharunderscore}}absorb\ meet{\isaliteral{5F}{\isacharunderscore}}join{\isaliteral{5F}{\isacharunderscore}}absorb%
\endisataginvisible
{\isafoldinvisible}%
%
@@ -1126,11 +1126,11 @@
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{locale}\isamarkupfalse%
-\ total{\isacharunderscore}order\ {\isacharequal}\ partial{\isacharunderscore}order\ {\isacharplus}\isanewline
-\ \ \ \ \isakeyword{assumes}\ total{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y\ {\isasymor}\ y\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\isanewline
+\ total{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{3D}{\isacharequal}}\ partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{2B}{\isacharplus}}\isanewline
+\ \ \ \ \isakeyword{assumes}\ total{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C6F723E}{\isasymor}}\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ {\isacharparenleft}\isakeyword{in}\ total{\isacharunderscore}order{\isacharparenright}\ less{\isacharunderscore}total{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqsubset}\ y\ {\isasymor}\ x\ {\isacharequal}\ y\ {\isasymor}\ y\ {\isasymsqsubset}\ x{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{in}\ total{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{29}{\isacharparenright}}\ less{\isaliteral{5F}{\isacharunderscore}}total{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C73717375627365743E}{\isasymsqsubset}}\ y\ {\isaliteral{5C3C6F723E}{\isasymor}}\ x\ {\isaliteral{3D}{\isacharequal}}\ y\ {\isaliteral{5C3C6F723E}{\isasymor}}\ y\ {\isaliteral{5C3C73717375627365743E}{\isasymsqsubset}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ \ \ %
@@ -1140,7 +1140,7 @@
\isacommand{using}\isamarkupfalse%
\ total\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}unfold\ less{\isacharunderscore}def{\isacharparenright}\ blast%
+\ {\isaliteral{28}{\isacharparenleft}}unfold\ less{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\ blast%
\endisatagproof
{\isafoldproof}%
%
@@ -1150,12 +1150,12 @@
\endisadelimproof
\isanewline
\ \ \isacommand{locale}\isamarkupfalse%
-\ distrib{\isacharunderscore}lattice\ {\isacharequal}\ lattice\ {\isacharplus}\isanewline
-\ \ \ \ \isakeyword{assumes}\ meet{\isacharunderscore}distr{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ {\isacharparenleft}y\ {\isasymsqunion}\ z{\isacharparenright}\ {\isacharequal}\ x\ {\isasymsqinter}\ y\ {\isasymsqunion}\ x\ {\isasymsqinter}\ z{\isachardoublequoteclose}\isanewline
+\ distrib{\isaliteral{5F}{\isacharunderscore}}lattice\ {\isaliteral{3D}{\isacharequal}}\ lattice\ {\isaliteral{2B}{\isacharplus}}\isanewline
+\ \ \ \ \isakeyword{assumes}\ meet{\isaliteral{5F}{\isacharunderscore}}distr{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\ \ \isacommand{lemma}\isamarkupfalse%
-\ {\isacharparenleft}\isakeyword{in}\ distrib{\isacharunderscore}lattice{\isacharparenright}\ join{\isacharunderscore}distr{\isacharcolon}\isanewline
-\ \ \ \ {\isachardoublequoteopen}x\ {\isasymsqunion}\ {\isacharparenleft}y\ {\isasymsqinter}\ z{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}x\ {\isasymsqunion}\ y{\isacharparenright}\ {\isasymsqinter}\ {\isacharparenleft}x\ {\isasymsqunion}\ z{\isacharparenright}{\isachardoublequoteclose}\ \ \isanewline
+\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{in}\ distrib{\isaliteral{5F}{\isacharunderscore}}lattice{\isaliteral{29}{\isacharparenright}}\ join{\isaliteral{5F}{\isacharunderscore}}distr{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \ \isanewline
%
\isadelimproof
\ \ \ \ %
@@ -1163,29 +1163,29 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqunion}\ {\isacharparenleft}y\ {\isasymsqinter}\ z{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}x\ {\isasymsqunion}\ {\isacharparenleft}x\ {\isasymsqinter}\ z{\isacharparenright}{\isacharparenright}\ {\isasymsqunion}\ {\isacharparenleft}y\ {\isasymsqinter}\ z{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ L{\isadigit{4}}{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ L{\isadigit{4}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isachardot}{\isachardot}{\isachardot}\ {\isacharequal}\ x\ {\isasymsqunion}\ {\isacharparenleft}{\isacharparenleft}x\ {\isasymsqinter}\ z{\isacharparenright}\ {\isasymsqunion}\ {\isacharparenleft}y\ {\isasymsqinter}\ z{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ L{\isadigit{2}}{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ L{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isachardot}{\isachardot}{\isachardot}\ {\isacharequal}\ x\ {\isasymsqunion}\ {\isacharparenleft}{\isacharparenleft}x\ {\isasymsqunion}\ y{\isacharparenright}\ {\isasymsqinter}\ z{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ L{\isadigit{1}}\ meet{\isacharunderscore}distr{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ L{\isadigit{1}}\ meet{\isaliteral{5F}{\isacharunderscore}}distr{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isachardot}{\isachardot}{\isachardot}\ {\isacharequal}\ {\isacharparenleft}{\isacharparenleft}x\ {\isasymsqunion}\ y{\isacharparenright}\ {\isasymsqinter}\ x{\isacharparenright}\ {\isasymsqunion}\ {\isacharparenleft}{\isacharparenleft}x\ {\isasymsqunion}\ y{\isacharparenright}\ {\isasymsqinter}\ z{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ L{\isadigit{1}}\ L{\isadigit{4}}{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ L{\isadigit{1}}\ L{\isadigit{4}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isachardot}{\isachardot}{\isachardot}\ {\isacharequal}\ {\isacharparenleft}x\ {\isasymsqunion}\ y{\isacharparenright}\ {\isasymsqinter}\ {\isacharparenleft}x\ {\isasymsqunion}\ z{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ meet{\isacharunderscore}distr{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ meet{\isaliteral{5F}{\isacharunderscore}}distr{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
%
@@ -1205,10 +1205,10 @@
\begin{center}
\subfigure[Declared hierarchy]{
\begin{tikzpicture}
- \node (po) at (0,0) {\isa{partial{\isacharunderscore}order}};
+ \node (po) at (0,0) {\isa{partial{\isaliteral{5F}{\isacharunderscore}}order}};
\node (lat) at (-1.5,-1) {\isa{lattice}};
- \node (dlat) at (-1.5,-2) {\isa{distrib{\isacharunderscore}lattice}};
- \node (to) at (1.5,-1) {\isa{total{\isacharunderscore}order}};
+ \node (dlat) at (-1.5,-2) {\isa{distrib{\isaliteral{5F}{\isacharunderscore}}lattice}};
+ \node (to) at (1.5,-1) {\isa{total{\isaliteral{5F}{\isacharunderscore}}order}};
\draw (po) -- (lat);
\draw (lat) -- (dlat);
\draw (po) -- (to);
@@ -1217,10 +1217,10 @@
} \\
\subfigure[Total orders are lattices]{
\begin{tikzpicture}
- \node (po) at (0,0) {\isa{partial{\isacharunderscore}order}};
+ \node (po) at (0,0) {\isa{partial{\isaliteral{5F}{\isacharunderscore}}order}};
\node (lat) at (0,-1) {\isa{lattice}};
- \node (dlat) at (-1.5,-2) {\isa{distrib{\isacharunderscore}lattice}};
- \node (to) at (1.5,-2) {\isa{total{\isacharunderscore}order}};
+ \node (dlat) at (-1.5,-2) {\isa{distrib{\isaliteral{5F}{\isacharunderscore}}lattice}};
+ \node (to) at (1.5,-2) {\isa{total{\isaliteral{5F}{\isacharunderscore}}order}};
\draw (po) -- (lat);
\draw (lat) -- (dlat);
\draw (lat) -- (to);
@@ -1229,10 +1229,10 @@
} \quad
\subfigure[Total orders are distributive lattices]{
\begin{tikzpicture}
- \node (po) at (0,0) {\isa{partial{\isacharunderscore}order}};
+ \node (po) at (0,0) {\isa{partial{\isaliteral{5F}{\isacharunderscore}}order}};
\node (lat) at (0,-1) {\isa{lattice}};
- \node (dlat) at (0,-2) {\isa{distrib{\isacharunderscore}lattice}};
- \node (to) at (0,-3) {\isa{total{\isacharunderscore}order}};
+ \node (dlat) at (0,-2) {\isa{distrib{\isaliteral{5F}{\isacharunderscore}}lattice}};
+ \node (to) at (0,-3) {\isa{total{\isaliteral{5F}{\isacharunderscore}}order}};
\draw (po) -- (lat);
\draw (lat) -- (dlat);
\draw (dlat) -- (to);
@@ -1269,7 +1269,7 @@
Consider the locale hierarchy from Figure~\ref{fig:lattices}(a).
Total orders are lattices, although this is not reflected here, and
definitions, theorems and other conclusions
- from \isa{lattice} are not available in \isa{total{\isacharunderscore}order}. To
+ from \isa{lattice} are not available in \isa{total{\isaliteral{5F}{\isacharunderscore}}order}. To
obtain the situation in Figure~\ref{fig:lattices}(b), it is
sufficient to add the conclusions of the latter locale to the former.
The \isakeyword{sublocale} command does exactly this.
@@ -1292,41 +1292,41 @@
%
\isatagvisible
\isacommand{sublocale}\isamarkupfalse%
-\ total{\isacharunderscore}order\ {\isasymsubseteq}\ lattice%
+\ total{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ lattice%
\begin{isamarkuptxt}%
\normalsize
- This enters the context of locale \isa{total{\isacharunderscore}order}, in
+ This enters the context of locale \isa{total{\isaliteral{5F}{\isacharunderscore}}order}, in
which the goal \begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ lattice\ op\ {\isasymsqsubseteq}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ lattice\ op\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}%
\end{isabelle} must be shown.
Now the
locale predicate needs to be unfolded --- for example, using its
definition or by introduction rules
provided by the locale package. For automation, the locale package
- provides the methods \isa{intro{\isacharunderscore}locales} and \isa{unfold{\isacharunderscore}locales}. They are aware of the
+ provides the methods \isa{intro{\isaliteral{5F}{\isacharunderscore}}locales} and \isa{unfold{\isaliteral{5F}{\isacharunderscore}}locales}. They are aware of the
current context and dependencies between locales and automatically
- discharge goals implied by these. While \isa{unfold{\isacharunderscore}locales}
- always unfolds locale predicates to assumptions, \isa{intro{\isacharunderscore}locales} only unfolds definitions along the locale
+ discharge goals implied by these. While \isa{unfold{\isaliteral{5F}{\isacharunderscore}}locales}
+ always unfolds locale predicates to assumptions, \isa{intro{\isaliteral{5F}{\isacharunderscore}}locales} only unfolds definitions along the locale
hierarchy, leaving a goal consisting of predicates defined by the
locale package. Occasionally the latter is of advantage since the goal
is smaller.
For the current goal, we would like to get hold of
the assumptions of \isa{lattice}, which need to be shown, hence
- \isa{unfold{\isacharunderscore}locales} is appropriate.%
+ \isa{unfold{\isaliteral{5F}{\isacharunderscore}}locales} is appropriate.%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \ \isacommand{proof}\isamarkupfalse%
-\ unfold{\isacharunderscore}locales%
+\ unfold{\isaliteral{5F}{\isacharunderscore}}locales%
\begin{isamarkuptxt}%
\normalsize
Since the fact that both lattices and total orders are partial
orders is already reflected in the locale hierarchy, the assumptions
- of \isa{partial{\isacharunderscore}order} are discharged automatically, and only the
+ of \isa{partial{\isaliteral{5F}{\isacharunderscore}}order} are discharged automatically, and only the
assumptions introduced in \isa{lattice} remain as subgoals
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ y{\isachardot}\ {\isasymexists}inf{\isachardot}\ is{\isacharunderscore}inf\ x\ y\ inf\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}x\ y{\isachardot}\ {\isasymexists}sup{\isachardot}\ is{\isacharunderscore}sup\ x\ y\ sup%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}inf{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ inf\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}sup{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ sup%
\end{isabelle}
The proof for the first subgoal is obtained by constructing an
infimum, whose existence is implied by totality.%
@@ -1336,12 +1336,12 @@
\ x\ y\isanewline
\ \ \ \ \isacommand{from}\isamarkupfalse%
\ total\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}is{\isacharunderscore}inf\ x\ y\ {\isacharparenleft}if\ x\ {\isasymsqsubseteq}\ y\ then\ x\ else\ y{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ {\isaliteral{28}{\isacharparenleft}}if\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ then\ x\ else\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}auto\ simp{\isacharcolon}\ is{\isacharunderscore}inf{\isacharunderscore}def{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}auto\ simp{\isaliteral{3A}{\isacharcolon}}\ is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymexists}inf{\isachardot}\ is{\isacharunderscore}inf\ x\ y\ inf{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}inf{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}inf\ x\ y\ inf{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\begin{isamarkuptxt}%
\normalsize
@@ -1368,12 +1368,12 @@
\ x\ y\isanewline
\ \ \ \ \isacommand{from}\isamarkupfalse%
\ total\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}is{\isacharunderscore}sup\ x\ y\ {\isacharparenleft}if\ x\ {\isasymsqsubseteq}\ y\ then\ y\ else\ x{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ {\isaliteral{28}{\isacharparenleft}}if\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ then\ y\ else\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}auto\ simp{\isacharcolon}\ is{\isacharunderscore}sup{\isacharunderscore}def{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}auto\ simp{\isaliteral{3A}{\isacharcolon}}\ is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymexists}sup{\isachardot}\ is{\isacharunderscore}sup\ x\ y\ sup{\isachardoublequoteclose}\ \isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}sup{\isaliteral{2E}{\isachardot}}\ is{\isaliteral{5F}{\isacharunderscore}}sup\ x\ y\ sup{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\endisataginvisible
{\isafoldinvisible}%
@@ -1402,7 +1402,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{sublocale}\isamarkupfalse%
-\ total{\isacharunderscore}order\ {\isasymsubseteq}\ distrib{\isacharunderscore}lattice\isanewline
+\ total{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ distrib{\isaliteral{5F}{\isacharunderscore}}lattice\isanewline
%
\isadelimproof
\ \ \ \ %
@@ -1410,62 +1410,62 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ unfold{\isacharunderscore}locales\isanewline
+\ unfold{\isaliteral{5F}{\isacharunderscore}}locales\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ x\ y\ z\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqinter}\ {\isacharparenleft}y\ {\isasymsqunion}\ z{\isacharparenright}\ {\isacharequal}\ x\ {\isasymsqinter}\ y\ {\isasymsqunion}\ x\ {\isasymsqinter}\ z{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isacharquery}l\ {\isacharequal}\ {\isacharquery}r{\isachardoublequoteclose}{\isacharparenright}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{is}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}l\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}r{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
Jacobson I, p.\ 462%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \ \ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
-\ \ \ \ \ \ \isacommand{{\isacharbraceleft}}\isamarkupfalse%
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
+\ \ \ \ \ \ \isacommand{{\isaliteral{7B}{\isacharbraceleft}}}\isamarkupfalse%
\ \isacommand{assume}\isamarkupfalse%
-\ c{\isacharcolon}\ {\isachardoublequoteopen}y\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\ {\isachardoublequoteopen}z\ {\isasymsqsubseteq}\ x{\isachardoublequoteclose}\isanewline
+\ c{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}z\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{from}\isamarkupfalse%
\ c\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}l\ {\isacharequal}\ y\ {\isasymsqunion}\ z{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}l\ {\isaliteral{3D}{\isacharequal}}\ y\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}metis\ c\ join{\isacharunderscore}connection{\isadigit{2}}\ join{\isacharunderscore}related{\isadigit{2}}\ meet{\isacharunderscore}related{\isadigit{2}}\ total{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}metis\ c\ join{\isaliteral{5F}{\isacharunderscore}}connection{\isadigit{2}}\ join{\isaliteral{5F}{\isacharunderscore}}related{\isadigit{2}}\ meet{\isaliteral{5F}{\isacharunderscore}}related{\isadigit{2}}\ total{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{from}\isamarkupfalse%
\ c\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isachardot}{\isachardot}{\isachardot}\ {\isacharequal}\ {\isacharquery}r{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}metis\ meet{\isacharunderscore}related{\isadigit{2}}{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}r{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}metis\ meet{\isaliteral{5F}{\isacharunderscore}}related{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}l\ {\isacharequal}\ {\isacharquery}r{\isachardoublequoteclose}\ \isacommand{{\isachardot}}\isamarkupfalse%
-\ \isacommand{{\isacharbraceright}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}l\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}r{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
+\ \isacommand{{\isaliteral{7D}{\isacharbraceright}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
-\ \ \ \ \ \ \isacommand{{\isacharbraceleft}}\isamarkupfalse%
+\ \ \ \ \ \ \isacommand{{\isaliteral{7B}{\isacharbraceleft}}}\isamarkupfalse%
\ \isacommand{assume}\isamarkupfalse%
-\ c{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y\ {\isasymor}\ x\ {\isasymsqsubseteq}\ z{\isachardoublequoteclose}\isanewline
+\ c{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C6F723E}{\isasymor}}\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{from}\isamarkupfalse%
\ c\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}l\ {\isacharequal}\ x{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}l\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}metis\ join{\isacharunderscore}connection{\isadigit{2}}\ join{\isacharunderscore}related{\isadigit{2}}\ meet{\isacharunderscore}connection\ total\ trans{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}metis\ join{\isaliteral{5F}{\isacharunderscore}}connection{\isadigit{2}}\ join{\isaliteral{5F}{\isacharunderscore}}related{\isadigit{2}}\ meet{\isaliteral{5F}{\isacharunderscore}}connection\ total\ trans{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{also}\isamarkupfalse%
\ \isacommand{from}\isamarkupfalse%
\ c\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isachardot}{\isachardot}{\isachardot}\ {\isacharequal}\ {\isacharquery}r{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}r{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}metis\ join{\isacharunderscore}commute\ join{\isacharunderscore}related{\isadigit{2}}\ meet{\isacharunderscore}connection\ meet{\isacharunderscore}related{\isadigit{2}}\ total{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}metis\ join{\isaliteral{5F}{\isacharunderscore}}commute\ join{\isaliteral{5F}{\isacharunderscore}}related{\isadigit{2}}\ meet{\isaliteral{5F}{\isacharunderscore}}connection\ meet{\isaliteral{5F}{\isacharunderscore}}related{\isadigit{2}}\ total{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \ \ \ \ \isacommand{finally}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharquery}l\ {\isacharequal}\ {\isacharquery}r{\isachardoublequoteclose}\ \isacommand{{\isachardot}}\isamarkupfalse%
-\ \isacommand{{\isacharbraceright}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{3F}{\isacharquery}}l\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}r{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
+\ \isacommand{{\isaliteral{7D}{\isacharbraceright}}}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\ \isacommand{note}\isamarkupfalse%
\ total\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isacharquery}thesis\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{3F}{\isacharquery}}thesis\ \isacommand{by}\isamarkupfalse%
\ blast\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
--- a/doc-src/Locales/Locales/document/Examples1.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/Locales/Locales/document/Examples1.tex Mon Nov 08 14:41:11 2010 +0100
@@ -42,8 +42,8 @@
Section~\ref{sec:local-interpretation}.
As an example, consider the type of integers \isa{int}. The
- relation \isa{op\ {\isasymle}} is a total order over \isa{int}. We start
- with the interpretation that \isa{op\ {\isasymle}} is a partial order. The
+ relation \isa{op\ {\isaliteral{5C3C6C653E}{\isasymle}}} is a total order over \isa{int}. We start
+ with the interpretation that \isa{op\ {\isaliteral{5C3C6C653E}{\isasymle}}} is a partial order. The
facilities of the interpretation command are explored gradually in
three versions.%
\end{isamarkuptext}%
@@ -57,7 +57,7 @@
\begin{isamarkuptext}%
The command \isakeyword{interpretation} is for the interpretation of
locale in theories. In the following example, the parameter of locale
- \isa{partial{\isacharunderscore}order} is replaced by \isa{op\ {\isasymle}} and the locale instance is interpreted in the current
+ \isa{partial{\isaliteral{5F}{\isacharunderscore}}order} is replaced by \isa{op\ {\isaliteral{5C3C6C653E}{\isasymle}}} and the locale instance is interpreted in the current
theory.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -68,12 +68,12 @@
%
\isatagvisible
\isacommand{interpretation}\isamarkupfalse%
-\ int{\isacharcolon}\ partial{\isacharunderscore}order\ {\isachardoublequoteopen}op\ {\isasymle}\ {\isacharcolon}{\isacharcolon}\ int\ {\isasymRightarrow}\ int\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}%
+\ int{\isaliteral{3A}{\isacharcolon}}\ partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{22}{\isachardoublequoteopen}}op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptxt}%
\normalsize
The argument of the command is a simple \emph{locale expression}
consisting of the name of the interpreted locale, which is
- preceded by the qualifier \isa{int{\isacharcolon}} and succeeded by a
+ preceded by the qualifier \isa{int{\isaliteral{3A}{\isacharcolon}}} and succeeded by a
white-space-separated list of terms, which provide a full
instantiation of the locale parameters. The parameters are referred
to by order of declaration, which is also the order in which
@@ -83,12 +83,12 @@
The command creates the goal
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ partial{\isacharunderscore}order\ op\ {\isasymle}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ partial{\isaliteral{5F}{\isacharunderscore}}order\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}%
\end{isabelle} which can be shown easily:%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ unfold{\isacharunderscore}locales\ auto%
+\ unfold{\isaliteral{5F}{\isacharunderscore}}locales\ auto%
\endisatagvisible
{\isafoldvisible}%
%
@@ -99,10 +99,10 @@
\begin{isamarkuptext}%
The effect of the command is that instances of all
conclusions of the locale are available in the theory, where names
- are prefixed by the qualifier. For example, transitivity for \isa{int} is named \isa{int{\isachardot}trans} and is the following
+ are prefixed by the qualifier. For example, transitivity for \isa{int} is named \isa{int{\isaliteral{2E}{\isachardot}}trans} and is the following
theorem:
\begin{isabelle}%
-\ \ {\isasymlbrakk}{\isacharquery}x\ {\isasymle}\ {\isacharquery}y{\isacharsemicolon}\ {\isacharquery}y\ {\isasymle}\ {\isacharquery}z{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}x\ {\isasymle}\ {\isacharquery}z%
+\ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3F}{\isacharquery}}y{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3F}{\isacharquery}}z{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3F}{\isacharquery}}z%
\end{isabelle}
It is not possible to reference this theorem simply as \isa{trans}. This prevents unwanted hiding of existing theorems of the
theory by an interpretation.%
@@ -117,20 +117,20 @@
Not only does the above interpretation qualify theorem names.
The prefix \isa{int} is applied to all names introduced in locale
conclusions including names introduced in definitions. The
- qualified name \isa{int{\isachardot}less} is short for
- the interpretation of the definition, which is \isa{partial{\isacharunderscore}order{\isachardot}less\ op\ {\isasymle}}.
+ qualified name \isa{int{\isaliteral{2E}{\isachardot}}less} is short for
+ the interpretation of the definition, which is \isa{partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}}.
Qualified name and expanded form may be used almost
interchangeably.%
-\footnote{Since \isa{op\ {\isasymle}} is polymorphic, for \isa{partial{\isacharunderscore}order{\isachardot}less\ op\ {\isasymle}} a
- more general type will be inferred than for \isa{int{\isachardot}less} which
+\footnote{Since \isa{op\ {\isaliteral{5C3C6C653E}{\isasymle}}} is polymorphic, for \isa{partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}} a
+ more general type will be inferred than for \isa{int{\isaliteral{2E}{\isachardot}}less} which
is over type \isa{int}.}
The latter is preferred on output, as for example in the theorem
- \isa{int{\isachardot}less{\isacharunderscore}le{\isacharunderscore}trans}: \begin{isabelle}%
-\ \ {\isasymlbrakk}partial{\isacharunderscore}order{\isachardot}less\ op\ {\isasymle}\ {\isacharquery}x\ {\isacharquery}y{\isacharsemicolon}\ {\isacharquery}y\ {\isasymle}\ {\isacharquery}z{\isasymrbrakk}\isanewline
-\isaindent{\ \ }{\isasymLongrightarrow}\ partial{\isacharunderscore}order{\isachardot}less\ op\ {\isasymle}\ {\isacharquery}x\ {\isacharquery}z%
+ \isa{int{\isaliteral{2E}{\isachardot}}less{\isaliteral{5F}{\isacharunderscore}}le{\isaliteral{5F}{\isacharunderscore}}trans}: \begin{isabelle}%
+\ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{3F}{\isacharquery}}y{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3F}{\isacharquery}}z{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ \ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{3F}{\isacharquery}}z%
\end{isabelle}
Both notations for the strict order are not satisfactory. The
- constant \isa{op\ {\isacharless}} is the strict order for \isa{int}.
+ constant \isa{op\ {\isaliteral{3C}{\isacharless}}} is the strict order for \isa{int}.
In order to allow for the desired replacement, interpretation
accepts \emph{equations} in addition to the parameter instantiation.
These follow the locale expression and are indicated with the
--- a/doc-src/Locales/Locales/document/Examples2.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/Locales/Locales/document/Examples2.tex Mon Nov 08 14:41:11 2010 +0100
@@ -29,32 +29,32 @@
%
\isatagvisible
\isacommand{interpretation}\isamarkupfalse%
-\ int{\isacharcolon}\ partial{\isacharunderscore}order\ {\isachardoublequoteopen}op\ {\isasymle}\ {\isacharcolon}{\isacharcolon}\ {\isacharbrackleft}int{\isacharcomma}\ int{\isacharbrackright}\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
-\ \ \ \ \isakeyword{where}\ {\isachardoublequoteopen}partial{\isacharunderscore}order{\isachardot}less\ op\ {\isasymle}\ {\isacharparenleft}x{\isacharcolon}{\isacharcolon}int{\isacharparenright}\ y\ {\isacharequal}\ {\isacharparenleft}x\ {\isacharless}\ y{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ int{\isaliteral{3A}{\isacharcolon}}\ partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{22}{\isachardoublequoteopen}}op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5B}{\isacharbrackleft}}int{\isaliteral{2C}{\isacharcomma}}\ int{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}int{\isaliteral{29}{\isacharparenright}}\ y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3C}{\isacharless}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}%
+\ {\isaliteral{2D}{\isacharminus}}%
\begin{isamarkuptxt}%
\normalsize The goals are now:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ partial{\isacharunderscore}order\ op\ {\isasymle}\isanewline
-\ {\isadigit{2}}{\isachardot}\ partial{\isacharunderscore}order{\isachardot}less\ op\ {\isasymle}\ x\ y\ {\isacharequal}\ {\isacharparenleft}x\ {\isacharless}\ y{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ partial{\isaliteral{5F}{\isacharunderscore}}order\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ x\ y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3C}{\isacharless}}\ y{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
- The proof that~\isa{{\isasymle}} is a partial order is as above.%
+ The proof that~\isa{{\isaliteral{5C3C6C653E}{\isasymle}}} is a partial order is as above.%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}partial{\isacharunderscore}order\ {\isacharparenleft}op\ {\isasymle}\ {\isacharcolon}{\isacharcolon}\ int\ {\isasymRightarrow}\ int\ {\isasymRightarrow}\ bool{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{28}{\isacharparenleft}}op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
-\ unfold{\isacharunderscore}locales\ auto%
+\ unfold{\isaliteral{5F}{\isacharunderscore}}locales\ auto%
\begin{isamarkuptxt}%
\normalsize The second goal is shown by unfolding the
- definition of \isa{partial{\isacharunderscore}order{\isachardot}less}.%
+ definition of \isa{partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less}.%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}partial{\isacharunderscore}order{\isachardot}less\ op\ {\isasymle}\ {\isacharparenleft}x{\isacharcolon}{\isacharcolon}int{\isacharparenright}\ y\ {\isacharequal}\ {\isacharparenleft}x\ {\isacharless}\ y{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}int{\isaliteral{29}{\isacharparenright}}\ y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3C}{\isacharless}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{unfolding}\isamarkupfalse%
-\ partial{\isacharunderscore}order{\isachardot}less{\isacharunderscore}def\ {\isacharbrackleft}OF\ {\isacharbackquoteopen}partial{\isacharunderscore}order\ op\ {\isasymle}{\isacharbackquoteclose}{\isacharbrackright}\isanewline
+\ partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less{\isaliteral{5F}{\isacharunderscore}}def\ {\isaliteral{5B}{\isacharbrackleft}}OF\ {\isaliteral{60}{\isacharbackquoteopen}}partial{\isaliteral{5F}{\isacharunderscore}}order\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}{\isaliteral{60}{\isacharbackquoteclose}}{\isaliteral{5D}{\isacharbrackright}}\isanewline
\ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
@@ -68,7 +68,7 @@
%
\begin{isamarkuptext}%
Note that the above proof is not in the context of the
- interpreted locale. Hence, the premise of \isa{partial{\isacharunderscore}order{\isachardot}less{\isacharunderscore}def} is discharged manually with \isa{OF}.%
+ interpreted locale. Hence, the premise of \isa{partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less{\isaliteral{5F}{\isacharunderscore}}def} is discharged manually with \isa{OF}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
--- a/doc-src/Locales/Locales/document/Examples3.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/Locales/Locales/document/Examples3.tex Mon Nov 08 14:41:11 2010 +0100
@@ -29,9 +29,9 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-In the above example, the fact that \isa{op\ {\isasymle}} is a partial
+In the above example, the fact that \isa{op\ {\isaliteral{5C3C6C653E}{\isasymle}}} is a partial
order for the integers was used in the second goal to
- discharge the premise in the definition of \isa{op\ {\isasymsqsubset}}. In
+ discharge the premise in the definition of \isa{op\ {\isaliteral{5C3C73717375627365743E}{\isasymsqsubset}}}. In
general, proofs of the equations not only may involve definitions
from the interpreted locale but arbitrarily complex arguments in the
context of the locale. Therefore is would be convenient to have the
@@ -48,22 +48,22 @@
%
\isatagvisible
\isacommand{interpretation}\isamarkupfalse%
-\ int{\isacharcolon}\ partial{\isacharunderscore}order\ {\isachardoublequoteopen}op\ {\isasymle}\ {\isacharcolon}{\isacharcolon}\ int\ {\isasymRightarrow}\ int\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
-\ \ \ \ \isakeyword{where}\ {\isachardoublequoteopen}partial{\isacharunderscore}order{\isachardot}less\ op\ {\isasymle}\ {\isacharparenleft}x{\isacharcolon}{\isacharcolon}int{\isacharparenright}\ y\ {\isacharequal}\ {\isacharparenleft}x\ {\isacharless}\ y{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ int{\isaliteral{3A}{\isacharcolon}}\ partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{22}{\isachardoublequoteopen}}op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}int{\isaliteral{29}{\isacharparenright}}\ y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3C}{\isacharless}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}partial{\isacharunderscore}order\ {\isacharparenleft}op\ {\isasymle}\ {\isacharcolon}{\isacharcolon}\ int\ {\isasymRightarrow}\ int\ {\isasymRightarrow}\ bool{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{28}{\isacharparenleft}}op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
-\ unfold{\isacharunderscore}locales\ auto\isanewline
+\ unfold{\isaliteral{5F}{\isacharunderscore}}locales\ auto\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{interpret}\isamarkupfalse%
-\ int{\isacharcolon}\ partial{\isacharunderscore}order\ {\isachardoublequoteopen}op\ {\isasymle}\ {\isacharcolon}{\isacharcolon}\ {\isacharbrackleft}int{\isacharcomma}\ int{\isacharbrackright}\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ int{\isaliteral{3A}{\isacharcolon}}\ partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{22}{\isachardoublequoteopen}}op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5B}{\isacharbrackleft}}int{\isaliteral{2C}{\isacharcomma}}\ int{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}partial{\isacharunderscore}order{\isachardot}less\ op\ {\isasymle}\ {\isacharparenleft}x{\isacharcolon}{\isacharcolon}int{\isacharparenright}\ y\ {\isacharequal}\ {\isacharparenleft}x\ {\isacharless}\ y{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}int{\isaliteral{29}{\isacharparenright}}\ y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3C}{\isacharless}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{unfolding}\isamarkupfalse%
-\ int{\isachardot}less{\isacharunderscore}def\ \isacommand{by}\isamarkupfalse%
+\ int{\isaliteral{2E}{\isachardot}}less{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
%
@@ -79,7 +79,7 @@
and proved by assumption (Isar short hand ``.''). It enriches the
local proof context by the theorems
also obtained in the interpretation from Section~\ref{sec:po-first},
- and \isa{int{\isachardot}less{\isacharunderscore}def} may directly be used to unfold the
+ and \isa{int{\isaliteral{2E}{\isachardot}}less{\isaliteral{5F}{\isacharunderscore}}def} may directly be used to unfold the
definition. Theorems from the local interpretation disappear after
leaving the proof context --- that is, after the succeeding
\isakeyword{next} or \isakeyword{qed} statement.%
@@ -92,8 +92,8 @@
%
\begin{isamarkuptext}%
Further interpretations are necessary for
- the other locales. In \isa{lattice} the operations~\isa{{\isasymsqinter}}
- and~\isa{{\isasymsqunion}} are substituted by \isa{min}
+ the other locales. In \isa{lattice} the operations~\isa{{\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}}
+ and~\isa{{\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}} are substituted by \isa{min}
and \isa{max}. The entire proof for the
interpretation is reproduced to give an example of a more
elaborate interpretation proof. Note that the equations are named
@@ -107,45 +107,45 @@
%
\isatagvisible
\isacommand{interpretation}\isamarkupfalse%
-\ int{\isacharcolon}\ lattice\ {\isachardoublequoteopen}op\ {\isasymle}\ {\isacharcolon}{\isacharcolon}\ int\ {\isasymRightarrow}\ int\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
-\ \ \ \ \isakeyword{where}\ int{\isacharunderscore}min{\isacharunderscore}eq{\isacharcolon}\ {\isachardoublequoteopen}lattice{\isachardot}meet\ op\ {\isasymle}\ {\isacharparenleft}x{\isacharcolon}{\isacharcolon}int{\isacharparenright}\ y\ {\isacharequal}\ min\ x\ y{\isachardoublequoteclose}\isanewline
-\ \ \ \ \ \ \isakeyword{and}\ int{\isacharunderscore}max{\isacharunderscore}eq{\isacharcolon}\ {\isachardoublequoteopen}lattice{\isachardot}join\ op\ {\isasymle}\ {\isacharparenleft}x{\isacharcolon}{\isacharcolon}int{\isacharparenright}\ y\ {\isacharequal}\ max\ x\ y{\isachardoublequoteclose}\isanewline
+\ int{\isaliteral{3A}{\isacharcolon}}\ lattice\ {\isaliteral{22}{\isachardoublequoteopen}}op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \isakeyword{where}\ int{\isaliteral{5F}{\isacharunderscore}}min{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}lattice{\isaliteral{2E}{\isachardot}}meet\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}int{\isaliteral{29}{\isacharparenright}}\ y\ {\isaliteral{3D}{\isacharequal}}\ min\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \ \ \isakeyword{and}\ int{\isaliteral{5F}{\isacharunderscore}}max{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}lattice{\isaliteral{2E}{\isachardot}}join\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}int{\isaliteral{29}{\isacharparenright}}\ y\ {\isaliteral{3D}{\isacharequal}}\ max\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharminus}\isanewline
+\ {\isaliteral{2D}{\isacharminus}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}lattice\ {\isacharparenleft}op\ {\isasymle}\ {\isacharcolon}{\isacharcolon}\ int\ {\isasymRightarrow}\ int\ {\isasymRightarrow}\ bool{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}lattice\ {\isaliteral{28}{\isacharparenleft}}op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptxt}%
\normalsize We have already shown that this is a partial
order,%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \ \ \ \ \ \isacommand{apply}\isamarkupfalse%
-\ unfold{\isacharunderscore}locales%
+\ unfold{\isaliteral{5F}{\isacharunderscore}}locales%
\begin{isamarkuptxt}%
\normalsize hence only the lattice axioms remain to be
shown.
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ y{\isachardot}\ {\isasymexists}inf{\isachardot}\ partial{\isacharunderscore}order{\isachardot}is{\isacharunderscore}inf\ op\ {\isasymle}\ x\ y\ inf\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}x\ y{\isachardot}\ {\isasymexists}sup{\isachardot}\ partial{\isacharunderscore}order{\isachardot}is{\isacharunderscore}sup\ op\ {\isasymle}\ x\ y\ sup%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}inf{\isaliteral{2E}{\isachardot}}\ partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}is{\isaliteral{5F}{\isacharunderscore}}inf\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ x\ y\ inf\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}sup{\isaliteral{2E}{\isachardot}}\ partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}is{\isaliteral{5F}{\isacharunderscore}}sup\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ x\ y\ sup%
\end{isabelle}
- By \isa{is{\isacharunderscore}inf} and \isa{is{\isacharunderscore}sup},%
+ By \isa{is{\isaliteral{5F}{\isacharunderscore}}inf} and \isa{is{\isaliteral{5F}{\isacharunderscore}}sup},%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \ \ \ \ \ \isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}unfold\ int{\isachardot}is{\isacharunderscore}inf{\isacharunderscore}def\ int{\isachardot}is{\isacharunderscore}sup{\isacharunderscore}def{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}unfold\ int{\isaliteral{2E}{\isachardot}}is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}def\ int{\isaliteral{2E}{\isachardot}}is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\normalsize the goals are transformed to these
statements:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ y{\isachardot}\ {\isasymexists}inf{\isasymle}x{\isachardot}\ inf\ {\isasymle}\ y\ {\isasymand}\ {\isacharparenleft}{\isasymforall}z{\isachardot}\ z\ {\isasymle}\ x\ {\isasymand}\ z\ {\isasymle}\ y\ {\isasymlongrightarrow}\ z\ {\isasymle}\ inf{\isacharparenright}\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}x\ y{\isachardot}\ {\isasymexists}sup{\isasymge}x{\isachardot}\ y\ {\isasymle}\ sup\ {\isasymand}\ {\isacharparenleft}{\isasymforall}z{\isachardot}\ x\ {\isasymle}\ z\ {\isasymand}\ y\ {\isasymle}\ z\ {\isasymlongrightarrow}\ sup\ {\isasymle}\ z{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}inf{\isaliteral{5C3C6C653E}{\isasymle}}x{\isaliteral{2E}{\isachardot}}\ inf\ {\isaliteral{5C3C6C653E}{\isasymle}}\ y\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}z{\isaliteral{2E}{\isachardot}}\ z\ {\isaliteral{5C3C6C653E}{\isasymle}}\ x\ {\isaliteral{5C3C616E643E}{\isasymand}}\ z\ {\isaliteral{5C3C6C653E}{\isasymle}}\ y\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ z\ {\isaliteral{5C3C6C653E}{\isasymle}}\ inf{\isaliteral{29}{\isacharparenright}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}sup{\isaliteral{5C3C67653E}{\isasymge}}x{\isaliteral{2E}{\isachardot}}\ y\ {\isaliteral{5C3C6C653E}{\isasymle}}\ sup\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}z{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C6C653E}{\isasymle}}\ z\ {\isaliteral{5C3C616E643E}{\isasymand}}\ y\ {\isaliteral{5C3C6C653E}{\isasymle}}\ z\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ sup\ {\isaliteral{5C3C6C653E}{\isasymle}}\ z{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
This is Presburger arithmetic, which can be solved by the
method \isa{arith}.%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
-\ arith{\isacharplus}%
+\ arith{\isaliteral{2B}{\isacharplus}}%
\begin{isamarkuptxt}%
\normalsize In order to show the equations, we put ourselves
in a situation where the lattice theorems can be used in a
@@ -154,16 +154,16 @@
\isamarkuptrue%
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{interpret}\isamarkupfalse%
-\ int{\isacharcolon}\ lattice\ {\isachardoublequoteopen}op\ {\isasymle}\ {\isacharcolon}{\isacharcolon}\ int\ {\isasymRightarrow}\ int\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ int{\isaliteral{3A}{\isacharcolon}}\ lattice\ {\isaliteral{22}{\isachardoublequoteopen}}op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}lattice{\isachardot}meet\ op\ {\isasymle}\ {\isacharparenleft}x{\isacharcolon}{\isacharcolon}int{\isacharparenright}\ y\ {\isacharequal}\ min\ x\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}lattice{\isaliteral{2E}{\isachardot}}meet\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}int{\isaliteral{29}{\isacharparenright}}\ y\ {\isaliteral{3D}{\isacharequal}}\ min\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}bestsimp\ simp{\isacharcolon}\ int{\isachardot}meet{\isacharunderscore}def\ int{\isachardot}is{\isacharunderscore}inf{\isacharunderscore}def{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}bestsimp\ simp{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{2E}{\isachardot}}meet{\isaliteral{5F}{\isacharunderscore}}def\ int{\isaliteral{2E}{\isachardot}}is{\isaliteral{5F}{\isacharunderscore}}inf{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}lattice{\isachardot}join\ op\ {\isasymle}\ {\isacharparenleft}x{\isacharcolon}{\isacharcolon}int{\isacharparenright}\ y\ {\isacharequal}\ max\ x\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}lattice{\isaliteral{2E}{\isachardot}}join\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}int{\isaliteral{29}{\isacharparenright}}\ y\ {\isaliteral{3D}{\isacharequal}}\ max\ x\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}bestsimp\ simp{\isacharcolon}\ int{\isachardot}join{\isacharunderscore}def\ int{\isachardot}is{\isacharunderscore}sup{\isacharunderscore}def{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}bestsimp\ simp{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{2E}{\isachardot}}join{\isaliteral{5F}{\isacharunderscore}}def\ int{\isaliteral{2E}{\isachardot}}is{\isaliteral{5F}{\isacharunderscore}}sup{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
%
\endisatagvisible
@@ -174,7 +174,7 @@
\endisadelimvisible
%
\begin{isamarkuptext}%
-Next follows that \isa{op\ {\isasymle}} is a total order, again for
+Next follows that \isa{op\ {\isaliteral{5C3C6C653E}{\isasymle}}} is a total order, again for
the integers.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -185,9 +185,9 @@
%
\isatagvisible
\isacommand{interpretation}\isamarkupfalse%
-\ int{\isacharcolon}\ total{\isacharunderscore}order\ {\isachardoublequoteopen}op\ {\isasymle}\ {\isacharcolon}{\isacharcolon}\ int\ {\isasymRightarrow}\ int\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
+\ int{\isaliteral{3A}{\isacharcolon}}\ total{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{22}{\isachardoublequoteopen}}op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ unfold{\isacharunderscore}locales\ arith%
+\ unfold{\isaliteral{5F}{\isacharunderscore}}locales\ arith%
\endisatagvisible
{\isafoldvisible}%
%
@@ -204,24 +204,24 @@
\vspace{2ex}
\begin{center}
\begin{tabular}{l}
- \isa{int{\isachardot}less{\isacharunderscore}def} from locale \isa{partial{\isacharunderscore}order}: \\
- \quad \isa{{\isacharparenleft}{\isacharquery}x\ {\isacharless}\ {\isacharquery}y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isacharquery}x\ {\isasymle}\ {\isacharquery}y\ {\isasymand}\ {\isacharquery}x\ {\isasymnoteq}\ {\isacharquery}y{\isacharparenright}} \\
- \isa{int{\isachardot}meet{\isacharunderscore}left} from locale \isa{lattice}: \\
- \quad \isa{min\ {\isacharquery}x\ {\isacharquery}y\ {\isasymle}\ {\isacharquery}x} \\
- \isa{int{\isachardot}join{\isacharunderscore}distr} from locale \isa{distrib{\isacharunderscore}lattice}: \\
- \quad \isa{max\ {\isacharquery}x\ {\isacharparenleft}min\ {\isacharquery}y\ {\isacharquery}z{\isacharparenright}\ {\isacharequal}\ min\ {\isacharparenleft}max\ {\isacharquery}x\ {\isacharquery}y{\isacharparenright}\ {\isacharparenleft}max\ {\isacharquery}x\ {\isacharquery}z{\isacharparenright}} \\
- \isa{int{\isachardot}less{\isacharunderscore}total} from locale \isa{total{\isacharunderscore}order}: \\
- \quad \isa{{\isacharquery}x\ {\isacharless}\ {\isacharquery}y\ {\isasymor}\ {\isacharquery}x\ {\isacharequal}\ {\isacharquery}y\ {\isasymor}\ {\isacharquery}y\ {\isacharless}\ {\isacharquery}x}
+ \isa{int{\isaliteral{2E}{\isachardot}}less{\isaliteral{5F}{\isacharunderscore}}def} from locale \isa{partial{\isaliteral{5F}{\isacharunderscore}}order}: \\
+ \quad \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{3C}{\isacharless}}\ {\isaliteral{3F}{\isacharquery}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{3F}{\isacharquery}}y{\isaliteral{29}{\isacharparenright}}} \\
+ \isa{int{\isaliteral{2E}{\isachardot}}meet{\isaliteral{5F}{\isacharunderscore}}left} from locale \isa{lattice}: \\
+ \quad \isa{min\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3F}{\isacharquery}}x} \\
+ \isa{int{\isaliteral{2E}{\isachardot}}join{\isaliteral{5F}{\isacharunderscore}}distr} from locale \isa{distrib{\isaliteral{5F}{\isacharunderscore}}lattice}: \\
+ \quad \isa{max\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{28}{\isacharparenleft}}min\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{3F}{\isacharquery}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ min\ {\isaliteral{28}{\isacharparenleft}}max\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{3F}{\isacharquery}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}max\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{3F}{\isacharquery}}z{\isaliteral{29}{\isacharparenright}}} \\
+ \isa{int{\isaliteral{2E}{\isachardot}}less{\isaliteral{5F}{\isacharunderscore}}total} from locale \isa{total{\isaliteral{5F}{\isacharunderscore}}order}: \\
+ \quad \isa{{\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{3C}{\isacharless}}\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{3C}{\isacharless}}\ {\isaliteral{3F}{\isacharquery}}x}
\end{tabular}
\end{center}
\hrule
-\caption{Interpreted theorems for~\isa{{\isasymle}} on the integers.}
+\caption{Interpreted theorems for~\isa{{\isaliteral{5C3C6C653E}{\isasymle}}} on the integers.}
\label{tab:int-lattice}
\end{table}
\begin{itemize}
\item
- Locale \isa{distrib{\isacharunderscore}lattice} was also interpreted. Since the
+ Locale \isa{distrib{\isaliteral{5F}{\isacharunderscore}}lattice} was also interpreted. Since the
locale hierarchy reflects that total orders are distributive
lattices, the interpretation of the latter was inserted
automatically with the interpretation of the former. In general,
@@ -230,9 +230,9 @@
the \isakeyword{sublocale} command. Existing interpretations are
skipped avoiding duplicate work.
\item
- The predicate \isa{op\ {\isacharless}} appears in theorem \isa{int{\isachardot}less{\isacharunderscore}total}
- although an equation for the replacement of \isa{op\ {\isasymsqsubset}} was only
- given in the interpretation of \isa{partial{\isacharunderscore}order}. The
+ The predicate \isa{op\ {\isaliteral{3C}{\isacharless}}} appears in theorem \isa{int{\isaliteral{2E}{\isachardot}}less{\isaliteral{5F}{\isacharunderscore}}total}
+ although an equation for the replacement of \isa{op\ {\isaliteral{5C3C73717375627365743E}{\isasymsqsubset}}} was only
+ given in the interpretation of \isa{partial{\isaliteral{5F}{\isacharunderscore}}order}. The
interpretation equations are pushed downwards the hierarchy for
related interpretations --- that is, for interpretations that share
the instances of parameters they have in common.
@@ -244,7 +244,7 @@
The interpretations for a locale $n$ within the current
theory may be inspected with \isakeyword{print\_interps}~$n$. This
prints the list of instances of $n$, for which interpretations exist.
- For example, \isakeyword{print\_interps} \isa{partial{\isacharunderscore}order}
+ For example, \isakeyword{print\_interps} \isa{partial{\isaliteral{5F}{\isacharunderscore}}order}
outputs the following:
\begin{small}
\begin{alltt}
@@ -268,18 +268,18 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-A map~\isa{{\isasymphi}} between partial orders~\isa{{\isasymsqsubseteq}} and~\isa{{\isasympreceq}}
- is called order preserving if \isa{x\ {\isasymsqsubseteq}\ y} implies \isa{{\isasymphi}\ x\ {\isasympreceq}\ {\isasymphi}\ y}. This situation is more complex than those encountered so
+A map~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} between partial orders~\isa{{\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}} and~\isa{{\isaliteral{5C3C7072656365713E}{\isasympreceq}}}
+ is called order preserving if \isa{x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y} implies \isa{{\isaliteral{5C3C7068693E}{\isasymphi}}\ x\ {\isaliteral{5C3C7072656365713E}{\isasympreceq}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\ y}. This situation is more complex than those encountered so
far: it involves two partial orders, and it is desirable to use the
existing locale for both.
- A locale for order preserving maps requires three parameters: \isa{le}~(\isakeyword{infixl}~\isa{{\isasymsqsubseteq}}) and \isa{le{\isacharprime}}~(\isakeyword{infixl}~\isa{{\isasympreceq}}) for the orders and~\isa{{\isasymphi}}
+ A locale for order preserving maps requires three parameters: \isa{le}~(\isakeyword{infixl}~\isa{{\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}}) and \isa{le{\isaliteral{27}{\isacharprime}}}~(\isakeyword{infixl}~\isa{{\isaliteral{5C3C7072656365713E}{\isasympreceq}}}) for the orders and~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}}
for the map.
In order to reuse the existing locale for partial orders, which has
the single parameter~\isa{le}, it must be imported twice, once
mapping its parameter to~\isa{le} from the new locale and once
- to~\isa{le{\isacharprime}}. This can be achieved with a compound locale
+ to~\isa{le{\isaliteral{27}{\isacharprime}}}. This can be achieved with a compound locale
expression.
In general, a locale expression is a sequence of \emph{locale instances}
@@ -298,7 +298,7 @@
import and in the \isakeyword{sublocale} command, they default to
optional.
- Since the parameters~\isa{le} and~\isa{le{\isacharprime}} are to be partial
+ Since the parameters~\isa{le} and~\isa{le{\isaliteral{27}{\isacharprime}}} are to be partial
orders, our locale for order preserving maps will import the these
instances:
\begin{small}
@@ -319,45 +319,45 @@
clause. The \isakeyword{for} clause is also where the syntax of these
parameters is declared.
- Two context elements for the map parameter~\isa{{\isasymphi}} and the
+ Two context elements for the map parameter~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} and the
assumptions that it is order preserving complete the locale
declaration.%
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{locale}\isamarkupfalse%
-\ order{\isacharunderscore}preserving\ {\isacharequal}\isanewline
-\ \ \ \ le{\isacharcolon}\ partial{\isacharunderscore}order\ le\ {\isacharplus}\ le{\isacharprime}{\isacharcolon}\ partial{\isacharunderscore}order\ le{\isacharprime}\isanewline
-\ \ \ \ \ \ \isakeyword{for}\ le\ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasymsqsubseteq}{\isachardoublequoteclose}\ {\isadigit{5}}{\isadigit{0}}{\isacharparenright}\ \isakeyword{and}\ le{\isacharprime}\ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasympreceq}{\isachardoublequoteclose}\ {\isadigit{5}}{\isadigit{0}}{\isacharparenright}\ {\isacharplus}\isanewline
-\ \ \ \ \isakeyword{fixes}\ {\isasymphi}\isanewline
-\ \ \ \ \isakeyword{assumes}\ hom{\isacharunderscore}le{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y\ {\isasymLongrightarrow}\ {\isasymphi}\ x\ {\isasympreceq}\ {\isasymphi}\ y{\isachardoublequoteclose}%
+\ order{\isaliteral{5F}{\isacharunderscore}}preserving\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ le{\isaliteral{3A}{\isacharcolon}}\ partial{\isaliteral{5F}{\isacharunderscore}}order\ le\ {\isaliteral{2B}{\isacharplus}}\ le{\isaliteral{27}{\isacharprime}}{\isaliteral{3A}{\isacharcolon}}\ partial{\isaliteral{5F}{\isacharunderscore}}order\ le{\isaliteral{27}{\isacharprime}}\isanewline
+\ \ \ \ \ \ \isakeyword{for}\ le\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{5}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ \isakeyword{and}\ le{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C7072656365713E}{\isasympreceq}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{5}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\isanewline
+\ \ \ \ \isakeyword{fixes}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isanewline
+\ \ \ \ \isakeyword{assumes}\ hom{\isaliteral{5F}{\isacharunderscore}}le{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\ x\ {\isaliteral{5C3C7072656365713E}{\isasympreceq}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\ y{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
Here are examples of theorems that are
available in the locale:
- \hspace*{1em}\isa{hom{\isacharunderscore}le}: \isa{{\isacharquery}x\ {\isasymsqsubseteq}\ {\isacharquery}y\ {\isasymLongrightarrow}\ {\isasymphi}\ {\isacharquery}x\ {\isasympreceq}\ {\isasymphi}\ {\isacharquery}y}
+ \hspace*{1em}\isa{hom{\isaliteral{5F}{\isacharunderscore}}le}: \isa{{\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C7072656365713E}{\isasympreceq}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\ {\isaliteral{3F}{\isacharquery}}y}
- \hspace*{1em}\isa{le{\isachardot}less{\isacharunderscore}le{\isacharunderscore}trans}: \isa{{\isasymlbrakk}{\isacharquery}x\ {\isasymsqsubset}\ {\isacharquery}y{\isacharsemicolon}\ {\isacharquery}y\ {\isasymsqsubseteq}\ {\isacharquery}z{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}x\ {\isasymsqsubset}\ {\isacharquery}z}
+ \hspace*{1em}\isa{le{\isaliteral{2E}{\isachardot}}less{\isaliteral{5F}{\isacharunderscore}}le{\isaliteral{5F}{\isacharunderscore}}trans}: \isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C73717375627365743E}{\isasymsqsubset}}\ {\isaliteral{3F}{\isacharquery}}y{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ {\isaliteral{3F}{\isacharquery}}z{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C73717375627365743E}{\isasymsqsubset}}\ {\isaliteral{3F}{\isacharquery}}z}
- \hspace*{1em}\isa{le{\isacharprime}{\isachardot}less{\isacharunderscore}le{\isacharunderscore}trans}:
+ \hspace*{1em}\isa{le{\isaliteral{27}{\isacharprime}}{\isaliteral{2E}{\isachardot}}less{\isaliteral{5F}{\isacharunderscore}}le{\isaliteral{5F}{\isacharunderscore}}trans}:
\begin{isabelle}%
-\ \ \ \ {\isasymlbrakk}partial{\isacharunderscore}order{\isachardot}less\ op\ {\isasympreceq}\ {\isacharquery}x\ {\isacharquery}y{\isacharsemicolon}\ {\isacharquery}y\ {\isasympreceq}\ {\isacharquery}z{\isasymrbrakk}\isanewline
-\isaindent{\ \ \ \ }{\isasymLongrightarrow}\ partial{\isacharunderscore}order{\isachardot}less\ op\ {\isasympreceq}\ {\isacharquery}x\ {\isacharquery}z%
+\ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ op\ {\isaliteral{5C3C7072656365713E}{\isasympreceq}}\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{3F}{\isacharquery}}y{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{5C3C7072656365713E}{\isasympreceq}}\ {\isaliteral{3F}{\isacharquery}}z{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ \ \ \ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ op\ {\isaliteral{5C3C7072656365713E}{\isasympreceq}}\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{3F}{\isacharquery}}z%
\end{isabelle}
While there is infix syntax for the strict operation associated to
- \isa{op\ {\isasymsqsubseteq}}, there is none for the strict version of \isa{op\ {\isasympreceq}}. The abbreviation \isa{less} with its infix syntax is only
+ \isa{op\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}}, there is none for the strict version of \isa{op\ {\isaliteral{5C3C7072656365713E}{\isasympreceq}}}. The abbreviation \isa{less} with its infix syntax is only
available for the original instance it was declared for. We may
- introduce the abbreviation \isa{less{\isacharprime}} with infix syntax~\isa{{\isasymprec}}
+ introduce the abbreviation \isa{less{\isaliteral{27}{\isacharprime}}} with infix syntax~\isa{{\isaliteral{5C3C707265633E}{\isasymprec}}}
with the following declaration:%
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{abbreviation}\isamarkupfalse%
-\ {\isacharparenleft}\isakeyword{in}\ order{\isacharunderscore}preserving{\isacharparenright}\isanewline
-\ \ \ \ less{\isacharprime}\ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasymprec}{\isachardoublequoteclose}\ {\isadigit{5}}{\isadigit{0}}{\isacharparenright}\ \isakeyword{where}\ {\isachardoublequoteopen}less{\isacharprime}\ {\isasymequiv}\ partial{\isacharunderscore}order{\isachardot}less\ le{\isacharprime}{\isachardoublequoteclose}%
+\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{in}\ order{\isaliteral{5F}{\isacharunderscore}}preserving{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ less{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C707265633E}{\isasymprec}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{5}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}less{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ le{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
Now the theorem is displayed nicely as
- \isa{le{\isacharprime}{\isachardot}less{\isacharunderscore}le{\isacharunderscore}trans}:
+ \isa{le{\isaliteral{27}{\isacharprime}}{\isaliteral{2E}{\isachardot}}less{\isaliteral{5F}{\isacharunderscore}}le{\isaliteral{5F}{\isacharunderscore}}trans}:
\begin{isabelle}%
-\ \ {\isasymlbrakk}{\isacharquery}x\ {\isasymprec}\ {\isacharquery}y{\isacharsemicolon}\ {\isacharquery}y\ {\isasympreceq}\ {\isacharquery}z{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}x\ {\isasymprec}\ {\isacharquery}z%
+\ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C707265633E}{\isasymprec}}\ {\isaliteral{3F}{\isacharquery}}y{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{5C3C7072656365713E}{\isasympreceq}}\ {\isaliteral{3F}{\isacharquery}}z{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C707265633E}{\isasymprec}}\ {\isaliteral{3F}{\isacharquery}}z%
\end{isabelle}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -375,7 +375,7 @@
\begin{isamarkuptext}%
It is possible to omit parameter instantiations. The
instantiation then defaults to the name of
- the parameter itself. For example, the locale expression \isa{partial{\isacharunderscore}order} is short for \isa{partial{\isacharunderscore}order\ le}, since the
+ the parameter itself. For example, the locale expression \isa{partial{\isaliteral{5F}{\isacharunderscore}}order} is short for \isa{partial{\isaliteral{5F}{\isacharunderscore}}order\ le}, since the
locale's single parameter is~\isa{le}. We took advantage of this
in the \isakeyword{sublocale} declarations of
Section~\ref{sec:changing-the-hierarchy}.%
@@ -405,7 +405,7 @@
locale parameters for which no parameter instantiation is given are
implicitly added, with their mixfix syntax, at the beginning of the
\isakeyword{for} clause. For example, in a locale declaration, the
- expression \isa{partial{\isacharunderscore}order} is short for
+ expression \isa{partial{\isaliteral{5F}{\isacharunderscore}}order} is short for
\begin{small}
\begin{alltt}
partial_order le \isakeyword{for} le (\isakeyword{infixl} "\(\sqsubseteq\)" 50)\textrm{.}
@@ -418,20 +418,20 @@
%
\begin{isamarkuptext}%
The following locale declarations provide more examples. A
- map~\isa{{\isasymphi}} is a lattice homomorphism if it preserves meet and
+ map~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}} is a lattice homomorphism if it preserves meet and
join.%
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{locale}\isamarkupfalse%
-\ lattice{\isacharunderscore}hom\ {\isacharequal}\isanewline
-\ \ \ \ le{\isacharcolon}\ lattice\ {\isacharplus}\ le{\isacharprime}{\isacharcolon}\ lattice\ le{\isacharprime}\ \isakeyword{for}\ le{\isacharprime}\ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasympreceq}{\isachardoublequoteclose}\ {\isadigit{5}}{\isadigit{0}}{\isacharparenright}\ {\isacharplus}\isanewline
-\ \ \ \ \isakeyword{fixes}\ {\isasymphi}\isanewline
-\ \ \ \ \isakeyword{assumes}\ hom{\isacharunderscore}meet{\isacharcolon}\ {\isachardoublequoteopen}{\isasymphi}\ {\isacharparenleft}x\ {\isasymsqinter}\ y{\isacharparenright}\ {\isacharequal}\ le{\isacharprime}{\isachardot}meet\ {\isacharparenleft}{\isasymphi}\ x{\isacharparenright}\ {\isacharparenleft}{\isasymphi}\ y{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ \ \ \ \ \isakeyword{and}\ hom{\isacharunderscore}join{\isacharcolon}\ {\isachardoublequoteopen}{\isasymphi}\ {\isacharparenleft}x\ {\isasymsqunion}\ y{\isacharparenright}\ {\isacharequal}\ le{\isacharprime}{\isachardot}join\ {\isacharparenleft}{\isasymphi}\ x{\isacharparenright}\ {\isacharparenleft}{\isasymphi}\ y{\isacharparenright}{\isachardoublequoteclose}%
+\ lattice{\isaliteral{5F}{\isacharunderscore}}hom\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ le{\isaliteral{3A}{\isacharcolon}}\ lattice\ {\isaliteral{2B}{\isacharplus}}\ le{\isaliteral{27}{\isacharprime}}{\isaliteral{3A}{\isacharcolon}}\ lattice\ le{\isaliteral{27}{\isacharprime}}\ \isakeyword{for}\ le{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C7072656365713E}{\isasympreceq}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{5}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\isanewline
+\ \ \ \ \isakeyword{fixes}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\isanewline
+\ \ \ \ \isakeyword{assumes}\ hom{\isaliteral{5F}{\isacharunderscore}}meet{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ le{\isaliteral{27}{\isacharprime}}{\isaliteral{2E}{\isachardot}}meet\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \ \ \isakeyword{and}\ hom{\isaliteral{5F}{\isacharunderscore}}join{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ le{\isaliteral{27}{\isacharprime}}{\isaliteral{2E}{\isachardot}}join\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
The parameter instantiation in the first instance of \isa{lattice} is omitted. This causes the parameter~\isa{le} to be
added to the \isakeyword{for} clause, and the locale has
- parameters~\isa{le},~\isa{le{\isacharprime}} and, of course,~\isa{{\isasymphi}}.
+ parameters~\isa{le},~\isa{le{\isaliteral{27}{\isacharprime}}} and, of course,~\isa{{\isaliteral{5C3C7068693E}{\isasymphi}}}.
Before turning to the second example, we complete the locale by
providing infix syntax for the meet and join operations of the
@@ -439,11 +439,11 @@
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{context}\isamarkupfalse%
-\ lattice{\isacharunderscore}hom\ \isakeyword{begin}\isanewline
+\ lattice{\isaliteral{5F}{\isacharunderscore}}hom\ \isakeyword{begin}\isanewline
\ \ \isacommand{abbreviation}\isamarkupfalse%
-\ meet{\isacharprime}\ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasymsqinter}{\isacharprime}{\isacharprime}{\isachardoublequoteclose}\ {\isadigit{5}}{\isadigit{0}}{\isacharparenright}\ \isakeyword{where}\ {\isachardoublequoteopen}meet{\isacharprime}\ {\isasymequiv}\ le{\isacharprime}{\isachardot}meet{\isachardoublequoteclose}\isanewline
+\ meet{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{5}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}meet{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ le{\isaliteral{27}{\isacharprime}}{\isaliteral{2E}{\isachardot}}meet{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{abbreviation}\isamarkupfalse%
-\ join{\isacharprime}\ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasymsqunion}{\isacharprime}{\isacharprime}{\isachardoublequoteclose}\ {\isadigit{5}}{\isadigit{0}}{\isacharparenright}\ \isakeyword{where}\ {\isachardoublequoteopen}join{\isacharprime}\ {\isasymequiv}\ le{\isacharprime}{\isachardot}join{\isachardoublequoteclose}\isanewline
+\ join{\isaliteral{27}{\isacharprime}}\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{5}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}join{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ le{\isaliteral{27}{\isacharprime}}{\isaliteral{2E}{\isachardot}}join{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{end}\isamarkupfalse%
%
\begin{isamarkuptext}%
@@ -453,12 +453,12 @@
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{locale}\isamarkupfalse%
-\ lattice{\isacharunderscore}end\ {\isacharequal}\ lattice{\isacharunderscore}hom\ {\isacharunderscore}\ le%
+\ lattice{\isaliteral{5F}{\isacharunderscore}}end\ {\isaliteral{3D}{\isacharequal}}\ lattice{\isaliteral{5F}{\isacharunderscore}}hom\ {\isaliteral{5F}{\isacharunderscore}}\ le%
\begin{isamarkuptext}%
-The notation~\isa{{\isacharunderscore}} enables to omit a parameter in a
+The notation~\isa{{\isaliteral{5F}{\isacharunderscore}}} enables to omit a parameter in a
positional instantiation. The omitted parameter,~\isa{le} becomes
the parameter of the declared locale and is, in the following
- position, used to instantiate the second parameter of \isa{lattice{\isacharunderscore}hom}. The effect is that of identifying the first in second
+ position, used to instantiate the second parameter of \isa{lattice{\isaliteral{5F}{\isacharunderscore}}hom}. The effect is that of identifying the first in second
parameter of the homomorphism locale.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -469,7 +469,7 @@
interpretation which is introduced below. Parameter instantiations
are indicated by $\sqsubseteq \mapsto \preceq$ etc. By looking at
the inheritance diagram it would seem
- that two identical copies of each of the locales \isa{partial{\isacharunderscore}order} and \isa{lattice} are imported by \isa{lattice{\isacharunderscore}end}. This is not the case! Inheritance paths with
+ that two identical copies of each of the locales \isa{partial{\isaliteral{5F}{\isacharunderscore}}order} and \isa{lattice} are imported by \isa{lattice{\isaliteral{5F}{\isacharunderscore}}end}. This is not the case! Inheritance paths with
identical morphisms are automatically detected and
the conclusions of the respective locales appear only once.
@@ -477,15 +477,15 @@
\hrule \vspace{2ex}
\begin{center}
\begin{tikzpicture}
- \node (o) at (0,0) {\isa{partial{\isacharunderscore}order}};
- \node (oh) at (1.5,-2) {\isa{order{\isacharunderscore}preserving}};
+ \node (o) at (0,0) {\isa{partial{\isaliteral{5F}{\isacharunderscore}}order}};
+ \node (oh) at (1.5,-2) {\isa{order{\isaliteral{5F}{\isacharunderscore}}preserving}};
\node (oh1) at (1.5,-0.7) {$\scriptscriptstyle \sqsubseteq \mapsto \sqsubseteq$};
\node (oh2) at (0,-1.3) {$\scriptscriptstyle \sqsubseteq \mapsto \preceq$};
\node (l) at (-1.5,-2) {\isa{lattice}};
- \node (lh) at (0,-4) {\isa{lattice{\isacharunderscore}hom}};
+ \node (lh) at (0,-4) {\isa{lattice{\isaliteral{5F}{\isacharunderscore}}hom}};
\node (lh1) at (0,-2.7) {$\scriptscriptstyle \sqsubseteq \mapsto \sqsubseteq$};
\node (lh2) at (-1.5,-3.3) {$\scriptscriptstyle \sqsubseteq \mapsto \preceq$};
- \node (le) at (0,-6) {\isa{lattice{\isacharunderscore}end}};
+ \node (le) at (0,-6) {\isa{lattice{\isaliteral{5F}{\isacharunderscore}}end}};
\node (le1) at (0,-4.8)
[anchor=west]{$\scriptscriptstyle \sqsubseteq \mapsto \sqsubseteq$};
\node (le2) at (0,-5.2)
@@ -513,30 +513,30 @@
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{sublocale}\isamarkupfalse%
-\ lattice{\isacharunderscore}hom\ {\isasymsubseteq}\ order{\isacharunderscore}preserving%
+\ lattice{\isaliteral{5F}{\isacharunderscore}}hom\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ order{\isaliteral{5F}{\isacharunderscore}}preserving%
\isadelimproof
\ %
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ unfold{\isacharunderscore}locales\isanewline
+\ unfold{\isaliteral{5F}{\isacharunderscore}}locales\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ x\ y\isanewline
\ \ \ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymsqsubseteq}\ y{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isacharequal}\ {\isacharparenleft}x\ {\isasymsqunion}\ y{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ le{\isachardot}join{\isacharunderscore}connection{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ le{\isaliteral{2E}{\isachardot}}join{\isaliteral{5F}{\isacharunderscore}}connection{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymphi}\ y\ {\isacharequal}\ {\isacharparenleft}{\isasymphi}\ x\ {\isasymsqunion}{\isacharprime}\ {\isasymphi}\ y{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ hom{\isacharunderscore}join\ {\isacharbrackleft}symmetric{\isacharbrackright}{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ hom{\isaliteral{5F}{\isacharunderscore}}join\ {\isaliteral{5B}{\isacharbrackleft}}symmetric{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymphi}\ x\ {\isasympreceq}\ {\isasymphi}\ y{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ le{\isacharprime}{\isachardot}join{\isacharunderscore}connection{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ x\ {\isaliteral{5C3C7072656365713E}{\isasympreceq}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\ y{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ le{\isaliteral{27}{\isacharprime}}{\isaliteral{2E}{\isachardot}}join{\isaliteral{5F}{\isacharunderscore}}connection{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
%
\endisatagproof
@@ -548,10 +548,10 @@
%
\begin{isamarkuptext}%
Theorems and other declarations --- syntax, in particular --- from
- the locale \isa{order{\isacharunderscore}preserving} are now active in \isa{lattice{\isacharunderscore}hom}, for example
- \isa{hom{\isacharunderscore}le}:
+ the locale \isa{order{\isaliteral{5F}{\isacharunderscore}}preserving} are now active in \isa{lattice{\isaliteral{5F}{\isacharunderscore}}hom}, for example
+ \isa{hom{\isaliteral{5F}{\isacharunderscore}}le}:
\begin{isabelle}%
-\ \ {\isacharquery}x\ {\isasymsqsubseteq}\ {\isacharquery}y\ {\isasymLongrightarrow}\ {\isasymphi}\ {\isacharquery}x\ {\isasympreceq}\ {\isasymphi}\ {\isacharquery}y%
+\ \ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ {\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C7072656365713E}{\isasympreceq}}\ {\isaliteral{5C3C7068693E}{\isasymphi}}\ {\isaliteral{3F}{\isacharquery}}y%
\end{isabelle}
This theorem will be useful in the following section.%
\end{isamarkuptext}%
@@ -565,9 +565,9 @@
There are situations where an interpretation is not possible
in the general case since the desired property is only valid if
certain conditions are fulfilled. Take, for example, the function
- \isa{{\isasymlambda}i{\isachardot}\ n\ {\isacharasterisk}\ i} that scales its argument by a constant factor.
+ \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}i{\isaliteral{2E}{\isachardot}}\ n\ {\isaliteral{2A}{\isacharasterisk}}\ i} that scales its argument by a constant factor.
This function is order preserving (and even a lattice endomorphism)
- with respect to \isa{op\ {\isasymle}} provided \isa{n\ {\isasymge}\ {\isadigit{0}}}.
+ with respect to \isa{op\ {\isaliteral{5C3C6C653E}{\isasymle}}} provided \isa{n\ {\isaliteral{5C3C67653E}{\isasymge}}\ {\isadigit{0}}}.
It is not possible to express this using a global interpretation,
because it is in general unspecified whether~\isa{n} is
@@ -582,9 +582,9 @@
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{locale}\isamarkupfalse%
-\ non{\isacharunderscore}negative\ {\isacharequal}\isanewline
-\ \ \ \ \isakeyword{fixes}\ n\ {\isacharcolon}{\isacharcolon}\ int\isanewline
-\ \ \ \ \isakeyword{assumes}\ non{\isacharunderscore}neg{\isacharcolon}\ {\isachardoublequoteopen}{\isadigit{0}}\ {\isasymle}\ n{\isachardoublequoteclose}%
+\ non{\isaliteral{5F}{\isacharunderscore}}negative\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \isakeyword{fixes}\ n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\isanewline
+\ \ \ \ \isakeyword{assumes}\ non{\isaliteral{5F}{\isacharunderscore}}neg{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{0}}\ {\isaliteral{5C3C6C653E}{\isasymle}}\ n{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
It is again convenient to make the interpretation in an
incremental fashion, first for order preserving maps, the for
@@ -592,8 +592,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{sublocale}\isamarkupfalse%
-\ non{\isacharunderscore}negative\ {\isasymsubseteq}\isanewline
-\ \ \ \ \ \ order{\isacharunderscore}preserving\ {\isachardoublequoteopen}op\ {\isasymle}{\isachardoublequoteclose}\ {\isachardoublequoteopen}op\ {\isasymle}{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isasymlambda}i{\isachardot}\ n\ {\isacharasterisk}\ i{\isachardoublequoteclose}\isanewline
+\ non{\isaliteral{5F}{\isacharunderscore}}negative\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\isanewline
+\ \ \ \ \ \ order{\isaliteral{5F}{\isacharunderscore}}preserving\ {\isaliteral{22}{\isachardoublequoteopen}}op\ {\isaliteral{5C3C6C653E}{\isasymle}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}op\ {\isaliteral{5C3C6C653E}{\isasymle}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}i{\isaliteral{2E}{\isachardot}}\ n\ {\isaliteral{2A}{\isacharasterisk}}\ i{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ \ \ %
@@ -601,8 +601,8 @@
%
\isatagproof
\isacommand{using}\isamarkupfalse%
-\ non{\isacharunderscore}neg\ \isacommand{by}\isamarkupfalse%
-\ unfold{\isacharunderscore}locales\ {\isacharparenleft}rule\ mult{\isacharunderscore}left{\isacharunderscore}mono{\isacharparenright}%
+\ non{\isaliteral{5F}{\isacharunderscore}}neg\ \isacommand{by}\isamarkupfalse%
+\ unfold{\isaliteral{5F}{\isacharunderscore}}locales\ {\isaliteral{28}{\isacharparenleft}}rule\ mult{\isaliteral{5F}{\isacharunderscore}}left{\isaliteral{5F}{\isacharunderscore}}mono{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -612,7 +612,7 @@
%
\begin{isamarkuptext}%
While the proof of the previous interpretation
- is straightforward from monotonicity lemmas for~\isa{op\ {\isacharasterisk}}, the
+ is straightforward from monotonicity lemmas for~\isa{op\ {\isaliteral{2A}{\isacharasterisk}}}, the
second proof follows a useful pattern.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -623,23 +623,23 @@
%
\isatagvisible
\isacommand{sublocale}\isamarkupfalse%
-\ non{\isacharunderscore}negative\ {\isasymsubseteq}\ lattice{\isacharunderscore}end\ {\isachardoublequoteopen}op\ {\isasymle}{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isasymlambda}i{\isachardot}\ n\ {\isacharasterisk}\ i{\isachardoublequoteclose}\isanewline
+\ non{\isaliteral{5F}{\isacharunderscore}}negative\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ lattice{\isaliteral{5F}{\isacharunderscore}}end\ {\isaliteral{22}{\isachardoublequoteopen}}op\ {\isaliteral{5C3C6C653E}{\isasymle}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}i{\isaliteral{2E}{\isachardot}}\ n\ {\isaliteral{2A}{\isacharasterisk}}\ i{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
-\ {\isacharparenleft}unfold{\isacharunderscore}locales{\isacharcomma}\ unfold\ int{\isacharunderscore}min{\isacharunderscore}eq\ int{\isacharunderscore}max{\isacharunderscore}eq{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}unfold{\isaliteral{5F}{\isacharunderscore}}locales{\isaliteral{2C}{\isacharcomma}}\ unfold\ int{\isaliteral{5F}{\isacharunderscore}}min{\isaliteral{5F}{\isacharunderscore}}eq\ int{\isaliteral{5F}{\isacharunderscore}}max{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\normalsize Unfolding the locale predicates \emph{and} the
interpretation equations immediately yields two subgoals that
reflect the core conjecture.
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ y{\isachardot}\ n\ {\isacharasterisk}\ min\ x\ y\ {\isacharequal}\ min\ {\isacharparenleft}n\ {\isacharasterisk}\ x{\isacharparenright}\ {\isacharparenleft}n\ {\isacharasterisk}\ y{\isacharparenright}\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}x\ y{\isachardot}\ n\ {\isacharasterisk}\ max\ x\ y\ {\isacharequal}\ max\ {\isacharparenleft}n\ {\isacharasterisk}\ x{\isacharparenright}\ {\isacharparenleft}n\ {\isacharasterisk}\ y{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{2E}{\isachardot}}\ n\ {\isaliteral{2A}{\isacharasterisk}}\ min\ x\ y\ {\isaliteral{3D}{\isacharequal}}\ min\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2A}{\isacharasterisk}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2A}{\isacharasterisk}}\ y{\isaliteral{29}{\isacharparenright}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y{\isaliteral{2E}{\isachardot}}\ n\ {\isaliteral{2A}{\isacharasterisk}}\ max\ x\ y\ {\isaliteral{3D}{\isacharequal}}\ max\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2A}{\isacharasterisk}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2A}{\isacharasterisk}}\ y{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
- It is now necessary to show, in the context of \isa{non{\isacharunderscore}negative}, that multiplication by~\isa{n} commutes with
+ It is now necessary to show, in the context of \isa{non{\isaliteral{5F}{\isacharunderscore}}negative}, that multiplication by~\isa{n} commutes with
\isa{min} and \isa{max}.%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \ \isacommand{qed}\isamarkupfalse%
-\ {\isacharparenleft}auto\ simp{\isacharcolon}\ hom{\isacharunderscore}le{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}auto\ simp{\isaliteral{3A}{\isacharcolon}}\ hom{\isaliteral{5F}{\isacharunderscore}}le{\isaliteral{29}{\isacharparenright}}%
\endisatagvisible
{\isafoldvisible}%
%
@@ -648,13 +648,13 @@
\endisadelimvisible
%
\begin{isamarkuptext}%
-The lemma \isa{hom{\isacharunderscore}le}
+The lemma \isa{hom{\isaliteral{5F}{\isacharunderscore}}le}
simplifies a proof that would have otherwise been lengthy and we may
consider making it a default rule for the simplifier:%
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{lemmas}\isamarkupfalse%
-\ {\isacharparenleft}\isakeyword{in}\ order{\isacharunderscore}preserving{\isacharparenright}\ hom{\isacharunderscore}le\ {\isacharbrackleft}simp{\isacharbrackright}%
+\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{in}\ order{\isaliteral{5F}{\isacharunderscore}}preserving{\isaliteral{29}{\isacharparenright}}\ hom{\isaliteral{5F}{\isacharunderscore}}le\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}%
\isamarkupsubsection{Avoiding Infinite Chains of Interpretations
\label{sec:infinite-chains}%
}
@@ -678,7 +678,7 @@
%
\isatagvisible
\isacommand{sublocale}\isamarkupfalse%
-\ partial{\isacharunderscore}order\ {\isasymsubseteq}\ f{\isacharcolon}\ partial{\isacharunderscore}order\ {\isachardoublequoteopen}{\isasymlambda}f\ g{\isachardot}\ {\isasymforall}x{\isachardot}\ f\ x\ {\isasymsqsubseteq}\ g\ x{\isachardoublequoteclose}\isanewline
+\ partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ f{\isaliteral{3A}{\isacharcolon}}\ partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}f\ g{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ f\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ g\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{oops}\isamarkupfalse%
%
\endisatagvisible
@@ -692,23 +692,23 @@
Unfortunately this is a cyclic interpretation that leads to an
infinite chain, namely
\begin{isabelle}%
-\ \ partial{\isacharunderscore}order\ {\isasymsubseteq}\ partial{\isacharunderscore}order\ {\isacharparenleft}{\isasymlambda}f\ g{\isachardot}\ {\isasymforall}x{\isachardot}\ f\ x\ {\isasymsqsubseteq}\ g\ x{\isacharparenright}\ {\isasymsubseteq}\isanewline
-\isaindent{\ \ }\ \ partial{\isacharunderscore}order\ {\isacharparenleft}{\isasymlambda}f\ g{\isachardot}\ {\isasymforall}x\ y{\isachardot}\ f\ x\ y\ {\isasymsqsubseteq}\ g\ x\ y{\isacharparenright}\ {\isasymsubseteq}\ \ {\isasymdots}%
+\ \ partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}f\ g{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ f\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ g\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\isanewline
+\isaindent{\ \ }\ \ partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}f\ g{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x\ y{\isaliteral{2E}{\isachardot}}\ f\ x\ y\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ g\ x\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ \ {\isaliteral{5C3C646F74733E}{\isasymdots}}%
\end{isabelle}
and the interpretation is rejected.
Instead it is necessary to declare a locale that is logically
- equivalent to \isa{partial{\isacharunderscore}order} but serves to collect facts
+ equivalent to \isa{partial{\isaliteral{5F}{\isacharunderscore}}order} but serves to collect facts
about functions spaces where the co-domain is a partial order, and
to make the interpretation in its context:%
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{locale}\isamarkupfalse%
-\ fun{\isacharunderscore}partial{\isacharunderscore}order\ {\isacharequal}\ partial{\isacharunderscore}order\isanewline
+\ fun{\isaliteral{5F}{\isacharunderscore}}partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{3D}{\isacharequal}}\ partial{\isaliteral{5F}{\isacharunderscore}}order\isanewline
\isanewline
\ \ \isacommand{sublocale}\isamarkupfalse%
-\ fun{\isacharunderscore}partial{\isacharunderscore}order\ {\isasymsubseteq}\isanewline
-\ \ \ \ \ \ f{\isacharcolon}\ partial{\isacharunderscore}order\ {\isachardoublequoteopen}{\isasymlambda}f\ g{\isachardot}\ {\isasymforall}x{\isachardot}\ f\ x\ {\isasymsqsubseteq}\ g\ x{\isachardoublequoteclose}\isanewline
+\ fun{\isaliteral{5F}{\isacharunderscore}}partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\isanewline
+\ \ \ \ \ \ f{\isaliteral{3A}{\isacharcolon}}\ partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}f\ g{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ f\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ g\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ \ \ %
@@ -716,7 +716,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ unfold{\isacharunderscore}locales\ {\isacharparenleft}fast{\isacharcomma}rule{\isacharcomma}fast{\isacharcomma}blast\ intro{\isacharcolon}\ trans{\isacharparenright}%
+\ unfold{\isaliteral{5F}{\isacharunderscore}}locales\ {\isaliteral{28}{\isacharparenleft}}fast{\isaliteral{2C}{\isacharcomma}}rule{\isaliteral{2C}{\isacharcomma}}fast{\isaliteral{2C}{\isacharcomma}}blast\ intro{\isaliteral{3A}{\isacharcolon}}\ trans{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -732,10 +732,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\ \ \isacommand{locale}\isamarkupfalse%
-\ fun{\isacharunderscore}lattice\ {\isacharequal}\ fun{\isacharunderscore}partial{\isacharunderscore}order\ {\isacharplus}\ lattice\isanewline
+\ fun{\isaliteral{5F}{\isacharunderscore}}lattice\ {\isaliteral{3D}{\isacharequal}}\ fun{\isaliteral{5F}{\isacharunderscore}}partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{2B}{\isacharplus}}\ lattice\isanewline
\isanewline
\ \ \isacommand{sublocale}\isamarkupfalse%
-\ fun{\isacharunderscore}lattice\ {\isasymsubseteq}\ f{\isacharcolon}\ lattice\ {\isachardoublequoteopen}{\isasymlambda}f\ g{\isachardot}\ {\isasymforall}x{\isachardot}\ f\ x\ {\isasymsqsubseteq}\ g\ x{\isachardoublequoteclose}\isanewline
+\ fun{\isaliteral{5F}{\isacharunderscore}}lattice\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ f{\isaliteral{3A}{\isacharcolon}}\ lattice\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}f\ g{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ f\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ g\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ \ \ %
@@ -743,19 +743,19 @@
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
-\ unfold{\isacharunderscore}locales\isanewline
+\ unfold{\isaliteral{5F}{\isacharunderscore}}locales\isanewline
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ f\ g\isanewline
\ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}partial{\isacharunderscore}order{\isachardot}is{\isacharunderscore}inf\ {\isacharparenleft}{\isasymlambda}f\ g{\isachardot}\ {\isasymforall}x{\isachardot}\ f\ x\ {\isasymsqsubseteq}\ g\ x{\isacharparenright}\ f\ g\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ f\ x\ {\isasymsqinter}\ g\ x{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}is{\isaliteral{5F}{\isacharunderscore}}inf\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}f\ g{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ f\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ g\ x{\isaliteral{29}{\isacharparenright}}\ f\ g\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ f\ x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ g\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}rule\ is{\isacharunderscore}infI{\isacharparenright}\ \isacommand{apply}\isamarkupfalse%
-\ rule{\isacharplus}\ \isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}drule\ spec{\isacharcomma}\ assumption{\isacharparenright}{\isacharplus}\ \isacommand{done}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}infI{\isaliteral{29}{\isacharparenright}}\ \isacommand{apply}\isamarkupfalse%
+\ rule{\isaliteral{2B}{\isacharplus}}\ \isacommand{apply}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}drule\ spec{\isaliteral{2C}{\isacharcomma}}\ assumption{\isaliteral{29}{\isacharparenright}}{\isaliteral{2B}{\isacharplus}}\ \isacommand{done}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymexists}inf{\isachardot}\ partial{\isacharunderscore}order{\isachardot}is{\isacharunderscore}inf\ {\isacharparenleft}{\isasymlambda}f\ g{\isachardot}\ {\isasymforall}x{\isachardot}\ f\ x\ {\isasymsqsubseteq}\ g\ x{\isacharparenright}\ f\ g\ inf{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}inf{\isaliteral{2E}{\isachardot}}\ partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}is{\isaliteral{5F}{\isacharunderscore}}inf\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}f\ g{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ f\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ g\ x{\isaliteral{29}{\isacharparenright}}\ f\ g\ inf{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ fast\isanewline
\ \ \isacommand{next}\isamarkupfalse%
@@ -763,15 +763,15 @@
\ \ \ \ \isacommand{fix}\isamarkupfalse%
\ f\ g\isanewline
\ \ \ \ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}partial{\isacharunderscore}order{\isachardot}is{\isacharunderscore}sup\ {\isacharparenleft}{\isasymlambda}f\ g{\isachardot}\ {\isasymforall}x{\isachardot}\ f\ x\ {\isasymsqsubseteq}\ g\ x{\isacharparenright}\ f\ g\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ f\ x\ {\isasymsqunion}\ g\ x{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}is{\isaliteral{5F}{\isacharunderscore}}sup\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}f\ g{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ f\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ g\ x{\isaliteral{29}{\isacharparenright}}\ f\ g\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ f\ x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ g\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}rule\ is{\isacharunderscore}supI{\isacharparenright}\ \isacommand{apply}\isamarkupfalse%
-\ rule{\isacharplus}\ \isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}drule\ spec{\isacharcomma}\ assumption{\isacharparenright}{\isacharplus}\ \isacommand{done}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ is{\isaliteral{5F}{\isacharunderscore}}supI{\isaliteral{29}{\isacharparenright}}\ \isacommand{apply}\isamarkupfalse%
+\ rule{\isaliteral{2B}{\isacharplus}}\ \isacommand{apply}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}drule\ spec{\isaliteral{2C}{\isacharcomma}}\ assumption{\isaliteral{29}{\isacharparenright}}{\isaliteral{2B}{\isacharplus}}\ \isacommand{done}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymexists}sup{\isachardot}\ partial{\isacharunderscore}order{\isachardot}is{\isacharunderscore}sup\ {\isacharparenleft}{\isasymlambda}f\ g{\isachardot}\ {\isasymforall}x{\isachardot}\ f\ x\ {\isasymsqsubseteq}\ g\ x{\isacharparenright}\ f\ g\ sup{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}sup{\isaliteral{2E}{\isachardot}}\ partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}is{\isaliteral{5F}{\isacharunderscore}}sup\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}f\ g{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ f\ x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ g\ x{\isaliteral{29}{\isacharparenright}}\ f\ g\ sup{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ fast\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
--- a/doc-src/Locales/Locales/document/root.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/Locales/Locales/document/root.tex Mon Nov 08 14:41:11 2010 +0100
@@ -1,9 +1,5 @@
\documentclass[11pt,a4paper]{article}
\usepackage{amsmath}
-\usepackage{ifpdf}
-\ifpdf\relax\else\def\pgfsysdriver{pgfsys-dvi.def}\fi
-\usepackage{tikz}
-\usepackage{subfigure}
\usepackage{../../../isabelle,../../../isabellesym}
\usepackage{verbatim}
\usepackage{alltt}
@@ -13,6 +9,11 @@
\usepackage{../../../pdfsetup}
+\usepackage{ifpdf}
+\ifpdf\relax\else\def\pgfsysdriver{pgfsys-dvi.def}\fi
+\usepackage{tikz}
+\usepackage{subfigure}
+
\isadroptag{theory}
\isafoldtag{proof}
--- a/doc-src/Main/Docs/document/Main_Doc.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/Main/Docs/document/Main_Doc.tex Mon Nov 08 14:41:11 2010 +0100
@@ -1,6 +1,6 @@
%
\begin{isabellebody}%
-\def\isabellecontext{Main{\isacharunderscore}Doc}%
+\def\isabellecontext{Main{\isaliteral{5F}{\isacharunderscore}}Doc}%
%
\isadelimtheory
%
@@ -35,21 +35,21 @@
\section{HOL}
-The basic logic: \isa{x\ {\isacharequal}\ y}, \isa{True}, \isa{False}, \isa{{\isasymnot}\ P}, \isa{P\ {\isasymand}\ Q}, \isa{P\ {\isasymor}\ Q}, \isa{P\ {\isasymlongrightarrow}\ Q}, \isa{{\isasymforall}x{\isachardot}\ P}, \isa{{\isasymexists}x{\isachardot}\ P}, \isa{{\isasymexists}{\isacharbang}x{\isachardot}\ P}, \isa{THE\ x{\isachardot}\ P}.
+The basic logic: \isa{x\ {\isaliteral{3D}{\isacharequal}}\ y}, \isa{True}, \isa{False}, \isa{{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ P}, \isa{P\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q}, \isa{P\ {\isaliteral{5C3C6F723E}{\isasymor}}\ Q}, \isa{P\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q}, \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ P}, \isa{{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ P}, \isa{{\isaliteral{5C3C6578697374733E}{\isasymexists}}{\isaliteral{21}{\isacharbang}}x{\isaliteral{2E}{\isachardot}}\ P}, \isa{THE\ x{\isaliteral{2E}{\isachardot}}\ P}.
\smallskip
\begin{tabular}{@ {} l @ {~::~} l @ {}}
-\isa{undefined} & \isa{{\isacharprime}a}\\
-\isa{default} & \isa{{\isacharprime}a}\\
+\isa{undefined} & \isa{{\isaliteral{27}{\isacharprime}}a}\\
+\isa{default} & \isa{{\isaliteral{27}{\isacharprime}}a}\\
\end{tabular}
\subsubsection*{Syntax}
\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
-\isa{x\ {\isasymnoteq}\ y} & \isa{{\isachardoublequote}{\isasymnot}\ {\isacharparenleft}x\ {\isacharequal}\ y{\isacharparenright}{\isachardoublequote}} & (\verb$~=$)\\
-\isa{{\isachardoublequote}P\ {\isasymlongleftrightarrow}\ Q{\isachardoublequote}} & \isa{P\ {\isacharequal}\ Q} \\
-\isa{if\ x\ then\ y\ else\ z} & \isa{{\isachardoublequote}If\ x\ y\ z{\isachardoublequote}}\\
-\isa{let\ x\ {\isacharequal}\ e\isactrlisub {\isadigit{1}}\ in\ e\isactrlisub {\isadigit{2}}} & \isa{{\isachardoublequote}Let\ e\isactrlisub {\isadigit{1}}\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ e\isactrlisub {\isadigit{2}}{\isacharparenright}{\isachardoublequote}}\\
+\isa{x\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ y} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & (\verb$~=$)\\
+\isa{{\isaliteral{22}{\isachardoublequote}}P\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ Q{\isaliteral{22}{\isachardoublequote}}} & \isa{P\ {\isaliteral{3D}{\isacharequal}}\ Q} \\
+\isa{if\ x\ then\ y\ else\ z} & \isa{{\isaliteral{22}{\isachardoublequote}}If\ x\ y\ z{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{let\ x\ {\isaliteral{3D}{\isacharequal}}\ e\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ in\ e\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}} & \isa{{\isaliteral{22}{\isachardoublequote}}Let\ e\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ e\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}\\
\end{supertabular}
@@ -60,26 +60,26 @@
\smallskip
\begin{supertabular}{@ {} l @ {~::~} l l @ {}}
-\isa{op\ {\isasymle}} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ bool} & (\verb$<=$)\\
-\isa{op\ {\isacharless}} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ bool}\\
-\isa{Least} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ bool{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{min} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{max} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{top} & \isa{{\isacharprime}a}\\
-\isa{bot} & \isa{{\isacharprime}a}\\
-\isa{mono} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ bool}\\
-\isa{strict{\isacharunderscore}mono} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ bool}\\
+\isa{op\ {\isaliteral{5C3C6C653E}{\isasymle}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool} & (\verb$<=$)\\
+\isa{op\ {\isaliteral{3C}{\isacharless}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{Least} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{min} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{max} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{top} & \isa{{\isaliteral{27}{\isacharprime}}a}\\
+\isa{bot} & \isa{{\isaliteral{27}{\isacharprime}}a}\\
+\isa{mono} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{strict{\isaliteral{5F}{\isacharunderscore}}mono} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
\end{supertabular}
\subsubsection*{Syntax}
\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
-\isa{{\isachardoublequote}x\ {\isasymge}\ y{\isachardoublequote}} & \isa{y\ {\isasymle}\ x} & (\verb$>=$)\\
-\isa{{\isachardoublequote}x\ {\isachargreater}\ y{\isachardoublequote}} & \isa{y\ {\isacharless}\ x}\\
-\isa{{\isasymforall}x{\isasymle}y{\isachardot}\ P} & \isa{{\isachardoublequote}{\isasymforall}x{\isachardot}\ x\ {\isasymle}\ y\ {\isasymlongrightarrow}\ P{\isachardoublequote}}\\
-\isa{{\isasymexists}x{\isasymle}y{\isachardot}\ P} & \isa{{\isachardoublequote}{\isasymexists}x{\isachardot}\ x\ {\isasymle}\ y\ {\isasymand}\ P{\isachardoublequote}}\\
+\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C67653E}{\isasymge}}\ y{\isaliteral{22}{\isachardoublequote}}} & \isa{y\ {\isaliteral{5C3C6C653E}{\isasymle}}\ x} & (\verb$>=$)\\
+\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{3E}{\isachargreater}}\ y{\isaliteral{22}{\isachardoublequote}}} & \isa{y\ {\isaliteral{3C}{\isacharless}}\ x}\\
+\isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{5C3C6C653E}{\isasymle}}y{\isaliteral{2E}{\isachardot}}\ P} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C6C653E}{\isasymle}}\ y\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ P{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{5C3C6C653E}{\isasymle}}y{\isaliteral{2E}{\isachardot}}\ P} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C6C653E}{\isasymle}}\ y\ {\isaliteral{5C3C616E643E}{\isasymand}}\ P{\isaliteral{22}{\isachardoublequote}}}\\
\multicolumn{2}{@ {}l@ {}}{Similarly for $<$, $\ge$ and $>$}\\
-\isa{LEAST\ x{\isachardot}\ P} & \isa{{\isachardoublequote}Least\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ P{\isacharparenright}{\isachardoublequote}}\\
+\isa{LEAST\ x{\isaliteral{2E}{\isachardot}}\ P} & \isa{{\isaliteral{22}{\isachardoublequote}}Least\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ P{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}\\
\end{supertabular}
@@ -89,220 +89,220 @@
latter in theory \isa{Set}).
\begin{tabular}{@ {} l @ {~::~} l @ {}}
-\isa{inf} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{sup} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{Inf} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{Sup} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}a}\\
+\isa{inf} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{sup} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{Inf} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{Sup} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
\end{tabular}
\subsubsection*{Syntax}
-Available by loading theory \isa{Lattice{\isacharunderscore}Syntax} in directory \isa{Library}.
+Available by loading theory \isa{Lattice{\isaliteral{5F}{\isacharunderscore}}Syntax} in directory \isa{Library}.
\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-\isa{{\isachardoublequote}x\ {\isasymsqsubseteq}\ y{\isachardoublequote}} & \isa{x\ {\isasymle}\ y}\\
-\isa{{\isachardoublequote}x\ {\isasymsqsubset}\ y{\isachardoublequote}} & \isa{x\ {\isacharless}\ y}\\
-\isa{{\isachardoublequote}x\ {\isasymsqinter}\ y{\isachardoublequote}} & \isa{inf\ x\ y}\\
-\isa{{\isachardoublequote}x\ {\isasymsqunion}\ y{\isachardoublequote}} & \isa{sup\ x\ y}\\
-\isa{{\isachardoublequote}{\isasymSqinter}\ A{\isachardoublequote}} & \isa{Sup\ A}\\
-\isa{{\isachardoublequote}{\isasymSqunion}\ A{\isachardoublequote}} & \isa{Inf\ A}\\
-\isa{{\isachardoublequote}{\isasymtop}{\isachardoublequote}} & \isa{top}\\
-\isa{{\isachardoublequote}{\isasymbottom}{\isachardoublequote}} & \isa{bot}\\
+\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C737173756273657465713E}{\isasymsqsubseteq}}\ y{\isaliteral{22}{\isachardoublequote}}} & \isa{x\ {\isaliteral{5C3C6C653E}{\isasymle}}\ y}\\
+\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C73717375627365743E}{\isasymsqsubset}}\ y{\isaliteral{22}{\isachardoublequote}}} & \isa{x\ {\isaliteral{3C}{\isacharless}}\ y}\\
+\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C7371696E7465723E}{\isasymsqinter}}\ y{\isaliteral{22}{\isachardoublequote}}} & \isa{inf\ x\ y}\\
+\isa{{\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{5C3C7371756E696F6E3E}{\isasymsqunion}}\ y{\isaliteral{22}{\isachardoublequote}}} & \isa{sup\ x\ y}\\
+\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C5371696E7465723E}{\isasymSqinter}}\ A{\isaliteral{22}{\isachardoublequote}}} & \isa{Sup\ A}\\
+\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C5371756E696F6E3E}{\isasymSqunion}}\ A{\isaliteral{22}{\isachardoublequote}}} & \isa{Inf\ A}\\
+\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C746F703E}{\isasymtop}}{\isaliteral{22}{\isachardoublequote}}} & \isa{top}\\
+\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C626F74746F6D3E}{\isasymbottom}}{\isaliteral{22}{\isachardoublequote}}} & \isa{bot}\\
\end{supertabular}
\section{Set}
-Sets are predicates: \isa{{\isachardoublequote}{\isacharprime}a\ set\ \ {\isacharequal}\ \ {\isacharprime}a\ {\isasymRightarrow}\ bool{\isachardoublequote}}
+Sets are predicates: \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a\ set\ \ {\isaliteral{3D}{\isacharequal}}\ \ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequote}}}
\bigskip
\begin{supertabular}{@ {} l @ {~::~} l l @ {}}
-\isa{{\isacharbraceleft}{\isacharbraceright}} & \isa{{\isacharprime}a\ set}\\
-\isa{insert} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
-\isa{Collect} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ bool{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
-\isa{op\ {\isasymin}} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ set\ {\isasymRightarrow}\ bool} & (\texttt{:})\\
-\isa{op\ {\isasymunion}} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}a\ set} & (\texttt{Un})\\
-\isa{op\ {\isasyminter}} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}a\ set} & (\texttt{Int})\\
-\isa{UNION} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ set{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}b\ set}\\
-\isa{INTER} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ set{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}b\ set}\\
-\isa{Union} & \isa{{\isacharprime}a\ set\ set\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
-\isa{Inter} & \isa{{\isacharprime}a\ set\ set\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
-\isa{Pow} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}a\ set\ set}\\
-\isa{UNIV} & \isa{{\isacharprime}a\ set}\\
-\isa{op\ {\isacharbackquote}} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}b\ set}\\
-\isa{Ball} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ bool{\isacharparenright}\ {\isasymRightarrow}\ bool}\\
-\isa{Bex} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ bool{\isacharparenright}\ {\isasymRightarrow}\ bool}\\
+\isa{{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{7D}{\isacharbraceright}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{insert} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{Collect} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{op\ {\isaliteral{5C3C696E3E}{\isasymin}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool} & (\texttt{:})\\
+\isa{op\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set} & (\texttt{Un})\\
+\isa{op\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set} & (\texttt{Int})\\
+\isa{UNION} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ set{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ set}\\
+\isa{INTER} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ set{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ set}\\
+\isa{Union} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{Inter} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{Pow} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set\ set}\\
+\isa{UNIV} & \isa{{\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{op\ {\isaliteral{60}{\isacharbackquote}}} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ set}\\
+\isa{Ball} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{Bex} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
\end{supertabular}
\subsubsection*{Syntax}
\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
-\isa{{\isacharbraceleft}x\isactrlisub {\isadigit{1}}{\isacharcomma}{\isasymdots}{\isacharcomma}x\isactrlisub n{\isacharbraceright}} & \isa{insert\ x\isactrlisub {\isadigit{1}}\ {\isacharparenleft}{\isasymdots}\ {\isacharparenleft}insert\ x\isactrlisub n\ {\isacharbraceleft}{\isacharbraceright}{\isacharparenright}{\isasymdots}{\isacharparenright}}\\
-\isa{x\ {\isasymnotin}\ A} & \isa{{\isachardoublequote}{\isasymnot}{\isacharparenleft}x\ {\isasymin}\ A{\isacharparenright}{\isachardoublequote}}\\
-\isa{A\ {\isasymsubseteq}\ B} & \isa{{\isachardoublequote}A\ {\isasymle}\ B{\isachardoublequote}}\\
-\isa{A\ {\isasymsubset}\ B} & \isa{{\isachardoublequote}A\ {\isacharless}\ B{\isachardoublequote}}\\
-\isa{{\isachardoublequote}A\ {\isasymsupseteq}\ B{\isachardoublequote}} & \isa{{\isachardoublequote}B\ {\isasymle}\ A{\isachardoublequote}}\\
-\isa{{\isachardoublequote}A\ {\isasymsupset}\ B{\isachardoublequote}} & \isa{{\isachardoublequote}B\ {\isacharless}\ A{\isachardoublequote}}\\
-\isa{{\isacharbraceleft}x{\isachardot}\ P{\isacharbraceright}} & \isa{{\isachardoublequote}Collect\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ P{\isacharparenright}{\isachardoublequote}}\\
-\isa{{\isasymUnion}x{\isasymin}I{\isachardot}\ A} & \isa{{\isachardoublequote}UNION\ I\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ A{\isacharparenright}{\isachardoublequote}} & (\texttt{UN})\\
-\isa{{\isasymUnion}x{\isachardot}\ A} & \isa{{\isachardoublequote}UNION\ UNIV\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ A{\isacharparenright}{\isachardoublequote}}\\
-\isa{{\isasymInter}x{\isasymin}I{\isachardot}\ A} & \isa{{\isachardoublequote}INTER\ I\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ A{\isacharparenright}{\isachardoublequote}} & (\texttt{INT})\\
-\isa{{\isasymInter}x{\isachardot}\ A} & \isa{{\isachardoublequote}INTER\ UNIV\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ A{\isacharparenright}{\isachardoublequote}}\\
-\isa{{\isasymforall}x{\isasymin}A{\isachardot}\ P} & \isa{{\isachardoublequote}Ball\ A\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ P{\isacharparenright}{\isachardoublequote}}\\
-\isa{{\isasymexists}x{\isasymin}A{\isachardot}\ P} & \isa{{\isachardoublequote}Bex\ A\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ P{\isacharparenright}{\isachardoublequote}}\\
-\isa{range\ f} & \isa{{\isachardoublequote}f\ {\isacharbackquote}\ UNIV{\isachardoublequote}}\\
+\isa{{\isaliteral{7B}{\isacharbraceleft}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{7D}{\isacharbraceright}}} & \isa{insert\ x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{28}{\isacharparenleft}}insert\ x\isaliteral{5C3C5E697375623E}{}\isactrlisub n\ {\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{29}{\isacharparenright}}}\\
+\isa{x\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ A} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{A\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ B} & \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C6C653E}{\isasymle}}\ B{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{A\ {\isaliteral{5C3C7375627365743E}{\isasymsubset}}\ B} & \isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{3C}{\isacharless}}\ B{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C73757073657465713E}{\isasymsupseteq}}\ B{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}B\ {\isaliteral{5C3C6C653E}{\isasymle}}\ A{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{5C3C7375707365743E}{\isasymsupset}}\ B{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}B\ {\isaliteral{3C}{\isacharless}}\ A{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{7B}{\isacharbraceleft}}x{\isaliteral{2E}{\isachardot}}\ P{\isaliteral{7D}{\isacharbraceright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}Collect\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ P{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{5C3C556E696F6E3E}{\isasymUnion}}x{\isaliteral{5C3C696E3E}{\isasymin}}I{\isaliteral{2E}{\isachardot}}\ A} & \isa{{\isaliteral{22}{\isachardoublequote}}UNION\ I\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & (\texttt{UN})\\
+\isa{{\isaliteral{5C3C556E696F6E3E}{\isasymUnion}}x{\isaliteral{2E}{\isachardot}}\ A} & \isa{{\isaliteral{22}{\isachardoublequote}}UNION\ UNIV\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{5C3C496E7465723E}{\isasymInter}}x{\isaliteral{5C3C696E3E}{\isasymin}}I{\isaliteral{2E}{\isachardot}}\ A} & \isa{{\isaliteral{22}{\isachardoublequote}}INTER\ I\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}} & (\texttt{INT})\\
+\isa{{\isaliteral{5C3C496E7465723E}{\isasymInter}}x{\isaliteral{2E}{\isachardot}}\ A} & \isa{{\isaliteral{22}{\isachardoublequote}}INTER\ UNIV\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{5C3C696E3E}{\isasymin}}A{\isaliteral{2E}{\isachardot}}\ P} & \isa{{\isaliteral{22}{\isachardoublequote}}Ball\ A\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ P{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{5C3C696E3E}{\isasymin}}A{\isaliteral{2E}{\isachardot}}\ P} & \isa{{\isaliteral{22}{\isachardoublequote}}Bex\ A\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ P{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{range\ f} & \isa{{\isaliteral{22}{\isachardoublequote}}f\ {\isaliteral{60}{\isacharbackquote}}\ UNIV{\isaliteral{22}{\isachardoublequote}}}\\
\end{supertabular}
\section{Fun}
\begin{supertabular}{@ {} l @ {~::~} l l @ {}}
-\isa{id} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{op\ {\isasymcirc}} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}c\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}c\ {\isasymRightarrow}\ {\isacharprime}b} & (\texttt{o})\\
-\isa{inj{\isacharunderscore}on} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ set\ {\isasymRightarrow}\ bool}\\
-\isa{inj} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ bool}\\
-\isa{surj} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ bool}\\
-\isa{bij} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ bool}\\
-\isa{bij{\isacharunderscore}betw} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}b\ set\ {\isasymRightarrow}\ bool}\\
-\isa{fun{\isacharunderscore}upd} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b}\\
+\isa{id} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{op\ {\isaliteral{5C3C636972633E}{\isasymcirc}}} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}c\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}c\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b} & (\texttt{o})\\
+\isa{inj{\isaliteral{5F}{\isacharunderscore}}on} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{inj} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{surj} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{bij} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{bij{\isaliteral{5F}{\isacharunderscore}}betw} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{fun{\isaliteral{5F}{\isacharunderscore}}upd} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b}\\
\end{supertabular}
\subsubsection*{Syntax}
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-\isa{f{\isacharparenleft}x\ {\isacharcolon}{\isacharequal}\ y{\isacharparenright}} & \isa{{\isachardoublequote}fun{\isacharunderscore}upd\ f\ x\ y{\isachardoublequote}}\\
-\isa{f{\isacharparenleft}x\isactrlisub {\isadigit{1}}{\isacharcolon}{\isacharequal}y\isactrlisub {\isadigit{1}}{\isacharcomma}{\isasymdots}{\isacharcomma}x\isactrlisub n{\isacharcolon}{\isacharequal}y\isactrlisub n{\isacharparenright}} & \isa{f{\isacharparenleft}x\isactrlisub {\isadigit{1}}{\isacharcolon}{\isacharequal}y\isactrlisub {\isadigit{1}}{\isacharparenright}{\isasymdots}{\isacharparenleft}x\isactrlisub n{\isacharcolon}{\isacharequal}y\isactrlisub n{\isacharparenright}}\\
+\isa{f{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{29}{\isacharparenright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}fun{\isaliteral{5F}{\isacharunderscore}}upd\ f\ x\ y{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{f{\isaliteral{28}{\isacharparenleft}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}y\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}y\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}} & \isa{f{\isaliteral{28}{\isacharparenleft}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}y\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{28}{\isacharparenleft}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}y\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}}\\
\end{tabular}
\section{Hilbert\_Choice}
-Hilbert's selection ($\varepsilon$) operator: \isa{SOME\ x{\isachardot}\ P}.
+Hilbert's selection ($\varepsilon$) operator: \isa{SOME\ x{\isaliteral{2E}{\isachardot}}\ P}.
\smallskip
\begin{tabular}{@ {} l @ {~::~} l @ {}}
-\isa{inv{\isacharunderscore}into} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}a}
+\isa{inv{\isaliteral{5F}{\isacharunderscore}}into} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}
\end{tabular}
\subsubsection*{Syntax}
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-\isa{inv} & \isa{{\isachardoublequote}inv{\isacharunderscore}into\ UNIV{\isachardoublequote}}
+\isa{inv} & \isa{{\isaliteral{22}{\isachardoublequote}}inv{\isaliteral{5F}{\isacharunderscore}}into\ UNIV{\isaliteral{22}{\isachardoublequote}}}
\end{tabular}
\section{Fixed Points}
Theory: \isa{Inductive}.
-Least and greatest fixed points in a complete lattice \isa{{\isacharprime}a}:
+Least and greatest fixed points in a complete lattice \isa{{\isaliteral{27}{\isacharprime}}a}:
\begin{tabular}{@ {} l @ {~::~} l @ {}}
-\isa{lfp} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{gfp} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a}\\
+\isa{lfp} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{gfp} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
\end{tabular}
-Note that in particular sets (\isa{{\isacharprime}a\ {\isasymRightarrow}\ bool}) are complete lattices.
+Note that in particular sets (\isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}) are complete lattices.
\section{Sum\_Type}
-Type constructor \isa{{\isacharplus}}.
+Type constructor \isa{{\isaliteral{2B}{\isacharplus}}}.
\begin{tabular}{@ {} l @ {~::~} l @ {}}
-\isa{Inl} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isacharplus}\ {\isacharprime}b}\\
-\isa{Inr} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ {\isacharplus}\ {\isacharprime}a}\\
-\isa{op\ {\isacharless}{\isacharplus}{\isachargreater}} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}b\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isacharplus}\ {\isacharprime}b{\isacharparenright}\ set}
+\isa{Inl} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{27}{\isacharprime}}b}\\
+\isa{Inr} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{op\ {\isaliteral{3C}{\isacharless}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{3E}{\isachargreater}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ set}
\end{tabular}
\section{Product\_Type}
-Types \isa{unit} and \isa{{\isasymtimes}}.
+Types \isa{unit} and \isa{{\isaliteral{5C3C74696D65733E}{\isasymtimes}}}.
\begin{supertabular}{@ {} l @ {~::~} l @ {}}
-\isa{{\isacharparenleft}{\isacharparenright}} & \isa{unit}\\
-\isa{Pair} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b}\\
-\isa{fst} & \isa{{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{snd} & \isa{{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}b}\\
-\isa{split} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}c{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}c}\\
-\isa{curry} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}c{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}c}\\
-\isa{Sigma} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ set{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b{\isacharparenright}\ set}\\
+\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}} & \isa{unit}\\
+\isa{Pair} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b}\\
+\isa{fst} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{snd} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b}\\
+\isa{split} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}c}\\
+\isa{curry} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}c}\\
+\isa{Sigma} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ set{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ set}\\
\end{supertabular}
\subsubsection*{Syntax}
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} ll @ {}}
-\isa{{\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}} & \isa{{\isachardoublequote}Pair\ a\ b{\isachardoublequote}}\\
-\isa{{\isasymlambda}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ t} & \isa{{\isachardoublequote}split\ {\isacharparenleft}{\isasymlambda}x\ y{\isachardot}\ t{\isacharparenright}{\isachardoublequote}}\\
-\isa{A\ {\isasymtimes}\ B} & \isa{Sigma\ A\ {\isacharparenleft}{\isasymlambda}\_{\isachardot}\ B{\isacharparenright}} & (\verb$<*>$)
+\isa{{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}Pair\ a\ b{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ t} & \isa{{\isaliteral{22}{\isachardoublequote}}split\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x\ y{\isaliteral{2E}{\isachardot}}\ t{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{A\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ B} & \isa{Sigma\ A\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}\_{\isaliteral{2E}{\isachardot}}\ B{\isaliteral{29}{\isacharparenright}}} & (\verb$<*>$)
\end{tabular}
Pairs may be nested. Nesting to the right is printed as a tuple,
-e.g.\ \mbox{\isa{{\isacharparenleft}a{\isacharcomma}\ b{\isacharcomma}\ c{\isacharparenright}}} is really \mbox{\isa{{\isacharparenleft}a{\isacharcomma}\ {\isacharparenleft}b{\isacharcomma}\ c{\isacharparenright}{\isacharparenright}}.}
+e.g.\ \mbox{\isa{{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{2C}{\isacharcomma}}\ c{\isaliteral{29}{\isacharparenright}}}} is really \mbox{\isa{{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}b{\isaliteral{2C}{\isacharcomma}}\ c{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}}.}
Pattern matching with pairs and tuples extends to all binders,
-e.g.\ \mbox{\isa{{\isasymforall}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isasymin}A{\isachardot}\ P},} \isa{{\isacharbraceleft}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ P{\isacharbraceright}}, etc.
+e.g.\ \mbox{\isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C696E3E}{\isasymin}}A{\isaliteral{2E}{\isachardot}}\ P},} \isa{{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ P{\isaliteral{7D}{\isacharbraceright}}}, etc.
\section{Relation}
\begin{supertabular}{@ {} l @ {~::~} l @ {}}
-\isa{converse} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}b\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set}\\
-\isa{op\ O} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}b\ {\isasymtimes}\ {\isacharprime}c{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}c{\isacharparenright}\ set}\\
-\isa{op\ {\isacharbackquote}{\isacharbackquote}} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}b\ set}\\
-\isa{inv{\isacharunderscore}image} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}b\ {\isasymtimes}\ {\isacharprime}b{\isacharparenright}\ set}\\
-\isa{Id{\isacharunderscore}on} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set}\\
-\isa{Id} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set}\\
-\isa{Domain} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
-\isa{Range} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharprime}b\ set}\\
-\isa{Field} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
-\isa{refl{\isacharunderscore}on} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ bool}\\
-\isa{refl} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ bool}\\
-\isa{sym} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ bool}\\
-\isa{antisym} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ bool}\\
-\isa{trans} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ bool}\\
-\isa{irrefl} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ bool}\\
-\isa{total{\isacharunderscore}on} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ bool}\\
-\isa{total} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ bool}\\
+\isa{converse} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{op\ O} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}c{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}c{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{op\ {\isaliteral{60}{\isacharbackquote}}{\isaliteral{60}{\isacharbackquote}}} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ set}\\
+\isa{inv{\isaliteral{5F}{\isacharunderscore}}image} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{Id{\isaliteral{5F}{\isacharunderscore}}on} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{Id} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{Domain} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{Range} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ set}\\
+\isa{Field} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{refl{\isaliteral{5F}{\isacharunderscore}}on} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{refl} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{sym} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{antisym} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{trans} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{irrefl} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{total{\isaliteral{5F}{\isacharunderscore}}on} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{total} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
\end{supertabular}
\subsubsection*{Syntax}
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
-\isa{r{\isasyminverse}} & \isa{{\isachardoublequote}converse\ r{\isachardoublequote}} & (\verb$^-1$)
+\isa{r{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}} & \isa{{\isaliteral{22}{\isachardoublequote}}converse\ r{\isaliteral{22}{\isachardoublequote}}} & (\verb$^-1$)
\end{tabular}
\section{Equiv\_Relations}
\begin{supertabular}{@ {} l @ {~::~} l @ {}}
-\isa{equiv} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ bool}\\
-\isa{op\ {\isacharslash}{\isacharslash}} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharprime}a\ set\ set}\\
-\isa{congruent} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ bool}\\
-\isa{congruent{\isadigit{2}}} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}b\ {\isasymtimes}\ {\isacharprime}b{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}c{\isacharparenright}\ {\isasymRightarrow}\ bool}\\
+\isa{equiv} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{op\ {\isaliteral{2F}{\isacharslash}}{\isaliteral{2F}{\isacharslash}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set\ set}\\
+\isa{congruent} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{congruent{\isadigit{2}}} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
%@ {const Equiv_Relations.} & @ {term_type_only Equiv_Relations. ""}\\
\end{supertabular}
\subsubsection*{Syntax}
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-\isa{f\ respects\ r} & \isa{{\isachardoublequote}congruent\ r\ f{\isachardoublequote}}\\
-\isa{f\ respects{\isadigit{2}}\ r} & \isa{{\isachardoublequote}congruent{\isadigit{2}}\ r\ r\ f{\isachardoublequote}}\\
+\isa{f\ respects\ r} & \isa{{\isaliteral{22}{\isachardoublequote}}congruent\ r\ f{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{f\ respects{\isadigit{2}}\ r} & \isa{{\isaliteral{22}{\isachardoublequote}}congruent{\isadigit{2}}\ r\ r\ f{\isaliteral{22}{\isachardoublequote}}}\\
\end{tabular}
\section{Transitive\_Closure}
\begin{tabular}{@ {} l @ {~::~} l @ {}}
-\isa{rtrancl} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set}\\
-\isa{trancl} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set}\\
-\isa{reflcl} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set}\\
-\isa{op\ {\isacharcircum}{\isacharcircum}} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set}\\
+\isa{rtrancl} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{trancl} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{reflcl} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{op\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set}\\
\end{tabular}
\subsubsection*{Syntax}
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
-\isa{r\isactrlsup {\isacharasterisk}} & \isa{{\isachardoublequote}rtrancl\ r{\isachardoublequote}} & (\verb$^*$)\\
-\isa{r\isactrlsup {\isacharplus}} & \isa{{\isachardoublequote}trancl\ r{\isachardoublequote}} & (\verb$^+$)\\
-\isa{r\isactrlsup {\isacharequal}} & \isa{{\isachardoublequote}reflcl\ r{\isachardoublequote}} & (\verb$^=$)
+\isa{r\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}} & \isa{{\isaliteral{22}{\isachardoublequote}}rtrancl\ r{\isaliteral{22}{\isachardoublequote}}} & (\verb$^*$)\\
+\isa{r\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2B}{\isacharplus}}} & \isa{{\isaliteral{22}{\isachardoublequote}}trancl\ r{\isaliteral{22}{\isachardoublequote}}} & (\verb$^+$)\\
+\isa{r\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{3D}{\isacharequal}}} & \isa{{\isaliteral{22}{\isachardoublequote}}reflcl\ r{\isaliteral{22}{\isachardoublequote}}} & (\verb$^=$)
\end{tabular}
@@ -313,42 +313,42 @@
overloaded operators:
\begin{supertabular}{@ {} l @ {~::~} l l @ {}}
-\isa{{\isadigit{0}}} & \isa{{\isacharprime}a}\\
-\isa{{\isadigit{1}}} & \isa{{\isacharprime}a}\\
-\isa{op\ {\isacharplus}} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{op\ {\isacharminus}} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{uminus} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a} & (\verb$-$)\\
-\isa{op\ {\isacharasterisk}} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{inverse} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{op\ {\isacharslash}} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{abs} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{sgn} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{op\ dvd} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ bool}\\
-\isa{op\ div} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{op\ mod} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a}\\
+\isa{{\isadigit{0}}} & \isa{{\isaliteral{27}{\isacharprime}}a}\\
+\isa{{\isadigit{1}}} & \isa{{\isaliteral{27}{\isacharprime}}a}\\
+\isa{op\ {\isaliteral{2B}{\isacharplus}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{op\ {\isaliteral{2D}{\isacharminus}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{uminus} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a} & (\verb$-$)\\
+\isa{op\ {\isaliteral{2A}{\isacharasterisk}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{inverse} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{op\ {\isaliteral{2F}{\isacharslash}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{abs} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{sgn} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{op\ dvd} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{op\ div} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{op\ mod} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
\end{supertabular}
\subsubsection*{Syntax}
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-\isa{{\isasymbar}x{\isasymbar}} & \isa{{\isachardoublequote}abs\ x{\isachardoublequote}}
+\isa{{\isaliteral{5C3C6261723E}{\isasymbar}}x{\isaliteral{5C3C6261723E}{\isasymbar}}} & \isa{{\isaliteral{22}{\isachardoublequote}}abs\ x{\isaliteral{22}{\isachardoublequote}}}
\end{tabular}
\section{Nat}
-\isa{\isacommand{datatype}\ nat\ {\isacharequal}\ {\isadigit{0}}\ {\isacharbar}\ Suc\ nat}
+\isa{\isacommand{datatype}\ nat\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\ {\isaliteral{7C}{\isacharbar}}\ Suc\ nat}
\bigskip
\begin{tabular}{@ {} lllllll @ {}}
-\isa{op\ {\isacharplus}} &
-\isa{op\ {\isacharminus}} &
-\isa{op\ {\isacharasterisk}} &
+\isa{op\ {\isaliteral{2B}{\isacharplus}}} &
+\isa{op\ {\isaliteral{2D}{\isacharminus}}} &
+\isa{op\ {\isaliteral{2A}{\isacharasterisk}}} &
\isa{op\ div}&
\isa{op\ mod}&
\isa{op\ dvd}\\
-\isa{op\ {\isasymle}} &
-\isa{op\ {\isacharless}} &
+\isa{op\ {\isaliteral{5C3C6C653E}{\isasymle}}} &
+\isa{op\ {\isaliteral{3C}{\isacharless}}} &
\isa{min} &
\isa{max} &
\isa{Min} &
@@ -356,9 +356,9 @@
\end{tabular}
\begin{tabular}{@ {} l @ {~::~} l @ {}}
-\isa{of{\isacharunderscore}nat} & \isa{nat\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{op\ {\isacharcircum}{\isacharcircum}} &
- \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a}
+\isa{of{\isaliteral{5F}{\isacharunderscore}}nat} & \isa{nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{op\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}} &
+ \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}
\end{tabular}
\section{Int}
@@ -367,16 +367,16 @@
\bigskip
\begin{tabular}{@ {} llllllll @ {}}
-\isa{op\ {\isacharplus}} &
-\isa{op\ {\isacharminus}} &
+\isa{op\ {\isaliteral{2B}{\isacharplus}}} &
+\isa{op\ {\isaliteral{2D}{\isacharminus}}} &
\isa{uminus} &
-\isa{op\ {\isacharasterisk}} &
-\isa{op\ {\isacharcircum}} &
+\isa{op\ {\isaliteral{2A}{\isacharasterisk}}} &
+\isa{op\ {\isaliteral{5E}{\isacharcircum}}} &
\isa{op\ div}&
\isa{op\ mod}&
\isa{op\ dvd}\\
-\isa{op\ {\isasymle}} &
-\isa{op\ {\isacharless}} &
+\isa{op\ {\isaliteral{5C3C6C653E}{\isasymle}}} &
+\isa{op\ {\isaliteral{3C}{\isacharless}}} &
\isa{min} &
\isa{max} &
\isa{Min} &
@@ -386,15 +386,15 @@
\end{tabular}
\begin{tabular}{@ {} l @ {~::~} l l @ {}}
-\isa{nat} & \isa{int\ {\isasymRightarrow}\ nat}\\
-\isa{of{\isacharunderscore}int} & \isa{int\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{{\isasymint}} & \isa{{\isacharprime}a\ set} & (\verb$Ints$)
+\isa{nat} & \isa{int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat}\\
+\isa{of{\isaliteral{5F}{\isacharunderscore}}int} & \isa{int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{{\isaliteral{5C3C696E743E}{\isasymint}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ set} & (\verb$Ints$)
\end{tabular}
\subsubsection*{Syntax}
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-\isa{int} & \isa{{\isachardoublequote}of{\isacharunderscore}nat{\isachardoublequote}}\\
+\isa{int} & \isa{{\isaliteral{22}{\isachardoublequote}}of{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{22}{\isachardoublequote}}}\\
\end{tabular}
@@ -402,159 +402,159 @@
\begin{supertabular}{@ {} l @ {~::~} l @ {}}
-\isa{finite} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ bool}\\
-\isa{card} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ nat}\\
-\isa{fold} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}b}\\
-\isa{fold{\isacharunderscore}image} & \isa{{\isacharparenleft}{\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}b}\\
-\isa{setsum} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}b}\\
-\isa{setprod} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}b}\\
+\isa{finite} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{card} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat}\\
+\isa{fold} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b}\\
+\isa{fold{\isaliteral{5F}{\isacharunderscore}}image} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b}\\
+\isa{setsum} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b}\\
+\isa{setprod} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b}\\
\end{supertabular}
\subsubsection*{Syntax}
\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
-\isa{{\isasymSum}A} & \isa{{\isachardoublequote}setsum\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ x{\isacharparenright}\ A{\isachardoublequote}} & (\verb$SUM$)\\
-\isa{{\isasymSum}x{\isasymin}A{\isachardot}\ t} & \isa{{\isachardoublequote}setsum\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ t{\isacharparenright}\ A{\isachardoublequote}}\\
-\isa{{\isachardoublequote}{\isasymSum}x{\isacharbar}P{\isachardot}\ t{\isachardoublequote}} & \isa{{\isasymSum}x\ {\isacharbar}\ P{\isachardot}\ t}\\
-\multicolumn{2}{@ {}l@ {}}{Similarly for \isa{{\isasymProd}} instead of \isa{{\isasymSum}}} & (\verb$PROD$)\\
+\isa{{\isaliteral{5C3C53756D3E}{\isasymSum}}A} & \isa{{\isaliteral{22}{\isachardoublequote}}setsum\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{29}{\isacharparenright}}\ A{\isaliteral{22}{\isachardoublequote}}} & (\verb$SUM$)\\
+\isa{{\isaliteral{5C3C53756D3E}{\isasymSum}}x{\isaliteral{5C3C696E3E}{\isasymin}}A{\isaliteral{2E}{\isachardot}}\ t} & \isa{{\isaliteral{22}{\isachardoublequote}}setsum\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ t{\isaliteral{29}{\isacharparenright}}\ A{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C53756D3E}{\isasymSum}}x{\isaliteral{7C}{\isacharbar}}P{\isaliteral{2E}{\isachardot}}\ t{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{5C3C53756D3E}{\isasymSum}}x\ {\isaliteral{7C}{\isacharbar}}\ P{\isaliteral{2E}{\isachardot}}\ t}\\
+\multicolumn{2}{@ {}l@ {}}{Similarly for \isa{{\isaliteral{5C3C50726F643E}{\isasymProd}}} instead of \isa{{\isaliteral{5C3C53756D3E}{\isasymSum}}}} & (\verb$PROD$)\\
\end{supertabular}
\section{Wellfounded}
\begin{supertabular}{@ {} l @ {~::~} l @ {}}
-\isa{wf} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ bool}\\
-\isa{acyclic} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ bool}\\
-\isa{acc} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
-\isa{measure} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ nat{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set}\\
-\isa{op\ {\isacharless}{\isacharasterisk}lex{\isacharasterisk}{\isachargreater}} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}b\ {\isasymtimes}\ {\isacharprime}b{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b{\isacharparenright}\ {\isasymtimes}\ {\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b{\isacharparenright}\ set}\\
-\isa{op\ {\isacharless}{\isacharasterisk}mlex{\isacharasterisk}{\isachargreater}} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ nat{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set}\\
-\isa{less{\isacharunderscore}than} & \isa{{\isacharparenleft}nat\ {\isasymtimes}\ nat{\isacharparenright}\ set}\\
-\isa{pred{\isacharunderscore}nat} & \isa{{\isacharparenleft}nat\ {\isasymtimes}\ nat{\isacharparenright}\ set}\\
+\isa{wf} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{acyclic} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{acc} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{measure} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{op\ {\isaliteral{3C}{\isacharless}}{\isaliteral{2A}{\isacharasterisk}}lex{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{3E}{\isachargreater}}} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{op\ {\isaliteral{3C}{\isacharless}}{\isaliteral{2A}{\isacharasterisk}}mlex{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{3E}{\isachargreater}}} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{less{\isaliteral{5F}{\isacharunderscore}}than} & \isa{{\isaliteral{28}{\isacharparenleft}}nat\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ nat{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{pred{\isaliteral{5F}{\isacharunderscore}}nat} & \isa{{\isaliteral{28}{\isacharparenleft}}nat\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ nat{\isaliteral{29}{\isacharparenright}}\ set}\\
\end{supertabular}
\section{SetInterval}
\begin{supertabular}{@ {} l @ {~::~} l @ {}}
-\isa{lessThan} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
-\isa{atMost} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
-\isa{greaterThan} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
-\isa{atLeast} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
-\isa{greaterThanLessThan} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
-\isa{atLeastLessThan} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
-\isa{greaterThanAtMost} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
-\isa{atLeastAtMost} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
+\isa{lessThan} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{atMost} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{greaterThan} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{atLeast} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{greaterThanLessThan} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{atLeastLessThan} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{greaterThanAtMost} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{atLeastAtMost} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
\end{supertabular}
\subsubsection*{Syntax}
\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-\isa{{\isacharbraceleft}{\isachardot}{\isachardot}{\isacharless}y{\isacharbraceright}} & \isa{{\isachardoublequote}lessThan\ y{\isachardoublequote}}\\
-\isa{{\isacharbraceleft}{\isachardot}{\isachardot}y{\isacharbraceright}} & \isa{{\isachardoublequote}atMost\ y{\isachardoublequote}}\\
-\isa{{\isacharbraceleft}x{\isacharless}{\isachardot}{\isachardot}{\isacharbraceright}} & \isa{{\isachardoublequote}greaterThan\ x{\isachardoublequote}}\\
-\isa{{\isacharbraceleft}x{\isachardot}{\isachardot}{\isacharbraceright}} & \isa{{\isachardoublequote}atLeast\ x{\isachardoublequote}}\\
-\isa{{\isacharbraceleft}x{\isacharless}{\isachardot}{\isachardot}{\isacharless}y{\isacharbraceright}} & \isa{{\isachardoublequote}greaterThanLessThan\ x\ y{\isachardoublequote}}\\
-\isa{{\isacharbraceleft}x{\isachardot}{\isachardot}{\isacharless}y{\isacharbraceright}} & \isa{{\isachardoublequote}atLeastLessThan\ x\ y{\isachardoublequote}}\\
-\isa{{\isacharbraceleft}x{\isacharless}{\isachardot}{\isachardot}y{\isacharbraceright}} & \isa{{\isachardoublequote}greaterThanAtMost\ x\ y{\isachardoublequote}}\\
-\isa{{\isacharbraceleft}x{\isachardot}{\isachardot}y{\isacharbraceright}} & \isa{{\isachardoublequote}atLeastAtMost\ x\ y{\isachardoublequote}}\\
-\isa{{\isasymUnion}\ i{\isasymle}n{\isachardot}\ A} & \isa{{\isachardoublequote}{\isasymUnion}\ i\ {\isasymin}\ {\isacharbraceleft}{\isachardot}{\isachardot}n{\isacharbraceright}{\isachardot}\ A{\isachardoublequote}}\\
-\isa{{\isasymUnion}\ i{\isacharless}n{\isachardot}\ A} & \isa{{\isachardoublequote}{\isasymUnion}\ i\ {\isasymin}\ {\isacharbraceleft}{\isachardot}{\isachardot}{\isacharless}n{\isacharbraceright}{\isachardot}\ A{\isachardoublequote}}\\
-\multicolumn{2}{@ {}l@ {}}{Similarly for \isa{{\isasymInter}} instead of \isa{{\isasymUnion}}}\\
-\isa{{\isasymSum}x\ {\isacharequal}\ a{\isachardot}{\isachardot}b{\isachardot}\ t} & \isa{{\isachardoublequote}setsum\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ t{\isacharparenright}\ {\isacharbraceleft}a{\isachardot}{\isachardot}b{\isacharbraceright}{\isachardoublequote}}\\
-\isa{{\isasymSum}x\ {\isacharequal}\ a{\isachardot}{\isachardot}{\isacharless}b{\isachardot}\ t} & \isa{{\isachardoublequote}setsum\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ t{\isacharparenright}\ {\isacharbraceleft}a{\isachardot}{\isachardot}{\isacharless}b{\isacharbraceright}{\isachardoublequote}}\\
-\isa{{\isasymSum}x{\isasymle}b{\isachardot}\ t} & \isa{{\isachardoublequote}setsum\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ t{\isacharparenright}\ {\isacharbraceleft}{\isachardot}{\isachardot}b{\isacharbraceright}{\isachardoublequote}}\\
-\isa{{\isasymSum}x{\isacharless}b{\isachardot}\ t} & \isa{{\isachardoublequote}setsum\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ t{\isacharparenright}\ {\isacharbraceleft}{\isachardot}{\isachardot}{\isacharless}b{\isacharbraceright}{\isachardoublequote}}\\
-\multicolumn{2}{@ {}l@ {}}{Similarly for \isa{{\isasymProd}} instead of \isa{{\isasymSum}}}\\
+\isa{{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{3C}{\isacharless}}y{\isaliteral{7D}{\isacharbraceright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}lessThan\ y{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}y{\isaliteral{7D}{\isacharbraceright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}atMost\ y{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{7B}{\isacharbraceleft}}x{\isaliteral{3C}{\isacharless}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{7D}{\isacharbraceright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}greaterThan\ x{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{7B}{\isacharbraceleft}}x{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{7D}{\isacharbraceright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}atLeast\ x{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{7B}{\isacharbraceleft}}x{\isaliteral{3C}{\isacharless}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{3C}{\isacharless}}y{\isaliteral{7D}{\isacharbraceright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}greaterThanLessThan\ x\ y{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{7B}{\isacharbraceleft}}x{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{3C}{\isacharless}}y{\isaliteral{7D}{\isacharbraceright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}atLeastLessThan\ x\ y{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{7B}{\isacharbraceleft}}x{\isaliteral{3C}{\isacharless}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}y{\isaliteral{7D}{\isacharbraceright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}greaterThanAtMost\ x\ y{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{7B}{\isacharbraceleft}}x{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}y{\isaliteral{7D}{\isacharbraceright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}atLeastAtMost\ x\ y{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{5C3C556E696F6E3E}{\isasymUnion}}\ i{\isaliteral{5C3C6C653E}{\isasymle}}n{\isaliteral{2E}{\isachardot}}\ A} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C556E696F6E3E}{\isasymUnion}}\ i\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}n{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{2E}{\isachardot}}\ A{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{5C3C556E696F6E3E}{\isasymUnion}}\ i{\isaliteral{3C}{\isacharless}}n{\isaliteral{2E}{\isachardot}}\ A} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C556E696F6E3E}{\isasymUnion}}\ i\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{3C}{\isacharless}}n{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{2E}{\isachardot}}\ A{\isaliteral{22}{\isachardoublequote}}}\\
+\multicolumn{2}{@ {}l@ {}}{Similarly for \isa{{\isaliteral{5C3C496E7465723E}{\isasymInter}}} instead of \isa{{\isaliteral{5C3C556E696F6E3E}{\isasymUnion}}}}\\
+\isa{{\isaliteral{5C3C53756D3E}{\isasymSum}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}b{\isaliteral{2E}{\isachardot}}\ t} & \isa{{\isaliteral{22}{\isachardoublequote}}setsum\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7B}{\isacharbraceleft}}a{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}b{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{5C3C53756D3E}{\isasymSum}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{3C}{\isacharless}}b{\isaliteral{2E}{\isachardot}}\ t} & \isa{{\isaliteral{22}{\isachardoublequote}}setsum\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7B}{\isacharbraceleft}}a{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{3C}{\isacharless}}b{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{5C3C53756D3E}{\isasymSum}}x{\isaliteral{5C3C6C653E}{\isasymle}}b{\isaliteral{2E}{\isachardot}}\ t} & \isa{{\isaliteral{22}{\isachardoublequote}}setsum\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}b{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{5C3C53756D3E}{\isasymSum}}x{\isaliteral{3C}{\isacharless}}b{\isaliteral{2E}{\isachardot}}\ t} & \isa{{\isaliteral{22}{\isachardoublequote}}setsum\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{3C}{\isacharless}}b{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequote}}}\\
+\multicolumn{2}{@ {}l@ {}}{Similarly for \isa{{\isaliteral{5C3C50726F643E}{\isasymProd}}} instead of \isa{{\isaliteral{5C3C53756D3E}{\isasymSum}}}}\\
\end{supertabular}
\section{Power}
\begin{tabular}{@ {} l @ {~::~} l @ {}}
-\isa{op\ {\isacharcircum}} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ {\isacharprime}a}
+\isa{op\ {\isaliteral{5E}{\isacharcircum}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}
\end{tabular}
\section{Option}
-\isa{\isacommand{datatype}\ {\isacharprime}a\ option\ {\isacharequal}\ None\ {\isacharbar}\ Some\ {\isacharprime}a}
+\isa{\isacommand{datatype}\ {\isaliteral{27}{\isacharprime}}a\ option\ {\isaliteral{3D}{\isacharequal}}\ None\ {\isaliteral{7C}{\isacharbar}}\ Some\ {\isaliteral{27}{\isacharprime}}a}
\bigskip
\begin{tabular}{@ {} l @ {~::~} l @ {}}
-\isa{the} & \isa{{\isacharprime}a\ option\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{Option{\isachardot}map} & \isa{{\isachardoublequote}{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ option\ {\isasymRightarrow}\ {\isacharprime}b\ option{\isachardoublequote}}\\
-\isa{Option{\isachardot}set} & \isa{{\isacharprime}a\ option\ {\isasymRightarrow}\ {\isacharprime}a\ set}
+\isa{the} & \isa{{\isaliteral{27}{\isacharprime}}a\ option\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{Option{\isaliteral{2E}{\isachardot}}map} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ option\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{Option{\isaliteral{2E}{\isachardot}}set} & \isa{{\isaliteral{27}{\isacharprime}}a\ option\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}
\end{tabular}
\section{List}
-\isa{\isacommand{datatype}\ {\isacharprime}a\ list\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbar}\ op\ {\isacharhash}\ {\isacharprime}a\ {\isacharparenleft}{\isacharprime}a\ list{\isacharparenright}}
+\isa{\isacommand{datatype}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7C}{\isacharbar}}\ op\ {\isaliteral{23}{\isacharhash}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{29}{\isacharparenright}}}
\bigskip
\begin{supertabular}{@ {} l @ {~::~} l @ {}}
-\isa{op\ {\isacharat}} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{butlast} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{concat} & \isa{{\isacharprime}a\ list\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{distinct} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ bool}\\
-\isa{drop} & \isa{nat\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{dropWhile} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ bool{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{filter} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ bool{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{foldl} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ list\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{foldr} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}b}\\
-\isa{hd} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{last} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{length} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ nat}\\
-\isa{lenlex} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ list\ {\isasymtimes}\ {\isacharprime}a\ list{\isacharparenright}\ set}\\
-\isa{lex} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ list\ {\isasymtimes}\ {\isacharprime}a\ list{\isacharparenright}\ set}\\
-\isa{lexn} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ list\ {\isasymtimes}\ {\isacharprime}a\ list{\isacharparenright}\ set}\\
-\isa{lexord} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ list\ {\isasymtimes}\ {\isacharprime}a\ list{\isacharparenright}\ set}\\
-\isa{listrel} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ list\ {\isasymtimes}\ {\isacharprime}a\ list{\isacharparenright}\ set}\\
-\isa{listrel{\isadigit{1}}} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ list\ {\isasymtimes}\ {\isacharprime}a\ list{\isacharparenright}\ set}\\
-\isa{lists} & \isa{{\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}a\ list\ set}\\
-\isa{listset} & \isa{{\isacharprime}a\ set\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list\ set}\\
-\isa{listsum} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{list{\isacharunderscore}all{\isadigit{2}}} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ bool{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}b\ list\ {\isasymRightarrow}\ bool}\\
-\isa{list{\isacharunderscore}update} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{map} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}b\ list}\\
-\isa{measures} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ nat{\isacharparenright}\ list\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set}\\
-\isa{op\ {\isacharbang}} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ {\isacharprime}a}\\
-\isa{remdups} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{removeAll} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{remove{\isadigit{1}}} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{replicate} & \isa{nat\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{rev} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{rotate} & \isa{nat\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{rotate{\isadigit{1}}} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{set} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
-\isa{sort} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{sorted} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ bool}\\
-\isa{splice} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{sublist} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharparenleft}nat\ {\isasymRightarrow}\ bool{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{take} & \isa{nat\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{takeWhile} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ bool{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{tl} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list}\\
-\isa{upt} & \isa{nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat\ list}\\
-\isa{upto} & \isa{int\ {\isasymRightarrow}\ int\ {\isasymRightarrow}\ int\ list}\\
-\isa{zip} & \isa{{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}b\ list\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b{\isacharparenright}\ list}\\
+\isa{op\ {\isaliteral{40}{\isacharat}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{butlast} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{concat} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{distinct} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{drop} & \isa{nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{dropWhile} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{filter} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{foldl} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{foldr} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b}\\
+\isa{hd} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{last} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{length} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat}\\
+\isa{lenlex} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{lex} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{lexn} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{lexord} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{listrel} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{listrel{\isadigit{1}}} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{lists} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ set}\\
+\isa{listset} & \isa{{\isaliteral{27}{\isacharprime}}a\ set\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ set}\\
+\isa{listsum} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{list{\isaliteral{5F}{\isacharunderscore}}all{\isadigit{2}}} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{list{\isaliteral{5F}{\isacharunderscore}}update} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{map} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ list}\\
+\isa{measures} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{29}{\isacharparenright}}\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set}\\
+\isa{op\ {\isaliteral{21}{\isacharbang}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a}\\
+\isa{remdups} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{removeAll} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{remove{\isadigit{1}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{replicate} & \isa{nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{rev} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{rotate} & \isa{nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{rotate{\isadigit{1}}} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{set} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{sort} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{sorted} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{splice} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{sublist} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{take} & \isa{nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{takeWhile} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{tl} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list}\\
+\isa{upt} & \isa{nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ list}\\
+\isa{upto} & \isa{int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int\ list}\\
+\isa{zip} & \isa{{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ list}\\
\end{supertabular}
\subsubsection*{Syntax}
\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-\isa{{\isacharbrackleft}x\isactrlisub {\isadigit{1}}{\isacharcomma}{\isasymdots}{\isacharcomma}x\isactrlisub n{\isacharbrackright}} & \isa{x\isactrlisub {\isadigit{1}}\ {\isacharhash}\ {\isasymdots}\ {\isacharhash}\ x\isactrlisub n\ {\isacharhash}\ {\isacharbrackleft}{\isacharbrackright}}\\
-\isa{{\isacharbrackleft}m{\isachardot}{\isachardot}{\isacharless}n{\isacharbrackright}} & \isa{{\isachardoublequote}upt\ m\ n{\isachardoublequote}}\\
-\isa{{\isacharbrackleft}i{\isachardot}{\isachardot}j{\isacharbrackright}} & \isa{{\isachardoublequote}upto\ i\ j{\isachardoublequote}}\\
-\isa{{\isacharbrackleft}e{\isachardot}\ x\ {\isasymleftarrow}\ xs{\isacharbrackright}} & \isa{map\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ e{\isacharparenright}\ xs}\\
-\isa{{\isacharbrackleft}x{\isasymleftarrow}xs\ {\isachardot}\ b{\isacharbrackright}} & \isa{{\isachardoublequote}filter\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ b{\isacharparenright}\ xs{\isachardoublequote}} \\
-\isa{xs{\isacharbrackleft}n\ {\isacharcolon}{\isacharequal}\ x{\isacharbrackright}} & \isa{{\isachardoublequote}list{\isacharunderscore}update\ xs\ n\ x{\isachardoublequote}}\\
-\isa{{\isasymSum}x{\isasymleftarrow}xs{\isachardot}\ e} & \isa{{\isachardoublequote}listsum\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ e{\isacharparenright}\ xs{\isacharparenright}{\isachardoublequote}}\\
+\isa{{\isaliteral{5B}{\isacharbrackleft}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{5D}{\isacharbrackright}}} & \isa{x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{23}{\isacharhash}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{23}{\isacharhash}}\ x\isaliteral{5C3C5E697375623E}{}\isactrlisub n\ {\isaliteral{23}{\isacharhash}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}}\\
+\isa{{\isaliteral{5B}{\isacharbrackleft}}m{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{3C}{\isacharless}}n{\isaliteral{5D}{\isacharbrackright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}upt\ m\ n{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{5B}{\isacharbrackleft}}i{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}j{\isaliteral{5D}{\isacharbrackright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}upto\ i\ j{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{5B}{\isacharbrackleft}}e{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}\ xs{\isaliteral{5D}{\isacharbrackright}}} & \isa{map\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ e{\isaliteral{29}{\isacharparenright}}\ xs}\\
+\isa{{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}xs\ {\isaliteral{2E}{\isachardot}}\ b{\isaliteral{5D}{\isacharbrackright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}filter\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ b{\isaliteral{29}{\isacharparenright}}\ xs{\isaliteral{22}{\isachardoublequote}}} \\
+\isa{xs{\isaliteral{5B}{\isacharbrackleft}}n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{5D}{\isacharbrackright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}list{\isaliteral{5F}{\isacharunderscore}}update\ xs\ n\ x{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{5C3C53756D3E}{\isasymSum}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}xs{\isaliteral{2E}{\isachardot}}\ e} & \isa{{\isaliteral{22}{\isachardoublequote}}listsum\ {\isaliteral{28}{\isacharparenleft}}map\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ e{\isaliteral{29}{\isacharparenright}}\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}\\
\end{supertabular}
\medskip
-List comprehension: \isa{{\isacharbrackleft}e{\isachardot}\ q\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ q\isactrlisub n{\isacharbrackright}} where each
-qualifier \isa{q\isactrlisub i} is either a generator \mbox{\isa{pat\ {\isasymleftarrow}\ e}} or a
+List comprehension: \isa{{\isaliteral{5B}{\isacharbrackleft}}e{\isaliteral{2E}{\isachardot}}\ q\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ q\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{5D}{\isacharbrackright}}} where each
+qualifier \isa{q\isaliteral{5C3C5E697375623E}{}\isactrlisub i} is either a generator \mbox{\isa{pat\ {\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}\ e}} or a
guard, i.e.\ boolean expression.
\section{Map}
@@ -562,29 +562,29 @@
Maps model partial functions and are often used as finite tables. However,
the domain of a map may be infinite.
-\isa{{\isacharprime}a\ {\isasymrightharpoonup}\ {\isacharprime}b\ \ {\isacharequal}\ \ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option}
+\isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C7269676874686172706F6F6E75703E}{\isasymrightharpoonup}}\ {\isaliteral{27}{\isacharprime}}b\ \ {\isaliteral{3D}{\isacharequal}}\ \ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option}
\bigskip
\begin{supertabular}{@ {} l @ {~::~} l @ {}}
-\isa{Map{\isachardot}empty} & \isa{{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option}\\
-\isa{op\ {\isacharplus}{\isacharplus}} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option}\\
-\isa{op\ {\isasymcirc}\isactrlsub m} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}c\ {\isasymRightarrow}\ {\isacharprime}a\ option{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}c\ {\isasymRightarrow}\ {\isacharprime}b\ option}\\
-\isa{op\ {\isacharbar}{\isacharbackquote}} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ set\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option}\\
-\isa{dom} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ set}\\
-\isa{ran} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}b\ set}\\
-\isa{op\ {\isasymsubseteq}\isactrlsub m} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option{\isacharparenright}\ {\isasymRightarrow}\ bool}\\
-\isa{map{\isacharunderscore}of} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b{\isacharparenright}\ list\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option}\\
-\isa{map{\isacharunderscore}upds} & \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}b\ list\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option}\\
+\isa{Map{\isaliteral{2E}{\isachardot}}empty} & \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option}\\
+\isa{op\ {\isaliteral{2B}{\isacharplus}}{\isaliteral{2B}{\isacharplus}}} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option}\\
+\isa{op\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}c\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ option{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}c\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option}\\
+\isa{op\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{60}{\isacharbackquote}}} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option}\\
+\isa{dom} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ set}\\
+\isa{ran} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ set}\\
+\isa{op\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\isaliteral{5C3C5E7375623E}{}\isactrlsub m} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}\\
+\isa{map{\isaliteral{5F}{\isacharunderscore}}of} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option}\\
+\isa{map{\isaliteral{5F}{\isacharunderscore}}upds} & \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ option}\\
\end{supertabular}
\subsubsection*{Syntax}
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-\isa{Map{\isachardot}empty} & \isa{{\isasymlambda}x{\isachardot}\ None}\\
-\isa{m{\isacharparenleft}x\ {\isasymmapsto}\ y{\isacharparenright}} & \isa{{\isachardoublequote}m{\isacharparenleft}x{\isacharcolon}{\isacharequal}Some\ y{\isacharparenright}{\isachardoublequote}}\\
-\isa{m{\isacharparenleft}x\isactrlisub {\isadigit{1}}{\isasymmapsto}y\isactrlisub {\isadigit{1}}{\isacharcomma}{\isasymdots}{\isacharcomma}x\isactrlisub n{\isasymmapsto}y\isactrlisub n{\isacharparenright}} & \isa{{\isachardoublequote}m{\isacharparenleft}x\isactrlisub {\isadigit{1}}{\isasymmapsto}y\isactrlisub {\isadigit{1}}{\isacharparenright}{\isasymdots}{\isacharparenleft}x\isactrlisub n{\isasymmapsto}y\isactrlisub n{\isacharparenright}{\isachardoublequote}}\\
-\isa{{\isacharbrackleft}x\isactrlisub {\isadigit{1}}{\isasymmapsto}y\isactrlisub {\isadigit{1}}{\isacharcomma}{\isasymdots}{\isacharcomma}x\isactrlisub n{\isasymmapsto}y\isactrlisub n{\isacharbrackright}} & \isa{{\isachardoublequote}Map{\isachardot}empty{\isacharparenleft}x\isactrlisub {\isadigit{1}}{\isasymmapsto}y\isactrlisub {\isadigit{1}}{\isacharcomma}{\isasymdots}{\isacharcomma}x\isactrlisub n{\isasymmapsto}y\isactrlisub n{\isacharparenright}{\isachardoublequote}}\\
-\isa{m{\isacharparenleft}xs\ {\isacharbrackleft}{\isasymmapsto}{\isacharbrackright}\ ys{\isacharparenright}} & \isa{{\isachardoublequote}map{\isacharunderscore}upds\ m\ xs\ ys{\isachardoublequote}}\\
+\isa{Map{\isaliteral{2E}{\isachardot}}empty} & \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ None}\\
+\isa{m{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}\ y{\isaliteral{29}{\isacharparenright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}m{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}Some\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{m{\isaliteral{28}{\isacharparenleft}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}y\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}y\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}m{\isaliteral{28}{\isacharparenleft}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}y\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{28}{\isacharparenleft}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}y\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{{\isaliteral{5B}{\isacharbrackleft}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}y\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}y\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{5D}{\isacharbrackright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}Map{\isaliteral{2E}{\isachardot}}empty{\isaliteral{28}{\isacharparenleft}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}y\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}x\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}y\isaliteral{5C3C5E697375623E}{}\isactrlisub n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}\\
+\isa{m{\isaliteral{28}{\isacharparenleft}}xs\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5C3C6D617073746F3E}{\isasymmapsto}}{\isaliteral{5D}{\isacharbrackright}}\ ys{\isaliteral{29}{\isacharparenright}}} & \isa{{\isaliteral{22}{\isachardoublequote}}map{\isaliteral{5F}{\isacharunderscore}}upds\ m\ xs\ ys{\isaliteral{22}{\isachardoublequote}}}\\
\end{tabular}%
\end{isamarkuptext}%
\isamarkuptrue%
--- a/doc-src/System/Thy/document/Basics.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/System/Thy/document/Basics.tex Mon Nov 08 14:41:11 2010 +0100
@@ -37,7 +37,7 @@
environment variables to all Isabelle executables (including tools
and user interfaces).
- \item The \emph{raw Isabelle process} (\indexref{}{executable}{isabelle-process}\hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isacharminus}process}}}}) runs logic sessions either interactively or in
+ \item The \emph{raw Isabelle process} (\indexref{}{executable}{isabelle-process}\hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isaliteral{2D}{\isacharminus}}process}}}}) runs logic sessions either interactively or in
batch mode. In particular, this view abstracts over the invocation
of the actual ML system to be used. Regular users rarely need to
care about the low-level process.
@@ -58,7 +58,7 @@
\begin{isamarkuptext}%
The Isabelle system heavily depends on the \emph{settings
mechanism}\indexbold{settings}. Essentially, this is a statically
- scoped collection of environment variables, such as \hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}HOME}}}}, \hyperlink{setting.ML-SYSTEM}{\mbox{\isa{\isatt{ML{\isacharunderscore}SYSTEM}}}}, \hyperlink{setting.ML-HOME}{\mbox{\isa{\isatt{ML{\isacharunderscore}HOME}}}}. These
+ scoped collection of environment variables, such as \hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME}}}}, \hyperlink{setting.ML-SYSTEM}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}SYSTEM}}}}, \hyperlink{setting.ML-HOME}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}HOME}}}}. These
variables are \emph{not} intended to be set directly from the shell,
though. Isabelle employs a somewhat more sophisticated scheme of
\emph{settings files} --- one for site-wide defaults, another for
@@ -71,7 +71,7 @@
their shell startup scripts, before being able to actually run the
program. Isabelle requires none such administrative chores of its
end-users --- the executables can be invoked straight away.
- Occasionally, users would still want to put the \hyperlink{file.$ISABELLE-HOME/bin}{\mbox{\isa{\isatt{{\isachardollar}ISABELLE{\isacharunderscore}HOME{\isacharslash}bin}}}} directory into their shell's search path, but
+ Occasionally, users would still want to put the \hyperlink{file.$ISABELLE-HOME/bin}{\mbox{\isa{\isatt{{\isaliteral{24}{\isachardollar}}ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME{\isaliteral{2F}{\isacharslash}}bin}}}} directory into their shell's search path, but
this is not required.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -90,17 +90,17 @@
\begin{enumerate}
- \item The special variable \indexdef{}{setting}{ISABELLE\_HOME}\hypertarget{setting.ISABELLE-HOME}{\hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}HOME}}}}} is
+ \item The special variable \indexdef{}{setting}{ISABELLE\_HOME}\hypertarget{setting.ISABELLE-HOME}{\hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME}}}}} is
determined automatically from the location of the binary that has
been run.
- You should not try to set \hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}HOME}}}} manually. Also
+ You should not try to set \hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME}}}} manually. Also
note that the Isabelle executables either have to be run from their
original location in the distribution directory, or via the
executable objects created by the \hyperlink{tool.install}{\mbox{\isa{\isatt{install}}}} utility. Symbolic
- links are admissible, but a plain copy of the \hyperlink{file.$ISABELLE-HOME/bin}{\mbox{\isa{\isatt{{\isachardollar}ISABELLE{\isacharunderscore}HOME{\isacharslash}bin}}}} files will not work!
+ links are admissible, but a plain copy of the \hyperlink{file.$ISABELLE-HOME/bin}{\mbox{\isa{\isatt{{\isaliteral{24}{\isachardollar}}ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME{\isaliteral{2F}{\isacharslash}}bin}}}} files will not work!
- \item The file \hyperlink{file.$ISABELLE-HOME/etc/settings}{\mbox{\isa{\isatt{{\isachardollar}ISABELLE{\isacharunderscore}HOME{\isacharslash}etc{\isacharslash}settings}}}} is run as a
+ \item The file \hyperlink{file.$ISABELLE-HOME/etc/settings}{\mbox{\isa{\isatt{{\isaliteral{24}{\isachardollar}}ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME{\isaliteral{2F}{\isacharslash}}etc{\isaliteral{2F}{\isacharslash}}settings}}}} is run as a
\indexref{}{executable}{bash}\hyperlink{executable.bash}{\mbox{\isa{\isatt{bash}}}} shell script with the auto-export option for
variables enabled.
@@ -108,19 +108,19 @@
thus providing the site-wide default settings. The Isabelle
distribution already contains a global settings file with sensible
defaults for most variables. When installing the system, only a few
- of these may have to be adapted (probably \hyperlink{setting.ML-SYSTEM}{\mbox{\isa{\isatt{ML{\isacharunderscore}SYSTEM}}}}
+ of these may have to be adapted (probably \hyperlink{setting.ML-SYSTEM}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}SYSTEM}}}}
etc.).
\item The file \verb|$ISABELLE_HOME_USER/etc/settings| (if it
exists) is run in the same way as the site default settings. Note
- that the variable \hyperlink{setting.ISABELLE-HOME-USER}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}HOME{\isacharunderscore}USER}}}} has already been set
+ that the variable \hyperlink{setting.ISABELLE-HOME-USER}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME{\isaliteral{5F}{\isacharunderscore}}USER}}}} has already been set
before --- usually to something like \verb|$HOME/.isabelle/IsabelleXXXX|.
Thus individual users may override the site-wide defaults. See also
- file \hyperlink{file.$ISABELLE-HOME/etc/user-settings.sample}{\mbox{\isa{\isatt{{\isachardollar}ISABELLE{\isacharunderscore}HOME{\isacharslash}etc{\isacharslash}user{\isacharminus}settings{\isachardot}sample}}}} in the
+ file \hyperlink{file.$ISABELLE-HOME/etc/user-settings.sample}{\mbox{\isa{\isatt{{\isaliteral{24}{\isachardollar}}ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME{\isaliteral{2F}{\isacharslash}}etc{\isaliteral{2F}{\isacharslash}}user{\isaliteral{2D}{\isacharminus}}settings{\isaliteral{2E}{\isachardot}}sample}}}} in the
distribution. Typically, a user settings file would contain only a
few lines, just the assigments that are really changed. One should
- definitely \emph{not} start with a full copy the basic \hyperlink{file.$ISABELLE-HOME/etc/settings}{\mbox{\isa{\isatt{{\isachardollar}ISABELLE{\isacharunderscore}HOME{\isacharslash}etc{\isacharslash}settings}}}}. This could cause very annoying
+ definitely \emph{not} start with a full copy the basic \hyperlink{file.$ISABELLE-HOME/etc/settings}{\mbox{\isa{\isatt{{\isaliteral{24}{\isachardollar}}ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME{\isaliteral{2F}{\isacharslash}}etc{\isaliteral{2F}{\isacharslash}}settings}}}}. This could cause very annoying
maintainance problems later, when the Isabelle installation is
updated or changed otherwise.
@@ -138,13 +138,13 @@
\begin{itemize}
- \item \indexdef{}{setting}{ISABELLE\_PROCESS}\hypertarget{setting.ISABELLE-PROCESS}{\hyperlink{setting.ISABELLE-PROCESS}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}PROCESS}}}}} and \indexdef{}{setting}{ISABELLE\_TOOL}\hypertarget{setting.ISABELLE-TOOL}{\hyperlink{setting.ISABELLE-TOOL}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}TOOL}}}}} are set
- automatically to the absolute path names of the \hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isacharminus}process}}}} and \hyperlink{executable.isabelle}{\mbox{\isa{\isatt{isabelle}}}} executables,
+ \item \indexdef{}{setting}{ISABELLE\_PROCESS}\hypertarget{setting.ISABELLE-PROCESS}{\hyperlink{setting.ISABELLE-PROCESS}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}PROCESS}}}}} and \indexdef{}{setting}{ISABELLE\_TOOL}\hypertarget{setting.ISABELLE-TOOL}{\hyperlink{setting.ISABELLE-TOOL}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}TOOL}}}}} are set
+ automatically to the absolute path names of the \hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isaliteral{2D}{\isacharminus}}process}}}} and \hyperlink{executable.isabelle}{\mbox{\isa{\isatt{isabelle}}}} executables,
respectively.
- \item \indexref{}{setting}{ISABELLE\_OUTPUT}\hyperlink{setting.ISABELLE-OUTPUT}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}OUTPUT}}}} will have the identifiers of
- the Isabelle distribution (cf.\ \hyperlink{setting.ISABELLE-IDENTIFIER}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}IDENTIFIER}}}}) and
- the ML system (cf.\ \hyperlink{setting.ML-IDENTIFIER}{\mbox{\isa{\isatt{ML{\isacharunderscore}IDENTIFIER}}}}) appended automatically
+ \item \indexref{}{setting}{ISABELLE\_OUTPUT}\hyperlink{setting.ISABELLE-OUTPUT}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}OUTPUT}}}} will have the identifiers of
+ the Isabelle distribution (cf.\ \hyperlink{setting.ISABELLE-IDENTIFIER}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}IDENTIFIER}}}}) and
+ the ML system (cf.\ \hyperlink{setting.ML-IDENTIFIER}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}IDENTIFIER}}}}) appended automatically
to its value.
\end{itemize}
@@ -163,110 +163,110 @@
This is a reference of common Isabelle settings variables. Note that
the list is somewhat open-ended. Third-party utilities or interfaces
may add their own selection. Variables that are special in some
- sense are marked with \isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}}.
+ sense are marked with \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}.
\begin{description}
- \item[\indexdef{}{setting}{ISABELLE\_HOME}\hypertarget{setting.ISABELLE-HOME}{\hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}HOME}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}}] is the
+ \item[\indexdef{}{setting}{ISABELLE\_HOME}\hypertarget{setting.ISABELLE-HOME}{\hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}] is the
location of the top-level Isabelle distribution directory. This is
automatically determined from the Isabelle executable that has been
- invoked. Do not attempt to set \hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}HOME}}}} yourself
+ invoked. Do not attempt to set \hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME}}}} yourself
from the shell!
- \item[\indexdef{}{setting}{ISABELLE\_HOME\_USER}\hypertarget{setting.ISABELLE-HOME-USER}{\hyperlink{setting.ISABELLE-HOME-USER}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}HOME{\isacharunderscore}USER}}}}}] is the user-specific
- counterpart of \hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}HOME}}}}. The default value is
+ \item[\indexdef{}{setting}{ISABELLE\_HOME\_USER}\hypertarget{setting.ISABELLE-HOME-USER}{\hyperlink{setting.ISABELLE-HOME-USER}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME{\isaliteral{5F}{\isacharunderscore}}USER}}}}}] is the user-specific
+ counterpart of \hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME}}}}. The default value is
relative to \verb|$HOME/.isabelle|, under rare circumstances
this may be changed in the global setting file. Typically, the
- \hyperlink{setting.ISABELLE-HOME-USER}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}HOME{\isacharunderscore}USER}}}} directory mimics \hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}HOME}}}} to some extend. In particular, site-wide defaults may
+ \hyperlink{setting.ISABELLE-HOME-USER}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME{\isaliteral{5F}{\isacharunderscore}}USER}}}} directory mimics \hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME}}}} to some extend. In particular, site-wide defaults may
be overridden by a private \verb|$ISABELLE_HOME_USER/etc/settings|.
- \item[\indexdef{}{setting}{ISABELLE\_PLATFORM}\hypertarget{setting.ISABELLE-PLATFORM}{\hyperlink{setting.ISABELLE-PLATFORM}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}PLATFORM}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}}] is automatically
+ \item[\indexdef{}{setting}{ISABELLE\_PLATFORM}\hypertarget{setting.ISABELLE-PLATFORM}{\hyperlink{setting.ISABELLE-PLATFORM}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}PLATFORM}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}] is automatically
set to a symbolic identifier for the underlying hardware and
operating system. The Isabelle platform identification always
refers to the 32 bit variant, even this is a 64 bit machine. Note
that the ML or Java runtime may have a different idea, depending on
which binaries are actually run.
- \item[\indexdef{}{setting}{ISABELLE\_PLATFORM64}\hypertarget{setting.ISABELLE-PLATFORM64}{\hyperlink{setting.ISABELLE-PLATFORM64}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}PLATFORM{\isadigit{6}}{\isadigit{4}}}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}}] is similar to
- \hyperlink{setting.ISABELLE-PLATFORM}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}PLATFORM}}}} but refers to the proper 64 bit variant
+ \item[\indexdef{}{setting}{ISABELLE\_PLATFORM64}\hypertarget{setting.ISABELLE-PLATFORM64}{\hyperlink{setting.ISABELLE-PLATFORM64}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}PLATFORM{\isadigit{6}}{\isadigit{4}}}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}] is similar to
+ \hyperlink{setting.ISABELLE-PLATFORM}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}PLATFORM}}}} but refers to the proper 64 bit variant
on a platform that supports this; the value is empty for 32 bit.
- \item[\indexdef{}{setting}{ISABELLE\_PROCESS}\hypertarget{setting.ISABELLE-PROCESS}{\hyperlink{setting.ISABELLE-PROCESS}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}PROCESS}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}}, \hyperlink{setting.ISABELLE-TOOL}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}TOOL}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}}] are automatically set to the full path
- names of the \hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isacharminus}process}}}} and \hyperlink{executable.isabelle}{\mbox{\isa{\isatt{isabelle}}}} executables, respectively. Thus other tools and scripts
- need not assume that the \hyperlink{file.$ISABELLE-HOME/bin}{\mbox{\isa{\isatt{{\isachardollar}ISABELLE{\isacharunderscore}HOME{\isacharslash}bin}}}} directory is
+ \item[\indexdef{}{setting}{ISABELLE\_PROCESS}\hypertarget{setting.ISABELLE-PROCESS}{\hyperlink{setting.ISABELLE-PROCESS}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}PROCESS}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}, \hyperlink{setting.ISABELLE-TOOL}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}TOOL}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}] are automatically set to the full path
+ names of the \hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isaliteral{2D}{\isacharminus}}process}}}} and \hyperlink{executable.isabelle}{\mbox{\isa{\isatt{isabelle}}}} executables, respectively. Thus other tools and scripts
+ need not assume that the \hyperlink{file.$ISABELLE-HOME/bin}{\mbox{\isa{\isatt{{\isaliteral{24}{\isachardollar}}ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME{\isaliteral{2F}{\isacharslash}}bin}}}} directory is
on the current search path of the shell.
- \item[\indexdef{}{setting}{ISABELLE\_IDENTIFIER}\hypertarget{setting.ISABELLE-IDENTIFIER}{\hyperlink{setting.ISABELLE-IDENTIFIER}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}IDENTIFIER}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}}] refers
+ \item[\indexdef{}{setting}{ISABELLE\_IDENTIFIER}\hypertarget{setting.ISABELLE-IDENTIFIER}{\hyperlink{setting.ISABELLE-IDENTIFIER}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}IDENTIFIER}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}] refers
to the name of this Isabelle distribution, e.g.\ ``\verb|Isabelle2008|''.
- \item[\indexdef{}{setting}{ML\_SYSTEM}\hypertarget{setting.ML-SYSTEM}{\hyperlink{setting.ML-SYSTEM}{\mbox{\isa{\isatt{ML{\isacharunderscore}SYSTEM}}}}}, \indexdef{}{setting}{ML\_HOME}\hypertarget{setting.ML-HOME}{\hyperlink{setting.ML-HOME}{\mbox{\isa{\isatt{ML{\isacharunderscore}HOME}}}}},
- \indexdef{}{setting}{ML\_OPTIONS}\hypertarget{setting.ML-OPTIONS}{\hyperlink{setting.ML-OPTIONS}{\mbox{\isa{\isatt{ML{\isacharunderscore}OPTIONS}}}}}, \indexdef{}{setting}{ML\_PLATFORM}\hypertarget{setting.ML-PLATFORM}{\hyperlink{setting.ML-PLATFORM}{\mbox{\isa{\isatt{ML{\isacharunderscore}PLATFORM}}}}}, \indexdef{}{setting}{ML\_IDENTIFIER}\hypertarget{setting.ML-IDENTIFIER}{\hyperlink{setting.ML-IDENTIFIER}{\mbox{\isa{\isatt{ML{\isacharunderscore}IDENTIFIER}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}}] specify the underlying ML system
+ \item[\indexdef{}{setting}{ML\_SYSTEM}\hypertarget{setting.ML-SYSTEM}{\hyperlink{setting.ML-SYSTEM}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}SYSTEM}}}}}, \indexdef{}{setting}{ML\_HOME}\hypertarget{setting.ML-HOME}{\hyperlink{setting.ML-HOME}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}HOME}}}}},
+ \indexdef{}{setting}{ML\_OPTIONS}\hypertarget{setting.ML-OPTIONS}{\hyperlink{setting.ML-OPTIONS}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}OPTIONS}}}}}, \indexdef{}{setting}{ML\_PLATFORM}\hypertarget{setting.ML-PLATFORM}{\hyperlink{setting.ML-PLATFORM}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}PLATFORM}}}}}, \indexdef{}{setting}{ML\_IDENTIFIER}\hypertarget{setting.ML-IDENTIFIER}{\hyperlink{setting.ML-IDENTIFIER}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}IDENTIFIER}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}] specify the underlying ML system
to be used for Isabelle. There is only a fixed set of admissable
- \hyperlink{setting.ML-SYSTEM}{\mbox{\isa{\isatt{ML{\isacharunderscore}SYSTEM}}}} names (see the \hyperlink{file.$ISABELLE-HOME/etc/settings}{\mbox{\isa{\isatt{{\isachardollar}ISABELLE{\isacharunderscore}HOME{\isacharslash}etc{\isacharslash}settings}}}} file of the distribution).
+ \hyperlink{setting.ML-SYSTEM}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}SYSTEM}}}} names (see the \hyperlink{file.$ISABELLE-HOME/etc/settings}{\mbox{\isa{\isatt{{\isaliteral{24}{\isachardollar}}ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME{\isaliteral{2F}{\isacharslash}}etc{\isaliteral{2F}{\isacharslash}}settings}}}} file of the distribution).
- The actual compiler binary will be run from the directory \hyperlink{setting.ML-HOME}{\mbox{\isa{\isatt{ML{\isacharunderscore}HOME}}}}, with \hyperlink{setting.ML-OPTIONS}{\mbox{\isa{\isatt{ML{\isacharunderscore}OPTIONS}}}} as first arguments on the
- command line. The optional \hyperlink{setting.ML-PLATFORM}{\mbox{\isa{\isatt{ML{\isacharunderscore}PLATFORM}}}} may specify the
+ The actual compiler binary will be run from the directory \hyperlink{setting.ML-HOME}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}HOME}}}}, with \hyperlink{setting.ML-OPTIONS}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}OPTIONS}}}} as first arguments on the
+ command line. The optional \hyperlink{setting.ML-PLATFORM}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}PLATFORM}}}} may specify the
binary format of ML heap images, which is useful for cross-platform
- installations. The value of \hyperlink{setting.ML-IDENTIFIER}{\mbox{\isa{\isatt{ML{\isacharunderscore}IDENTIFIER}}}} is
- automatically obtained by composing the values of \hyperlink{setting.ML-SYSTEM}{\mbox{\isa{\isatt{ML{\isacharunderscore}SYSTEM}}}}, \hyperlink{setting.ML-PLATFORM}{\mbox{\isa{\isatt{ML{\isacharunderscore}PLATFORM}}}} and the Isabelle version values.
+ installations. The value of \hyperlink{setting.ML-IDENTIFIER}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}IDENTIFIER}}}} is
+ automatically obtained by composing the values of \hyperlink{setting.ML-SYSTEM}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}SYSTEM}}}}, \hyperlink{setting.ML-PLATFORM}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}PLATFORM}}}} and the Isabelle version values.
- \item[\indexdef{}{setting}{ISABELLE\_PATH}\hypertarget{setting.ISABELLE-PATH}{\hyperlink{setting.ISABELLE-PATH}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}PATH}}}}}] is a list of directories
+ \item[\indexdef{}{setting}{ISABELLE\_PATH}\hypertarget{setting.ISABELLE-PATH}{\hyperlink{setting.ISABELLE-PATH}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}PATH}}}}}] is a list of directories
(separated by colons) where Isabelle logic images may reside. When
- looking up heaps files, the value of \hyperlink{setting.ML-IDENTIFIER}{\mbox{\isa{\isatt{ML{\isacharunderscore}IDENTIFIER}}}} is
+ looking up heaps files, the value of \hyperlink{setting.ML-IDENTIFIER}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}IDENTIFIER}}}} is
appended to each component internally.
- \item[\indexdef{}{setting}{ISABELLE\_OUTPUT}\hypertarget{setting.ISABELLE-OUTPUT}{\hyperlink{setting.ISABELLE-OUTPUT}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}OUTPUT}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}}] is a
+ \item[\indexdef{}{setting}{ISABELLE\_OUTPUT}\hypertarget{setting.ISABELLE-OUTPUT}{\hyperlink{setting.ISABELLE-OUTPUT}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}OUTPUT}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}] is a
directory where output heap files should be stored by default. The
ML system and Isabelle version identifier is appended here, too.
- \item[\indexdef{}{setting}{ISABELLE\_BROWSER\_INFO}\hypertarget{setting.ISABELLE-BROWSER-INFO}{\hyperlink{setting.ISABELLE-BROWSER-INFO}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}BROWSER{\isacharunderscore}INFO}}}}}] is the directory where
+ \item[\indexdef{}{setting}{ISABELLE\_BROWSER\_INFO}\hypertarget{setting.ISABELLE-BROWSER-INFO}{\hyperlink{setting.ISABELLE-BROWSER-INFO}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}BROWSER{\isaliteral{5F}{\isacharunderscore}}INFO}}}}}] is the directory where
theory browser information (HTML text, graph data, and printable
documents) is stored (see also \secref{sec:info}). The default
value is \verb|$ISABELLE_HOME_USER/browser_info|.
- \item[\indexdef{}{setting}{ISABELLE\_LOGIC}\hypertarget{setting.ISABELLE-LOGIC}{\hyperlink{setting.ISABELLE-LOGIC}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}LOGIC}}}}}] specifies the default logic to
+ \item[\indexdef{}{setting}{ISABELLE\_LOGIC}\hypertarget{setting.ISABELLE-LOGIC}{\hyperlink{setting.ISABELLE-LOGIC}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}LOGIC}}}}}] specifies the default logic to
load if none is given explicitely by the user. The default value is
\verb|HOL|.
- \item[\indexdef{}{setting}{ISABELLE\_LINE\_EDITOR}\hypertarget{setting.ISABELLE-LINE-EDITOR}{\hyperlink{setting.ISABELLE-LINE-EDITOR}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}LINE{\isacharunderscore}EDITOR}}}}}] specifies the default
+ \item[\indexdef{}{setting}{ISABELLE\_LINE\_EDITOR}\hypertarget{setting.ISABELLE-LINE-EDITOR}{\hyperlink{setting.ISABELLE-LINE-EDITOR}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}LINE{\isaliteral{5F}{\isacharunderscore}}EDITOR}}}}}] specifies the default
line editor for the \indexref{}{tool}{tty}\hyperlink{tool.tty}{\mbox{\isa{\isatt{tty}}}} interface.
- \item[\indexdef{}{setting}{ISABELLE\_USEDIR\_OPTIONS}\hypertarget{setting.ISABELLE-USEDIR-OPTIONS}{\hyperlink{setting.ISABELLE-USEDIR-OPTIONS}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}USEDIR{\isacharunderscore}OPTIONS}}}}}] is implicitly prefixed
+ \item[\indexdef{}{setting}{ISABELLE\_USEDIR\_OPTIONS}\hypertarget{setting.ISABELLE-USEDIR-OPTIONS}{\hyperlink{setting.ISABELLE-USEDIR-OPTIONS}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}USEDIR{\isaliteral{5F}{\isacharunderscore}}OPTIONS}}}}}] is implicitly prefixed
to the command line of any \indexref{}{tool}{usedir}\hyperlink{tool.usedir}{\mbox{\isa{\isatt{usedir}}}} invocation. This
typically contains compilation options for object-logics --- \hyperlink{tool.usedir}{\mbox{\isa{\isatt{usedir}}}} is the basic utility for managing logic sessions (cf.\ the
\verb|IsaMakefile|s in the distribution).
- \item[\indexdef{}{setting}{ISABELLE\_FILE\_IDENT}\hypertarget{setting.ISABELLE-FILE-IDENT}{\hyperlink{setting.ISABELLE-FILE-IDENT}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}FILE{\isacharunderscore}IDENT}}}}}] specifies a shell command
+ \item[\indexdef{}{setting}{ISABELLE\_FILE\_IDENT}\hypertarget{setting.ISABELLE-FILE-IDENT}{\hyperlink{setting.ISABELLE-FILE-IDENT}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}FILE{\isaliteral{5F}{\isacharunderscore}}IDENT}}}}}] specifies a shell command
for producing a source file identification, based on the actual
content instead of the full physical path and date stamp (which is
the default). A typical identification would produce a ``digest'' of
the text, using a cryptographic hash function like SHA-1, for
example.
- \item[\indexdef{}{setting}{ISABELLE\_LATEX}\hypertarget{setting.ISABELLE-LATEX}{\hyperlink{setting.ISABELLE-LATEX}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}LATEX}}}}}, \indexdef{}{setting}{ISABELLE\_PDFLATEX}\hypertarget{setting.ISABELLE-PDFLATEX}{\hyperlink{setting.ISABELLE-PDFLATEX}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}PDFLATEX}}}}}, \indexdef{}{setting}{ISABELLE\_BIBTEX}\hypertarget{setting.ISABELLE-BIBTEX}{\hyperlink{setting.ISABELLE-BIBTEX}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}BIBTEX}}}}}, \indexdef{}{setting}{ISABELLE\_DVIPS}\hypertarget{setting.ISABELLE-DVIPS}{\hyperlink{setting.ISABELLE-DVIPS}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}DVIPS}}}}}] refer to {\LaTeX} related tools for Isabelle
+ \item[\indexdef{}{setting}{ISABELLE\_LATEX}\hypertarget{setting.ISABELLE-LATEX}{\hyperlink{setting.ISABELLE-LATEX}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}LATEX}}}}}, \indexdef{}{setting}{ISABELLE\_PDFLATEX}\hypertarget{setting.ISABELLE-PDFLATEX}{\hyperlink{setting.ISABELLE-PDFLATEX}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}PDFLATEX}}}}}, \indexdef{}{setting}{ISABELLE\_BIBTEX}\hypertarget{setting.ISABELLE-BIBTEX}{\hyperlink{setting.ISABELLE-BIBTEX}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}BIBTEX}}}}}, \indexdef{}{setting}{ISABELLE\_DVIPS}\hypertarget{setting.ISABELLE-DVIPS}{\hyperlink{setting.ISABELLE-DVIPS}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}DVIPS}}}}}] refer to {\LaTeX} related tools for Isabelle
document preparation (see also \secref{sec:tool-latex}).
- \item[\indexdef{}{setting}{ISABELLE\_TOOLS}\hypertarget{setting.ISABELLE-TOOLS}{\hyperlink{setting.ISABELLE-TOOLS}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}TOOLS}}}}}] is a colon separated list of
+ \item[\indexdef{}{setting}{ISABELLE\_TOOLS}\hypertarget{setting.ISABELLE-TOOLS}{\hyperlink{setting.ISABELLE-TOOLS}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}TOOLS}}}}}] is a colon separated list of
directories that are scanned by \hyperlink{executable.isabelle}{\mbox{\isa{\isatt{isabelle}}}} for external
utility programs (see also \secref{sec:isabelle-tool}).
- \item[\indexdef{}{setting}{ISABELLE\_DOCS}\hypertarget{setting.ISABELLE-DOCS}{\hyperlink{setting.ISABELLE-DOCS}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}DOCS}}}}}] is a colon separated list of
+ \item[\indexdef{}{setting}{ISABELLE\_DOCS}\hypertarget{setting.ISABELLE-DOCS}{\hyperlink{setting.ISABELLE-DOCS}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}DOCS}}}}}] is a colon separated list of
directories with documentation files.
- \item[\indexdef{}{setting}{ISABELLE\_DOC\_FORMAT}\hypertarget{setting.ISABELLE-DOC-FORMAT}{\hyperlink{setting.ISABELLE-DOC-FORMAT}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}DOC{\isacharunderscore}FORMAT}}}}}] specifies the preferred
+ \item[\indexdef{}{setting}{ISABELLE\_DOC\_FORMAT}\hypertarget{setting.ISABELLE-DOC-FORMAT}{\hyperlink{setting.ISABELLE-DOC-FORMAT}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}DOC{\isaliteral{5F}{\isacharunderscore}}FORMAT}}}}}] specifies the preferred
document format, typically \verb|dvi| or \verb|pdf|.
- \item[\indexdef{}{setting}{DVI\_VIEWER}\hypertarget{setting.DVI-VIEWER}{\hyperlink{setting.DVI-VIEWER}{\mbox{\isa{\isatt{DVI{\isacharunderscore}VIEWER}}}}}] specifies the command to be used
+ \item[\indexdef{}{setting}{DVI\_VIEWER}\hypertarget{setting.DVI-VIEWER}{\hyperlink{setting.DVI-VIEWER}{\mbox{\isa{\isatt{DVI{\isaliteral{5F}{\isacharunderscore}}VIEWER}}}}}] specifies the command to be used
for displaying \verb|dvi| files.
- \item[\indexdef{}{setting}{PDF\_VIEWER}\hypertarget{setting.PDF-VIEWER}{\hyperlink{setting.PDF-VIEWER}{\mbox{\isa{\isatt{PDF{\isacharunderscore}VIEWER}}}}}] specifies the command to be used
+ \item[\indexdef{}{setting}{PDF\_VIEWER}\hypertarget{setting.PDF-VIEWER}{\hyperlink{setting.PDF-VIEWER}{\mbox{\isa{\isatt{PDF{\isaliteral{5F}{\isacharunderscore}}VIEWER}}}}}] specifies the command to be used
for displaying \verb|pdf| files.
- \item[\indexdef{}{setting}{PRINT\_COMMAND}\hypertarget{setting.PRINT-COMMAND}{\hyperlink{setting.PRINT-COMMAND}{\mbox{\isa{\isatt{PRINT{\isacharunderscore}COMMAND}}}}}] specifies the standard printer
+ \item[\indexdef{}{setting}{PRINT\_COMMAND}\hypertarget{setting.PRINT-COMMAND}{\hyperlink{setting.PRINT-COMMAND}{\mbox{\isa{\isatt{PRINT{\isaliteral{5F}{\isacharunderscore}}COMMAND}}}}}] specifies the standard printer
spool command, which is expected to accept \verb|ps| files.
- \item[\indexdef{}{setting}{ISABELLE\_TMP\_PREFIX}\hypertarget{setting.ISABELLE-TMP-PREFIX}{\hyperlink{setting.ISABELLE-TMP-PREFIX}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}TMP{\isacharunderscore}PREFIX}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}}] is the
- prefix from which any running \hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isacharminus}process}}}}
+ \item[\indexdef{}{setting}{ISABELLE\_TMP\_PREFIX}\hypertarget{setting.ISABELLE-TMP-PREFIX}{\hyperlink{setting.ISABELLE-TMP-PREFIX}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}TMP{\isaliteral{5F}{\isacharunderscore}}PREFIX}}}}}\isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}] is the
+ prefix from which any running \hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isaliteral{2D}{\isacharminus}}process}}}}
derives an individual directory for temporary files. The default is
somewhere in \verb|/tmp|.
@@ -300,7 +300,7 @@
\end{ttbox}
Components can also add to existing Isabelle settings such as
- \indexdef{}{setting}{ISABELLE\_TOOLS}\hypertarget{setting.ISABELLE-TOOLS}{\hyperlink{setting.ISABELLE-TOOLS}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}TOOLS}}}}}, in order to provide
+ \indexdef{}{setting}{ISABELLE\_TOOLS}\hypertarget{setting.ISABELLE-TOOLS}{\hyperlink{setting.ISABELLE-TOOLS}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}TOOLS}}}}}, in order to provide
component-specific tools that can be invoked by end-users. For
example:
@@ -315,9 +315,9 @@
\end{itemize}
- The root of component initialization is \hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}HOME}}}}
+ The root of component initialization is \hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME}}}}
itself. After initializing all of its sub-components recursively,
- \hyperlink{setting.ISABELLE-HOME-USER}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}HOME{\isacharunderscore}USER}}}} is included in the same manner (if
+ \hyperlink{setting.ISABELLE-HOME-USER}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME{\isaliteral{5F}{\isacharunderscore}}USER}}}} is included in the same manner (if
that directory exists). Thus users can easily add private
components to \verb|$ISABELLE_HOME_USER/etc/components|.
@@ -332,7 +332,7 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-The \indexdef{}{executable}{isabelle-process}\hypertarget{executable.isabelle-process}{\hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isacharminus}process}}}}} executable runs bare-bones
+The \indexdef{}{executable}{isabelle-process}\hypertarget{executable.isabelle-process}{\hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isaliteral{2D}{\isacharminus}}process}}}}} executable runs bare-bones
Isabelle logic sessions --- either interactively or in batch mode.
It provides an abstraction over the underlying ML system, and over
the actual heap file locations. Its usage is:
@@ -361,11 +361,11 @@
\end{ttbox}
Input files without path specifications are looked up in the
- \hyperlink{setting.ISABELLE-PATH}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}PATH}}}} setting, which may consist of multiple
+ \hyperlink{setting.ISABELLE-PATH}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}PATH}}}} setting, which may consist of multiple
components separated by colons --- these are tried in the given
- order with the value of \hyperlink{setting.ML-IDENTIFIER}{\mbox{\isa{\isatt{ML{\isacharunderscore}IDENTIFIER}}}} appended
+ order with the value of \hyperlink{setting.ML-IDENTIFIER}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}IDENTIFIER}}}} appended
internally. In a similar way, base names are relative to the
- directory specified by \hyperlink{setting.ISABELLE-OUTPUT}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}OUTPUT}}}}. In any case,
+ directory specified by \hyperlink{setting.ISABELLE-OUTPUT}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}OUTPUT}}}}. In any case,
actual file locations may also be given by including at least one
slash (\verb|/|) in the name (hint: use \verb|./| to
refer to the current directory).%
@@ -423,7 +423,7 @@
\medskip The \verb|-W| option makes Isabelle enter a special
process wrapper for interaction via the Isabelle/Scala layer, see
- also \hyperlink{file.~~/src/Pure/System/isabelle-process.scala}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}Pure{\isacharslash}System{\isacharslash}isabelle{\isacharunderscore}process{\isachardot}scala}}}}. The
+ also \hyperlink{file.~~/src/Pure/System/isabelle-process.scala}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}Pure{\isaliteral{2F}{\isacharslash}}System{\isaliteral{2F}{\isacharslash}}isabelle{\isaliteral{5F}{\isacharunderscore}}process{\isaliteral{2E}{\isachardot}}scala}}}}. The
protocol between the ML and JVM process is private to the
implementation.
@@ -439,15 +439,15 @@
%
\begin{isamarkuptext}%
Run an interactive session of the default object-logic (as specified
- by the \hyperlink{setting.ISABELLE-LOGIC}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}LOGIC}}}} setting) like this:
+ by the \hyperlink{setting.ISABELLE-LOGIC}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}LOGIC}}}} setting) like this:
\begin{ttbox}
isabelle-process
\end{ttbox}
- Usually \hyperlink{setting.ISABELLE-LOGIC}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}LOGIC}}}} refers to one of the standard
+ Usually \hyperlink{setting.ISABELLE-LOGIC}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}LOGIC}}}} refers to one of the standard
logic images, which are read-only by default. A writable session
--- based on \verb|FOL|, but output to \verb|Foo| (in the
- directory specified by the \hyperlink{setting.ISABELLE-OUTPUT}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}OUTPUT}}}} setting) ---
+ directory specified by the \hyperlink{setting.ISABELLE-OUTPUT}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}OUTPUT}}}} setting) ---
may be invoked as follows:
\begin{ttbox}
isabelle-process FOL Foo
@@ -505,7 +505,7 @@
In principle, Isabelle tools are ordinary executable scripts that
are run within the Isabelle settings environment, see
\secref{sec:settings}. The set of available tools is collected by
- \hyperlink{executable.isabelle}{\mbox{\isa{\isatt{isabelle}}}} from the directories listed in the \hyperlink{setting.ISABELLE-TOOLS}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}TOOLS}}}} setting. Do not try to call the scripts directly
+ \hyperlink{executable.isabelle}{\mbox{\isa{\isatt{isabelle}}}} from the directories listed in the \hyperlink{setting.ISABELLE-TOOLS}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}TOOLS}}}} setting. Do not try to call the scripts directly
from the shell. Neither should you add the tool directories to your
shell's search path!%
\end{isamarkuptext}%
--- a/doc-src/System/Thy/document/Interfaces.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/System/Thy/document/Interfaces.tex Mon Nov 08 14:41:11 2010 +0100
@@ -73,15 +73,15 @@
\begin{description}
- \item[\indexdef{}{setting}{PROOFGENERAL\_HOME}\hypertarget{setting.PROOFGENERAL-HOME}{\hyperlink{setting.PROOFGENERAL-HOME}{\mbox{\isa{\isatt{PROOFGENERAL{\isacharunderscore}HOME}}}}}] points to the main
+ \item[\indexdef{}{setting}{PROOFGENERAL\_HOME}\hypertarget{setting.PROOFGENERAL-HOME}{\hyperlink{setting.PROOFGENERAL-HOME}{\mbox{\isa{\isatt{PROOFGENERAL{\isaliteral{5F}{\isacharunderscore}}HOME}}}}}] points to the main
installation directory of the Proof General distribution. The
default settings try to locate this in a number of standard places,
notably \verb|$ISABELLE_HOME/contrib/ProofGeneral|.
- \item[\indexdef{}{setting}{PROOFGENERAL\_OPTIONS}\hypertarget{setting.PROOFGENERAL-OPTIONS}{\hyperlink{setting.PROOFGENERAL-OPTIONS}{\mbox{\isa{\isatt{PROOFGENERAL{\isacharunderscore}OPTIONS}}}}}] is implicitly prefixed to
+ \item[\indexdef{}{setting}{PROOFGENERAL\_OPTIONS}\hypertarget{setting.PROOFGENERAL-OPTIONS}{\hyperlink{setting.PROOFGENERAL-OPTIONS}{\mbox{\isa{\isatt{PROOFGENERAL{\isaliteral{5F}{\isacharunderscore}}OPTIONS}}}}}] is implicitly prefixed to
the command line of any invocation of the Proof General \verb|interface| script.
- \item[\indexdef{}{setting}{XSYMBOL\_INSTALLFONTS}\hypertarget{setting.XSYMBOL-INSTALLFONTS}{\hyperlink{setting.XSYMBOL-INSTALLFONTS}{\mbox{\isa{\isatt{XSYMBOL{\isacharunderscore}INSTALLFONTS}}}}}] may contain a small shell
+ \item[\indexdef{}{setting}{XSYMBOL\_INSTALLFONTS}\hypertarget{setting.XSYMBOL-INSTALLFONTS}{\hyperlink{setting.XSYMBOL-INSTALLFONTS}{\mbox{\isa{\isatt{XSYMBOL{\isaliteral{5F}{\isacharunderscore}}INSTALLFONTS}}}}}] may contain a small shell
script to install the X11 fonts required for the X-Symbols mode of
Proof General. This is only relevant if the X11 display server runs
on a different machine than the Emacs application, with a different
--- a/doc-src/System/Thy/document/Misc.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/System/Thy/document/Misc.tex Mon Nov 08 14:41:11 2010 +0100
@@ -46,7 +46,7 @@
\medskip The \verb|-c| option causes the input file to be
removed after use. The program for viewing \verb|dvi| files is
- determined by the \hyperlink{setting.DVI-VIEWER}{\mbox{\isa{\isatt{DVI{\isacharunderscore}VIEWER}}}} setting.%
+ determined by the \hyperlink{setting.DVI-VIEWER}{\mbox{\isa{\isatt{DVI{\isaliteral{5F}{\isacharunderscore}}VIEWER}}}} setting.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -66,10 +66,10 @@
of these identifiers may be specified as the first argument in order
to have the corresponding document displayed.
- \medskip The \hyperlink{setting.ISABELLE-DOCS}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}DOCS}}}} setting specifies the list of
+ \medskip The \hyperlink{setting.ISABELLE-DOCS}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}DOCS}}}} setting specifies the list of
directories (separated by colons) to be scanned for documentations.
The program for viewing \verb|dvi| files is determined by the
- \hyperlink{setting.DVI-VIEWER}{\mbox{\isa{\isatt{DVI{\isacharunderscore}VIEWER}}}} setting.%
+ \hyperlink{setting.DVI-VIEWER}{\mbox{\isa{\isatt{DVI{\isaliteral{5F}{\isacharunderscore}}VIEWER}}}} setting.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -79,7 +79,7 @@
%
\begin{isamarkuptext}%
The \indexdef{}{tool}{findlogics}\hypertarget{tool.findlogics}{\hyperlink{tool.findlogics}{\mbox{\isa{\isatt{findlogics}}}}} utility traverses all directories
- specified in \hyperlink{setting.ISABELLE-PATH}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}PATH}}}}, looking for Isabelle logic
+ specified in \hyperlink{setting.ISABELLE-PATH}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}PATH}}}}, looking for Isabelle logic
images. Its usage is:
\begin{ttbox}
Usage: findlogics
@@ -88,8 +88,8 @@
\end{ttbox}
The base names of all files found on the path are printed --- sorted
- and with duplicates removed. Also note that lookup in \hyperlink{setting.ISABELLE-PATH}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}PATH}}}} includes the current values of \hyperlink{setting.ML-SYSTEM}{\mbox{\isa{\isatt{ML{\isacharunderscore}SYSTEM}}}}
- and \hyperlink{setting.ML-PLATFORM}{\mbox{\isa{\isatt{ML{\isacharunderscore}PLATFORM}}}}. Thus switching to another ML compiler
+ and with duplicates removed. Also note that lookup in \hyperlink{setting.ISABELLE-PATH}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}PATH}}}} includes the current values of \hyperlink{setting.ML-SYSTEM}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}SYSTEM}}}}
+ and \hyperlink{setting.ML-PLATFORM}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}PLATFORM}}}}. Thus switching to another ML compiler
may change the set of logic images available.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -152,9 +152,9 @@
ISABELLE_OUTPUT="\$ISABELLE_HOME_USER/heaps"
\end{ttbox}
- Note how the \hyperlink{setting.ML-IDENTIFIER}{\mbox{\isa{\isatt{ML{\isacharunderscore}IDENTIFIER}}}} value got appended
+ Note how the \hyperlink{setting.ML-IDENTIFIER}{\mbox{\isa{\isatt{ML{\isaliteral{5F}{\isacharunderscore}}IDENTIFIER}}}} value got appended
automatically to each path component. This is a special feature of
- \hyperlink{setting.ISABELLE-OUTPUT}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}OUTPUT}}}}.%
+ \hyperlink{setting.ISABELLE-OUTPUT}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}OUTPUT}}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -180,10 +180,10 @@
\end{ttbox}
The \verb|-d| option overrides the current Isabelle
- distribution directory as determined by \hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}HOME}}}}.
+ distribution directory as determined by \hyperlink{setting.ISABELLE-HOME}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME}}}}.
The \verb|-p| option installs executable wrapper scripts for
- \hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isacharminus}process}}}}, \hyperlink{executable.isabelle}{\mbox{\isa{\isatt{isabelle}}}},
+ \hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isaliteral{2D}{\isacharminus}}process}}}}, \hyperlink{executable.isabelle}{\mbox{\isa{\isatt{isabelle}}}},
\hyperlink{executable.Isabelle}{\mbox{\isa{\isatt{Isabelle}}}}, containing proper absolute references to the
Isabelle distribution directory. A typical \verb|DIR|
specification would be some directory expected to be in the shell's
@@ -250,7 +250,7 @@
\begin{isamarkuptext}%
Refer to the \verb|IsaMakefile|s of the Isabelle distribution's
object-logics as a model for your own developments. For example,
- see \hyperlink{file.~~/src/FOL/IsaMakefile}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}FOL{\isacharslash}IsaMakefile}}}}.%
+ see \hyperlink{file.~~/src/FOL/IsaMakefile}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}FOL{\isaliteral{2F}{\isacharslash}}IsaMakefile}}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -289,7 +289,7 @@
\end{ttbox}
The \verb|-c| option causes the input file to be removed
- after use. The printer spool command is determined by the \hyperlink{setting.PRINT-COMMAND}{\mbox{\isa{\isatt{PRINT{\isacharunderscore}COMMAND}}}} setting.%
+ after use. The printer spool command is determined by the \hyperlink{setting.PRINT-COMMAND}{\mbox{\isa{\isatt{PRINT{\isaliteral{5F}{\isacharunderscore}}COMMAND}}}} setting.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -343,31 +343,31 @@
comments).
\item Markup elements are represented via ASCII control characters
- \isa{{\isachardoublequote}\isactrlbold X\ {\isacharequal}\ {\isadigit{5}}{\isachardoublequote}} and \isa{{\isachardoublequote}\isactrlbold Y\ {\isacharequal}\ {\isadigit{6}}{\isachardoublequote}} as follows:
+ \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E626F6C643E}{}\isactrlbold X\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{5}}{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E626F6C643E}{}\isactrlbold Y\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{6}}{\isaliteral{22}{\isachardoublequote}}} as follows:
\begin{tabular}{ll}
XML & YXML \\\hline
- \verb|<|\isa{{\isachardoublequote}name\ attribute{\isachardoublequote}}\verb|=|\isa{{\isachardoublequote}value\ {\isasymdots}{\isachardoublequote}}\verb|>| &
- \isa{{\isachardoublequote}\isactrlbold X\isactrlbold Yname\isactrlbold Yattribute{\isachardoublequote}}\verb|=|\isa{{\isachardoublequote}value{\isasymdots}\isactrlbold X{\isachardoublequote}} \\
- \verb|</|\isa{name}\verb|>| & \isa{{\isachardoublequote}\isactrlbold X\isactrlbold Y\isactrlbold X{\isachardoublequote}} \\
+ \verb|<|\isa{{\isaliteral{22}{\isachardoublequote}}name\ attribute{\isaliteral{22}{\isachardoublequote}}}\verb|=|\isa{{\isaliteral{22}{\isachardoublequote}}value\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{22}{\isachardoublequote}}}\verb|>| &
+ \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E626F6C643E}{}\isactrlbold X\isaliteral{5C3C5E626F6C643E}{}\isactrlbold Yname\isaliteral{5C3C5E626F6C643E}{}\isactrlbold Yattribute{\isaliteral{22}{\isachardoublequote}}}\verb|=|\isa{{\isaliteral{22}{\isachardoublequote}}value{\isaliteral{5C3C646F74733E}{\isasymdots}}\isaliteral{5C3C5E626F6C643E}{}\isactrlbold X{\isaliteral{22}{\isachardoublequote}}} \\
+ \verb|</|\isa{name}\verb|>| & \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E626F6C643E}{}\isactrlbold X\isaliteral{5C3C5E626F6C643E}{}\isactrlbold Y\isaliteral{5C3C5E626F6C643E}{}\isactrlbold X{\isaliteral{22}{\isachardoublequote}}} \\
\end{tabular}
There is no special case for empty body text, i.e.\ \verb|<foo/>| is treated like \verb|<foo></foo>|. Also note that
- \isa{{\isachardoublequote}\isactrlbold X{\isachardoublequote}} and \isa{{\isachardoublequote}\isactrlbold Y{\isachardoublequote}} may never occur in
+ \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E626F6C643E}{}\isactrlbold X{\isaliteral{22}{\isachardoublequote}}} and \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E626F6C643E}{}\isactrlbold Y{\isaliteral{22}{\isachardoublequote}}} may never occur in
well-formed XML documents.
\end{enumerate}
Parsing YXML is pretty straight-forward: split the text into chunks
- separated by \isa{{\isachardoublequote}\isactrlbold X{\isachardoublequote}}, then split each chunk into
- sub-chunks separated by \isa{{\isachardoublequote}\isactrlbold Y{\isachardoublequote}}. Markup chunks start
+ separated by \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E626F6C643E}{}\isactrlbold X{\isaliteral{22}{\isachardoublequote}}}, then split each chunk into
+ sub-chunks separated by \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E626F6C643E}{}\isactrlbold Y{\isaliteral{22}{\isachardoublequote}}}. Markup chunks start
with an empty sub-chunk, and a second empty sub-chunk indicates
close of an element. Any other non-empty chunk consists of plain
- text. For example, see \hyperlink{file.~~/src/Pure/General/yxml.ML}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}Pure{\isacharslash}General{\isacharslash}yxml{\isachardot}ML}}}} or
- \hyperlink{file.~~/src/Pure/General/yxml.scala}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}Pure{\isacharslash}General{\isacharslash}yxml{\isachardot}scala}}}}.
+ text. For example, see \hyperlink{file.~~/src/Pure/General/yxml.ML}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}Pure{\isaliteral{2F}{\isacharslash}}General{\isaliteral{2F}{\isacharslash}}yxml{\isaliteral{2E}{\isachardot}}ML}}}} or
+ \hyperlink{file.~~/src/Pure/General/yxml.scala}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}Pure{\isaliteral{2F}{\isacharslash}}General{\isaliteral{2F}{\isacharslash}}yxml{\isaliteral{2E}{\isachardot}}scala}}}}.
YXML documents may be detected quickly by checking that the first
- two characters are \isa{{\isachardoublequote}\isactrlbold X\isactrlbold Y{\isachardoublequote}}.%
+ two characters are \isa{{\isaliteral{22}{\isachardoublequote}}\isaliteral{5C3C5E626F6C643E}{}\isactrlbold X\isaliteral{5C3C5E626F6C643E}{}\isactrlbold Y{\isaliteral{22}{\isachardoublequote}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
--- a/doc-src/System/Thy/document/Presentation.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/System/Thy/document/Presentation.tex Mon Nov 08 14:41:11 2010 +0100
@@ -34,7 +34,7 @@
The Isabelle tools \indexref{}{tool}{mkdir}\hyperlink{tool.mkdir}{\mbox{\isa{\isatt{mkdir}}}} and \indexref{}{tool}{make}\hyperlink{tool.make}{\mbox{\isa{\isatt{make}}}} provide
the primary means for managing Isabelle sessions, including proper
setup for presentation. Here the \indexref{}{tool}{usedir}\hyperlink{tool.usedir}{\mbox{\isa{\isatt{usedir}}}} tool takes care
- to let \indexref{}{executable}{isabelle-process}\hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isacharminus}process}}}} process run any
+ to let \indexref{}{executable}{isabelle-process}\hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isaliteral{2D}{\isacharminus}}process}}}} process run any
additional stages required for document preparation, notably the
tools \indexref{}{tool}{document}\hyperlink{tool.document}{\mbox{\isa{\isatt{document}}}} and \indexref{}{tool}{latex}\hyperlink{tool.latex}{\mbox{\isa{\isatt{latex}}}}. The complete tool
chain for managing batch-mode Isabelle sessions is illustrated in
@@ -53,7 +53,7 @@
\verb|isabelle| \hyperlink{tool.usedir}{\mbox{\isa{\isatt{usedir}}}} & part of the standard
\verb|IsaMakefile| entry of a session; \\
- \hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isacharminus}process}}}} & run through \verb|isabelle| \indexref{}{tool}{usedir}\hyperlink{tool.usedir}{\mbox{\isa{\isatt{usedir}}}}; \\
+ \hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isaliteral{2D}{\isacharminus}}process}}}} & run through \verb|isabelle| \indexref{}{tool}{usedir}\hyperlink{tool.usedir}{\mbox{\isa{\isatt{usedir}}}}; \\
\verb|isabelle| \indexref{}{tool}{document}\hyperlink{tool.document}{\mbox{\isa{\isatt{document}}}} & run by the Isabelle
process if document preparation is enabled; \\
@@ -96,14 +96,14 @@
The easiest way to let Isabelle generate theory browsing information
for existing sessions is to append ``\verb|-i true|'' to the
- \indexref{}{setting}{ISABELLE\_USEDIR\_OPTIONS}\hyperlink{setting.ISABELLE-USEDIR-OPTIONS}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}USEDIR{\isacharunderscore}OPTIONS}}}} before invoking \verb|isabelle| \hyperlink{tool.make}{\mbox{\isa{\isatt{make}}}} (or \hyperlink{file.$ISABELLE-HOME/build}{\mbox{\isa{\isatt{{\isachardollar}ISABELLE{\isacharunderscore}HOME{\isacharslash}build}}}}). For
+ \indexref{}{setting}{ISABELLE\_USEDIR\_OPTIONS}\hyperlink{setting.ISABELLE-USEDIR-OPTIONS}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}USEDIR{\isaliteral{5F}{\isacharunderscore}}OPTIONS}}}} before invoking \verb|isabelle| \hyperlink{tool.make}{\mbox{\isa{\isatt{make}}}} (or \hyperlink{file.$ISABELLE-HOME/build}{\mbox{\isa{\isatt{{\isaliteral{24}{\isachardollar}}ISABELLE{\isaliteral{5F}{\isacharunderscore}}HOME{\isaliteral{2F}{\isacharslash}}build}}}}). For
example, add something like this to your Isabelle settings file
\begin{ttbox}
ISABELLE_USEDIR_OPTIONS="-i true"
\end{ttbox}
- and then change into the \hyperlink{file.~~/src/FOL}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}FOL}}}} directory and run
+ and then change into the \hyperlink{file.~~/src/FOL}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}FOL}}}} directory and run
\verb|isabelle| \hyperlink{tool.make}{\mbox{\isa{\isatt{make}}}}, or even \verb|isabelle|
\hyperlink{tool.make}{\mbox{\isa{\isatt{make}}}}~\verb|all|. The presentation output will appear
in \verb|ISABELLE_BROWSER_INFO/FOL|, which usually refers to
@@ -111,7 +111,7 @@
\verb|-v true| will make the internal runs of \hyperlink{tool.usedir}{\mbox{\isa{\isatt{usedir}}}}
more explicit about such details.
- Many standard Isabelle sessions (such as \hyperlink{file.~~/src/HOL/ex}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}HOL{\isacharslash}ex}}}})
+ Many standard Isabelle sessions (such as \hyperlink{file.~~/src/HOL/ex}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}HOL{\isaliteral{2F}{\isacharslash}}ex}}}})
also provide actual printable documents. These are prepared
automatically as well if enabled like this, using the \verb|-d| option
\begin{ttbox}
@@ -124,7 +124,7 @@
well, see \secref{sec:tool-document} for further details.
\bigskip The theory browsing information is stored in a
- sub-directory directory determined by the \indexref{}{setting}{ISABELLE\_BROWSER\_INFO}\hyperlink{setting.ISABELLE-BROWSER-INFO}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}BROWSER{\isacharunderscore}INFO}}}} setting plus a prefix corresponding to the
+ sub-directory directory determined by the \indexref{}{setting}{ISABELLE\_BROWSER\_INFO}\hyperlink{setting.ISABELLE-BROWSER-INFO}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}BROWSER{\isaliteral{5F}{\isacharunderscore}}INFO}}}} setting plus a prefix corresponding to the
session identifier (according to the tree structure of sub-sessions
by default). A complete WWW view of all standard object-logics and
examples of the Isabelle distribution is available at the usual
@@ -138,7 +138,7 @@
\end{center}
\medskip In order to present your own theories on the web, simply
- copy the corresponding subdirectory from \hyperlink{setting.ISABELLE-BROWSER-INFO}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}BROWSER{\isacharunderscore}INFO}}}} to your WWW server, having generated browser
+ copy the corresponding subdirectory from \hyperlink{setting.ISABELLE-BROWSER-INFO}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}BROWSER{\isaliteral{5F}{\isacharunderscore}}INFO}}}} to your WWW server, having generated browser
info like this:
\begin{ttbox}
isabelle usedir -i true HOL Foo
@@ -204,7 +204,7 @@
-o FILE output to FILE (ps, eps, pdf)
\end{ttbox}
When no filename is specified, the browser automatically changes to
- the directory \hyperlink{setting.ISABELLE-BROWSER-INFO}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}BROWSER{\isacharunderscore}INFO}}}}.
+ the directory \hyperlink{setting.ISABELLE-BROWSER-INFO}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}BROWSER{\isaliteral{5F}{\isacharunderscore}}INFO}}}}.
\medskip The \verb|-b| option indicates that this is for
administrative build only, i.e.\ no browser popup if no files are
@@ -327,8 +327,8 @@
\begin{center}\small
\begin{tabular}{rcl}
- \isa{graph} & \isa{{\isachardoublequote}{\isacharequal}{\isachardoublequote}} & \isa{{\isachardoublequote}{\isacharbraceleft}\ vertex{\isachardoublequote}}~\verb|;|~\isa{{\isachardoublequote}{\isacharbraceright}{\isacharplus}{\isachardoublequote}} \\
- \isa{vertex} & \isa{{\isachardoublequote}{\isacharequal}{\isachardoublequote}} & \isa{{\isachardoublequote}vertex{\isacharunderscore}name\ vertex{\isacharunderscore}ID\ dir{\isacharunderscore}name\ {\isacharbrackleft}{\isachardoublequote}}~\verb|+|~\isa{{\isachardoublequote}{\isacharbrackright}\ path\ {\isacharbrackleft}{\isachardoublequote}}~\verb|<|~\isa{{\isachardoublequote}{\isacharbar}{\isachardoublequote}}~\verb|>|~\isa{{\isachardoublequote}{\isacharbrackright}\ {\isacharbraceleft}\ vertex{\isacharunderscore}ID\ {\isacharbraceright}{\isacharasterisk}{\isachardoublequote}}
+ \isa{graph} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7B}{\isacharbraceleft}}\ vertex{\isaliteral{22}{\isachardoublequote}}}~\verb|;|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{22}{\isachardoublequote}}} \\
+ \isa{vertex} & \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}} & \isa{{\isaliteral{22}{\isachardoublequote}}vertex{\isaliteral{5F}{\isacharunderscore}}name\ vertex{\isaliteral{5F}{\isacharunderscore}}ID\ dir{\isaliteral{5F}{\isacharunderscore}}name\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}}~\verb|+|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}\ path\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}}~\verb|<|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}}~\verb|>|~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7B}{\isacharbraceleft}}\ vertex{\isaliteral{5F}{\isacharunderscore}}ID\ {\isaliteral{7D}{\isacharbraceright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequote}}}
\end{tabular}
\end{center}
@@ -336,14 +336,14 @@
\begin{description}
- \item[\isa{vertex{\isacharunderscore}name}] The name of the vertex.
+ \item[\isa{vertex{\isaliteral{5F}{\isacharunderscore}}name}] The name of the vertex.
- \item[\isa{vertex{\isacharunderscore}ID}] The vertex identifier. Note that there may
+ \item[\isa{vertex{\isaliteral{5F}{\isacharunderscore}}ID}] The vertex identifier. Note that there may
be several vertices with equal names, whereas identifiers must be
unique.
- \item[\isa{dir{\isacharunderscore}name}] The name of the ``directory'' the vertex
- should be placed in. A ``\verb|+|'' sign after \isa{dir{\isacharunderscore}name} indicates that the nodes in the directory are initially
+ \item[\isa{dir{\isaliteral{5F}{\isacharunderscore}}name}] The name of the ``directory'' the vertex
+ should be placed in. A ``\verb|+|'' sign after \isa{dir{\isaliteral{5F}{\isacharunderscore}}name} indicates that the nodes in the directory are initially
visible. Directories are initially invisible by default.
\item[\isa{path}] The path of the corresponding theory file. This
@@ -451,7 +451,7 @@
manual editing of the generated \verb|IsaMakefile|, which is
meant to cover all of the sub-session directories at the same time
(this is the deeper reasong why \verb|IsaMakefile| is not made
- part of the initial session directory created by \verb|isabelle| \hyperlink{tool.mkdir}{\mbox{\isa{\isatt{mkdir}}}}). See \hyperlink{file.~~/src/HOL/IsaMakefile}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}HOL{\isacharslash}IsaMakefile}}}} for
+ part of the initial session directory created by \verb|isabelle| \hyperlink{tool.mkdir}{\mbox{\isa{\isatt{mkdir}}}}). See \hyperlink{file.~~/src/HOL/IsaMakefile}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}HOL{\isaliteral{2F}{\isacharslash}}IsaMakefile}}}} for
a full-blown example.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -498,7 +498,7 @@
ML_OPTIONS=-H 500
\end{ttbox}
- Note that the value of the \indexref{}{setting}{ISABELLE\_USEDIR\_OPTIONS}\hyperlink{setting.ISABELLE-USEDIR-OPTIONS}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}USEDIR{\isacharunderscore}OPTIONS}}}}
+ Note that the value of the \indexref{}{setting}{ISABELLE\_USEDIR\_OPTIONS}\hyperlink{setting.ISABELLE-USEDIR-OPTIONS}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}USEDIR{\isaliteral{5F}{\isacharunderscore}}OPTIONS}}}}
setting is implicitly prefixed to \emph{any} \hyperlink{tool.usedir}{\mbox{\isa{\isatt{usedir}}}}
call. Since the \verb|IsaMakefile|s of all object-logics
distributed with Isabelle just invoke \hyperlink{tool.usedir}{\mbox{\isa{\isatt{usedir}}}} for the real
@@ -517,7 +517,7 @@
mode} (enabled through the \verb|-b| option) and
\emph{example mode} (default).
- Calling \hyperlink{tool.usedir}{\mbox{\isa{\isatt{usedir}}}} with \verb|-b| runs \hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isacharminus}process}}}} with input image \verb|LOGIC| and output to
+ Calling \hyperlink{tool.usedir}{\mbox{\isa{\isatt{usedir}}}} with \verb|-b| runs \hyperlink{executable.isabelle-process}{\mbox{\isa{\isatt{isabelle{\isaliteral{2D}{\isacharminus}}process}}}} with input image \verb|LOGIC| and output to
\verb|NAME|, as provided on the command line. This will be a
batch session, running \verb|ROOT.ML| from the current
directory and then quitting. It is assumed that \verb|ROOT.ML|
@@ -621,7 +621,7 @@
\begin{isamarkuptext}%
Refer to the \verb|IsaMakefile|s of the Isabelle distribution's
object-logics as a model for your own developments. For example,
- see \hyperlink{file.~~/src/FOL/IsaMakefile}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}src{\isacharslash}FOL{\isacharslash}IsaMakefile}}}}. The Isabelle \indexref{}{tool}{mkdir}\hyperlink{tool.mkdir}{\mbox{\isa{\isatt{mkdir}}}} tool creates \verb|IsaMakefile|s with proper invocation
+ see \hyperlink{file.~~/src/FOL/IsaMakefile}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}FOL{\isaliteral{2F}{\isacharslash}}IsaMakefile}}}}. The Isabelle \indexref{}{tool}{mkdir}\hyperlink{tool.mkdir}{\mbox{\isa{\isatt{mkdir}}}} tool creates \verb|IsaMakefile|s with proper invocation
of \hyperlink{tool.usedir}{\mbox{\isa{\isatt{usedir}}}} as well.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -670,7 +670,7 @@
fold text tagged as \isa{foo}. The builtin default is equivalent
to the tag specification ``\verb|+theory,+proof,+ML,+visible,-invisible|''; see also the {\LaTeX}
macros \verb|\isakeeptag|, \verb|\isadroptag|, and
- \verb|\isafoldtag|, in \hyperlink{file.~~/lib/texinputs/isabelle.sty}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}lib{\isacharslash}texinputs{\isacharslash}isabelle{\isachardot}sty}}}}.
+ \verb|\isafoldtag|, in \hyperlink{file.~~/lib/texinputs/isabelle.sty}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}lib{\isaliteral{2F}{\isacharslash}}texinputs{\isaliteral{2F}{\isacharslash}}isabelle{\isaliteral{2E}{\isachardot}}sty}}}}.
\medskip Document preparation requires a properly setup ``\verb|document|'' directory within the logic session sources. This
directory is supposed to contain all the files needed to produce the
@@ -692,7 +692,7 @@
\medskip When running the session, Isabelle copies the original
\verb|document| directory into its proper place within
- \hyperlink{setting.ISABELLE-BROWSER-INFO}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}BROWSER{\isacharunderscore}INFO}}}} according to the session path.
+ \hyperlink{setting.ISABELLE-BROWSER-INFO}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}BROWSER{\isaliteral{5F}{\isacharunderscore}}INFO}}}} according to the session path.
Then, for any processed theory \isa{A} some {\LaTeX} source is
generated and put there as \isa{A}\verb|.tex|.
Furthermore, a list of all generated theory files is put into
@@ -701,7 +701,7 @@
containing all the theories.
The {\LaTeX} versions of the theories require some macros defined in
- \hyperlink{file.~~/lib/texinputs/isabelle.sty}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}lib{\isacharslash}texinputs{\isacharslash}isabelle{\isachardot}sty}}}}. Doing \verb|\usepackage{isabelle}| in \verb|root.tex| should be fine;
+ \hyperlink{file.~~/lib/texinputs/isabelle.sty}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}lib{\isaliteral{2F}{\isacharslash}}texinputs{\isaliteral{2F}{\isacharslash}}isabelle{\isaliteral{2E}{\isachardot}}sty}}}}. Doing \verb|\usepackage{isabelle}| in \verb|root.tex| should be fine;
the underlying Isabelle \hyperlink{tool.latex}{\mbox{\isa{\isatt{latex}}}} tool already includes an
appropriate path specification for {\TeX} inputs.
@@ -710,11 +710,11 @@
contains a standard set of {\LaTeX} macro definitions \verb|\isasym|\isa{foo} corresponding to \verb|\|\verb|<|\isa{foo}\verb|>|, see \cite{isabelle-implementation} for a
complete list of predefined Isabelle symbols. Users may invent
further symbols as well, just by providing {\LaTeX} macros in a
- similar fashion as in \hyperlink{file.~~/lib/texinputs/isabellesym.sty}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}lib{\isacharslash}texinputs{\isacharslash}isabellesym{\isachardot}sty}}}} of
+ similar fashion as in \hyperlink{file.~~/lib/texinputs/isabellesym.sty}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}lib{\isaliteral{2F}{\isacharslash}}texinputs{\isaliteral{2F}{\isacharslash}}isabellesym{\isaliteral{2E}{\isachardot}}sty}}}} of
the distribution.
For proper setup of DVI and PDF documents (with hyperlinks and
- bookmarks), we recommend to include \hyperlink{file.~~/lib/texinputs/pdfsetup.sty}{\mbox{\isa{\isatt{{\isachartilde}{\isachartilde}{\isacharslash}lib{\isacharslash}texinputs{\isacharslash}pdfsetup{\isachardot}sty}}}} as well.
+ bookmarks), we recommend to include \hyperlink{file.~~/lib/texinputs/pdfsetup.sty}{\mbox{\isa{\isatt{{\isaliteral{7E}{\isachartilde}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{2F}{\isacharslash}}lib{\isaliteral{2F}{\isacharslash}}texinputs{\isaliteral{2F}{\isacharslash}}pdfsetup{\isaliteral{2E}{\isachardot}}sty}}}} as well.
\medskip As a final step of document preparation within Isabelle,
\verb|isabelle| \hyperlink{tool.document}{\mbox{\isa{\isatt{document}}}}~\verb|-c| is run on the
@@ -752,7 +752,7 @@
according to the given output format: \hyperlink{executable.latex}{\mbox{\isa{\isatt{latex}}}},
\hyperlink{executable.pdflatex}{\mbox{\isa{\isatt{pdflatex}}}}, \hyperlink{executable.dvips}{\mbox{\isa{\isatt{dvips}}}}, \hyperlink{executable.bibtex}{\mbox{\isa{\isatt{bibtex}}}}
(for \verb|bbl|), and \hyperlink{executable.makeindex}{\mbox{\isa{\isatt{makeindex}}}} (for \verb|idx|). The actual commands are determined from the settings
- environment (\hyperlink{setting.ISABELLE-LATEX}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}LATEX}}}} etc.).
+ environment (\hyperlink{setting.ISABELLE-LATEX}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}LATEX}}}} etc.).
The \verb|sty| output format causes the Isabelle style files to
be updated from the distribution. This is useful in special
@@ -773,7 +773,7 @@
Invoking \verb|isabelle| \hyperlink{tool.latex}{\mbox{\isa{\isatt{latex}}}} by hand may be
occasionally useful when debugging failed attempts of the automatic
document preparation stage of batch-mode Isabelle. The abortive
- process leaves the sources at a certain place within \hyperlink{setting.ISABELLE-BROWSER-INFO}{\mbox{\isa{\isatt{ISABELLE{\isacharunderscore}BROWSER{\isacharunderscore}INFO}}}}, see the runtime error message for details.
+ process leaves the sources at a certain place within \hyperlink{setting.ISABELLE-BROWSER-INFO}{\mbox{\isa{\isatt{ISABELLE{\isaliteral{5F}{\isacharunderscore}}BROWSER{\isaliteral{5F}{\isacharunderscore}}INFO}}}}, see the runtime error message for details.
This enables users to inspect {\LaTeX} runs in further detail, e.g.\
like this:
\begin{ttbox}
--- a/doc-src/TutorialI/Advanced/document/simp.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Advanced/document/simp.tex Mon Nov 08 14:41:11 2010 +0100
@@ -41,33 +41,33 @@
of $P \Imp Q$, it is legal to use the assumption $P$.
For $\Imp$ this policy is hardwired, but
contextual information can also be made available for other
-operators. For example, \isa{xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymlongrightarrow}\ xs\ {\isacharat}\ xs\ {\isacharequal}\ xs} simplifies to \isa{True} because we may use \isa{xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}} when simplifying \isa{xs\ {\isacharat}\ xs\ {\isacharequal}\ xs}. The generation of contextual information during simplification is
+operators. For example, \isa{xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ xs\ {\isaliteral{40}{\isacharat}}\ xs\ {\isaliteral{3D}{\isacharequal}}\ xs} simplifies to \isa{True} because we may use \isa{xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}} when simplifying \isa{xs\ {\isaliteral{40}{\isacharat}}\ xs\ {\isaliteral{3D}{\isacharequal}}\ xs}. The generation of contextual information during simplification is
controlled by so-called \bfindex{congruence rules}. This is the one for
-\isa{{\isasymlongrightarrow}}:
+\isa{{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}}:
\begin{isabelle}%
-\ \ \ \ \ {\isasymlbrakk}P\ {\isacharequal}\ P{\isacharprime}{\isacharsemicolon}\ P{\isacharprime}\ {\isasymLongrightarrow}\ Q\ {\isacharequal}\ Q{\isacharprime}{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharparenleft}P\ {\isasymlongrightarrow}\ Q{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}P{\isacharprime}\ {\isasymlongrightarrow}\ Q{\isacharprime}{\isacharparenright}%
+\ \ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}P\ {\isaliteral{3D}{\isacharequal}}\ P{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ P{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Q\ {\isaliteral{3D}{\isacharequal}}\ Q{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}P\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}P{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
It should be read as follows:
-In order to simplify \isa{P\ {\isasymlongrightarrow}\ Q} to \isa{P{\isacharprime}\ {\isasymlongrightarrow}\ Q{\isacharprime}},
-simplify \isa{P} to \isa{P{\isacharprime}}
-and assume \isa{P{\isacharprime}} when simplifying \isa{Q} to \isa{Q{\isacharprime}}.
+In order to simplify \isa{P\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q} to \isa{P{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ Q{\isaliteral{27}{\isacharprime}}},
+simplify \isa{P} to \isa{P{\isaliteral{27}{\isacharprime}}}
+and assume \isa{P{\isaliteral{27}{\isacharprime}}} when simplifying \isa{Q} to \isa{Q{\isaliteral{27}{\isacharprime}}}.
Here are some more examples. The congruence rules for bounded
quantifiers supply contextual information about the bound variable:
\begin{isabelle}%
-\ \ \ \ \ {\isasymlbrakk}A\ {\isacharequal}\ B{\isacharsemicolon}\ {\isasymAnd}x{\isachardot}\ x\ {\isasymin}\ B\ {\isasymLongrightarrow}\ P\ x\ {\isacharequal}\ Q\ x{\isasymrbrakk}\isanewline
-\isaindent{\ \ \ \ \ }{\isasymLongrightarrow}\ {\isacharparenleft}{\isasymforall}x{\isasymin}A{\isachardot}\ P\ x{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isasymforall}x{\isasymin}B{\isachardot}\ Q\ x{\isacharparenright}%
+\ \ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}A\ {\isaliteral{3D}{\isacharequal}}\ B{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ x\ {\isaliteral{3D}{\isacharequal}}\ Q\ x{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ \ \ \ \ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{5C3C696E3E}{\isasymin}}A{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{5C3C696E3E}{\isasymin}}B{\isaliteral{2E}{\isachardot}}\ Q\ x{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
One congruence rule for conditional expressions supplies contextual
information for simplifying the \isa{then} and \isa{else} cases:
\begin{isabelle}%
-\ \ \ \ \ {\isasymlbrakk}b\ {\isacharequal}\ c{\isacharsemicolon}\ c\ {\isasymLongrightarrow}\ x\ {\isacharequal}\ u{\isacharsemicolon}\ {\isasymnot}\ c\ {\isasymLongrightarrow}\ y\ {\isacharequal}\ v{\isasymrbrakk}\isanewline
-\isaindent{\ \ \ \ \ }{\isasymLongrightarrow}\ {\isacharparenleft}if\ b\ then\ x\ else\ y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}if\ c\ then\ u\ else\ v{\isacharparenright}%
+\ \ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}b\ {\isaliteral{3D}{\isacharequal}}\ c{\isaliteral{3B}{\isacharsemicolon}}\ c\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{3D}{\isacharequal}}\ u{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ c\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ y\ {\isaliteral{3D}{\isacharequal}}\ v{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ \ \ \ \ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}if\ b\ then\ x\ else\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ c\ then\ u\ else\ v{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
An alternative congruence rule for conditional expressions
actually \emph{prevents} simplification of some arguments:
\begin{isabelle}%
-\ \ \ \ \ b\ {\isacharequal}\ c\ {\isasymLongrightarrow}\ {\isacharparenleft}if\ b\ then\ x\ else\ y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}if\ c\ then\ x\ else\ y{\isacharparenright}%
+\ \ \ \ \ b\ {\isaliteral{3D}{\isacharequal}}\ c\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}if\ b\ then\ x\ else\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ c\ then\ x\ else\ y{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
Only the first argument is simplified; the others remain unchanged.
This makes simplification much faster and is faithful to the evaluation
@@ -78,18 +78,18 @@
You can declare your own congruence rules with the attribute \attrdx{cong},
either globally, in the usual manner,
\begin{quote}
-\isacommand{declare} \textit{theorem-name} \isa{{\isacharbrackleft}cong{\isacharbrackright}}
+\isacommand{declare} \textit{theorem-name} \isa{{\isaliteral{5B}{\isacharbrackleft}}cong{\isaliteral{5D}{\isacharbrackright}}}
\end{quote}
or locally in a \isa{simp} call by adding the modifier
\begin{quote}
-\isa{cong{\isacharcolon}} \textit{list of theorem names}
+\isa{cong{\isaliteral{3A}{\isacharcolon}}} \textit{list of theorem names}
\end{quote}
The effect is reversed by \isa{cong\ del} instead of \isa{cong}.
\begin{warn}
-The congruence rule \isa{conj{\isacharunderscore}cong}
+The congruence rule \isa{conj{\isaliteral{5F}{\isacharunderscore}}cong}
\begin{isabelle}%
-\ \ \ \ \ {\isasymlbrakk}P\ {\isacharequal}\ P{\isacharprime}{\isacharsemicolon}\ P{\isacharprime}\ {\isasymLongrightarrow}\ Q\ {\isacharequal}\ Q{\isacharprime}{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharparenleft}P\ {\isasymand}\ Q{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}P{\isacharprime}\ {\isasymand}\ Q{\isacharprime}{\isacharparenright}%
+\ \ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}P\ {\isaliteral{3D}{\isacharequal}}\ P{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ P{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Q\ {\isaliteral{3D}{\isacharequal}}\ Q{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}P\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}P{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\par\noindent
is occasionally useful but is not a default rule; you have to declare it explicitly.
@@ -105,15 +105,15 @@
\index{rewrite rules!permutative|bold}%
An equation is a \textbf{permutative rewrite rule} if the left-hand
side and right-hand side are the same up to renaming of variables. The most
-common permutative rule is commutativity: \isa{x\ {\isacharplus}\ y\ {\isacharequal}\ y\ {\isacharplus}\ x}. Other examples
-include \isa{x\ {\isacharminus}\ y\ {\isacharminus}\ z\ {\isacharequal}\ x\ {\isacharminus}\ z\ {\isacharminus}\ y} in arithmetic and \isa{insert\ x\ {\isacharparenleft}insert\ y\ A{\isacharparenright}\ {\isacharequal}\ insert\ y\ {\isacharparenleft}insert\ x\ A{\isacharparenright}} for sets. Such rules are problematic because
+common permutative rule is commutativity: \isa{x\ {\isaliteral{2B}{\isacharplus}}\ y\ {\isaliteral{3D}{\isacharequal}}\ y\ {\isaliteral{2B}{\isacharplus}}\ x}. Other examples
+include \isa{x\ {\isaliteral{2D}{\isacharminus}}\ y\ {\isaliteral{2D}{\isacharminus}}\ z\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{2D}{\isacharminus}}\ z\ {\isaliteral{2D}{\isacharminus}}\ y} in arithmetic and \isa{insert\ x\ {\isaliteral{28}{\isacharparenleft}}insert\ y\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ insert\ y\ {\isaliteral{28}{\isacharparenleft}}insert\ x\ A{\isaliteral{29}{\isacharparenright}}} for sets. Such rules are problematic because
once they apply, they can be used forever. The simplifier is aware of this
danger and treats permutative rules by means of a special strategy, called
\bfindex{ordered rewriting}: a permutative rewrite
rule is only applied if the term becomes smaller with respect to a fixed
lexicographic ordering on terms. For example, commutativity rewrites
-\isa{b\ {\isacharplus}\ a} to \isa{a\ {\isacharplus}\ b}, but then stops because \isa{a\ {\isacharplus}\ b} is strictly
-smaller than \isa{b\ {\isacharplus}\ a}. Permutative rewrite rules can be turned into
+\isa{b\ {\isaliteral{2B}{\isacharplus}}\ a} to \isa{a\ {\isaliteral{2B}{\isacharplus}}\ b}, but then stops because \isa{a\ {\isaliteral{2B}{\isacharplus}}\ b} is strictly
+smaller than \isa{b\ {\isaliteral{2B}{\isacharplus}}\ a}. Permutative rewrite rules can be turned into
simplification rules in the usual manner via the \isa{simp} attribute; the
simplifier recognizes their special status automatically.
@@ -136,7 +136,7 @@
\[\def\maps#1{~\stackrel{#1}{\leadsto}~}
f(f(b,c),a) \maps{A} f(b,f(c,a)) \maps{C} f(b,f(a,c)) \maps{LC} f(a,f(b,c)) \]
-Note that ordered rewriting for \isa{{\isacharplus}} and \isa{{\isacharasterisk}} on numbers is rarely
+Note that ordered rewriting for \isa{{\isaliteral{2B}{\isacharplus}}} and \isa{{\isaliteral{2A}{\isacharasterisk}}} on numbers is rarely
necessary because the built-in arithmetic prover often succeeds without
such tricks.%
\end{isamarkuptext}%
@@ -172,22 +172,22 @@
Each occurrence of an unknown is of the form
$\Var{f}~x@1~\dots~x@n$, where the $x@i$ are distinct bound
variables. Thus all ordinary rewrite rules, where all unknowns are
-of base type, for example \isa{{\isacharquery}a\ {\isacharplus}\ {\isacharquery}b\ {\isacharplus}\ {\isacharquery}c\ {\isacharequal}\ {\isacharquery}a\ {\isacharplus}\ {\isacharparenleft}{\isacharquery}b\ {\isacharplus}\ {\isacharquery}c{\isacharparenright}}, are acceptable: if an unknown is
+of base type, for example \isa{{\isaliteral{3F}{\isacharquery}}a\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{3F}{\isacharquery}}b\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{3F}{\isacharquery}}c\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}a\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}b\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{3F}{\isacharquery}}c{\isaliteral{29}{\isacharparenright}}}, are acceptable: if an unknown is
of base type, it cannot have any arguments. Additionally, the rule
-\isa{{\isacharparenleft}{\isasymforall}x{\isachardot}\ {\isacharquery}P\ x\ {\isasymand}\ {\isacharquery}Q\ x{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isacharparenleft}{\isasymforall}x{\isachardot}\ {\isacharquery}P\ x{\isacharparenright}\ {\isasymand}\ {\isacharparenleft}{\isasymforall}x{\isachardot}\ {\isacharquery}Q\ x{\isacharparenright}{\isacharparenright}} is also acceptable, in
-both directions: all arguments of the unknowns \isa{{\isacharquery}P} and
-\isa{{\isacharquery}Q} are distinct bound variables.
+\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}P\ x\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{3F}{\isacharquery}}Q\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}P\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}Q\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}} is also acceptable, in
+both directions: all arguments of the unknowns \isa{{\isaliteral{3F}{\isacharquery}}P} and
+\isa{{\isaliteral{3F}{\isacharquery}}Q} are distinct bound variables.
If the left-hand side is not a higher-order pattern, all is not lost.
The simplifier will still try to apply the rule provided it
matches directly: without much $\lambda$-calculus hocus
-pocus. For example, \isa{{\isacharparenleft}{\isacharquery}f\ {\isacharquery}x\ {\isasymin}\ range\ {\isacharquery}f{\isacharparenright}\ {\isacharequal}\ True} rewrites
-\isa{g\ a\ {\isasymin}\ range\ g} to \isa{True}, but will fail to match
-\isa{g{\isacharparenleft}h\ b{\isacharparenright}\ {\isasymin}\ range{\isacharparenleft}{\isasymlambda}x{\isachardot}\ g{\isacharparenleft}h\ x{\isacharparenright}{\isacharparenright}}. However, you can
+pocus. For example, \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}f\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ range\ {\isaliteral{3F}{\isacharquery}}f{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ True} rewrites
+\isa{g\ a\ {\isaliteral{5C3C696E3E}{\isasymin}}\ range\ g} to \isa{True}, but will fail to match
+\isa{g{\isaliteral{28}{\isacharparenleft}}h\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ range{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ g{\isaliteral{28}{\isacharparenleft}}h\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}}. However, you can
eliminate the offending subterms --- those that are not patterns ---
by adding new variables and conditions.
-In our example, we eliminate \isa{{\isacharquery}f\ {\isacharquery}x} and obtain
- \isa{{\isacharquery}y\ {\isacharequal}\ {\isacharquery}f\ {\isacharquery}x\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isacharquery}y\ {\isasymin}\ range\ {\isacharquery}f{\isacharparenright}\ {\isacharequal}\ True}, which is fine
+In our example, we eliminate \isa{{\isaliteral{3F}{\isacharquery}}f\ {\isaliteral{3F}{\isacharquery}}x} and obtain
+ \isa{{\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}f\ {\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ range\ {\isaliteral{3F}{\isacharquery}}f{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ True}, which is fine
as a conditional rewrite rule since conditions can be arbitrary
terms. However, this trick is not a panacea because the newly
introduced conditions may be hard to solve.
@@ -205,8 +205,8 @@
\label{sec:simp-preprocessor}
When a theorem is declared a simplification rule, it need not be a
conditional equation already. The simplifier will turn it into a set of
-conditional equations automatically. For example, \isa{f\ x\ {\isacharequal}\ g\ x\ {\isasymand}\ h\ x\ {\isacharequal}\ k\ x} becomes the two separate
-simplification rules \isa{f\ x\ {\isacharequal}\ g\ x} and \isa{h\ x\ {\isacharequal}\ k\ x}. In
+conditional equations automatically. For example, \isa{f\ x\ {\isaliteral{3D}{\isacharequal}}\ g\ x\ {\isaliteral{5C3C616E643E}{\isasymand}}\ h\ x\ {\isaliteral{3D}{\isacharequal}}\ k\ x} becomes the two separate
+simplification rules \isa{f\ x\ {\isaliteral{3D}{\isacharequal}}\ g\ x} and \isa{h\ x\ {\isaliteral{3D}{\isacharequal}}\ k\ x}. In
general, the input theorem is converted as follows:
\begin{eqnarray}
\neg P &\mapsto& P = \hbox{\isa{False}} \nonumber\\
@@ -220,10 +220,10 @@
Once this conversion process is finished, all remaining non-equations
$P$ are turned into trivial equations $P =\isa{True}$.
For example, the formula
-\begin{center}\isa{{\isacharparenleft}p\ {\isasymlongrightarrow}\ t\ {\isacharequal}\ u\ {\isasymand}\ {\isasymnot}\ r{\isacharparenright}\ {\isasymand}\ s}\end{center}
+\begin{center}\isa{{\isaliteral{28}{\isacharparenleft}}p\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ t\ {\isaliteral{3D}{\isacharequal}}\ u\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ r{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ s}\end{center}
is converted into the three rules
\begin{center}
-\isa{p\ {\isasymLongrightarrow}\ t\ {\isacharequal}\ u},\quad \isa{p\ {\isasymLongrightarrow}\ r\ {\isacharequal}\ False},\quad \isa{s\ {\isacharequal}\ True}.
+\isa{p\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ t\ {\isaliteral{3D}{\isacharequal}}\ u},\quad \isa{p\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ r\ {\isaliteral{3D}{\isacharequal}}\ False},\quad \isa{s\ {\isaliteral{3D}{\isacharequal}}\ True}.
\end{center}
\index{simplification rule|)}
\index{simplification|)}%
--- a/doc-src/TutorialI/CTL/document/Base.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/CTL/document/Base.tex Mon Nov 08 14:41:11 2010 +0100
@@ -30,7 +30,7 @@
we consider a simple modal logic called propositional dynamic
logic (PDL)\@. We then proceed to the temporal logic CTL, which is
used in many real
-model checkers. In each case we give both a traditional semantics (\isa{{\isasymTurnstile}}) and a
+model checkers. In each case we give both a traditional semantics (\isa{{\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}}) and a
recursive function \isa{mc} that maps a formula into the set of all states of
the system where the formula is valid. If the system has a finite number of
states, \isa{mc} is directly executable: it is a model checker, albeit an
@@ -89,7 +89,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{consts}\isamarkupfalse%
-\ M\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}state\ {\isasymtimes}\ state{\isacharparenright}set{\isachardoublequoteclose}%
+\ M\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}state\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ state{\isaliteral{29}{\isacharparenright}}set{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
This is Isabelle's way of declaring a constant without defining it.
@@ -97,14 +97,14 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{typedecl}\isamarkupfalse%
-\ {\isachardoublequoteopen}atom{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}atom{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
and a \emph{labelling function}%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{consts}\isamarkupfalse%
-\ L\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}state\ {\isasymRightarrow}\ atom\ set{\isachardoublequoteclose}%
+\ L\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}state\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ atom\ set{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
telling us which atomic propositions are true in each state.%
--- a/doc-src/TutorialI/CTL/document/CTL.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/CTL/document/CTL.tex Mon Nov 08 14:41:11 2010 +0100
@@ -28,7 +28,7 @@
\isa{formula} by a new constructor%
\end{isamarkuptext}%
\isamarkuptrue%
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ AF\ formula%
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ AF\ formula%
\begin{isamarkuptext}%
\noindent
which stands for ``\emph{A}lways in the \emph{F}uture'':
@@ -38,8 +38,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{definition}\isamarkupfalse%
-\ Paths\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}state\ {\isasymRightarrow}\ {\isacharparenleft}nat\ {\isasymRightarrow}\ state{\isacharparenright}set{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}Paths\ s\ {\isasymequiv}\ {\isacharbraceleft}p{\isachardot}\ s\ {\isacharequal}\ p\ {\isadigit{0}}\ {\isasymand}\ {\isacharparenleft}{\isasymforall}i{\isachardot}\ {\isacharparenleft}p\ i{\isacharcomma}\ p{\isacharparenleft}i{\isacharplus}{\isadigit{1}}{\isacharparenright}{\isacharparenright}\ {\isasymin}\ M{\isacharparenright}{\isacharbraceright}{\isachardoublequoteclose}%
+\ Paths\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}state\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ state{\isaliteral{29}{\isacharparenright}}set{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}Paths\ s\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{7B}{\isacharbraceleft}}p{\isaliteral{2E}{\isachardot}}\ s\ {\isaliteral{3D}{\isacharequal}}\ p\ {\isadigit{0}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}p\ i{\isaliteral{2C}{\isacharcomma}}\ p{\isaliteral{28}{\isacharparenleft}}i{\isaliteral{2B}{\isacharplus}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M{\isaliteral{29}{\isacharparenright}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
This definition allows a succinct statement of the semantics of \isa{AF}:
@@ -49,7 +49,7 @@
a new datatype and a new function.}%
\end{isamarkuptext}%
\isamarkuptrue%
-{\isachardoublequoteopen}s\ {\isasymTurnstile}\ AF\ f\ \ \ \ {\isacharequal}\ {\isacharparenleft}{\isasymforall}p\ {\isasymin}\ Paths\ s{\isachardot}\ {\isasymexists}i{\isachardot}\ p\ i\ {\isasymTurnstile}\ f{\isacharparenright}{\isachardoublequoteclose}%
+{\isaliteral{22}{\isachardoublequoteopen}}s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ AF\ f\ \ \ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}p\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Paths\ s{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}i{\isaliteral{2E}{\isachardot}}\ p\ i\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ f{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
Model checking \isa{AF} involves a function which
@@ -57,15 +57,15 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{definition}\isamarkupfalse%
-\ af\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}state\ set\ {\isasymRightarrow}\ state\ set\ {\isasymRightarrow}\ state\ set{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}af\ A\ T\ {\isasymequiv}\ A\ {\isasymunion}\ {\isacharbraceleft}s{\isachardot}\ {\isasymforall}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymlongrightarrow}\ t\ {\isasymin}\ T{\isacharbraceright}{\isachardoublequoteclose}%
+\ af\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}state\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ state\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ state\ set{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}af\ A\ T\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ A\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ {\isaliteral{7B}{\isacharbraceleft}}s{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ T{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
-Now we define \isa{mc\ {\isacharparenleft}AF\ f{\isacharparenright}} as the least set \isa{T} that includes
+Now we define \isa{mc\ {\isaliteral{28}{\isacharparenleft}}AF\ f{\isaliteral{29}{\isacharparenright}}} as the least set \isa{T} that includes
\isa{mc\ f} and all states all of whose direct successors are in \isa{T}:%
\end{isamarkuptext}%
\isamarkuptrue%
-{\isachardoublequoteopen}mc{\isacharparenleft}AF\ f{\isacharparenright}\ \ \ \ {\isacharequal}\ lfp{\isacharparenleft}af{\isacharparenleft}mc\ f{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
+{\isaliteral{22}{\isachardoublequoteopen}}mc{\isaliteral{28}{\isacharparenleft}}AF\ f{\isaliteral{29}{\isacharparenright}}\ \ \ \ {\isaliteral{3D}{\isacharequal}}\ lfp{\isaliteral{28}{\isacharparenleft}}af{\isaliteral{28}{\isacharparenleft}}mc\ f{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
Because \isa{af} is monotone in its second argument (and also its first, but
@@ -73,7 +73,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ mono{\isacharunderscore}af{\isacharcolon}\ {\isachardoublequoteopen}mono{\isacharparenleft}af\ A{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ mono{\isaliteral{5F}{\isacharunderscore}}af{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}mono{\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -81,7 +81,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp\ add{\isacharcolon}\ mono{\isacharunderscore}def\ af{\isacharunderscore}def{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ mono{\isaliteral{5F}{\isacharunderscore}}def\ af{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
\ blast\isanewline
\isacommand{done}\isamarkupfalse%
@@ -120,14 +120,14 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-All we need to prove now is \isa{mc\ {\isacharparenleft}AF\ f{\isacharparenright}\ {\isacharequal}\ {\isacharbraceleft}s{\isachardot}\ s\ {\isasymTurnstile}\ AF\ f{\isacharbraceright}}, which states
-that \isa{mc} and \isa{{\isasymTurnstile}} agree for \isa{AF}\@.
+All we need to prove now is \isa{mc\ {\isaliteral{28}{\isacharparenleft}}AF\ f{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}s{\isaliteral{2E}{\isachardot}}\ s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ AF\ f{\isaliteral{7D}{\isacharbraceright}}}, which states
+that \isa{mc} and \isa{{\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}} agree for \isa{AF}\@.
This time we prove the two inclusions separately, starting
with the easy one:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ AF{\isacharunderscore}lemma{\isadigit{1}}{\isacharcolon}\ {\isachardoublequoteopen}lfp{\isacharparenleft}af\ A{\isacharparenright}\ {\isasymsubseteq}\ {\isacharbraceleft}s{\isachardot}\ {\isasymforall}p\ {\isasymin}\ Paths\ s{\isachardot}\ {\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A{\isacharbraceright}{\isachardoublequoteclose}%
+\ AF{\isaliteral{5F}{\isacharunderscore}}lemma{\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}lfp{\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ {\isaliteral{7B}{\isacharbraceleft}}s{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}p\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Paths\ s{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}i{\isaliteral{2E}{\isachardot}}\ p\ i\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -140,34 +140,34 @@
for a change, we do not use fixed point induction. Park-induction,
named after David Park, is weaker but sufficient for this proof:
\begin{center}
-\isa{f\ S\ {\isasymle}\ S\ {\isasymLongrightarrow}\ lfp\ f\ {\isasymle}\ S} \hfill (\isa{lfp{\isacharunderscore}lowerbound})
+\isa{f\ S\ {\isaliteral{5C3C6C653E}{\isasymle}}\ S\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ lfp\ f\ {\isaliteral{5C3C6C653E}{\isasymle}}\ S} \hfill (\isa{lfp{\isaliteral{5F}{\isacharunderscore}}lowerbound})
\end{center}
-The instance of the premise \isa{f\ S\ {\isasymsubseteq}\ S} is proved pointwise,
+The instance of the premise \isa{f\ S\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ S} is proved pointwise,
a decision that \isa{auto} takes for us:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ lfp{\isacharunderscore}lowerbound{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule\ lfp{\isaliteral{5F}{\isacharunderscore}}lowerbound{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto\ simp\ add{\isacharcolon}\ af{\isacharunderscore}def\ Paths{\isacharunderscore}def{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}auto\ simp\ add{\isaliteral{3A}{\isacharcolon}}\ af{\isaliteral{5F}{\isacharunderscore}}def\ Paths{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}p{\isachardot}\ {\isasymlbrakk}{\isasymforall}t{\isachardot}\ {\isacharparenleft}p\ {\isadigit{0}}{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymlongrightarrow}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}p{\isachardot}\ {\isasymlbrakk}{\isasymforall}t{\isachardot}\ }{\isacharparenleft}{\isasymforall}p{\isachardot}\ t\ {\isacharequal}\ p\ {\isadigit{0}}\ {\isasymand}\ {\isacharparenleft}{\isasymforall}i{\isachardot}\ {\isacharparenleft}p\ i{\isacharcomma}\ p\ {\isacharparenleft}Suc\ i{\isacharparenright}{\isacharparenright}\ {\isasymin}\ M{\isacharparenright}\ {\isasymlongrightarrow}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}p{\isachardot}\ {\isasymlbrakk}{\isasymforall}t{\isachardot}\ {\isacharparenleft}{\isasymforall}p{\isachardot}\ }{\isacharparenleft}{\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}p{\isachardot}\ \ }{\isasymforall}i{\isachardot}\ {\isacharparenleft}p\ i{\isacharcomma}\ p\ {\isacharparenleft}Suc\ i{\isacharparenright}{\isacharparenright}\ {\isasymin}\ M{\isasymrbrakk}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}p{\isachardot}\ }{\isasymLongrightarrow}\ {\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}p{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}p\ {\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}p{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}t{\isaliteral{2E}{\isachardot}}\ }{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}p{\isaliteral{2E}{\isachardot}}\ t\ {\isaliteral{3D}{\isacharequal}}\ p\ {\isadigit{0}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}p\ i{\isaliteral{2C}{\isacharcomma}}\ p\ {\isaliteral{28}{\isacharparenleft}}Suc\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}p{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}p{\isaliteral{2E}{\isachardot}}\ }{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}i{\isaliteral{2E}{\isachardot}}\ p\ i\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}p{\isaliteral{2E}{\isachardot}}\ \ }{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}p\ i{\isaliteral{2C}{\isacharcomma}}\ p\ {\isaliteral{28}{\isacharparenleft}}Suc\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}p{\isaliteral{2E}{\isachardot}}\ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}i{\isaliteral{2E}{\isachardot}}\ p\ i\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A%
\end{isabelle}
In this remaining case, we set \isa{t} to \isa{p\ {\isadigit{1}}}.
The rest is automatic, which is surprising because it involves
-finding the instantiation \isa{{\isasymlambda}i{\isachardot}\ p\ {\isacharparenleft}i\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}}
-for \isa{{\isasymforall}p}.%
+finding the instantiation \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}i{\isaliteral{2E}{\isachardot}}\ p\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}}
+for \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}p}.%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}erule{\isacharunderscore}tac\ x\ {\isacharequal}\ {\isachardoublequoteopen}p\ {\isadigit{1}}{\isachardoublequoteclose}\ \isakeyword{in}\ allE{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}erule{\isaliteral{5F}{\isacharunderscore}}tac\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequoteopen}}p\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{in}\ allE{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}auto{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -179,11 +179,11 @@
%
\begin{isamarkuptext}%
The opposite inclusion is proved by contradiction: if some state
-\isa{s} is not in \isa{lfp\ {\isacharparenleft}af\ A{\isacharparenright}}, then we can construct an
+\isa{s} is not in \isa{lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}}, then we can construct an
infinite \isa{A}-avoiding path starting from~\isa{s}. The reason is
that by unfolding \isa{lfp} we find that if \isa{s} is not in
-\isa{lfp\ {\isacharparenleft}af\ A{\isacharparenright}}, then \isa{s} is not in \isa{A} and there is a
-direct successor of \isa{s} that is again not in \mbox{\isa{lfp\ {\isacharparenleft}af\ A{\isacharparenright}}}. Iterating this argument yields the promised infinite
+\isa{lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}}, then \isa{s} is not in \isa{A} and there is a
+direct successor of \isa{s} that is again not in \mbox{\isa{lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}}}. Iterating this argument yields the promised infinite
\isa{A}-avoiding path. Let us formalize this sketch.
The one-step argument in the sketch above
@@ -191,8 +191,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ not{\isacharunderscore}in{\isacharunderscore}lfp{\isacharunderscore}afD{\isacharcolon}\isanewline
-\ {\isachardoublequoteopen}s\ {\isasymnotin}\ lfp{\isacharparenleft}af\ A{\isacharparenright}\ {\isasymLongrightarrow}\ s\ {\isasymnotin}\ A\ {\isasymand}\ {\isacharparenleft}{\isasymexists}\ t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ t\ {\isasymnotin}\ lfp{\isacharparenleft}af\ A{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ not{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{5F}{\isacharunderscore}}lfp{\isaliteral{5F}{\isacharunderscore}}afD{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}s\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ lfp{\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ s\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}\ t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ t\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ lfp{\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -200,11 +200,11 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}erule\ contrapos{\isacharunderscore}np{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}erule\ contrapos{\isaliteral{5F}{\isacharunderscore}}np{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}subst\ lfp{\isacharunderscore}unfold{\isacharbrackleft}OF\ mono{\isacharunderscore}af{\isacharbrackright}{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}subst\ lfp{\isaliteral{5F}{\isacharunderscore}}unfold{\isaliteral{5B}{\isacharbrackleft}}OF\ mono{\isaliteral{5F}{\isacharunderscore}}af{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp\ add{\isacharcolon}\ af{\isacharunderscore}def{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ af{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -216,7 +216,7 @@
%
\begin{isamarkuptext}%
\noindent
-We assume the negation of the conclusion and prove \isa{s\ {\isasymin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}}.
+We assume the negation of the conclusion and prove \isa{s\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}}.
Unfolding \isa{lfp} once and
simplifying with the definition of \isa{af} finishes the proof.
@@ -225,13 +225,13 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ path\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}state\ {\isasymRightarrow}\ {\isacharparenleft}state\ {\isasymRightarrow}\ bool{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}nat\ {\isasymRightarrow}\ state{\isacharparenright}{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}path\ s\ Q\ {\isadigit{0}}\ {\isacharequal}\ s{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}path\ s\ Q\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}SOME\ t{\isachardot}\ {\isacharparenleft}path\ s\ Q\ n{\isacharcomma}t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ Q\ t{\isacharparenright}{\isachardoublequoteclose}%
+\ path\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}state\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}state\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ state{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}path\ s\ Q\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ s{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}path\ s\ Q\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}SOME\ t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}path\ s\ Q\ n{\isaliteral{2C}{\isacharcomma}}t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q\ t{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
-Element \isa{n\ {\isacharplus}\ {\isadigit{1}}} on this path is some arbitrary successor
-\isa{t} of element \isa{n} such that \isa{Q\ t} holds. Remember that \isa{SOME\ t{\isachardot}\ R\ t}
+Element \isa{n\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}} on this path is some arbitrary successor
+\isa{t} of element \isa{n} such that \isa{Q\ t} holds. Remember that \isa{SOME\ t{\isaliteral{2E}{\isachardot}}\ R\ t}
is some arbitrary but fixed \isa{t} such that \isa{R\ t} holds (see \S\ref{sec:SOME}). Of
course, such a \isa{t} need not exist, but that is of no
concern to us since we will only use \isa{path} when a
@@ -242,9 +242,9 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ infinity{\isacharunderscore}lemma{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}{\isasymlbrakk}\ Q\ s{\isacharsemicolon}\ {\isasymforall}s{\isachardot}\ Q\ s\ {\isasymlongrightarrow}\ {\isacharparenleft}{\isasymexists}\ t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ Q\ t{\isacharparenright}\ {\isasymrbrakk}\ {\isasymLongrightarrow}\isanewline
-\ \ \ {\isasymexists}p{\isasymin}Paths\ s{\isachardot}\ {\isasymforall}i{\isachardot}\ Q{\isacharparenleft}p\ i{\isacharparenright}{\isachardoublequoteclose}%
+\ infinity{\isaliteral{5F}{\isacharunderscore}}lemma{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ Q\ s{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}s{\isaliteral{2E}{\isachardot}}\ Q\ s\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}\ t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\isanewline
+\ \ \ {\isaliteral{5C3C6578697374733E}{\isasymexists}}p{\isaliteral{5C3C696E3E}{\isasymin}}Paths\ s{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{2E}{\isachardot}}\ Q{\isaliteral{28}{\isacharparenleft}}p\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -258,66 +258,66 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}subgoal{\isacharunderscore}tac\isanewline
-\ \ {\isachardoublequoteopen}{\isasymexists}p{\isachardot}\ s\ {\isacharequal}\ p\ {\isadigit{0}}\ {\isasymand}\ {\isacharparenleft}{\isasymforall}i{\isacharcolon}{\isacharcolon}nat{\isachardot}\ {\isacharparenleft}p\ i{\isacharcomma}\ p{\isacharparenleft}i{\isacharplus}{\isadigit{1}}{\isacharparenright}{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ Q{\isacharparenleft}p\ i{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}subgoal{\isaliteral{5F}{\isacharunderscore}}tac\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}p{\isaliteral{2E}{\isachardot}}\ s\ {\isaliteral{3D}{\isacharequal}}\ p\ {\isadigit{0}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}p\ i{\isaliteral{2C}{\isacharcomma}}\ p{\isaliteral{28}{\isacharparenleft}}i{\isaliteral{2B}{\isacharplus}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q{\isaliteral{28}{\isacharparenleft}}p\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
From this proposition the original goal follows easily:%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp\ add{\isacharcolon}\ Paths{\isacharunderscore}def{\isacharcomma}\ blast{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ Paths{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{2C}{\isacharcomma}}\ blast{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
The new subgoal is proved by providing the witness \isa{path\ s\ Q} for \isa{p}:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule{\isacharunderscore}tac\ x\ {\isacharequal}\ {\isachardoublequoteopen}path\ s\ Q{\isachardoublequoteclose}\ \isakeyword{in}\ exI{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule{\isaliteral{5F}{\isacharunderscore}}tac\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequoteopen}}path\ s\ Q{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{in}\ exI{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}clarsimp{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}clarsimp{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
After simplification and clarification, the subgoal has the following form:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}i{\isachardot}\ {\isasymlbrakk}Q\ s{\isacharsemicolon}\ {\isasymforall}s{\isachardot}\ Q\ s\ {\isasymlongrightarrow}\ {\isacharparenleft}{\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ Q\ t{\isacharparenright}{\isasymrbrakk}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}i{\isachardot}\ }{\isasymLongrightarrow}\ {\isacharparenleft}path\ s\ Q\ i{\isacharcomma}\ SOME\ t{\isachardot}\ {\isacharparenleft}path\ s\ Q\ i{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ Q\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}i{\isachardot}\ {\isasymLongrightarrow}\ }Q\ {\isacharparenleft}path\ s\ Q\ i{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}i{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}Q\ s{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}s{\isaliteral{2E}{\isachardot}}\ Q\ s\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q\ t{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}i{\isaliteral{2E}{\isachardot}}\ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}path\ s\ Q\ i{\isaliteral{2C}{\isacharcomma}}\ SOME\ t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}path\ s\ Q\ i{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}i{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ }Q\ {\isaliteral{28}{\isacharparenleft}}path\ s\ Q\ i{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
It invites a proof by induction on \isa{i}:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ i{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ i{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
After simplification, the base case boils down to
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymlbrakk}Q\ s{\isacharsemicolon}\ {\isasymforall}s{\isachardot}\ Q\ s\ {\isasymlongrightarrow}\ {\isacharparenleft}{\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ Q\ t{\isacharparenright}{\isasymrbrakk}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ }{\isasymLongrightarrow}\ {\isacharparenleft}s{\isacharcomma}\ SOME\ t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ Q\ t{\isacharparenright}\ {\isasymin}\ M%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}Q\ s{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}s{\isaliteral{2E}{\isachardot}}\ Q\ s\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q\ t{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ SOME\ t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M%
\end{isabelle}
-The conclusion looks exceedingly trivial: after all, \isa{t} is chosen such that \isa{{\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M}
+The conclusion looks exceedingly trivial: after all, \isa{t} is chosen such that \isa{{\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M}
holds. However, we first have to show that such a \isa{t} actually exists! This reasoning
-is embodied in the theorem \isa{someI{\isadigit{2}}{\isacharunderscore}ex}:
+is embodied in the theorem \isa{someI{\isadigit{2}}{\isaliteral{5F}{\isacharunderscore}}ex}:
\begin{isabelle}%
-\ \ \ \ \ {\isasymlbrakk}{\isasymexists}a{\isachardot}\ {\isacharquery}P\ a{\isacharsemicolon}\ {\isasymAnd}x{\isachardot}\ {\isacharquery}P\ x\ {\isasymLongrightarrow}\ {\isacharquery}Q\ x{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}Q\ {\isacharparenleft}SOME\ x{\isachardot}\ {\isacharquery}P\ x{\isacharparenright}%
+\ \ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}a{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}P\ a{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}P\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}Q\ x{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}Q\ {\isaliteral{28}{\isacharparenleft}}SOME\ x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}P\ x{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
-When we apply this theorem as an introduction rule, \isa{{\isacharquery}P\ x} becomes
-\isa{{\isacharparenleft}s{\isacharcomma}\ x{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ Q\ x} and \isa{{\isacharquery}Q\ x} becomes \isa{{\isacharparenleft}s{\isacharcomma}\ x{\isacharparenright}\ {\isasymin}\ M} and we have to prove
-two subgoals: \isa{{\isasymexists}a{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ a{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ Q\ a}, which follows from the assumptions, and
-\isa{{\isacharparenleft}s{\isacharcomma}\ x{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ Q\ x\ {\isasymLongrightarrow}\ {\isacharparenleft}s{\isacharcomma}\ x{\isacharparenright}\ {\isasymin}\ M}, which is trivial. Thus it is not surprising that
+When we apply this theorem as an introduction rule, \isa{{\isaliteral{3F}{\isacharquery}}P\ x} becomes
+\isa{{\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q\ x} and \isa{{\isaliteral{3F}{\isacharquery}}Q\ x} becomes \isa{{\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M} and we have to prove
+two subgoals: \isa{{\isaliteral{5C3C6578697374733E}{\isasymexists}}a{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q\ a}, which follows from the assumptions, and
+\isa{{\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M}, which is trivial. Thus it is not surprising that
\isa{fast} can prove the base case quickly:%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}fast\ intro{\isacharcolon}\ someI{\isadigit{2}}{\isacharunderscore}ex{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}fast\ intro{\isaliteral{3A}{\isacharcolon}}\ someI{\isadigit{2}}{\isaliteral{5F}{\isacharunderscore}}ex{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
What is worth noting here is that we have used \methdx{fast} rather than
\isa{blast}. The reason is that \isa{blast} would fail because it cannot
-cope with \isa{someI{\isadigit{2}}{\isacharunderscore}ex}: unifying its conclusion with the current
+cope with \isa{someI{\isadigit{2}}{\isaliteral{5F}{\isacharunderscore}}ex}: unifying its conclusion with the current
subgoal is non-trivial because of the nested schematic variables. For
efficiency reasons \isa{blast} does not even attempt such unifications.
Although \isa{fast} can in principle cope with complicated unification
@@ -327,22 +327,22 @@
The induction step is similar, but more involved, because now we face nested
occurrences of \isa{SOME}. As a result, \isa{fast} is no longer able to
-solve the subgoal and we apply \isa{someI{\isadigit{2}}{\isacharunderscore}ex} by hand. We merely
+solve the subgoal and we apply \isa{someI{\isadigit{2}}{\isaliteral{5F}{\isacharunderscore}}ex} by hand. We merely
show the proof commands but do not describe the details:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ someI{\isadigit{2}}{\isacharunderscore}ex{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule\ someI{\isadigit{2}}{\isaliteral{5F}{\isacharunderscore}}ex{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}blast{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}blast{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ someI{\isadigit{2}}{\isacharunderscore}ex{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule\ someI{\isadigit{2}}{\isaliteral{5F}{\isacharunderscore}}ex{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}blast{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}blast{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}blast{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}blast{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -355,14 +355,14 @@
\begin{isamarkuptext}%
Function \isa{path} has fulfilled its purpose now and can be forgotten.
It was merely defined to provide the witness in the proof of the
-\isa{infinity{\isacharunderscore}lemma}. Aficionados of minimal proofs might like to know
+\isa{infinity{\isaliteral{5F}{\isacharunderscore}}lemma}. Aficionados of minimal proofs might like to know
that we could have given the witness without having to define a new function:
the term
\begin{isabelle}%
-\ \ \ \ \ nat{\isacharunderscore}rec\ s\ {\isacharparenleft}{\isasymlambda}n\ t{\isachardot}\ SOME\ u{\isachardot}\ {\isacharparenleft}t{\isacharcomma}\ u{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ Q\ u{\isacharparenright}%
+\ \ \ \ \ nat{\isaliteral{5F}{\isacharunderscore}}rec\ s\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}n\ t{\isaliteral{2E}{\isachardot}}\ SOME\ u{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{2C}{\isacharcomma}}\ u{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q\ u{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
is extensionally equal to \isa{path\ s\ Q},
-where \isa{nat{\isacharunderscore}rec} is the predefined primitive recursor on \isa{nat}.%
+where \isa{nat{\isaliteral{5F}{\isacharunderscore}}rec} is the predefined primitive recursor on \isa{nat}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -380,11 +380,11 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-At last we can prove the opposite direction of \isa{AF{\isacharunderscore}lemma{\isadigit{1}}}:%
+At last we can prove the opposite direction of \isa{AF{\isaliteral{5F}{\isacharunderscore}}lemma{\isadigit{1}}}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ AF{\isacharunderscore}lemma{\isadigit{2}}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharbraceleft}s{\isachardot}\ {\isasymforall}p\ {\isasymin}\ Paths\ s{\isachardot}\ {\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A{\isacharbraceright}\ {\isasymsubseteq}\ lfp{\isacharparenleft}af\ A{\isacharparenright}{\isachardoublequoteclose}%
+\ AF{\isaliteral{5F}{\isacharunderscore}}lemma{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7B}{\isacharbraceleft}}s{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}p\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Paths\ s{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}i{\isaliteral{2E}{\isachardot}}\ p\ i\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{7D}{\isacharbraceright}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ lfp{\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -397,32 +397,32 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ subsetI{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule\ subsetI{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}erule\ contrapos{\isacharunderscore}pp{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}erule\ contrapos{\isaliteral{5F}{\isacharunderscore}}pp{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
\ simp%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x{\isachardot}\ x\ {\isasymnotin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymexists}p{\isasymin}Paths\ x{\isachardot}\ {\isasymforall}i{\isachardot}\ p\ i\ {\isasymnotin}\ A%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}p{\isaliteral{5C3C696E3E}{\isasymin}}Paths\ x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{2E}{\isachardot}}\ p\ i\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ A%
\end{isabelle}
-Applying the \isa{infinity{\isacharunderscore}lemma} as a destruction rule leaves two subgoals, the second
-premise of \isa{infinity{\isacharunderscore}lemma} and the original subgoal:%
+Applying the \isa{infinity{\isaliteral{5F}{\isacharunderscore}}lemma} as a destruction rule leaves two subgoals, the second
+premise of \isa{infinity{\isaliteral{5F}{\isacharunderscore}}lemma} and the original subgoal:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}drule\ infinity{\isacharunderscore}lemma{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}drule\ infinity{\isaliteral{5F}{\isacharunderscore}}lemma{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x{\isachardot}\ {\isasymforall}s{\isachardot}\ s\ {\isasymnotin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}\ {\isasymlongrightarrow}\ {\isacharparenleft}{\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ t\ {\isasymnotin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}{\isacharparenright}\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}x{\isachardot}\ {\isasymexists}p{\isasymin}Paths\ x{\isachardot}\ {\isasymforall}i{\isachardot}\ p\ i\ {\isasymnotin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}\ {\isasymLongrightarrow}\isanewline
-\isaindent{\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}x{\isachardot}\ }{\isasymexists}p{\isasymin}Paths\ x{\isachardot}\ {\isasymforall}i{\isachardot}\ p\ i\ {\isasymnotin}\ A%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}s{\isaliteral{2E}{\isachardot}}\ s\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ t\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}p{\isaliteral{5C3C696E3E}{\isasymin}}Paths\ x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{2E}{\isachardot}}\ p\ i\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\isanewline
+\isaindent{\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ }{\isaliteral{5C3C6578697374733E}{\isasymexists}}p{\isaliteral{5C3C696E3E}{\isasymin}}Paths\ x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{2E}{\isachardot}}\ p\ i\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ A%
\end{isabelle}
Both are solved automatically:%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto\ dest{\isacharcolon}\ not{\isacharunderscore}in{\isacharunderscore}lfp{\isacharunderscore}afD{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}auto\ dest{\isaliteral{3A}{\isacharcolon}}\ not{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{5F}{\isacharunderscore}}lfp{\isaliteral{5F}{\isacharunderscore}}afD{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -438,12 +438,12 @@
simpler arguments.
The main theorem is proved as for PDL, except that we also derive the
-necessary equality \isa{lfp{\isacharparenleft}af\ A{\isacharparenright}\ {\isacharequal}\ {\isachardot}{\isachardot}{\isachardot}} by combining
-\isa{AF{\isacharunderscore}lemma{\isadigit{1}}} and \isa{AF{\isacharunderscore}lemma{\isadigit{2}}} on the spot:%
+necessary equality \isa{lfp{\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}} by combining
+\isa{AF{\isaliteral{5F}{\isacharunderscore}}lemma{\isadigit{1}}} and \isa{AF{\isaliteral{5F}{\isacharunderscore}}lemma{\isadigit{2}}} on the spot:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ {\isachardoublequoteopen}mc\ f\ {\isacharequal}\ {\isacharbraceleft}s{\isachardot}\ s\ {\isasymTurnstile}\ f{\isacharbraceright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}mc\ f\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}s{\isaliteral{2E}{\isachardot}}\ s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ f{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -451,9 +451,9 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ f{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ f{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto\ simp\ add{\isacharcolon}\ EF{\isacharunderscore}lemma\ equalityI{\isacharbrackleft}OF\ AF{\isacharunderscore}lemma{\isadigit{1}}\ AF{\isacharunderscore}lemma{\isadigit{2}}{\isacharbrackright}{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}auto\ simp\ add{\isaliteral{3A}{\isacharcolon}}\ EF{\isaliteral{5F}{\isacharunderscore}}lemma\ equalityI{\isaliteral{5B}{\isacharbrackleft}}OF\ AF{\isaliteral{5F}{\isacharunderscore}}lemma{\isadigit{1}}\ AF{\isaliteral{5F}{\isacharunderscore}}lemma{\isadigit{2}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -472,27 +472,27 @@
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
\isanewline
-until{\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}state\ set\ {\isasymRightarrow}\ state\ set\ {\isasymRightarrow}\ state\ {\isasymRightarrow}\ state\ list\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}until\ A\ B\ s\ {\isacharbrackleft}{\isacharbrackright}\ \ \ \ {\isacharequal}\ {\isacharparenleft}s\ {\isasymin}\ B{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}until\ A\ B\ s\ {\isacharparenleft}t{\isacharhash}p{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}s\ {\isasymin}\ A\ {\isasymand}\ {\isacharparenleft}s{\isacharcomma}t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ until\ A\ B\ t\ p{\isacharparenright}{\isachardoublequoteclose}%
+until{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}state\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ state\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ state\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ state\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}until\ A\ B\ s\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ \ \ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}s\ {\isaliteral{5C3C696E3E}{\isasymin}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}until\ A\ B\ s\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{23}{\isacharhash}}p{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}s\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ until\ A\ B\ t\ p{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
Expressing the semantics of \isa{EU} is now straightforward:
\begin{isabelle}%
-\ \ \ \ \ s\ {\isasymTurnstile}\ EU\ f\ g\ {\isacharequal}\ {\isacharparenleft}{\isasymexists}p{\isachardot}\ until\ {\isacharbraceleft}t{\isachardot}\ t\ {\isasymTurnstile}\ f{\isacharbraceright}\ {\isacharbraceleft}t{\isachardot}\ t\ {\isasymTurnstile}\ g{\isacharbraceright}\ s\ p{\isacharparenright}%
+\ \ \ \ \ s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ EU\ f\ g\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}p{\isaliteral{2E}{\isachardot}}\ until\ {\isaliteral{7B}{\isacharbraceleft}}t{\isaliteral{2E}{\isachardot}}\ t\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ f{\isaliteral{7D}{\isacharbraceright}}\ {\isaliteral{7B}{\isacharbraceleft}}t{\isaliteral{2E}{\isachardot}}\ t\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ g{\isaliteral{7D}{\isacharbraceright}}\ s\ p{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
Note that \isa{EU} is not definable in terms of the other operators!
Model checking \isa{EU} is again a least fixed point construction:
\begin{isabelle}%
-\ \ \ \ \ mc{\isacharparenleft}EU\ f\ g{\isacharparenright}\ {\isacharequal}\ lfp{\isacharparenleft}{\isasymlambda}T{\isachardot}\ mc\ g\ {\isasymunion}\ mc\ f\ {\isasyminter}\ {\isacharparenleft}M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}\ T{\isacharparenright}{\isacharparenright}%
+\ \ \ \ \ mc{\isaliteral{28}{\isacharparenleft}}EU\ f\ g{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ lfp{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}T{\isaliteral{2E}{\isachardot}}\ mc\ g\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ mc\ f\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ {\isaliteral{28}{\isacharparenleft}}M{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{60}{\isacharbackquote}}{\isaliteral{60}{\isacharbackquote}}\ T{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\begin{exercise}
Extend the datatype of formulae by the above until operator
and prove the equivalence between semantics and model checking, i.e.\ that
\begin{isabelle}%
-\ \ \ \ \ mc\ {\isacharparenleft}EU\ f\ g{\isacharparenright}\ {\isacharequal}\ {\isacharbraceleft}s{\isachardot}\ s\ {\isasymTurnstile}\ EU\ f\ g{\isacharbraceright}%
+\ \ \ \ \ mc\ {\isaliteral{28}{\isacharparenleft}}EU\ f\ g{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}s{\isaliteral{2E}{\isachardot}}\ s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ EU\ f\ g{\isaliteral{7D}{\isacharbraceright}}%
\end{isabelle}
%For readability you may want to annotate {term EU} with its customary syntax
%{text[display]"| EU formula formula E[_ U _]"}
@@ -546,10 +546,10 @@
our model checkers. It is clear that if all sets are finite, they can be
represented as lists and the usual set operations are easily
implemented. Only \isa{lfp} requires a little thought. Fortunately, theory
-\isa{While{\isacharunderscore}Combinator} in the Library~\cite{HOL-Library} provides a
+\isa{While{\isaliteral{5F}{\isacharunderscore}}Combinator} in the Library~\cite{HOL-Library} provides a
theorem stating that in the case of finite sets and a monotone
function~\isa{F}, the value of \mbox{\isa{lfp\ F}} can be computed by
-iterated application of \isa{F} to~\isa{{\isacharbraceleft}{\isacharbraceright}} until a fixed point is
+iterated application of \isa{F} to~\isa{{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{7D}{\isacharbraceright}}} until a fixed point is
reached. It is actually possible to generate executable functional programs
from HOL definitions, but that is beyond the scope of the tutorial.%
\index{CTL|)}%
--- a/doc-src/TutorialI/CTL/document/CTLind.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/CTL/document/CTLind.tex Mon Nov 08 14:41:11 2010 +0100
@@ -27,42 +27,42 @@
show how inductive definitions can simplify proofs.
In \S\ref{sec:CTL} we gave a fairly involved proof of the correctness of a
model checker for CTL\@. In particular the proof of the
-\isa{infinity{\isacharunderscore}lemma} on the way to \isa{AF{\isacharunderscore}lemma{\isadigit{2}}} is not as
+\isa{infinity{\isaliteral{5F}{\isacharunderscore}}lemma} on the way to \isa{AF{\isaliteral{5F}{\isacharunderscore}}lemma{\isadigit{2}}} is not as
simple as one might expect, due to the \isa{SOME} operator
-involved. Below we give a simpler proof of \isa{AF{\isacharunderscore}lemma{\isadigit{2}}}
+involved. Below we give a simpler proof of \isa{AF{\isaliteral{5F}{\isacharunderscore}}lemma{\isadigit{2}}}
based on an auxiliary inductive definition.
Let us call a (finite or infinite) path \emph{\isa{A}-avoiding} if it does
-not touch any node in the set \isa{A}. Then \isa{AF{\isacharunderscore}lemma{\isadigit{2}}} says
+not touch any node in the set \isa{A}. Then \isa{AF{\isaliteral{5F}{\isacharunderscore}}lemma{\isadigit{2}}} says
that if no infinite path from some state \isa{s} is \isa{A}-avoiding,
-then \isa{s\ {\isasymin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}}. We prove this by inductively defining the set
+then \isa{s\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}}. We prove this by inductively defining the set
\isa{Avoid\ s\ A} of states reachable from \isa{s} by a finite \isa{A}-avoiding path:
% Second proof of opposite direction, directly by well-founded induction
% on the initial segment of M that avoids A.%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{inductive{\isacharunderscore}set}\isamarkupfalse%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse%
\isanewline
-\ \ Avoid\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}state\ {\isasymRightarrow}\ state\ set\ {\isasymRightarrow}\ state\ set{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{for}\ s\ {\isacharcolon}{\isacharcolon}\ state\ \isakeyword{and}\ A\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}state\ set{\isachardoublequoteclose}\isanewline
+\ \ Avoid\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}state\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ state\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ state\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{for}\ s\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ state\ \isakeyword{and}\ A\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}state\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ \ \ {\isachardoublequoteopen}s\ {\isasymin}\ Avoid\ s\ A{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}{\isasymlbrakk}\ t\ {\isasymin}\ Avoid\ s\ A{\isacharsemicolon}\ t\ {\isasymnotin}\ A{\isacharsemicolon}\ {\isacharparenleft}t{\isacharcomma}u{\isacharparenright}\ {\isasymin}\ M\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ u\ {\isasymin}\ Avoid\ s\ A{\isachardoublequoteclose}%
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}s\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Avoid\ s\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Avoid\ s\ A{\isaliteral{3B}{\isacharsemicolon}}\ t\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ A{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{2C}{\isacharcomma}}u{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ u\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Avoid\ s\ A{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
It is easy to see that for any infinite \isa{A}-avoiding path \isa{f}
-with \isa{f\ {\isadigit{0}}\ {\isasymin}\ Avoid\ s\ A} there is an infinite \isa{A}-avoiding path
+with \isa{f\ {\isadigit{0}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Avoid\ s\ A} there is an infinite \isa{A}-avoiding path
starting with \isa{s} because (by definition of \isa{Avoid}) there is a
finite \isa{A}-avoiding path from \isa{s} to \isa{f\ {\isadigit{0}}}.
-The proof is by induction on \isa{f\ {\isadigit{0}}\ {\isasymin}\ Avoid\ s\ A}. However,
+The proof is by induction on \isa{f\ {\isadigit{0}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Avoid\ s\ A}. However,
this requires the following
reformulation, as explained in \S\ref{sec:ind-var-in-prems} above;
-the \isa{rule{\isacharunderscore}format} directive undoes the reformulation after the proof.%
+the \isa{rule{\isaliteral{5F}{\isacharunderscore}}format} directive undoes the reformulation after the proof.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ ex{\isacharunderscore}infinite{\isacharunderscore}path{\isacharbrackleft}rule{\isacharunderscore}format{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}t\ {\isasymin}\ Avoid\ s\ A\ \ {\isasymLongrightarrow}\isanewline
-\ \ \ {\isasymforall}f{\isasymin}Paths\ t{\isachardot}\ {\isacharparenleft}{\isasymforall}i{\isachardot}\ f\ i\ {\isasymnotin}\ A{\isacharparenright}\ {\isasymlongrightarrow}\ {\isacharparenleft}{\isasymexists}p{\isasymin}Paths\ s{\isachardot}\ {\isasymforall}i{\isachardot}\ p\ i\ {\isasymnotin}\ A{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ ex{\isaliteral{5F}{\isacharunderscore}}infinite{\isaliteral{5F}{\isacharunderscore}}path{\isaliteral{5B}{\isacharbrackleft}}rule{\isaliteral{5F}{\isacharunderscore}}format{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Avoid\ s\ A\ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\isanewline
+\ \ \ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}f{\isaliteral{5C3C696E3E}{\isasymin}}Paths\ t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{2E}{\isachardot}}\ f\ i\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}p{\isaliteral{5C3C696E3E}{\isasymin}}Paths\ s{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{2E}{\isachardot}}\ p\ i\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -70,15 +70,15 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}erule\ Avoid{\isachardot}induct{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}erule\ Avoid{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}blast{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}blast{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}clarify{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}clarify{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}drule{\isacharunderscore}tac\ x\ {\isacharequal}\ {\isachardoublequoteopen}{\isasymlambda}i{\isachardot}\ case\ i\ of\ {\isadigit{0}}\ {\isasymRightarrow}\ t\ {\isacharbar}\ Suc\ i\ {\isasymRightarrow}\ f\ i{\isachardoublequoteclose}\ \isakeyword{in}\ bspec{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}drule{\isaliteral{5F}{\isacharunderscore}}tac\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}i{\isaliteral{2E}{\isachardot}}\ case\ i\ of\ {\isadigit{0}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ t\ {\isaliteral{7C}{\isacharbar}}\ Suc\ i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ f\ i{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{in}\ bspec{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}\ Paths{\isacharunderscore}def\ split{\isacharcolon}\ nat{\isachardot}split{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{5F}{\isacharunderscore}}all\ add{\isaliteral{3A}{\isacharcolon}}\ Paths{\isaliteral{5F}{\isacharunderscore}}def\ split{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{2E}{\isachardot}}split{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -90,24 +90,24 @@
%
\begin{isamarkuptext}%
\noindent
-The base case (\isa{t\ {\isacharequal}\ s}) is trivial and proved by \isa{blast}.
+The base case (\isa{t\ {\isaliteral{3D}{\isacharequal}}\ s}) is trivial and proved by \isa{blast}.
In the induction step, we have an infinite \isa{A}-avoiding path \isa{f}
starting from \isa{u}, a successor of \isa{t}. Now we simply instantiate
-the \isa{{\isasymforall}f{\isasymin}Paths\ t} in the induction hypothesis by the path starting with
+the \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}f{\isaliteral{5C3C696E3E}{\isasymin}}Paths\ t} in the induction hypothesis by the path starting with
\isa{t} and continuing with \isa{f}. That is what the above $\lambda$-term
expresses. Simplification shows that this is a path starting with \isa{t}
and that the instantiated induction hypothesis implies the conclusion.
Now we come to the key lemma. Assuming that no infinite \isa{A}-avoiding
-path starts from \isa{s}, we want to show \isa{s\ {\isasymin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}}. For the
+path starts from \isa{s}, we want to show \isa{s\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}}. For the
inductive proof this must be generalized to the statement that every point \isa{t}
``between'' \isa{s} and \isa{A}, in other words all of \isa{Avoid\ s\ A},
-is contained in \isa{lfp\ {\isacharparenleft}af\ A{\isacharparenright}}:%
+is contained in \isa{lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ Avoid{\isacharunderscore}in{\isacharunderscore}lfp{\isacharbrackleft}rule{\isacharunderscore}format{\isacharparenleft}no{\isacharunderscore}asm{\isacharparenright}{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}{\isasymforall}p{\isasymin}Paths\ s{\isachardot}\ {\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A\ {\isasymLongrightarrow}\ t\ {\isasymin}\ Avoid\ s\ A\ {\isasymlongrightarrow}\ t\ {\isasymin}\ lfp{\isacharparenleft}af\ A{\isacharparenright}{\isachardoublequoteclose}%
+\ Avoid{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{5F}{\isacharunderscore}}lfp{\isaliteral{5B}{\isacharbrackleft}}rule{\isaliteral{5F}{\isacharunderscore}}format{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}p{\isaliteral{5C3C696E3E}{\isasymin}}Paths\ s{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}i{\isaliteral{2E}{\isachardot}}\ p\ i\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Avoid\ s\ A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lfp{\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -116,16 +116,16 @@
%
\begin{isamarkuptxt}%
\noindent
-The proof is by induction on the ``distance'' between \isa{t} and \isa{A}. Remember that \isa{lfp\ {\isacharparenleft}af\ A{\isacharparenright}\ {\isacharequal}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}}.
-If \isa{t} is already in \isa{A}, then \isa{t\ {\isasymin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}} is
+The proof is by induction on the ``distance'' between \isa{t} and \isa{A}. Remember that \isa{lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ A\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ M{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{60}{\isacharbackquote}}{\isaliteral{60}{\isacharbackquote}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}}.
+If \isa{t} is already in \isa{A}, then \isa{t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}} is
trivial. If \isa{t} is not in \isa{A} but all successors are in
-\isa{lfp\ {\isacharparenleft}af\ A{\isacharparenright}} (induction hypothesis), then \isa{t\ {\isasymin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}} is
+\isa{lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}} (induction hypothesis), then \isa{t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}} is
again trivial.
The formal counterpart of this proof sketch is a well-founded induction
-on~\isa{M} restricted to \isa{Avoid\ s\ A\ {\isacharminus}\ A}, roughly speaking:
+on~\isa{M} restricted to \isa{Avoid\ s\ A\ {\isaliteral{2D}{\isacharminus}}\ A}, roughly speaking:
\begin{isabelle}%
-\ \ \ \ \ {\isacharbraceleft}{\isacharparenleft}y{\isacharcomma}\ x{\isacharparenright}{\isachardot}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ x\ {\isasymin}\ Avoid\ s\ A\ {\isasymand}\ x\ {\isasymnotin}\ A{\isacharbraceright}%
+\ \ \ \ \ {\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Avoid\ s\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ x\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ A{\isaliteral{7D}{\isacharbraceright}}%
\end{isabelle}
As we shall see presently, the absence of infinite \isa{A}-avoiding paths
starting from \isa{s} implies well-foundedness of this relation. For the
@@ -133,62 +133,62 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}subgoal{\isacharunderscore}tac\ {\isachardoublequoteopen}wf{\isacharbraceleft}{\isacharparenleft}y{\isacharcomma}x{\isacharparenright}{\isachardot}\ {\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ x\ {\isasymin}\ Avoid\ s\ A\ {\isasymand}\ x\ {\isasymnotin}\ A{\isacharbraceright}{\isachardoublequoteclose}{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}subgoal{\isaliteral{5F}{\isacharunderscore}}tac\ {\isaliteral{22}{\isachardoublequoteopen}}wf{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}x{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Avoid\ s\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ x\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ A{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}erule{\isacharunderscore}tac\ a\ {\isacharequal}\ t\ \isakeyword{in}\ wf{\isacharunderscore}induct{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}erule{\isaliteral{5F}{\isacharunderscore}}tac\ a\ {\isaliteral{3D}{\isacharequal}}\ t\ \isakeyword{in}\ wf{\isaliteral{5F}{\isacharunderscore}}induct{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}clarsimp{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}clarsimp{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}t{\isachardot}\ {\isasymlbrakk}{\isasymforall}p{\isasymin}Paths\ s{\isachardot}\ {\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A{\isacharsemicolon}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}t{\isachardot}\ \ }{\isasymforall}y{\isachardot}\ {\isacharparenleft}t{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ t\ {\isasymnotin}\ A\ {\isasymlongrightarrow}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}t{\isachardot}\ \ {\isasymforall}y{\isachardot}\ }y\ {\isasymin}\ Avoid\ s\ A\ {\isasymlongrightarrow}\ y\ {\isasymin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}{\isacharsemicolon}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}t{\isachardot}\ \ }t\ {\isasymin}\ Avoid\ s\ A{\isasymrbrakk}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}t{\isachardot}\ }{\isasymLongrightarrow}\ t\ {\isasymin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymforall}p{\isasymin}Paths\ s{\isachardot}\ {\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A\ {\isasymLongrightarrow}\isanewline
-\isaindent{\ {\isadigit{2}}{\isachardot}\ }wf\ {\isacharbraceleft}{\isacharparenleft}y{\isacharcomma}\ x{\isacharparenright}{\isachardot}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ x\ {\isasymin}\ Avoid\ s\ A\ {\isasymand}\ x\ {\isasymnotin}\ A{\isacharbraceright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}p{\isaliteral{5C3C696E3E}{\isasymin}}Paths\ s{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}i{\isaliteral{2E}{\isachardot}}\ p\ i\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}t{\isaliteral{2E}{\isachardot}}\ \ }{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}y{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ t\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}t{\isaliteral{2E}{\isachardot}}\ \ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}y{\isaliteral{2E}{\isachardot}}\ }y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Avoid\ s\ A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}t{\isaliteral{2E}{\isachardot}}\ \ }t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Avoid\ s\ A{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}t{\isaliteral{2E}{\isachardot}}\ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}p{\isaliteral{5C3C696E3E}{\isasymin}}Paths\ s{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}i{\isaliteral{2E}{\isachardot}}\ p\ i\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\isanewline
+\isaindent{\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ }wf\ {\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Avoid\ s\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ x\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ A{\isaliteral{7D}{\isacharbraceright}}%
\end{isabelle}
-Now the induction hypothesis states that if \isa{t\ {\isasymnotin}\ A}
+Now the induction hypothesis states that if \isa{t\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ A}
then all successors of \isa{t} that are in \isa{Avoid\ s\ A} are in
-\isa{lfp\ {\isacharparenleft}af\ A{\isacharparenright}}. Unfolding \isa{lfp} in the conclusion of the first
+\isa{lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}}. Unfolding \isa{lfp} in the conclusion of the first
subgoal once, we have to prove that \isa{t} is in \isa{A} or all successors
-of \isa{t} are in \isa{lfp\ {\isacharparenleft}af\ A{\isacharparenright}}. But if \isa{t} is not in \isa{A},
+of \isa{t} are in \isa{lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}}. But if \isa{t} is not in \isa{A},
the second
\isa{Avoid}-rule implies that all successors of \isa{t} are in
-\isa{Avoid\ s\ A}, because we also assume \isa{t\ {\isasymin}\ Avoid\ s\ A}.
+\isa{Avoid\ s\ A}, because we also assume \isa{t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Avoid\ s\ A}.
Hence, by the induction hypothesis, all successors of \isa{t} are indeed in
-\isa{lfp\ {\isacharparenleft}af\ A{\isacharparenright}}. Mechanically:%
+\isa{lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}}. Mechanically:%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}subst\ lfp{\isacharunderscore}unfold{\isacharbrackleft}OF\ mono{\isacharunderscore}af{\isacharbrackright}{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}subst\ lfp{\isaliteral{5F}{\isacharunderscore}}unfold{\isaliteral{5B}{\isacharbrackleft}}OF\ mono{\isaliteral{5F}{\isacharunderscore}}af{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp\ {\isacharparenleft}no{\isacharunderscore}asm{\isacharparenright}\ add{\isacharcolon}\ af{\isacharunderscore}def{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}simp\ {\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{29}{\isacharparenright}}\ add{\isaliteral{3A}{\isacharcolon}}\ af{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}blast\ intro{\isacharcolon}\ Avoid{\isachardot}intros{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}blast\ intro{\isaliteral{3A}{\isacharcolon}}\ Avoid{\isaliteral{2E}{\isachardot}}intros{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
Having proved the main goal, we return to the proof obligation that the
relation used above is indeed well-founded. This is proved by contradiction: if
the relation is not well-founded then there exists an infinite \isa{A}-avoiding path all in \isa{Avoid\ s\ A}, by theorem
-\isa{wf{\isacharunderscore}iff{\isacharunderscore}no{\isacharunderscore}infinite{\isacharunderscore}down{\isacharunderscore}chain}:
+\isa{wf{\isaliteral{5F}{\isacharunderscore}}iff{\isaliteral{5F}{\isacharunderscore}}no{\isaliteral{5F}{\isacharunderscore}}infinite{\isaliteral{5F}{\isacharunderscore}}down{\isaliteral{5F}{\isacharunderscore}}chain}:
\begin{isabelle}%
-\ \ \ \ \ wf\ r\ {\isacharequal}\ {\isacharparenleft}{\isasymnot}\ {\isacharparenleft}{\isasymexists}f{\isachardot}\ {\isasymforall}i{\isachardot}\ {\isacharparenleft}f\ {\isacharparenleft}Suc\ i{\isacharparenright}{\isacharcomma}\ f\ i{\isacharparenright}\ {\isasymin}\ r{\isacharparenright}{\isacharparenright}%
+\ \ \ \ \ wf\ r\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}f{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}Suc\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ f\ i{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
-From lemma \isa{ex{\isacharunderscore}infinite{\isacharunderscore}path} the existence of an infinite
+From lemma \isa{ex{\isaliteral{5F}{\isacharunderscore}}infinite{\isaliteral{5F}{\isacharunderscore}}path} the existence of an infinite
\isa{A}-avoiding path starting in \isa{s} follows, contradiction.%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}erule\ contrapos{\isacharunderscore}pp{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}erule\ contrapos{\isaliteral{5F}{\isacharunderscore}}pp{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp\ add{\isacharcolon}\ wf{\isacharunderscore}iff{\isacharunderscore}no{\isacharunderscore}infinite{\isacharunderscore}down{\isacharunderscore}chain{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ wf{\isaliteral{5F}{\isacharunderscore}}iff{\isaliteral{5F}{\isacharunderscore}}no{\isaliteral{5F}{\isacharunderscore}}infinite{\isaliteral{5F}{\isacharunderscore}}down{\isaliteral{5F}{\isacharunderscore}}chain{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}erule\ exE{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}erule\ exE{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ ex{\isacharunderscore}infinite{\isacharunderscore}path{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule\ ex{\isaliteral{5F}{\isacharunderscore}}infinite{\isaliteral{5F}{\isacharunderscore}}path{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto\ simp\ add{\isacharcolon}\ Paths{\isacharunderscore}def{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}auto\ simp\ add{\isaliteral{3A}{\isacharcolon}}\ Paths{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -199,23 +199,23 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-The \isa{{\isacharparenleft}no{\isacharunderscore}asm{\isacharparenright}} modifier of the \isa{rule{\isacharunderscore}format} directive in the
+The \isa{{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{29}{\isacharparenright}}} modifier of the \isa{rule{\isaliteral{5F}{\isacharunderscore}}format} directive in the
statement of the lemma means
-that the assumption is left unchanged; otherwise the \isa{{\isasymforall}p}
+that the assumption is left unchanged; otherwise the \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}p}
would be turned
-into a \isa{{\isasymAnd}p}, which would complicate matters below. As it is,
-\isa{Avoid{\isacharunderscore}in{\isacharunderscore}lfp} is now
+into a \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}p}, which would complicate matters below. As it is,
+\isa{Avoid{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{5F}{\isacharunderscore}}lfp} is now
\begin{isabelle}%
-\ \ \ \ \ {\isasymlbrakk}{\isasymforall}p{\isasymin}Paths\ s{\isachardot}\ {\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A{\isacharsemicolon}\ t\ {\isasymin}\ Avoid\ s\ A{\isasymrbrakk}\ {\isasymLongrightarrow}\ t\ {\isasymin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}%
+\ \ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}p{\isaliteral{5C3C696E3E}{\isasymin}}Paths\ s{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}i{\isaliteral{2E}{\isachardot}}\ p\ i\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{3B}{\isacharsemicolon}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Avoid\ s\ A{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
-The main theorem is simply the corollary where \isa{t\ {\isacharequal}\ s},
-when the assumption \isa{t\ {\isasymin}\ Avoid\ s\ A} is trivially true
+The main theorem is simply the corollary where \isa{t\ {\isaliteral{3D}{\isacharequal}}\ s},
+when the assumption \isa{t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Avoid\ s\ A} is trivially true
by the first \isa{Avoid}-rule. Isabelle confirms this:%
\index{CTL|)}%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ AF{\isacharunderscore}lemma{\isadigit{2}}{\isacharcolon}\ \ {\isachardoublequoteopen}{\isacharbraceleft}s{\isachardot}\ {\isasymforall}p\ {\isasymin}\ Paths\ s{\isachardot}\ {\isasymexists}\ i{\isachardot}\ p\ i\ {\isasymin}\ A{\isacharbraceright}\ {\isasymsubseteq}\ lfp{\isacharparenleft}af\ A{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ AF{\isaliteral{5F}{\isacharunderscore}}lemma{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7B}{\isacharbraceleft}}s{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}p\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Paths\ s{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}\ i{\isaliteral{2E}{\isachardot}}\ p\ i\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{7D}{\isacharbraceright}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ lfp{\isaliteral{28}{\isacharparenleft}}af\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -223,7 +223,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-{\isacharparenleft}auto\ elim{\isacharcolon}\ Avoid{\isacharunderscore}in{\isacharunderscore}lfp\ intro{\isacharcolon}\ Avoid{\isachardot}intros{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}auto\ elim{\isaliteral{3A}{\isacharcolon}}\ Avoid{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{5F}{\isacharunderscore}}lfp\ intro{\isaliteral{3A}{\isacharcolon}}\ Avoid{\isaliteral{2E}{\isachardot}}intros{\isaliteral{29}{\isacharparenright}}\isanewline
\isanewline
%
\endisatagproof
--- a/doc-src/TutorialI/CTL/document/PDL.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/CTL/document/PDL.tex Mon Nov 08 14:41:11 2010 +0100
@@ -31,34 +31,34 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ formula\ {\isacharequal}\ Atom\ {\isachardoublequoteopen}atom{\isachardoublequoteclose}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Neg\ formula\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ And\ formula\ formula\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ AX\ formula\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ EF\ formula%
+\ formula\ {\isaliteral{3D}{\isacharequal}}\ Atom\ {\isaliteral{22}{\isachardoublequoteopen}}atom{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Neg\ formula\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ And\ formula\ formula\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ AX\ formula\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ EF\ formula%
\begin{isamarkuptext}%
\noindent
This resembles the boolean expression case study in
\S\ref{sec:boolex}.
A validity relation between states and formulae specifies the semantics.
-The syntax annotation allows us to write \isa{s\ {\isasymTurnstile}\ f} instead of
+The syntax annotation allows us to write \isa{s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ f} instead of
\hbox{\isa{valid\ s\ f}}. The definition is by recursion over the syntax:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ valid\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}state\ {\isasymRightarrow}\ formula\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \ \ {\isacharparenleft}{\isachardoublequoteopen}{\isacharparenleft}{\isacharunderscore}\ {\isasymTurnstile}\ {\isacharunderscore}{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbrackleft}{\isadigit{8}}{\isadigit{0}}{\isacharcomma}{\isadigit{8}}{\isadigit{0}}{\isacharbrackright}\ {\isadigit{8}}{\isadigit{0}}{\isacharparenright}\isanewline
+\ valid\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}state\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ formula\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{8}}{\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}{\isadigit{8}}{\isadigit{0}}{\isaliteral{5D}{\isacharbrackright}}\ {\isadigit{8}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isakeyword{where}\isanewline
-{\isachardoublequoteopen}s\ {\isasymTurnstile}\ Atom\ a\ \ {\isacharequal}\ {\isacharparenleft}a\ {\isasymin}\ L\ s{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}s\ {\isasymTurnstile}\ Neg\ f\ \ \ {\isacharequal}\ {\isacharparenleft}{\isasymnot}{\isacharparenleft}s\ {\isasymTurnstile}\ f{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}s\ {\isasymTurnstile}\ And\ f\ g\ {\isacharequal}\ {\isacharparenleft}s\ {\isasymTurnstile}\ f\ {\isasymand}\ s\ {\isasymTurnstile}\ g{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}s\ {\isasymTurnstile}\ AX\ f\ \ \ \ {\isacharequal}\ {\isacharparenleft}{\isasymforall}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}t{\isacharparenright}\ {\isasymin}\ M\ {\isasymlongrightarrow}\ t\ {\isasymTurnstile}\ f{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}s\ {\isasymTurnstile}\ EF\ f\ \ \ \ {\isacharequal}\ {\isacharparenleft}{\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}t{\isacharparenright}\ {\isasymin}\ M\isactrlsup {\isacharasterisk}\ {\isasymand}\ t\ {\isasymTurnstile}\ f{\isacharparenright}{\isachardoublequoteclose}%
+{\isaliteral{22}{\isachardoublequoteopen}}s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ Atom\ a\ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{5C3C696E3E}{\isasymin}}\ L\ s{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ Neg\ f\ \ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}{\isaliteral{28}{\isacharparenleft}}s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ f{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ And\ f\ g\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ f\ {\isaliteral{5C3C616E643E}{\isasymand}}\ s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ g{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ AX\ f\ \ \ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ t\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ f{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ EF\ f\ \ \ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ t\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ f{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
The first three equations should be self-explanatory. The temporal formula
\isa{AX\ f} means that \isa{f} is true in \emph{A}ll ne\emph{X}t states whereas
\isa{EF\ f} means that there \emph{E}xists some \emph{F}uture state in which \isa{f} is
-true. The future is expressed via \isa{\isactrlsup {\isacharasterisk}}, the reflexive transitive
+true. The future is expressed via \isa{\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}}, the reflexive transitive
closure. Because of reflexivity, the future includes the present.
Now we come to the model checker itself. It maps a formula into the
@@ -67,21 +67,21 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ mc\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}formula\ {\isasymRightarrow}\ state\ set{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}mc{\isacharparenleft}Atom\ a{\isacharparenright}\ \ {\isacharequal}\ {\isacharbraceleft}s{\isachardot}\ a\ {\isasymin}\ L\ s{\isacharbraceright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}mc{\isacharparenleft}Neg\ f{\isacharparenright}\ \ \ {\isacharequal}\ {\isacharminus}mc\ f{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}mc{\isacharparenleft}And\ f\ g{\isacharparenright}\ {\isacharequal}\ mc\ f\ {\isasyminter}\ mc\ g{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}mc{\isacharparenleft}AX\ f{\isacharparenright}\ \ \ \ {\isacharequal}\ {\isacharbraceleft}s{\isachardot}\ {\isasymforall}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}t{\isacharparenright}\ {\isasymin}\ M\ \ {\isasymlongrightarrow}\ t\ {\isasymin}\ mc\ f{\isacharbraceright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}mc{\isacharparenleft}EF\ f{\isacharparenright}\ \ \ \ {\isacharequal}\ lfp{\isacharparenleft}{\isasymlambda}T{\isachardot}\ mc\ f\ {\isasymunion}\ {\isacharparenleft}M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}\ T{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
+\ mc\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}formula\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ state\ set{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}mc{\isaliteral{28}{\isacharparenleft}}Atom\ a{\isaliteral{29}{\isacharparenright}}\ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}s{\isaliteral{2E}{\isachardot}}\ a\ {\isaliteral{5C3C696E3E}{\isasymin}}\ L\ s{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}mc{\isaliteral{28}{\isacharparenleft}}Neg\ f{\isaliteral{29}{\isacharparenright}}\ \ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}mc\ f{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}mc{\isaliteral{28}{\isacharparenleft}}And\ f\ g{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ mc\ f\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ mc\ g{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}mc{\isaliteral{28}{\isacharparenleft}}AX\ f{\isaliteral{29}{\isacharparenright}}\ \ \ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}s{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ \ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ mc\ f{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}mc{\isaliteral{28}{\isacharparenleft}}EF\ f{\isaliteral{29}{\isacharparenright}}\ \ \ \ {\isaliteral{3D}{\isacharequal}}\ lfp{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}T{\isaliteral{2E}{\isachardot}}\ mc\ f\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ {\isaliteral{28}{\isacharparenleft}}M{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{60}{\isacharbackquote}}{\isaliteral{60}{\isacharbackquote}}\ T{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
Only the equation for \isa{EF} deserves some comments. Remember that the
-postfix \isa{{\isasyminverse}} and the infix \isa{{\isacharbackquote}{\isacharbackquote}} are predefined and denote the
+postfix \isa{{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}} and the infix \isa{{\isaliteral{60}{\isacharbackquote}}{\isaliteral{60}{\isacharbackquote}}} are predefined and denote the
converse of a relation and the image of a set under a relation. Thus
-\isa{M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}\ T} is the set of all predecessors of \isa{T} and the least
-fixed point (\isa{lfp}) of \isa{{\isasymlambda}T{\isachardot}\ mc\ f\ {\isasymunion}\ M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}\ T} is the least set
+\isa{M{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{60}{\isacharbackquote}}{\isaliteral{60}{\isacharbackquote}}\ T} is the set of all predecessors of \isa{T} and the least
+fixed point (\isa{lfp}) of \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}T{\isaliteral{2E}{\isachardot}}\ mc\ f\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ M{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{60}{\isacharbackquote}}{\isaliteral{60}{\isacharbackquote}}\ T} is the least set
\isa{T} containing \isa{mc\ f} and all predecessors of \isa{T}. If you
-find it hard to see that \isa{mc\ {\isacharparenleft}EF\ f{\isacharparenright}} contains exactly those states from
+find it hard to see that \isa{mc\ {\isaliteral{28}{\isacharparenleft}}EF\ f{\isaliteral{29}{\isacharparenright}}} contains exactly those states from
which there is a path to a state where \isa{f} is true, do not worry --- this
will be proved in a moment.
@@ -90,7 +90,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ mono{\isacharunderscore}ef{\isacharcolon}\ {\isachardoublequoteopen}mono{\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ {\isacharparenleft}M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}\ T{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ mono{\isaliteral{5F}{\isacharunderscore}}ef{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}mono{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}T{\isaliteral{2E}{\isachardot}}\ A\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ {\isaliteral{28}{\isacharparenleft}}M{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{60}{\isacharbackquote}}{\isaliteral{60}{\isacharbackquote}}\ T{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -98,7 +98,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ monoI{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule\ monoI{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
\ blast\isanewline
\isacommand{done}\isamarkupfalse%
@@ -117,8 +117,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ EF{\isacharunderscore}lemma{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}lfp{\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ {\isacharparenleft}M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}\ T{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharbraceleft}s{\isachardot}\ {\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}t{\isacharparenright}\ {\isasymin}\ M\isactrlsup {\isacharasterisk}\ {\isasymand}\ t\ {\isasymin}\ A{\isacharbraceright}{\isachardoublequoteclose}%
+\ EF{\isaliteral{5F}{\isacharunderscore}}lemma{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}lfp{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}T{\isaliteral{2E}{\isachardot}}\ A\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ {\isaliteral{28}{\isacharparenleft}}M{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{60}{\isacharbackquote}}{\isaliteral{60}{\isacharbackquote}}\ T{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}s{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -132,26 +132,26 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ equalityI{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule\ equalityI{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ subsetI{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule\ subsetI{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
Simplification leaves us with the following first subgoal
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}s{\isachardot}\ s\ {\isasymin}\ lfp\ {\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}\ T{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\isactrlsup {\isacharasterisk}\ {\isasymand}\ t\ {\isasymin}\ A%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}s{\isaliteral{2E}{\isachardot}}\ s\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}T{\isaliteral{2E}{\isachardot}}\ A\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ M{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{60}{\isacharbackquote}}{\isaliteral{60}{\isacharbackquote}}\ T{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A%
\end{isabelle}
which is proved by \isa{lfp}-induction:%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}erule\ lfp{\isacharunderscore}induct{\isacharunderscore}set{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}erule\ lfp{\isaliteral{5F}{\isacharunderscore}}induct{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ mono{\isacharunderscore}ef{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule\ mono{\isaliteral{5F}{\isacharunderscore}}ef{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
Having disposed of the monotonicity subgoal,
@@ -166,68 +166,68 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}blast\ intro{\isacharcolon}\ rtrancl{\isacharunderscore}trans{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}blast\ intro{\isaliteral{3A}{\isacharcolon}}\ rtrancl{\isaliteral{5F}{\isacharunderscore}}trans{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
We now return to the second set inclusion subgoal, which is again proved
pointwise:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ subsetI{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule\ subsetI{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp{\isacharcomma}\ clarify{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{2C}{\isacharcomma}}\ clarify{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
After simplification and clarification we are left with
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ t{\isachardot}\ {\isasymlbrakk}{\isacharparenleft}x{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\isactrlsup {\isacharasterisk}{\isacharsemicolon}\ t\ {\isasymin}\ A{\isasymrbrakk}\ {\isasymLongrightarrow}\ x\ {\isasymin}\ lfp\ {\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}\ T{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\ t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{3B}{\isacharsemicolon}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}T{\isaliteral{2E}{\isachardot}}\ A\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ M{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{60}{\isacharbackquote}}{\isaliteral{60}{\isacharbackquote}}\ T{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
-This goal is proved by induction on \isa{{\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\isactrlsup {\isacharasterisk}}. But since the model
+This goal is proved by induction on \isa{{\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}}. But since the model
checker works backwards (from \isa{t} to \isa{s}), we cannot use the
-induction theorem \isa{rtrancl{\isacharunderscore}induct}: it works in the
+induction theorem \isa{rtrancl{\isaliteral{5F}{\isacharunderscore}}induct}: it works in the
forward direction. Fortunately the converse induction theorem
-\isa{converse{\isacharunderscore}rtrancl{\isacharunderscore}induct} already exists:
+\isa{converse{\isaliteral{5F}{\isacharunderscore}}rtrancl{\isaliteral{5F}{\isacharunderscore}}induct} already exists:
\begin{isabelle}%
-\ \ \ \ \ {\isasymlbrakk}{\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\ {\isasymin}\ r\isactrlsup {\isacharasterisk}{\isacharsemicolon}\ P\ b{\isacharsemicolon}\isanewline
-\isaindent{\ \ \ \ \ \ }{\isasymAnd}y\ z{\isachardot}\ {\isasymlbrakk}{\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharsemicolon}\ {\isacharparenleft}z{\isacharcomma}\ b{\isacharparenright}\ {\isasymin}\ r\isactrlsup {\isacharasterisk}{\isacharsemicolon}\ P\ z{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ y{\isasymrbrakk}\isanewline
-\isaindent{\ \ \ \ \ }{\isasymLongrightarrow}\ P\ a%
+\ \ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{3B}{\isacharsemicolon}}\ P\ b{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ \ \ \ \ \ }{\isaliteral{5C3C416E643E}{\isasymAnd}}y\ z{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}z{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{3B}{\isacharsemicolon}}\ P\ z{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ y{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ \ \ \ \ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ a%
\end{isabelle}
-It says that if \isa{{\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\ {\isasymin}\ r\isactrlsup {\isacharasterisk}} and we know \isa{P\ b} then we can infer
+It says that if \isa{{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}} and we know \isa{P\ b} then we can infer
\isa{P\ a} provided each step backwards from a predecessor \isa{z} of
\isa{b} preserves \isa{P}.%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}erule\ converse{\isacharunderscore}rtrancl{\isacharunderscore}induct{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}erule\ converse{\isaliteral{5F}{\isacharunderscore}}rtrancl{\isaliteral{5F}{\isacharunderscore}}induct{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
The base case
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ t{\isachardot}\ t\ {\isasymin}\ A\ {\isasymLongrightarrow}\ t\ {\isasymin}\ lfp\ {\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}\ T{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\ t{\isaliteral{2E}{\isachardot}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}T{\isaliteral{2E}{\isachardot}}\ A\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ M{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{60}{\isacharbackquote}}{\isaliteral{60}{\isacharbackquote}}\ T{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
is solved by unrolling \isa{lfp} once%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}subst\ lfp{\isacharunderscore}unfold{\isacharbrackleft}OF\ mono{\isacharunderscore}ef{\isacharbrackright}{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}subst\ lfp{\isaliteral{5F}{\isacharunderscore}}unfold{\isaliteral{5B}{\isacharbrackleft}}OF\ mono{\isaliteral{5F}{\isacharunderscore}}ef{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ t{\isachardot}\ t\ {\isasymin}\ A\ {\isasymLongrightarrow}\ t\ {\isasymin}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}\ lfp\ {\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharbackquote}{\isacharbackquote}\ T{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\ t{\isaliteral{2E}{\isachardot}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ M{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{60}{\isacharbackquote}}{\isaliteral{60}{\isacharbackquote}}\ lfp\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}T{\isaliteral{2E}{\isachardot}}\ A\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ M{\isaliteral{5C3C696E76657273653E}{\isasyminverse}}\ {\isaliteral{60}{\isacharbackquote}}{\isaliteral{60}{\isacharbackquote}}\ T{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
and disposing of the resulting trivial subgoal automatically:%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}blast{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}blast{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
The proof of the induction step is identical to the one for the base case:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}subst\ lfp{\isacharunderscore}unfold{\isacharbrackleft}OF\ mono{\isacharunderscore}ef{\isacharbrackright}{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}subst\ lfp{\isaliteral{5F}{\isacharunderscore}}unfold{\isaliteral{5B}{\isacharbrackleft}}OF\ mono{\isaliteral{5F}{\isacharunderscore}}ef{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}blast{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}blast{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -243,7 +243,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ {\isachardoublequoteopen}mc\ f\ {\isacharequal}\ {\isacharbraceleft}s{\isachardot}\ s\ {\isasymTurnstile}\ f{\isacharbraceright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}mc\ f\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{7B}{\isacharbraceleft}}s{\isaliteral{2E}{\isachardot}}\ s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ f{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -251,9 +251,9 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ f{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ f{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto\ simp\ add{\isacharcolon}\ EF{\isacharunderscore}lemma{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}auto\ simp\ add{\isaliteral{3A}{\isacharcolon}}\ EF{\isaliteral{5F}{\isacharunderscore}}lemma{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -268,16 +268,16 @@
\isa{AX} has a dual operator \isa{EN}
(``there exists a next state such that'')%
\footnote{We cannot use the customary \isa{EX}: it is reserved
-as the \textsc{ascii}-equivalent of \isa{{\isasymexists}}.}
+as the \textsc{ascii}-equivalent of \isa{{\isaliteral{5C3C6578697374733E}{\isasymexists}}}.}
with the intended semantics
\begin{isabelle}%
-\ \ \ \ \ s\ {\isasymTurnstile}\ EN\ f\ {\isacharequal}\ {\isacharparenleft}{\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ t\ {\isasymTurnstile}\ f{\isacharparenright}%
+\ \ \ \ \ s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ EN\ f\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}t{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ M\ {\isaliteral{5C3C616E643E}{\isasymand}}\ t\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ f{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
Fortunately, \isa{EN\ f} can already be expressed as a PDL formula. How?
Show that the semantics for \isa{EF} satisfies the following recursion equation:
\begin{isabelle}%
-\ \ \ \ \ s\ {\isasymTurnstile}\ EF\ f\ {\isacharequal}\ {\isacharparenleft}s\ {\isasymTurnstile}\ f\ {\isasymor}\ s\ {\isasymTurnstile}\ EN\ {\isacharparenleft}EF\ f{\isacharparenright}{\isacharparenright}%
+\ \ \ \ \ s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ EF\ f\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ f\ {\isaliteral{5C3C6F723E}{\isasymor}}\ s\ {\isaliteral{5C3C5475726E7374696C653E}{\isasymTurnstile}}\ EN\ {\isaliteral{28}{\isacharparenleft}}EF\ f{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\end{exercise}
\index{PDL|)}%
--- a/doc-src/TutorialI/CodeGen/document/CodeGen.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/CodeGen/document/CodeGen.tex Mon Nov 08 14:41:11 2010 +0100
@@ -32,11 +32,11 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{types}\isamarkupfalse%
-\ {\isacharprime}v\ binop\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharprime}v\ {\isasymRightarrow}\ {\isacharprime}v\ {\isasymRightarrow}\ {\isacharprime}v{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{27}{\isacharprime}}v\ binop\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}v\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}v\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}v{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isacommand{datatype}\isamarkupfalse%
-\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}expr\ {\isacharequal}\ Cex\ {\isacharprime}v\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Vex\ {\isacharprime}a\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Bex\ {\isachardoublequoteopen}{\isacharprime}v\ binop{\isachardoublequoteclose}\ \ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}expr{\isachardoublequoteclose}\ \ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}expr{\isachardoublequoteclose}%
+\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}expr\ {\isaliteral{3D}{\isacharequal}}\ Cex\ {\isaliteral{27}{\isacharprime}}v\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Vex\ {\isaliteral{27}{\isacharprime}}a\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Bex\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}v\ binop{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}expr{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}expr{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
The three constructors represent constants, variables and the application of
@@ -47,10 +47,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ {\isachardoublequoteopen}value{\isachardoublequoteclose}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}expr\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}v{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}v{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}value\ {\isacharparenleft}Cex\ v{\isacharparenright}\ env\ {\isacharequal}\ v{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}value\ {\isacharparenleft}Vex\ a{\isacharparenright}\ env\ {\isacharequal}\ env\ a{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}value\ {\isacharparenleft}Bex\ f\ e{\isadigit{1}}\ e{\isadigit{2}}{\isacharparenright}\ env\ {\isacharequal}\ f\ {\isacharparenleft}value\ e{\isadigit{1}}\ env{\isacharparenright}\ {\isacharparenleft}value\ e{\isadigit{2}}\ env{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}value{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}expr\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}v{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}value\ {\isaliteral{28}{\isacharparenleft}}Cex\ v{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ v{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}value\ {\isaliteral{28}{\isacharparenleft}}Vex\ a{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ env\ a{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}value\ {\isaliteral{28}{\isacharparenleft}}Bex\ f\ e{\isadigit{1}}\ e{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ f\ {\isaliteral{28}{\isacharparenleft}}value\ e{\isadigit{1}}\ env{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}value\ e{\isadigit{2}}\ env{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
The stack machine has three instructions: load a constant value onto the
stack, load the contents of an address onto the stack, and apply a
@@ -59,9 +59,9 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}\ instr\ {\isacharequal}\ Const\ {\isacharprime}v\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Load\ {\isacharprime}a\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Apply\ {\isachardoublequoteopen}{\isacharprime}v\ binop{\isachardoublequoteclose}%
+\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}\ instr\ {\isaliteral{3D}{\isacharequal}}\ Const\ {\isaliteral{27}{\isacharprime}}v\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Load\ {\isaliteral{27}{\isacharprime}}a\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Apply\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}v\ binop{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
The execution of the stack machine is modelled by a function
\isa{exec} that takes a list of instructions, a store (modelled as a
@@ -72,13 +72,13 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ exec\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}instr\ list\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a{\isasymRightarrow}{\isacharprime}v{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}v\ list\ {\isasymRightarrow}\ {\isacharprime}v\ list{\isachardoublequoteclose}\isanewline
+\ exec\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}instr\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}v\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}v\ list{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-{\isachardoublequoteopen}exec\ {\isacharbrackleft}{\isacharbrackright}\ s\ vs\ {\isacharequal}\ vs{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}exec\ {\isacharparenleft}i{\isacharhash}is{\isacharparenright}\ s\ vs\ {\isacharequal}\ {\isacharparenleft}case\ i\ of\isanewline
-\ \ \ \ Const\ v\ \ {\isasymRightarrow}\ exec\ is\ s\ {\isacharparenleft}v{\isacharhash}vs{\isacharparenright}\isanewline
-\ \ {\isacharbar}\ Load\ a\ \ \ {\isasymRightarrow}\ exec\ is\ s\ {\isacharparenleft}{\isacharparenleft}s\ a{\isacharparenright}{\isacharhash}vs{\isacharparenright}\isanewline
-\ \ {\isacharbar}\ Apply\ f\ \ {\isasymRightarrow}\ exec\ is\ s\ {\isacharparenleft}{\isacharparenleft}f\ {\isacharparenleft}hd\ vs{\isacharparenright}\ {\isacharparenleft}hd{\isacharparenleft}tl\ vs{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharhash}{\isacharparenleft}tl{\isacharparenleft}tl\ vs{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
+{\isaliteral{22}{\isachardoublequoteopen}}exec\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ s\ vs\ {\isaliteral{3D}{\isacharequal}}\ vs{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}exec\ {\isaliteral{28}{\isacharparenleft}}i{\isaliteral{23}{\isacharhash}}is{\isaliteral{29}{\isacharparenright}}\ s\ vs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}case\ i\ of\isanewline
+\ \ \ \ Const\ v\ \ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ exec\ is\ s\ {\isaliteral{28}{\isacharparenleft}}v{\isaliteral{23}{\isacharhash}}vs{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ Load\ a\ \ \ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ exec\ is\ s\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}s\ a{\isaliteral{29}{\isacharparenright}}{\isaliteral{23}{\isacharhash}}vs{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ Apply\ f\ \ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ exec\ is\ s\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}hd\ vs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}hd{\isaliteral{28}{\isacharparenleft}}tl\ vs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{23}{\isacharhash}}{\isaliteral{28}{\isacharparenleft}}tl{\isaliteral{28}{\isacharparenleft}}tl\ vs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
Recall that \isa{hd} and \isa{tl}
@@ -94,17 +94,17 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ compile\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}expr\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}instr\ list{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}compile\ {\isacharparenleft}Cex\ v{\isacharparenright}\ \ \ \ \ \ \ {\isacharequal}\ {\isacharbrackleft}Const\ v{\isacharbrackright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}compile\ {\isacharparenleft}Vex\ a{\isacharparenright}\ \ \ \ \ \ \ {\isacharequal}\ {\isacharbrackleft}Load\ a{\isacharbrackright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}compile\ {\isacharparenleft}Bex\ f\ e{\isadigit{1}}\ e{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}compile\ e{\isadigit{2}}{\isacharparenright}\ {\isacharat}\ {\isacharparenleft}compile\ e{\isadigit{1}}{\isacharparenright}\ {\isacharat}\ {\isacharbrackleft}Apply\ f{\isacharbrackright}{\isachardoublequoteclose}%
+\ compile\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}expr\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}instr\ list{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}compile\ {\isaliteral{28}{\isacharparenleft}}Cex\ v{\isaliteral{29}{\isacharparenright}}\ \ \ \ \ \ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}Const\ v{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}compile\ {\isaliteral{28}{\isacharparenleft}}Vex\ a{\isaliteral{29}{\isacharparenright}}\ \ \ \ \ \ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}Load\ a{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}compile\ {\isaliteral{28}{\isacharparenleft}}Bex\ f\ e{\isadigit{1}}\ e{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}compile\ e{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{28}{\isacharparenleft}}compile\ e{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{5B}{\isacharbrackleft}}Apply\ f{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
Now we have to prove the correctness of the compiler, i.e.\ that the
execution of a compiled expression results in the value of the expression:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ {\isachardoublequoteopen}exec\ {\isacharparenleft}compile\ e{\isacharparenright}\ s\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}value\ e\ s{\isacharbrackright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}exec\ {\isaliteral{28}{\isacharparenleft}}compile\ e{\isaliteral{29}{\isacharparenright}}\ s\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}value\ e\ s{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -124,7 +124,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymforall}vs{\isachardot}\ exec\ {\isacharparenleft}compile\ e{\isacharparenright}\ s\ vs\ {\isacharequal}\ {\isacharparenleft}value\ e\ s{\isacharparenright}\ {\isacharhash}\ vs{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}vs{\isaliteral{2E}{\isachardot}}\ exec\ {\isaliteral{28}{\isacharparenleft}}compile\ e{\isaliteral{29}{\isacharparenright}}\ s\ vs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}value\ e\ s{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{23}{\isacharhash}}\ vs{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -146,8 +146,8 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ exec{\isacharunderscore}app{\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}{\isasymforall}vs{\isachardot}\ exec\ {\isacharparenleft}xs{\isacharat}ys{\isacharparenright}\ s\ vs\ {\isacharequal}\ exec\ ys\ s\ {\isacharparenleft}exec\ xs\ s\ vs{\isacharparenright}{\isachardoublequoteclose}%
+\ exec{\isaliteral{5F}{\isacharunderscore}}app{\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}vs{\isaliteral{2E}{\isachardot}}\ exec\ {\isaliteral{28}{\isacharparenleft}}xs{\isaliteral{40}{\isacharat}}ys{\isaliteral{29}{\isacharparenright}}\ s\ vs\ {\isaliteral{3D}{\isacharequal}}\ exec\ ys\ s\ {\isaliteral{28}{\isacharparenleft}}exec\ xs\ s\ vs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -163,7 +163,7 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharcomma}\ simp{\isacharcomma}\ simp\ split{\isacharcolon}\ instr{\isachardot}split{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ xs{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{2C}{\isacharcomma}}\ simp\ split{\isaliteral{3A}{\isacharcolon}}\ instr{\isaliteral{2E}{\isachardot}}split{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -185,7 +185,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharcomma}\ simp{\isacharunderscore}all\ split{\isacharcolon}\ instr{\isachardot}split{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ xs{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{5F}{\isacharunderscore}}all\ split{\isaliteral{3A}{\isacharcolon}}\ instr{\isaliteral{2E}{\isachardot}}split{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -197,7 +197,7 @@
\noindent
Although this is more compact, it is less clear for the reader of the proof.
-We could now go back and prove \isa{exec\ {\isacharparenleft}compile\ e{\isacharparenright}\ s\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}value\ e\ s{\isacharbrackright}}
+We could now go back and prove \isa{exec\ {\isaliteral{28}{\isacharparenleft}}compile\ e{\isaliteral{29}{\isacharparenright}}\ s\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}value\ e\ s{\isaliteral{5D}{\isacharbrackright}}}
merely by simplification with the generalized version we just proved.
However, this is unnecessary because the generalized version fully subsumes
its instance.%
--- a/doc-src/TutorialI/Datatype/document/ABexpr.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Datatype/document/ABexpr.tex Mon Nov 08 14:41:11 2010 +0100
@@ -31,14 +31,14 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ {\isacharprime}a\ aexp\ {\isacharequal}\ IF\ \ \ {\isachardoublequoteopen}{\isacharprime}a\ bexp{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isacharprime}a\ aexp{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isacharprime}a\ aexp{\isachardoublequoteclose}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Sum\ \ {\isachardoublequoteopen}{\isacharprime}a\ aexp{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isacharprime}a\ aexp{\isachardoublequoteclose}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Diff\ {\isachardoublequoteopen}{\isacharprime}a\ aexp{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isacharprime}a\ aexp{\isachardoublequoteclose}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Var\ {\isacharprime}a\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Num\ nat\isanewline
-\isakeyword{and}\ \ \ \ \ \ {\isacharprime}a\ bexp\ {\isacharequal}\ Less\ {\isachardoublequoteopen}{\isacharprime}a\ aexp{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isacharprime}a\ aexp{\isachardoublequoteclose}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ And\ \ {\isachardoublequoteopen}{\isacharprime}a\ bexp{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isacharprime}a\ bexp{\isachardoublequoteclose}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Neg\ \ {\isachardoublequoteopen}{\isacharprime}a\ bexp{\isachardoublequoteclose}%
+\ {\isaliteral{27}{\isacharprime}}a\ aexp\ {\isaliteral{3D}{\isacharequal}}\ IF\ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ bexp{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Sum\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Diff\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Var\ {\isaliteral{27}{\isacharprime}}a\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Num\ nat\isanewline
+\isakeyword{and}\ \ \ \ \ \ {\isaliteral{27}{\isacharprime}}a\ bexp\ {\isaliteral{3D}{\isacharequal}}\ Less\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ And\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ bexp{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ bexp{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Neg\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ bexp{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
Type \isa{aexp} is similar to \isa{expr} in \S\ref{sec:ExprCompiler},
@@ -50,23 +50,23 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ evala\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ aexp\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ nat{\isacharparenright}\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-\ \ \ \ \ \ \ \ \ evalb\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ bexp\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ nat{\isacharparenright}\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}evala\ {\isacharparenleft}IF\ b\ a{\isadigit{1}}\ a{\isadigit{2}}{\isacharparenright}\ env\ {\isacharequal}\isanewline
-\ \ \ {\isacharparenleft}if\ evalb\ b\ env\ then\ evala\ a{\isadigit{1}}\ env\ else\ evala\ a{\isadigit{2}}\ env{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}evala\ {\isacharparenleft}Sum\ a{\isadigit{1}}\ a{\isadigit{2}}{\isacharparenright}\ env\ {\isacharequal}\ evala\ a{\isadigit{1}}\ env\ {\isacharplus}\ evala\ a{\isadigit{2}}\ env{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}evala\ {\isacharparenleft}Diff\ a{\isadigit{1}}\ a{\isadigit{2}}{\isacharparenright}\ env\ {\isacharequal}\ evala\ a{\isadigit{1}}\ env\ {\isacharminus}\ evala\ a{\isadigit{2}}\ env{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}evala\ {\isacharparenleft}Var\ v{\isacharparenright}\ env\ {\isacharequal}\ env\ v{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}evala\ {\isacharparenleft}Num\ n{\isacharparenright}\ env\ {\isacharequal}\ n{\isachardoublequoteclose}\ {\isacharbar}\isanewline
+\ evala\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ aexp\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+\ \ \ \ \ \ \ \ \ evalb\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ bexp\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}evala\ {\isaliteral{28}{\isacharparenleft}}IF\ b\ a{\isadigit{1}}\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ {\isaliteral{28}{\isacharparenleft}}if\ evalb\ b\ env\ then\ evala\ a{\isadigit{1}}\ env\ else\ evala\ a{\isadigit{2}}\ env{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}evala\ {\isaliteral{28}{\isacharparenleft}}Sum\ a{\isadigit{1}}\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ evala\ a{\isadigit{1}}\ env\ {\isaliteral{2B}{\isacharplus}}\ evala\ a{\isadigit{2}}\ env{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}evala\ {\isaliteral{28}{\isacharparenleft}}Diff\ a{\isadigit{1}}\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ evala\ a{\isadigit{1}}\ env\ {\isaliteral{2D}{\isacharminus}}\ evala\ a{\isadigit{2}}\ env{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}evala\ {\isaliteral{28}{\isacharparenleft}}Var\ v{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ env\ v{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}evala\ {\isaliteral{28}{\isacharparenleft}}Num\ n{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
\isanewline
-{\isachardoublequoteopen}evalb\ {\isacharparenleft}Less\ a{\isadigit{1}}\ a{\isadigit{2}}{\isacharparenright}\ env\ {\isacharequal}\ {\isacharparenleft}evala\ a{\isadigit{1}}\ env\ {\isacharless}\ evala\ a{\isadigit{2}}\ env{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}evalb\ {\isacharparenleft}And\ b{\isadigit{1}}\ b{\isadigit{2}}{\isacharparenright}\ env\ {\isacharequal}\ {\isacharparenleft}evalb\ b{\isadigit{1}}\ env\ {\isasymand}\ evalb\ b{\isadigit{2}}\ env{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}evalb\ {\isacharparenleft}Neg\ b{\isacharparenright}\ env\ {\isacharequal}\ {\isacharparenleft}{\isasymnot}\ evalb\ b\ env{\isacharparenright}{\isachardoublequoteclose}%
+{\isaliteral{22}{\isachardoublequoteopen}}evalb\ {\isaliteral{28}{\isacharparenleft}}Less\ a{\isadigit{1}}\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}evala\ a{\isadigit{1}}\ env\ {\isaliteral{3C}{\isacharless}}\ evala\ a{\isadigit{2}}\ env{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}evalb\ {\isaliteral{28}{\isacharparenleft}}And\ b{\isadigit{1}}\ b{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}evalb\ b{\isadigit{1}}\ env\ {\isaliteral{5C3C616E643E}{\isasymand}}\ evalb\ b{\isadigit{2}}\ env{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}evalb\ {\isaliteral{28}{\isacharparenleft}}Neg\ b{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ evalb\ b\ env{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
Both take an expression and an environment (a mapping from variables
-\isa{{\isacharprime}a} to values \isa{nat}) and return its arithmetic/boolean
+\isa{{\isaliteral{27}{\isacharprime}}a} to values \isa{nat}) and return its arithmetic/boolean
value. Since the datatypes are mutually recursive, so are functions
that operate on them. Hence they need to be defined in a single
\isacommand{primrec} section. Notice the \isakeyword{and} separating
@@ -78,24 +78,24 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ substa\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ aexp{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ aexp\ {\isasymRightarrow}\ {\isacharprime}b\ aexp{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-\ \ \ \ \ \ \ \ \ substb\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ aexp{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ bexp\ {\isasymRightarrow}\ {\isacharprime}b\ bexp{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}substa\ s\ {\isacharparenleft}IF\ b\ a{\isadigit{1}}\ a{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ IF\ {\isacharparenleft}substb\ s\ b{\isacharparenright}\ {\isacharparenleft}substa\ s\ a{\isadigit{1}}{\isacharparenright}\ {\isacharparenleft}substa\ s\ a{\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}substa\ s\ {\isacharparenleft}Sum\ a{\isadigit{1}}\ a{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ Sum\ {\isacharparenleft}substa\ s\ a{\isadigit{1}}{\isacharparenright}\ {\isacharparenleft}substa\ s\ a{\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}substa\ s\ {\isacharparenleft}Diff\ a{\isadigit{1}}\ a{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ Diff\ {\isacharparenleft}substa\ s\ a{\isadigit{1}}{\isacharparenright}\ {\isacharparenleft}substa\ s\ a{\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}substa\ s\ {\isacharparenleft}Var\ v{\isacharparenright}\ {\isacharequal}\ s\ v{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}substa\ s\ {\isacharparenleft}Num\ n{\isacharparenright}\ {\isacharequal}\ Num\ n{\isachardoublequoteclose}\ {\isacharbar}\isanewline
+\ substa\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ aexp{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ aexp\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ aexp{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+\ \ \ \ \ \ \ \ \ substb\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ aexp{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ bexp\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ bexp{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}substa\ s\ {\isaliteral{28}{\isacharparenleft}}IF\ b\ a{\isadigit{1}}\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ IF\ {\isaliteral{28}{\isacharparenleft}}substb\ s\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}substa\ s\ a{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}substa\ s\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}substa\ s\ {\isaliteral{28}{\isacharparenleft}}Sum\ a{\isadigit{1}}\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Sum\ {\isaliteral{28}{\isacharparenleft}}substa\ s\ a{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}substa\ s\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}substa\ s\ {\isaliteral{28}{\isacharparenleft}}Diff\ a{\isadigit{1}}\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Diff\ {\isaliteral{28}{\isacharparenleft}}substa\ s\ a{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}substa\ s\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}substa\ s\ {\isaliteral{28}{\isacharparenleft}}Var\ v{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ s\ v{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}substa\ s\ {\isaliteral{28}{\isacharparenleft}}Num\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Num\ n{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
\isanewline
-{\isachardoublequoteopen}substb\ s\ {\isacharparenleft}Less\ a{\isadigit{1}}\ a{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ Less\ {\isacharparenleft}substa\ s\ a{\isadigit{1}}{\isacharparenright}\ {\isacharparenleft}substa\ s\ a{\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}substb\ s\ {\isacharparenleft}And\ b{\isadigit{1}}\ b{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ And\ {\isacharparenleft}substb\ s\ b{\isadigit{1}}{\isacharparenright}\ {\isacharparenleft}substb\ s\ b{\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}substb\ s\ {\isacharparenleft}Neg\ b{\isacharparenright}\ {\isacharequal}\ Neg\ {\isacharparenleft}substb\ s\ b{\isacharparenright}{\isachardoublequoteclose}%
+{\isaliteral{22}{\isachardoublequoteopen}}substb\ s\ {\isaliteral{28}{\isacharparenleft}}Less\ a{\isadigit{1}}\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Less\ {\isaliteral{28}{\isacharparenleft}}substa\ s\ a{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}substa\ s\ a{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}substb\ s\ {\isaliteral{28}{\isacharparenleft}}And\ b{\isadigit{1}}\ b{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ And\ {\isaliteral{28}{\isacharparenleft}}substb\ s\ b{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}substb\ s\ b{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}substb\ s\ {\isaliteral{28}{\isacharparenleft}}Neg\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Neg\ {\isaliteral{28}{\isacharparenleft}}substb\ s\ b{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
Their first argument is a function mapping variables to expressions, the
substitution. It is applied to all variables in the second argument. As a
-result, the type of variables in the expression may change from \isa{{\isacharprime}a}
-to \isa{{\isacharprime}b}. Note that there are only arithmetic and no boolean variables.
+result, the type of variables in the expression may change from \isa{{\isaliteral{27}{\isacharprime}}a}
+to \isa{{\isaliteral{27}{\isacharprime}}b}. Note that there are only arithmetic and no boolean variables.
Now we can prove a fundamental theorem about the interaction between
evaluation and substitution: applying a substitution $s$ to an expression $a$
@@ -108,8 +108,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}evala\ {\isacharparenleft}substa\ s\ a{\isacharparenright}\ env\ {\isacharequal}\ evala\ a\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ evala\ {\isacharparenleft}s\ x{\isacharparenright}\ env{\isacharparenright}\ {\isasymand}\isanewline
-\ \ \ \ \ \ \ \ evalb\ {\isacharparenleft}substb\ s\ b{\isacharparenright}\ env\ {\isacharequal}\ evalb\ b\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ evala\ {\isacharparenleft}s\ x{\isacharparenright}\ env{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}evala\ {\isaliteral{28}{\isacharparenleft}}substa\ s\ a{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ evala\ a\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ evala\ {\isaliteral{28}{\isacharparenleft}}s\ x{\isaliteral{29}{\isacharparenright}}\ env{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\isanewline
+\ \ \ \ \ \ \ \ evalb\ {\isaliteral{28}{\isacharparenleft}}substb\ s\ b{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ evalb\ b\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ evala\ {\isaliteral{28}{\isacharparenleft}}s\ x{\isaliteral{29}{\isacharparenright}}\ env{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -117,13 +117,13 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ a\ \isakeyword{and}\ b{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ a\ \isakeyword{and}\ b{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent The resulting 8 goals (one for each constructor) are proved in one fell swoop:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-\ simp{\isacharunderscore}all%
+\ simp{\isaliteral{5F}{\isacharunderscore}}all%
\endisatagproof
{\isafoldproof}%
%
@@ -137,11 +137,11 @@
\[ P@1(x@1)\ \land \dots \land P@n(x@n) \]
where each variable $x@i$ is of type $\tau@i$. Induction is started by
\begin{isabelle}
-\isacommand{apply}\isa{{\isacharparenleft}induct{\isacharunderscore}tac} $x@1$ \isacommand{and} \dots\ \isacommand{and} $x@n$\isa{{\isacharparenright}}
+\isacommand{apply}\isa{{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac} $x@1$ \isacommand{and} \dots\ \isacommand{and} $x@n$\isa{{\isaliteral{29}{\isacharparenright}}}
\end{isabelle}
\begin{exercise}
- Define a function \isa{norma} of type \isa{{\isacharprime}a\ aexp\ {\isasymRightarrow}\ {\isacharprime}a\ aexp} that
+ Define a function \isa{norma} of type \isa{{\isaliteral{27}{\isacharprime}}a\ aexp\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ aexp} that
replaces \isa{IF}s with complex boolean conditions by nested
\isa{IF}s; it should eliminate the constructors
\isa{And} and \isa{Neg}, leaving only \isa{Less}.
@@ -149,7 +149,7 @@
preserves the value of an expression and that the result of \isa{norma}
is really normal, i.e.\ no more \isa{And}s and \isa{Neg}s occur in
it. ({\em Hint:} proceed as in \S\ref{sec:boolex} and read the discussion
- of type annotations following lemma \isa{subst{\isacharunderscore}id} below).
+ of type annotations following lemma \isa{subst{\isaliteral{5F}{\isacharunderscore}}id} below).
\end{exercise}%
\end{isamarkuptext}%
\isamarkuptrue%
--- a/doc-src/TutorialI/Datatype/document/Fundata.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Datatype/document/Fundata.tex Mon Nov 08 14:41:11 2010 +0100
@@ -15,45 +15,45 @@
%
\endisadelimtheory
\isacommand{datatype}\isamarkupfalse%
-\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}i{\isacharparenright}bigtree\ {\isacharequal}\ Tip\ {\isacharbar}\ Br\ {\isacharprime}a\ {\isachardoublequoteopen}{\isacharprime}i\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}i{\isacharparenright}bigtree{\isachardoublequoteclose}%
+\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}i{\isaliteral{29}{\isacharparenright}}bigtree\ {\isaliteral{3D}{\isacharequal}}\ Tip\ {\isaliteral{7C}{\isacharbar}}\ Br\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}i\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}i{\isaliteral{29}{\isacharparenright}}bigtree{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
-Parameter \isa{{\isacharprime}a} is the type of values stored in
-the \isa{Br}anches of the tree, whereas \isa{{\isacharprime}i} is the index
-type over which the tree branches. If \isa{{\isacharprime}i} is instantiated to
+Parameter \isa{{\isaliteral{27}{\isacharprime}}a} is the type of values stored in
+the \isa{Br}anches of the tree, whereas \isa{{\isaliteral{27}{\isacharprime}}i} is the index
+type over which the tree branches. If \isa{{\isaliteral{27}{\isacharprime}}i} is instantiated to
\isa{bool}, the result is a binary tree; if it is instantiated to
\isa{nat}, we have an infinitely branching tree because each node
has as many subtrees as there are natural numbers. How can we possibly
write down such a tree? Using functional notation! For example, the term
\begin{isabelle}%
-\ \ \ \ \ Br\ {\isadigit{0}}\ {\isacharparenleft}{\isasymlambda}i{\isachardot}\ Br\ i\ {\isacharparenleft}{\isasymlambda}n{\isachardot}\ Tip{\isacharparenright}{\isacharparenright}%
+\ \ \ \ \ Br\ {\isadigit{0}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}i{\isaliteral{2E}{\isachardot}}\ Br\ i\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}n{\isaliteral{2E}{\isachardot}}\ Tip{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
-of type \isa{{\isacharparenleft}nat{\isacharcomma}\ nat{\isacharparenright}\ bigtree} is the tree whose
+of type \isa{{\isaliteral{28}{\isacharparenleft}}nat{\isaliteral{2C}{\isacharcomma}}\ nat{\isaliteral{29}{\isacharparenright}}\ bigtree} is the tree whose
root is labeled with 0 and whose $i$th subtree is labeled with $i$ and
has merely \isa{Tip}s as further subtrees.
-Function \isa{map{\isacharunderscore}bt} applies a function to all labels in a \isa{bigtree}:%
+Function \isa{map{\isaliteral{5F}{\isacharunderscore}}bt} applies a function to all labels in a \isa{bigtree}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ map{\isacharunderscore}bt\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}i{\isacharparenright}bigtree\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}b{\isacharcomma}{\isacharprime}i{\isacharparenright}bigtree{\isachardoublequoteclose}\isanewline
+\ map{\isaliteral{5F}{\isacharunderscore}}bt\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}i{\isaliteral{29}{\isacharparenright}}bigtree\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}b{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}i{\isaliteral{29}{\isacharparenright}}bigtree{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-{\isachardoublequoteopen}map{\isacharunderscore}bt\ f\ Tip\ \ \ \ \ \ {\isacharequal}\ Tip{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}map{\isacharunderscore}bt\ f\ {\isacharparenleft}Br\ a\ F{\isacharparenright}\ {\isacharequal}\ Br\ {\isacharparenleft}f\ a{\isacharparenright}\ {\isacharparenleft}{\isasymlambda}i{\isachardot}\ map{\isacharunderscore}bt\ f\ {\isacharparenleft}F\ i{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
+{\isaliteral{22}{\isachardoublequoteopen}}map{\isaliteral{5F}{\isacharunderscore}}bt\ f\ Tip\ \ \ \ \ \ {\isaliteral{3D}{\isacharequal}}\ Tip{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}map{\isaliteral{5F}{\isacharunderscore}}bt\ f\ {\isaliteral{28}{\isacharparenleft}}Br\ a\ F{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Br\ {\isaliteral{28}{\isacharparenleft}}f\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}i{\isaliteral{2E}{\isachardot}}\ map{\isaliteral{5F}{\isacharunderscore}}bt\ f\ {\isaliteral{28}{\isacharparenleft}}F\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent This is a valid \isacommand{primrec} definition because the
-recursive calls of \isa{map{\isacharunderscore}bt} involve only subtrees of
+recursive calls of \isa{map{\isaliteral{5F}{\isacharunderscore}}bt} involve only subtrees of
\isa{F}, which is itself a subterm of the left-hand side. Thus termination
is assured. The seasoned functional programmer might try expressing
-\isa{{\isasymlambda}i{\isachardot}\ map{\isacharunderscore}bt\ f\ {\isacharparenleft}F\ i{\isacharparenright}} as \isa{map{\isacharunderscore}bt\ f\ {\isasymcirc}\ F}, which Isabelle
-however will reject. Applying \isa{map{\isacharunderscore}bt} to only one of its arguments
+\isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}i{\isaliteral{2E}{\isachardot}}\ map{\isaliteral{5F}{\isacharunderscore}}bt\ f\ {\isaliteral{28}{\isacharparenleft}}F\ i{\isaliteral{29}{\isacharparenright}}} as \isa{map{\isaliteral{5F}{\isacharunderscore}}bt\ f\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ F}, which Isabelle
+however will reject. Applying \isa{map{\isaliteral{5F}{\isacharunderscore}}bt} to only one of its arguments
makes the termination proof less obvious.
The following lemma has a simple proof by induction:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}map{\isacharunderscore}bt\ {\isacharparenleft}g\ o\ f{\isacharparenright}\ T\ {\isacharequal}\ map{\isacharunderscore}bt\ g\ {\isacharparenleft}map{\isacharunderscore}bt\ f\ T{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}map{\isaliteral{5F}{\isacharunderscore}}bt\ {\isaliteral{28}{\isacharparenleft}}g\ o\ f{\isaliteral{29}{\isacharparenright}}\ T\ {\isaliteral{3D}{\isacharequal}}\ map{\isaliteral{5F}{\isacharunderscore}}bt\ g\ {\isaliteral{28}{\isacharparenleft}}map{\isaliteral{5F}{\isacharunderscore}}bt\ f\ T{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -61,7 +61,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ T{\isacharcomma}\ simp{\isacharunderscore}all{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ T{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -82,9 +82,9 @@
Because of the function type, the proof state after induction looks unusual.
Notice the quantified induction hypothesis:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ map{\isacharunderscore}bt\ {\isacharparenleft}g\ {\isasymcirc}\ f{\isacharparenright}\ Tip\ {\isacharequal}\ map{\isacharunderscore}bt\ g\ {\isacharparenleft}map{\isacharunderscore}bt\ f\ Tip{\isacharparenright}\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}a\ F{\isachardot}\ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ map{\isacharunderscore}bt\ {\isacharparenleft}g\ {\isasymcirc}\ f{\isacharparenright}\ {\isacharparenleft}F\ x{\isacharparenright}\ {\isacharequal}\ map{\isacharunderscore}bt\ g\ {\isacharparenleft}map{\isacharunderscore}bt\ f\ {\isacharparenleft}F\ x{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isasymLongrightarrow}\isanewline
-\isaindent{\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}a\ F{\isachardot}\ }map{\isacharunderscore}bt\ {\isacharparenleft}g\ {\isasymcirc}\ f{\isacharparenright}\ {\isacharparenleft}Br\ a\ F{\isacharparenright}\ {\isacharequal}\ map{\isacharunderscore}bt\ g\ {\isacharparenleft}map{\isacharunderscore}bt\ f\ {\isacharparenleft}Br\ a\ F{\isacharparenright}{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ map{\isaliteral{5F}{\isacharunderscore}}bt\ {\isaliteral{28}{\isacharparenleft}}g\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ f{\isaliteral{29}{\isacharparenright}}\ Tip\ {\isaliteral{3D}{\isacharequal}}\ map{\isaliteral{5F}{\isacharunderscore}}bt\ g\ {\isaliteral{28}{\isacharparenleft}}map{\isaliteral{5F}{\isacharunderscore}}bt\ f\ Tip{\isaliteral{29}{\isacharparenright}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a\ F{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ map{\isaliteral{5F}{\isacharunderscore}}bt\ {\isaliteral{28}{\isacharparenleft}}g\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ f{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}F\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ map{\isaliteral{5F}{\isacharunderscore}}bt\ g\ {\isaliteral{28}{\isacharparenleft}}map{\isaliteral{5F}{\isacharunderscore}}bt\ f\ {\isaliteral{28}{\isacharparenleft}}F\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\isanewline
+\isaindent{\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a\ F{\isaliteral{2E}{\isachardot}}\ }map{\isaliteral{5F}{\isacharunderscore}}bt\ {\isaliteral{28}{\isacharparenleft}}g\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ f{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}Br\ a\ F{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ map{\isaliteral{5F}{\isacharunderscore}}bt\ g\ {\isaliteral{28}{\isacharparenleft}}map{\isaliteral{5F}{\isacharunderscore}}bt\ f\ {\isaliteral{28}{\isacharparenleft}}Br\ a\ F{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
--- a/doc-src/TutorialI/Datatype/document/Nested.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Datatype/document/Nested.tex Mon Nov 08 14:41:11 2010 +0100
@@ -26,14 +26,14 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ {\isacharparenleft}{\isacharprime}v{\isacharcomma}{\isacharprime}f{\isacharparenright}{\isachardoublequoteopen}term{\isachardoublequoteclose}\ {\isacharequal}\ Var\ {\isacharprime}v\ {\isacharbar}\ App\ {\isacharprime}f\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}v{\isacharcomma}{\isacharprime}f{\isacharparenright}term\ list{\isachardoublequoteclose}%
+\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteopen}}term{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{3D}{\isacharequal}}\ Var\ {\isaliteral{27}{\isacharprime}}v\ {\isaliteral{7C}{\isacharbar}}\ App\ {\isaliteral{27}{\isacharprime}}f\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}term\ list{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
Note that we need to quote \isa{term} on the left to avoid confusion with
the Isabelle command \isacommand{term}.
-Parameter \isa{{\isacharprime}v} is the type of variables and \isa{{\isacharprime}f} the type of
+Parameter \isa{{\isaliteral{27}{\isacharprime}}v} is the type of variables and \isa{{\isaliteral{27}{\isacharprime}}f} the type of
function symbols.
-A mathematical term like $f(x,g(y))$ becomes \isa{App\ f\ {\isacharbrackleft}Var\ x{\isacharcomma}\ App\ g\ {\isacharbrackleft}Var\ y{\isacharbrackright}{\isacharbrackright}}, where \isa{f}, \isa{g}, \isa{x}, \isa{y} are
+A mathematical term like $f(x,g(y))$ becomes \isa{App\ f\ {\isaliteral{5B}{\isacharbrackleft}}Var\ x{\isaliteral{2C}{\isacharcomma}}\ App\ g\ {\isaliteral{5B}{\isacharbrackleft}}Var\ y{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5D}{\isacharbrackright}}}, where \isa{f}, \isa{g}, \isa{x}, \isa{y} are
suitable values, e.g.\ numbers or strings.
What complicates the definition of \isa{term} is the nested occurrence of
@@ -58,19 +58,19 @@
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
\isanewline
-subst\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}v{\isasymRightarrow}{\isacharparenleft}{\isacharprime}v{\isacharcomma}{\isacharprime}f{\isacharparenright}term{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}v{\isacharcomma}{\isacharprime}f{\isacharparenright}term\ \ \ \ \ \ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}v{\isacharcomma}{\isacharprime}f{\isacharparenright}term{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-substs{\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}v{\isasymRightarrow}{\isacharparenleft}{\isacharprime}v{\isacharcomma}{\isacharprime}f{\isacharparenright}term{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}v{\isacharcomma}{\isacharprime}f{\isacharparenright}term\ list\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}v{\isacharcomma}{\isacharprime}f{\isacharparenright}term\ list{\isachardoublequoteclose}\isanewline
+subst\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}term{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}term\ \ \ \ \ \ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}term{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+substs{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}term{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}term\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}term\ list{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-{\isachardoublequoteopen}subst\ s\ {\isacharparenleft}Var\ x{\isacharparenright}\ {\isacharequal}\ s\ x{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-\ \ subst{\isacharunderscore}App{\isacharcolon}\isanewline
-{\isachardoublequoteopen}subst\ s\ {\isacharparenleft}App\ f\ ts{\isacharparenright}\ {\isacharequal}\ App\ f\ {\isacharparenleft}substs\ s\ ts{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}subst\ s\ {\isaliteral{28}{\isacharparenleft}}Var\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ s\ x{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+\ \ subst{\isaliteral{5F}{\isacharunderscore}}App{\isaliteral{3A}{\isacharcolon}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}subst\ s\ {\isaliteral{28}{\isacharparenleft}}App\ f\ ts{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ App\ f\ {\isaliteral{28}{\isacharparenleft}}substs\ s\ ts{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
\isanewline
-{\isachardoublequoteopen}substs\ s\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}substs\ s\ {\isacharparenleft}t\ {\isacharhash}\ ts{\isacharparenright}\ {\isacharequal}\ subst\ s\ t\ {\isacharhash}\ substs\ s\ ts{\isachardoublequoteclose}%
+{\isaliteral{22}{\isachardoublequoteopen}}substs\ s\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}substs\ s\ {\isaliteral{28}{\isacharparenleft}}t\ {\isaliteral{23}{\isacharhash}}\ ts{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ subst\ s\ t\ {\isaliteral{23}{\isacharhash}}\ substs\ s\ ts{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
Individual equations in a \commdx{primrec} definition may be
-named as shown for \isa{subst{\isacharunderscore}App}.
+named as shown for \isa{subst{\isaliteral{5F}{\isacharunderscore}}App}.
The significance of this device will become apparent below.
Similarly, when proving a statement about terms inductively, we need
@@ -80,8 +80,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ subst{\isacharunderscore}id{\isacharcolon}\ {\isachardoublequoteopen}subst\ \ Var\ t\ \ {\isacharequal}\ {\isacharparenleft}t\ {\isacharcolon}{\isacharcolon}{\isacharparenleft}{\isacharprime}v{\isacharcomma}{\isacharprime}f{\isacharparenright}term{\isacharparenright}\ \ {\isasymand}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ substs\ Var\ ts\ {\isacharequal}\ {\isacharparenleft}ts{\isacharcolon}{\isacharcolon}{\isacharparenleft}{\isacharprime}v{\isacharcomma}{\isacharprime}f{\isacharparenright}term\ list{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ subst{\isaliteral{5F}{\isacharunderscore}}id{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}subst\ \ Var\ t\ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}term{\isaliteral{29}{\isacharparenright}}\ \ {\isaliteral{5C3C616E643E}{\isasymand}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ substs\ Var\ ts\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}ts{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}term\ list{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -89,7 +89,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ t\ \isakeyword{and}\ ts{\isacharcomma}\ simp{\isacharunderscore}all{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ t\ \isakeyword{and}\ ts{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -102,36 +102,36 @@
\begin{isamarkuptext}%
\noindent
Note that \isa{Var} is the identity substitution because by definition it
-leaves variables unchanged: \isa{subst\ Var\ {\isacharparenleft}Var\ x{\isacharparenright}\ {\isacharequal}\ Var\ x}. Note also
+leaves variables unchanged: \isa{subst\ Var\ {\isaliteral{28}{\isacharparenleft}}Var\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Var\ x}. Note also
that the type annotations are necessary because otherwise there is nothing in
the goal to enforce that both halves of the goal talk about the same type
-parameters \isa{{\isacharparenleft}{\isacharprime}v{\isacharcomma}{\isacharprime}f{\isacharparenright}}. As a result, induction would fail
+parameters \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}}. As a result, induction would fail
because the two halves of the goal would be unrelated.
\begin{exercise}
The fact that substitution distributes over composition can be expressed
roughly as follows:
\begin{isabelle}%
-\ \ \ \ \ subst\ {\isacharparenleft}f\ {\isasymcirc}\ g{\isacharparenright}\ t\ {\isacharequal}\ subst\ f\ {\isacharparenleft}subst\ g\ t{\isacharparenright}%
+\ \ \ \ \ subst\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{5C3C636972633E}{\isasymcirc}}\ g{\isaliteral{29}{\isacharparenright}}\ t\ {\isaliteral{3D}{\isacharequal}}\ subst\ f\ {\isaliteral{28}{\isacharparenleft}}subst\ g\ t{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
Correct this statement (you will find that it does not type-check),
-strengthen it, and prove it. (Note: \isa{{\isasymcirc}} is function composition;
-its definition is found in theorem \isa{o{\isacharunderscore}def}).
+strengthen it, and prove it. (Note: \isa{{\isaliteral{5C3C636972633E}{\isasymcirc}}} is function composition;
+its definition is found in theorem \isa{o{\isaliteral{5F}{\isacharunderscore}}def}).
\end{exercise}
\begin{exercise}\label{ex:trev-trev}
- Define a function \isa{trev} of type \isa{{\isacharparenleft}{\isacharprime}v{\isacharcomma}\ {\isacharprime}f{\isacharparenright}\ Nested{\isachardot}term\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}v{\isacharcomma}\ {\isacharprime}f{\isacharparenright}\ Nested{\isachardot}term}
+ Define a function \isa{trev} of type \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}\ Nested{\isaliteral{2E}{\isachardot}}term\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}\ Nested{\isaliteral{2E}{\isachardot}}term}
that recursively reverses the order of arguments of all function symbols in a
- term. Prove that \isa{trev\ {\isacharparenleft}trev\ t{\isacharparenright}\ {\isacharequal}\ t}.
+ term. Prove that \isa{trev\ {\isaliteral{28}{\isacharparenleft}}trev\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ t}.
\end{exercise}
The experienced functional programmer may feel that our definition of
\isa{subst} is too complicated in that \isa{substs} is
unnecessary. The \isa{App}-case can be defined directly as
\begin{isabelle}%
-\ \ \ \ \ subst\ s\ {\isacharparenleft}App\ f\ ts{\isacharparenright}\ {\isacharequal}\ App\ f\ {\isacharparenleft}map\ {\isacharparenleft}subst\ s{\isacharparenright}\ ts{\isacharparenright}%
+\ \ \ \ \ subst\ s\ {\isaliteral{28}{\isacharparenleft}}App\ f\ ts{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ App\ f\ {\isaliteral{28}{\isacharparenleft}}map\ {\isaliteral{28}{\isacharparenleft}}subst\ s{\isaliteral{29}{\isacharparenright}}\ ts{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
where \isa{map} is the standard list function such that
-\isa{map\ f\ {\isacharbrackleft}x{\isadigit{1}}{\isacharcomma}{\isachardot}{\isachardot}{\isachardot}{\isacharcomma}xn{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}f\ x{\isadigit{1}}{\isacharcomma}{\isachardot}{\isachardot}{\isachardot}{\isacharcomma}f\ xn{\isacharbrackright}}. This is true, but Isabelle
+\isa{map\ f\ {\isaliteral{5B}{\isacharbrackleft}}x{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2C}{\isacharcomma}}xn{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}f\ x{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2C}{\isacharcomma}}f\ xn{\isaliteral{5D}{\isacharbrackright}}}. This is true, but Isabelle
insists on the conjunctive format. Fortunately, we can easily \emph{prove}
that the suggested equation holds:%
\end{isamarkuptext}%
@@ -177,7 +177,7 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}subst\ s\ {\isacharparenleft}App\ f\ ts{\isacharparenright}\ {\isacharequal}\ App\ f\ {\isacharparenleft}map\ {\isacharparenleft}subst\ s{\isacharparenright}\ ts{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}subst\ s\ {\isaliteral{28}{\isacharparenleft}}App\ f\ ts{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ App\ f\ {\isaliteral{28}{\isacharparenleft}}map\ {\isaliteral{28}{\isacharparenleft}}subst\ s{\isaliteral{29}{\isacharparenright}}\ ts{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -185,7 +185,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ ts{\isacharcomma}\ simp{\isacharunderscore}all{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ ts{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -202,7 +202,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{declare}\isamarkupfalse%
-\ subst{\isacharunderscore}App\ {\isacharbrackleft}simp\ del{\isacharbrackright}%
+\ subst{\isaliteral{5F}{\isacharunderscore}}App\ {\isaliteral{5B}{\isacharbrackleft}}simp\ del{\isaliteral{5D}{\isacharbrackright}}%
\begin{isamarkuptext}%
\noindent The advantage is that now we have replaced \isa{substs} by \isa{map}, we can profit from the large number of
pre-proved lemmas about \isa{map}. Unfortunately, inductive proofs
@@ -217,7 +217,7 @@
Of course, you may also combine mutual and nested recursion of datatypes. For example,
constructor \isa{Sum} in \S\ref{sec:datatype-mut-rec} could take a list of
-expressions as its argument: \isa{Sum}~\isa{{\isachardoublequote}{\isacharprime}a\ aexp\ list{\isachardoublequote}}.%
+expressions as its argument: \isa{Sum}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a\ aexp\ list{\isaliteral{22}{\isachardoublequote}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
--- a/doc-src/TutorialI/Datatype/document/unfoldnested.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Datatype/document/unfoldnested.tex Mon Nov 08 14:41:11 2010 +0100
@@ -15,8 +15,8 @@
%
\endisadelimtheory
\isacommand{datatype}\isamarkupfalse%
-\ {\isacharparenleft}{\isacharprime}v{\isacharcomma}{\isacharprime}f{\isacharparenright}{\isachardoublequoteopen}term{\isachardoublequoteclose}\ {\isacharequal}\ Var\ {\isacharprime}v\ {\isacharbar}\ App\ {\isacharprime}f\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}v{\isacharcomma}{\isacharprime}f{\isacharparenright}term{\isacharunderscore}list{\isachardoublequoteclose}\isanewline
-\isakeyword{and}\ {\isacharparenleft}{\isacharprime}v{\isacharcomma}{\isacharprime}f{\isacharparenright}term{\isacharunderscore}list\ {\isacharequal}\ Nil\ {\isacharbar}\ Cons\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}v{\isacharcomma}{\isacharprime}f{\isacharparenright}term{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}v{\isacharcomma}{\isacharprime}f{\isacharparenright}term{\isacharunderscore}list{\isachardoublequoteclose}%
+\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteopen}}term{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{3D}{\isacharequal}}\ Var\ {\isaliteral{27}{\isacharprime}}v\ {\isaliteral{7C}{\isacharbar}}\ App\ {\isaliteral{27}{\isacharprime}}f\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}term{\isaliteral{5F}{\isacharunderscore}}list{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\isakeyword{and}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}term{\isaliteral{5F}{\isacharunderscore}}list\ {\isaliteral{3D}{\isacharequal}}\ Nil\ {\isaliteral{7C}{\isacharbar}}\ Cons\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}term{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}f{\isaliteral{29}{\isacharparenright}}term{\isaliteral{5F}{\isacharunderscore}}list{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimtheory
%
\endisadelimtheory
--- a/doc-src/TutorialI/Documents/document/Documents.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Documents/document/Documents.tex Mon Nov 08 14:41:11 2010 +0100
@@ -46,7 +46,7 @@
such as \isacommand{definition} and \isacommand{primrec} --- and also
\isacommand{datatype}, which declares constructor operations.
Type-constructors may be annotated as well, although this is less
- frequently encountered in practice (the infix type \isa{{\isasymtimes}} comes
+ frequently encountered in practice (the infix type \isa{{\isaliteral{5C3C74696D65733E}{\isasymtimes}}} comes
to mind).
Infix declarations\index{infix annotations} provide a useful special
@@ -55,38 +55,38 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{definition}\isamarkupfalse%
-\ xor\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}bool\ {\isasymRightarrow}\ bool\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharplus}{\isacharbrackright}{\isachardoublequoteclose}\ {\isadigit{6}}{\isadigit{0}}{\isacharparenright}\isanewline
-\isakeyword{where}\ {\isachardoublequoteopen}A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B\ {\isasymequiv}\ {\isacharparenleft}A\ {\isasymand}\ {\isasymnot}\ B{\isacharparenright}\ {\isasymor}\ {\isacharparenleft}{\isasymnot}\ A\ {\isasymand}\ B{\isacharparenright}{\isachardoublequoteclose}%
+\ xor\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}bool\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{6}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}\ B\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
-\noindent Now \isa{xor\ A\ B} and \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B} refer to the
+\noindent Now \isa{xor\ A\ B} and \isa{A\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}\ B} refer to the
same expression internally. Any curried function with at least two
arguments may be given infix syntax. For partial applications with
fewer than two operands, there is a notation using the prefix~\isa{op}. For instance, \isa{xor} without arguments is represented as
- \isa{op\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}}; together with ordinary function application, this
- turns \isa{xor\ A} into \isa{op\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ A}.
+ \isa{op\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}}; together with ordinary function application, this
+ turns \isa{xor\ A} into \isa{op\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}\ A}.
The keyword \isakeyword{infixl} seen above specifies an
infix operator that is nested to the \emph{left}: in iterated
applications the more complex expression appears on the left-hand
- side, and \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ C} stands for \isa{{\isacharparenleft}A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B{\isacharparenright}\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ C}. Similarly, \isakeyword{infixr} means nesting to the
- \emph{right}, reading \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ C} as \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ {\isacharparenleft}B\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ C{\isacharparenright}}. A \emph{non-oriented} declaration via \isakeyword{infix}
- would render \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ C} illegal, but demand explicit
+ side, and \isa{A\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}\ B\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}\ C} stands for \isa{{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}\ C}. Similarly, \isakeyword{infixr} means nesting to the
+ \emph{right}, reading \isa{A\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}\ B\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}\ C} as \isa{A\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{28}{\isacharparenleft}}B\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}\ C{\isaliteral{29}{\isacharparenright}}}. A \emph{non-oriented} declaration via \isakeyword{infix}
+ would render \isa{A\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}\ B\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}\ C} illegal, but demand explicit
parentheses to indicate the intended grouping.
- The string \isa{{\isachardoublequote}{\isacharbrackleft}{\isacharplus}{\isacharbrackright}{\isachardoublequote}} in our annotation refers to the
+ The string \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}} in our annotation refers to the
concrete syntax to represent the operator (a literal token), while
the number \isa{{\isadigit{6}}{\isadigit{0}}} determines the precedence of the construct:
the syntactic priorities of the arguments and result. Isabelle/HOL
already uses up many popular combinations of ASCII symbols for its
- own use, including both \isa{{\isacharplus}} and \isa{{\isacharplus}{\isacharplus}}. Longer
+ own use, including both \isa{{\isaliteral{2B}{\isacharplus}}} and \isa{{\isaliteral{2B}{\isacharplus}}{\isaliteral{2B}{\isacharplus}}}. Longer
character combinations are more likely to be still available for
- user extensions, such as our~\isa{{\isacharbrackleft}{\isacharplus}{\isacharbrackright}}.
+ user extensions, such as our~\isa{{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}}.
Operator precedences have a range of 0--1000. Very low or high
priorities are reserved for the meta-logic. HOL syntax mainly uses
- the range of 10--100: the equality infix \isa{{\isacharequal}} is centered at
- 50; logical connectives (like \isa{{\isasymor}} and \isa{{\isasymand}}) are
- below 50; algebraic ones (like \isa{{\isacharplus}} and \isa{{\isacharasterisk}}) are
+ the range of 10--100: the equality infix \isa{{\isaliteral{3D}{\isacharequal}}} is centered at
+ 50; logical connectives (like \isa{{\isaliteral{5C3C6F723E}{\isasymor}}} and \isa{{\isaliteral{5C3C616E643E}{\isasymand}}}) are
+ below 50; algebraic ones (like \isa{{\isaliteral{2B}{\isacharplus}}} and \isa{{\isaliteral{2A}{\isacharasterisk}}}) are
above 50. User syntax should strive to coexist with common HOL
forms, or use the mostly unused range 100--900.%
\end{isamarkuptext}%
@@ -120,7 +120,7 @@
interpretation is left to further front-end tools. For example, the
user-interface of Proof~General + X-Symbol and the Isabelle document
processor (see \S\ref{sec:document-preparation}) display the
- \verb,\,\verb,<forall>, symbol as~\isa{{\isasymforall}}.
+ \verb,\,\verb,<forall>, symbol as~\isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}}.
A list of standard Isabelle symbols is given in
\cite{isabelle-isar-ref}. You may introduce your own
@@ -130,13 +130,13 @@
few predefined control symbols, such as \verb,\,\verb,<^sub>, and
\verb,\,\verb,<^sup>, for sub- and superscript of the subsequent
printable symbol, respectively. For example, \verb,A\<^sup>\<star>, is
- output as \isa{A\isactrlsup {\isasymstar}}.
+ output as \isa{A\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{5C3C737461723E}{\isasymstar}}}.
A number of symbols are considered letters by the Isabelle lexer and
can be used as part of identifiers. These are the greek letters
- \isa{{\isasymalpha}} (\verb+\+\verb+<alpha>+), \isa{{\isasymbeta}}
- (\verb+\+\verb+<beta>+), etc. (excluding \isa{{\isasymlambda}}),
- special letters like \isa{{\isasymA}} (\verb+\+\verb+<A>+) and \isa{{\isasymAA}} (\verb+\+\verb+<AA>+), and the control symbols
+ \isa{{\isaliteral{5C3C616C7068613E}{\isasymalpha}}} (\verb+\+\verb+<alpha>+), \isa{{\isaliteral{5C3C626574613E}{\isasymbeta}}}
+ (\verb+\+\verb+<beta>+), etc. (excluding \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}}),
+ special letters like \isa{{\isaliteral{5C3C413E}{\isasymA}}} (\verb+\+\verb+<A>+) and \isa{{\isaliteral{5C3C41413E}{\isasymAA}}} (\verb+\+\verb+<AA>+), and the control symbols
\verb+\+\verb+<^isub>+ and \verb+\+\verb+<^isup>+ for single letter
sub and super scripts. This means that the input
@@ -144,8 +144,8 @@
{\small\noindent \verb,\,\verb,<forall>\,\verb,<alpha>\<^isub>1.,~\verb,\,\verb,<alpha>\<^isub>1 = \,\verb,<Pi>\<^isup>\<A>,}
\medskip
- \noindent is recognized as the term \isa{{\isasymforall}{\isasymalpha}\isactrlisub {\isadigit{1}}{\isachardot}\ {\isasymalpha}\isactrlisub {\isadigit{1}}\ {\isacharequal}\ {\isasymPi}\isactrlisup {\isasymA}}
- by Isabelle. Note that \isa{{\isasymPi}\isactrlisup {\isasymA}} is a single
+ \noindent is recognized as the term \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C50693E}{\isasymPi}}\isaliteral{5C3C5E697375703E}{}\isactrlisup {\isaliteral{5C3C413E}{\isasymA}}}
+ by Isabelle. Note that \isa{{\isaliteral{5C3C50693E}{\isasymPi}}\isaliteral{5C3C5E697375703E}{}\isactrlisup {\isaliteral{5C3C413E}{\isasymA}}} is a single
syntactic entity, not an exponentiation.
Replacing our previous definition of \isa{xor} by the
@@ -166,8 +166,8 @@
%
\endisadelimML
\isacommand{definition}\isamarkupfalse%
-\ xor\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}bool\ {\isasymRightarrow}\ bool\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasymoplus}{\isachardoublequoteclose}\ {\isadigit{6}}{\isadigit{0}}{\isacharparenright}\isanewline
-\isakeyword{where}\ {\isachardoublequoteopen}A\ {\isasymoplus}\ B\ {\isasymequiv}\ {\isacharparenleft}A\ {\isasymand}\ {\isasymnot}\ B{\isacharparenright}\ {\isasymor}\ {\isacharparenleft}{\isasymnot}\ A\ {\isasymand}\ B{\isacharparenright}{\isachardoublequoteclose}%
+\ xor\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}bool\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F706C75733E}{\isasymoplus}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{6}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ B\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimML
%
\endisadelimML
@@ -183,7 +183,7 @@
%
\begin{isamarkuptext}%
\noindent The X-Symbol package within Proof~General provides several
- input methods to enter \isa{{\isasymoplus}} in the text. If all fails one may
+ input methods to enter \isa{{\isaliteral{5C3C6F706C75733E}{\isasymoplus}}} in the text. If all fails one may
just type a named entity \verb,\,\verb,<oplus>, by hand; the
corresponding symbol will be displayed after further input.
@@ -208,11 +208,11 @@
%
\endisadelimML
\isacommand{definition}\isamarkupfalse%
-\ xor\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}bool\ {\isasymRightarrow}\ bool\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharplus}{\isacharbrackright}{\isasymignore}{\isachardoublequoteclose}\ {\isadigit{6}}{\isadigit{0}}{\isacharparenright}\isanewline
-\isakeyword{where}\ {\isachardoublequoteopen}A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}{\isasymignore}\ B\ {\isasymequiv}\ {\isacharparenleft}A\ {\isasymand}\ {\isasymnot}\ B{\isacharparenright}\ {\isasymor}\ {\isacharparenleft}{\isasymnot}\ A\ {\isasymand}\ B{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ xor\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}bool\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5C3C69676E6F72653E}{\isasymignore}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{6}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5C3C69676E6F72653E}{\isasymignore}}\ B\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{notation}\isamarkupfalse%
-\ {\isacharparenleft}xsymbols{\isacharparenright}\ xor\ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasymoplus}{\isasymignore}{\isachardoublequoteclose}\ {\isadigit{6}}{\isadigit{0}}{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}xsymbols{\isaliteral{29}{\isacharparenright}}\ xor\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F706C75733E}{\isasymoplus}}{\isaliteral{5C3C69676E6F72653E}{\isasymignore}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{6}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}%
\isadelimML
%
\endisadelimML
@@ -230,9 +230,9 @@
\noindent
The \commdx{notation} command associates a mixfix
annotation with a known constant. The print mode specification,
-here \isa{{\isacharparenleft}xsymbols{\isacharparenright}}, is optional.
+here \isa{{\isaliteral{28}{\isacharparenleft}}xsymbols{\isaliteral{29}{\isacharparenright}}}, is optional.
-We may now write \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B} or \isa{A\ {\isasymoplus}\ B} in input, while
+We may now write \isa{A\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2B}{\isacharplus}}{\isaliteral{5D}{\isacharbrackright}}\ B} or \isa{A\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ B} in input, while
output uses the nicer syntax of $xsymbols$ whenever that print mode is
active. Such an arrangement is particularly useful for interactive
development, where users may type ASCII text and see mathematical
@@ -252,17 +252,17 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ currency\ {\isacharequal}\isanewline
-\ \ \ \ Euro\ nat\ \ \ \ {\isacharparenleft}{\isachardoublequoteopen}{\isasymeuro}{\isachardoublequoteclose}{\isacharparenright}\isanewline
-\ \ {\isacharbar}\ Pounds\ nat\ \ {\isacharparenleft}{\isachardoublequoteopen}{\isasympounds}{\isachardoublequoteclose}{\isacharparenright}\isanewline
-\ \ {\isacharbar}\ Yen\ nat\ \ \ \ \ {\isacharparenleft}{\isachardoublequoteopen}{\isasymyen}{\isachardoublequoteclose}{\isacharparenright}\isanewline
-\ \ {\isacharbar}\ Dollar\ nat\ \ {\isacharparenleft}{\isachardoublequoteopen}{\isachardollar}{\isachardoublequoteclose}{\isacharparenright}%
+\ currency\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ Euro\ nat\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6575726F3E}{\isasymeuro}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ Pounds\ nat\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C706F756E64733E}{\isasympounds}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ Yen\ nat\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C79656E3E}{\isasymyen}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ Dollar\ nat\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{24}{\isachardollar}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptext}%
\noindent Here the mixfix annotations on the rightmost column happen
to consist of a single Isabelle symbol each: \verb,\,\verb,<euro>,,
\verb,\,\verb,<pounds>,, \verb,\,\verb,<yen>,, and \verb,$,. Recall
- that a constructor like \isa{Euro} actually is a function \isa{nat\ {\isasymRightarrow}\ currency}. The expression \isa{Euro\ {\isadigit{1}}{\isadigit{0}}} will be
- printed as \isa{{\isasymeuro}\ {\isadigit{1}}{\isadigit{0}}}; only the head of the application is
+ that a constructor like \isa{Euro} actually is a function \isa{nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ currency}. The expression \isa{Euro\ {\isadigit{1}}{\isadigit{0}}} will be
+ printed as \isa{{\isaliteral{5C3C6575726F3E}{\isasymeuro}}\ {\isadigit{1}}{\isadigit{0}}}; only the head of the application is
subject to our concrete syntax. This rather simple form already
achieves conformance with notational standards of the European
Commission.
@@ -278,7 +278,7 @@
\begin{isamarkuptext}%
Mixfix syntax annotations merely decorate particular constant
application forms with concrete syntax, for instance replacing
-\isa{xor\ A\ B} by \isa{A\ {\isasymoplus}\ B}. Occasionally, the relationship
+\isa{xor\ A\ B} by \isa{A\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ B}. Occasionally, the relationship
between some piece of notation and its internal form is more
complicated. Here we need \emph{abbreviations}.
@@ -288,34 +288,34 @@
simple mechanism for syntactic macros.
A typical use of abbreviations is to introduce relational notation for
-membership in a set of pairs, replacing \isa{{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ sim} by
-\isa{x\ {\isasymapprox}\ y}. We assume that a constant \isa{sim} of type
-\isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set} has been introduced at this point.%
+membership in a set of pairs, replacing \isa{{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ sim} by
+\isa{x\ {\isaliteral{5C3C617070726F783E}{\isasymapprox}}\ y}. We assume that a constant \isa{sim} of type
+\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ set} has been introduced at this point.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{abbreviation}\isamarkupfalse%
-\ sim{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \ \ {\isacharparenleft}\isakeyword{infix}\ {\isachardoublequoteopen}{\isasymapprox}{\isachardoublequoteclose}\ {\isadigit{5}}{\isadigit{0}}{\isacharparenright}\isanewline
-\isakeyword{where}\ {\isachardoublequoteopen}x\ {\isasymapprox}\ y\ \ {\isasymequiv}\ \ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ sim{\isachardoublequoteclose}%
+\ sim{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infix}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C617070726F783E}{\isasymapprox}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{5}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C617070726F783E}{\isasymapprox}}\ y\ \ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ \ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ sim{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent The given meta-equality is used as a rewrite rule
-after parsing (replacing \mbox{\isa{x\ {\isasymapprox}\ y}} by \isa{{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ sim}) and before printing (turning \isa{{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ sim} back into
-\mbox{\isa{x\ {\isasymapprox}\ y}}). The name of the dummy constant \isa{sim{\isadigit{2}}}
+after parsing (replacing \mbox{\isa{x\ {\isaliteral{5C3C617070726F783E}{\isasymapprox}}\ y}} by \isa{{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ sim}) and before printing (turning \isa{{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ sim} back into
+\mbox{\isa{x\ {\isaliteral{5C3C617070726F783E}{\isasymapprox}}\ y}}). The name of the dummy constant \isa{sim{\isadigit{2}}}
does not matter, as long as it is unique.
Another common application of abbreviations is to
provide variant versions of fundamental relational expressions, such
-as \isa{{\isasymnoteq}} for negated equalities. The following declaration
+as \isa{{\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}} for negated equalities. The following declaration
stems from Isabelle/HOL itself:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{abbreviation}\isamarkupfalse%
-\ not{\isacharunderscore}equal\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isachartilde}{\isacharequal}{\isasymignore}{\isachardoublequoteclose}\ {\isadigit{5}}{\isadigit{0}}{\isacharparenright}\isanewline
-\isakeyword{where}\ {\isachardoublequoteopen}x\ {\isachartilde}{\isacharequal}{\isasymignore}\ y\ \ {\isasymequiv}\ \ {\isasymnot}\ {\isacharparenleft}x\ {\isacharequal}\ y{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ not{\isaliteral{5F}{\isacharunderscore}}equal\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7E}{\isachartilde}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{5C3C69676E6F72653E}{\isasymignore}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{5}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{7E}{\isachartilde}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{5C3C69676E6F72653E}{\isasymignore}}\ y\ \ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ \ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{notation}\isamarkupfalse%
-\ {\isacharparenleft}xsymbols{\isacharparenright}\ not{\isacharunderscore}equal\ {\isacharparenleft}\isakeyword{infix}\ {\isachardoublequoteopen}{\isasymnoteq}{\isasymignore}{\isachardoublequoteclose}\ {\isadigit{5}}{\isadigit{0}}{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}xsymbols{\isaliteral{29}{\isacharparenright}}\ not{\isaliteral{5F}{\isacharunderscore}}equal\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infix}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}{\isaliteral{5C3C69676E6F72653E}{\isasymignore}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{5}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptext}%
-\noindent The notation \isa{{\isasymnoteq}} is introduced separately to restrict it
+\noindent The notation \isa{{\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}} is introduced separately to restrict it
to the \emph{xsymbols} mode.
Abbreviations are appropriate when the defined concept is a
@@ -357,20 +357,20 @@
\begin{quotation}
%
\begin{isamarkuptext}%
-The following datatype definition of \isa{{\isacharprime}a\ bintree} models
- binary trees with nodes being decorated by elements of type \isa{{\isacharprime}a}.%
+The following datatype definition of \isa{{\isaliteral{27}{\isacharprime}}a\ bintree} models
+ binary trees with nodes being decorated by elements of type \isa{{\isaliteral{27}{\isacharprime}}a}.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ {\isacharprime}a\ bintree\ {\isacharequal}\isanewline
-\ \ \ \ \ Leaf\ {\isacharbar}\ Branch\ {\isacharprime}a\ \ {\isachardoublequoteopen}{\isacharprime}a\ bintree{\isachardoublequoteclose}\ \ {\isachardoublequoteopen}{\isacharprime}a\ bintree{\isachardoublequoteclose}%
+\ {\isaliteral{27}{\isacharprime}}a\ bintree\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ Leaf\ {\isaliteral{7C}{\isacharbar}}\ Branch\ {\isaliteral{27}{\isacharprime}}a\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ bintree{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ bintree{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent The datatype induction rule generated here is of the form
\begin{isabelle}%
-\ {\isasymlbrakk}P\ Leaf{\isacharsemicolon}\isanewline
-\isaindent{\ \ }{\isasymAnd}a\ bintree{\isadigit{1}}\ bintree{\isadigit{2}}{\isachardot}\isanewline
-\isaindent{\ \ \ \ \ }{\isasymlbrakk}P\ bintree{\isadigit{1}}{\isacharsemicolon}\ P\ bintree{\isadigit{2}}{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}Branch\ a\ bintree{\isadigit{1}}\ bintree{\isadigit{2}}{\isacharparenright}{\isasymrbrakk}\isanewline
-\isaindent{\ }{\isasymLongrightarrow}\ P\ bintree%
+\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}P\ Leaf{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ \ }{\isaliteral{5C3C416E643E}{\isasymAnd}}a\ bintree{\isadigit{1}}\ bintree{\isadigit{2}}{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ \ \ \ \ }{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}P\ bintree{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\ P\ bintree{\isadigit{2}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ {\isaliteral{28}{\isacharparenleft}}Branch\ a\ bintree{\isadigit{1}}\ bintree{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ bintree%
\end{isabelle}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -529,8 +529,8 @@
\medskip
From the Isabelle perspective, each markup command takes a single
- $text$ argument (delimited by \verb,",~\isa{{\isasymdots}}~\verb,", or
- \verb,{,\verb,*,~\isa{{\isasymdots}}~\verb,*,\verb,},). After stripping any
+ $text$ argument (delimited by \verb,",~\isa{{\isaliteral{5C3C646F74733E}{\isasymdots}}}~\verb,", or
+ \verb,{,\verb,*,~\isa{{\isaliteral{5C3C646F74733E}{\isasymdots}}}~\verb,*,\verb,},). After stripping any
surrounding white space, the argument is passed to a {\LaTeX} macro
\verb,\isamarkupXYZ, for command \isakeyword{XYZ}. These macros are
defined in \verb,isabelle.sty, according to the meaning given in the
@@ -599,7 +599,7 @@
%
\begin{isamarkuptext}%
Isabelle \bfindex{source comments}, which are of the form
- \verb,(,\verb,*,~\isa{{\isasymdots}}~\verb,*,\verb,),, essentially act like
+ \verb,(,\verb,*,~\isa{{\isaliteral{5C3C646F74733E}{\isasymdots}}}~\verb,*,\verb,),, essentially act like
white space and do not really contribute to the content. They
mainly serve technical purposes to mark certain oddities in the raw
input text. In contrast, \bfindex{formal comments} are portions of
@@ -609,14 +609,14 @@
\medskip Marginal comments are part of each command's concrete
syntax \cite{isabelle-ref}; the common form is ``\verb,--,~$text$''
- where $text$ is delimited by \verb,",\isa{{\isasymdots}}\verb,", or
- \verb,{,\verb,*,~\isa{{\isasymdots}}~\verb,*,\verb,}, as before. Multiple
+ where $text$ is delimited by \verb,",\isa{{\isaliteral{5C3C646F74733E}{\isasymdots}}}\verb,", or
+ \verb,{,\verb,*,~\isa{{\isaliteral{5C3C646F74733E}{\isasymdots}}}~\verb,*,\verb,}, as before. Multiple
marginal comments may be given at the same time. Here is a simple
example:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isacharminus}{\isacharminus}{\isachargreater}\ A{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ %
\isamarkupcmt{a triviality of propositional logic%
}
@@ -632,7 +632,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ impI{\isacharparenright}\ %
+\ {\isaliteral{28}{\isacharparenleft}}rule\ impI{\isaliteral{29}{\isacharparenright}}\ %
\isamarkupcmt{implicit assumption step involved here%
}
%
@@ -692,7 +692,7 @@
for types, terms, or theorems as in the formal part of a theory.
\medskip This sentence demonstrates quotations and antiquotations:
- \isa{{\isasymlambda}x\ y{\isachardot}\ x} is a well-typed term.
+ \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x\ y{\isaliteral{2E}{\isachardot}}\ x} is a well-typed term.
\medskip\noindent The output above was produced as follows:
\begin{ttbox}
@@ -703,14 +703,14 @@
\end{ttbox}\vspace{-\medskipamount}
The notational change from the ASCII character~\verb,%, to the
- symbol~\isa{{\isasymlambda}} reveals that Isabelle printed this term, after
+ symbol~\isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}} reveals that Isabelle printed this term, after
parsing and type-checking. Document preparation enables symbolic
output by default.
\medskip The next example includes an option to show the type of all
variables. The antiquotation
\texttt{{\at}}\verb,{term [show_types] "%x y. x"}, produces the
- output \isa{{\isasymlambda}{\isacharparenleft}x{\isasymColon}{\isacharprime}a{\isacharparenright}\ y{\isasymColon}{\isacharprime}b{\isachardot}\ x}. Type inference has figured
+ output \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ y{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}b{\isaliteral{2E}{\isachardot}}\ x}. Type inference has figured
out the most general typings in the present theory context. Terms
may acquire different typings due to constraints imposed by their
environment; within a proof, for example, variables are given the
@@ -748,7 +748,7 @@
virtue is that the string $s$ is processed as Isabelle output,
interpreting Isabelle symbols appropriately.
- For example, \texttt{\at}\verb,{text "\<forall>\<exists>"}, produces \isa{{\isasymforall}{\isasymexists}}, according to the standard interpretation of these symbol
+ For example, \texttt{\at}\verb,{text "\<forall>\<exists>"}, produces \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}}, according to the standard interpretation of these symbol
(cf.\ \S\ref{sec:doc-prep-symbols}). Thus we achieve consistent
mathematical notation in both the formal and informal parts of the
document very easily, independently of the term language of
@@ -847,14 +847,14 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isacharequal}\ x{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}%
\isadeliminvisible
\ %
\endisadeliminvisible
%
\isataginvisible
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{29}{\isacharparenright}}%
\endisataginvisible
{\isafoldinvisible}%
%
@@ -883,7 +883,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymnoteq}\ {\isacharparenleft}{\isadigit{0}}{\isacharcolon}{\isacharcolon}int{\isacharparenright}\ {\isasymLongrightarrow}\ {\isadigit{0}}\ {\isacharless}\ x\ {\isacharasterisk}\ x{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}int{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isadigit{0}}\ {\isaliteral{3C}{\isacharless}}\ x\ {\isaliteral{2A}{\isacharasterisk}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -891,7 +891,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}auto{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}auto{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
--- a/doc-src/TutorialI/Fun/document/fun0.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Fun/document/fun0.tex Mon Nov 08 14:41:11 2010 +0100
@@ -23,10 +23,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
-\ fib\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}fib\ {\isadigit{0}}\ {\isacharequal}\ {\isadigit{0}}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}fib\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}fib\ {\isacharparenleft}Suc{\isacharparenleft}Suc\ x{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ fib\ x\ {\isacharplus}\ fib\ {\isacharparenleft}Suc\ x{\isacharparenright}{\isachardoublequoteclose}%
+\ fib\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}fib\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}fib\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}fib\ {\isaliteral{28}{\isacharparenleft}}Suc{\isaliteral{28}{\isacharparenleft}}Suc\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ fib\ x\ {\isaliteral{2B}{\isacharplus}}\ fib\ {\isaliteral{28}{\isacharparenleft}}Suc\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
This resembles ordinary functional programming languages. Note the obligatory
@@ -39,10 +39,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
-\ sep\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}sep\ a\ {\isacharbrackleft}{\isacharbrackright}\ \ \ \ \ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}sep\ a\ {\isacharbrackleft}x{\isacharbrackright}\ \ \ \ {\isacharequal}\ {\isacharbrackleft}x{\isacharbrackright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}sep\ a\ {\isacharparenleft}x{\isacharhash}y{\isacharhash}zs{\isacharparenright}\ {\isacharequal}\ x\ {\isacharhash}\ a\ {\isacharhash}\ sep\ a\ {\isacharparenleft}y{\isacharhash}zs{\isacharparenright}{\isachardoublequoteclose}%
+\ sep\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}sep\ a\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ \ \ \ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}sep\ a\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}\ \ \ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}sep\ a\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{23}{\isacharhash}}y{\isaliteral{23}{\isacharhash}}zs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{23}{\isacharhash}}\ a\ {\isaliteral{23}{\isacharhash}}\ sep\ a\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{23}{\isacharhash}}zs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
This time the length of the list decreases with the
@@ -53,24 +53,24 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
-\ last\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}last\ {\isacharbrackleft}x{\isacharbrackright}\ \ \ \ \ \ {\isacharequal}\ x{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}last\ {\isacharparenleft}{\isacharunderscore}{\isacharhash}y{\isacharhash}zs{\isacharparenright}\ {\isacharequal}\ last\ {\isacharparenleft}y{\isacharhash}zs{\isacharparenright}{\isachardoublequoteclose}%
+\ last\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}last\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}\ \ \ \ \ \ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}last\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{23}{\isacharhash}}y{\isaliteral{23}{\isacharhash}}zs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ last\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{23}{\isacharhash}}zs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
Overlapping patterns are disambiguated by taking the order of equations into
account, just as in functional programming:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
-\ sep{\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}sep{\isadigit{1}}\ a\ {\isacharparenleft}x{\isacharhash}y{\isacharhash}zs{\isacharparenright}\ {\isacharequal}\ x\ {\isacharhash}\ a\ {\isacharhash}\ sep{\isadigit{1}}\ a\ {\isacharparenleft}y{\isacharhash}zs{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}sep{\isadigit{1}}\ {\isacharunderscore}\ xs\ \ \ \ \ \ \ {\isacharequal}\ xs{\isachardoublequoteclose}%
+\ sep{\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}sep{\isadigit{1}}\ a\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{23}{\isacharhash}}y{\isaliteral{23}{\isacharhash}}zs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{23}{\isacharhash}}\ a\ {\isaliteral{23}{\isacharhash}}\ sep{\isadigit{1}}\ a\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{23}{\isacharhash}}zs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}sep{\isadigit{1}}\ {\isaliteral{5F}{\isacharunderscore}}\ xs\ \ \ \ \ \ \ {\isaliteral{3D}{\isacharequal}}\ xs{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
To guarantee that the second equation can only be applied if the first
one does not match, Isabelle internally replaces the second equation
-by the two possibilities that are left: \isa{sep{\isadigit{1}}\ a\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}} and
-\isa{sep{\isadigit{1}}\ a\ {\isacharbrackleft}x{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}x{\isacharbrackright}}. Thus the functions \isa{sep} and
+by the two possibilities that are left: \isa{sep{\isadigit{1}}\ a\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}} and
+\isa{sep{\isadigit{1}}\ a\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}}. Thus the functions \isa{sep} and
\isa{sep{\isadigit{1}}} are identical.
Because of its pattern matching syntax, \isacommand{fun} is also useful
@@ -78,15 +78,15 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
-\ swap{\isadigit{1}}{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}swap{\isadigit{1}}{\isadigit{2}}\ {\isacharparenleft}x{\isacharhash}y{\isacharhash}zs{\isacharparenright}\ {\isacharequal}\ y{\isacharhash}x{\isacharhash}zs{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}swap{\isadigit{1}}{\isadigit{2}}\ zs\ \ \ \ \ \ \ {\isacharequal}\ zs{\isachardoublequoteclose}%
+\ swap{\isadigit{1}}{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}swap{\isadigit{1}}{\isadigit{2}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{23}{\isacharhash}}y{\isaliteral{23}{\isacharhash}}zs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{23}{\isacharhash}}x{\isaliteral{23}{\isacharhash}}zs{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}swap{\isadigit{1}}{\isadigit{2}}\ zs\ \ \ \ \ \ \ {\isaliteral{3D}{\isacharequal}}\ zs{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
After a function~$f$ has been defined via \isacommand{fun},
its defining equations (or variants derived from them) are available
-under the name $f$\isa{{\isachardot}simps} as theorems.
+under the name $f$\isa{{\isaliteral{2E}{\isachardot}}simps} as theorems.
For example, look (via \isacommand{thm}) at
-\isa{sep{\isachardot}simps} and \isa{sep{\isadigit{1}}{\isachardot}simps} to see that they define
+\isa{sep{\isaliteral{2E}{\isachardot}}simps} and \isa{sep{\isadigit{1}}{\isaliteral{2E}{\isachardot}}simps} to see that they define
the same function. What is more, those equations are automatically declared as
simplification rules.
@@ -107,10 +107,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
-\ ack{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}ack{\isadigit{2}}\ n\ {\isadigit{0}}\ {\isacharequal}\ Suc\ n{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}ack{\isadigit{2}}\ {\isadigit{0}}\ {\isacharparenleft}Suc\ m{\isacharparenright}\ {\isacharequal}\ ack{\isadigit{2}}\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}\ m{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}ack{\isadigit{2}}\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharparenleft}Suc\ m{\isacharparenright}\ {\isacharequal}\ ack{\isadigit{2}}\ {\isacharparenleft}ack{\isadigit{2}}\ n\ {\isacharparenleft}Suc\ m{\isacharparenright}{\isacharparenright}\ m{\isachardoublequoteclose}%
+\ ack{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}ack{\isadigit{2}}\ n\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ Suc\ n{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}ack{\isadigit{2}}\ {\isadigit{0}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ m{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ ack{\isadigit{2}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ m{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}ack{\isadigit{2}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ m{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ ack{\isadigit{2}}\ {\isaliteral{28}{\isacharparenleft}}ack{\isadigit{2}}\ n\ {\isaliteral{28}{\isacharparenleft}}Suc\ m{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ m{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
The order of arguments has no influence on whether
\isacommand{fun} can prove termination of a function. For more details
@@ -129,14 +129,14 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
-\ gcd\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}gcd\ m\ n\ {\isacharequal}\ {\isacharparenleft}if\ n{\isacharequal}{\isadigit{0}}\ then\ m\ else\ gcd\ n\ {\isacharparenleft}m\ mod\ n{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
+\ gcd\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}gcd\ m\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ n{\isaliteral{3D}{\isacharequal}}{\isadigit{0}}\ then\ m\ else\ gcd\ n\ {\isaliteral{28}{\isacharparenleft}}m\ mod\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
The second argument decreases with each recursive call.
The termination condition
\begin{isabelle}%
-\ \ \ \ \ n\ {\isasymnoteq}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ m\ mod\ n\ {\isacharless}\ n%
+\ \ \ \ \ n\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ m\ mod\ n\ {\isaliteral{3C}{\isacharless}}\ n%
\end{isabelle}
is proved automatically because it is already present as a lemma in
HOL\@. Thus the recursion equation becomes a simplification
@@ -148,23 +148,23 @@
condition simplifies to \isa{True} or \isa{False}. For
example, simplification reduces
\begin{isabelle}%
-\ \ \ \ \ gcd\ m\ n\ {\isacharequal}\ k%
+\ \ \ \ \ gcd\ m\ n\ {\isaliteral{3D}{\isacharequal}}\ k%
\end{isabelle}
in one step to
\begin{isabelle}%
-\ \ \ \ \ {\isacharparenleft}if\ n\ {\isacharequal}\ {\isadigit{0}}\ then\ m\ else\ gcd\ n\ {\isacharparenleft}m\ mod\ n{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ k%
+\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}if\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\ then\ m\ else\ gcd\ n\ {\isaliteral{28}{\isacharparenleft}}m\ mod\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ k%
\end{isabelle}
where the condition cannot be reduced further, and splitting leads to
\begin{isabelle}%
-\ \ \ \ \ {\isacharparenleft}n\ {\isacharequal}\ {\isadigit{0}}\ {\isasymlongrightarrow}\ m\ {\isacharequal}\ k{\isacharparenright}\ {\isasymand}\ {\isacharparenleft}n\ {\isasymnoteq}\ {\isadigit{0}}\ {\isasymlongrightarrow}\ gcd\ n\ {\isacharparenleft}m\ mod\ n{\isacharparenright}\ {\isacharequal}\ k{\isacharparenright}%
+\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ m\ {\isaliteral{3D}{\isacharequal}}\ k{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ gcd\ n\ {\isaliteral{28}{\isacharparenleft}}m\ mod\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ k{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
-Since the recursive call \isa{gcd\ n\ {\isacharparenleft}m\ mod\ n{\isacharparenright}} is no longer protected by
+Since the recursive call \isa{gcd\ n\ {\isaliteral{28}{\isacharparenleft}}m\ mod\ n{\isaliteral{29}{\isacharparenright}}} is no longer protected by
an \isa{if}, it is unfolded again, which leads to an infinite chain of
simplification steps. Fortunately, this problem can be avoided in many
different ways.
The most radical solution is to disable the offending theorem
-\isa{split{\isacharunderscore}if},
+\isa{split{\isaliteral{5F}{\isacharunderscore}}if},
as shown in \S\ref{sec:AutoCaseSplits}. However, we do not recommend this
approach: you will often have to invoke the rule explicitly when
\isa{if} is involved.
@@ -175,13 +175,13 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
-\ gcd{\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}gcd{\isadigit{1}}\ m\ {\isadigit{0}}\ {\isacharequal}\ m{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}gcd{\isadigit{1}}\ m\ n\ {\isacharequal}\ gcd{\isadigit{1}}\ n\ {\isacharparenleft}m\ mod\ n{\isacharparenright}{\isachardoublequoteclose}%
+\ gcd{\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}gcd{\isadigit{1}}\ m\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ m{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}gcd{\isadigit{1}}\ m\ n\ {\isaliteral{3D}{\isacharequal}}\ gcd{\isadigit{1}}\ n\ {\isaliteral{28}{\isacharparenleft}}m\ mod\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
The order of equations is important: it hides the side condition
-\isa{n\ {\isasymnoteq}\ {\isadigit{0}}}. Unfortunately, not all conditionals can be
+\isa{n\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}}. Unfortunately, not all conditionals can be
expressed by pattern matching.
A simple alternative is to replace \isa{if} by \isa{case},
@@ -189,8 +189,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
-\ gcd{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}gcd{\isadigit{2}}\ m\ n\ {\isacharequal}\ {\isacharparenleft}case\ n{\isacharequal}{\isadigit{0}}\ of\ True\ {\isasymRightarrow}\ m\ {\isacharbar}\ False\ {\isasymRightarrow}\ gcd{\isadigit{2}}\ n\ {\isacharparenleft}m\ mod\ n{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
+\ gcd{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}gcd{\isadigit{2}}\ m\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}case\ n{\isaliteral{3D}{\isacharequal}}{\isadigit{0}}\ of\ True\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ m\ {\isaliteral{7C}{\isacharbar}}\ False\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ gcd{\isadigit{2}}\ n\ {\isaliteral{28}{\isacharparenleft}}m\ mod\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
This is probably the neatest solution next to pattern matching, and it is
@@ -202,7 +202,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}gcd\ m\ {\isadigit{0}}\ {\isacharequal}\ m{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}gcd\ m\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ m{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -210,7 +210,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -222,7 +222,7 @@
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}n\ {\isasymnoteq}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ gcd\ m\ n\ {\isacharequal}\ gcd\ n\ {\isacharparenleft}m\ mod\ n{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}n\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{0}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ gcd\ m\ n\ {\isaliteral{3D}{\isacharequal}}\ gcd\ n\ {\isaliteral{28}{\isacharparenleft}}m\ mod\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -230,7 +230,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -247,7 +247,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{declare}\isamarkupfalse%
-\ gcd{\isachardot}simps\ {\isacharbrackleft}simp\ del{\isacharbrackright}%
+\ gcd{\isaliteral{2E}{\isachardot}}simps\ {\isaliteral{5B}{\isacharbrackleft}}simp\ del{\isaliteral{5D}{\isacharbrackright}}%
\begin{isamarkuptext}%
\index{induction!recursion|(}
\index{recursion induction|(}
@@ -260,7 +260,7 @@
again induction. But this time the structural form of induction that comes
with datatypes is unlikely to work well --- otherwise we could have defined the
function by \isacommand{primrec}. Therefore \isacommand{fun} automatically
-proves a suitable induction rule $f$\isa{{\isachardot}induct} that follows the
+proves a suitable induction rule $f$\isa{{\isaliteral{2E}{\isachardot}}induct} that follows the
recursion pattern of the particular function $f$. We call this
\textbf{recursion induction}. Roughly speaking, it
requires you to prove for each \isacommand{fun} equation that the property
@@ -270,7 +270,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}map\ f\ {\isacharparenleft}sep\ x\ xs{\isacharparenright}\ {\isacharequal}\ sep\ {\isacharparenleft}f\ x{\isacharparenright}\ {\isacharparenleft}map\ f\ xs{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}map\ f\ {\isaliteral{28}{\isacharparenleft}}sep\ x\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ sep\ {\isaliteral{28}{\isacharparenleft}}f\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}map\ f\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -285,23 +285,23 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ x\ xs\ rule{\isacharcolon}\ sep{\isachardot}induct{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ x\ xs\ rule{\isaliteral{3A}{\isacharcolon}}\ sep{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
The resulting proof state has three subgoals corresponding to the three
clauses for \isa{sep}:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}a{\isachardot}\ map\ f\ {\isacharparenleft}sep\ a\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\ sep\ {\isacharparenleft}f\ a{\isacharparenright}\ {\isacharparenleft}map\ f\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}a\ x{\isachardot}\ map\ f\ {\isacharparenleft}sep\ a\ {\isacharbrackleft}x{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\ sep\ {\isacharparenleft}f\ a{\isacharparenright}\ {\isacharparenleft}map\ f\ {\isacharbrackleft}x{\isacharbrackright}{\isacharparenright}\isanewline
-\ {\isadigit{3}}{\isachardot}\ {\isasymAnd}a\ x\ y\ zs{\isachardot}\isanewline
-\isaindent{\ {\isadigit{3}}{\isachardot}\ \ \ \ }map\ f\ {\isacharparenleft}sep\ a\ {\isacharparenleft}y\ {\isacharhash}\ zs{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ sep\ {\isacharparenleft}f\ a{\isacharparenright}\ {\isacharparenleft}map\ f\ {\isacharparenleft}y\ {\isacharhash}\ zs{\isacharparenright}{\isacharparenright}\ {\isasymLongrightarrow}\isanewline
-\isaindent{\ {\isadigit{3}}{\isachardot}\ \ \ \ }map\ f\ {\isacharparenleft}sep\ a\ {\isacharparenleft}x\ {\isacharhash}\ y\ {\isacharhash}\ zs{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ sep\ {\isacharparenleft}f\ a{\isacharparenright}\ {\isacharparenleft}map\ f\ {\isacharparenleft}x\ {\isacharhash}\ y\ {\isacharhash}\ zs{\isacharparenright}{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a{\isaliteral{2E}{\isachardot}}\ map\ f\ {\isaliteral{28}{\isacharparenleft}}sep\ a\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ sep\ {\isaliteral{28}{\isacharparenleft}}f\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}map\ f\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a\ x{\isaliteral{2E}{\isachardot}}\ map\ f\ {\isaliteral{28}{\isacharparenleft}}sep\ a\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ sep\ {\isaliteral{28}{\isacharparenleft}}f\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}map\ f\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ {\isadigit{3}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a\ x\ y\ zs{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{3}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }map\ f\ {\isaliteral{28}{\isacharparenleft}}sep\ a\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{23}{\isacharhash}}\ zs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ sep\ {\isaliteral{28}{\isacharparenleft}}f\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}map\ f\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{23}{\isacharhash}}\ zs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\isanewline
+\isaindent{\ {\isadigit{3}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }map\ f\ {\isaliteral{28}{\isacharparenleft}}sep\ a\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ y\ {\isaliteral{23}{\isacharhash}}\ zs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ sep\ {\isaliteral{28}{\isacharparenleft}}f\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}map\ f\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ y\ {\isaliteral{23}{\isacharhash}}\ zs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
The rest is pure simplification:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-\ simp{\isacharunderscore}all\isanewline
+\ simp{\isaliteral{5F}{\isacharunderscore}}all\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -319,12 +319,12 @@
In general, the format of invoking recursion induction is
\begin{quote}
-\isacommand{apply}\isa{{\isacharparenleft}induct{\isacharunderscore}tac} $x@1 \dots x@n$ \isa{rule{\isacharcolon}} $f$\isa{{\isachardot}induct{\isacharparenright}}
+\isacommand{apply}\isa{{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac} $x@1 \dots x@n$ \isa{rule{\isaliteral{3A}{\isacharcolon}}} $f$\isa{{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}}
\end{quote}\index{*induct_tac (method)}%
where $x@1~\dots~x@n$ is a list of free variables in the subgoal and $f$ the
name of a function that takes $n$ arguments. Usually the subgoal will
contain the term $f x@1 \dots x@n$ but this need not be the case. The
-induction rules do not mention $f$ at all. Here is \isa{sep{\isachardot}induct}:
+induction rules do not mention $f$ at all. Here is \isa{sep{\isaliteral{2E}{\isachardot}}induct}:
\begin{isabelle}
{\isasymlbrakk}~{\isasymAnd}a.~P~a~[];\isanewline
~~{\isasymAnd}a~x.~P~a~[x];\isanewline
--- a/doc-src/TutorialI/Ifexpr/document/Ifexpr.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Ifexpr/document/Ifexpr.tex Mon Nov 08 14:41:11 2010 +0100
@@ -38,30 +38,30 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ boolex\ {\isacharequal}\ Const\ bool\ {\isacharbar}\ Var\ nat\ {\isacharbar}\ Neg\ boolex\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ And\ boolex\ boolex%
+\ boolex\ {\isaliteral{3D}{\isacharequal}}\ Const\ bool\ {\isaliteral{7C}{\isacharbar}}\ Var\ nat\ {\isaliteral{7C}{\isacharbar}}\ Neg\ boolex\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ And\ boolex\ boolex%
\begin{isamarkuptext}%
\noindent
The two constants are represented by \isa{Const\ True} and
\isa{Const\ False}. Variables are represented by terms of the form
\isa{Var\ n}, where \isa{n} is a natural number (type \isa{nat}).
For example, the formula $P@0 \land \neg P@1$ is represented by the term
-\isa{And\ {\isacharparenleft}Var\ {\isadigit{0}}{\isacharparenright}\ {\isacharparenleft}Neg\ {\isacharparenleft}Var\ {\isadigit{1}}{\isacharparenright}{\isacharparenright}}.
+\isa{And\ {\isaliteral{28}{\isacharparenleft}}Var\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}Neg\ {\isaliteral{28}{\isacharparenleft}}Var\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}}.
\subsubsection{The Value of a Boolean Expression}
The value of a boolean expression depends on the value of its variables.
Hence the function \isa{value} takes an additional parameter, an
-\emph{environment} of type \isa{nat\ {\isasymRightarrow}\ bool}, which maps variables to their
+\emph{environment} of type \isa{nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}, which maps variables to their
values:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ {\isachardoublequoteopen}value{\isachardoublequoteclose}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}boolex\ {\isasymRightarrow}\ {\isacharparenleft}nat\ {\isasymRightarrow}\ bool{\isacharparenright}\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}value\ {\isacharparenleft}Const\ b{\isacharparenright}\ env\ {\isacharequal}\ b{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}value\ {\isacharparenleft}Var\ x{\isacharparenright}\ \ \ env\ {\isacharequal}\ env\ x{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}value\ {\isacharparenleft}Neg\ b{\isacharparenright}\ \ \ env\ {\isacharequal}\ {\isacharparenleft}{\isasymnot}\ value\ b\ env{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}value\ {\isacharparenleft}And\ b\ c{\isacharparenright}\ env\ {\isacharequal}\ {\isacharparenleft}value\ b\ env\ {\isasymand}\ value\ c\ env{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}value{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}boolex\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}value\ {\isaliteral{28}{\isacharparenleft}}Const\ b{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}value\ {\isaliteral{28}{\isacharparenleft}}Var\ x{\isaliteral{29}{\isacharparenright}}\ \ \ env\ {\isaliteral{3D}{\isacharequal}}\ env\ x{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}value\ {\isaliteral{28}{\isacharparenleft}}Neg\ b{\isaliteral{29}{\isacharparenright}}\ \ \ env\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ value\ b\ env{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}value\ {\isaliteral{28}{\isacharparenleft}}And\ b\ c{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}value\ b\ env\ {\isaliteral{5C3C616E643E}{\isasymand}}\ value\ c\ env{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
\subsubsection{If-Expressions}
@@ -73,18 +73,18 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ ifex\ {\isacharequal}\ CIF\ bool\ {\isacharbar}\ VIF\ nat\ {\isacharbar}\ IF\ ifex\ ifex\ ifex%
+\ ifex\ {\isaliteral{3D}{\isacharequal}}\ CIF\ bool\ {\isaliteral{7C}{\isacharbar}}\ VIF\ nat\ {\isaliteral{7C}{\isacharbar}}\ IF\ ifex\ ifex\ ifex%
\begin{isamarkuptext}%
\noindent
The evaluation of If-expressions proceeds as for \isa{boolex}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ valif\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}ifex\ {\isasymRightarrow}\ {\isacharparenleft}nat\ {\isasymRightarrow}\ bool{\isacharparenright}\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}valif\ {\isacharparenleft}CIF\ b{\isacharparenright}\ \ \ \ env\ {\isacharequal}\ b{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}valif\ {\isacharparenleft}VIF\ x{\isacharparenright}\ \ \ \ env\ {\isacharequal}\ env\ x{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}valif\ {\isacharparenleft}IF\ b\ t\ e{\isacharparenright}\ env\ {\isacharequal}\ {\isacharparenleft}if\ valif\ b\ env\ then\ valif\ t\ env\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ else\ valif\ e\ env{\isacharparenright}{\isachardoublequoteclose}%
+\ valif\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}ifex\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}valif\ {\isaliteral{28}{\isacharparenleft}}CIF\ b{\isaliteral{29}{\isacharparenright}}\ \ \ \ env\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}valif\ {\isaliteral{28}{\isacharparenleft}}VIF\ x{\isaliteral{29}{\isacharparenright}}\ \ \ \ env\ {\isaliteral{3D}{\isacharequal}}\ env\ x{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}valif\ {\isaliteral{28}{\isacharparenleft}}IF\ b\ t\ e{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ valif\ b\ env\ then\ valif\ t\ env\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ else\ valif\ e\ env{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\subsubsection{Converting Boolean and If-Expressions}
@@ -94,11 +94,11 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ bool{\isadigit{2}}if\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}boolex\ {\isasymRightarrow}\ ifex{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}bool{\isadigit{2}}if\ {\isacharparenleft}Const\ b{\isacharparenright}\ {\isacharequal}\ CIF\ b{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}bool{\isadigit{2}}if\ {\isacharparenleft}Var\ x{\isacharparenright}\ \ \ {\isacharequal}\ VIF\ x{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}bool{\isadigit{2}}if\ {\isacharparenleft}Neg\ b{\isacharparenright}\ \ \ {\isacharequal}\ IF\ {\isacharparenleft}bool{\isadigit{2}}if\ b{\isacharparenright}\ {\isacharparenleft}CIF\ False{\isacharparenright}\ {\isacharparenleft}CIF\ True{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}bool{\isadigit{2}}if\ {\isacharparenleft}And\ b\ c{\isacharparenright}\ {\isacharequal}\ IF\ {\isacharparenleft}bool{\isadigit{2}}if\ b{\isacharparenright}\ {\isacharparenleft}bool{\isadigit{2}}if\ c{\isacharparenright}\ {\isacharparenleft}CIF\ False{\isacharparenright}{\isachardoublequoteclose}%
+\ bool{\isadigit{2}}if\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}boolex\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ ifex{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}bool{\isadigit{2}}if\ {\isaliteral{28}{\isacharparenleft}}Const\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ CIF\ b{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}bool{\isadigit{2}}if\ {\isaliteral{28}{\isacharparenleft}}Var\ x{\isaliteral{29}{\isacharparenright}}\ \ \ {\isaliteral{3D}{\isacharequal}}\ VIF\ x{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}bool{\isadigit{2}}if\ {\isaliteral{28}{\isacharparenleft}}Neg\ b{\isaliteral{29}{\isacharparenright}}\ \ \ {\isaliteral{3D}{\isacharequal}}\ IF\ {\isaliteral{28}{\isacharparenleft}}bool{\isadigit{2}}if\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}CIF\ False{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}CIF\ True{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}bool{\isadigit{2}}if\ {\isaliteral{28}{\isacharparenleft}}And\ b\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ IF\ {\isaliteral{28}{\isacharparenleft}}bool{\isadigit{2}}if\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}bool{\isadigit{2}}if\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}CIF\ False{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
At last, we have something we can verify: that \isa{bool{\isadigit{2}}if} preserves the
@@ -106,7 +106,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}valif\ {\isacharparenleft}bool{\isadigit{2}}if\ b{\isacharparenright}\ env\ {\isacharequal}\ value\ b\ env{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}valif\ {\isaliteral{28}{\isacharparenleft}}bool{\isadigit{2}}if\ b{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ value\ b\ env{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -119,9 +119,9 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ b{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ b{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}auto{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -139,22 +139,22 @@
More interesting is the transformation of If-expressions into a normal form
where the first argument of \isa{IF} cannot be another \isa{IF} but
must be a constant or variable. Such a normal form can be computed by
-repeatedly replacing a subterm of the form \isa{IF\ {\isacharparenleft}IF\ b\ x\ y{\isacharparenright}\ z\ u} by
-\isa{IF\ b\ {\isacharparenleft}IF\ x\ z\ u{\isacharparenright}\ {\isacharparenleft}IF\ y\ z\ u{\isacharparenright}}, which has the same value. The following
+repeatedly replacing a subterm of the form \isa{IF\ {\isaliteral{28}{\isacharparenleft}}IF\ b\ x\ y{\isaliteral{29}{\isacharparenright}}\ z\ u} by
+\isa{IF\ b\ {\isaliteral{28}{\isacharparenleft}}IF\ x\ z\ u{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}IF\ y\ z\ u{\isaliteral{29}{\isacharparenright}}}, which has the same value. The following
primitive recursive functions perform this task:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ normif\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}ifex\ {\isasymRightarrow}\ ifex\ {\isasymRightarrow}\ ifex\ {\isasymRightarrow}\ ifex{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}normif\ {\isacharparenleft}CIF\ b{\isacharparenright}\ \ \ \ t\ e\ {\isacharequal}\ IF\ {\isacharparenleft}CIF\ b{\isacharparenright}\ t\ e{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}normif\ {\isacharparenleft}VIF\ x{\isacharparenright}\ \ \ \ t\ e\ {\isacharequal}\ IF\ {\isacharparenleft}VIF\ x{\isacharparenright}\ t\ e{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}normif\ {\isacharparenleft}IF\ b\ t\ e{\isacharparenright}\ u\ f\ {\isacharequal}\ normif\ b\ {\isacharparenleft}normif\ t\ u\ f{\isacharparenright}\ {\isacharparenleft}normif\ e\ u\ f{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ normif\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}ifex\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ ifex\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ ifex\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ ifex{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}normif\ {\isaliteral{28}{\isacharparenleft}}CIF\ b{\isaliteral{29}{\isacharparenright}}\ \ \ \ t\ e\ {\isaliteral{3D}{\isacharequal}}\ IF\ {\isaliteral{28}{\isacharparenleft}}CIF\ b{\isaliteral{29}{\isacharparenright}}\ t\ e{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}normif\ {\isaliteral{28}{\isacharparenleft}}VIF\ x{\isaliteral{29}{\isacharparenright}}\ \ \ \ t\ e\ {\isaliteral{3D}{\isacharequal}}\ IF\ {\isaliteral{28}{\isacharparenleft}}VIF\ x{\isaliteral{29}{\isacharparenright}}\ t\ e{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}normif\ {\isaliteral{28}{\isacharparenleft}}IF\ b\ t\ e{\isaliteral{29}{\isacharparenright}}\ u\ f\ {\isaliteral{3D}{\isacharequal}}\ normif\ b\ {\isaliteral{28}{\isacharparenleft}}normif\ t\ u\ f{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}normif\ e\ u\ f{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{primrec}\isamarkupfalse%
-\ norm\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}ifex\ {\isasymRightarrow}\ ifex{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}norm\ {\isacharparenleft}CIF\ b{\isacharparenright}\ \ \ \ {\isacharequal}\ CIF\ b{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}norm\ {\isacharparenleft}VIF\ x{\isacharparenright}\ \ \ \ {\isacharequal}\ VIF\ x{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}norm\ {\isacharparenleft}IF\ b\ t\ e{\isacharparenright}\ {\isacharequal}\ normif\ b\ {\isacharparenleft}norm\ t{\isacharparenright}\ {\isacharparenleft}norm\ e{\isacharparenright}{\isachardoublequoteclose}%
+\ norm\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}ifex\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ ifex{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}norm\ {\isaliteral{28}{\isacharparenleft}}CIF\ b{\isaliteral{29}{\isacharparenright}}\ \ \ \ {\isaliteral{3D}{\isacharequal}}\ CIF\ b{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}norm\ {\isaliteral{28}{\isacharparenleft}}VIF\ x{\isaliteral{29}{\isacharparenright}}\ \ \ \ {\isaliteral{3D}{\isacharequal}}\ VIF\ x{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}norm\ {\isaliteral{28}{\isacharparenleft}}IF\ b\ t\ e{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ normif\ b\ {\isaliteral{28}{\isacharparenleft}}norm\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}norm\ e{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
Their interplay is tricky; we leave it to you to develop an
@@ -163,7 +163,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ {\isachardoublequoteopen}valif\ {\isacharparenleft}norm\ b{\isacharparenright}\ env\ {\isacharequal}\ valif\ b\ env{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}valif\ {\isaliteral{28}{\isacharparenleft}}norm\ b{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ valif\ b\ env{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -184,8 +184,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}{\isasymforall}t\ e{\isachardot}\ valif\ {\isacharparenleft}normif\ b\ t\ e{\isacharparenright}\ env\ {\isacharequal}\ valif\ {\isacharparenleft}IF\ b\ t\ e{\isacharparenright}\ env{\isachardoublequoteclose}%
+\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}t\ e{\isaliteral{2E}{\isachardot}}\ valif\ {\isaliteral{28}{\isacharparenleft}}normif\ b\ t\ e{\isaliteral{29}{\isacharparenright}}\ env\ {\isaliteral{3D}{\isacharequal}}\ valif\ {\isaliteral{28}{\isacharparenleft}}IF\ b\ t\ e{\isaliteral{29}{\isacharparenright}}\ env{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -215,26 +215,26 @@
\begin{isamarkuptext}%
\noindent
Note that the lemma does not have a name, but is implicitly used in the proof
-of the theorem shown above because of the \isa{{\isacharbrackleft}simp{\isacharbrackright}} attribute.
+of the theorem shown above because of the \isa{{\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}} attribute.
But how can we be sure that \isa{norm} really produces a normal form in
the above sense? We define a function that tests If-expressions for normality:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ normal\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}ifex\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}normal{\isacharparenleft}CIF\ b{\isacharparenright}\ {\isacharequal}\ True{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}normal{\isacharparenleft}VIF\ x{\isacharparenright}\ {\isacharequal}\ True{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}normal{\isacharparenleft}IF\ b\ t\ e{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}normal\ t\ {\isasymand}\ normal\ e\ {\isasymand}\isanewline
-\ \ \ \ \ {\isacharparenleft}case\ b\ of\ CIF\ b\ {\isasymRightarrow}\ True\ {\isacharbar}\ VIF\ x\ {\isasymRightarrow}\ True\ {\isacharbar}\ IF\ x\ y\ z\ {\isasymRightarrow}\ False{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
+\ normal\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}ifex\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}normal{\isaliteral{28}{\isacharparenleft}}CIF\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ True{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}normal{\isaliteral{28}{\isacharparenleft}}VIF\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ True{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}normal{\isaliteral{28}{\isacharparenleft}}IF\ b\ t\ e{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}normal\ t\ {\isaliteral{5C3C616E643E}{\isasymand}}\ normal\ e\ {\isaliteral{5C3C616E643E}{\isasymand}}\isanewline
+\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}case\ b\ of\ CIF\ b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ True\ {\isaliteral{7C}{\isacharbar}}\ VIF\ x\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ True\ {\isaliteral{7C}{\isacharbar}}\ IF\ x\ y\ z\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ False{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
-Now we prove \isa{normal\ {\isacharparenleft}norm\ b{\isacharparenright}}. Of course, this requires a lemma about
+Now we prove \isa{normal\ {\isaliteral{28}{\isacharparenleft}}norm\ b{\isaliteral{29}{\isacharparenright}}}. Of course, this requires a lemma about
normality of \isa{normif}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymforall}t\ e{\isachardot}\ normal{\isacharparenleft}normif\ b\ t\ e{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}normal\ t\ {\isasymand}\ normal\ e{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}t\ e{\isaliteral{2E}{\isachardot}}\ normal{\isaliteral{28}{\isacharparenleft}}normif\ b\ t\ e{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}normal\ t\ {\isaliteral{5C3C616E643E}{\isasymand}}\ normal\ e{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -266,15 +266,15 @@
How do we come up with the required lemmas? Try to prove the main theorems
without them and study carefully what \isa{auto} leaves unproved. This
can provide the clue. The necessity of universal quantification
-(\isa{{\isasymforall}t\ e}) in the two lemmas is explained in
+(\isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}t\ e}) in the two lemmas is explained in
\S\ref{sec:InductionHeuristics}
\begin{exercise}
We strengthen the definition of a \isa{normal} If-expression as follows:
the first argument of all \isa{IF}s must be a variable. Adapt the above
development to this changed requirement. (Hint: you may need to formulate
- some of the goals as implications (\isa{{\isasymlongrightarrow}}) rather than
- equalities (\isa{{\isacharequal}}).)
+ some of the goals as implications (\isa{{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}}) rather than
+ equalities (\isa{{\isaliteral{3D}{\isacharequal}}}).)
\end{exercise}
\index{boolean expressions example|)}%
\end{isamarkuptext}%
--- a/doc-src/TutorialI/Inductive/document/AB.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Inductive/document/AB.tex Mon Nov 08 14:41:11 2010 +0100
@@ -42,14 +42,14 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ alfa\ {\isacharequal}\ a\ {\isacharbar}\ b%
+\ alfa\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{7C}{\isacharbar}}\ b%
\begin{isamarkuptext}%
\noindent
For convenience we include the following easy lemmas as simplification rules:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}x\ {\isasymnoteq}\ a{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}x\ {\isacharequal}\ b{\isacharparenright}\ {\isasymand}\ {\isacharparenleft}x\ {\isasymnoteq}\ b{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}x\ {\isacharequal}\ a{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -57,7 +57,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}case{\isacharunderscore}tac\ x{\isacharcomma}\ auto{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}case{\isaliteral{5F}{\isacharunderscore}}tac\ x{\isaliteral{2C}{\isacharcomma}}\ auto{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -74,21 +74,21 @@
of \isa{S}, \isa{A} and~\isa{B}:%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{inductive{\isacharunderscore}set}\isamarkupfalse%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse%
\isanewline
-\ \ S\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}alfa\ list\ set{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-\ \ A\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}alfa\ list\ set{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-\ \ B\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}alfa\ list\ set{\isachardoublequoteclose}\isanewline
+\ \ S\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}alfa\ list\ set{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+\ \ A\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}alfa\ list\ set{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+\ \ B\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}alfa\ list\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharbrackright}\ {\isasymin}\ S{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}w\ {\isasymin}\ A\ {\isasymLongrightarrow}\ b{\isacharhash}w\ {\isasymin}\ S{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}w\ {\isasymin}\ B\ {\isasymLongrightarrow}\ a{\isacharhash}w\ {\isasymin}\ S{\isachardoublequoteclose}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ S{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}w\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ b{\isaliteral{23}{\isacharhash}}w\ {\isaliteral{5C3C696E3E}{\isasymin}}\ S{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}w\ {\isaliteral{5C3C696E3E}{\isasymin}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a{\isaliteral{23}{\isacharhash}}w\ {\isaliteral{5C3C696E3E}{\isasymin}}\ S{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}w\ {\isasymin}\ S\ \ \ \ \ \ \ \ {\isasymLongrightarrow}\ a{\isacharhash}w\ \ \ {\isasymin}\ A{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}{\isasymlbrakk}\ v{\isasymin}A{\isacharsemicolon}\ w{\isasymin}A\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ b{\isacharhash}v{\isacharat}w\ {\isasymin}\ A{\isachardoublequoteclose}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}w\ {\isaliteral{5C3C696E3E}{\isasymin}}\ S\ \ \ \ \ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a{\isaliteral{23}{\isacharhash}}w\ \ \ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ v{\isaliteral{5C3C696E3E}{\isasymin}}A{\isaliteral{3B}{\isacharsemicolon}}\ w{\isaliteral{5C3C696E3E}{\isasymin}}A\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ b{\isaliteral{23}{\isacharhash}}v{\isaliteral{40}{\isacharat}}w\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}w\ {\isasymin}\ S\ \ \ \ \ \ \ \ \ \ \ \ {\isasymLongrightarrow}\ b{\isacharhash}w\ \ \ {\isasymin}\ B{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}{\isasymlbrakk}\ v\ {\isasymin}\ B{\isacharsemicolon}\ w\ {\isasymin}\ B\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ a{\isacharhash}v{\isacharat}w\ {\isasymin}\ B{\isachardoublequoteclose}%
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}w\ {\isaliteral{5C3C696E3E}{\isasymin}}\ S\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ b{\isaliteral{23}{\isacharhash}}w\ \ \ {\isaliteral{5C3C696E3E}{\isasymin}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ v\ {\isaliteral{5C3C696E3E}{\isasymin}}\ B{\isaliteral{3B}{\isacharsemicolon}}\ w\ {\isaliteral{5C3C696E3E}{\isasymin}}\ B\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a{\isaliteral{23}{\isacharhash}}v{\isaliteral{40}{\isacharat}}w\ {\isaliteral{5C3C696E3E}{\isasymin}}\ B{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
First we show that all words in \isa{S} contain the same number of \isa{a}'s and \isa{b}'s. Since the definition of \isa{S} is by mutual
@@ -97,10 +97,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ correctness{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}{\isacharparenleft}w\ {\isasymin}\ S\ {\isasymlongrightarrow}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}{\isacharparenright}\ \ \ \ \ {\isasymand}\isanewline
-\ \ \ {\isacharparenleft}w\ {\isasymin}\ A\ {\isasymlongrightarrow}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}\ {\isasymand}\isanewline
-\ \ \ {\isacharparenleft}w\ {\isasymin}\ B\ {\isasymlongrightarrow}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}{\isachardoublequoteclose}%
+\ correctness{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}w\ {\isaliteral{5C3C696E3E}{\isasymin}}\ S\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}w{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}a{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}w{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}b{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ \ \ \ \ {\isaliteral{5C3C616E643E}{\isasymand}}\isanewline
+\ \ \ {\isaliteral{28}{\isacharparenleft}}w\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}w{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}a{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}w{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}b{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\isanewline
+\ \ \ {\isaliteral{28}{\isacharparenleft}}w\ {\isaliteral{5C3C696E3E}{\isasymin}}\ B\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}w{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}b{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}w{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}a{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -109,14 +109,14 @@
%
\begin{isamarkuptxt}%
\noindent
-These propositions are expressed with the help of the predefined \isa{filter} function on lists, which has the convenient syntax \isa{{\isacharbrackleft}x{\isasymleftarrow}xs{\isachardot}\ P\ x{\isacharbrackright}}, the list of all elements \isa{x} in \isa{xs} such that \isa{P\ x}
+These propositions are expressed with the help of the predefined \isa{filter} function on lists, which has the convenient syntax \isa{{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}xs{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{5D}{\isacharbrackright}}}, the list of all elements \isa{x} in \isa{xs} such that \isa{P\ x}
holds. Remember that on lists \isa{size} and \isa{length} are synonymous.
The proof itself is by rule induction and afterwards automatic:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ S{\isacharunderscore}A{\isacharunderscore}B{\isachardot}induct{\isacharcomma}\ auto{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ S{\isaliteral{5F}{\isacharunderscore}}A{\isaliteral{5F}{\isacharunderscore}}B{\isaliteral{2E}{\isachardot}}induct{\isaliteral{2C}{\isacharcomma}}\ auto{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -141,13 +141,13 @@
word. We start with 0 and end (at the right end) with 2. Since each move to the
right increases or decreases the difference by 1, we must have passed through
1 on our way from 0 to 2. Formally, we appeal to the following discrete
-intermediate value theorem \isa{nat{\isadigit{0}}{\isacharunderscore}intermed{\isacharunderscore}int{\isacharunderscore}val}
+intermediate value theorem \isa{nat{\isadigit{0}}{\isaliteral{5F}{\isacharunderscore}}intermed{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{5F}{\isacharunderscore}}val}
\begin{isabelle}%
-\ \ \ \ \ {\isasymlbrakk}{\isasymforall}i{\isacharless}n{\isachardot}\ {\isasymbar}f\ {\isacharparenleft}i\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}\ {\isacharminus}\ f\ i{\isasymbar}\ {\isasymle}\ {\isadigit{1}}{\isacharsemicolon}\ f\ {\isadigit{0}}\ {\isasymle}\ k{\isacharsemicolon}\ k\ {\isasymle}\ f\ n{\isasymrbrakk}\isanewline
-\isaindent{\ \ \ \ \ }{\isasymLongrightarrow}\ {\isasymexists}i{\isasymle}n{\isachardot}\ f\ i\ {\isacharequal}\ k%
+\ \ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{3C}{\isacharless}}n{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6261723E}{\isasymbar}}f\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2D}{\isacharminus}}\ f\ i{\isaliteral{5C3C6261723E}{\isasymbar}}\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\ f\ {\isadigit{0}}\ {\isaliteral{5C3C6C653E}{\isasymle}}\ k{\isaliteral{3B}{\isacharsemicolon}}\ k\ {\isaliteral{5C3C6C653E}{\isasymle}}\ f\ n{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ \ \ \ \ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}i{\isaliteral{5C3C6C653E}{\isasymle}}n{\isaliteral{2E}{\isachardot}}\ f\ i\ {\isaliteral{3D}{\isacharequal}}\ k%
\end{isabelle}
-where \isa{f} is of type \isa{nat\ {\isasymRightarrow}\ int}, \isa{int} are the integers,
-\isa{{\isasymbar}{\isachardot}{\isasymbar}} is the absolute value function\footnote{See
+where \isa{f} is of type \isa{nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int}, \isa{int} are the integers,
+\isa{{\isaliteral{5C3C6261723E}{\isasymbar}}{\isaliteral{2E}{\isachardot}}{\isaliteral{5C3C6261723E}{\isasymbar}}} is the absolute value function\footnote{See
Table~\ref{tab:ascii} in the Appendix for the correct \textsc{ascii}
syntax.}, and \isa{{\isadigit{1}}} is the integer 1 (see \S\ref{sec:numbers}).
@@ -160,9 +160,9 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ step{\isadigit{1}}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymforall}i\ {\isacharless}\ size\ w{\isachardot}\isanewline
-\ \ {\isasymbar}{\isacharparenleft}int{\isacharparenleft}size{\isacharbrackleft}x{\isasymleftarrow}take\ {\isacharparenleft}i{\isacharplus}{\isadigit{1}}{\isacharparenright}\ w{\isachardot}\ P\ x{\isacharbrackright}{\isacharparenright}{\isacharminus}int{\isacharparenleft}size{\isacharbrackleft}x{\isasymleftarrow}take\ {\isacharparenleft}i{\isacharplus}{\isadigit{1}}{\isacharparenright}\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharparenright}{\isacharparenright}\isanewline
-\ \ \ {\isacharminus}\ {\isacharparenleft}int{\isacharparenleft}size{\isacharbrackleft}x{\isasymleftarrow}take\ i\ w{\isachardot}\ P\ x{\isacharbrackright}{\isacharparenright}{\isacharminus}int{\isacharparenleft}size{\isacharbrackleft}x{\isasymleftarrow}take\ i\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharparenright}{\isacharparenright}{\isasymbar}\ {\isasymle}\ {\isadigit{1}}{\isachardoublequoteclose}%
+\ step{\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i\ {\isaliteral{3C}{\isacharless}}\ size\ w{\isaliteral{2E}{\isachardot}}\isanewline
+\ \ {\isaliteral{5C3C6261723E}{\isasymbar}}{\isaliteral{28}{\isacharparenleft}}int{\isaliteral{28}{\isacharparenleft}}size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}take\ {\isaliteral{28}{\isacharparenleft}}i{\isaliteral{2B}{\isacharplus}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ w{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2D}{\isacharminus}}int{\isaliteral{28}{\isacharparenleft}}size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}take\ {\isaliteral{28}{\isacharparenleft}}i{\isaliteral{2B}{\isacharplus}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ w{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}P\ x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{28}{\isacharparenleft}}int{\isaliteral{28}{\isacharparenleft}}size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}take\ i\ w{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2D}{\isacharminus}}int{\isaliteral{28}{\isacharparenleft}}size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}take\ i\ w{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}P\ x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C6261723E}{\isasymbar}}\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -172,7 +172,7 @@
\begin{isamarkuptxt}%
\noindent
The lemma is a bit hard to read because of the coercion function
-\isa{int\ {\isacharcolon}{\isacharcolon}\ nat\ {\isasymRightarrow}\ int}. It is required because \isa{size} returns
+\isa{int\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int}. It is required because \isa{size} returns
a natural number, but subtraction on type~\isa{nat} will do the wrong thing.
Function \isa{take} is predefined and \isa{take\ i\ xs} is the prefix of
length \isa{i} of \isa{xs}; below we also need \isa{drop\ i\ xs}, which
@@ -184,9 +184,9 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ w{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ w{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto\ simp\ add{\isacharcolon}\ abs{\isacharunderscore}if\ take{\isacharunderscore}Cons\ split{\isacharcolon}\ nat{\isachardot}split{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}auto\ simp\ add{\isaliteral{3A}{\isacharcolon}}\ abs{\isaliteral{5F}{\isacharunderscore}}if\ take{\isaliteral{5F}{\isacharunderscore}}Cons\ split{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{2E}{\isachardot}}split{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -201,9 +201,9 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ part{\isadigit{1}}{\isacharcolon}\isanewline
-\ {\isachardoublequoteopen}size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharplus}{\isadigit{2}}\ {\isasymLongrightarrow}\isanewline
-\ \ {\isasymexists}i{\isasymle}size\ w{\isachardot}\ size{\isacharbrackleft}x{\isasymleftarrow}take\ i\ w{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}take\ i\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharplus}{\isadigit{1}}{\isachardoublequoteclose}%
+\ part{\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}w{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}w{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}P\ x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2B}{\isacharplus}}{\isadigit{2}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\isanewline
+\ \ {\isaliteral{5C3C6578697374733E}{\isasymexists}}i{\isaliteral{5C3C6C653E}{\isasymle}}size\ w{\isaliteral{2E}{\isachardot}}\ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}take\ i\ w{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}take\ i\ w{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}P\ x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2B}{\isacharplus}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -218,7 +218,7 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}insert\ nat{\isadigit{0}}{\isacharunderscore}intermed{\isacharunderscore}int{\isacharunderscore}val{\isacharbrackleft}OF\ step{\isadigit{1}}{\isacharcomma}\ of\ {\isachardoublequoteopen}P{\isachardoublequoteclose}\ {\isachardoublequoteopen}w{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isadigit{1}}{\isachardoublequoteclose}{\isacharbrackright}{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}insert\ nat{\isadigit{0}}{\isaliteral{5F}{\isacharunderscore}}intermed{\isaliteral{5F}{\isacharunderscore}}int{\isaliteral{5F}{\isacharunderscore}}val{\isaliteral{5B}{\isacharbrackleft}}OF\ step{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ of\ {\isaliteral{22}{\isachardoublequoteopen}}P{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}w{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{by}\isamarkupfalse%
\ force%
\endisatagproof
@@ -236,11 +236,11 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ part{\isadigit{2}}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}{\isasymlbrakk}size{\isacharbrackleft}x{\isasymleftarrow}take\ i\ w\ {\isacharat}\ drop\ i\ w{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharequal}\isanewline
-\ \ \ \ size{\isacharbrackleft}x{\isasymleftarrow}take\ i\ w\ {\isacharat}\ drop\ i\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharplus}{\isadigit{2}}{\isacharsemicolon}\isanewline
-\ \ \ \ size{\isacharbrackleft}x{\isasymleftarrow}take\ i\ w{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}take\ i\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharplus}{\isadigit{1}}{\isasymrbrakk}\isanewline
-\ \ \ {\isasymLongrightarrow}\ size{\isacharbrackleft}x{\isasymleftarrow}drop\ i\ w{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}drop\ i\ w{\isachardot}\ {\isasymnot}P\ x{\isacharbrackright}{\isacharplus}{\isadigit{1}}{\isachardoublequoteclose}\isanewline
+\ part{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}take\ i\ w\ {\isaliteral{40}{\isacharat}}\ drop\ i\ w{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}take\ i\ w\ {\isaliteral{40}{\isacharat}}\ drop\ i\ w{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}P\ x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2B}{\isacharplus}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}take\ i\ w{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}take\ i\ w{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}P\ x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2B}{\isacharplus}}{\isadigit{1}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}drop\ i\ w{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}drop\ i\ w{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}P\ x{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2B}{\isacharplus}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -248,7 +248,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-{\isacharparenleft}simp\ del{\isacharcolon}\ append{\isacharunderscore}take{\isacharunderscore}drop{\isacharunderscore}id{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp\ del{\isaliteral{3A}{\isacharcolon}}\ append{\isaliteral{5F}{\isacharunderscore}}take{\isaliteral{5F}{\isacharunderscore}}drop{\isaliteral{5F}{\isacharunderscore}}id{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -260,12 +260,12 @@
\noindent
In the proof we have disabled the normally useful lemma
\begin{isabelle}
-\isa{take\ n\ xs\ {\isacharat}\ drop\ n\ xs\ {\isacharequal}\ xs}
+\isa{take\ n\ xs\ {\isaliteral{40}{\isacharat}}\ drop\ n\ xs\ {\isaliteral{3D}{\isacharequal}}\ xs}
\rulename{append_take_drop_id}
\end{isabelle}
to allow the simplifier to apply the following lemma instead:
\begin{isabelle}%
-\ \ \ \ \ {\isacharbrackleft}x{\isasymin}xs{\isacharat}ys{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}x{\isasymin}xs{\isachardot}\ P\ x{\isacharbrackright}\ {\isacharat}\ {\isacharbrackleft}x{\isasymin}ys{\isachardot}\ P\ x{\isacharbrackright}%
+\ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C696E3E}{\isasymin}}xs{\isaliteral{40}{\isacharat}}ys{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C696E3E}{\isasymin}}xs{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C696E3E}{\isasymin}}ys{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{5D}{\isacharbrackright}}%
\end{isabelle}
To dispose of trivial cases automatically, the rules of the inductive
@@ -273,7 +273,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{declare}\isamarkupfalse%
-\ S{\isacharunderscore}A{\isacharunderscore}B{\isachardot}intros{\isacharbrackleft}simp{\isacharbrackright}%
+\ S{\isaliteral{5F}{\isacharunderscore}}A{\isaliteral{5F}{\isacharunderscore}}B{\isaliteral{2E}{\isachardot}}intros{\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}%
\begin{isamarkuptext}%
\noindent
This could have been done earlier but was not necessary so far.
@@ -284,10 +284,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ completeness{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}{\isacharparenleft}size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}\ \ \ \ \ {\isasymlongrightarrow}\ w\ {\isasymin}\ S{\isacharparenright}\ {\isasymand}\isanewline
-\ \ \ {\isacharparenleft}size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}\ {\isasymlongrightarrow}\ w\ {\isasymin}\ A{\isacharparenright}\ {\isasymand}\isanewline
-\ \ \ {\isacharparenleft}size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}b{\isacharbrackright}\ {\isacharequal}\ size{\isacharbrackleft}x{\isasymleftarrow}w{\isachardot}\ x{\isacharequal}a{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}\ {\isasymlongrightarrow}\ w\ {\isasymin}\ B{\isacharparenright}{\isachardoublequoteclose}%
+\ completeness{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}w{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}a{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}w{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}b{\isaliteral{5D}{\isacharbrackright}}\ \ \ \ \ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ w\ {\isaliteral{5C3C696E3E}{\isasymin}}\ S{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\isanewline
+\ \ \ {\isaliteral{28}{\isacharparenleft}}size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}w{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}a{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}w{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}b{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ w\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\isanewline
+\ \ \ {\isaliteral{28}{\isacharparenleft}}size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}w{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}b{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ size{\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}w{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}a{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ w\ {\isaliteral{5C3C696E3E}{\isasymin}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -299,16 +299,16 @@
The proof is by induction on \isa{w}. Structural induction would fail here
because, as we can see from the grammar, we need to make bigger steps than
merely appending a single letter at the front. Hence we induct on the length
-of \isa{w}, using the induction rule \isa{length{\isacharunderscore}induct}:%
+of \isa{w}, using the induction rule \isa{length{\isaliteral{5F}{\isacharunderscore}}induct}:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ w\ rule{\isacharcolon}\ length{\isacharunderscore}induct{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ w\ rule{\isaliteral{3A}{\isacharcolon}}\ length{\isaliteral{5F}{\isacharunderscore}}induct{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rename{\isacharunderscore}tac\ w{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}rename{\isaliteral{5F}{\isacharunderscore}}tac\ w{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
-The \isa{rule} parameter tells \isa{induct{\isacharunderscore}tac} explicitly which induction
+The \isa{rule} parameter tells \isa{induct{\isaliteral{5F}{\isacharunderscore}}tac} explicitly which induction
rule to use. For details see \S\ref{sec:complete-ind} below.
In this case the result is that we may assume the lemma already
holds for all words shorter than \isa{w}. Because the induction step renames
@@ -319,18 +319,18 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}case{\isacharunderscore}tac\ w{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}case{\isaliteral{5F}{\isacharunderscore}}tac\ w{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp{\isacharunderscore}all{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
Simplification disposes of the base case and leaves only a conjunction
of two step cases to be proved:
-if \isa{w\ {\isacharequal}\ a\ {\isacharhash}\ v} and \begin{isabelle}%
-\ \ \ \ \ length\ {\isacharparenleft}if\ x\ {\isacharequal}\ a\ then\ {\isacharbrackleft}x\ {\isasymin}\ v{\isacharbrackright}\ else\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\isanewline
-\isaindent{\ \ \ \ \ }length\ {\isacharparenleft}if\ x\ {\isacharequal}\ b\ then\ {\isacharbrackleft}x\ {\isasymin}\ v{\isacharbrackright}\ else\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharplus}\ {\isadigit{2}}%
+if \isa{w\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{23}{\isacharhash}}\ v} and \begin{isabelle}%
+\ \ \ \ \ length\ {\isaliteral{28}{\isacharparenleft}}if\ x\ {\isaliteral{3D}{\isacharequal}}\ a\ then\ {\isaliteral{5B}{\isacharbrackleft}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ v{\isaliteral{5D}{\isacharbrackright}}\ else\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\isaindent{\ \ \ \ \ }length\ {\isaliteral{28}{\isacharparenleft}}if\ x\ {\isaliteral{3D}{\isacharequal}}\ b\ then\ {\isaliteral{5B}{\isacharbrackleft}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ v{\isaliteral{5D}{\isacharbrackright}}\ else\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{2}}%
\end{isabelle} then
-\isa{b\ {\isacharhash}\ v\ {\isasymin}\ A}, and similarly for \isa{w\ {\isacharequal}\ b\ {\isacharhash}\ v}.
+\isa{b\ {\isaliteral{23}{\isacharhash}}\ v\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A}, and similarly for \isa{w\ {\isaliteral{3D}{\isacharequal}}\ b\ {\isaliteral{23}{\isacharhash}}\ v}.
We only consider the first case in detail.
After breaking the conjunction up into two cases, we can apply
@@ -338,77 +338,77 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ conjI{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule\ conjI{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}clarify{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}clarify{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}frule\ part{\isadigit{1}}{\isacharbrackleft}of\ {\isachardoublequoteopen}{\isasymlambda}x{\isachardot}\ x{\isacharequal}a{\isachardoublequoteclose}{\isacharcomma}\ simplified{\isacharbrackright}{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}frule\ part{\isadigit{1}}{\isaliteral{5B}{\isacharbrackleft}}of\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}a{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{2C}{\isacharcomma}}\ simplified{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}clarify{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}clarify{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
-This yields an index \isa{i\ {\isasymle}\ length\ v} such that
+This yields an index \isa{i\ {\isaliteral{5C3C6C653E}{\isasymle}}\ length\ v} such that
\begin{isabelle}%
-\ \ \ \ \ length\ {\isacharbrackleft}x{\isasymleftarrow}take\ i\ v\ {\isachardot}\ x\ {\isacharequal}\ a{\isacharbrackright}\ {\isacharequal}\ length\ {\isacharbrackleft}x{\isasymleftarrow}take\ i\ v\ {\isachardot}\ x\ {\isacharequal}\ b{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}%
+\ \ \ \ \ length\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}take\ i\ v\ {\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ length\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}take\ i\ v\ {\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}%
\end{isabelle}
With the help of \isa{part{\isadigit{2}}} it follows that
\begin{isabelle}%
-\ \ \ \ \ length\ {\isacharbrackleft}x{\isasymleftarrow}drop\ i\ v\ {\isachardot}\ x\ {\isacharequal}\ a{\isacharbrackright}\ {\isacharequal}\ length\ {\isacharbrackleft}x{\isasymleftarrow}drop\ i\ v\ {\isachardot}\ x\ {\isacharequal}\ b{\isacharbrackright}\ {\isacharplus}\ {\isadigit{1}}%
+\ \ \ \ \ length\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}drop\ i\ v\ {\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ length\ {\isaliteral{5B}{\isacharbrackleft}}x{\isaliteral{5C3C6C6566746172726F773E}{\isasymleftarrow}}drop\ i\ v\ {\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}drule\ part{\isadigit{2}}{\isacharbrackleft}of\ {\isachardoublequoteopen}{\isasymlambda}x{\isachardot}\ x{\isacharequal}a{\isachardoublequoteclose}{\isacharcomma}\ simplified{\isacharbrackright}{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}drule\ part{\isadigit{2}}{\isaliteral{5B}{\isacharbrackleft}}of\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}a{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{2C}{\isacharcomma}}\ simplified{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}assumption{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}assumption{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
-Now it is time to decompose \isa{v} in the conclusion \isa{b\ {\isacharhash}\ v\ {\isasymin}\ A}
-into \isa{take\ i\ v\ {\isacharat}\ drop\ i\ v},%
+Now it is time to decompose \isa{v} in the conclusion \isa{b\ {\isaliteral{23}{\isacharhash}}\ v\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A}
+into \isa{take\ i\ v\ {\isaliteral{40}{\isacharat}}\ drop\ i\ v},%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule{\isacharunderscore}tac\ n{\isadigit{1}}{\isacharequal}i\ \isakeyword{and}\ t{\isacharequal}v\ \isakeyword{in}\ subst{\isacharbrackleft}OF\ append{\isacharunderscore}take{\isacharunderscore}drop{\isacharunderscore}id{\isacharbrackright}{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}rule{\isaliteral{5F}{\isacharunderscore}}tac\ n{\isadigit{1}}{\isaliteral{3D}{\isacharequal}}i\ \isakeyword{and}\ t{\isaliteral{3D}{\isacharequal}}v\ \isakeyword{in}\ subst{\isaliteral{5B}{\isacharbrackleft}}OF\ append{\isaliteral{5F}{\isacharunderscore}}take{\isaliteral{5F}{\isacharunderscore}}drop{\isaliteral{5F}{\isacharunderscore}}id{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
(the variables \isa{n{\isadigit{1}}} and \isa{t} are the result of composing the
-theorems \isa{subst} and \isa{append{\isacharunderscore}take{\isacharunderscore}drop{\isacharunderscore}id})
+theorems \isa{subst} and \isa{append{\isaliteral{5F}{\isacharunderscore}}take{\isaliteral{5F}{\isacharunderscore}}drop{\isaliteral{5F}{\isacharunderscore}}id})
after which the appropriate rule of the grammar reduces the goal
-to the two subgoals \isa{take\ i\ v\ {\isasymin}\ A} and \isa{drop\ i\ v\ {\isasymin}\ A}:%
+to the two subgoals \isa{take\ i\ v\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A} and \isa{drop\ i\ v\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A}:%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ S{\isacharunderscore}A{\isacharunderscore}B{\isachardot}intros{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}rule\ S{\isaliteral{5F}{\isacharunderscore}}A{\isaliteral{5F}{\isacharunderscore}}B{\isaliteral{2E}{\isachardot}}intros{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
Both subgoals follow from the induction hypothesis because both \isa{take\ i\ v} and \isa{drop\ i\ v} are shorter than \isa{w}:%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}force\ simp\ add{\isacharcolon}\ min{\isacharunderscore}less{\isacharunderscore}iff{\isacharunderscore}disj{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}force\ simp\ add{\isaliteral{3A}{\isacharcolon}}\ min{\isaliteral{5F}{\isacharunderscore}}less{\isaliteral{5F}{\isacharunderscore}}iff{\isaliteral{5F}{\isacharunderscore}}disj{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}force\ split\ add{\isacharcolon}\ nat{\isacharunderscore}diff{\isacharunderscore}split{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}force\ split\ add{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{5F}{\isacharunderscore}}diff{\isaliteral{5F}{\isacharunderscore}}split{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
-The case \isa{w\ {\isacharequal}\ b\ {\isacharhash}\ v} is proved analogously:%
+The case \isa{w\ {\isaliteral{3D}{\isacharequal}}\ b\ {\isaliteral{23}{\isacharhash}}\ v} is proved analogously:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}clarify{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}clarify{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}frule\ part{\isadigit{1}}{\isacharbrackleft}of\ {\isachardoublequoteopen}{\isasymlambda}x{\isachardot}\ x{\isacharequal}b{\isachardoublequoteclose}{\isacharcomma}\ simplified{\isacharbrackright}{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}frule\ part{\isadigit{1}}{\isaliteral{5B}{\isacharbrackleft}}of\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}b{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{2C}{\isacharcomma}}\ simplified{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}clarify{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}clarify{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}drule\ part{\isadigit{2}}{\isacharbrackleft}of\ {\isachardoublequoteopen}{\isasymlambda}x{\isachardot}\ x{\isacharequal}b{\isachardoublequoteclose}{\isacharcomma}\ simplified{\isacharbrackright}{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}drule\ part{\isadigit{2}}{\isaliteral{5B}{\isacharbrackleft}}of\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}b{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{2C}{\isacharcomma}}\ simplified{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}assumption{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}assumption{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule{\isacharunderscore}tac\ n{\isadigit{1}}{\isacharequal}i\ \isakeyword{and}\ t{\isacharequal}v\ \isakeyword{in}\ subst{\isacharbrackleft}OF\ append{\isacharunderscore}take{\isacharunderscore}drop{\isacharunderscore}id{\isacharbrackright}{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule{\isaliteral{5F}{\isacharunderscore}}tac\ n{\isadigit{1}}{\isaliteral{3D}{\isacharequal}}i\ \isakeyword{and}\ t{\isaliteral{3D}{\isacharequal}}v\ \isakeyword{in}\ subst{\isaliteral{5B}{\isacharbrackleft}}OF\ append{\isaliteral{5F}{\isacharunderscore}}take{\isaliteral{5F}{\isacharunderscore}}drop{\isaliteral{5F}{\isacharunderscore}}id{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ S{\isacharunderscore}A{\isacharunderscore}B{\isachardot}intros{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule\ S{\isaliteral{5F}{\isacharunderscore}}A{\isaliteral{5F}{\isacharunderscore}}B{\isaliteral{2E}{\isachardot}}intros{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}force\ simp\ add{\isacharcolon}\ min{\isacharunderscore}less{\isacharunderscore}iff{\isacharunderscore}disj{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}force\ simp\ add{\isaliteral{3A}{\isacharcolon}}\ min{\isaliteral{5F}{\isacharunderscore}}less{\isaliteral{5F}{\isacharunderscore}}iff{\isaliteral{5F}{\isacharunderscore}}disj{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{by}\isamarkupfalse%
-{\isacharparenleft}force\ simp\ add{\isacharcolon}\ min{\isacharunderscore}less{\isacharunderscore}iff{\isacharunderscore}disj\ split\ add{\isacharcolon}\ nat{\isacharunderscore}diff{\isacharunderscore}split{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}force\ simp\ add{\isaliteral{3A}{\isacharcolon}}\ min{\isaliteral{5F}{\isacharunderscore}}less{\isaliteral{5F}{\isacharunderscore}}iff{\isaliteral{5F}{\isacharunderscore}}disj\ split\ add{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{5F}{\isacharunderscore}}diff{\isaliteral{5F}{\isacharunderscore}}split{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -429,7 +429,7 @@
length of a word. This deprives them of the beauty of rule induction,
and in the easy direction (correctness) their reasoning is more
detailed than our \isa{auto}. For the hard part (completeness), they
-consider just one of the cases that our \isa{simp{\isacharunderscore}all} disposes of
+consider just one of the cases that our \isa{simp{\isaliteral{5F}{\isacharunderscore}}all} disposes of
automatically. Then they conclude the proof by saying about the
remaining cases: ``We do this in a manner similar to our method of
proof for part (1); this part is left to the reader''. But this is
--- a/doc-src/TutorialI/Inductive/document/Advanced.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Inductive/document/Advanced.tex Mon Nov 08 14:41:11 2010 +0100
@@ -42,7 +42,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ {\isacharprime}f\ gterm\ {\isacharequal}\ Apply\ {\isacharprime}f\ {\isachardoublequoteopen}{\isacharprime}f\ gterm\ list{\isachardoublequoteclose}%
+\ {\isaliteral{27}{\isacharprime}}f\ gterm\ {\isaliteral{3D}{\isacharequal}}\ Apply\ {\isaliteral{27}{\isacharprime}}f\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}f\ gterm\ list{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
To try it out, we declare a datatype of some integer operations:
integer constants, the unary minus operator and the addition
@@ -50,16 +50,16 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ integer{\isacharunderscore}op\ {\isacharequal}\ Number\ int\ {\isacharbar}\ UnaryMinus\ {\isacharbar}\ Plus%
+\ integer{\isaliteral{5F}{\isacharunderscore}}op\ {\isaliteral{3D}{\isacharequal}}\ Number\ int\ {\isaliteral{7C}{\isacharbar}}\ UnaryMinus\ {\isaliteral{7C}{\isacharbar}}\ Plus%
\begin{isamarkuptext}%
-Now the type \isa{integer{\isacharunderscore}op\ gterm} denotes the ground
+Now the type \isa{integer{\isaliteral{5F}{\isacharunderscore}}op\ gterm} denotes the ground
terms built over those symbols.
The type constructor \isa{gterm} can be generalized to a function
over sets. It returns
the set of ground terms that can be formed over a set \isa{F} of function symbols. For
example, we could consider the set of ground terms formed from the finite
-set \isa{{\isacharbraceleft}Number\ {\isadigit{2}}{\isacharcomma}\ UnaryMinus{\isacharcomma}\ Plus{\isacharbraceright}}.
+set \isa{{\isaliteral{7B}{\isacharbraceleft}}Number\ {\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ UnaryMinus{\isaliteral{2C}{\isacharcomma}}\ Plus{\isaliteral{7D}{\isacharbraceright}}}.
This concept is inductive. If we have a list \isa{args} of ground terms
over~\isa{F} and a function symbol \isa{f} in \isa{F}, then we
@@ -74,13 +74,13 @@
list.%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{inductive{\isacharunderscore}set}\isamarkupfalse%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse%
\isanewline
-\ \ gterms\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}f\ set\ {\isasymRightarrow}\ {\isacharprime}f\ gterm\ set{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{for}\ F\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}f\ set{\isachardoublequoteclose}\isanewline
+\ \ gterms\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}f\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}f\ gterm\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{for}\ F\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}f\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-step{\isacharbrackleft}intro{\isacharbang}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymlbrakk}{\isasymforall}t\ {\isasymin}\ set\ args{\isachardot}\ t\ {\isasymin}\ gterms\ F{\isacharsemicolon}\ \ f\ {\isasymin}\ F{\isasymrbrakk}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isasymLongrightarrow}\ {\isacharparenleft}Apply\ f\ args{\isacharparenright}\ {\isasymin}\ gterms\ F{\isachardoublequoteclose}%
+step{\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ set\ args{\isaliteral{2E}{\isachardot}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ F{\isaliteral{3B}{\isacharsemicolon}}\ \ f\ {\isaliteral{5C3C696E3E}{\isasymin}}\ F{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}Apply\ f\ args{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ F{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
To demonstrate a proof from this definition, let us
show that the function \isa{gterms}
@@ -88,7 +88,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ gterms{\isacharunderscore}mono{\isacharcolon}\ {\isachardoublequoteopen}F{\isasymsubseteq}G\ {\isasymLongrightarrow}\ gterms\ F\ {\isasymsubseteq}\ gterms\ G{\isachardoublequoteclose}\isanewline
+\ gterms{\isaliteral{5F}{\isacharunderscore}}mono{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}F{\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}G\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ gterms\ F\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ gterms\ G{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -98,7 +98,7 @@
\isacommand{apply}\isamarkupfalse%
\ clarify\isanewline
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}erule\ gterms{\isachardot}induct{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}erule\ gterms{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
\ blast\isanewline
\isacommand{done}\isamarkupfalse%
@@ -124,9 +124,9 @@
\isa{gterms\ F}. (We could have used \isa{intro\ subsetI}.) We then
apply rule induction. Here is the resulting subgoal:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ args\ f{\isachardot}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymlbrakk}F\ {\isasymsubseteq}\ G{\isacharsemicolon}\ {\isasymforall}t{\isasymin}set\ args{\isachardot}\ t\ {\isasymin}\ gterms\ F\ {\isasymand}\ t\ {\isasymin}\ gterms\ G{\isacharsemicolon}\ f\ {\isasymin}\ F{\isasymrbrakk}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymLongrightarrow}\ Apply\ f\ args\ {\isasymin}\ gterms\ G%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\ args\ f{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}F\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ G{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}t{\isaliteral{5C3C696E3E}{\isasymin}}set\ args{\isaliteral{2E}{\isachardot}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ F\ {\isaliteral{5C3C616E643E}{\isasymand}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ G{\isaliteral{3B}{\isacharsemicolon}}\ f\ {\isaliteral{5C3C696E3E}{\isasymin}}\ F{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Apply\ f\ args\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ G%
\end{isabelle}
The assumptions state that \isa{f} belongs
to~\isa{F}, which is included in~\isa{G}, and that every element of the list \isa{args} is
@@ -146,8 +146,8 @@
Why do we call this function \isa{gterms} instead
of \isa{gterm}? A constant may have the same name as a type. However,
name clashes could arise in the theorems that Isabelle generates.
-Our choice of names keeps \isa{gterms{\isachardot}induct} separate from
-\isa{gterm{\isachardot}induct}.
+Our choice of names keeps \isa{gterms{\isaliteral{2E}{\isachardot}}induct} separate from
+\isa{gterm{\isaliteral{2E}{\isachardot}}induct}.
\end{warn}
Call a term \textbf{well-formed} if each symbol occurring in it is applied
@@ -162,14 +162,14 @@
term.%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{inductive{\isacharunderscore}set}\isamarkupfalse%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse%
\isanewline
-\ \ well{\isacharunderscore}formed{\isacharunderscore}gterm\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}f\ {\isasymRightarrow}\ nat{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}f\ gterm\ set{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{for}\ arity\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}f\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\isanewline
+\ \ well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}f\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}f\ gterm\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{for}\ arity\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}f\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-step{\isacharbrackleft}intro{\isacharbang}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymlbrakk}{\isasymforall}t\ {\isasymin}\ set\ args{\isachardot}\ t\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity{\isacharsemicolon}\ \ \isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ length\ args\ {\isacharequal}\ arity\ f{\isasymrbrakk}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isasymLongrightarrow}\ {\isacharparenleft}Apply\ f\ args{\isacharparenright}\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity{\isachardoublequoteclose}%
+step{\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ set\ args{\isaliteral{2E}{\isachardot}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm\ arity{\isaliteral{3B}{\isacharsemicolon}}\ \ \isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ length\ args\ {\isaliteral{3D}{\isacharequal}}\ arity\ f{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}Apply\ f\ args{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm\ arity{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
The inductive definition neatly captures the reasoning above.
The universal quantification over the
@@ -200,22 +200,22 @@
direct, if more obscure, than using a universal quantifier.%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{inductive{\isacharunderscore}set}\isamarkupfalse%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse%
\isanewline
-\ \ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}f\ {\isasymRightarrow}\ nat{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}f\ gterm\ set{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{for}\ arity\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}f\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\isanewline
+\ \ well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}f\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}f\ gterm\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{for}\ arity\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}f\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-step{\isacharbrackleft}intro{\isacharbang}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymlbrakk}args\ {\isasymin}\ lists\ {\isacharparenleft}well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity{\isacharparenright}{\isacharsemicolon}\ \ \isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ length\ args\ {\isacharequal}\ arity\ f{\isasymrbrakk}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isasymLongrightarrow}\ {\isacharparenleft}Apply\ f\ args{\isacharparenright}\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity{\isachardoublequoteclose}\isanewline
-\isakeyword{monos}\ lists{\isacharunderscore}mono%
+step{\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}args\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lists\ {\isaliteral{28}{\isacharparenleft}}well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm{\isaliteral{27}{\isacharprime}}\ arity{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ length\ args\ {\isaliteral{3D}{\isacharequal}}\ arity\ f{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}Apply\ f\ args{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm{\isaliteral{27}{\isacharprime}}\ arity{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\isakeyword{monos}\ lists{\isaliteral{5F}{\isacharunderscore}}mono%
\begin{isamarkuptext}%
-We cite the theorem \isa{lists{\isacharunderscore}mono} to justify
+We cite the theorem \isa{lists{\isaliteral{5F}{\isacharunderscore}}mono} to justify
using the function \isa{lists}.%
\footnote{This particular theorem is installed by default already, but we
include the \isakeyword{monos} declaration in order to illustrate its syntax.}
\begin{isabelle}%
-A\ {\isasymsubseteq}\ B\ {\isasymLongrightarrow}\ lists\ A\ {\isasymsubseteq}\ lists\ B\rulename{lists{\isacharunderscore}mono}%
+A\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ B\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ lists\ A\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ lists\ B\rulename{lists{\isaliteral{5F}{\isacharunderscore}}mono}%
\end{isabelle}
Why must the function be monotone? An inductive definition describes
an iterative construction: each element of the set is constructed by a
@@ -223,8 +223,8 @@
elements of \isa{even} are constructed by finitely many applications of
the rules
\begin{isabelle}%
-{\isadigit{0}}\ {\isasymin}\ even\isasep\isanewline%
-n\ {\isasymin}\ even\ {\isasymLongrightarrow}\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isasymin}\ even%
+{\isadigit{0}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\isasep\isanewline%
+n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even%
\end{isabelle}
All references to a set in its
inductive definition must be positive. Applications of an
@@ -232,8 +232,8 @@
construction process to converge.
The following pair of rules do not constitute an inductive definition:
\begin{trivlist}
-\item \isa{{\isadigit{0}}\ {\isasymin}\ even}
-\item \isa{n\ {\isasymnotin}\ even\ {\isasymLongrightarrow}\ Suc\ n\ {\isasymin}\ even}
+\item \isa{{\isadigit{0}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even}
+\item \isa{n\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ even\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Suc\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even}
\end{trivlist}
Showing that 4 is even using these rules requires showing that 3 is not
even. It is far from trivial to show that this set of rules
@@ -242,7 +242,7 @@
Even with its use of the function \isa{lists}, the premise of our
introduction rule is positive:
\begin{isabelle}%
-args\ {\isasymin}\ lists\ {\isacharparenleft}well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity{\isacharparenright}%
+args\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lists\ {\isaliteral{28}{\isacharparenleft}}well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm{\isaliteral{27}{\isacharprime}}\ arity{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
To apply the rule we construct a list \isa{args} of previously
constructed well-formed terms. We obtain a
@@ -265,7 +265,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity\ {\isasymsubseteq}\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm\ arity\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm{\isaliteral{27}{\isacharprime}}\ arity{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -275,7 +275,7 @@
\isacommand{apply}\isamarkupfalse%
\ clarify\isanewline
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}erule\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isachardot}induct{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}erule\ well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
\ auto\isanewline
\isacommand{done}\isamarkupfalse%
@@ -295,14 +295,14 @@
%
\begin{isamarkuptxt}%
The \isa{clarify} method gives
-us an element of \isa{well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity} on which to perform
+us an element of \isa{well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm\ arity} on which to perform
induction. The resulting subgoal can be proved automatically:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ args\ f{\isachardot}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymlbrakk}{\isasymforall}t{\isasymin}set\ args{\isachardot}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ {\isasymlbrakk}\ \ \ }t\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity\ {\isasymand}\ t\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity{\isacharsemicolon}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ \ }length\ args\ {\isacharequal}\ arity\ f{\isasymrbrakk}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymLongrightarrow}\ Apply\ f\ args\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\ args\ f{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}t{\isaliteral{5C3C696E3E}{\isasymin}}set\ args{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ \ \ }t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm\ arity\ {\isaliteral{5C3C616E643E}{\isasymand}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm{\isaliteral{27}{\isacharprime}}\ arity{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ \ }length\ args\ {\isaliteral{3D}{\isacharequal}}\ arity\ f{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Apply\ f\ args\ {\isaliteral{5C3C696E3E}{\isasymin}}\ well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm{\isaliteral{27}{\isacharprime}}\ arity%
\end{isabelle}
This proof resembles the one given in
{\S}\ref{sec:gterm-datatype} above, especially in the form of the
@@ -317,7 +317,7 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity\ {\isasymsubseteq}\ well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm{\isaliteral{27}{\isacharprime}}\ arity\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm\ arity{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -327,7 +327,7 @@
\isacommand{apply}\isamarkupfalse%
\ clarify\isanewline
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}erule\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}{\isachardot}induct{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}erule\ well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm{\isaliteral{27}{\isacharprime}}{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
\ auto\isanewline
\isacommand{done}\isamarkupfalse%
@@ -349,28 +349,28 @@
The proof script is virtually identical,
but the subgoal after applying induction may be surprising:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ args\ f{\isachardot}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymlbrakk}args\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ {\isasymlbrakk}}{\isasymin}\ lists\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ {\isasymlbrakk}{\isasymin}\ \ }{\isacharparenleft}well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity\ {\isasyminter}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ {\isasymlbrakk}{\isasymin}\ \ {\isacharparenleft}}{\isacharbraceleft}a{\isachardot}\ a\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity{\isacharbraceright}{\isacharparenright}{\isacharsemicolon}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ \ }length\ args\ {\isacharequal}\ arity\ f{\isasymrbrakk}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymLongrightarrow}\ Apply\ f\ args\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\ args\ f{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}args\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}}{\isaliteral{5C3C696E3E}{\isasymin}}\ lists\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C696E3E}{\isasymin}}\ \ }{\isaliteral{28}{\isacharparenleft}}well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm{\isaliteral{27}{\isacharprime}}\ arity\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C696E3E}{\isasymin}}\ \ {\isaliteral{28}{\isacharparenleft}}}{\isaliteral{7B}{\isacharbraceleft}}a{\isaliteral{2E}{\isachardot}}\ a\ {\isaliteral{5C3C696E3E}{\isasymin}}\ well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm\ arity{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ \ }length\ args\ {\isaliteral{3D}{\isacharequal}}\ arity\ f{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Apply\ f\ args\ {\isaliteral{5C3C696E3E}{\isasymin}}\ well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm\ arity%
\end{isabelle}
The induction hypothesis contains an application of \isa{lists}. Using a
monotone function in the inductive definition always has this effect. The
subgoal may look uninviting, but fortunately
\isa{lists} distributes over intersection:
\begin{isabelle}%
-listsp\ {\isacharparenleft}{\isacharparenleft}{\isasymlambda}x{\isachardot}\ x\ {\isasymin}\ A{\isacharparenright}\ {\isasyminter}\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ x\ {\isasymin}\ B{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ x\ {\isasymin}\ lists\ A{\isacharparenright}\ {\isasyminter}\ {\isacharparenleft}{\isasymlambda}x{\isachardot}\ x\ {\isasymin}\ lists\ B{\isacharparenright}\rulename{lists{\isacharunderscore}Int{\isacharunderscore}eq}%
+listsp\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lists\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lists\ B{\isaliteral{29}{\isacharparenright}}\rulename{lists{\isaliteral{5F}{\isacharunderscore}}Int{\isaliteral{5F}{\isacharunderscore}}eq}%
\end{isabelle}
Thanks to this default simplification rule, the induction hypothesis
is quickly replaced by its two parts:
\begin{trivlist}
-\item \isa{args\ {\isasymin}\ lists\ {\isacharparenleft}well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity{\isacharparenright}}
-\item \isa{args\ {\isasymin}\ lists\ {\isacharparenleft}well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity{\isacharparenright}}
+\item \isa{args\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lists\ {\isaliteral{28}{\isacharparenleft}}well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm{\isaliteral{27}{\isacharprime}}\ arity{\isaliteral{29}{\isacharparenright}}}
+\item \isa{args\ {\isaliteral{5C3C696E3E}{\isasymin}}\ lists\ {\isaliteral{28}{\isacharparenleft}}well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm\ arity{\isaliteral{29}{\isacharparenright}}}
\end{trivlist}
-Invoking the rule \isa{well{\isacharunderscore}formed{\isacharunderscore}gterm{\isachardot}step} completes the proof. The
+Invoking the rule \isa{well{\isaliteral{5F}{\isacharunderscore}}formed{\isaliteral{5F}{\isacharunderscore}}gterm{\isaliteral{2E}{\isachardot}}step} completes the proof. The
call to \isa{auto} does all this work.
This example is typical of how monotone functions
@@ -378,7 +378,7 @@
distribute over intersection. Monotonicity implies one direction of
this set equality; we have this theorem:
\begin{isabelle}%
-mono\ f\ {\isasymLongrightarrow}\ f\ {\isacharparenleft}A\ {\isasyminter}\ B{\isacharparenright}\ {\isasymsubseteq}\ f\ A\ {\isasyminter}\ f\ B\rulename{mono{\isacharunderscore}Int}%
+mono\ f\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ f\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ f\ A\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ f\ B\rulename{mono{\isaliteral{5F}{\isacharunderscore}}Int}%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
@@ -397,16 +397,16 @@
\begin{isamarkuptext}%
\index{rule inversion|(}%
Does \isa{gterms} distribute over intersection? We have proved that this
-function is monotone, so \isa{mono{\isacharunderscore}Int} gives one of the inclusions. The
+function is monotone, so \isa{mono{\isaliteral{5F}{\isacharunderscore}}Int} gives one of the inclusions. The
opposite inclusion asserts that if \isa{t} is a ground term over both of the
sets
\isa{F} and~\isa{G} then it is also a ground term over their intersection,
-\isa{F\ {\isasyminter}\ G}.%
+\isa{F\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ G}.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ gterms{\isacharunderscore}IntI{\isacharcolon}\isanewline
-\ \ \ \ \ {\isachardoublequoteopen}t\ {\isasymin}\ gterms\ F\ {\isasymLongrightarrow}\ t\ {\isasymin}\ gterms\ G\ {\isasymlongrightarrow}\ t\ {\isasymin}\ gterms\ {\isacharparenleft}F{\isasyminter}G{\isacharparenright}{\isachardoublequoteclose}%
+\ gterms{\isaliteral{5F}{\isacharunderscore}}IntI{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ F\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ G\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ {\isaliteral{28}{\isacharparenleft}}F{\isaliteral{5C3C696E7465723E}{\isasyminter}}G{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -422,32 +422,32 @@
%
\begin{isamarkuptext}%
Attempting this proof, we get the assumption
-\isa{Apply\ f\ args\ {\isasymin}\ gterms\ G}, which cannot be broken down.
+\isa{Apply\ f\ args\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ G}, which cannot be broken down.
It looks like a job for rule inversion:\cmmdx{inductive\protect\_cases}%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{inductive{\isacharunderscore}cases}\isamarkupfalse%
-\ gterm{\isacharunderscore}Apply{\isacharunderscore}elim\ {\isacharbrackleft}elim{\isacharbang}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}Apply\ f\ args\ {\isasymin}\ gterms\ F{\isachardoublequoteclose}%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}cases}\isamarkupfalse%
+\ gterm{\isaliteral{5F}{\isacharunderscore}}Apply{\isaliteral{5F}{\isacharunderscore}}elim\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}Apply\ f\ args\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ F{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
Here is the result.
\begin{isabelle}%
-{\isasymlbrakk}Apply\ f\ args\ {\isasymin}\ gterms\ F{\isacharsemicolon}\isanewline
-\isaindent{\ }{\isasymlbrakk}{\isasymforall}t{\isasymin}set\ args{\isachardot}\ t\ {\isasymin}\ gterms\ F{\isacharsemicolon}\ f\ {\isasymin}\ F{\isasymrbrakk}\ {\isasymLongrightarrow}\ P{\isasymrbrakk}\isanewline
-{\isasymLongrightarrow}\ P\rulename{gterm{\isacharunderscore}Apply{\isacharunderscore}elim}%
+{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}Apply\ f\ args\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ F{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ }{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}t{\isaliteral{5C3C696E3E}{\isasymin}}set\ args{\isaliteral{2E}{\isachardot}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ F{\isaliteral{3B}{\isacharsemicolon}}\ f\ {\isaliteral{5C3C696E3E}{\isasymin}}\ F{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\rulename{gterm{\isaliteral{5F}{\isacharunderscore}}Apply{\isaliteral{5F}{\isacharunderscore}}elim}%
\end{isabelle}
This rule replaces an assumption about \isa{Apply\ f\ args} by
assumptions about \isa{f} and~\isa{args}.
No cases are discarded (there was only one to begin
with) but the rule applies specifically to the pattern \isa{Apply\ f\ args}.
It can be applied repeatedly as an elimination rule without looping, so we
-have given the \isa{elim{\isacharbang}} attribute.
+have given the \isa{elim{\isaliteral{21}{\isacharbang}}} attribute.
Now we can prove the other half of that distributive law.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ gterms{\isacharunderscore}IntI\ {\isacharbrackleft}rule{\isacharunderscore}format{\isacharcomma}\ intro{\isacharbang}{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ \ {\isachardoublequoteopen}t\ {\isasymin}\ gterms\ F\ {\isasymLongrightarrow}\ t\ {\isasymin}\ gterms\ G\ {\isasymlongrightarrow}\ t\ {\isasymin}\ gterms\ {\isacharparenleft}F{\isasyminter}G{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ gterms{\isaliteral{5F}{\isacharunderscore}}IntI\ {\isaliteral{5B}{\isacharbrackleft}}rule{\isaliteral{5F}{\isacharunderscore}}format{\isaliteral{2C}{\isacharcomma}}\ intro{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ F\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ G\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ {\isaliteral{28}{\isacharparenleft}}F{\isaliteral{5C3C696E7465723E}{\isasyminter}}G{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -455,7 +455,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}erule\ gterms{\isachardot}induct{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}erule\ gterms{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
\ blast\isanewline
\isacommand{done}\isamarkupfalse%
@@ -477,19 +477,19 @@
The proof begins with rule induction over the definition of
\isa{gterms}, which leaves a single subgoal:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}args\ f{\isachardot}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymlbrakk}{\isasymforall}t{\isasymin}set\ args{\isachardot}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ {\isasymlbrakk}\ \ \ }t\ {\isasymin}\ gterms\ F\ {\isasymand}\ {\isacharparenleft}t\ {\isasymin}\ gterms\ G\ {\isasymlongrightarrow}\ t\ {\isasymin}\ gterms\ {\isacharparenleft}F\ {\isasyminter}\ G{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ \ }f\ {\isasymin}\ F{\isasymrbrakk}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymLongrightarrow}\ Apply\ f\ args\ {\isasymin}\ gterms\ G\ {\isasymlongrightarrow}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ {\isasymLongrightarrow}\ }Apply\ f\ args\ {\isasymin}\ gterms\ {\isacharparenleft}F\ {\isasyminter}\ G{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}args\ f{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}t{\isaliteral{5C3C696E3E}{\isasymin}}set\ args{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ \ \ }t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ F\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ G\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ t\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ {\isaliteral{28}{\isacharparenleft}}F\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ G{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ \ }f\ {\isaliteral{5C3C696E3E}{\isasymin}}\ F{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Apply\ f\ args\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ G\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ }Apply\ f\ args\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ {\isaliteral{28}{\isacharparenleft}}F\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ G{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
-To prove this, we assume \isa{Apply\ f\ args\ {\isasymin}\ gterms\ G}. Rule inversion,
-in the form of \isa{gterm{\isacharunderscore}Apply{\isacharunderscore}elim}, infers
+To prove this, we assume \isa{Apply\ f\ args\ {\isaliteral{5C3C696E3E}{\isasymin}}\ gterms\ G}. Rule inversion,
+in the form of \isa{gterm{\isaliteral{5F}{\isacharunderscore}}Apply{\isaliteral{5F}{\isacharunderscore}}elim}, infers
that every element of \isa{args} belongs to
\isa{gterms\ G}; hence (by the induction hypothesis) it belongs
-to \isa{gterms\ {\isacharparenleft}F\ {\isasyminter}\ G{\isacharparenright}}. Rule inversion also yields
-\isa{f\ {\isasymin}\ G} and hence \isa{f\ {\isasymin}\ F\ {\isasyminter}\ G}.
+to \isa{gterms\ {\isaliteral{28}{\isacharparenleft}}F\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ G{\isaliteral{29}{\isacharparenright}}}. Rule inversion also yields
+\isa{f\ {\isaliteral{5C3C696E3E}{\isasymin}}\ G} and hence \isa{f\ {\isaliteral{5C3C696E3E}{\isasymin}}\ F\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ G}.
All of this reasoning is done by \isa{blast}.
\smallskip
@@ -504,8 +504,8 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ gterms{\isacharunderscore}Int{\isacharunderscore}eq\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ \ {\isachardoublequoteopen}gterms\ {\isacharparenleft}F\ {\isasyminter}\ G{\isacharparenright}\ {\isacharequal}\ gterms\ F\ {\isasyminter}\ gterms\ G{\isachardoublequoteclose}\isanewline
+\ gterms{\isaliteral{5F}{\isacharunderscore}}Int{\isaliteral{5F}{\isacharunderscore}}eq\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}gterms\ {\isaliteral{28}{\isacharparenleft}}F\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ G{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ gterms\ F\ {\isaliteral{5C3C696E7465723E}{\isasyminter}}\ gterms\ G{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -513,7 +513,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}blast\ intro{\isacharbang}{\isacharcolon}\ mono{\isacharunderscore}Int\ monoI\ gterms{\isacharunderscore}mono{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}blast\ intro{\isaliteral{21}{\isacharbang}}{\isaliteral{3A}{\isacharcolon}}\ mono{\isaliteral{5F}{\isacharunderscore}}Int\ monoI\ gterms{\isaliteral{5F}{\isacharunderscore}}mono{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -533,10 +533,10 @@
list of argument types paired with the result type.
Complete this inductive definition:
\begin{isabelle}
-\isacommand{inductive{\isacharunderscore}set}\isamarkupfalse%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse%
\isanewline
-\ \ well{\isacharunderscore}typed{\isacharunderscore}gterm\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}f\ {\isasymRightarrow}\ {\isacharprime}t\ list\ {\isacharasterisk}\ {\isacharprime}t{\isacharparenright}\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}f\ gterm\ {\isacharasterisk}\ {\isacharprime}t{\isacharparenright}set{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{for}\ sig\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}f\ {\isasymRightarrow}\ {\isacharprime}t\ list\ {\isacharasterisk}\ {\isacharprime}t{\isachardoublequoteclose}%
+\ \ well{\isaliteral{5F}{\isacharunderscore}}typed{\isaliteral{5F}{\isacharunderscore}}gterm\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}f\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}t\ list\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{27}{\isacharprime}}t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}f\ gterm\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{27}{\isacharprime}}t{\isaliteral{29}{\isacharparenright}}set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{for}\ sig\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}f\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}t\ list\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{27}{\isacharprime}}t{\isaliteral{22}{\isachardoublequoteclose}}%
\end{isabelle}
\end{exercise}
\end{isamarkuptext}
--- a/doc-src/TutorialI/Inductive/document/Even.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Inductive/document/Even.tex Mon Nov 08 14:41:11 2010 +0100
@@ -39,10 +39,10 @@
a set of natural numbers with the desired properties.%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{inductive{\isacharunderscore}set}\isamarkupfalse%
-\ even\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ set{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-zero{\isacharbrackleft}intro{\isacharbang}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isadigit{0}}\ {\isasymin}\ even{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-step{\isacharbrackleft}intro{\isacharbang}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}n\ {\isasymin}\ even\ {\isasymLongrightarrow}\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}\ {\isasymin}\ even{\isachardoublequoteclose}%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse%
+\ even\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ set{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+zero{\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{0}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+step{\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
An inductive definition consists of introduction rules. The first one
above states that 0 is even; the second states that if $n$ is even, then so
@@ -54,8 +54,8 @@
rule for case analysis and an induction rule. We can refer to these
theorems by automatically-generated names. Here are two examples:
\begin{isabelle}%
-{\isadigit{0}}\ {\isasymin}\ even\rulename{even{\isachardot}zero}\par\smallskip%
-n\ {\isasymin}\ even\ {\isasymLongrightarrow}\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isasymin}\ even\rulename{even{\isachardot}step}%
+{\isadigit{0}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\rulename{even{\isaliteral{2E}{\isachardot}}zero}\par\smallskip%
+n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\rulename{even{\isaliteral{2E}{\isachardot}}step}%
\end{isabelle}
The introduction rules can be given attributes. Here
@@ -80,7 +80,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ two{\isacharunderscore}times{\isacharunderscore}even{\isacharbrackleft}intro{\isacharbang}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isadigit{2}}{\isacharasterisk}k\ {\isasymin}\ even{\isachardoublequoteclose}\isanewline
+\ two{\isaliteral{5F}{\isacharunderscore}}times{\isaliteral{5F}{\isacharunderscore}}even{\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{2}}{\isaliteral{2A}{\isacharasterisk}}k\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -88,7 +88,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}induct{\isacharunderscore}tac\ k{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ k{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
\ auto\isanewline
\isacommand{done}\isamarkupfalse%
@@ -111,8 +111,8 @@
The first step is induction on the natural number \isa{k}, which leaves
two subgoals:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isadigit{2}}\ {\isacharasterisk}\ {\isadigit{0}}\ {\isasymin}\ even\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ {\isadigit{2}}\ {\isacharasterisk}\ n\ {\isasymin}\ even\ {\isasymLongrightarrow}\ {\isadigit{2}}\ {\isacharasterisk}\ Suc\ n\ {\isasymin}\ even%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isadigit{0}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ {\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ Suc\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even%
\end{isabelle}
Here \isa{auto} simplifies both subgoals so that they match the introduction
rules, which are then applied automatically.
@@ -120,7 +120,7 @@
Our ultimate goal is to prove the equivalence between the traditional
definition of \isa{even} (using the divides relation) and our inductive
definition. One direction of this equivalence is immediate by the lemma
-just proved, whose \isa{intro{\isacharbang}} attribute ensures it is applied automatically.%
+just proved, whose \isa{intro{\isaliteral{21}{\isacharbang}}} attribute ensures it is applied automatically.%
\end{isamarkuptxt}%
\isamarkuptrue%
%
@@ -131,7 +131,7 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ dvd{\isacharunderscore}imp{\isacharunderscore}even{\isacharcolon}\ {\isachardoublequoteopen}{\isadigit{2}}\ dvd\ n\ {\isasymLongrightarrow}\ n\ {\isasymin}\ even{\isachardoublequoteclose}\isanewline
+\ dvd{\isaliteral{5F}{\isacharunderscore}}imp{\isaliteral{5F}{\isacharunderscore}}even{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{2}}\ dvd\ n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -139,7 +139,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}auto\ simp\ add{\isacharcolon}\ dvd{\isacharunderscore}def{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}auto\ simp\ add{\isaliteral{3A}{\isacharcolon}}\ dvd{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -157,9 +157,9 @@
\isa{even}, Isabelle has
generated an induction rule:
\begin{isabelle}%
-{\isasymlbrakk}x\ {\isasymin}\ even{\isacharsemicolon}\ P\ {\isadigit{0}}{\isacharsemicolon}\isanewline
-\isaindent{\ }{\isasymAnd}n{\isachardot}\ {\isasymlbrakk}n\ {\isasymin}\ even{\isacharsemicolon}\ P\ n{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}{\isasymrbrakk}\isanewline
-{\isasymLongrightarrow}\ P\ x\rulename{even{\isachardot}induct}%
+{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{3B}{\isacharsemicolon}}\ P\ {\isadigit{0}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ }{\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{3B}{\isacharsemicolon}}\ P\ n{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ x\rulename{even{\isaliteral{2E}{\isachardot}}induct}%
\end{isabelle}
A property \isa{P} holds for every even number provided it
holds for~\isa{{\isadigit{0}}} and is closed under the operation
@@ -178,7 +178,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ even{\isacharunderscore}imp{\isacharunderscore}dvd{\isacharcolon}\ {\isachardoublequoteopen}n\ {\isasymin}\ even\ {\isasymLongrightarrow}\ {\isadigit{2}}\ dvd\ n{\isachardoublequoteclose}%
+\ even{\isaliteral{5F}{\isacharunderscore}}imp{\isaliteral{5F}{\isacharunderscore}}dvd{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isadigit{2}}\ dvd\ n{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -186,44 +186,44 @@
\isatagproof
%
\begin{isamarkuptxt}%
-We begin by applying induction. Note that \isa{even{\isachardot}induct} has the form
+We begin by applying induction. Note that \isa{even{\isaliteral{2E}{\isachardot}}induct} has the form
of an elimination rule, so we use the method \isa{erule}. We get two
subgoals:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}erule\ even{\isachardot}induct{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}erule\ even{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isadigit{2}}\ dvd\ {\isadigit{0}}\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ {\isasymlbrakk}n\ {\isasymin}\ even{\isacharsemicolon}\ {\isadigit{2}}\ dvd\ n{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isadigit{2}}\ dvd\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isadigit{2}}\ dvd\ {\isadigit{0}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{3B}{\isacharsemicolon}}\ {\isadigit{2}}\ dvd\ n{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isadigit{2}}\ dvd\ Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
We unfold the definition of \isa{dvd} in both subgoals, proving the first
one and simplifying the second:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}\ dvd{\isacharunderscore}def{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{5F}{\isacharunderscore}}all\ add{\isaliteral{3A}{\isacharcolon}}\ dvd{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ {\isasymlbrakk}n\ {\isasymin}\ even{\isacharsemicolon}\ {\isasymexists}k{\isachardot}\ n\ {\isacharequal}\ {\isadigit{2}}\ {\isacharasterisk}\ k{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isasymexists}k{\isachardot}\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ {\isadigit{2}}\ {\isacharasterisk}\ k%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}k{\isaliteral{2E}{\isachardot}}\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ k{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}k{\isaliteral{2E}{\isachardot}}\ Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ k%
\end{isabelle}
The next command eliminates the existential quantifier from the assumption
-and replaces \isa{n} by \isa{{\isadigit{2}}\ {\isacharasterisk}\ k}.%
+and replaces \isa{n} by \isa{{\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ k}.%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
\ clarify%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}n\ k{\isachardot}\ {\isadigit{2}}\ {\isacharasterisk}\ k\ {\isasymin}\ even\ {\isasymLongrightarrow}\ {\isasymexists}ka{\isachardot}\ Suc\ {\isacharparenleft}Suc\ {\isacharparenleft}{\isadigit{2}}\ {\isacharasterisk}\ k{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isadigit{2}}\ {\isacharasterisk}\ ka%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n\ k{\isaliteral{2E}{\isachardot}}\ {\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ k\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}ka{\isaliteral{2E}{\isachardot}}\ Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ k{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ ka%
\end{isabelle}
To conclude, we tell Isabelle that the desired value is
\isa{Suc\ k}. With this hint, the subgoal falls to \isa{simp}.%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}rule{\isacharunderscore}tac\ x\ {\isacharequal}\ {\isachardoublequoteopen}Suc\ k{\isachardoublequoteclose}\ \isakeyword{in}\ exI{\isacharcomma}\ simp{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}rule{\isaliteral{5F}{\isacharunderscore}}tac\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequoteopen}}Suc\ k{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{in}\ exI{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -239,7 +239,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ even{\isacharunderscore}iff{\isacharunderscore}dvd{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}n\ {\isasymin}\ even{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isadigit{2}}\ dvd\ n{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ even{\isaliteral{5F}{\isacharunderscore}}iff{\isaliteral{5F}{\isacharunderscore}}dvd{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}\ dvd\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -247,7 +247,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}blast\ intro{\isacharcolon}\ dvd{\isacharunderscore}imp{\isacharunderscore}even\ even{\isacharunderscore}imp{\isacharunderscore}dvd{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}blast\ intro{\isaliteral{3A}{\isacharcolon}}\ dvd{\isaliteral{5F}{\isacharunderscore}}imp{\isaliteral{5F}{\isacharunderscore}}even\ even{\isaliteral{5F}{\isacharunderscore}}imp{\isaliteral{5F}{\isacharunderscore}}dvd{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -269,7 +269,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isasymin}\ even\ {\isasymLongrightarrow}\ n\ {\isasymin}\ even{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -277,7 +277,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}erule\ even{\isachardot}induct{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}erule\ even{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{oops}\isamarkupfalse%
%
\endisatagproof
@@ -294,12 +294,12 @@
\isatagproof
%
\begin{isamarkuptxt}%
-Rule induction finds no occurrences of \isa{Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}} in the
+Rule induction finds no occurrences of \isa{Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}} in the
conclusion, which it therefore leaves unchanged. (Look at
-\isa{even{\isachardot}induct} to see why this happens.) We have these subgoals:
+\isa{even{\isaliteral{2E}{\isachardot}}induct} to see why this happens.) We have these subgoals:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ n\ {\isasymin}\ even\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}na{\isachardot}\ {\isasymlbrakk}na\ {\isasymin}\ even{\isacharsemicolon}\ n\ {\isasymin}\ even{\isasymrbrakk}\ {\isasymLongrightarrow}\ n\ {\isasymin}\ even%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}na{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}na\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{3B}{\isacharsemicolon}}\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even%
\end{isabelle}
The first one is hopeless. Rule induction on
a non-variable term discards information, and usually fails.
@@ -317,7 +317,7 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ even{\isacharunderscore}imp{\isacharunderscore}even{\isacharunderscore}minus{\isacharunderscore}{\isadigit{2}}{\isacharcolon}\ {\isachardoublequoteopen}n\ {\isasymin}\ even\ {\isasymLongrightarrow}\ n\ {\isacharminus}\ {\isadigit{2}}\ {\isasymin}\ even{\isachardoublequoteclose}\isanewline
+\ even{\isaliteral{5F}{\isacharunderscore}}imp{\isaliteral{5F}{\isacharunderscore}}even{\isaliteral{5F}{\isacharunderscore}}minus{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{2}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -325,7 +325,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}erule\ even{\isachardot}induct{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}erule\ even{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
\ auto\isanewline
\isacommand{done}\isamarkupfalse%
@@ -346,11 +346,11 @@
\begin{isamarkuptxt}%
This lemma is trivially inductive. Here are the subgoals:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isadigit{0}}\ {\isacharminus}\ {\isadigit{2}}\ {\isasymin}\ even\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ {\isasymlbrakk}n\ {\isasymin}\ even{\isacharsemicolon}\ n\ {\isacharminus}\ {\isadigit{2}}\ {\isasymin}\ even{\isasymrbrakk}\ {\isasymLongrightarrow}\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharminus}\ {\isadigit{2}}\ {\isasymin}\ even%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isadigit{0}}\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{2}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{3B}{\isacharsemicolon}}\ n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{2}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{2}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even%
\end{isabelle}
-The first is trivial because \isa{{\isadigit{0}}\ {\isacharminus}\ {\isadigit{2}}} simplifies to \isa{{\isadigit{0}}}, which is
-even. The second is trivial too: \isa{Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharminus}\ {\isadigit{2}}} simplifies to
+The first is trivial because \isa{{\isadigit{0}}\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{2}}} simplifies to \isa{{\isadigit{0}}}, which is
+even. The second is trivial too: \isa{Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{2}}} simplifies to
\isa{n}, matching the assumption.%
\index{rule induction|)} %the sequel isn't really about induction
@@ -366,7 +366,7 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ Suc{\isacharunderscore}Suc{\isacharunderscore}even{\isacharunderscore}imp{\isacharunderscore}even{\isacharcolon}\ {\isachardoublequoteopen}Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isasymin}\ even\ {\isasymLongrightarrow}\ n\ {\isasymin}\ even{\isachardoublequoteclose}\isanewline
+\ Suc{\isaliteral{5F}{\isacharunderscore}}Suc{\isaliteral{5F}{\isacharunderscore}}even{\isaliteral{5F}{\isacharunderscore}}imp{\isaliteral{5F}{\isacharunderscore}}even{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -374,7 +374,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}drule\ even{\isacharunderscore}imp{\isacharunderscore}even{\isacharunderscore}minus{\isacharunderscore}{\isadigit{2}}{\isacharcomma}\ simp{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}drule\ even{\isaliteral{5F}{\isacharunderscore}}imp{\isaliteral{5F}{\isacharunderscore}}even{\isaliteral{5F}{\isacharunderscore}}minus{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -383,13 +383,13 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-We have just proved the converse of the introduction rule \isa{even{\isachardot}step}.
+We have just proved the converse of the introduction rule \isa{even{\isaliteral{2E}{\isachardot}}step}.
This suggests proving the following equivalence. We give it the
\attrdx{iff} attribute because of its obvious value for simplification.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}iff{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharparenleft}Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}\ {\isasymin}\ even{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}n\ {\isasymin}\ even{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}iff{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -397,7 +397,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}blast\ dest{\isacharcolon}\ Suc{\isacharunderscore}Suc{\isacharunderscore}even{\isacharunderscore}imp{\isacharunderscore}even{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}blast\ dest{\isaliteral{3A}{\isacharcolon}}\ Suc{\isaliteral{5F}{\isacharunderscore}}Suc{\isaliteral{5F}{\isacharunderscore}}even{\isaliteral{5F}{\isacharunderscore}}imp{\isaliteral{5F}{\isacharunderscore}}even{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -419,60 +419,60 @@
Recall that \isa{even} is the minimal set closed under these two rules:
\begin{isabelle}%
-{\isadigit{0}}\ {\isasymin}\ even\isasep\isanewline%
-n\ {\isasymin}\ even\ {\isasymLongrightarrow}\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isasymin}\ even%
+{\isadigit{0}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\isasep\isanewline%
+n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even%
\end{isabelle}
Minimality means that \isa{even} contains only the elements that these
rules force it to contain. If we are told that \isa{a}
belongs to
\isa{even} then there are only two possibilities. Either \isa{a} is \isa{{\isadigit{0}}}
-or else \isa{a} has the form \isa{Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}}, for some suitable \isa{n}
+or else \isa{a} has the form \isa{Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}}, for some suitable \isa{n}
that belongs to
\isa{even}. That is the gist of the \isa{cases} rule, which Isabelle proves
for us when it accepts an inductive definition:
\begin{isabelle}%
-{\isasymlbrakk}a\ {\isasymin}\ even{\isacharsemicolon}\ a\ {\isacharequal}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ P{\isacharsemicolon}\isanewline
-\isaindent{\ }{\isasymAnd}n{\isachardot}\ {\isasymlbrakk}a\ {\isacharequal}\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharsemicolon}\ n\ {\isasymin}\ even{\isasymrbrakk}\ {\isasymLongrightarrow}\ P{\isasymrbrakk}\isanewline
-{\isasymLongrightarrow}\ P\rulename{even{\isachardot}cases}%
+{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}a\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{3B}{\isacharsemicolon}}\ a\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ }{\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}a\ {\isaliteral{3D}{\isacharequal}}\ Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\rulename{even{\isaliteral{2E}{\isachardot}}cases}%
\end{isabelle}
This general rule is less useful than instances of it for
specific patterns. For example, if \isa{a} has the form
-\isa{Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}} then the first case becomes irrelevant, while the second
+\isa{Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}} then the first case becomes irrelevant, while the second
case tells us that \isa{n} belongs to \isa{even}. Isabelle will generate
this instance for us:%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{inductive{\isacharunderscore}cases}\isamarkupfalse%
-\ Suc{\isacharunderscore}Suc{\isacharunderscore}cases\ {\isacharbrackleft}elim{\isacharbang}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}Suc{\isacharparenleft}Suc\ n{\isacharparenright}\ {\isasymin}\ even{\isachardoublequoteclose}%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}cases}\isamarkupfalse%
+\ Suc{\isaliteral{5F}{\isacharunderscore}}Suc{\isaliteral{5F}{\isacharunderscore}}cases\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}Suc{\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
The \commdx{inductive\protect\_cases} command generates an instance of
the \isa{cases} rule for the supplied pattern and gives it the supplied name:
\begin{isabelle}%
-{\isasymlbrakk}Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isasymin}\ even{\isacharsemicolon}\ n\ {\isasymin}\ even\ {\isasymLongrightarrow}\ P{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\rulename{Suc{\isacharunderscore}Suc{\isacharunderscore}cases}%
+{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{3B}{\isacharsemicolon}}\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\rulename{Suc{\isaliteral{5F}{\isacharunderscore}}Suc{\isaliteral{5F}{\isacharunderscore}}cases}%
\end{isabelle}
-Applying this as an elimination rule yields one case where \isa{even{\isachardot}cases}
+Applying this as an elimination rule yields one case where \isa{even{\isaliteral{2E}{\isachardot}}cases}
would yield two. Rule inversion works well when the conclusions of the
-introduction rules involve datatype constructors like \isa{Suc} and \isa{{\isacharhash}}
+introduction rules involve datatype constructors like \isa{Suc} and \isa{{\isaliteral{23}{\isacharhash}}}
(list ``cons''); freeness reasoning discards all but one or two cases.
In the \isacommand{inductive\_cases} command we supplied an
-attribute, \isa{elim{\isacharbang}},
+attribute, \isa{elim{\isaliteral{21}{\isacharbang}}},
\index{elim"!@\isa {elim"!} (attribute)}%
indicating that this elimination rule can be
applied aggressively. The original
\isa{cases} rule would loop if used in that manner because the
pattern~\isa{a} matches everything.
-The rule \isa{Suc{\isacharunderscore}Suc{\isacharunderscore}cases} is equivalent to the following implication:
+The rule \isa{Suc{\isaliteral{5F}{\isacharunderscore}}Suc{\isaliteral{5F}{\isacharunderscore}}cases} is equivalent to the following implication:
\begin{isabelle}%
-Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isasymin}\ even\ {\isasymLongrightarrow}\ n\ {\isasymin}\ even%
+Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even%
\end{isabelle}
Just above we devoted some effort to reaching precisely
this result. Yet we could have obtained it by a one-line declaration,
-dispensing with the lemma \isa{even{\isacharunderscore}imp{\isacharunderscore}even{\isacharunderscore}minus{\isacharunderscore}{\isadigit{2}}}.
+dispensing with the lemma \isa{even{\isaliteral{5F}{\isacharunderscore}}imp{\isaliteral{5F}{\isacharunderscore}}even{\isaliteral{5F}{\isacharunderscore}}minus{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}}.
This example also justifies the terminology
\textbf{rule inversion}: the new rule inverts the introduction rule
-\isa{even{\isachardot}step}. In general, a rule can be inverted when the set of elements
+\isa{even{\isaliteral{2E}{\isachardot}}step}. In general, a rule can be inverted when the set of elements
it introduces is disjoint from those of the other introduction rules.
For one-off applications of rule inversion, use the \methdx{ind_cases} method.
@@ -486,7 +486,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}ind{\isacharunderscore}cases\ {\isachardoublequoteopen}Suc{\isacharparenleft}Suc\ n{\isacharparenright}\ {\isasymin}\ even{\isachardoublequoteclose}{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}ind{\isaliteral{5F}{\isacharunderscore}}cases\ {\isaliteral{22}{\isachardoublequoteopen}}Suc{\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -501,7 +501,7 @@
To summarize, every inductive definition produces a \isa{cases} rule. The
\commdx{inductive\protect\_cases} command stores an instance of the
\isa{cases} rule for a given pattern. Within a proof, the
-\isa{ind{\isacharunderscore}cases} method applies an instance of the \isa{cases}
+\isa{ind{\isaliteral{5F}{\isacharunderscore}}cases} method applies an instance of the \isa{cases}
rule.
The even numbers example has shown how inductive definitions can be
--- a/doc-src/TutorialI/Inductive/document/Mutual.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Inductive/document/Mutual.tex Mon Nov 08 14:41:11 2010 +0100
@@ -25,23 +25,23 @@
natural numbers:%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{inductive{\isacharunderscore}set}\isamarkupfalse%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse%
\isanewline
-\ \ Even\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ set{\isachardoublequoteclose}\ \isakeyword{and}\isanewline
-\ \ Odd\ \ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ set{\isachardoublequoteclose}\isanewline
+\ \ Even\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ set{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
+\ \ Odd\ \ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ zero{\isacharcolon}\ \ {\isachardoublequoteopen}{\isadigit{0}}\ {\isasymin}\ Even{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ EvenI{\isacharcolon}\ {\isachardoublequoteopen}n\ {\isasymin}\ Odd\ {\isasymLongrightarrow}\ Suc\ n\ {\isasymin}\ Even{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ OddI{\isacharcolon}\ \ {\isachardoublequoteopen}n\ {\isasymin}\ Even\ {\isasymLongrightarrow}\ Suc\ n\ {\isasymin}\ Odd{\isachardoublequoteclose}%
+\ \ zero{\isaliteral{3A}{\isacharcolon}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{0}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Even{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ EvenI{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Odd\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Suc\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Even{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ OddI{\isaliteral{3A}{\isacharcolon}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Even\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Suc\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Odd{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
The mutually inductive definition of multiple sets is no different from
that of a single set, except for induction: just as for mutually recursive
datatypes, induction needs to involve all the simultaneously defined sets. In
-the above case, the induction rule is called \isa{Even{\isacharunderscore}Odd{\isachardot}induct}
+the above case, the induction rule is called \isa{Even{\isaliteral{5F}{\isacharunderscore}}Odd{\isaliteral{2E}{\isachardot}}induct}
(simply concatenate the names of the sets involved) and has the conclusion
\begin{isabelle}%
-\ \ \ \ \ {\isacharparenleft}{\isacharquery}x\ {\isasymin}\ Even\ {\isasymlongrightarrow}\ {\isacharquery}P\ {\isacharquery}x{\isacharparenright}\ {\isasymand}\ {\isacharparenleft}{\isacharquery}y\ {\isasymin}\ Odd\ {\isasymlongrightarrow}\ {\isacharquery}Q\ {\isacharquery}y{\isacharparenright}%
+\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Even\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{3F}{\isacharquery}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Odd\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}Q\ {\isaliteral{3F}{\isacharquery}}y{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
If we want to prove that all even numbers are divisible by two, we have to
@@ -49,7 +49,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}m\ {\isasymin}\ Even\ {\isasymlongrightarrow}\ {\isadigit{2}}\ dvd\ m{\isacharparenright}\ {\isasymand}\ {\isacharparenleft}n\ {\isasymin}\ Odd\ {\isasymlongrightarrow}\ {\isadigit{2}}\ dvd\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}m\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Even\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isadigit{2}}\ dvd\ m{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Odd\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isadigit{2}}\ dvd\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -64,12 +64,12 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ Even{\isacharunderscore}Odd{\isachardot}induct{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}rule\ Even{\isaliteral{5F}{\isacharunderscore}}Odd{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isadigit{2}}\ dvd\ {\isadigit{0}}\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ {\isasymlbrakk}n\ {\isasymin}\ Odd{\isacharsemicolon}\ {\isadigit{2}}\ dvd\ Suc\ n{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isadigit{2}}\ dvd\ Suc\ n\isanewline
-\ {\isadigit{3}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ {\isasymlbrakk}n\ {\isasymin}\ Even{\isacharsemicolon}\ {\isadigit{2}}\ dvd\ n{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isadigit{2}}\ dvd\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isadigit{2}}\ dvd\ {\isadigit{0}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Odd{\isaliteral{3B}{\isacharsemicolon}}\ {\isadigit{2}}\ dvd\ Suc\ n{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isadigit{2}}\ dvd\ Suc\ n\isanewline
+\ {\isadigit{3}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ Even{\isaliteral{3B}{\isacharsemicolon}}\ {\isadigit{2}}\ dvd\ n{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isadigit{2}}\ dvd\ Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
The first two subgoals are proved by simplification and the final one can be
proved in the same manner as in \S\ref{sec:rule-induction}
@@ -95,19 +95,19 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{inductive}\isamarkupfalse%
-\ evn\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-zero{\isacharcolon}\ {\isachardoublequoteopen}evn\ {\isadigit{0}}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-step{\isacharcolon}\ {\isachardoublequoteopen}evn\ n\ {\isasymLongrightarrow}\ evn{\isacharparenleft}Suc{\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
+\ evn\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+zero{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}evn\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+step{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}evn\ n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ evn{\isaliteral{28}{\isacharparenleft}}Suc{\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent Everything works as before, except that
you write \commdx{inductive} instead of \isacommand{inductive\_set} and
-\isa{evn\ n} instead of \isa{n\ {\isasymin}\ even}.
+\isa{evn\ n} instead of \isa{n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ even}.
When defining an n-ary relation as a predicate, it is recommended to curry
-the predicate: its type should be \mbox{\isa{{\isasymtau}\isactrlisub {\isadigit{1}}\ {\isasymRightarrow}\ {\isasymdots}\ {\isasymRightarrow}\ {\isasymtau}\isactrlisub n\ {\isasymRightarrow}\ bool}}
+the predicate: its type should be \mbox{\isa{{\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}}
rather than
-\isa{{\isasymtau}\isactrlisub {\isadigit{1}}\ {\isasymtimes}\ {\isasymdots}\ {\isasymtimes}\ {\isasymtau}\isactrlisub n\ {\isasymRightarrow}\ bool}. The curried version facilitates inductions.
+\isa{{\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub n\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}. The curried version facilitates inductions.
-When should you choose sets and when predicates? If you intend to combine your notion with set theoretic notation, define it as an inductive set. If not, define it as an inductive predicate, thus avoiding the \isa{{\isasymin}} notation. But note that predicates of more than one argument cannot be combined with the usual set theoretic operators: \isa{P\ {\isasymunion}\ Q} is not well-typed if \isa{P{\isacharcomma}\ Q\ {\isacharcolon}{\isacharcolon}\ {\isasymtau}\isactrlisub {\isadigit{1}}\ {\isasymRightarrow}\ {\isasymtau}\isactrlisub {\isadigit{2}}\ {\isasymRightarrow}\ bool}, you have to write \isa{{\isasymlambda}x\ y{\isachardot}\ P\ x\ y\ {\isasymand}\ Q\ x\ y} instead.
+When should you choose sets and when predicates? If you intend to combine your notion with set theoretic notation, define it as an inductive set. If not, define it as an inductive predicate, thus avoiding the \isa{{\isaliteral{5C3C696E3E}{\isasymin}}} notation. But note that predicates of more than one argument cannot be combined with the usual set theoretic operators: \isa{P\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ Q} is not well-typed if \isa{P{\isaliteral{2C}{\isacharcomma}}\ Q\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5C3C7461753E}{\isasymtau}}\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool}, you have to write \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x\ y{\isaliteral{2E}{\isachardot}}\ P\ x\ y\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Q\ x\ y} instead.
\index{inductive predicates|)}%
\end{isamarkuptext}%
\isamarkuptrue%
--- a/doc-src/TutorialI/Inductive/document/Star.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Inductive/document/Star.tex Mon Nov 08 14:41:11 2010 +0100
@@ -27,26 +27,26 @@
Relations too can be defined inductively, since they are just sets of pairs.
A perfect example is the function that maps a relation to its
reflexive transitive closure. This concept was already
-introduced in \S\ref{sec:Relations}, where the operator \isa{\isactrlsup {\isacharasterisk}} was
+introduced in \S\ref{sec:Relations}, where the operator \isa{\isaliteral{5C3C5E7375703E}{}\isactrlsup {\isaliteral{2A}{\isacharasterisk}}} was
defined as a least fixed point because inductive definitions were not yet
available. But now they are:%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{inductive{\isacharunderscore}set}\isamarkupfalse%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse%
\isanewline
-\ \ rtc\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}set{\isachardoublequoteclose}\ \ \ {\isacharparenleft}{\isachardoublequoteopen}{\isacharunderscore}{\isacharasterisk}{\isachardoublequoteclose}\ {\isacharbrackleft}{\isadigit{1}}{\isadigit{0}}{\isadigit{0}}{\isadigit{0}}{\isacharbrackright}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isacharparenright}\isanewline
-\ \ \isakeyword{for}\ r\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}set{\isachardoublequoteclose}\isanewline
+\ \ rtc\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}set{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isadigit{0}}{\isadigit{0}}{\isadigit{0}}{\isaliteral{5D}{\isacharbrackright}}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \isakeyword{for}\ r\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ rtc{\isacharunderscore}refl{\isacharbrackleft}iff{\isacharbrackright}{\isacharcolon}\ \ {\isachardoublequoteopen}{\isacharparenleft}x{\isacharcomma}x{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ rtc{\isacharunderscore}step{\isacharcolon}\ \ \ \ \ \ \ {\isachardoublequoteopen}{\isasymlbrakk}\ {\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ r{\isacharsemicolon}\ {\isacharparenleft}y{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharparenleft}x{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}%
+\ \ rtc{\isaliteral{5F}{\isacharunderscore}}refl{\isaliteral{5B}{\isacharbrackleft}}iff{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ rtc{\isaliteral{5F}{\isacharunderscore}}step{\isaliteral{3A}{\isacharcolon}}\ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
The function \isa{rtc} is annotated with concrete syntax: instead of
-\isa{rtc\ r} we can write \isa{r{\isacharasterisk}}. The actual definition
+\isa{rtc\ r} we can write \isa{r{\isaliteral{2A}{\isacharasterisk}}}. The actual definition
consists of two rules. Reflexivity is obvious and is immediately given the
\isa{iff} attribute to increase automation. The
-second rule, \isa{rtc{\isacharunderscore}step}, says that we can always add one more
-\isa{r}-step to the left. Although we could make \isa{rtc{\isacharunderscore}step} an
+second rule, \isa{rtc{\isaliteral{5F}{\isacharunderscore}}step}, says that we can always add one more
+\isa{r}-step to the left. Although we could make \isa{rtc{\isaliteral{5F}{\isacharunderscore}}step} an
introduction rule, this is dangerous: the recursion in the second premise
slows down and may even kill the automatic tactics.
@@ -58,7 +58,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ r\ {\isasymLongrightarrow}\ {\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -66,7 +66,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-{\isacharparenleft}blast\ intro{\isacharcolon}\ rtc{\isacharunderscore}step{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}blast\ intro{\isaliteral{3A}{\isacharcolon}}\ rtc{\isaliteral{5F}{\isacharunderscore}}step{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -78,22 +78,22 @@
\noindent
Although the lemma itself is an unremarkable consequence of the basic rules,
it has the advantage that it can be declared an introduction rule without the
-danger of killing the automatic tactics because \isa{r{\isacharasterisk}} occurs only in
+danger of killing the automatic tactics because \isa{r{\isaliteral{2A}{\isacharasterisk}}} occurs only in
the conclusion and not in the premise. Thus some proofs that would otherwise
-need \isa{rtc{\isacharunderscore}step} can now be found automatically. The proof also
-shows that \isa{blast} is able to handle \isa{rtc{\isacharunderscore}step}. But
+need \isa{rtc{\isaliteral{5F}{\isacharunderscore}}step} can now be found automatically. The proof also
+shows that \isa{blast} is able to handle \isa{rtc{\isaliteral{5F}{\isacharunderscore}}step}. But
some of the other automatic tactics are more sensitive, and even \isa{blast} can be lead astray in the presence of large numbers of rules.
To prove transitivity, we need rule induction, i.e.\ theorem
-\isa{rtc{\isachardot}induct}:
+\isa{rtc{\isaliteral{2E}{\isachardot}}induct}:
\begin{isabelle}%
-\ \ \ \ \ {\isasymlbrakk}{\isacharparenleft}{\isacharquery}x{\isadigit{1}}{\isachardot}{\isadigit{0}}{\isacharcomma}\ {\isacharquery}x{\isadigit{2}}{\isachardot}{\isadigit{0}}{\isacharparenright}\ {\isasymin}\ {\isacharquery}r{\isacharasterisk}{\isacharsemicolon}\ {\isasymAnd}x{\isachardot}\ {\isacharquery}P\ x\ x{\isacharsemicolon}\isanewline
-\isaindent{\ \ \ \ \ \ }{\isasymAnd}x\ y\ z{\isachardot}\ {\isasymlbrakk}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ {\isacharquery}r{\isacharsemicolon}\ {\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ {\isacharquery}r{\isacharasterisk}{\isacharsemicolon}\ {\isacharquery}P\ y\ z{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}P\ x\ z{\isasymrbrakk}\isanewline
-\isaindent{\ \ \ \ \ }{\isasymLongrightarrow}\ {\isacharquery}P\ {\isacharquery}x{\isadigit{1}}{\isachardot}{\isadigit{0}}\ {\isacharquery}x{\isadigit{2}}{\isachardot}{\isadigit{0}}%
+\ \ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}x{\isadigit{1}}{\isaliteral{2E}{\isachardot}}{\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}x{\isadigit{2}}{\isaliteral{2E}{\isachardot}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{3F}{\isacharquery}}r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{3F}{\isacharquery}}P\ x\ x{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ \ \ \ \ \ }{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y\ z{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{3F}{\isacharquery}}r{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{3F}{\isacharquery}}r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{3F}{\isacharquery}}P\ y\ z{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}P\ x\ z{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ \ \ \ \ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{3F}{\isacharquery}}x{\isadigit{1}}{\isaliteral{2E}{\isachardot}}{\isadigit{0}}\ {\isaliteral{3F}{\isacharquery}}x{\isadigit{2}}{\isaliteral{2E}{\isachardot}}{\isadigit{0}}%
\end{isabelle}
-It says that \isa{{\isacharquery}P} holds for an arbitrary pair \isa{{\isacharparenleft}{\isacharquery}x{\isadigit{1}}{\isachardot}{\isadigit{0}}{\isacharcomma}\ {\isacharquery}x{\isadigit{2}}{\isachardot}{\isadigit{0}}{\isacharparenright}\ {\isasymin}\ {\isacharquery}r{\isacharasterisk}}
-if \isa{{\isacharquery}P} is preserved by all rules of the inductive definition,
-i.e.\ if \isa{{\isacharquery}P} holds for the conclusion provided it holds for the
+It says that \isa{{\isaliteral{3F}{\isacharquery}}P} holds for an arbitrary pair \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{3F}{\isacharquery}}x{\isadigit{1}}{\isaliteral{2E}{\isachardot}}{\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}x{\isadigit{2}}{\isaliteral{2E}{\isachardot}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{3F}{\isacharquery}}r{\isaliteral{2A}{\isacharasterisk}}}
+if \isa{{\isaliteral{3F}{\isacharquery}}P} is preserved by all rules of the inductive definition,
+i.e.\ if \isa{{\isaliteral{3F}{\isacharquery}}P} holds for the conclusion provided it holds for the
premises. In general, rule induction for an $n$-ary inductive relation $R$
expects a premise of the form $(x@1,\dots,x@n) \in R$.
@@ -101,7 +101,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ rtc{\isacharunderscore}trans{\isacharcolon}\ {\isachardoublequoteopen}{\isasymlbrakk}\ {\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isacharsemicolon}\ {\isacharparenleft}y{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharparenleft}x{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}\isanewline
+\ rtc{\isaliteral{5F}{\isacharunderscore}}trans{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -109,30 +109,30 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}erule\ rtc{\isachardot}induct{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}erule\ rtc{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
Unfortunately, even the base case is a problem:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x{\isachardot}\ {\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymLongrightarrow}\ {\isacharparenleft}x{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}%
\end{isabelle}
We have to abandon this proof attempt.
-To understand what is going on, let us look again at \isa{rtc{\isachardot}induct}.
+To understand what is going on, let us look again at \isa{rtc{\isaliteral{2E}{\isachardot}}induct}.
In the above application of \isa{erule}, the first premise of
-\isa{rtc{\isachardot}induct} is unified with the first suitable assumption, which
-is \isa{{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}} rather than \isa{{\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}}. Although that
+\isa{rtc{\isaliteral{2E}{\isachardot}}induct} is unified with the first suitable assumption, which
+is \isa{{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}} rather than \isa{{\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}}. Although that
is what we want, it is merely due to the order in which the assumptions occur
in the subgoal, which it is not good practice to rely on. As a result,
-\isa{{\isacharquery}xb} becomes \isa{x}, \isa{{\isacharquery}xa} becomes
-\isa{y} and \isa{{\isacharquery}P} becomes \isa{{\isasymlambda}u\ v{\isachardot}\ {\isacharparenleft}u{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}}, thus
+\isa{{\isaliteral{3F}{\isacharquery}}xb} becomes \isa{x}, \isa{{\isaliteral{3F}{\isacharquery}}xa} becomes
+\isa{y} and \isa{{\isaliteral{3F}{\isacharquery}}P} becomes \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}u\ v{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}u{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}}, thus
yielding the above subgoal. So what went wrong?
-When looking at the instantiation of \isa{{\isacharquery}P} we see that it does not
+When looking at the instantiation of \isa{{\isaliteral{3F}{\isacharquery}}P} we see that it does not
depend on its second parameter at all. The reason is that in our original
-goal, of the pair \isa{{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}} only \isa{x} appears also in the
+goal, of the pair \isa{{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}} only \isa{x} appears also in the
conclusion, but not \isa{y}. Thus our induction statement is too
general. Fortunately, it can easily be specialized:
-transfer the additional premise \isa{{\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}} into the conclusion:%
+transfer the additional premise \isa{{\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}} into the conclusion:%
\end{isamarkuptxt}%
\isamarkuptrue%
%
@@ -143,8 +143,8 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ rtc{\isacharunderscore}trans{\isacharbrackleft}rule{\isacharunderscore}format{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymLongrightarrow}\ {\isacharparenleft}y{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymlongrightarrow}\ {\isacharparenleft}x{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}%
+\ rtc{\isaliteral{5F}{\isacharunderscore}}trans{\isaliteral{5B}{\isacharbrackleft}}rule{\isaliteral{5F}{\isacharunderscore}}format{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -160,28 +160,28 @@
using $\longrightarrow$.
\end{quote}
A similar heuristic for other kinds of inductions is formulated in
-\S\ref{sec:ind-var-in-prems}. The \isa{rule{\isacharunderscore}format} directive turns
-\isa{{\isasymlongrightarrow}} back into \isa{{\isasymLongrightarrow}}: in the end we obtain the original
+\S\ref{sec:ind-var-in-prems}. The \isa{rule{\isaliteral{5F}{\isacharunderscore}}format} directive turns
+\isa{{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}} back into \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}}: in the end we obtain the original
statement of our lemma.%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}erule\ rtc{\isachardot}induct{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}erule\ rtc{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
Now induction produces two subgoals which are both proved automatically:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x{\isachardot}\ {\isacharparenleft}x{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymlongrightarrow}\ {\isacharparenleft}x{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}x\ y\ za{\isachardot}\isanewline
-\isaindent{\ {\isadigit{2}}{\isachardot}\ \ \ \ }{\isasymlbrakk}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ r{\isacharsemicolon}\ {\isacharparenleft}y{\isacharcomma}\ za{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isacharsemicolon}\ {\isacharparenleft}za{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymlongrightarrow}\ {\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isasymrbrakk}\isanewline
-\isaindent{\ {\isadigit{2}}{\isachardot}\ \ \ \ }{\isasymLongrightarrow}\ {\isacharparenleft}za{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymlongrightarrow}\ {\isacharparenleft}x{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y\ za{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ za{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}za{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}za{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}blast{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}blast{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}blast\ intro{\isacharcolon}\ rtc{\isacharunderscore}step{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}blast\ intro{\isaliteral{3A}{\isacharcolon}}\ rtc{\isaliteral{5F}{\isacharunderscore}}step{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -192,19 +192,19 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-Let us now prove that \isa{r{\isacharasterisk}} is really the reflexive transitive closure
+Let us now prove that \isa{r{\isaliteral{2A}{\isacharasterisk}}} is really the reflexive transitive closure
of \isa{r}, i.e.\ the least reflexive and transitive
relation containing \isa{r}. The latter is easily formalized%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{inductive{\isacharunderscore}set}\isamarkupfalse%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse%
\isanewline
-\ \ rtc{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}set{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{for}\ r\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}set{\isachardoublequoteclose}\isanewline
+\ \ rtc{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{for}\ r\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ r\ {\isasymLongrightarrow}\ {\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ rtc{\isadigit{2}}\ r{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}{\isacharparenleft}x{\isacharcomma}x{\isacharparenright}\ {\isasymin}\ rtc{\isadigit{2}}\ r{\isachardoublequoteclose}\isanewline
-{\isacharbar}\ {\isachardoublequoteopen}{\isasymlbrakk}\ {\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ rtc{\isadigit{2}}\ r{\isacharsemicolon}\ {\isacharparenleft}y{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ rtc{\isadigit{2}}\ r\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharparenleft}x{\isacharcomma}z{\isacharparenright}\ {\isasymin}\ rtc{\isadigit{2}}\ r{\isachardoublequoteclose}%
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ rtc{\isadigit{2}}\ r{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ rtc{\isadigit{2}}\ r{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ rtc{\isadigit{2}}\ r{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ rtc{\isadigit{2}}\ r\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ rtc{\isadigit{2}}\ r{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
and the equivalence of the two definitions is easily shown by the obvious rule
@@ -212,7 +212,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ rtc{\isadigit{2}}\ r\ {\isasymLongrightarrow}\ {\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ rtc{\isadigit{2}}\ r\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -220,13 +220,13 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}erule\ rtc{\isadigit{2}}{\isachardot}induct{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}erule\ rtc{\isadigit{2}}{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}blast{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}blast{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}blast{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}blast{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}blast\ intro{\isacharcolon}\ rtc{\isacharunderscore}trans{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}blast\ intro{\isaliteral{3A}{\isacharcolon}}\ rtc{\isaliteral{5F}{\isacharunderscore}}trans{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -238,7 +238,7 @@
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymLongrightarrow}\ {\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isasymin}\ rtc{\isadigit{2}}\ r{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ rtc{\isadigit{2}}\ r{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -246,11 +246,11 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}erule\ rtc{\isachardot}induct{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}erule\ rtc{\isaliteral{2E}{\isachardot}}induct{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}blast\ intro{\isacharcolon}\ rtc{\isadigit{2}}{\isachardot}intros{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}blast\ intro{\isaliteral{3A}{\isacharcolon}}\ rtc{\isadigit{2}}{\isaliteral{2E}{\isachardot}}intros{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}blast\ intro{\isacharcolon}\ rtc{\isadigit{2}}{\isachardot}intros{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}blast\ intro{\isaliteral{3A}{\isacharcolon}}\ rtc{\isadigit{2}}{\isaliteral{2E}{\isachardot}}intros{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -263,21 +263,21 @@
\begin{isamarkuptext}%
So why did we start with the first definition? Because it is simpler. It
contains only two rules, and the single step rule is simpler than
-transitivity. As a consequence, \isa{rtc{\isachardot}induct} is simpler than
-\isa{rtc{\isadigit{2}}{\isachardot}induct}. Since inductive proofs are hard enough
+transitivity. As a consequence, \isa{rtc{\isaliteral{2E}{\isachardot}}induct} is simpler than
+\isa{rtc{\isadigit{2}}{\isaliteral{2E}{\isachardot}}induct}. Since inductive proofs are hard enough
anyway, we should always pick the simplest induction schema available.
Hence \isa{rtc} is the definition of choice.
\index{reflexive transitive closure!defining inductively|)}
\begin{exercise}\label{ex:converse-rtc-step}
-Show that the converse of \isa{rtc{\isacharunderscore}step} also holds:
+Show that the converse of \isa{rtc{\isaliteral{5F}{\isacharunderscore}}step} also holds:
\begin{isabelle}%
-\ \ \ \ \ {\isasymlbrakk}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isacharsemicolon}\ {\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharparenleft}x{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}%
+\ \ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ r{\isaliteral{2A}{\isacharasterisk}}%
\end{isabelle}
\end{exercise}
\begin{exercise}
Repeat the development of this section, but starting with a definition of
-\isa{rtc} where \isa{rtc{\isacharunderscore}step} is replaced by its converse as shown
+\isa{rtc} where \isa{rtc{\isaliteral{5F}{\isacharunderscore}}step} is replaced by its converse as shown
in exercise~\ref{ex:converse-rtc-step}.
\end{exercise}%
\end{isamarkuptext}%
--- a/doc-src/TutorialI/Misc/document/AdvancedInd.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Misc/document/AdvancedInd.tex Mon Nov 08 14:41:11 2010 +0100
@@ -40,7 +40,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymLongrightarrow}\ hd{\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharequal}\ last\ xs{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}xs\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ hd{\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ last\ xs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -48,7 +48,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ xs{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
But induction produces the warning
@@ -57,14 +57,14 @@
\end{quote}
and leads to the base case
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymLongrightarrow}\ hd\ {\isacharparenleft}rev\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\ last\ {\isacharbrackleft}{\isacharbrackright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ xs\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ hd\ {\isaliteral{28}{\isacharparenleft}}rev\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ last\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}%
\end{isabelle}
Simplification reduces the base case to this:
\begin{isabelle}
\ 1.\ xs\ {\isasymnoteq}\ []\ {\isasymLongrightarrow}\ hd\ []\ =\ last\ []
\end{isabelle}
We cannot prove this equality because we do not know what \isa{hd} and
-\isa{last} return when applied to \isa{{\isacharbrackleft}{\isacharbrackright}}.
+\isa{last} return when applied to \isa{{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}}.
We should not have ignored the warning. Because the induction
formula is only the conclusion, induction does not affect the occurrence of \isa{xs} in the premises.
@@ -73,12 +73,12 @@
heuristic applies to rule inductions; see \S\ref{sec:rtc}.}
\begin{quote}
\emph{Pull all occurrences of the induction variable into the conclusion
-using \isa{{\isasymlongrightarrow}}.}
+using \isa{{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}}.}
\end{quote}
Thus we should state the lemma as an ordinary
-implication~(\isa{{\isasymlongrightarrow}}), letting
+implication~(\isa{{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}}), letting
\attrdx{rule_format} (\S\ref{sec:forward}) convert the
-result to the usual \isa{{\isasymLongrightarrow}} form:%
+result to the usual \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}} form:%
\end{isamarkuptxt}%
\isamarkuptrue%
%
@@ -89,7 +89,7 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ hd{\isacharunderscore}rev\ {\isacharbrackleft}rule{\isacharunderscore}format{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymlongrightarrow}\ hd{\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharequal}\ last\ xs{\isachardoublequoteclose}%
+\ hd{\isaliteral{5F}{\isacharunderscore}}rev\ {\isaliteral{5B}{\isacharbrackleft}}rule{\isaliteral{5F}{\isacharunderscore}}format{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}xs\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ hd{\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ last\ xs{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -100,7 +100,7 @@
\noindent
This time, induction leaves us with a trivial base case:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymlongrightarrow}\ hd\ {\isacharparenleft}rev\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\ last\ {\isacharbrackleft}{\isacharbrackright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ hd\ {\isaliteral{28}{\isacharparenleft}}rev\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ last\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}%
\end{isabelle}
And \isa{auto} completes the proof.
@@ -108,9 +108,9 @@
induction variable, you should turn the conclusion $C$ into
\[ A@1 \longrightarrow \cdots A@n \longrightarrow C. \]
Additionally, you may also have to universally quantify some other variables,
-which can yield a fairly complex conclusion. However, \isa{rule{\isacharunderscore}format}
-can remove any number of occurrences of \isa{{\isasymforall}} and
-\isa{{\isasymlongrightarrow}}.
+which can yield a fairly complex conclusion. However, \isa{rule{\isaliteral{5F}{\isacharunderscore}}format}
+can remove any number of occurrences of \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}} and
+\isa{{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}}.
\index{induction!on a term}%
A second reason why your proposition may not be amenable to induction is that
@@ -133,7 +133,7 @@
For an example see \S\ref{sec:CTL-revisited} below.
Of course, all premises that share free variables with $t$ need to be pulled into
-the conclusion as well, under the \isa{{\isasymforall}}, again using \isa{{\isasymlongrightarrow}} as shown above.
+the conclusion as well, under the \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}}, again using \isa{{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}} as shown above.
Readers who are puzzled by the form of statement
(\ref{eqn:ind-over-term}) above should remember that the
@@ -179,33 +179,33 @@
induction, where you prove $P(n)$ under the assumption that $P(m)$
holds for all $m<n$. In Isabelle, this is the theorem \tdx{nat_less_induct}:
\begin{isabelle}%
-\ \ \ \ \ {\isacharparenleft}{\isasymAnd}n{\isachardot}\ {\isasymforall}m{\isacharless}n{\isachardot}\ P\ m\ {\isasymLongrightarrow}\ P\ n{\isacharparenright}\ {\isasymLongrightarrow}\ P\ n%
+\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}m{\isaliteral{3C}{\isacharless}}n{\isaliteral{2E}{\isachardot}}\ P\ m\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ n%
\end{isabelle}
As an application, we prove a property of the following
function:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{consts}\isamarkupfalse%
-\ f\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\isanewline
+\ f\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isacommand{axioms}\isamarkupfalse%
-\ f{\isacharunderscore}ax{\isacharcolon}\ {\isachardoublequoteopen}f{\isacharparenleft}f{\isacharparenleft}n{\isacharparenright}{\isacharparenright}\ {\isacharless}\ f{\isacharparenleft}Suc{\isacharparenleft}n{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
+\ f{\isaliteral{5F}{\isacharunderscore}}ax{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}f{\isaliteral{28}{\isacharparenleft}}f{\isaliteral{28}{\isacharparenleft}}n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3C}{\isacharless}}\ f{\isaliteral{28}{\isacharparenleft}}Suc{\isaliteral{28}{\isacharparenleft}}n{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\begin{warn}
We discourage the use of axioms because of the danger of
-inconsistencies. Axiom \isa{f{\isacharunderscore}ax} does
+inconsistencies. Axiom \isa{f{\isaliteral{5F}{\isacharunderscore}}ax} does
not introduce an inconsistency because, for example, the identity function
satisfies it. Axioms can be useful in exploratory developments, say when
you assume some well-known theorems so that you can quickly demonstrate some
point about methodology. If your example turns into a substantial proof
development, you should replace axioms by theorems.
\end{warn}\noindent
-The axiom for \isa{f} implies \isa{n\ {\isasymle}\ f\ n}, which can
+The axiom for \isa{f} implies \isa{n\ {\isaliteral{5C3C6C653E}{\isasymle}}\ f\ n}, which can
be proved by induction on \mbox{\isa{f\ n}}. Following the recipe outlined
above, we have to phrase the proposition as follows to allow induction:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ f{\isacharunderscore}incr{\isacharunderscore}lem{\isacharcolon}\ {\isachardoublequoteopen}{\isasymforall}i{\isachardot}\ k\ {\isacharequal}\ f\ i\ {\isasymlongrightarrow}\ i\ {\isasymle}\ f\ i{\isachardoublequoteclose}%
+\ f{\isaliteral{5F}{\isacharunderscore}}incr{\isaliteral{5F}{\isacharunderscore}}lem{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{2E}{\isachardot}}\ k\ {\isaliteral{3D}{\isacharequal}}\ f\ i\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ i\ {\isaliteral{5C3C6C653E}{\isasymle}}\ f\ i{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -214,39 +214,39 @@
%
\begin{isamarkuptxt}%
\noindent
-To perform induction on \isa{k} using \isa{nat{\isacharunderscore}less{\isacharunderscore}induct}, we use
+To perform induction on \isa{k} using \isa{nat{\isaliteral{5F}{\isacharunderscore}}less{\isaliteral{5F}{\isacharunderscore}}induct}, we use
the same general induction method as for recursion induction (see
\S\ref{sec:fun-induction}):%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ k\ rule{\isacharcolon}\ nat{\isacharunderscore}less{\isacharunderscore}induct{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ k\ rule{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{5F}{\isacharunderscore}}less{\isaliteral{5F}{\isacharunderscore}}induct{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
We get the following proof state:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}n{\isachardot}\ {\isasymforall}m{\isacharless}n{\isachardot}\ {\isasymforall}i{\isachardot}\ m\ {\isacharequal}\ f\ i\ {\isasymlongrightarrow}\ i\ {\isasymle}\ f\ i\ {\isasymLongrightarrow}\ {\isasymforall}i{\isachardot}\ n\ {\isacharequal}\ f\ i\ {\isasymlongrightarrow}\ i\ {\isasymle}\ f\ i%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}m{\isaliteral{3C}{\isacharless}}n{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{2E}{\isachardot}}\ m\ {\isaliteral{3D}{\isacharequal}}\ f\ i\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ i\ {\isaliteral{5C3C6C653E}{\isasymle}}\ f\ i\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{2E}{\isachardot}}\ n\ {\isaliteral{3D}{\isacharequal}}\ f\ i\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ i\ {\isaliteral{5C3C6C653E}{\isasymle}}\ f\ i%
\end{isabelle}
-After stripping the \isa{{\isasymforall}i}, the proof continues with a case
-distinction on \isa{i}. The case \isa{i\ {\isacharequal}\ {\isadigit{0}}} is trivial and we focus on
+After stripping the \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i}, the proof continues with a case
+distinction on \isa{i}. The case \isa{i\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}} is trivial and we focus on
the other case:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule\ allI{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule\ allI{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}case{\isacharunderscore}tac\ i{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}case{\isaliteral{5F}{\isacharunderscore}}tac\ i{\isaliteral{29}{\isacharparenright}}\isanewline
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}n\ i\ nat{\isachardot}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymlbrakk}{\isasymforall}m{\isacharless}n{\isachardot}\ {\isasymforall}i{\isachardot}\ m\ {\isacharequal}\ f\ i\ {\isasymlongrightarrow}\ i\ {\isasymle}\ f\ i{\isacharsemicolon}\ i\ {\isacharequal}\ Suc\ nat{\isasymrbrakk}\ {\isasymLongrightarrow}\ n\ {\isacharequal}\ f\ i\ {\isasymlongrightarrow}\ i\ {\isasymle}\ f\ i%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}n\ i\ nat{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}m{\isaliteral{3C}{\isacharless}}n{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{2E}{\isachardot}}\ m\ {\isaliteral{3D}{\isacharequal}}\ f\ i\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ i\ {\isaliteral{5C3C6C653E}{\isasymle}}\ f\ i{\isaliteral{3B}{\isacharsemicolon}}\ i\ {\isaliteral{3D}{\isacharequal}}\ Suc\ nat{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ n\ {\isaliteral{3D}{\isacharequal}}\ f\ i\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ i\ {\isaliteral{5C3C6C653E}{\isasymle}}\ f\ i%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{by}\isamarkupfalse%
-{\isacharparenleft}blast\ intro{\isacharbang}{\isacharcolon}\ f{\isacharunderscore}ax\ Suc{\isacharunderscore}leI\ intro{\isacharcolon}\ le{\isacharunderscore}less{\isacharunderscore}trans{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}blast\ intro{\isaliteral{21}{\isacharbang}}{\isaliteral{3A}{\isacharcolon}}\ f{\isaliteral{5F}{\isacharunderscore}}ax\ Suc{\isaliteral{5F}{\isacharunderscore}}leI\ intro{\isaliteral{3A}{\isacharcolon}}\ le{\isaliteral{5F}{\isacharunderscore}}less{\isaliteral{5F}{\isacharunderscore}}trans{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -258,42 +258,42 @@
\noindent
If you find the last step puzzling, here are the two lemmas it employs:
\begin{isabelle}
-\isa{m\ {\isacharless}\ n\ {\isasymLongrightarrow}\ Suc\ m\ {\isasymle}\ n}
+\isa{m\ {\isaliteral{3C}{\isacharless}}\ n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Suc\ m\ {\isaliteral{5C3C6C653E}{\isasymle}}\ n}
\rulename{Suc_leI}\isanewline
-\isa{{\isasymlbrakk}x\ {\isasymle}\ y{\isacharsemicolon}\ y\ {\isacharless}\ z{\isasymrbrakk}\ {\isasymLongrightarrow}\ x\ {\isacharless}\ z}
+\isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}x\ {\isaliteral{5C3C6C653E}{\isasymle}}\ y{\isaliteral{3B}{\isacharsemicolon}}\ y\ {\isaliteral{3C}{\isacharless}}\ z{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ x\ {\isaliteral{3C}{\isacharless}}\ z}
\rulename{le_less_trans}
\end{isabelle}
%
The proof goes like this (writing \isa{j} instead of \isa{nat}).
-Since \isa{i\ {\isacharequal}\ Suc\ j} it suffices to show
-\hbox{\isa{j\ {\isacharless}\ f\ {\isacharparenleft}Suc\ j{\isacharparenright}}},
-by \isa{Suc{\isacharunderscore}leI}\@. This is
-proved as follows. From \isa{f{\isacharunderscore}ax} we have \isa{f\ {\isacharparenleft}f\ j{\isacharparenright}\ {\isacharless}\ f\ {\isacharparenleft}Suc\ j{\isacharparenright}}
-(1) which implies \isa{f\ j\ {\isasymle}\ f\ {\isacharparenleft}f\ j{\isacharparenright}} by the induction hypothesis.
-Using (1) once more we obtain \isa{f\ j\ {\isacharless}\ f\ {\isacharparenleft}Suc\ j{\isacharparenright}} (2) by the transitivity
-rule \isa{le{\isacharunderscore}less{\isacharunderscore}trans}.
-Using the induction hypothesis once more we obtain \isa{j\ {\isasymle}\ f\ j}
-which, together with (2) yields \isa{j\ {\isacharless}\ f\ {\isacharparenleft}Suc\ j{\isacharparenright}} (again by
-\isa{le{\isacharunderscore}less{\isacharunderscore}trans}).
+Since \isa{i\ {\isaliteral{3D}{\isacharequal}}\ Suc\ j} it suffices to show
+\hbox{\isa{j\ {\isaliteral{3C}{\isacharless}}\ f\ {\isaliteral{28}{\isacharparenleft}}Suc\ j{\isaliteral{29}{\isacharparenright}}}},
+by \isa{Suc{\isaliteral{5F}{\isacharunderscore}}leI}\@. This is
+proved as follows. From \isa{f{\isaliteral{5F}{\isacharunderscore}}ax} we have \isa{f\ {\isaliteral{28}{\isacharparenleft}}f\ j{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3C}{\isacharless}}\ f\ {\isaliteral{28}{\isacharparenleft}}Suc\ j{\isaliteral{29}{\isacharparenright}}}
+(1) which implies \isa{f\ j\ {\isaliteral{5C3C6C653E}{\isasymle}}\ f\ {\isaliteral{28}{\isacharparenleft}}f\ j{\isaliteral{29}{\isacharparenright}}} by the induction hypothesis.
+Using (1) once more we obtain \isa{f\ j\ {\isaliteral{3C}{\isacharless}}\ f\ {\isaliteral{28}{\isacharparenleft}}Suc\ j{\isaliteral{29}{\isacharparenright}}} (2) by the transitivity
+rule \isa{le{\isaliteral{5F}{\isacharunderscore}}less{\isaliteral{5F}{\isacharunderscore}}trans}.
+Using the induction hypothesis once more we obtain \isa{j\ {\isaliteral{5C3C6C653E}{\isasymle}}\ f\ j}
+which, together with (2) yields \isa{j\ {\isaliteral{3C}{\isacharless}}\ f\ {\isaliteral{28}{\isacharparenleft}}Suc\ j{\isaliteral{29}{\isacharparenright}}} (again by
+\isa{le{\isaliteral{5F}{\isacharunderscore}}less{\isaliteral{5F}{\isacharunderscore}}trans}).
This last step shows both the power and the danger of automatic proofs. They
will usually not tell you how the proof goes, because it can be hard to
translate the internal proof into a human-readable format. Automatic
proofs are easy to write but hard to read and understand.
-The desired result, \isa{i\ {\isasymle}\ f\ i}, follows from \isa{f{\isacharunderscore}incr{\isacharunderscore}lem}:%
+The desired result, \isa{i\ {\isaliteral{5C3C6C653E}{\isasymle}}\ f\ i}, follows from \isa{f{\isaliteral{5F}{\isacharunderscore}}incr{\isaliteral{5F}{\isacharunderscore}}lem}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemmas}\isamarkupfalse%
-\ f{\isacharunderscore}incr\ {\isacharequal}\ f{\isacharunderscore}incr{\isacharunderscore}lem{\isacharbrackleft}rule{\isacharunderscore}format{\isacharcomma}\ OF\ refl{\isacharbrackright}%
+\ f{\isaliteral{5F}{\isacharunderscore}}incr\ {\isaliteral{3D}{\isacharequal}}\ f{\isaliteral{5F}{\isacharunderscore}}incr{\isaliteral{5F}{\isacharunderscore}}lem{\isaliteral{5B}{\isacharbrackleft}}rule{\isaliteral{5F}{\isacharunderscore}}format{\isaliteral{2C}{\isacharcomma}}\ OF\ refl{\isaliteral{5D}{\isacharbrackright}}%
\begin{isamarkuptext}%
\noindent
-The final \isa{refl} gets rid of the premise \isa{{\isacharquery}k\ {\isacharequal}\ f\ {\isacharquery}i}.
+The final \isa{refl} gets rid of the premise \isa{{\isaliteral{3F}{\isacharquery}}k\ {\isaliteral{3D}{\isacharequal}}\ f\ {\isaliteral{3F}{\isacharquery}}i}.
We could have included this derivation in the original statement of the lemma:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ f{\isacharunderscore}incr{\isacharbrackleft}rule{\isacharunderscore}format{\isacharcomma}\ OF\ refl{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymforall}i{\isachardot}\ k\ {\isacharequal}\ f\ i\ {\isasymlongrightarrow}\ i\ {\isasymle}\ f\ i{\isachardoublequoteclose}%
+\ f{\isaliteral{5F}{\isacharunderscore}}incr{\isaliteral{5B}{\isacharbrackleft}}rule{\isaliteral{5F}{\isacharunderscore}}format{\isaliteral{2C}{\isacharcomma}}\ OF\ refl{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}i{\isaliteral{2E}{\isachardot}}\ k\ {\isaliteral{3D}{\isacharequal}}\ f\ i\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ i\ {\isaliteral{5C3C6C653E}{\isasymle}}\ f\ i{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -317,18 +317,18 @@
whose conclusion is of the form ${?}P~?x@1 \dots ?x@n$, in which case the
format is
\begin{quote}
-\isacommand{apply}\isa{{\isacharparenleft}induct{\isacharunderscore}tac} $y@1 \dots y@n$ \isa{rule{\isacharcolon}} $r$\isa{{\isacharparenright}}
+\isacommand{apply}\isa{{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac} $y@1 \dots y@n$ \isa{rule{\isaliteral{3A}{\isacharcolon}}} $r$\isa{{\isaliteral{29}{\isacharparenright}}}
\end{quote}
where $y@1, \dots, y@n$ are variables in the conclusion of the first subgoal.
-A further useful induction rule is \isa{length{\isacharunderscore}induct},
+A further useful induction rule is \isa{length{\isaliteral{5F}{\isacharunderscore}}induct},
induction on the length of a list\indexbold{*length_induct}
\begin{isabelle}%
-\ \ \ \ \ {\isacharparenleft}{\isasymAnd}xs{\isachardot}\ {\isasymforall}ys{\isachardot}\ length\ ys\ {\isacharless}\ length\ xs\ {\isasymlongrightarrow}\ P\ ys\ {\isasymLongrightarrow}\ P\ xs{\isacharparenright}\ {\isasymLongrightarrow}\ P\ xs%
+\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}xs{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}ys{\isaliteral{2E}{\isachardot}}\ length\ ys\ {\isaliteral{3C}{\isacharless}}\ length\ xs\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ P\ ys\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ xs%
\end{isabelle}
-which is a special case of \isa{measure{\isacharunderscore}induct}
+which is a special case of \isa{measure{\isaliteral{5F}{\isacharunderscore}}induct}
\begin{isabelle}%
-\ \ \ \ \ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ {\isasymforall}y{\isachardot}\ f\ y\ {\isacharless}\ f\ x\ {\isasymlongrightarrow}\ P\ y\ {\isasymLongrightarrow}\ P\ x{\isacharparenright}\ {\isasymLongrightarrow}\ P\ a%
+\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}y{\isaliteral{2E}{\isachardot}}\ f\ y\ {\isaliteral{3C}{\isacharless}}\ f\ x\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ P\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ a%
\end{isabelle}
where \isa{f} may be any function into type \isa{nat}.%
\end{isamarkuptext}%
@@ -343,13 +343,13 @@
\index{induction!deriving new schemas}%
Induction schemas are ordinary theorems and you can derive new ones
whenever you wish. This section shows you how, using the example
-of \isa{nat{\isacharunderscore}less{\isacharunderscore}induct}. Assume we only have structural induction
+of \isa{nat{\isaliteral{5F}{\isacharunderscore}}less{\isaliteral{5F}{\isacharunderscore}}induct}. Assume we only have structural induction
available for \isa{nat} and want to derive complete induction. We
must generalize the statement as shown:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ induct{\isacharunderscore}lem{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isasymAnd}n{\isacharcolon}{\isacharcolon}nat{\isachardot}\ {\isasymforall}m{\isacharless}n{\isachardot}\ P\ m\ {\isasymLongrightarrow}\ P\ n{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymforall}m{\isacharless}n{\isachardot}\ P\ m{\isachardoublequoteclose}\isanewline
+\ induct{\isaliteral{5F}{\isacharunderscore}}lem{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}m{\isaliteral{3C}{\isacharless}}n{\isaliteral{2E}{\isachardot}}\ P\ m\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}m{\isaliteral{3C}{\isacharless}}n{\isaliteral{2E}{\isachardot}}\ P\ m{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -357,18 +357,18 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ n{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ n{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
-The base case is vacuously true. For the induction step (\isa{m\ {\isacharless}\ Suc\ n}) we distinguish two cases: case \isa{m\ {\isacharless}\ n} is true by induction
-hypothesis and case \isa{m\ {\isacharequal}\ n} follows from the assumption, again using
+The base case is vacuously true. For the induction step (\isa{m\ {\isaliteral{3C}{\isacharless}}\ Suc\ n}) we distinguish two cases: case \isa{m\ {\isaliteral{3C}{\isacharless}}\ n} is true by induction
+hypothesis and case \isa{m\ {\isaliteral{3D}{\isacharequal}}\ n} follows from the assumption, again using
the induction hypothesis:%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}blast{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}blast{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{by}\isamarkupfalse%
-{\isacharparenleft}blast\ elim{\isacharcolon}\ less{\isacharunderscore}SucE{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}blast\ elim{\isaliteral{3A}{\isacharcolon}}\ less{\isaliteral{5F}{\isacharunderscore}}SucE{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -378,21 +378,21 @@
%
\begin{isamarkuptext}%
\noindent
-The elimination rule \isa{less{\isacharunderscore}SucE} expresses the case distinction:
+The elimination rule \isa{less{\isaliteral{5F}{\isacharunderscore}}SucE} expresses the case distinction:
\begin{isabelle}%
-\ \ \ \ \ {\isasymlbrakk}m\ {\isacharless}\ Suc\ n{\isacharsemicolon}\ m\ {\isacharless}\ n\ {\isasymLongrightarrow}\ P{\isacharsemicolon}\ m\ {\isacharequal}\ n\ {\isasymLongrightarrow}\ P{\isasymrbrakk}\ {\isasymLongrightarrow}\ P%
+\ \ \ \ \ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}m\ {\isaliteral{3C}{\isacharless}}\ Suc\ n{\isaliteral{3B}{\isacharsemicolon}}\ m\ {\isaliteral{3C}{\isacharless}}\ n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{3B}{\isacharsemicolon}}\ m\ {\isaliteral{3D}{\isacharequal}}\ n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P%
\end{isabelle}
Now it is straightforward to derive the original version of
-\isa{nat{\isacharunderscore}less{\isacharunderscore}induct} by manipulating the conclusion of the above
+\isa{nat{\isaliteral{5F}{\isacharunderscore}}less{\isaliteral{5F}{\isacharunderscore}}induct} by manipulating the conclusion of the above
lemma: instantiate \isa{n} by \isa{Suc\ n} and \isa{m} by \isa{n}
-and remove the trivial condition \isa{n\ {\isacharless}\ Suc\ n}. Fortunately, this
+and remove the trivial condition \isa{n\ {\isaliteral{3C}{\isacharless}}\ Suc\ n}. Fortunately, this
happens automatically when we add the lemma as a new premise to the
desired goal:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ nat{\isacharunderscore}less{\isacharunderscore}induct{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isasymAnd}n{\isacharcolon}{\isacharcolon}nat{\isachardot}\ {\isasymforall}m{\isacharless}n{\isachardot}\ P\ m\ {\isasymLongrightarrow}\ P\ n{\isacharparenright}\ {\isasymLongrightarrow}\ P\ n{\isachardoublequoteclose}\isanewline
+\ nat{\isaliteral{5F}{\isacharunderscore}}less{\isaliteral{5F}{\isacharunderscore}}induct{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}n{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}m{\isaliteral{3C}{\isacharless}}n{\isaliteral{2E}{\isachardot}}\ P\ m\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ n{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -400,7 +400,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-{\isacharparenleft}insert\ induct{\isacharunderscore}lem{\isacharcomma}\ blast{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}insert\ induct{\isaliteral{5F}{\isacharunderscore}}lem{\isaliteral{2C}{\isacharcomma}}\ blast{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -411,8 +411,8 @@
\begin{isamarkuptext}%
HOL already provides the mother of
all inductions, well-founded induction (see \S\ref{sec:Well-founded}). For
-example theorem \isa{nat{\isacharunderscore}less{\isacharunderscore}induct} is
-a special case of \isa{wf{\isacharunderscore}induct} where \isa{r} is \isa{{\isacharless}} on
+example theorem \isa{nat{\isaliteral{5F}{\isacharunderscore}}less{\isaliteral{5F}{\isacharunderscore}}induct} is
+a special case of \isa{wf{\isaliteral{5F}{\isacharunderscore}}induct} where \isa{r} is \isa{{\isaliteral{3C}{\isacharless}}} on
\isa{nat}. The details can be found in theory \isa{Wellfounded_Recursion}.%
\end{isamarkuptext}%
\isamarkuptrue%
--- a/doc-src/TutorialI/Misc/document/Itrev.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Misc/document/Itrev.tex Mon Nov 08 14:41:11 2010 +0100
@@ -46,15 +46,15 @@
\emph{Do induction on argument number $i$ if the function is defined by
recursion in argument number $i$.}
\end{quote}
-When we look at the proof of \isa{{\isacharparenleft}xs{\isacharat}ys{\isacharparenright}\ {\isacharat}\ zs\ {\isacharequal}\ xs\ {\isacharat}\ {\isacharparenleft}ys{\isacharat}zs{\isacharparenright}}
+When we look at the proof of \isa{{\isaliteral{28}{\isacharparenleft}}xs{\isaliteral{40}{\isacharat}}ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{40}{\isacharat}}\ zs\ {\isaliteral{3D}{\isacharequal}}\ xs\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{28}{\isacharparenleft}}ys{\isaliteral{40}{\isacharat}}zs{\isaliteral{29}{\isacharparenright}}}
in \S\ref{sec:intro-proof} we find
\begin{itemize}
-\item \isa{{\isacharat}} is recursive in
+\item \isa{{\isaliteral{40}{\isacharat}}} is recursive in
the first argument
\item \isa{xs} occurs only as the first argument of
-\isa{{\isacharat}}
+\isa{{\isaliteral{40}{\isacharat}}}
\item both \isa{ys} and \isa{zs} occur at least once as
-the second argument of \isa{{\isacharat}}
+the second argument of \isa{{\isaliteral{40}{\isacharat}}}
\end{itemize}
Hence it is natural to perform induction on~\isa{xs}.
@@ -65,16 +65,16 @@
step to go through. Let us illustrate the idea with an example.
Function \cdx{rev} has quadratic worst-case running time
-because it calls function \isa{{\isacharat}} for each element of the list and
-\isa{{\isacharat}} is linear in its first argument. A linear time version of
+because it calls function \isa{{\isaliteral{40}{\isacharat}}} for each element of the list and
+\isa{{\isaliteral{40}{\isacharat}}} is linear in its first argument. A linear time version of
\isa{rev} reqires an extra argument where the result is accumulated
-gradually, using only~\isa{{\isacharhash}}:%
+gradually, using only~\isa{{\isaliteral{23}{\isacharhash}}}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ itrev\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}itrev\ {\isacharbrackleft}{\isacharbrackright}\ \ \ \ \ ys\ {\isacharequal}\ ys{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}itrev\ {\isacharparenleft}x{\isacharhash}xs{\isacharparenright}\ ys\ {\isacharequal}\ itrev\ xs\ {\isacharparenleft}x{\isacharhash}ys{\isacharparenright}{\isachardoublequoteclose}%
+\ itrev\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}itrev\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ \ \ \ \ ys\ {\isaliteral{3D}{\isacharequal}}\ ys{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}itrev\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{23}{\isacharhash}}xs{\isaliteral{29}{\isacharparenright}}\ ys\ {\isaliteral{3D}{\isacharequal}}\ itrev\ xs\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{23}{\isacharhash}}ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
The behaviour of \cdx{itrev} is simple: it reverses
@@ -88,7 +88,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}itrev\ xs\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ rev\ xs{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}itrev\ xs\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ rev\ xs{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -101,22 +101,22 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharcomma}\ simp{\isacharunderscore}all{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ xs{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
Unfortunately, this attempt does not prove
the induction step:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}a\ list{\isachardot}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }itrev\ list\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ rev\ list\ {\isasymLongrightarrow}\ itrev\ list\ {\isacharbrackleft}a{\isacharbrackright}\ {\isacharequal}\ rev\ list\ {\isacharat}\ {\isacharbrackleft}a{\isacharbrackright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a\ list{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }itrev\ list\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ rev\ list\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ itrev\ list\ {\isaliteral{5B}{\isacharbrackleft}}a{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ rev\ list\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{5B}{\isacharbrackleft}}a{\isaliteral{5D}{\isacharbrackright}}%
\end{isabelle}
The induction hypothesis is too weak. The fixed
-argument,~\isa{{\isacharbrackleft}{\isacharbrackright}}, prevents it from rewriting the conclusion.
+argument,~\isa{{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}}, prevents it from rewriting the conclusion.
This example suggests a heuristic:
\begin{quote}\index{generalizing induction formulae}%
\emph{Generalize goals for induction by replacing constants by variables.}
\end{quote}
-Of course one cannot do this na\"{\i}vely: \isa{itrev\ xs\ ys\ {\isacharequal}\ rev\ xs} is
+Of course one cannot do this na\"{\i}vely: \isa{itrev\ xs\ ys\ {\isaliteral{3D}{\isacharequal}}\ rev\ xs} is
just not true. The correct generalization is%
\end{isamarkuptxt}%
\isamarkuptrue%
@@ -128,7 +128,7 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}itrev\ xs\ ys\ {\isacharequal}\ rev\ xs\ {\isacharat}\ ys{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}itrev\ xs\ ys\ {\isaliteral{3D}{\isacharequal}}\ rev\ xs\ {\isaliteral{40}{\isacharat}}\ ys{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -137,7 +137,7 @@
%
\begin{isamarkuptxt}%
\noindent
-If \isa{ys} is replaced by \isa{{\isacharbrackleft}{\isacharbrackright}}, the right-hand side simplifies to
+If \isa{ys} is replaced by \isa{{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}}, the right-hand side simplifies to
\isa{rev\ xs}, as required.
In this instance it was easy to guess the right generalization.
@@ -147,14 +147,14 @@
induction, and we repeat our proof attempt. Unfortunately, we are still
not there:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}a\ list{\isachardot}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }itrev\ list\ ys\ {\isacharequal}\ rev\ list\ {\isacharat}\ ys\ {\isasymLongrightarrow}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }itrev\ list\ {\isacharparenleft}a\ {\isacharhash}\ ys{\isacharparenright}\ {\isacharequal}\ rev\ list\ {\isacharat}\ a\ {\isacharhash}\ ys%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a\ list{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }itrev\ list\ ys\ {\isaliteral{3D}{\isacharequal}}\ rev\ list\ {\isaliteral{40}{\isacharat}}\ ys\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }itrev\ list\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{23}{\isacharhash}}\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rev\ list\ {\isaliteral{40}{\isacharat}}\ a\ {\isaliteral{23}{\isacharhash}}\ ys%
\end{isabelle}
The induction hypothesis is still too weak, but this time it takes no
intuition to generalize: the problem is that \isa{ys} is fixed throughout
the subgoal, but the induction hypothesis needs to be applied with
-\isa{a\ {\isacharhash}\ ys} instead of \isa{ys}. Hence we prove the theorem
+\isa{a\ {\isaliteral{23}{\isacharhash}}\ ys} instead of \isa{ys}. Hence we prove the theorem
for all \isa{ys} instead of a fixed one:%
\end{isamarkuptxt}%
\isamarkuptrue%
@@ -166,7 +166,7 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymforall}ys{\isachardot}\ itrev\ xs\ ys\ {\isacharequal}\ rev\ xs\ {\isacharat}\ ys{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}ys{\isaliteral{2E}{\isachardot}}\ itrev\ xs\ ys\ {\isaliteral{3D}{\isacharequal}}\ rev\ xs\ {\isaliteral{40}{\isacharat}}\ ys{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -203,8 +203,8 @@
than the left-hand side.}
\end{quote}
This heuristic is tricky to apply because it is not obvious that
-\isa{rev\ xs\ {\isacharat}\ ys} is simpler than \isa{itrev\ xs\ ys}. But see what
-happens if you try to prove \isa{rev\ xs\ {\isacharat}\ ys\ {\isacharequal}\ itrev\ xs\ ys}!
+\isa{rev\ xs\ {\isaliteral{40}{\isacharat}}\ ys} is simpler than \isa{itrev\ xs\ ys}. But see what
+happens if you try to prove \isa{rev\ xs\ {\isaliteral{40}{\isacharat}}\ ys\ {\isaliteral{3D}{\isacharequal}}\ itrev\ xs\ ys}!
If you have tried these heuristics and still find your
induction does not go through, and no obvious lemma suggests itself, you may
--- a/doc-src/TutorialI/Misc/document/Option2.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Misc/document/Option2.tex Mon Nov 08 14:41:11 2010 +0100
@@ -22,7 +22,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ {\isacharprime}a\ option\ {\isacharequal}\ None\ {\isacharbar}\ Some\ {\isacharprime}a%
+\ {\isaliteral{27}{\isacharprime}}a\ option\ {\isaliteral{3D}{\isacharequal}}\ None\ {\isaliteral{7C}{\isacharbar}}\ Some\ {\isaliteral{27}{\isacharprime}}a%
\begin{isamarkuptext}%
\noindent
Frequently one needs to add a distinguished element to some existing type.
--- a/doc-src/TutorialI/Misc/document/Plus.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Misc/document/Plus.tex Mon Nov 08 14:41:11 2010 +0100
@@ -20,9 +20,9 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ add\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}add\ m\ {\isadigit{0}}\ {\isacharequal}\ m{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}add\ m\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ add\ {\isacharparenleft}Suc\ m{\isacharparenright}\ n{\isachardoublequoteclose}%
+\ add\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}add\ m\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ m{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}add\ m\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ add\ {\isaliteral{28}{\isacharparenleft}}Suc\ m{\isaliteral{29}{\isacharparenright}}\ n{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent and prove%
\end{isamarkuptext}%
@@ -41,7 +41,7 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}add\ m\ n\ {\isacharequal}\ m{\isacharplus}n{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}add\ m\ n\ {\isaliteral{3D}{\isacharequal}}\ m{\isaliteral{2B}{\isacharplus}}n{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
--- a/doc-src/TutorialI/Misc/document/Tree.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Misc/document/Tree.tex Mon Nov 08 14:41:11 2010 +0100
@@ -21,7 +21,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ {\isacharprime}a\ tree\ {\isacharequal}\ Tip\ {\isacharbar}\ Node\ {\isachardoublequoteopen}{\isacharprime}a\ tree{\isachardoublequoteclose}\ {\isacharprime}a\ {\isachardoublequoteopen}{\isacharprime}a\ tree{\isachardoublequoteclose}%
+\ {\isaliteral{27}{\isacharprime}}a\ tree\ {\isaliteral{3D}{\isacharequal}}\ Tip\ {\isaliteral{7C}{\isacharbar}}\ Node\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ tree{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ tree{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
Define a function \isa{mirror} that mirrors a binary tree
@@ -29,7 +29,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ mirror{\isacharunderscore}mirror{\isacharcolon}\ {\isachardoublequoteopen}mirror{\isacharparenleft}mirror\ t{\isacharparenright}\ {\isacharequal}\ t{\isachardoublequoteclose}%
+\ mirror{\isaliteral{5F}{\isacharunderscore}}mirror{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}mirror{\isaliteral{28}{\isacharparenleft}}mirror\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ t{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -50,7 +50,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}flatten{\isacharparenleft}mirror\ t{\isacharparenright}\ {\isacharequal}\ rev{\isacharparenleft}flatten\ t{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}flatten{\isaliteral{28}{\isacharparenleft}}mirror\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rev{\isaliteral{28}{\isacharparenleft}}flatten\ t{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
--- a/doc-src/TutorialI/Misc/document/Tree2.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Misc/document/Tree2.tex Mon Nov 08 14:41:11 2010 +0100
@@ -18,12 +18,12 @@
\begin{isamarkuptext}%
\noindent In Exercise~\ref{ex:Tree} we defined a function
\isa{flatten} from trees to lists. The straightforward version of
-\isa{flatten} is based on \isa{{\isacharat}} and is thus, like \isa{rev},
+\isa{flatten} is based on \isa{{\isaliteral{40}{\isacharat}}} and is thus, like \isa{rev},
quadratic. A linear time version of \isa{flatten} again reqires an extra
argument, the accumulator. Define%
\end{isamarkuptext}%
\isamarkuptrue%
-flatten{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ tree\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequoteclose}%
+flatten{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ tree\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent and prove%
\end{isamarkuptext}%
@@ -42,7 +42,7 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}flatten{\isadigit{2}}\ t\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ flatten\ t{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}flatten{\isadigit{2}}\ t\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ flatten\ t{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
--- a/doc-src/TutorialI/Misc/document/appendix.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Misc/document/appendix.tex Mon Nov 08 14:41:11 2010 +0100
@@ -21,21 +21,21 @@
\begin{tabular}{lll}
Constant & Type & Syntax \\
\hline
-\isa{{\isadigit{0}}} & \isa{{\isacharprime}a{\isasymColon}zero} \\
-\isa{{\isadigit{1}}} & \isa{{\isacharprime}a{\isasymColon}one} \\
-\isa{plus} & \isa{{\isacharprime}a{\isasymColon}plus\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}plus\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}plus} & (infixl $+$ 65) \\
-\isa{minus} & \isa{{\isacharprime}a{\isasymColon}minus\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}minus\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}minus} & (infixl $-$ 65) \\
-\isa{uminus} & \isa{{\isacharprime}a{\isasymColon}uminus\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}uminus} & $- x$ \\
-\isa{times} & \isa{{\isacharprime}a{\isasymColon}times\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}times\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}times} & (infixl $*$ 70) \\
-\isa{divide} & \isa{{\isacharprime}a{\isasymColon}inverse\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}inverse\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}inverse} & (infixl $/$ 70) \\
-\isa{Divides{\isachardot}div} & \isa{{\isacharprime}a{\isasymColon}div\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}div\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}div} & (infixl $div$ 70) \\
-\isa{Divides{\isachardot}mod} & \isa{{\isacharprime}a{\isasymColon}div\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}div\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}div} & (infixl $mod$ 70) \\
-\isa{abs} & \isa{{\isacharprime}a{\isasymColon}abs\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}abs} & ${\mid} x {\mid}$ \\
-\isa{sgn} & \isa{{\isacharprime}a{\isasymColon}sgn\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}sgn} \\
-\isa{less{\isacharunderscore}eq} & \isa{{\isacharprime}a{\isasymColon}ord\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}ord\ {\isasymRightarrow}\ bool} & (infixl $\le$ 50) \\
-\isa{less} & \isa{{\isacharprime}a{\isasymColon}ord\ {\isasymRightarrow}\ {\isacharprime}a{\isasymColon}ord\ {\isasymRightarrow}\ bool} & (infixl $<$ 50) \\
-\isa{top} & \isa{{\isacharprime}a{\isasymColon}top} \\
-\isa{bot} & \isa{{\isacharprime}a{\isasymColon}bot}
+\isa{{\isadigit{0}}} & \isa{{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}zero} \\
+\isa{{\isadigit{1}}} & \isa{{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}one} \\
+\isa{plus} & \isa{{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}plus\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}plus\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}plus} & (infixl $+$ 65) \\
+\isa{minus} & \isa{{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}minus\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}minus\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}minus} & (infixl $-$ 65) \\
+\isa{uminus} & \isa{{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}uminus\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}uminus} & $- x$ \\
+\isa{times} & \isa{{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}times\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}times\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}times} & (infixl $*$ 70) \\
+\isa{divide} & \isa{{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}inverse\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}inverse\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}inverse} & (infixl $/$ 70) \\
+\isa{Divides{\isaliteral{2E}{\isachardot}}div} & \isa{{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}div\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}div\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}div} & (infixl $div$ 70) \\
+\isa{Divides{\isaliteral{2E}{\isachardot}}mod} & \isa{{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}div\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}div\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}div} & (infixl $mod$ 70) \\
+\isa{abs} & \isa{{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}abs\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}abs} & ${\mid} x {\mid}$ \\
+\isa{sgn} & \isa{{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}sgn\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}sgn} \\
+\isa{less{\isaliteral{5F}{\isacharunderscore}}eq} & \isa{{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}ord\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}ord\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool} & (infixl $\le$ 50) \\
+\isa{less} & \isa{{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}ord\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}ord\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool} & (infixl $<$ 50) \\
+\isa{top} & \isa{{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}top} \\
+\isa{bot} & \isa{{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}bot}
\end{tabular}
\caption{Important Overloaded Constants in Main}
\label{tab:overloading}
--- a/doc-src/TutorialI/Misc/document/case_exprs.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Misc/document/case_exprs.tex Mon Nov 08 14:41:11 2010 +0100
@@ -1,6 +1,6 @@
%
\begin{isabellebody}%
-\def\isabellecontext{case{\isacharunderscore}exprs}%
+\def\isabellecontext{case{\isaliteral{5F}{\isacharunderscore}}exprs}%
%
\isadelimtheory
%
@@ -21,22 +21,22 @@
HOL also features \isa{case}-expressions for analyzing
elements of a datatype. For example,
\begin{isabelle}%
-\ \ \ \ \ case\ xs\ of\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymRightarrow}\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbar}\ y\ {\isacharhash}\ ys\ {\isasymRightarrow}\ y%
+\ \ \ \ \ case\ xs\ of\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7C}{\isacharbar}}\ y\ {\isaliteral{23}{\isacharhash}}\ ys\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ y%
\end{isabelle}
-evaluates to \isa{{\isacharbrackleft}{\isacharbrackright}} if \isa{xs} is \isa{{\isacharbrackleft}{\isacharbrackright}} and to \isa{y} if
-\isa{xs} is \isa{y\ {\isacharhash}\ ys}. (Since the result in both branches must be of
-the same type, it follows that \isa{y} is of type \isa{{\isacharprime}a\ list} and hence
-that \isa{xs} is of type \isa{{\isacharprime}a\ list\ list}.)
+evaluates to \isa{{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}} if \isa{xs} is \isa{{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}} and to \isa{y} if
+\isa{xs} is \isa{y\ {\isaliteral{23}{\isacharhash}}\ ys}. (Since the result in both branches must be of
+the same type, it follows that \isa{y} is of type \isa{{\isaliteral{27}{\isacharprime}}a\ list} and hence
+that \isa{xs} is of type \isa{{\isaliteral{27}{\isacharprime}}a\ list\ list}.)
In general, case expressions are of the form
\[
\begin{array}{c}
-\isa{case}~e~\isa{of}\ pattern@1~\isa{{\isasymRightarrow}}~e@1\ \isa{{\isacharbar}}\ \dots\
- \isa{{\isacharbar}}~pattern@m~\isa{{\isasymRightarrow}}~e@m
+\isa{case}~e~\isa{of}\ pattern@1~\isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}}~e@1\ \isa{{\isaliteral{7C}{\isacharbar}}}\ \dots\
+ \isa{{\isaliteral{7C}{\isacharbar}}}~pattern@m~\isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}}~e@m
\end{array}
\]
Like in functional programming, patterns are expressions consisting of
-datatype constructors (e.g. \isa{{\isacharbrackleft}{\isacharbrackright}} and \isa{{\isacharhash}})
+datatype constructors (e.g. \isa{{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}} and \isa{{\isaliteral{23}{\isacharhash}}})
and variables, including the wildcard ``\verb$_$''.
Not all cases need to be covered and the order of cases matters.
However, one is well-advised not to wallow in complex patterns because
@@ -68,7 +68,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}case\ xs\ of\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymRightarrow}\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbar}\ y{\isacharhash}ys\ {\isasymRightarrow}\ xs{\isacharparenright}\ {\isacharequal}\ xs{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}case\ xs\ of\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7C}{\isacharbar}}\ y{\isaliteral{23}{\isacharhash}}ys\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ xs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -76,20 +76,20 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}case{\isacharunderscore}tac\ xs{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}case{\isaliteral{5F}{\isacharunderscore}}tac\ xs{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
results in the proof state
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymLongrightarrow}\ {\isacharparenleft}case\ xs\ of\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymRightarrow}\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbar}\ y\ {\isacharhash}\ ys\ {\isasymRightarrow}\ xs{\isacharparenright}\ {\isacharequal}\ xs\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}a\ list{\isachardot}\isanewline
-\isaindent{\ {\isadigit{2}}{\isachardot}\ \ \ \ }xs\ {\isacharequal}\ a\ {\isacharhash}\ list\ {\isasymLongrightarrow}\ {\isacharparenleft}case\ xs\ of\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymRightarrow}\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbar}\ y\ {\isacharhash}\ ys\ {\isasymRightarrow}\ xs{\isacharparenright}\ {\isacharequal}\ xs%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}case\ xs\ of\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7C}{\isacharbar}}\ y\ {\isaliteral{23}{\isacharhash}}\ ys\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ xs\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a\ list{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }xs\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{23}{\isacharhash}}\ list\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}case\ xs\ of\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7C}{\isacharbar}}\ y\ {\isaliteral{23}{\isacharhash}}\ ys\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ xs%
\end{isabelle}
which is solved automatically:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}auto{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -107,11 +107,11 @@
Induction is only allowed on free (or \isasymAnd-bound) variables that
should not occur among the assumptions of the subgoal; see
\S\ref{sec:ind-var-in-prems} for details. Case distinction
- (\isa{case{\isacharunderscore}tac}) works for arbitrary terms, which need to be
- quoted if they are non-atomic. However, apart from \isa{{\isasymAnd}}-bound
+ (\isa{case{\isaliteral{5F}{\isacharunderscore}}tac}) works for arbitrary terms, which need to be
+ quoted if they are non-atomic. However, apart from \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}}-bound
variables, the terms must not contain variables that are bound outside.
- For example, given the goal \isa{{\isasymforall}xs{\isachardot}\ xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymor}\ {\isacharparenleft}{\isasymexists}y\ ys{\isachardot}\ xs\ {\isacharequal}\ y\ {\isacharhash}\ ys{\isacharparenright}},
- \isa{case{\isacharunderscore}tac\ xs} will not work as expected because Isabelle interprets
+ For example, given the goal \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}xs{\isaliteral{2E}{\isachardot}}\ xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}y\ ys{\isaliteral{2E}{\isachardot}}\ xs\ {\isaliteral{3D}{\isacharequal}}\ y\ {\isaliteral{23}{\isacharhash}}\ ys{\isaliteral{29}{\isacharparenright}}},
+ \isa{case{\isaliteral{5F}{\isacharunderscore}}tac\ xs} will not work as expected because Isabelle interprets
the \isa{xs} as a new free variable distinct from the bound
\isa{xs} in the goal.
\end{warn}%
--- a/doc-src/TutorialI/Misc/document/fakenat.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Misc/document/fakenat.tex Mon Nov 08 14:41:11 2010 +0100
@@ -22,7 +22,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ nat\ {\isacharequal}\ {\isadigit{0}}\ {\isacharbar}\ Suc\ nat%
+\ nat\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\ {\isaliteral{7C}{\isacharbar}}\ Suc\ nat%
\isadelimtheory
%
\endisadelimtheory
--- a/doc-src/TutorialI/Misc/document/natsum.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Misc/document/natsum.tex Mon Nov 08 14:41:11 2010 +0100
@@ -19,22 +19,22 @@
\noindent
In particular, there are \isa{case}-expressions, for example
\begin{isabelle}%
-\ \ \ \ \ case\ n\ of\ {\isadigit{0}}\ {\isasymRightarrow}\ {\isadigit{0}}\ {\isacharbar}\ Suc\ m\ {\isasymRightarrow}\ m%
+\ \ \ \ \ case\ n\ of\ {\isadigit{0}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isadigit{0}}\ {\isaliteral{7C}{\isacharbar}}\ Suc\ m\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ m%
\end{isabelle}
primitive recursion, for example%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ sum\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}sum\ {\isadigit{0}}\ {\isacharequal}\ {\isadigit{0}}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}sum\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ Suc\ n\ {\isacharplus}\ sum\ n{\isachardoublequoteclose}%
+\ sum\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}sum\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}sum\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Suc\ n\ {\isaliteral{2B}{\isacharplus}}\ sum\ n{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
and induction, for example%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}sum\ n\ {\isacharplus}\ sum\ n\ {\isacharequal}\ n{\isacharasterisk}{\isacharparenleft}Suc\ n{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}sum\ n\ {\isaliteral{2B}{\isacharplus}}\ sum\ n\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -42,9 +42,9 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ n{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ n{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}auto{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -63,9 +63,9 @@
\sdx{div}, \sdx{mod}, \cdx{min} and
\cdx{max} are predefined, as are the relations
\isadxboldpos{\isasymle}{$HOL2arithrel} and
-\isadxboldpos{<}{$HOL2arithrel}. As usual, \isa{m\ {\isacharminus}\ n\ {\isacharequal}\ {\isadigit{0}}} if
-\isa{m\ {\isacharless}\ n}. There is even a least number operation
-\sdx{LEAST}\@. For example, \isa{{\isacharparenleft}LEAST\ n{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ n{\isacharparenright}\ {\isacharequal}\ Suc\ {\isadigit{0}}}.
+\isadxboldpos{<}{$HOL2arithrel}. As usual, \isa{m\ {\isaliteral{2D}{\isacharminus}}\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}} if
+\isa{m\ {\isaliteral{3C}{\isacharless}}\ n}. There is even a least number operation
+\sdx{LEAST}\@. For example, \isa{{\isaliteral{28}{\isacharparenleft}}LEAST\ n{\isaliteral{2E}{\isachardot}}\ {\isadigit{0}}\ {\isaliteral{3C}{\isacharless}}\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Suc\ {\isadigit{0}}}.
\begin{warn}\index{overloading}
The constants \cdx{0} and \cdx{1} and the operations
\isadxboldpos{+}{$HOL2arithfun}, \isadxboldpos{-}{$HOL2arithfun},
@@ -73,16 +73,16 @@
\cdx{max}, \isadxboldpos{\isasymle}{$HOL2arithrel} and
\isadxboldpos{<}{$HOL2arithrel} are overloaded: they are available
not just for natural numbers but for other types as well.
- For example, given the goal \isa{x\ {\isacharplus}\ {\isadigit{0}}\ {\isacharequal}\ x}, there is nothing to indicate
+ For example, given the goal \isa{x\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ x}, there is nothing to indicate
that you are talking about natural numbers. Hence Isabelle can only infer
- that \isa{x} is of some arbitrary type where \isa{{\isadigit{0}}} and \isa{{\isacharplus}} are
+ that \isa{x} is of some arbitrary type where \isa{{\isadigit{0}}} and \isa{{\isaliteral{2B}{\isacharplus}}} are
declared. As a consequence, you will be unable to prove the
goal. To alert you to such pitfalls, Isabelle flags numerals without a
- fixed type in its output: \isa{x\ {\isacharplus}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isacharequal}\ x}. (In the absence of a numeral,
+ fixed type in its output: \isa{x\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ x}. (In the absence of a numeral,
it may take you some time to realize what has happened if \pgmenu{Show
Types} is not set). In this particular example, you need to include
- an explicit type constraint, for example \isa{x{\isacharplus}{\isadigit{0}}\ {\isacharequal}\ {\isacharparenleft}x{\isacharcolon}{\isacharcolon}nat{\isacharparenright}}. If there
- is enough contextual information this may not be necessary: \isa{Suc\ x\ {\isacharequal}\ x} automatically implies \isa{x{\isacharcolon}{\isacharcolon}nat} because \isa{Suc} is not
+ an explicit type constraint, for example \isa{x{\isaliteral{2B}{\isacharplus}}{\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{29}{\isacharparenright}}}. If there
+ is enough contextual information this may not be necessary: \isa{Suc\ x\ {\isaliteral{3D}{\isacharequal}}\ x} automatically implies \isa{x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat} because \isa{Suc} is not
overloaded.
For details on overloading see \S\ref{sec:overloading}.
@@ -91,12 +91,12 @@
\end{warn}
\begin{warn}
The symbols \isadxboldpos{>}{$HOL2arithrel} and
- \isadxboldpos{\isasymge}{$HOL2arithrel} are merely syntax: \isa{x\ {\isachargreater}\ y}
- stands for \isa{y\ {\isacharless}\ x} and similary for \isa{{\isasymge}} and
- \isa{{\isasymle}}.
+ \isadxboldpos{\isasymge}{$HOL2arithrel} are merely syntax: \isa{x\ {\isaliteral{3E}{\isachargreater}}\ y}
+ stands for \isa{y\ {\isaliteral{3C}{\isacharless}}\ x} and similary for \isa{{\isaliteral{5C3C67653E}{\isasymge}}} and
+ \isa{{\isaliteral{5C3C6C653E}{\isasymle}}}.
\end{warn}
\begin{warn}
- Constant \isa{{\isadigit{1}}{\isacharcolon}{\isacharcolon}nat} is defined to equal \isa{Suc\ {\isadigit{0}}}. This definition
+ Constant \isa{{\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat} is defined to equal \isa{Suc\ {\isadigit{0}}}. This definition
(see \S\ref{sec:ConstDefinitions}) is unfolded automatically by some
tactics (like \isa{auto}, \isa{simp} and \isa{arith}) but not by
others (especially the single step tactics in Chapter~\ref{chap:rules}).
@@ -110,7 +110,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymlbrakk}\ {\isasymnot}\ m\ {\isacharless}\ n{\isacharsemicolon}\ m\ {\isacharless}\ n\ {\isacharplus}\ {\isacharparenleft}{\isadigit{1}}{\isacharcolon}{\isacharcolon}nat{\isacharparenright}\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ m\ {\isacharequal}\ n{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ m\ {\isaliteral{3C}{\isacharless}}\ n{\isaliteral{3B}{\isacharsemicolon}}\ m\ {\isaliteral{3C}{\isacharless}}\ n\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ m\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -132,7 +132,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}m\ {\isasymnoteq}\ {\isacharparenleft}n{\isacharcolon}{\isacharcolon}nat{\isacharparenright}\ {\isasymLongrightarrow}\ m\ {\isacharless}\ n\ {\isasymor}\ n\ {\isacharless}\ m{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}m\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{28}{\isacharparenleft}}n{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ m\ {\isaliteral{3C}{\isacharless}}\ n\ {\isaliteral{5C3C6F723E}{\isasymor}}\ n\ {\isaliteral{3C}{\isacharless}}\ m{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -149,15 +149,15 @@
\begin{isamarkuptext}%
\noindent The method \methdx{arith} is more general. It attempts to
prove the first subgoal provided it is a \textbf{linear arithmetic} formula.
-Such formulas may involve the usual logical connectives (\isa{{\isasymnot}},
-\isa{{\isasymand}}, \isa{{\isasymor}}, \isa{{\isasymlongrightarrow}}, \isa{{\isacharequal}},
-\isa{{\isasymforall}}, \isa{{\isasymexists}}), the relations \isa{{\isacharequal}},
-\isa{{\isasymle}} and \isa{{\isacharless}}, and the operations \isa{{\isacharplus}}, \isa{{\isacharminus}},
+Such formulas may involve the usual logical connectives (\isa{{\isaliteral{5C3C6E6F743E}{\isasymnot}}},
+\isa{{\isaliteral{5C3C616E643E}{\isasymand}}}, \isa{{\isaliteral{5C3C6F723E}{\isasymor}}}, \isa{{\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}}, \isa{{\isaliteral{3D}{\isacharequal}}},
+\isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}}, \isa{{\isaliteral{5C3C6578697374733E}{\isasymexists}}}), the relations \isa{{\isaliteral{3D}{\isacharequal}}},
+\isa{{\isaliteral{5C3C6C653E}{\isasymle}}} and \isa{{\isaliteral{3C}{\isacharless}}}, and the operations \isa{{\isaliteral{2B}{\isacharplus}}}, \isa{{\isaliteral{2D}{\isacharminus}}},
\isa{min} and \isa{max}. For example,%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}min\ i\ {\isacharparenleft}max\ j\ {\isacharparenleft}k{\isacharasterisk}k{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ max\ {\isacharparenleft}min\ {\isacharparenleft}k{\isacharasterisk}k{\isacharparenright}\ i{\isacharparenright}\ {\isacharparenleft}min\ i\ {\isacharparenleft}j{\isacharcolon}{\isacharcolon}nat{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}min\ i\ {\isaliteral{28}{\isacharparenleft}}max\ j\ {\isaliteral{28}{\isacharparenleft}}k{\isaliteral{2A}{\isacharasterisk}}k{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ max\ {\isaliteral{28}{\isacharparenleft}}min\ {\isaliteral{28}{\isacharparenleft}}k{\isaliteral{2A}{\isacharasterisk}}k{\isaliteral{29}{\isacharparenright}}\ i{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}min\ i\ {\isaliteral{28}{\isacharparenleft}}j{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -165,7 +165,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}arith{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}arith{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -175,11 +175,11 @@
%
\begin{isamarkuptext}%
\noindent
-succeeds because \isa{k\ {\isacharasterisk}\ k} can be treated as atomic. In contrast,%
+succeeds because \isa{k\ {\isaliteral{2A}{\isacharasterisk}}\ k} can be treated as atomic. In contrast,%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}n{\isacharasterisk}n\ {\isacharequal}\ n{\isacharplus}{\isadigit{1}}\ {\isasymLongrightarrow}\ n{\isacharequal}{\isadigit{0}}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}n{\isaliteral{2A}{\isacharasterisk}}n\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{2B}{\isacharplus}}{\isadigit{1}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ n{\isaliteral{3D}{\isacharequal}}{\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
--- a/doc-src/TutorialI/Misc/document/pairs.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Misc/document/pairs.tex Mon Nov 08 14:41:11 2010 +0100
@@ -35,7 +35,7 @@
as a degenerate product with 0 components.
\item
Products, like type \isa{nat}, are datatypes, which means
-in particular that \isa{induct{\isacharunderscore}tac} and \isa{case{\isacharunderscore}tac} are applicable to
+in particular that \isa{induct{\isaliteral{5F}{\isacharunderscore}}tac} and \isa{case{\isaliteral{5F}{\isacharunderscore}}tac} are applicable to
terms of product type.
Both split the term into a number of variables corresponding to the tuple structure
(up to 7 components).
--- a/doc-src/TutorialI/Misc/document/prime_def.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Misc/document/prime_def.tex Mon Nov 08 14:41:11 2010 +0100
@@ -1,6 +1,6 @@
%
\begin{isabellebody}%
-\def\isabellecontext{prime{\isacharunderscore}def}%
+\def\isabellecontext{prime{\isaliteral{5F}{\isacharunderscore}}def}%
%
\isadelimtheory
%
@@ -21,14 +21,14 @@
variables on the right-hand side. Consider the following, flawed definition
(where \isa{dvd} means ``divides''):
\begin{isabelle}%
-\ \ \ \ \ {\isachardoublequote}prime\ p\ {\isasymequiv}\ {\isadigit{1}}\ {\isacharless}\ p\ {\isasymand}\ {\isacharparenleft}m\ dvd\ p\ {\isasymlongrightarrow}\ m\ {\isacharequal}\ {\isadigit{1}}\ {\isasymor}\ m\ {\isacharequal}\ p{\isacharparenright}{\isachardoublequote}%
+\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}prime\ p\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isadigit{1}}\ {\isaliteral{3C}{\isacharless}}\ p\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}m\ dvd\ p\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ m\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ m\ {\isaliteral{3D}{\isacharequal}}\ p{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}%
\end{isabelle}
\par\noindent\hangindent=0pt
Isabelle rejects this ``definition'' because of the extra \isa{m} on the
right-hand side, which would introduce an inconsistency (why?).
The correct version is
\begin{isabelle}%
-\ \ \ \ \ {\isachardoublequote}prime\ p\ {\isasymequiv}\ {\isadigit{1}}\ {\isacharless}\ p\ {\isasymand}\ {\isacharparenleft}{\isasymforall}m{\isachardot}\ m\ dvd\ p\ {\isasymlongrightarrow}\ m\ {\isacharequal}\ {\isadigit{1}}\ {\isasymor}\ m\ {\isacharequal}\ p{\isacharparenright}{\isachardoublequote}%
+\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}prime\ p\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isadigit{1}}\ {\isaliteral{3C}{\isacharless}}\ p\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}m{\isaliteral{2E}{\isachardot}}\ m\ dvd\ p\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ m\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ m\ {\isaliteral{3D}{\isacharequal}}\ p{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}%
\end{isabelle}
\end{warn}%
\end{isamarkuptext}%
--- a/doc-src/TutorialI/Misc/document/simp.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Misc/document/simp.tex Mon Nov 08 14:41:11 2010 +0100
@@ -22,7 +22,7 @@
\begin{isamarkuptext}%
\index{simplification rules}
To facilitate simplification,
-the attribute \isa{{\isacharbrackleft}simp{\isacharbrackright}}\index{*simp (attribute)}
+the attribute \isa{{\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}}\index{*simp (attribute)}
declares theorems to be simplification rules, which the simplifier
will use automatically. In addition, \isacommand{datatype} and
\isacommand{primrec} declarations (and a few others)
@@ -33,14 +33,14 @@
Nearly any theorem can become a simplification
rule. The simplifier will try to transform it into an equation.
For example, the theorem
-\isa{{\isasymnot}\ P} is turned into \isa{P\ {\isacharequal}\ False}. The details
+\isa{{\isaliteral{5C3C6E6F743E}{\isasymnot}}\ P} is turned into \isa{P\ {\isaliteral{3D}{\isacharequal}}\ False}. The details
are explained in \S\ref{sec:SimpHow}.
The simplification attribute of theorems can be turned on and off:%
\index{*simp del (attribute)}
\begin{quote}
-\isacommand{declare} \textit{theorem-name}\isa{{\isacharbrackleft}simp{\isacharbrackright}}\\
-\isacommand{declare} \textit{theorem-name}\isa{{\isacharbrackleft}simp\ del{\isacharbrackright}}
+\isacommand{declare} \textit{theorem-name}\isa{{\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}}\\
+\isacommand{declare} \textit{theorem-name}\isa{{\isaliteral{5B}{\isacharbrackleft}}simp\ del{\isaliteral{5D}{\isacharbrackright}}}
\end{quote}
Only equations that really simplify, like \isa{rev\
{\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharequal}\ xs} and
@@ -99,17 +99,17 @@
the set of simplification rules used in a simplification step by adding rules
to it and/or deleting rules from it. The two modifiers for this are
\begin{quote}
-\isa{add{\isacharcolon}} \textit{list of theorem names}\index{*add (modifier)}\\
-\isa{del{\isacharcolon}} \textit{list of theorem names}\index{*del (modifier)}
+\isa{add{\isaliteral{3A}{\isacharcolon}}} \textit{list of theorem names}\index{*add (modifier)}\\
+\isa{del{\isaliteral{3A}{\isacharcolon}}} \textit{list of theorem names}\index{*del (modifier)}
\end{quote}
Or you can use a specific list of theorems and omit all others:
\begin{quote}
-\isa{only{\isacharcolon}} \textit{list of theorem names}\index{*only (modifier)}
+\isa{only{\isaliteral{3A}{\isacharcolon}}} \textit{list of theorem names}\index{*only (modifier)}
\end{quote}
In this example, we invoke the simplifier, adding two distributive
laws:
\begin{quote}
-\isacommand{apply}\isa{{\isacharparenleft}simp\ add{\isacharcolon}\ mod{\isacharunderscore}mult{\isacharunderscore}distrib\ add{\isacharunderscore}mult{\isacharunderscore}distrib{\isacharparenright}}
+\isacommand{apply}\isa{{\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ mod{\isaliteral{5F}{\isacharunderscore}}mult{\isaliteral{5F}{\isacharunderscore}}distrib\ add{\isaliteral{5F}{\isacharunderscore}}mult{\isaliteral{5F}{\isacharunderscore}}distrib{\isaliteral{29}{\isacharparenright}}}
\end{quote}%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -125,7 +125,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymlbrakk}\ xs\ {\isacharat}\ zs\ {\isacharequal}\ ys\ {\isacharat}\ xs{\isacharsemicolon}\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharat}\ xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharat}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ ys\ {\isacharequal}\ zs{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ xs\ {\isaliteral{40}{\isacharat}}\ zs\ {\isaliteral{3D}{\isacharequal}}\ ys\ {\isaliteral{40}{\isacharat}}\ xs{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{40}{\isacharat}}\ xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ ys\ {\isaliteral{3D}{\isacharequal}}\ zs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -145,15 +145,15 @@
%
\begin{isamarkuptext}%
\noindent
-The second assumption simplifies to \isa{xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}}, which in turn
-simplifies the first assumption to \isa{zs\ {\isacharequal}\ ys}, thus reducing the
-conclusion to \isa{ys\ {\isacharequal}\ ys} and hence to \isa{True}.
+The second assumption simplifies to \isa{xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}}, which in turn
+simplifies the first assumption to \isa{zs\ {\isaliteral{3D}{\isacharequal}}\ ys}, thus reducing the
+conclusion to \isa{ys\ {\isaliteral{3D}{\isacharequal}}\ ys} and hence to \isa{True}.
In some cases, using the assumptions can lead to nontermination:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymforall}x{\isachardot}\ f\ x\ {\isacharequal}\ g\ {\isacharparenleft}f\ {\isacharparenleft}g\ x{\isacharparenright}{\isacharparenright}\ {\isasymLongrightarrow}\ f\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ f\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharat}\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ f\ x\ {\isaliteral{3D}{\isacharequal}}\ g\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}g\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ f\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ f\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -163,14 +163,14 @@
\begin{isamarkuptxt}%
\noindent
An unmodified application of \isa{simp} loops. The culprit is the
-simplification rule \isa{f\ x\ {\isacharequal}\ g\ {\isacharparenleft}f\ {\isacharparenleft}g\ x{\isacharparenright}{\isacharparenright}}, which is extracted from
+simplification rule \isa{f\ x\ {\isaliteral{3D}{\isacharequal}}\ g\ {\isaliteral{28}{\isacharparenleft}}f\ {\isaliteral{28}{\isacharparenleft}}g\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}}, which is extracted from
the assumption. (Isabelle notices certain simple forms of
nontermination but not this one.) The problem can be circumvented by
telling the simplifier to ignore the assumptions:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp\ {\isacharparenleft}no{\isacharunderscore}asm{\isacharparenright}{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}simp\ {\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -184,12 +184,12 @@
\noindent
Three modifiers influence the treatment of assumptions:
\begin{description}
-\item[\isa{{\isacharparenleft}no{\isacharunderscore}asm{\isacharparenright}}]\index{*no_asm (modifier)}
+\item[\isa{{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{29}{\isacharparenright}}}]\index{*no_asm (modifier)}
means that assumptions are completely ignored.
-\item[\isa{{\isacharparenleft}no{\isacharunderscore}asm{\isacharunderscore}simp{\isacharparenright}}]\index{*no_asm_simp (modifier)}
+\item[\isa{{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{29}{\isacharparenright}}}]\index{*no_asm_simp (modifier)}
means that the assumptions are not simplified but
are used in the simplification of the conclusion.
-\item[\isa{{\isacharparenleft}no{\isacharunderscore}asm{\isacharunderscore}use{\isacharparenright}}]\index{*no_asm_use (modifier)}
+\item[\isa{{\isaliteral{28}{\isacharparenleft}}no{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{5F}{\isacharunderscore}}use{\isaliteral{29}{\isacharparenright}}}]\index{*no_asm_use (modifier)}
means that the assumptions are simplified but are not
used in the simplification of each other or the conclusion.
\end{description}
@@ -226,15 +226,15 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{definition}\isamarkupfalse%
-\ xor\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}bool\ {\isasymRightarrow}\ bool\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}xor\ A\ B\ {\isasymequiv}\ {\isacharparenleft}A\ {\isasymand}\ {\isasymnot}B{\isacharparenright}\ {\isasymor}\ {\isacharparenleft}{\isasymnot}A\ {\isasymand}\ B{\isacharparenright}{\isachardoublequoteclose}%
+\ xor\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}bool\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}xor\ A\ B\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
we may want to prove%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}xor\ A\ {\isacharparenleft}{\isasymnot}A{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}xor\ A\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6E6F743E}{\isasymnot}}A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -248,12 +248,12 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp\ only{\isacharcolon}\ xor{\isacharunderscore}def{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp\ only{\isaliteral{3A}{\isacharcolon}}\ xor{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
In this particular case, the resulting goal
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ A\ {\isasymand}\ {\isasymnot}\ {\isasymnot}\ A\ {\isasymor}\ {\isasymnot}\ A\ {\isasymand}\ {\isasymnot}\ A%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}\ A%
\end{isabelle}
can be proved by simplification. Thus we could have proved the lemma outright by%
\end{isamarkuptxt}%
@@ -272,7 +272,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp\ add{\isacharcolon}\ xor{\isacharunderscore}def{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ xor{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -313,7 +313,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}let\ xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ in\ xs{\isacharat}ys{\isacharat}xs{\isacharparenright}\ {\isacharequal}\ ys{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}let\ xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ in\ xs{\isaliteral{40}{\isacharat}}ys{\isaliteral{40}{\isacharat}}xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ ys{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -321,7 +321,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp\ add{\isacharcolon}\ Let{\isacharunderscore}def{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ Let{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -333,12 +333,12 @@
%
\begin{isamarkuptext}%
If, in a particular context, there is no danger of a combinatorial explosion
-of nested \isa{let}s, you could even simplify with \isa{Let{\isacharunderscore}def} by
+of nested \isa{let}s, you could even simplify with \isa{Let{\isaliteral{5F}{\isacharunderscore}}def} by
default:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{declare}\isamarkupfalse%
-\ Let{\isacharunderscore}def\ {\isacharbrackleft}simp{\isacharbrackright}%
+\ Let{\isaliteral{5F}{\isacharunderscore}}def\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}%
\isamarkupsubsection{Conditional Simplification Rules%
}
\isamarkuptrue%
@@ -350,7 +350,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ hd{\isacharunderscore}Cons{\isacharunderscore}tl{\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\ \ {\isasymLongrightarrow}\ \ hd\ xs\ {\isacharhash}\ tl\ xs\ {\isacharequal}\ xs{\isachardoublequoteclose}\isanewline
+\ hd{\isaliteral{5F}{\isacharunderscore}}Cons{\isaliteral{5F}{\isacharunderscore}}tl{\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}xs\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ \ hd\ xs\ {\isaliteral{23}{\isacharhash}}\ tl\ xs\ {\isaliteral{3D}{\isacharequal}}\ xs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -358,7 +358,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}case{\isacharunderscore}tac\ xs{\isacharcomma}\ simp{\isacharcomma}\ simp{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}case{\isaliteral{5F}{\isacharunderscore}}tac\ xs{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -372,13 +372,13 @@
\noindent
Note the use of ``\ttindexboldpos{,}{$Isar}'' to string together a
sequence of methods. Assuming that the simplification rule
-\isa{{\isacharparenleft}rev\ xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}}
+\isa{{\isaliteral{28}{\isacharparenleft}}rev\ xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}}
is present as well,
the lemma below is proved by plain simplification:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymLongrightarrow}\ hd{\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharhash}\ tl{\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharequal}\ rev\ xs{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}xs\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ hd{\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{23}{\isacharhash}}\ tl{\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rev\ xs{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -394,10 +394,10 @@
%
\begin{isamarkuptext}%
\noindent
-The conditional equation \isa{hd{\isacharunderscore}Cons{\isacharunderscore}tl} above
-can simplify \isa{hd\ {\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharhash}\ tl\ {\isacharparenleft}rev\ xs{\isacharparenright}} to \isa{rev\ xs}
-because the corresponding precondition \isa{rev\ xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}}
-simplifies to \isa{xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}}, which is exactly the local
+The conditional equation \isa{hd{\isaliteral{5F}{\isacharunderscore}}Cons{\isaliteral{5F}{\isacharunderscore}}tl} above
+can simplify \isa{hd\ {\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{23}{\isacharhash}}\ tl\ {\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}} to \isa{rev\ xs}
+because the corresponding precondition \isa{rev\ xs\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}}
+simplifies to \isa{xs\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}}, which is exactly the local
assumption of the subgoal.%
\end{isamarkuptext}%
\isamarkuptrue%
@@ -414,7 +414,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymforall}xs{\isachardot}\ if\ xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ then\ rev\ xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ else\ rev\ xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}xs{\isaliteral{2E}{\isachardot}}\ if\ xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ then\ rev\ xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ else\ rev\ xs\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -427,16 +427,16 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}split\ split{\isacharunderscore}if{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}split\ split{\isaliteral{5F}{\isacharunderscore}}if{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymforall}xs{\isachardot}\ {\isacharparenleft}xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymlongrightarrow}\ rev\ xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isasymand}\ {\isacharparenleft}xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymlongrightarrow}\ rev\ xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}xs{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ rev\ xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}xs\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ rev\ xs\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
where \tdx{split_if} is a theorem that expresses splitting of
\isa{if}s. Because
splitting the \isa{if}s is usually the right proof strategy, the
-simplifier does it automatically. Try \isacommand{apply}\isa{{\isacharparenleft}simp{\isacharparenright}}
+simplifier does it automatically. Try \isacommand{apply}\isa{{\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{29}{\isacharparenright}}}
on the initial goal above.
This splitting idea generalizes from \isa{if} to \sdx{case}.
@@ -451,7 +451,7 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}case\ xs\ of\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymRightarrow}\ zs\ {\isacharbar}\ y{\isacharhash}ys\ {\isasymRightarrow}\ y{\isacharhash}{\isacharparenleft}ys{\isacharat}zs{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ xs{\isacharat}zs{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}case\ xs\ of\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ zs\ {\isaliteral{7C}{\isacharbar}}\ y{\isaliteral{23}{\isacharhash}}ys\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ y{\isaliteral{23}{\isacharhash}}{\isaliteral{28}{\isacharparenleft}}ys{\isaliteral{40}{\isacharat}}zs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ xs{\isaliteral{40}{\isacharat}}zs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -459,11 +459,11 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}split\ list{\isachardot}split{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}split\ list{\isaliteral{2E}{\isachardot}}split{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isacharparenleft}xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymlongrightarrow}\ zs\ {\isacharequal}\ xs\ {\isacharat}\ zs{\isacharparenright}\ {\isasymand}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ }{\isacharparenleft}{\isasymforall}a\ list{\isachardot}\ xs\ {\isacharequal}\ a\ {\isacharhash}\ list\ {\isasymlongrightarrow}\ a\ {\isacharhash}\ list\ {\isacharat}\ zs\ {\isacharequal}\ xs\ {\isacharat}\ zs{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ zs\ {\isaliteral{3D}{\isacharequal}}\ xs\ {\isaliteral{40}{\isacharat}}\ zs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ }{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}a\ list{\isaliteral{2E}{\isachardot}}\ xs\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{23}{\isacharhash}}\ list\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ a\ {\isaliteral{23}{\isacharhash}}\ list\ {\isaliteral{40}{\isacharat}}\ zs\ {\isaliteral{3D}{\isacharequal}}\ xs\ {\isaliteral{40}{\isacharat}}\ zs{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
The simplifier does not split
\isa{case}-expressions, as it does \isa{if}-expressions,
@@ -488,7 +488,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp\ split{\isacharcolon}\ list{\isachardot}split{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp\ split{\isaliteral{3A}{\isacharcolon}}\ list{\isaliteral{2E}{\isachardot}}split{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -498,15 +498,15 @@
%
\begin{isamarkuptext}%
\noindent
-whereas \isacommand{apply}\isa{{\isacharparenleft}simp{\isacharparenright}} alone will not succeed.
+whereas \isacommand{apply}\isa{{\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{29}{\isacharparenright}}} alone will not succeed.
Every datatype $t$ comes with a theorem
-$t$\isa{{\isachardot}split} which can be declared to be a \bfindex{split rule} either
+$t$\isa{{\isaliteral{2E}{\isachardot}}split} which can be declared to be a \bfindex{split rule} either
locally as above, or by giving it the \attrdx{split} attribute globally:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{declare}\isamarkupfalse%
-\ list{\isachardot}split\ {\isacharbrackleft}split{\isacharbrackright}%
+\ list{\isaliteral{2E}{\isachardot}}split\ {\isaliteral{5B}{\isacharbrackleft}}split{\isaliteral{5D}{\isacharbrackright}}%
\begin{isamarkuptext}%
\noindent
The \isa{split} attribute can be removed with the \isa{del} modifier,
@@ -520,7 +520,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp\ split\ del{\isacharcolon}\ split{\isacharunderscore}if{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp\ split\ del{\isaliteral{3A}{\isacharcolon}}\ split{\isaliteral{5F}{\isacharunderscore}}if{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -534,7 +534,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{declare}\isamarkupfalse%
-\ list{\isachardot}split\ {\isacharbrackleft}split\ del{\isacharbrackright}%
+\ list{\isaliteral{2E}{\isachardot}}split\ {\isaliteral{5B}{\isacharbrackleft}}split\ del{\isaliteral{5D}{\isacharbrackright}}%
\begin{isamarkuptext}%
Polished proofs typically perform splitting within \isa{simp} rather than
invoking the \isa{split} method. However, if a goal contains
@@ -545,11 +545,11 @@
The split rules shown above are intended to affect only the subgoal's
conclusion. If you want to split an \isa{if} or \isa{case}-expression
in the assumptions, you have to apply \tdx{split_if_asm} or
-$t$\isa{{\isachardot}split{\isacharunderscore}asm}:%
+$t$\isa{{\isaliteral{2E}{\isachardot}}split{\isaliteral{5F}{\isacharunderscore}}asm}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}if\ xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ then\ ys\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\ else\ ys\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymLongrightarrow}\ xs\ {\isacharat}\ ys\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}if\ xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ then\ ys\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ else\ ys\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ xs\ {\isaliteral{40}{\isacharat}}\ ys\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -557,18 +557,18 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}split\ split{\isacharunderscore}if{\isacharunderscore}asm{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}split\ split{\isaliteral{5F}{\isacharunderscore}}if{\isaliteral{5F}{\isacharunderscore}}asm{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
Unlike splitting the conclusion, this step creates two
-separate subgoals, which here can be solved by \isa{simp{\isacharunderscore}all}:
+separate subgoals, which here can be solved by \isa{simp{\isaliteral{5F}{\isacharunderscore}}all}:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymlbrakk}xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isacharsemicolon}\ ys\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ xs\ {\isacharat}\ ys\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymlbrakk}xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}{\isacharsemicolon}\ ys\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ xs\ {\isacharat}\ ys\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}xs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\ ys\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ xs\ {\isaliteral{40}{\isacharat}}\ ys\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}xs\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\ ys\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ xs\ {\isaliteral{40}{\isacharat}}\ ys\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}%
\end{isabelle}
If you need to split both in the assumptions and the conclusion,
-use $t$\isa{{\isachardot}splits} which subsumes $t$\isa{{\isachardot}split} and
-$t$\isa{{\isachardot}split{\isacharunderscore}asm}. Analogously, there is \isa{if{\isacharunderscore}splits}.
+use $t$\isa{{\isaliteral{2E}{\isachardot}}splits} which subsumes $t$\isa{{\isaliteral{2E}{\isachardot}}split} and
+$t$\isa{{\isaliteral{2E}{\isachardot}}split{\isaliteral{5F}{\isacharunderscore}}asm}. Analogously, there is \isa{if{\isaliteral{5F}{\isacharunderscore}}splits}.
\begin{warn}
The simplifier merely simplifies the condition of an
@@ -600,7 +600,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}rev\ {\isacharbrackleft}a{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}rev\ {\isaliteral{5B}{\isacharbrackleft}}a{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -608,7 +608,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -673,7 +673,7 @@
%
\isatagproof
\isacommand{using}\isamarkupfalse%
-\ {\isacharbrackleft}{\isacharbrackleft}trace{\isacharunderscore}simp{\isacharequal}true{\isacharbrackright}{\isacharbrackright}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5B}{\isacharbrackleft}}trace{\isaliteral{5F}{\isacharunderscore}}simp{\isaliteral{3D}{\isacharequal}}true{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5D}{\isacharbrackright}}\isanewline
\isacommand{apply}\isamarkupfalse%
\ simp%
\endisatagproof
@@ -737,11 +737,11 @@
\end{ttbox}
This finds \emph{all} equations---not just those with a \isa{simp} attribute---whose conclusion has the form
\begin{isabelle}%
-\ \ \ \ \ {\isacharunderscore}\ {\isacharasterisk}\ {\isacharparenleft}{\isacharunderscore}\ {\isacharplus}\ {\isacharunderscore}{\isacharparenright}\ {\isacharequal}\ {\isasymdots}%
+\ \ \ \ \ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}%
\end{isabelle}
It only finds equations that can simplify the given pattern
at the root, not somewhere inside: for example, equations of the form
-\isa{{\isacharunderscore}\ {\isacharplus}\ {\isacharunderscore}\ {\isacharequal}\ {\isasymdots}} do not match.
+\isa{{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}} do not match.
You may also search for theorems by name---you merely
need to specify a substring. For example, you could search for all
@@ -767,7 +767,7 @@
"_ + _" -"_ - _" -simp: "_ * (_ + _)" name: assoc
\end{ttbox}
looks for theorems containing plus but not minus, and which do not simplify
-\mbox{\isa{{\isacharunderscore}\ {\isacharasterisk}\ {\isacharparenleft}{\isacharunderscore}\ {\isacharplus}\ {\isacharunderscore}{\isacharparenright}}} at the root, and whose name contains \texttt{assoc}.
+\mbox{\isa{{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}}} at the root, and whose name contains \texttt{assoc}.
Further search criteria are explained in \S\ref{sec:find2}.
--- a/doc-src/TutorialI/Misc/document/types.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Misc/document/types.tex Mon Nov 08 14:41:11 2010 +0100
@@ -15,9 +15,9 @@
%
\endisadelimtheory
\isacommand{types}\isamarkupfalse%
-\ number\ \ \ \ \ \ \ {\isacharequal}\ nat\isanewline
-\ \ \ \ \ \ gate\ \ \ \ \ \ \ \ \ {\isacharequal}\ {\isachardoublequoteopen}bool\ {\isasymRightarrow}\ bool\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
-\ \ \ \ \ \ {\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}b{\isacharparenright}alist\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b{\isacharparenright}list{\isachardoublequoteclose}%
+\ number\ \ \ \ \ \ \ {\isaliteral{3D}{\isacharequal}}\ nat\isanewline
+\ \ \ \ \ \ gate\ \ \ \ \ \ \ \ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequoteopen}}bool\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}alist\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{29}{\isacharparenright}}list{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
Internally all synonyms are fully expanded. As a consequence Isabelle's
@@ -39,9 +39,9 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{definition}\isamarkupfalse%
-\ nand\ {\isacharcolon}{\isacharcolon}\ gate\ \isakeyword{where}\ {\isachardoublequoteopen}nand\ A\ B\ {\isasymequiv}\ {\isasymnot}{\isacharparenleft}A\ {\isasymand}\ B{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ nand\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ gate\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}nand\ A\ B\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isacommand{definition}\isamarkupfalse%
-\ xor\ \ {\isacharcolon}{\isacharcolon}\ gate\ \isakeyword{where}\ {\isachardoublequoteopen}xor\ \ A\ B\ {\isasymequiv}\ A\ {\isasymand}\ {\isasymnot}B\ {\isasymor}\ {\isasymnot}A\ {\isasymand}\ B{\isachardoublequoteclose}%
+\ xor\ \ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ gate\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}xor\ \ A\ B\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}B\ {\isaliteral{5C3C6F723E}{\isasymor}}\ {\isaliteral{5C3C6E6F743E}{\isasymnot}}A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent%
The symbol \indexboldpos{\isasymequiv}{$IsaEq} is a special form of equality
@@ -49,7 +49,7 @@
Pattern-matching is not allowed: each definition must be of
the form $f\,x@1\,\dots\,x@n~\isasymequiv~t$.
Section~\ref{sec:Simp-with-Defs} explains how definitions are used
-in proofs. The default name of each definition is $f$\isa{{\isacharunderscore}def}, where
+in proofs. The default name of each definition is $f$\isa{{\isaliteral{5F}{\isacharunderscore}}def}, where
$f$ is the name of the defined constant.%
\end{isamarkuptext}%
\isamarkuptrue%
--- a/doc-src/TutorialI/Protocol/document/Event.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Protocol/document/Event.tex Mon Nov 08 14:41:11 2010 +0100
@@ -466,7 +466,7 @@
\emph{events}. The most important event, \isa{Says\ A\ B\ X}, expresses
$A\to B : X$, which is the attempt by~$A$ to send~$B$ the message~$X$.
A trace is simply a list, constructed in reverse
-using~\isa{{\isacharhash}}. Other event types include reception of messages (when
+using~\isa{{\isaliteral{23}{\isacharhash}}}. Other event types include reception of messages (when
we want to make it explicit) and an agent's storing a fact.
Sometimes the protocol requires an agent to generate a new nonce. The
@@ -476,7 +476,7 @@
The function \isa{used} has a straightforward
recursive definition. Here is the case for \isa{Says} event:
\begin{isabelle}%
-\ \ \ \ \ used\ {\isacharparenleft}Says\ A\ B\ X\ {\isacharhash}\ evs{\isacharparenright}\ {\isacharequal}\ parts\ {\isacharbraceleft}X{\isacharbraceright}\ {\isasymunion}\ used\ evs%
+\ \ \ \ \ used\ {\isaliteral{28}{\isacharparenleft}}Says\ A\ B\ X\ {\isaliteral{23}{\isacharhash}}\ evs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ parts\ {\isaliteral{7B}{\isacharbraceleft}}X{\isaliteral{7D}{\isacharbraceright}}\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ used\ evs%
\end{isabelle}
The function \isa{knows} formalizes an agent's knowledge. Mostly we only
@@ -486,14 +486,14 @@
of compromised users. After each \isa{Says} event, the spy learns the
message that was sent:
\begin{isabelle}%
-\ \ \ \ \ knows\ Spy\ {\isacharparenleft}Says\ A\ B\ X\ {\isacharhash}\ evs{\isacharparenright}\ {\isacharequal}\ insert\ X\ {\isacharparenleft}knows\ Spy\ evs{\isacharparenright}%
+\ \ \ \ \ knows\ Spy\ {\isaliteral{28}{\isacharparenleft}}Says\ A\ B\ X\ {\isaliteral{23}{\isacharhash}}\ evs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ insert\ X\ {\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evs{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
Combinations of functions express other important
sets of messages derived from~\isa{evs}:
\begin{itemize}
-\item \isa{analz\ {\isacharparenleft}knows\ Spy\ evs{\isacharparenright}} is everything that the spy could
+\item \isa{analz\ {\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evs{\isaliteral{29}{\isacharparenright}}} is everything that the spy could
learn by decryption
-\item \isa{synth\ {\isacharparenleft}analz\ {\isacharparenleft}knows\ Spy\ evs{\isacharparenright}{\isacharparenright}} is everything that the spy
+\item \isa{synth\ {\isaliteral{28}{\isacharparenleft}}analz\ {\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}} is everything that the spy
could generate
\end{itemize}%
\end{isamarkuptext}%
--- a/doc-src/TutorialI/Protocol/document/Message.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Protocol/document/Message.tex Mon Nov 08 14:41:11 2010 +0100
@@ -41,16 +41,16 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ agent\ {\isacharequal}\ Server\ {\isacharbar}\ Friend\ nat\ {\isacharbar}\ Spy%
+\ agent\ {\isaliteral{3D}{\isacharequal}}\ Server\ {\isaliteral{7C}{\isacharbar}}\ Friend\ nat\ {\isaliteral{7C}{\isacharbar}}\ Spy%
\begin{isamarkuptext}%
Keys are just natural numbers. Function \isa{invKey} maps a public key to
the matching private key, and vice versa:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{types}\isamarkupfalse%
-\ key\ {\isacharequal}\ nat\isanewline
+\ key\ {\isaliteral{3D}{\isacharequal}}\ nat\isanewline
\isacommand{consts}\isamarkupfalse%
-\ invKey\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}key\ {\isasymRightarrow}\ key{\isachardoublequoteclose}%
+\ invKey\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}key\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ key{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -72,11 +72,11 @@
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
\isanewline
-\ \ \ \ \ msg\ {\isacharequal}\ Agent\ \ agent\isanewline
-\ \ \ \ \ \ \ \ \ {\isacharbar}\ Nonce\ \ nat\isanewline
-\ \ \ \ \ \ \ \ \ {\isacharbar}\ Key\ \ \ \ key\isanewline
-\ \ \ \ \ \ \ \ \ {\isacharbar}\ MPair\ \ msg\ msg\isanewline
-\ \ \ \ \ \ \ \ \ {\isacharbar}\ Crypt\ \ key\ msg%
+\ \ \ \ \ msg\ {\isaliteral{3D}{\isacharequal}}\ Agent\ \ agent\isanewline
+\ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Nonce\ \ nat\isanewline
+\ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Key\ \ \ \ key\isanewline
+\ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ MPair\ \ msg\ msg\isanewline
+\ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Crypt\ \ key\ msg%
\begin{isamarkuptext}%
\noindent
The notation $\comp{X\sb 1,\ldots X\sb{n-1},X\sb n}$
@@ -85,7 +85,7 @@
Since datatype constructors are injective, we have the theorem
\begin{isabelle}%
-Crypt\ K\ X\ {\isacharequal}\ Crypt\ K{\isacharprime}\ X{\isacharprime}\ {\isasymLongrightarrow}\ K\ {\isacharequal}\ K{\isacharprime}\ {\isasymand}\ X\ {\isacharequal}\ X{\isacharprime}%
+Crypt\ K\ X\ {\isaliteral{3D}{\isacharequal}}\ Crypt\ K{\isaliteral{27}{\isacharprime}}\ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ K\ {\isaliteral{3D}{\isacharequal}}\ K{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ X\ {\isaliteral{3D}{\isacharequal}}\ X{\isaliteral{27}{\isacharprime}}%
\end{isabelle}
A ciphertext can be decrypted using only one key and
can yield only one plaintext. In the real world, decryption with the
@@ -672,17 +672,17 @@
defined inductively.%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{inductive{\isacharunderscore}set}\isamarkupfalse%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse%
\isanewline
-\ \ analz\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}msg\ set\ {\isasymRightarrow}\ msg\ set{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{for}\ H\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}msg\ set{\isachardoublequoteclose}\isanewline
+\ \ analz\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}msg\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ msg\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{for}\ H\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}msg\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isakeyword{where}\isanewline
-\ \ \ \ Inj\ {\isacharbrackleft}intro{\isacharcomma}simp{\isacharbrackright}\ {\isacharcolon}\ {\isachardoublequoteopen}X\ {\isasymin}\ H\ {\isasymLongrightarrow}\ X\ {\isasymin}\ analz\ H{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ Fst{\isacharcolon}\ \ \ \ \ {\isachardoublequoteopen}{\isasymlbrace}X{\isacharcomma}Y{\isasymrbrace}\ {\isasymin}\ analz\ H\ {\isasymLongrightarrow}\ X\ {\isasymin}\ analz\ H{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ Snd{\isacharcolon}\ \ \ \ \ {\isachardoublequoteopen}{\isasymlbrace}X{\isacharcomma}Y{\isasymrbrace}\ {\isasymin}\ analz\ H\ {\isasymLongrightarrow}\ Y\ {\isasymin}\ analz\ H{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ Decrypt\ {\isacharbrackleft}dest{\isacharbrackright}{\isacharcolon}\ \isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ {\isachardoublequoteopen}{\isasymlbrakk}Crypt\ K\ X\ {\isasymin}\ analz\ H{\isacharsemicolon}\ Key{\isacharparenleft}invKey\ K{\isacharparenright}\ {\isasymin}\ analz\ H{\isasymrbrakk}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isasymLongrightarrow}\ X\ {\isasymin}\ analz\ H{\isachardoublequoteclose}%
+\ \ \ \ Inj\ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{2C}{\isacharcomma}}simp{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ H\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ Fst{\isaliteral{3A}{\isacharcolon}}\ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}X{\isaliteral{2C}{\isacharcomma}}Y{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ Snd{\isaliteral{3A}{\isacharcolon}}\ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}X{\isaliteral{2C}{\isacharcomma}}Y{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ Decrypt\ {\isaliteral{5B}{\isacharbrackleft}}dest{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ \isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}Crypt\ K\ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H{\isaliteral{3B}{\isacharsemicolon}}\ Key{\isaliteral{28}{\isacharparenleft}}invKey\ K{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -1104,26 +1104,26 @@
message encrypted with key~$K$ if he has the matching key,~$K^{-1}$.
Properties proved by rule induction include the following:
\begin{isabelle}%
-G\ {\isasymsubseteq}\ H\ {\isasymLongrightarrow}\ analz\ G\ {\isasymsubseteq}\ analz\ H\rulename{analz{\isacharunderscore}mono}\par\smallskip%
-analz\ {\isacharparenleft}analz\ H{\isacharparenright}\ {\isacharequal}\ analz\ H\rulename{analz{\isacharunderscore}idem}%
+G\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ H\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ analz\ G\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ analz\ H\rulename{analz{\isaliteral{5F}{\isacharunderscore}}mono}\par\smallskip%
+analz\ {\isaliteral{28}{\isacharparenleft}}analz\ H{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ analz\ H\rulename{analz{\isaliteral{5F}{\isacharunderscore}}idem}%
\end{isabelle}
The set of fake messages that an intruder could invent
-starting from~\isa{H} is \isa{synth{\isacharparenleft}analz\ H{\isacharparenright}}, where \isa{synth\ H}
+starting from~\isa{H} is \isa{synth{\isaliteral{28}{\isacharparenleft}}analz\ H{\isaliteral{29}{\isacharparenright}}}, where \isa{synth\ H}
formalizes what the adversary can build from the set of messages~$H$.%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{inductive{\isacharunderscore}set}\isamarkupfalse%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse%
\isanewline
-\ \ synth\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}msg\ set\ {\isasymRightarrow}\ msg\ set{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{for}\ H\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}msg\ set{\isachardoublequoteclose}\isanewline
+\ \ synth\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}msg\ set\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ msg\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{for}\ H\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}msg\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isakeyword{where}\isanewline
-\ \ \ \ Inj\ \ \ \ {\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}X\ {\isasymin}\ H\ {\isasymLongrightarrow}\ X\ {\isasymin}\ synth\ H{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ Agent\ \ {\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}Agent\ agt\ {\isasymin}\ synth\ H{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ MPair\ \ {\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isachardoublequoteopen}{\isasymlbrakk}X\ {\isasymin}\ synth\ H{\isacharsemicolon}\ \ Y\ {\isasymin}\ synth\ H{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isasymlbrace}X{\isacharcomma}Y{\isasymrbrace}\ {\isasymin}\ synth\ H{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ Crypt\ \ {\isacharbrackleft}intro{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isachardoublequoteopen}{\isasymlbrakk}X\ {\isasymin}\ synth\ H{\isacharsemicolon}\ \ Key\ K\ {\isasymin}\ H{\isasymrbrakk}\ {\isasymLongrightarrow}\ Crypt\ K\ X\ {\isasymin}\ synth\ H{\isachardoublequoteclose}%
+\ \ \ \ Inj\ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ H\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ Agent\ \ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}Agent\ agt\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ MPair\ \ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H{\isaliteral{3B}{\isacharsemicolon}}\ \ Y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}X{\isaliteral{2C}{\isacharcomma}}Y{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ Crypt\ \ {\isaliteral{5B}{\isacharbrackleft}}intro{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H{\isaliteral{3B}{\isacharsemicolon}}\ \ Key\ K\ {\isaliteral{5C3C696E3E}{\isasymin}}\ H{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Crypt\ K\ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -1172,18 +1172,18 @@
Like \isa{analz}, this set operator is monotone and idempotent. It also
satisfies an interesting equation involving \isa{analz}:
\begin{isabelle}%
-analz\ {\isacharparenleft}synth\ H{\isacharparenright}\ {\isacharequal}\ analz\ H\ {\isasymunion}\ synth\ H\rulename{analz{\isacharunderscore}synth}%
+analz\ {\isaliteral{28}{\isacharparenleft}}synth\ H{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ analz\ H\ {\isaliteral{5C3C756E696F6E3E}{\isasymunion}}\ synth\ H\rulename{analz{\isaliteral{5F}{\isacharunderscore}}synth}%
\end{isabelle}
Rule inversion plays a major role in reasoning about \isa{synth}, through
declarations such as this one:%
\end{isamarkuptext}%
\isamarkuptrue%
-\isacommand{inductive{\isacharunderscore}cases}\isamarkupfalse%
-\ Nonce{\isacharunderscore}synth\ {\isacharbrackleft}elim{\isacharbang}{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}Nonce\ n\ {\isasymin}\ synth\ H{\isachardoublequoteclose}%
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}cases}\isamarkupfalse%
+\ Nonce{\isaliteral{5F}{\isacharunderscore}}synth\ {\isaliteral{5B}{\isacharbrackleft}}elim{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}Nonce\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
The resulting elimination rule replaces every assumption of the form
-\isa{Nonce\ n\ {\isasymin}\ synth\ H} by \isa{Nonce\ n\ {\isasymin}\ H},
+\isa{Nonce\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ H} by \isa{Nonce\ n\ {\isaliteral{5C3C696E3E}{\isasymin}}\ H},
expressing that a nonce cannot be guessed.
A third operator, \isa{parts}, is useful for stating correctness
@@ -1194,7 +1194,7 @@
Its definition resembles that of \isa{analz} except in the rule
corresponding to the constructor \isa{Crypt}:
\begin{isabelle}%
-\ \ \ \ \ Crypt\ K\ X\ {\isasymin}\ parts\ H\ {\isasymLongrightarrow}\ X\ {\isasymin}\ parts\ H%
+\ \ \ \ \ Crypt\ K\ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ parts\ H\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ parts\ H%
\end{isabelle}
The body of an encrypted message is always regarded as part of it. We can
use \isa{parts} to express general well-formedness properties of a protocol,
--- a/doc-src/TutorialI/Protocol/document/NS_Public.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Protocol/document/NS_Public.tex Mon Nov 08 14:41:11 2010 +0100
@@ -1,6 +1,6 @@
%
\begin{isabellebody}%
-\def\isabellecontext{NS{\isacharunderscore}Public}%
+\def\isabellecontext{NS{\isaliteral{5F}{\isacharunderscore}}Public}%
%
\isadelimtheory
%
@@ -21,33 +21,33 @@
%
\begin{figure}
\begin{isabelle}
-\isacommand{inductive{\isacharunderscore}set}\isamarkupfalse%
-\ ns{\isacharunderscore}public\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}event\ list\ set{\isachardoublequoteclose}\isanewline
+\isacommand{inductive{\isaliteral{5F}{\isacharunderscore}}set}\isamarkupfalse%
+\ ns{\isaliteral{5F}{\isacharunderscore}}public\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}event\ list\ set{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isakeyword{where}\isanewline
\isanewline
-\ \ \ Nil{\isacharcolon}\ \ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharbrackright}\ {\isasymin}\ ns{\isacharunderscore}public{\isachardoublequoteclose}\isanewline
+\ \ \ Nil{\isaliteral{3A}{\isacharcolon}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isanewline
-\ {\isacharbar}\ Fake{\isacharcolon}\ {\isachardoublequoteopen}{\isasymlbrakk}evsf\ {\isasymin}\ ns{\isacharunderscore}public{\isacharsemicolon}\ \ X\ {\isasymin}\ synth\ {\isacharparenleft}analz\ {\isacharparenleft}knows\ Spy\ evsf{\isacharparenright}{\isacharparenright}{\isasymrbrakk}\isanewline
-\ \ \ \ \ \ \ \ \ \ {\isasymLongrightarrow}\ Says\ Spy\ B\ X\ \ {\isacharhash}\ evsf\ {\isasymin}\ ns{\isacharunderscore}public{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{7C}{\isacharbar}}\ Fake{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}evsf\ {\isaliteral{5C3C696E3E}{\isasymin}}\ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{3B}{\isacharsemicolon}}\ \ X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ {\isaliteral{28}{\isacharparenleft}}analz\ {\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evsf{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\ \ \ \ \ \ \ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Says\ Spy\ B\ X\ \ {\isaliteral{23}{\isacharhash}}\ evsf\ {\isaliteral{5C3C696E3E}{\isasymin}}\ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isanewline
-\ {\isacharbar}\ NS{\isadigit{1}}{\isacharcolon}\ \ {\isachardoublequoteopen}{\isasymlbrakk}evs{\isadigit{1}}\ {\isasymin}\ ns{\isacharunderscore}public{\isacharsemicolon}\ \ Nonce\ NA\ {\isasymnotin}\ used\ evs{\isadigit{1}}{\isasymrbrakk}\isanewline
-\ \ \ \ \ \ \ \ \ \ {\isasymLongrightarrow}\ Says\ A\ B\ {\isacharparenleft}Crypt\ {\isacharparenleft}pubK\ B{\isacharparenright}\ {\isasymlbrace}Nonce\ NA{\isacharcomma}\ Agent\ A{\isasymrbrace}{\isacharparenright}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharhash}\ evs{\isadigit{1}}\ \ {\isasymin}\ \ ns{\isacharunderscore}public{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{7C}{\isacharbar}}\ NS{\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}evs{\isadigit{1}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{3B}{\isacharsemicolon}}\ \ Nonce\ NA\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ used\ evs{\isadigit{1}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\ \ \ \ \ \ \ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Says\ A\ B\ {\isaliteral{28}{\isacharparenleft}}Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}Nonce\ NA{\isaliteral{2C}{\isacharcomma}}\ Agent\ A{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{23}{\isacharhash}}\ evs{\isadigit{1}}\ \ {\isaliteral{5C3C696E3E}{\isasymin}}\ \ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isanewline
-\ {\isacharbar}\ NS{\isadigit{2}}{\isacharcolon}\ \ {\isachardoublequoteopen}{\isasymlbrakk}evs{\isadigit{2}}\ {\isasymin}\ ns{\isacharunderscore}public{\isacharsemicolon}\ \ Nonce\ NB\ {\isasymnotin}\ used\ evs{\isadigit{2}}{\isacharsemicolon}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ Says\ A{\isacharprime}\ B\ {\isacharparenleft}Crypt\ {\isacharparenleft}pubK\ B{\isacharparenright}\ {\isasymlbrace}Nonce\ NA{\isacharcomma}\ Agent\ A{\isasymrbrace}{\isacharparenright}\ {\isasymin}\ set\ evs{\isadigit{2}}{\isasymrbrakk}\isanewline
-\ \ \ \ \ \ \ \ \ \ {\isasymLongrightarrow}\ Says\ B\ A\ {\isacharparenleft}Crypt\ {\isacharparenleft}pubK\ A{\isacharparenright}\ {\isasymlbrace}Nonce\ NA{\isacharcomma}\ Nonce\ NB{\isacharcomma}\ Agent\ B{\isasymrbrace}{\isacharparenright}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharhash}\ evs{\isadigit{2}}\ \ {\isasymin}\ \ ns{\isacharunderscore}public{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{7C}{\isacharbar}}\ NS{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}evs{\isadigit{2}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{3B}{\isacharsemicolon}}\ \ Nonce\ NB\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ used\ evs{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ Says\ A{\isaliteral{27}{\isacharprime}}\ B\ {\isaliteral{28}{\isacharparenleft}}Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}Nonce\ NA{\isaliteral{2C}{\isacharcomma}}\ Agent\ A{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ set\ evs{\isadigit{2}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\ \ \ \ \ \ \ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Says\ B\ A\ {\isaliteral{28}{\isacharparenleft}}Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}Nonce\ NA{\isaliteral{2C}{\isacharcomma}}\ Nonce\ NB{\isaliteral{2C}{\isacharcomma}}\ Agent\ B{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{23}{\isacharhash}}\ evs{\isadigit{2}}\ \ {\isaliteral{5C3C696E3E}{\isasymin}}\ \ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isanewline
-\ {\isacharbar}\ NS{\isadigit{3}}{\isacharcolon}\ \ {\isachardoublequoteopen}{\isasymlbrakk}evs{\isadigit{3}}\ {\isasymin}\ ns{\isacharunderscore}public{\isacharsemicolon}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ Says\ A\ \ B\ {\isacharparenleft}Crypt\ {\isacharparenleft}pubK\ B{\isacharparenright}\ {\isasymlbrace}Nonce\ NA{\isacharcomma}\ Agent\ A{\isasymrbrace}{\isacharparenright}\ {\isasymin}\ set\ evs{\isadigit{3}}{\isacharsemicolon}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ Says\ B{\isacharprime}\ A\ {\isacharparenleft}Crypt\ {\isacharparenleft}pubK\ A{\isacharparenright}\ {\isasymlbrace}Nonce\ NA{\isacharcomma}\ Nonce\ NB{\isacharcomma}\ Agent\ B{\isasymrbrace}{\isacharparenright}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isasymin}\ set\ evs{\isadigit{3}}{\isasymrbrakk}\isanewline
-\ \ \ \ \ \ \ \ \ \ {\isasymLongrightarrow}\ Says\ A\ B\ {\isacharparenleft}Crypt\ {\isacharparenleft}pubK\ B{\isacharparenright}\ {\isacharparenleft}Nonce\ NB{\isacharparenright}{\isacharparenright}\ {\isacharhash}\ evs{\isadigit{3}}\ {\isasymin}\ ns{\isacharunderscore}public{\isachardoublequoteclose}%
+\ {\isaliteral{7C}{\isacharbar}}\ NS{\isadigit{3}}{\isaliteral{3A}{\isacharcolon}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}evs{\isadigit{3}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ Says\ A\ \ B\ {\isaliteral{28}{\isacharparenleft}}Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}Nonce\ NA{\isaliteral{2C}{\isacharcomma}}\ Agent\ A{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ set\ evs{\isadigit{3}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ Says\ B{\isaliteral{27}{\isacharprime}}\ A\ {\isaliteral{28}{\isacharparenleft}}Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}Nonce\ NA{\isaliteral{2C}{\isacharcomma}}\ Nonce\ NB{\isaliteral{2C}{\isacharcomma}}\ Agent\ B{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5C3C696E3E}{\isasymin}}\ set\ evs{\isadigit{3}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\ \ \ \ \ \ \ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Says\ A\ B\ {\isaliteral{28}{\isacharparenleft}}Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}Nonce\ NB{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{23}{\isacharhash}}\ evs{\isadigit{3}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{22}{\isachardoublequoteclose}}%
\end{isabelle}
\caption{An Inductive Protocol Definition}\label{fig:ns_public}
\end{figure}
@@ -65,7 +65,7 @@
Each protocol step is specified by a rule of an inductive definition. An
event trace has type \isa{event\ list}, so we declare the constant
-\isa{ns{\isacharunderscore}public} to be a set of such traces.
+\isa{ns{\isaliteral{5F}{\isacharunderscore}}public} to be a set of such traces.
Figure~\ref{fig:ns_public} presents the inductive definition. The
\isa{Nil} rule introduces the empty trace. The \isa{Fake} rule models the
@@ -78,14 +78,14 @@
Here is a detailed explanation of rule \isa{NS{\isadigit{2}}}.
A trace containing an event of the form
\begin{isabelle}%
-\ \ \ \ \ Says\ A{\isacharprime}\ B\ {\isacharparenleft}Crypt\ {\isacharparenleft}pubK\ B{\isacharparenright}\ {\isasymlbrace}Nonce\ NA{\isacharcomma}\ Agent\ A{\isasymrbrace}{\isacharparenright}%
+\ \ \ \ \ Says\ A{\isaliteral{27}{\isacharprime}}\ B\ {\isaliteral{28}{\isacharparenleft}}Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}Nonce\ NA{\isaliteral{2C}{\isacharcomma}}\ Agent\ A{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
may be extended by an event of the form
\begin{isabelle}%
-\ \ \ \ \ Says\ B\ A\ {\isacharparenleft}Crypt\ {\isacharparenleft}pubK\ A{\isacharparenright}\ {\isasymlbrace}Nonce\ NA{\isacharcomma}\ Nonce\ NB{\isacharcomma}\ Agent\ B{\isasymrbrace}{\isacharparenright}%
+\ \ \ \ \ Says\ B\ A\ {\isaliteral{28}{\isacharparenleft}}Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}Nonce\ NA{\isaliteral{2C}{\isacharcomma}}\ Nonce\ NB{\isaliteral{2C}{\isacharcomma}}\ Agent\ B{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
-where \isa{NB} is a fresh nonce: \isa{Nonce\ NB\ {\isasymnotin}\ used\ evs{\isadigit{2}}}.
-Writing the sender as \isa{A{\isacharprime}} indicates that \isa{B} does not
+where \isa{NB} is a fresh nonce: \isa{Nonce\ NB\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ used\ evs{\isadigit{2}}}.
+Writing the sender as \isa{A{\isaliteral{27}{\isacharprime}}} indicates that \isa{B} does not
know who sent the message. Calling the trace variable \isa{evs{\isadigit{2}}} rather
than simply \isa{evs} helps us know where we are in a proof after many
case-splits: every subgoal mentioning \isa{evs{\isadigit{2}}} involves message~2 of the
@@ -117,7 +117,7 @@
\begin{isamarkuptext}%
Secrecy properties can be hard to prove. The conclusion of a typical
secrecy theorem is
-\isa{X\ {\isasymnotin}\ analz\ {\isacharparenleft}knows\ Spy\ evs{\isacharparenright}}. The difficulty arises from
+\isa{X\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ analz\ {\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evs{\isaliteral{29}{\isacharparenright}}}. The difficulty arises from
having to reason about \isa{analz}, or less formally, showing that the spy
can never learn~\isa{X}. Much easier is to prove that \isa{X} can never
occur at all. Such \emph{regularity} properties are typically expressed
@@ -132,9 +132,9 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ Spy{\isacharunderscore}see{\isacharunderscore}priK\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ \ \ {\isachardoublequoteopen}evs\ {\isasymin}\ ns{\isacharunderscore}public\isanewline
-\ \ \ \ \ \ \ {\isasymLongrightarrow}\ {\isacharparenleft}Key\ {\isacharparenleft}priK\ A{\isacharparenright}\ {\isasymin}\ parts\ {\isacharparenleft}knows\ Spy\ evs{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}A\ {\isasymin}\ bad{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ Spy{\isaliteral{5F}{\isacharunderscore}}see{\isaliteral{5F}{\isacharunderscore}}priK\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}evs\ {\isaliteral{5C3C696E3E}{\isasymin}}\ ns{\isaliteral{5F}{\isacharunderscore}}public\isanewline
+\ \ \ \ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}Key\ {\isaliteral{28}{\isacharparenleft}}priK\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ parts\ {\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evs{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C696E3E}{\isasymin}}\ bad{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -142,10 +142,10 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}erule\ ns{\isacharunderscore}public{\isachardot}induct{\isacharcomma}\ simp{\isacharunderscore}all{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}erule\ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{2E}{\isachardot}}induct{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
The induction yields five subgoals, one for each rule in the definition of
-\isa{ns{\isacharunderscore}public}. The idea is to prove that the protocol property holds initially
+\isa{ns{\isaliteral{5F}{\isacharunderscore}}public}. The idea is to prove that the protocol property holds initially
(rule \isa{Nil}), is preserved by each of the legitimate protocol steps (rules
\isa{NS{\isadigit{1}}}--\isa{{\isadigit{3}}}), and even is preserved in the face of anything the
spy can do (rule \isa{Fake}).
@@ -154,12 +154,12 @@
at all, so only \isa{Fake} is relevant. Indeed, simplification leaves
only the \isa{Fake} case, as indicated by the variable name \isa{evsf}:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}evsf\ X{\isachardot}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymlbrakk}evsf\ {\isasymin}\ ns{\isacharunderscore}public{\isacharsemicolon}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ \ }{\isacharparenleft}Key\ {\isacharparenleft}priK\ A{\isacharparenright}\ {\isasymin}\ parts\ {\isacharparenleft}knows\ Spy\ evsf{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}A\ {\isasymin}\ bad{\isacharparenright}{\isacharsemicolon}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ \ }X\ {\isasymin}\ synth\ {\isacharparenleft}analz\ {\isacharparenleft}knows\ Spy\ evsf{\isacharparenright}{\isacharparenright}{\isasymrbrakk}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymLongrightarrow}\ {\isacharparenleft}Key\ {\isacharparenleft}priK\ A{\isacharparenright}\ {\isasymin}\ parts\ {\isacharparenleft}insert\ X\ {\isacharparenleft}knows\ Spy\ evsf{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharequal}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ {\isasymLongrightarrow}\ }{\isacharparenleft}A\ {\isasymin}\ bad{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}evsf\ X{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}evsf\ {\isaliteral{5C3C696E3E}{\isasymin}}\ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ \ }{\isaliteral{28}{\isacharparenleft}}Key\ {\isaliteral{28}{\isacharparenleft}}priK\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ parts\ {\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evsf{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C696E3E}{\isasymin}}\ bad{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ \ }X\ {\isaliteral{5C3C696E3E}{\isasymin}}\ synth\ {\isaliteral{28}{\isacharparenleft}}analz\ {\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evsf{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}Key\ {\isaliteral{28}{\isacharparenleft}}priK\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ parts\ {\isaliteral{28}{\isacharparenleft}}insert\ X\ {\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evsf{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ }{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{5C3C696E3E}{\isasymin}}\ bad{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
@@ -199,16 +199,16 @@
always choose fresh values as nonces; only the spy might reuse a value,
and he doesn't know this particular value. The proof script is short:
induction, simplification, \isa{blast}. The first line uses the rule
-\isa{rev{\isacharunderscore}mp} to prepare the induction by moving two assumptions into the
+\isa{rev{\isaliteral{5F}{\isacharunderscore}}mp} to prepare the induction by moving two assumptions into the
induction formula.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ no{\isacharunderscore}nonce{\isacharunderscore}NS{\isadigit{1}}{\isacharunderscore}NS{\isadigit{2}}{\isacharcolon}\isanewline
-\ \ \ \ {\isachardoublequoteopen}{\isasymlbrakk}Crypt\ {\isacharparenleft}pubK\ C{\isacharparenright}\ {\isasymlbrace}NA{\isacharprime}{\isacharcomma}\ Nonce\ NA{\isacharcomma}\ Agent\ D{\isasymrbrace}\ {\isasymin}\ parts\ {\isacharparenleft}knows\ Spy\ evs{\isacharparenright}{\isacharsemicolon}\isanewline
-\ \ \ \ \ \ Crypt\ {\isacharparenleft}pubK\ B{\isacharparenright}\ {\isasymlbrace}Nonce\ NA{\isacharcomma}\ Agent\ A{\isasymrbrace}\ {\isasymin}\ parts\ {\isacharparenleft}knows\ Spy\ evs{\isacharparenright}{\isacharsemicolon}\isanewline
-\ \ \ \ \ \ evs\ {\isasymin}\ ns{\isacharunderscore}public{\isasymrbrakk}\isanewline
-\ \ \ \ \ {\isasymLongrightarrow}\ Nonce\ NA\ {\isasymin}\ analz\ {\isacharparenleft}knows\ Spy\ evs{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ no{\isaliteral{5F}{\isacharunderscore}}nonce{\isaliteral{5F}{\isacharunderscore}}NS{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}NS{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ C{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}NA{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ Nonce\ NA{\isaliteral{2C}{\isacharcomma}}\ Agent\ D{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ parts\ {\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evs{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ \ \ Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}Nonce\ NA{\isaliteral{2C}{\isacharcomma}}\ Agent\ A{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ parts\ {\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evs{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ \ \ evs\ {\isaliteral{5C3C696E3E}{\isasymin}}\ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\ \ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Nonce\ NA\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ {\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -216,11 +216,11 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}erule\ rev{\isacharunderscore}mp{\isacharcomma}\ erule\ rev{\isacharunderscore}mp{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}erule\ rev{\isaliteral{5F}{\isacharunderscore}}mp{\isaliteral{2C}{\isacharcomma}}\ erule\ rev{\isaliteral{5F}{\isacharunderscore}}mp{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}erule\ ns{\isacharunderscore}public{\isachardot}induct{\isacharcomma}\ simp{\isacharunderscore}all{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}erule\ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{2E}{\isachardot}}induct{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}blast\ intro{\isacharcolon}\ analz{\isacharunderscore}insertI{\isacharparenright}{\isacharplus}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}blast\ intro{\isaliteral{3A}{\isacharcolon}}\ analz{\isaliteral{5F}{\isacharunderscore}}insertI{\isaliteral{29}{\isacharparenright}}{\isaliteral{2B}{\isacharplus}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -237,11 +237,11 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ unique{\isacharunderscore}NA{\isacharcolon}\isanewline
-\ \ \ \ \ {\isachardoublequoteopen}{\isasymlbrakk}Crypt{\isacharparenleft}pubK\ B{\isacharparenright}\ \ {\isasymlbrace}Nonce\ NA{\isacharcomma}\ Agent\ A\ {\isasymrbrace}\ {\isasymin}\ parts{\isacharparenleft}knows\ Spy\ evs{\isacharparenright}{\isacharsemicolon}\isanewline
-\ \ \ \ \ \ \ Crypt{\isacharparenleft}pubK\ B{\isacharprime}{\isacharparenright}\ {\isasymlbrace}Nonce\ NA{\isacharcomma}\ Agent\ A{\isacharprime}{\isasymrbrace}\ {\isasymin}\ parts{\isacharparenleft}knows\ Spy\ evs{\isacharparenright}{\isacharsemicolon}\isanewline
-\ \ \ \ \ \ \ Nonce\ NA\ {\isasymnotin}\ analz\ {\isacharparenleft}knows\ Spy\ evs{\isacharparenright}{\isacharsemicolon}\ evs\ {\isasymin}\ ns{\isacharunderscore}public{\isasymrbrakk}\isanewline
-\ \ \ \ \ \ {\isasymLongrightarrow}\ A{\isacharequal}A{\isacharprime}\ {\isasymand}\ B{\isacharequal}B{\isacharprime}{\isachardoublequoteclose}%
+\ unique{\isaliteral{5F}{\isacharunderscore}}NA{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}Crypt{\isaliteral{28}{\isacharparenleft}}pubK\ B{\isaliteral{29}{\isacharparenright}}\ \ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}Nonce\ NA{\isaliteral{2C}{\isacharcomma}}\ Agent\ A\ {\isaliteral{5C3C7262726163653E}{\isasymrbrace}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ parts{\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evs{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ \ \ \ Crypt{\isaliteral{28}{\isacharparenleft}}pubK\ B{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}Nonce\ NA{\isaliteral{2C}{\isacharcomma}}\ Agent\ A{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ parts{\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evs{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ \ \ \ \ Nonce\ NA\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ analz\ {\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evs{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ evs\ {\isaliteral{5C3C696E3E}{\isasymin}}\ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\ \ \ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ A{\isaliteral{3D}{\isacharequal}}A{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B{\isaliteral{3D}{\isacharequal}}B{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -332,10 +332,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ Spy{\isacharunderscore}not{\isacharunderscore}see{\isacharunderscore}NB\ {\isacharbrackleft}dest{\isacharbrackright}{\isacharcolon}\isanewline
-\ {\isachardoublequoteopen}{\isasymlbrakk}Says\ B\ A\ {\isacharparenleft}Crypt\ {\isacharparenleft}pubK\ A{\isacharparenright}\ {\isasymlbrace}Nonce\ NA{\isacharcomma}\ Nonce\ NB{\isacharcomma}\ Agent\ B{\isasymrbrace}{\isacharparenright}\ {\isasymin}\ set\ evs{\isacharsemicolon}\isanewline
-\ \ \ A\ {\isasymnotin}\ bad{\isacharsemicolon}\ \ B\ {\isasymnotin}\ bad{\isacharsemicolon}\ \ evs\ {\isasymin}\ ns{\isacharunderscore}public{\isasymrbrakk}\isanewline
-\ \ {\isasymLongrightarrow}\ Nonce\ NB\ {\isasymnotin}\ analz\ {\isacharparenleft}knows\ Spy\ evs{\isacharparenright}{\isachardoublequoteclose}%
+\ Spy{\isaliteral{5F}{\isacharunderscore}}not{\isaliteral{5F}{\isacharunderscore}}see{\isaliteral{5F}{\isacharunderscore}}NB\ {\isaliteral{5B}{\isacharbrackleft}}dest{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}Says\ B\ A\ {\isaliteral{28}{\isacharparenleft}}Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}Nonce\ NA{\isaliteral{2C}{\isacharcomma}}\ Nonce\ NB{\isaliteral{2C}{\isacharcomma}}\ Agent\ B{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ set\ evs{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ A\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ bad{\isaliteral{3B}{\isacharsemicolon}}\ \ B\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ bad{\isaliteral{3B}{\isacharsemicolon}}\ \ evs\ {\isaliteral{5C3C696E3E}{\isasymin}}\ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Nonce\ NB\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ analz\ {\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -348,7 +348,7 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}erule\ rev{\isacharunderscore}mp{\isacharcomma}\ erule\ ns{\isacharunderscore}public{\isachardot}induct{\isacharcomma}\ simp{\isacharunderscore}all{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}erule\ rev{\isaliteral{5F}{\isacharunderscore}}mp{\isaliteral{2C}{\isacharcomma}}\ erule\ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{2E}{\isachardot}}induct{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
The proof states are too complicated to present in full.
Let's examine the simplest subgoal, that for message~1. The following
@@ -362,29 +362,29 @@
In the Isabelle subgoal, instead of primed variables like $B'$ and $Na'$
we have \isa{Ba} and~\isa{NAa}:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}evs{\isadigit{1}}\ NAa\ Ba{\isachardot}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymlbrakk}A\ {\isasymnotin}\ bad{\isacharsemicolon}\ B\ {\isasymnotin}\ bad{\isacharsemicolon}\ evs{\isadigit{1}}\ {\isasymin}\ ns{\isacharunderscore}public{\isacharsemicolon}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ \ }Says\ B\ A\ {\isacharparenleft}Crypt\ {\isacharparenleft}pubK\ A{\isacharparenright}\ {\isasymlbrace}Nonce\ NA{\isacharcomma}\ Nonce\ NB{\isacharcomma}\ Agent\ B{\isasymrbrace}{\isacharparenright}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ \ }{\isasymin}\ set\ evs{\isadigit{1}}\ {\isasymlongrightarrow}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ \ }Nonce\ NB\ {\isasymnotin}\ analz\ {\isacharparenleft}knows\ Spy\ evs{\isadigit{1}}{\isacharparenright}{\isacharsemicolon}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ \ }Nonce\ NAa\ {\isasymnotin}\ used\ evs{\isadigit{1}}{\isasymrbrakk}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymLongrightarrow}\ Ba\ {\isasymin}\ bad\ {\isasymlongrightarrow}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ {\isasymLongrightarrow}\ }Says\ B\ A\ {\isacharparenleft}Crypt\ {\isacharparenleft}pubK\ A{\isacharparenright}\ {\isasymlbrace}Nonce\ NA{\isacharcomma}\ Nonce\ NB{\isacharcomma}\ Agent\ B{\isasymrbrace}{\isacharparenright}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ {\isasymLongrightarrow}\ }{\isasymin}\ set\ evs{\isadigit{1}}\ {\isasymlongrightarrow}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ {\isasymLongrightarrow}\ }NB\ {\isasymnoteq}\ NAa%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}evs{\isadigit{1}}\ NAa\ Ba{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}A\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ bad{\isaliteral{3B}{\isacharsemicolon}}\ B\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ bad{\isaliteral{3B}{\isacharsemicolon}}\ evs{\isadigit{1}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ \ }Says\ B\ A\ {\isaliteral{28}{\isacharparenleft}}Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}Nonce\ NA{\isaliteral{2C}{\isacharcomma}}\ Nonce\ NB{\isaliteral{2C}{\isacharcomma}}\ Agent\ B{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ \ }{\isaliteral{5C3C696E3E}{\isasymin}}\ set\ evs{\isadigit{1}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ \ }Nonce\ NB\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ analz\ {\isaliteral{28}{\isacharparenleft}}knows\ Spy\ evs{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ \ }Nonce\ NAa\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ used\ evs{\isadigit{1}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Ba\ {\isaliteral{5C3C696E3E}{\isasymin}}\ bad\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ }Says\ B\ A\ {\isaliteral{28}{\isacharparenleft}}Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}Nonce\ NA{\isaliteral{2C}{\isacharcomma}}\ Nonce\ NB{\isaliteral{2C}{\isacharcomma}}\ Agent\ B{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ }{\isaliteral{5C3C696E3E}{\isasymin}}\ set\ evs{\isadigit{1}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ }NB\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ NAa%
\end{isabelle}
The simplifier has used a
default simplification rule that does a case
analysis for each encrypted message on whether or not the decryption key
is compromised.
\begin{isabelle}%
-analz\ {\isacharparenleft}insert\ {\isacharparenleft}Crypt\ K\ X{\isacharparenright}\ H{\isacharparenright}\ {\isacharequal}\isanewline
-{\isacharparenleft}if\ Key\ {\isacharparenleft}invKey\ K{\isacharparenright}\ {\isasymin}\ analz\ H\isanewline
-\isaindent{{\isacharparenleft}}then\ insert\ {\isacharparenleft}Crypt\ K\ X{\isacharparenright}\ {\isacharparenleft}analz\ {\isacharparenleft}insert\ X\ H{\isacharparenright}{\isacharparenright}\isanewline
-\isaindent{{\isacharparenleft}}else\ insert\ {\isacharparenleft}Crypt\ K\ X{\isacharparenright}\ {\isacharparenleft}analz\ H{\isacharparenright}{\isacharparenright}\rulename{analz{\isacharunderscore}Crypt{\isacharunderscore}if}%
+analz\ {\isaliteral{28}{\isacharparenleft}}insert\ {\isaliteral{28}{\isacharparenleft}}Crypt\ K\ X{\isaliteral{29}{\isacharparenright}}\ H{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+{\isaliteral{28}{\isacharparenleft}}if\ Key\ {\isaliteral{28}{\isacharparenleft}}invKey\ K{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ analz\ H\isanewline
+\isaindent{{\isaliteral{28}{\isacharparenleft}}}then\ insert\ {\isaliteral{28}{\isacharparenleft}}Crypt\ K\ X{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}analz\ {\isaliteral{28}{\isacharparenleft}}insert\ X\ H{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\isaindent{{\isaliteral{28}{\isacharparenleft}}}else\ insert\ {\isaliteral{28}{\isacharparenleft}}Crypt\ K\ X{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}analz\ H{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\rulename{analz{\isaliteral{5F}{\isacharunderscore}}Crypt{\isaliteral{5F}{\isacharunderscore}}if}%
\end{isabelle}
-The simplifier has also used \isa{Spy{\isacharunderscore}see{\isacharunderscore}priK}, proved in
-{\S}\ref{sec:regularity} above, to yield \isa{Ba\ {\isasymin}\ bad}.
+The simplifier has also used \isa{Spy{\isaliteral{5F}{\isacharunderscore}}see{\isaliteral{5F}{\isacharunderscore}}priK}, proved in
+{\S}\ref{sec:regularity} above, to yield \isa{Ba\ {\isaliteral{5C3C696E3E}{\isasymin}}\ bad}.
Recall that this subgoal concerns the case
where the last message to be sent was
@@ -392,9 +392,9 @@
This message can compromise $Nb$ only if $Nb=Na'$ and $B'$ is compromised,
allowing the spy to decrypt the message. The Isabelle subgoal says
precisely this, if we allow for its choice of variable names.
-Proving \isa{NB\ {\isasymnoteq}\ NAa} is easy: \isa{NB} was
+Proving \isa{NB\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ NAa} is easy: \isa{NB} was
sent earlier, while \isa{NAa} is fresh; formally, we have
-the assumption \isa{Nonce\ NAa\ {\isasymnotin}\ used\ evs{\isadigit{1}}}.
+the assumption \isa{Nonce\ NAa\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ used\ evs{\isadigit{1}}}.
Note that our reasoning concerned \isa{B}'s participation in another
run. Agents may engage in several runs concurrently, and some attacks work
@@ -405,7 +405,7 @@
the very message mentioned in the theorem statement.
Some of the cases are proved by unicity, others by
the induction hypothesis. For all those complications, the proofs are
-automatic by \isa{blast} with the theorem \isa{no{\isacharunderscore}nonce{\isacharunderscore}NS{\isadigit{1}}{\isacharunderscore}NS{\isadigit{2}}}.
+automatic by \isa{blast} with the theorem \isa{no{\isaliteral{5F}{\isacharunderscore}}nonce{\isaliteral{5F}{\isacharunderscore}}NS{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}NS{\isadigit{2}}}.
The remaining theorems about the protocol are not hard to prove. The
following one asserts a form of \emph{authenticity}: if
@@ -435,11 +435,11 @@
%
\endisadelimproof
\isacommand{theorem}\isamarkupfalse%
-\ B{\isacharunderscore}trusts{\isacharunderscore}NS{\isadigit{3}}{\isacharcolon}\isanewline
-\ {\isachardoublequoteopen}{\isasymlbrakk}Says\ B\ A\ \ {\isacharparenleft}Crypt\ {\isacharparenleft}pubK\ A{\isacharparenright}\ {\isasymlbrace}Nonce\ NA{\isacharcomma}\ Nonce\ NB{\isacharcomma}\ Agent\ B{\isasymrbrace}{\isacharparenright}\ {\isasymin}\ set\ evs{\isacharsemicolon}\isanewline
-\ \ \ Says\ A{\isacharprime}\ B\ {\isacharparenleft}Crypt\ {\isacharparenleft}pubK\ B{\isacharparenright}\ {\isacharparenleft}Nonce\ NB{\isacharparenright}{\isacharparenright}\ {\isasymin}\ set\ evs{\isacharsemicolon}\isanewline
-\ \ \ A\ {\isasymnotin}\ bad{\isacharsemicolon}\ \ B\ {\isasymnotin}\ bad{\isacharsemicolon}\ \ evs\ {\isasymin}\ ns{\isacharunderscore}public{\isasymrbrakk}\isanewline
-\ \ {\isasymLongrightarrow}\ Says\ A\ B\ {\isacharparenleft}Crypt\ {\isacharparenleft}pubK\ B{\isacharparenright}\ {\isacharparenleft}Nonce\ NB{\isacharparenright}{\isacharparenright}\ {\isasymin}\ set\ evs{\isachardoublequoteclose}%
+\ B{\isaliteral{5F}{\isacharunderscore}}trusts{\isaliteral{5F}{\isacharunderscore}}NS{\isadigit{3}}{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}Says\ B\ A\ \ {\isaliteral{28}{\isacharparenleft}}Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ A{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}Nonce\ NA{\isaliteral{2C}{\isacharcomma}}\ Nonce\ NB{\isaliteral{2C}{\isacharcomma}}\ Agent\ B{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ set\ evs{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ Says\ A{\isaliteral{27}{\isacharprime}}\ B\ {\isaliteral{28}{\isacharparenleft}}Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}Nonce\ NB{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ set\ evs{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\ \ \ A\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ bad{\isaliteral{3B}{\isacharsemicolon}}\ \ B\ {\isaliteral{5C3C6E6F74696E3E}{\isasymnotin}}\ bad{\isaliteral{3B}{\isacharsemicolon}}\ \ evs\ {\isaliteral{5C3C696E3E}{\isasymin}}\ ns{\isaliteral{5F}{\isacharunderscore}}public{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\ \ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Says\ A\ B\ {\isaliteral{28}{\isacharparenleft}}Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}Nonce\ NB{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ set\ evs{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -471,7 +471,7 @@
run by sending an instance of message~1 involving the nonce~\isa{NA}\@.
For this theorem, the conclusion is
\begin{isabelle}%
-Says\ A\ B\ {\isacharparenleft}Crypt\ {\isacharparenleft}pubK\ B{\isacharparenright}\ {\isasymlbrace}Nonce\ NA{\isacharcomma}\ Agent\ A{\isasymrbrace}{\isacharparenright}\ {\isasymin}\ set\ evs%
+Says\ A\ B\ {\isaliteral{28}{\isacharparenleft}}Crypt\ {\isaliteral{28}{\isacharparenleft}}pubK\ B{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C62726163653E}{\isasymlbrace}}Nonce\ NA{\isaliteral{2C}{\isacharcomma}}\ Agent\ A{\isaliteral{5C3C7262726163653E}{\isasymrbrace}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C696E3E}{\isasymin}}\ set\ evs%
\end{isabelle}
Analogous theorems can be proved for~\isa{A}, stating that nonce~\isa{NA}
remains secret and that message~2 really originates with~\isa{B}. Even the
--- a/doc-src/TutorialI/Protocol/document/Public.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Protocol/document/Public.tex Mon Nov 08 14:41:11 2010 +0100
@@ -24,10 +24,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{consts}\isamarkupfalse%
-\ pubK\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}agent\ {\isasymRightarrow}\ key{\isachardoublequoteclose}\isanewline
+\ pubK\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}agent\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ key{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isacommand{abbreviation}\isamarkupfalse%
-\ priK\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}agent\ {\isasymRightarrow}\ key{\isachardoublequoteclose}\isanewline
-\isakeyword{where}\ {\isachardoublequoteopen}priK\ x\ \ {\isasymequiv}\ \ invKey{\isacharparenleft}pubK\ x{\isacharparenright}{\isachardoublequoteclose}%
+\ priK\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}agent\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ key{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}priK\ x\ \ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ \ invKey{\isaliteral{28}{\isacharparenleft}}pubK\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
The set \isa{bad} consists of those agents whose private keys are known to
@@ -40,8 +40,8 @@
\isamarkuptrue%
\isacommand{axioms}\isamarkupfalse%
\isanewline
-\ \ inj{\isacharunderscore}pubK{\isacharcolon}\ \ \ \ \ \ \ \ {\isachardoublequoteopen}inj\ pubK{\isachardoublequoteclose}\isanewline
-\ \ priK{\isacharunderscore}neq{\isacharunderscore}pubK{\isacharcolon}\ \ \ {\isachardoublequoteopen}priK\ A\ {\isasymnoteq}\ pubK\ B{\isachardoublequoteclose}%
+\ \ inj{\isaliteral{5F}{\isacharunderscore}}pubK{\isaliteral{3A}{\isacharcolon}}\ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}inj\ pubK{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ priK{\isaliteral{5F}{\isacharunderscore}}neq{\isaliteral{5F}{\isacharunderscore}}pubK{\isaliteral{3A}{\isacharcolon}}\ \ \ {\isaliteral{22}{\isachardoublequoteopen}}priK\ A\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ pubK\ B{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
--- a/doc-src/TutorialI/Rules/document/find2.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Rules/document/find2.tex Mon Nov 08 14:41:11 2010 +0100
@@ -31,10 +31,10 @@
\texttt{intro}, \texttt{elim} and \texttt{dest}.
For example, given the goal \begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ A\ {\isasymand}\ B%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B%
\end{isabelle}
you can click on \pgmenu{Find} and type in the search expression
-\texttt{intro}. You will be shown a few rules ending in \isa{{\isasymLongrightarrow}\ {\isacharquery}P\ {\isasymand}\ {\isacharquery}Q},
+\texttt{intro}. You will be shown a few rules ending in \isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{3F}{\isacharquery}}Q},
among them \isa{conjI}\@. You may even discover that
the very theorem you are trying to prove is already in the
database. Given the goal%
@@ -57,17 +57,17 @@
\begin{isamarkuptxt}%
\vspace{-\bigskipamount}
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ A\ {\isasymlongrightarrow}\ A%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ A\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ A%
\end{isabelle}
the search for \texttt{intro} finds not just \isa{impI}
-but also \isa{imp{\isacharunderscore}refl}: \isa{{\isacharquery}P\ {\isasymlongrightarrow}\ {\isacharquery}P}.
+but also \isa{imp{\isaliteral{5F}{\isacharunderscore}}refl}: \isa{{\isaliteral{3F}{\isacharquery}}P\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{3F}{\isacharquery}}P}.
As before, search criteria can be combined freely: for example,
\begin{ttbox}
"_ \at\ _" intro
\end{ttbox}
searches for all introduction rules that match the current goal and
-mention the \isa{{\isacharat}} function.
+mention the \isa{{\isaliteral{40}{\isacharat}}} function.
Searching for elimination and destruction rules via \texttt{elim} and
\texttt{dest} is analogous to \texttt{intro} but takes the assumptions
--- a/doc-src/TutorialI/ToyList/document/ToyList.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/ToyList/document/ToyList.tex Mon Nov 08 14:41:11 2010 +0100
@@ -29,8 +29,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ {\isacharprime}a\ list\ {\isacharequal}\ Nil\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharparenleft}{\isachardoublequoteopen}{\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}{\isacharparenright}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Cons\ {\isacharprime}a\ {\isachardoublequoteopen}{\isacharprime}a\ list{\isachardoublequoteclose}\ \ \ \ \ \ \ \ \ \ \ \ {\isacharparenleft}\isakeyword{infixr}\ {\isachardoublequoteopen}{\isacharhash}{\isachardoublequoteclose}\ {\isadigit{6}}{\isadigit{5}}{\isacharparenright}%
+\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{3D}{\isacharequal}}\ Nil\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Cons\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{22}{\isachardoublequoteclose}}\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixr}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{23}{\isacharhash}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{6}}{\isadigit{5}}{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptext}%
\noindent
The datatype\index{datatype@\isacommand {datatype} (command)}
@@ -42,15 +42,15 @@
\isa{False}. Because this notation quickly becomes unwieldy, the
datatype declaration is annotated with an alternative syntax: instead of
\isa{Nil} and \isa{Cons x xs} we can write
-\isa{{\isacharbrackleft}{\isacharbrackright}}\index{$HOL2list@\isa{[]}|bold} and
-\isa{x\ {\isacharhash}\ xs}\index{$HOL2list@\isa{\#}|bold}. In fact, this
+\isa{{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}}\index{$HOL2list@\isa{[]}|bold} and
+\isa{x\ {\isaliteral{23}{\isacharhash}}\ xs}\index{$HOL2list@\isa{\#}|bold}. In fact, this
alternative syntax is the familiar one. Thus the list \isa{Cons True
-(Cons False Nil)} becomes \isa{True\ {\isacharhash}\ False\ {\isacharhash}\ {\isacharbrackleft}{\isacharbrackright}}. The annotation
+(Cons False Nil)} becomes \isa{True\ {\isaliteral{23}{\isacharhash}}\ False\ {\isaliteral{23}{\isacharhash}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}}. The annotation
\isacommand{infixr}\index{infixr@\isacommand{infixr} (annotation)}
-means that \isa{{\isacharhash}} associates to
-the right: the term \isa{x\ {\isacharhash}\ y\ {\isacharhash}\ z} is read as \isa{x\ {\isacharhash}\ {\isacharparenleft}y\ {\isacharhash}\ z{\isacharparenright}}
-and not as \isa{{\isacharparenleft}x\ {\isacharhash}\ y{\isacharparenright}\ {\isacharhash}\ z}.
-The \isa{{\isadigit{6}}{\isadigit{5}}} is the priority of the infix \isa{{\isacharhash}}.
+means that \isa{{\isaliteral{23}{\isacharhash}}} associates to
+the right: the term \isa{x\ {\isaliteral{23}{\isacharhash}}\ y\ {\isaliteral{23}{\isacharhash}}\ z} is read as \isa{x\ {\isaliteral{23}{\isacharhash}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{23}{\isacharhash}}\ z{\isaliteral{29}{\isacharparenright}}}
+and not as \isa{{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{23}{\isacharhash}}\ z}.
+The \isa{{\isadigit{6}}{\isadigit{5}}} is the priority of the infix \isa{{\isaliteral{23}{\isacharhash}}}.
\begin{warn}
Syntax annotations can be powerful, but they are difficult to master and
@@ -64,25 +64,25 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ app\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{infixr}\ {\isachardoublequoteopen}{\isacharat}{\isachardoublequoteclose}\ {\isadigit{6}}{\isadigit{5}}{\isacharparenright}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}{\isacharbrackleft}{\isacharbrackright}\ {\isacharat}\ ys\ \ \ \ \ \ \ {\isacharequal}\ ys{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}{\isacharparenleft}x\ {\isacharhash}\ xs{\isacharparenright}\ {\isacharat}\ ys\ {\isacharequal}\ x\ {\isacharhash}\ {\isacharparenleft}xs\ {\isacharat}\ ys{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ app\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixr}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{40}{\isacharat}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{6}}{\isadigit{5}}{\isaliteral{29}{\isacharparenright}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{40}{\isacharat}}\ ys\ \ \ \ \ \ \ {\isaliteral{3D}{\isacharequal}}\ ys{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{40}{\isacharat}}\ ys\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{23}{\isacharhash}}\ {\isaliteral{28}{\isacharparenleft}}xs\ {\isaliteral{40}{\isacharat}}\ ys{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{primrec}\isamarkupfalse%
-\ rev\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}rev\ {\isacharbrackleft}{\isacharbrackright}\ \ \ \ \ \ \ \ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}rev\ {\isacharparenleft}x\ {\isacharhash}\ xs{\isacharparenright}\ \ {\isacharequal}\ {\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharat}\ {\isacharparenleft}x\ {\isacharhash}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isachardoublequoteclose}%
+\ rev\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}rev\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ \ \ \ \ \ \ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}rev\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ xs{\isaliteral{29}{\isacharparenright}}\ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{23}{\isacharhash}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
Each function definition is of the form
\begin{center}
-\isacommand{primrec} \textit{name} \isa{{\isacharcolon}{\isacharcolon}} \textit{type} \textit{(optional syntax)} \isakeyword{where} \textit{equations}
+\isacommand{primrec} \textit{name} \isa{{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}} \textit{type} \textit{(optional syntax)} \isakeyword{where} \textit{equations}
\end{center}
-The equations must be separated by \isa{{\isacharbar}}.
+The equations must be separated by \isa{{\isaliteral{7C}{\isacharbar}}}.
%
Function \isa{app} is annotated with concrete syntax. Instead of the
prefix syntax \isa{app\ xs\ ys} the infix
-\isa{xs\ {\isacharat}\ ys}\index{$HOL2list@\isa{\at}|bold} becomes the preferred
+\isa{xs\ {\isaliteral{40}{\isacharat}}\ ys}\index{$HOL2list@\isa{\at}|bold} becomes the preferred
form.
\index{*rev (constant)|(}\index{append function|(}
@@ -133,21 +133,21 @@
Assuming you have processed the declarations and definitions of
\texttt{ToyList} presented so far, you may want to test your
functions by running them. For example, what is the value of
-\isa{rev\ {\isacharparenleft}True\ {\isacharhash}\ False\ {\isacharhash}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}}? Command%
+\isa{rev\ {\isaliteral{28}{\isacharparenleft}}True\ {\isaliteral{23}{\isacharhash}}\ False\ {\isaliteral{23}{\isacharhash}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}}? Command%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{value}\isamarkupfalse%
-\ {\isachardoublequoteopen}rev\ {\isacharparenleft}True\ {\isacharhash}\ False\ {\isacharhash}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}rev\ {\isaliteral{28}{\isacharparenleft}}True\ {\isaliteral{23}{\isacharhash}}\ False\ {\isaliteral{23}{\isacharhash}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
-\noindent yields the correct result \isa{False\ {\isacharhash}\ True\ {\isacharhash}\ {\isacharbrackleft}{\isacharbrackright}}.
+\noindent yields the correct result \isa{False\ {\isaliteral{23}{\isacharhash}}\ True\ {\isaliteral{23}{\isacharhash}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}}.
But we can go beyond mere functional programming and evaluate terms with
variables in them, executing functions symbolically:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{value}\isamarkupfalse%
-\ {\isachardoublequoteopen}rev\ {\isacharparenleft}a\ {\isacharhash}\ b\ {\isacharhash}\ c\ {\isacharhash}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}rev\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{23}{\isacharhash}}\ b\ {\isaliteral{23}{\isacharhash}}\ c\ {\isaliteral{23}{\isacharhash}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
-\noindent yields \isa{c\ {\isacharhash}\ b\ {\isacharhash}\ a\ {\isacharhash}\ {\isacharbrackleft}{\isacharbrackright}}.
+\noindent yields \isa{c\ {\isaliteral{23}{\isacharhash}}\ b\ {\isaliteral{23}{\isacharhash}}\ a\ {\isaliteral{23}{\isacharhash}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}}.
\section{An Introductory Proof}
\label{sec:intro-proof}
@@ -164,7 +164,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ rev{\isacharunderscore}rev\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}rev{\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharequal}\ xs{\isachardoublequoteclose}%
+\ rev{\isaliteral{5F}{\isacharunderscore}}rev\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}rev{\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ xs{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -177,19 +177,19 @@
This \isacommand{theorem} command does several things:
\begin{itemize}
\item
-It establishes a new theorem to be proved, namely \isa{rev\ {\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharequal}\ xs}.
+It establishes a new theorem to be proved, namely \isa{rev\ {\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ xs}.
\item
-It gives that theorem the name \isa{rev{\isacharunderscore}rev}, for later reference.
+It gives that theorem the name \isa{rev{\isaliteral{5F}{\isacharunderscore}}rev}, for later reference.
\item
It tells Isabelle (via the bracketed attribute \attrdx{simp}) to take the eventual theorem as a simplification rule: future proofs involving
-simplification will replace occurrences of \isa{rev\ {\isacharparenleft}rev\ xs{\isacharparenright}} by
+simplification will replace occurrences of \isa{rev\ {\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}} by
\isa{xs}.
\end{itemize}
The name and the simplification attribute are optional.
Isabelle's response is to print the initial proof state consisting
of some header information (like how many subgoals there are) followed by
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ rev\ {\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharequal}\ xs%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ rev\ {\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ xs%
\end{isabelle}
For compactness reasons we omit the header in this tutorial.
Until we have finished a proof, the \rmindex{proof state} proper
@@ -206,13 +206,13 @@
set the flag \isa{Proof.show_main_goal}\index{*show_main_goal (flag)}
--- this flag used to be set by default.)
-Let us now get back to \isa{rev\ {\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharequal}\ xs}. Properties of recursively
+Let us now get back to \isa{rev\ {\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ xs}. Properties of recursively
defined functions are best established by induction. In this case there is
nothing obvious except induction on \isa{xs}:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ xs{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent\index{*induct_tac (method)}%
This tells Isabelle to perform induction on variable \isa{xs}. The suffix
@@ -222,9 +222,9 @@
two subgoals, namely the base case (\isa{Nil}) and the induction step
(\isa{Cons}):
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ rev\ {\isacharparenleft}rev\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}a\ list{\isachardot}\isanewline
-\isaindent{\ {\isadigit{2}}{\isachardot}\ \ \ \ }rev\ {\isacharparenleft}rev\ list{\isacharparenright}\ {\isacharequal}\ list\ {\isasymLongrightarrow}\ rev\ {\isacharparenleft}rev\ {\isacharparenleft}a\ {\isacharhash}\ list{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ a\ {\isacharhash}\ list%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ rev\ {\isaliteral{28}{\isacharparenleft}}rev\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\isanewline
+\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a\ list{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }rev\ {\isaliteral{28}{\isacharparenleft}}rev\ list{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ list\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ rev\ {\isaliteral{28}{\isacharparenleft}}rev\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{23}{\isacharhash}}\ list{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{23}{\isacharhash}}\ list%
\end{isabelle}
The induction step is an example of the general format of a subgoal:\index{subgoals}
@@ -239,7 +239,7 @@
conclusion}\index{conclusion!of subgoal} is the actual proposition to be proved.
Typical proof steps
that add new assumptions are induction and case distinction. In our example
-the only assumption is the induction hypothesis \isa{rev\ {\isacharparenleft}rev\ list{\isacharparenright}\ {\isacharequal}\ list}, where \isa{list} is a variable name chosen by Isabelle. If there
+the only assumption is the induction hypothesis \isa{rev\ {\isaliteral{28}{\isacharparenleft}}rev\ list{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ list}, where \isa{list} is a variable name chosen by Isabelle. If there
are multiple assumptions, they are enclosed in the bracket pair
\indexboldpos{\isasymlbrakk}{$Isabrl} and
\indexboldpos{\isasymrbrakk}{$Isabrr} and separated by semicolons.
@@ -248,17 +248,17 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}auto{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
This command tells Isabelle to apply a proof strategy called
\isa{auto} to all subgoals. Essentially, \isa{auto} tries to
simplify the subgoals. In our case, subgoal~1 is solved completely (thanks
-to the equation \isa{rev\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}}) and disappears; the simplified version
+to the equation \isa{rev\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}}) and disappears; the simplified version
of subgoal~2 becomes the new subgoal~1:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}a\ list{\isachardot}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }rev\ {\isacharparenleft}rev\ list{\isacharparenright}\ {\isacharequal}\ list\ {\isasymLongrightarrow}\ rev\ {\isacharparenleft}rev\ list\ {\isacharat}\ a\ {\isacharhash}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ {\isacharequal}\ a\ {\isacharhash}\ list%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a\ list{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }rev\ {\isaliteral{28}{\isacharparenleft}}rev\ list{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ list\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ rev\ {\isaliteral{28}{\isacharparenleft}}rev\ list\ {\isaliteral{40}{\isacharat}}\ a\ {\isaliteral{23}{\isacharhash}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{23}{\isacharhash}}\ list%
\end{isabelle}
In order to simplify this subgoal further, a lemma suggests itself.%
\end{isamarkuptxt}%
@@ -282,7 +282,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ rev{\isacharunderscore}app\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}rev{\isacharparenleft}xs\ {\isacharat}\ ys{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}rev\ ys{\isacharparenright}\ {\isacharat}\ {\isacharparenleft}rev\ xs{\isacharparenright}{\isachardoublequoteclose}%
+\ rev{\isaliteral{5F}{\isacharunderscore}}app\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}rev{\isaliteral{28}{\isacharparenleft}}xs\ {\isaliteral{40}{\isacharat}}\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}rev\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -296,22 +296,22 @@
\emph{theorem} and \emph{lemma} pretty much interchangeably, too.
There are two variables that we could induct on: \isa{xs} and
-\isa{ys}. Because \isa{{\isacharat}} is defined by recursion on
+\isa{ys}. Because \isa{{\isaliteral{40}{\isacharat}}} is defined by recursion on
the first argument, \isa{xs} is the correct one:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ xs{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
This time not even the base case is solved automatically:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}auto{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ rev\ ys\ {\isacharequal}\ rev\ ys\ {\isacharat}\ {\isacharbrackleft}{\isacharbrackright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ rev\ ys\ {\isaliteral{3D}{\isacharequal}}\ rev\ ys\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}%
\end{isabelle}
Again, we need to abandon this proof attempt and prove another simple lemma
first. In the future the step of abandoning an incomplete proof before
@@ -335,7 +335,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ app{\isacharunderscore}Nil{\isadigit{2}}\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}xs\ {\isacharat}\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ xs{\isachardoublequoteclose}\isanewline
+\ app{\isaliteral{5F}{\isacharunderscore}}Nil{\isadigit{2}}\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}xs\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ xs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -343,15 +343,15 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ xs{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}auto{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
-It works, yielding the desired message \isa{No\ subgoals{\isacharbang}}:
+It works, yielding the desired message \isa{No\ subgoals{\isaliteral{21}{\isacharbang}}}:
\begin{isabelle}%
-xs\ {\isacharat}\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ xs\isanewline
-No\ subgoals{\isacharbang}%
+xs\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ xs\isanewline
+No\ subgoals{\isaliteral{21}{\isacharbang}}%
\end{isabelle}
We still need to confirm that the proof is now finished:%
\end{isamarkuptxt}%
@@ -373,16 +373,16 @@
% Instead of \isacommand{apply} followed by a dot, you can simply write
% \isacommand{by}\indexbold{by}, which we do most of the time.
-Notice that in lemma \isa{app{\isacharunderscore}Nil{\isadigit{2}}},
+Notice that in lemma \isa{app{\isaliteral{5F}{\isacharunderscore}}Nil{\isadigit{2}}},
as printed out after the final \isacommand{done}, the free variable \isa{xs} has been
-replaced by the unknown \isa{{\isacharquery}xs}, just as explained in
+replaced by the unknown \isa{{\isaliteral{3F}{\isacharquery}}xs}, just as explained in
\S\ref{sec:variables}.
Going back to the proof of the first lemma%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ rev{\isacharunderscore}app\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}rev{\isacharparenleft}xs\ {\isacharat}\ ys{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}rev\ ys{\isacharparenright}\ {\isacharat}\ {\isacharparenleft}rev\ xs{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ rev{\isaliteral{5F}{\isacharunderscore}}app\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}rev{\isaliteral{28}{\isacharparenleft}}xs\ {\isaliteral{40}{\isacharat}}\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}rev\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -390,25 +390,25 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ xs{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}auto{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
we find that this time \isa{auto} solves the base case, but the
induction step merely simplifies to
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}a\ list{\isachardot}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }rev\ {\isacharparenleft}list\ {\isacharat}\ ys{\isacharparenright}\ {\isacharequal}\ rev\ ys\ {\isacharat}\ rev\ list\ {\isasymLongrightarrow}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isacharparenleft}rev\ ys\ {\isacharat}\ rev\ list{\isacharparenright}\ {\isacharat}\ a\ {\isacharhash}\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ rev\ ys\ {\isacharat}\ rev\ list\ {\isacharat}\ a\ {\isacharhash}\ {\isacharbrackleft}{\isacharbrackright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a\ list{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }rev\ {\isaliteral{28}{\isacharparenleft}}list\ {\isaliteral{40}{\isacharat}}\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rev\ ys\ {\isaliteral{40}{\isacharat}}\ rev\ list\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{28}{\isacharparenleft}}rev\ ys\ {\isaliteral{40}{\isacharat}}\ rev\ list{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{40}{\isacharat}}\ a\ {\isaliteral{23}{\isacharhash}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ rev\ ys\ {\isaliteral{40}{\isacharat}}\ rev\ list\ {\isaliteral{40}{\isacharat}}\ a\ {\isaliteral{23}{\isacharhash}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}%
\end{isabelle}
-Now we need to remember that \isa{{\isacharat}} associates to the right, and that
-\isa{{\isacharhash}} and \isa{{\isacharat}} have the same priority (namely the \isa{{\isadigit{6}}{\isadigit{5}}}
+Now we need to remember that \isa{{\isaliteral{40}{\isacharat}}} associates to the right, and that
+\isa{{\isaliteral{23}{\isacharhash}}} and \isa{{\isaliteral{40}{\isacharat}}} have the same priority (namely the \isa{{\isadigit{6}}{\isadigit{5}}}
in their \isacommand{infixr} annotation). Thus the conclusion really is
\begin{isabelle}
~~~~~(rev~ys~@~rev~list)~@~(a~\#~[])~=~rev~ys~@~(rev~list~@~(a~\#~[]))
\end{isabelle}
-and the missing lemma is associativity of \isa{{\isacharat}}.%
+and the missing lemma is associativity of \isa{{\isaliteral{40}{\isacharat}}}.%
\end{isamarkuptxt}%
\isamarkuptrue%
%
@@ -429,7 +429,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ app{\isacharunderscore}assoc\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}xs\ {\isacharat}\ ys{\isacharparenright}\ {\isacharat}\ zs\ {\isacharequal}\ xs\ {\isacharat}\ {\isacharparenleft}ys\ {\isacharat}\ zs{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ app{\isaliteral{5F}{\isacharunderscore}}assoc\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}xs\ {\isaliteral{40}{\isacharat}}\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{40}{\isacharat}}\ zs\ {\isaliteral{3D}{\isacharequal}}\ xs\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{28}{\isacharparenleft}}ys\ {\isaliteral{40}{\isacharat}}\ zs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -437,9 +437,9 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ xs{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}auto{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -455,7 +455,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ rev{\isacharunderscore}app\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}rev{\isacharparenleft}xs\ {\isacharat}\ ys{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}rev\ ys{\isacharparenright}\ {\isacharat}\ {\isacharparenleft}rev\ xs{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ rev{\isaliteral{5F}{\isacharunderscore}}app\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}rev{\isaliteral{28}{\isacharparenleft}}xs\ {\isaliteral{40}{\isacharat}}\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}rev\ ys{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{40}{\isacharat}}\ {\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -463,9 +463,9 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ xs{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}auto{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -481,7 +481,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ rev{\isacharunderscore}rev\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}rev{\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharequal}\ xs{\isachardoublequoteclose}\isanewline
+\ rev{\isaliteral{5F}{\isacharunderscore}}rev\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}rev{\isaliteral{28}{\isacharparenleft}}rev\ xs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ xs{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -489,9 +489,9 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ xs{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}auto{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
--- a/doc-src/TutorialI/Trie/document/Trie.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Trie/document/Trie.tex Mon Nov 08 14:41:11 2010 +0100
@@ -19,12 +19,12 @@
To minimize running time, each node of a trie should contain an array that maps
letters to subtries. We have chosen a
representation where the subtries are held in an association list, i.e.\ a
-list of (letter,trie) pairs. Abstracting over the alphabet \isa{{\isacharprime}a} and the
-values \isa{{\isacharprime}v} we define a trie as follows:%
+list of (letter,trie) pairs. Abstracting over the alphabet \isa{{\isaliteral{27}{\isacharprime}}a} and the
+values \isa{{\isaliteral{27}{\isacharprime}}v} we define a trie as follows:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}trie\ {\isacharequal}\ Trie\ \ {\isachardoublequoteopen}{\isacharprime}v\ option{\isachardoublequoteclose}\ \ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a\ {\isacharasterisk}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}trie{\isacharparenright}list{\isachardoublequoteclose}%
+\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}trie\ {\isaliteral{3D}{\isacharequal}}\ Trie\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}v\ option{\isaliteral{22}{\isachardoublequoteclose}}\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}trie{\isaliteral{29}{\isacharparenright}}list{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
\index{datatypes!and nested recursion}%
@@ -35,11 +35,11 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ {\isachardoublequoteopen}value{\isachardoublequoteclose}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}trie\ {\isasymRightarrow}\ {\isacharprime}v\ option{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}value{\isacharparenleft}Trie\ ov\ al{\isacharparenright}\ {\isacharequal}\ ov{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}value{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}trie\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}v\ option{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}value{\isaliteral{28}{\isacharparenleft}}Trie\ ov\ al{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ ov{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isacommand{primrec}\isamarkupfalse%
-\ alist\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}trie\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isacharasterisk}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}trie{\isacharparenright}list{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}alist{\isacharparenleft}Trie\ ov\ al{\isacharparenright}\ {\isacharequal}\ al{\isachardoublequoteclose}%
+\ alist\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}trie\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}trie{\isaliteral{29}{\isacharparenright}}list{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}alist{\isaliteral{28}{\isacharparenleft}}Trie\ ov\ al{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ al{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
Association lists come with a generic lookup function. Its result
@@ -47,10 +47,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ assoc\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}key\ {\isacharasterisk}\ {\isacharprime}val{\isacharparenright}list\ {\isasymRightarrow}\ {\isacharprime}key\ {\isasymRightarrow}\ {\isacharprime}val\ option{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}assoc\ {\isacharbrackleft}{\isacharbrackright}\ x\ {\isacharequal}\ None{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}assoc\ {\isacharparenleft}p{\isacharhash}ps{\isacharparenright}\ x\ {\isacharequal}\isanewline
-\ \ \ {\isacharparenleft}let\ {\isacharparenleft}a{\isacharcomma}b{\isacharparenright}\ {\isacharequal}\ p\ in\ if\ a{\isacharequal}x\ then\ Some\ b\ else\ assoc\ ps\ x{\isacharparenright}{\isachardoublequoteclose}%
+\ assoc\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}key\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{27}{\isacharprime}}val{\isaliteral{29}{\isacharparenright}}list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}key\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}val\ option{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}assoc\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ x\ {\isaliteral{3D}{\isacharequal}}\ None{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}assoc\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{23}{\isacharhash}}ps{\isaliteral{29}{\isacharparenright}}\ x\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ {\isaliteral{28}{\isacharparenleft}}let\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ p\ in\ if\ a{\isaliteral{3D}{\isacharequal}}x\ then\ Some\ b\ else\ assoc\ ps\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
Now we can define the lookup function for tries. It descends into the trie
examining the letters of the search string one by one. As
@@ -59,19 +59,19 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ lookup\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}trie\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}v\ option{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}lookup\ t\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ value\ t{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}lookup\ t\ {\isacharparenleft}a{\isacharhash}as{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}case\ assoc\ {\isacharparenleft}alist\ t{\isacharparenright}\ a\ of\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ None\ {\isasymRightarrow}\ None\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharbar}\ Some\ at\ {\isasymRightarrow}\ lookup\ at\ as{\isacharparenright}{\isachardoublequoteclose}%
+\ lookup\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}trie\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}v\ option{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}lookup\ t\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\ value\ t{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}lookup\ t\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{23}{\isacharhash}}as{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}case\ assoc\ {\isaliteral{28}{\isacharparenleft}}alist\ t{\isaliteral{29}{\isacharparenright}}\ a\ of\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ None\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ None\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{7C}{\isacharbar}}\ Some\ at\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ lookup\ at\ as{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
As a first simple property we prove that looking up a string in the empty
-trie \isa{Trie\ None\ {\isacharbrackleft}{\isacharbrackright}} always returns \isa{None}. The proof merely
+trie \isa{Trie\ None\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}} always returns \isa{None}. The proof merely
distinguishes the two cases whether the search string is empty or not:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}lookup\ {\isacharparenleft}Trie\ None\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}\ as\ {\isacharequal}\ None{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}lookup\ {\isaliteral{28}{\isacharparenleft}}Trie\ None\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ as\ {\isaliteral{3D}{\isacharequal}}\ None{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -79,7 +79,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}case{\isacharunderscore}tac\ as{\isacharcomma}\ simp{\isacharunderscore}all{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}case{\isaliteral{5F}{\isacharunderscore}}tac\ as{\isaliteral{2C}{\isacharcomma}}\ simp{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -96,12 +96,12 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ update{\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}trie\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}v\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}{\isacharprime}v{\isacharparenright}trie{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}update\ t\ {\isacharbrackleft}{\isacharbrackright}\ \ \ \ \ v\ {\isacharequal}\ Trie\ {\isacharparenleft}Some\ v{\isacharparenright}\ {\isacharparenleft}alist\ t{\isacharparenright}{\isachardoublequoteclose}\ {\isacharbar}\isanewline
-{\isachardoublequoteopen}update\ t\ {\isacharparenleft}a{\isacharhash}as{\isacharparenright}\ v\ {\isacharequal}\isanewline
-\ \ \ {\isacharparenleft}let\ tt\ {\isacharequal}\ {\isacharparenleft}case\ assoc\ {\isacharparenleft}alist\ t{\isacharparenright}\ a\ of\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ None\ {\isasymRightarrow}\ Trie\ None\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharbar}\ Some\ at\ {\isasymRightarrow}\ at{\isacharparenright}\isanewline
-\ \ \ \ in\ Trie\ {\isacharparenleft}value\ t{\isacharparenright}\ {\isacharparenleft}{\isacharparenleft}a{\isacharcomma}update\ tt\ as\ v{\isacharparenright}\ {\isacharhash}\ alist\ t{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
+\ update{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}trie\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ list\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}v\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}{\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}trie{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}update\ t\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ \ \ \ \ v\ {\isaliteral{3D}{\isacharequal}}\ Trie\ {\isaliteral{28}{\isacharparenleft}}Some\ v{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}alist\ t{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{7C}{\isacharbar}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}update\ t\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{23}{\isacharhash}}as{\isaliteral{29}{\isacharparenright}}\ v\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ {\isaliteral{28}{\isacharparenleft}}let\ tt\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}case\ assoc\ {\isaliteral{28}{\isacharparenleft}}alist\ t{\isaliteral{29}{\isacharparenright}}\ a\ of\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ None\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ Trie\ None\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{7C}{\isacharbar}}\ Some\ at\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ at{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \ \ in\ Trie\ {\isaliteral{28}{\isacharparenleft}}value\ t{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}update\ tt\ as\ v{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{23}{\isacharhash}}\ alist\ t{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
The base case is obvious. In the recursive case the subtrie
@@ -117,7 +117,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{declare}\isamarkupfalse%
-\ Let{\isacharunderscore}def{\isacharbrackleft}simp{\isacharbrackright}\ option{\isachardot}split{\isacharbrackleft}split{\isacharbrackright}%
+\ Let{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{5B}{\isacharbrackleft}}simp{\isaliteral{5D}{\isacharbrackright}}\ option{\isaliteral{2E}{\isachardot}}split{\isaliteral{5B}{\isacharbrackleft}}split{\isaliteral{5D}{\isacharbrackright}}%
\begin{isamarkuptext}%
\noindent
The reason becomes clear when looking (probably after a failed proof
@@ -129,8 +129,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{theorem}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymforall}t\ v\ bs{\isachardot}\ lookup\ {\isacharparenleft}update\ t\ as\ v{\isacharparenright}\ bs\ {\isacharequal}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharparenleft}if\ as{\isacharequal}bs\ then\ Some\ v\ else\ lookup\ t\ bs{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}t\ v\ bs{\isaliteral{2E}{\isachardot}}\ lookup\ {\isaliteral{28}{\isacharparenleft}}update\ t\ as\ v{\isaliteral{29}{\isacharparenright}}\ bs\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}if\ as{\isaliteral{3D}{\isacharequal}}bs\ then\ Some\ v\ else\ lookup\ t\ bs{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -149,7 +149,7 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ as{\isacharcomma}\ auto{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ as{\isaliteral{2C}{\isacharcomma}}\ auto{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
Unfortunately, this time we are left with three intimidating looking subgoals:
@@ -164,7 +164,7 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}case{\isacharunderscore}tac{\isacharbrackleft}{\isacharbang}{\isacharbrackright}\ bs{\isacharcomma}\ auto{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}case{\isaliteral{5F}{\isacharunderscore}}tac{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}\ bs{\isaliteral{2C}{\isacharcomma}}\ auto{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -178,14 +178,14 @@
\noindent
\index{subgoal numbering}%
All methods ending in \isa{tac} take an optional first argument that
-specifies the range of subgoals they are applied to, where \isa{{\isacharbrackleft}{\isacharbang}{\isacharbrackright}} means
-all subgoals, i.e.\ \isa{{\isacharbrackleft}{\isadigit{1}}{\isacharminus}{\isadigit{3}}{\isacharbrackright}} in our case. Individual subgoal numbers,
-e.g. \isa{{\isacharbrackleft}{\isadigit{2}}{\isacharbrackright}} are also allowed.
+specifies the range of subgoals they are applied to, where \isa{{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{21}{\isacharbang}}{\isaliteral{5D}{\isacharbrackright}}} means
+all subgoals, i.e.\ \isa{{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{2D}{\isacharminus}}{\isadigit{3}}{\isaliteral{5D}{\isacharbrackright}}} in our case. Individual subgoal numbers,
+e.g. \isa{{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{2}}{\isaliteral{5D}{\isacharbrackright}}} are also allowed.
This proof may look surprisingly straightforward. However, note that this
comes at a cost: the proof script is unreadable because the intermediate
proof states are invisible, and we rely on the (possibly brittle) magic of
-\isa{auto} (\isa{simp{\isacharunderscore}all} will not do --- try it) to split the subgoals
+\isa{auto} (\isa{simp{\isaliteral{5F}{\isacharunderscore}}all} will not do --- try it) to split the subgoals
of the induction up in such a way that case distinction on \isa{bs} makes
sense and solves the proof.
@@ -207,8 +207,8 @@
\begin{exercise}
Conceptually, each node contains a mapping from letters to optional
subtries. Above we have implemented this by means of an association
- list. Replay the development replacing \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isacharprime}v{\isacharparenright}\ trie{\isacharparenright}\ list}
- with \isa{{\isacharprime}a\ {\isasymrightharpoonup}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isacharprime}v{\isacharparenright}\ trie}.
+ list. Replay the development replacing \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}\ trie{\isaliteral{29}{\isacharparenright}}\ list}
+ with \isa{{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{27}{\isacharprime}}v{\isaliteral{29}{\isacharparenright}}\ trie\ option}.
\end{exercise}%
\end{isamarkuptext}%
\isamarkuptrue%
--- a/doc-src/TutorialI/Types/document/Axioms.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Types/document/Axioms.tex Mon Nov 08 14:41:11 2010 +0100
@@ -40,20 +40,20 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{class}\isamarkupfalse%
-\ semigroup\ {\isacharequal}\ plus\ {\isacharplus}\isanewline
-\ \ \isakeyword{assumes}\ assoc{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}x\ {\isasymoplus}\ y{\isacharparenright}\ {\isasymoplus}\ z\ {\isacharequal}\ x\ {\isasymoplus}\ {\isacharparenleft}y\ {\isasymoplus}\ z{\isacharparenright}{\isachardoublequoteclose}%
+\ semigroup\ {\isaliteral{3D}{\isacharequal}}\ plus\ {\isaliteral{2B}{\isacharplus}}\isanewline
+\ \ \isakeyword{assumes}\ assoc{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ z\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent This \hyperlink{command.class}{\mbox{\isa{\isacommand{class}}}} specification requires that
-all instances of \isa{semigroup} obey \hyperlink{fact.assoc:}{\mbox{\isa{assoc{\isacharcolon}}}}~\isa{{\isachardoublequote}{\isasymAnd}x\ y\ z\ {\isasymColon}\ {\isacharprime}a{\isasymColon}semigroup{\isachardot}\ {\isacharparenleft}x\ {\isasymoplus}\ y{\isacharparenright}\ {\isasymoplus}\ z\ {\isacharequal}\ x\ {\isasymoplus}\ {\isacharparenleft}y\ {\isasymoplus}\ z{\isacharparenright}{\isachardoublequote}}.
+all instances of \isa{semigroup} obey \hyperlink{fact.assoc:}{\mbox{\isa{assoc{\isaliteral{3A}{\isacharcolon}}}}}~\isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C416E643E}{\isasymAnd}}x\ y\ z\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}semigroup{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ z\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}.
We can use this class axiom to derive further abstract theorems
relative to class \isa{semigroup}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ assoc{\isacharunderscore}left{\isacharcolon}\isanewline
-\ \ \isakeyword{fixes}\ x\ y\ z\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a{\isasymColon}semigroup{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{shows}\ {\isachardoublequoteopen}x\ {\isasymoplus}\ {\isacharparenleft}y\ {\isasymoplus}\ z{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}x\ {\isasymoplus}\ y{\isacharparenright}\ {\isasymoplus}\ z{\isachardoublequoteclose}\isanewline
+\ assoc{\isaliteral{5F}{\isacharunderscore}}left{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \isakeyword{fixes}\ x\ y\ z\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}semigroup{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -62,7 +62,7 @@
\isatagproof
\isacommand{using}\isamarkupfalse%
\ assoc\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}rule\ sym{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ sym{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -71,7 +71,7 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-\noindent The \isa{semigroup} constraint on type \isa{{\isacharprime}a} restricts instantiations of \isa{{\isacharprime}a} to types of class
+\noindent The \isa{semigroup} constraint on type \isa{{\isaliteral{27}{\isacharprime}}a} restricts instantiations of \isa{{\isaliteral{27}{\isacharprime}}a} to types of class
\isa{semigroup} and during the proof enables us to use the fact
\hyperlink{fact.assoc}{\mbox{\isa{assoc}}} whose type parameter is itself constrained to class
\isa{semigroup}. The main advantage of classes is that theorems
@@ -82,7 +82,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{instantiation}\isamarkupfalse%
-\ nat\ {\isacharcolon}{\isacharcolon}\ semigroup\isanewline
+\ nat\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ semigroup\isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{instance}\isamarkupfalse%
@@ -96,15 +96,15 @@
%
\begin{isamarkuptxt}%
\noindent The proof opens with a default proof step, which for
-instance judgements invokes method \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isacharunderscore}classes}}}.%
+instance judgements invokes method \hyperlink{method.intro-classes}{\mbox{\isa{intro{\isaliteral{5F}{\isacharunderscore}}classes}}}.%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \ \isacommand{fix}\isamarkupfalse%
-\ m\ n\ q\ {\isacharcolon}{\isacharcolon}\ nat\isanewline
+\ m\ n\ q\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}m\ {\isasymoplus}\ n{\isacharparenright}\ {\isasymoplus}\ q\ {\isacharequal}\ m\ {\isasymoplus}\ {\isacharparenleft}n\ {\isasymoplus}\ q{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}m\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ q\ {\isaliteral{3D}{\isacharequal}}\ m\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ q{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ m{\isacharparenright}\ simp{\isacharunderscore}all\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}induct\ m{\isaliteral{29}{\isacharparenright}}\ simp{\isaliteral{5F}{\isacharunderscore}}all\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
@@ -123,7 +123,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{instantiation}\isamarkupfalse%
-\ prod\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}semigroup{\isacharcomma}\ semigroup{\isacharparenright}\ semigroup\isanewline
+\ prod\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}semigroup{\isaliteral{2C}{\isacharcomma}}\ semigroup{\isaliteral{29}{\isacharparenright}}\ semigroup\isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{instance}\isamarkupfalse%
@@ -136,11 +136,11 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
-\ p\isactrlisub {\isadigit{1}}\ p\isactrlisub {\isadigit{2}}\ p\isactrlisub {\isadigit{3}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a{\isasymColon}semigroup\ {\isasymtimes}\ {\isacharprime}b{\isasymColon}semigroup{\isachardoublequoteclose}\isanewline
+\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{3}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}semigroup\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}semigroup{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}p\isactrlisub {\isadigit{1}}\ {\isasymoplus}\ p\isactrlisub {\isadigit{2}}\ {\isasymoplus}\ p\isactrlisub {\isadigit{3}}\ {\isacharequal}\ p\isactrlisub {\isadigit{1}}\ {\isasymoplus}\ {\isacharparenleft}p\isactrlisub {\isadigit{2}}\ {\isasymoplus}\ p\isactrlisub {\isadigit{3}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{3}}\ {\isaliteral{3D}{\isacharequal}}\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ {\isaliteral{28}{\isacharparenleft}}p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{3}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}cases\ p\isactrlisub {\isadigit{1}}{\isacharcomma}\ cases\ p\isactrlisub {\isadigit{2}}{\isacharcomma}\ cases\ p\isactrlisub {\isadigit{3}}{\isacharparenright}\ {\isacharparenleft}simp\ add{\isacharcolon}\ assoc{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}cases\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ cases\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ cases\ p\isaliteral{5C3C5E697375623E}{}\isactrlisub {\isadigit{3}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ assoc{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent Associativity of product semigroups is established
using the hypothetical associativity \hyperlink{fact.assoc}{\mbox{\isa{assoc}}} of the type
@@ -173,9 +173,9 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{class}\isamarkupfalse%
-\ monoidl\ {\isacharequal}\ semigroup\ {\isacharplus}\isanewline
-\ \ \isakeyword{fixes}\ neutral\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a{\isachardoublequoteclose}\ {\isacharparenleft}{\isachardoublequoteopen}{\isasymzero}{\isachardoublequoteclose}{\isacharparenright}\isanewline
-\ \ \isakeyword{assumes}\ neutl{\isacharcolon}\ {\isachardoublequoteopen}{\isasymzero}\ {\isasymoplus}\ x\ {\isacharequal}\ x{\isachardoublequoteclose}%
+\ monoidl\ {\isaliteral{3D}{\isacharequal}}\ semigroup\ {\isaliteral{2B}{\isacharplus}}\isanewline
+\ \ \isakeyword{fixes}\ neutral\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C7A65726F3E}{\isasymzero}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \isakeyword{assumes}\ neutl{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C7A65726F3E}{\isasymzero}}\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ x\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent Again, we prove some instances, by providing
suitable parameter definitions and proofs for the additional
@@ -183,12 +183,12 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{instantiation}\isamarkupfalse%
-\ nat\ {\isacharcolon}{\isacharcolon}\ monoidl\isanewline
+\ nat\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ monoidl\isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{definition}\isamarkupfalse%
\isanewline
-\ \ neutral{\isacharunderscore}nat{\isacharunderscore}def{\isacharcolon}\ {\isachardoublequoteopen}{\isasymzero}\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}nat{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ neutral{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C7A65726F3E}{\isasymzero}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{instance}\isamarkupfalse%
%
@@ -200,11 +200,11 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
-\ n\ {\isacharcolon}{\isacharcolon}\ nat\isanewline
+\ n\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ nat\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymzero}\ {\isasymoplus}\ n\ {\isacharequal}\ n{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C7A65726F3E}{\isasymzero}}\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ n\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{unfolding}\isamarkupfalse%
-\ neutral{\isacharunderscore}nat{\isacharunderscore}def\ \isacommand{by}\isamarkupfalse%
+\ neutral{\isaliteral{5F}{\isacharunderscore}}nat{\isaliteral{5F}{\isacharunderscore}}def\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -226,12 +226,12 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{instantiation}\isamarkupfalse%
-\ prod\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}monoidl{\isacharcomma}\ monoidl{\isacharparenright}\ monoidl\isanewline
+\ prod\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}monoidl{\isaliteral{2C}{\isacharcomma}}\ monoidl{\isaliteral{29}{\isacharparenright}}\ monoidl\isanewline
\isakeyword{begin}\isanewline
\isanewline
\isacommand{definition}\isamarkupfalse%
\isanewline
-\ \ neutral{\isacharunderscore}prod{\isacharunderscore}def{\isacharcolon}\ {\isachardoublequoteopen}{\isasymzero}\ {\isacharequal}\ {\isacharparenleft}{\isasymzero}{\isacharcomma}\ {\isasymzero}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ \ neutral{\isaliteral{5F}{\isacharunderscore}}prod{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C7A65726F3E}{\isasymzero}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C7A65726F3E}{\isasymzero}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C7A65726F3E}{\isasymzero}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isanewline
\isacommand{instance}\isamarkupfalse%
%
@@ -243,11 +243,11 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{fix}\isamarkupfalse%
-\ p\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a{\isasymColon}monoidl\ {\isasymtimes}\ {\isacharprime}b{\isasymColon}monoidl{\isachardoublequoteclose}\isanewline
+\ p\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}monoidl\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}monoidl{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymzero}\ {\isasymoplus}\ p\ {\isacharequal}\ p{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C7A65726F3E}{\isasymzero}}\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ p\ {\isaliteral{3D}{\isacharequal}}\ p{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}cases\ p{\isacharparenright}\ {\isacharparenleft}simp\ add{\isacharcolon}\ neutral{\isacharunderscore}prod{\isacharunderscore}def\ neutl{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}cases\ p{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ neutral{\isaliteral{5F}{\isacharunderscore}}prod{\isaliteral{5F}{\isacharunderscore}}def\ neutl{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
@@ -267,8 +267,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{class}\isamarkupfalse%
-\ monoid\ {\isacharequal}\ monoidl\ {\isacharplus}\isanewline
-\ \ \isakeyword{assumes}\ neutr{\isacharcolon}\ {\isachardoublequoteopen}x\ {\isasymoplus}\ {\isasymzero}\ {\isacharequal}\ x{\isachardoublequoteclose}%
+\ monoid\ {\isaliteral{3D}{\isacharequal}}\ monoidl\ {\isaliteral{2B}{\isacharplus}}\isanewline
+\ \ \isakeyword{assumes}\ neutr{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ {\isaliteral{5C3C7A65726F3E}{\isasymzero}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent Corresponding instances for \isa{nat} and products
are left as an exercise to the reader.%
@@ -284,18 +284,18 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{class}\isamarkupfalse%
-\ group\ {\isacharequal}\ monoidl\ {\isacharplus}\isanewline
-\ \ \isakeyword{fixes}\ inv\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\ {\isacharparenleft}{\isachardoublequoteopen}{\isasymdiv}\ {\isacharunderscore}{\isachardoublequoteclose}\ {\isacharbrackleft}{\isadigit{8}}{\isadigit{1}}{\isacharbrackright}\ {\isadigit{8}}{\isadigit{0}}{\isacharparenright}\isanewline
-\ \ \isakeyword{assumes}\ invl{\isacharcolon}\ {\isachardoublequoteopen}{\isasymdiv}\ x\ {\isasymoplus}\ x\ {\isacharequal}\ {\isasymzero}{\isachardoublequoteclose}%
+\ group\ {\isaliteral{3D}{\isacharequal}}\ monoidl\ {\isaliteral{2B}{\isacharplus}}\isanewline
+\ \ \isakeyword{fixes}\ inv\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6469763E}{\isasymdiv}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{8}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}\ {\isadigit{8}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
+\ \ \isakeyword{assumes}\ invl{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6469763E}{\isasymdiv}}\ x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C7A65726F3E}{\isasymzero}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent We continue with a further example for abstract
proofs relative to type classes:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ left{\isacharunderscore}cancel{\isacharcolon}\isanewline
-\ \ \isakeyword{fixes}\ x\ y\ z\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a{\isasymColon}group{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{shows}\ {\isachardoublequoteopen}x\ {\isasymoplus}\ y\ {\isacharequal}\ x\ {\isasymoplus}\ z\ {\isasymlongleftrightarrow}\ y\ {\isacharequal}\ z{\isachardoublequoteclose}\isanewline
+\ left{\isaliteral{5F}{\isacharunderscore}}cancel{\isaliteral{3A}{\isacharcolon}}\isanewline
+\ \ \isakeyword{fixes}\ x\ y\ z\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}group{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ \isakeyword{shows}\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ y\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ z\ {\isaliteral{5C3C6C6F6E676C65667472696768746172726F773E}{\isasymlongleftrightarrow}}\ y\ {\isaliteral{3D}{\isacharequal}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -305,26 +305,26 @@
\isacommand{proof}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymoplus}\ y\ {\isacharequal}\ x\ {\isasymoplus}\ z{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ y\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdiv}\ x\ {\isasymoplus}\ {\isacharparenleft}x\ {\isasymoplus}\ y{\isacharparenright}\ {\isacharequal}\ {\isasymdiv}\ x\ {\isasymoplus}\ {\isacharparenleft}x\ {\isasymoplus}\ z{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6469763E}{\isasymdiv}}\ x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6469763E}{\isasymdiv}}\ x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}{\isasymdiv}\ x\ {\isasymoplus}\ x{\isacharparenright}\ {\isasymoplus}\ y\ {\isacharequal}\ {\isacharparenleft}{\isasymdiv}\ x\ {\isasymoplus}\ x{\isacharparenright}\ {\isasymoplus}\ z{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ assoc{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6469763E}{\isasymdiv}}\ x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6469763E}{\isasymdiv}}\ x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ assoc{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isacharequal}\ z{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ invl\ neutl{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{3D}{\isacharequal}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ invl\ neutl{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{next}\isamarkupfalse%
\isanewline
\ \ \isacommand{assume}\isamarkupfalse%
-\ {\isachardoublequoteopen}y\ {\isacharequal}\ z{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}y\ {\isaliteral{3D}{\isacharequal}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymoplus}\ y\ {\isacharequal}\ x\ {\isasymoplus}\ z{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ y\ {\isaliteral{3D}{\isacharequal}}\ x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ z{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
\ simp\isanewline
\isacommand{qed}\isamarkupfalse%
%
@@ -342,7 +342,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{instance}\isamarkupfalse%
-\ group\ {\isasymsubseteq}\ monoid\isanewline
+\ group\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ monoid\isanewline
%
\isadelimproof
%
@@ -355,17 +355,17 @@
\ x\isanewline
\ \ \isacommand{from}\isamarkupfalse%
\ invl\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdiv}\ x\ {\isasymoplus}\ x\ {\isacharequal}\ {\isasymzero}{\isachardoublequoteclose}\ \isacommand{{\isachardot}}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6469763E}{\isasymdiv}}\ x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C7A65726F3E}{\isasymzero}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{have}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymdiv}\ x\ {\isasymoplus}\ {\isacharparenleft}x\ {\isasymoplus}\ {\isasymzero}{\isacharparenright}\ {\isacharequal}\ {\isasymdiv}\ x\ {\isasymoplus}\ x{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6469763E}{\isasymdiv}}\ x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ {\isaliteral{5C3C7A65726F3E}{\isasymzero}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6469763E}{\isasymdiv}}\ x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ neutl\ invl\ assoc\ {\isacharbrackleft}symmetric{\isacharbrackright}{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ neutl\ invl\ assoc\ {\isaliteral{5B}{\isacharbrackleft}}symmetric{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{then}\isamarkupfalse%
\ \isacommand{show}\isamarkupfalse%
-\ {\isachardoublequoteopen}x\ {\isasymoplus}\ {\isasymzero}\ {\isacharequal}\ x{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ left{\isacharunderscore}cancel{\isacharparenright}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ {\isaliteral{5C3C7A65726F3E}{\isasymzero}}\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\ \isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ left{\isaliteral{5F}{\isacharunderscore}}cancel{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
@@ -406,7 +406,7 @@
\end{picture}
\caption{Subclass relationship of monoids and groups:
before and after establishing the relationship
- \isa{group\ {\isasymsubseteq}\ monoid}; transitive edges are left out.}
+ \isa{group\ {\isaliteral{5C3C73756273657465713E}{\isasymsubseteq}}\ monoid}; transitive edges are left out.}
\label{fig:subclass}
\end{center}
\end{figure}%
@@ -447,7 +447,7 @@
\begin{isamarkuptext}%
In our algebra example, we have started with a \emph{syntactic
class} \isa{plus} which only specifies operations but no axioms; it
-would have been also possible to start immediately with class \isa{semigroup}, specifying the \isa{{\isasymoplus}} operation and associativity at
+would have been also possible to start immediately with class \isa{semigroup}, specifying the \isa{{\isaliteral{5C3C6F706C75733E}{\isasymoplus}}} operation and associativity at
the same time.
Which approach is more appropriate depends. Usually it is more
@@ -463,8 +463,8 @@
\emph{with} axioms.
Further note that classes may contain axioms but \emph{no} operations.
-An example is class \isa{finite} from theory \hyperlink{theory.Finite-Set}{\mbox{\isa{Finite{\isacharunderscore}Set}}}
-which specifies a type to be finite: \isa{{\isachardoublequote}finite\ {\isacharparenleft}UNIV\ {\isasymColon}\ {\isacharprime}a{\isasymColon}finite\ set{\isacharparenright}{\isachardoublequote}}.%
+An example is class \isa{finite} from theory \hyperlink{theory.Finite-Set}{\mbox{\isa{Finite{\isaliteral{5F}{\isacharunderscore}}Set}}}
+which specifies a type to be finite: \isa{{\isaliteral{22}{\isachardoublequote}}finite\ {\isaliteral{28}{\isacharparenleft}}UNIV\ {\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}finite\ set{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
--- a/doc-src/TutorialI/Types/document/Numbers.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Types/document/Numbers.tex Mon Nov 08 14:41:11 2010 +0100
@@ -9,7 +9,7 @@
\isatagtheory
\isacommand{theory}\isamarkupfalse%
\ Numbers\isanewline
-\isakeyword{imports}\ Complex{\isacharunderscore}Main\isanewline
+\isakeyword{imports}\ Complex{\isaliteral{5F}{\isacharunderscore}}Main\isanewline
\isakeyword{begin}%
\endisatagtheory
{\isafoldtheory}%
@@ -26,7 +26,7 @@
%
\isatagML
\isacommand{ML}\isamarkupfalse%
-\ {\isachardoublequoteopen}Pretty{\isachardot}margin{\isacharunderscore}default\ {\isacharcolon}{\isacharequal}\ {\isadigit{6}}{\isadigit{4}}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}Pretty{\isaliteral{2E}{\isachardot}}margin{\isaliteral{5F}{\isacharunderscore}}default\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ {\isadigit{6}}{\isadigit{4}}{\isaliteral{22}{\isachardoublequoteclose}}%
\endisatagML
{\isafoldML}%
%
@@ -35,13 +35,13 @@
%
\endisadelimML
\isacommand{declare}\isamarkupfalse%
-\ {\isacharbrackleft}{\isacharbrackleft}thy{\isacharunderscore}output{\isacharunderscore}indent\ {\isacharequal}\ {\isadigit{0}}{\isacharbrackright}{\isacharbrackright}%
+\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5B}{\isacharbrackleft}}thy{\isaliteral{5F}{\isacharunderscore}}output{\isaliteral{5F}{\isacharunderscore}}indent\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5D}{\isacharbrackright}}%
\begin{isamarkuptext}%
numeric literals; default simprules; can re-orient%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isadigit{2}}\ {\isacharasterisk}\ m\ {\isacharequal}\ m\ {\isacharplus}\ m{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ m\ {\isaliteral{3D}{\isacharequal}}\ m\ {\isaliteral{2B}{\isacharplus}}\ m{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -50,7 +50,7 @@
%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isacharparenleft}{\isadigit{2}}{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isacharasterisk}\ m\ {\isacharequal}\ m\ {\isacharplus}\ m%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ m\ {\isaliteral{3D}{\isacharequal}}\ m\ {\isaliteral{2B}{\isacharplus}}\ m%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
@@ -65,49 +65,49 @@
\isanewline
\isanewline
\isacommand{consts}\isamarkupfalse%
-\ h\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\isanewline
+\ h\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isacommand{recdef}\isamarkupfalse%
-\ h\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceright}{\isachardoublequoteclose}\isanewline
-{\isachardoublequoteopen}h\ i\ {\isacharequal}\ {\isacharparenleft}if\ i\ {\isacharequal}\ {\isadigit{3}}\ then\ {\isadigit{2}}\ else\ i{\isacharparenright}{\isachardoublequoteclose}%
+\ h\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}h\ i\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ i\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{3}}\ then\ {\isadigit{2}}\ else\ i{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
-\isa{h\ {\isadigit{3}}\ {\isacharequal}\ {\isadigit{2}}}
-\isa{h\ i\ {\isacharequal}\ i}%
+\isa{h\ {\isadigit{3}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{2}}}
+\isa{h\ i\ {\isaliteral{3D}{\isacharequal}}\ i}%
\end{isamarkuptext}%
\isamarkuptrue%
%
\begin{isamarkuptext}%
\begin{isabelle}%
-Numeral{\isadigit{0}}\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}%
+Numeral{\isadigit{0}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\rulename{numeral_0_eq_0}
\begin{isabelle}%
-Numeral{\isadigit{1}}\ {\isacharequal}\ {\isacharparenleft}{\isadigit{1}}{\isasymColon}{\isacharprime}a{\isacharparenright}%
+Numeral{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\rulename{numeral_1_eq_1}
\begin{isabelle}%
-{\isadigit{2}}\ {\isacharplus}\ n\ {\isacharequal}\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}%
+{\isadigit{2}}\ {\isaliteral{2B}{\isacharplus}}\ n\ {\isaliteral{3D}{\isacharequal}}\ Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\rulename{add_2_eq_Suc}
\begin{isabelle}%
-n\ {\isacharplus}\ {\isadigit{2}}\ {\isacharequal}\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}%
+n\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ Suc\ {\isaliteral{28}{\isacharparenleft}}Suc\ n{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\rulename{add_2_eq_Suc'}
\begin{isabelle}%
-a\ {\isacharplus}\ b\ {\isacharplus}\ c\ {\isacharequal}\ a\ {\isacharplus}\ {\isacharparenleft}b\ {\isacharplus}\ c{\isacharparenright}%
+a\ {\isaliteral{2B}{\isacharplus}}\ b\ {\isaliteral{2B}{\isacharplus}}\ c\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}b\ {\isaliteral{2B}{\isacharplus}}\ c{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\rulename{add_assoc}
\begin{isabelle}%
-a\ {\isacharplus}\ b\ {\isacharequal}\ b\ {\isacharplus}\ a%
+a\ {\isaliteral{2B}{\isacharplus}}\ b\ {\isaliteral{3D}{\isacharequal}}\ b\ {\isaliteral{2B}{\isacharplus}}\ a%
\end{isabelle}
\rulename{add_commute}
\begin{isabelle}%
-b\ {\isacharplus}\ {\isacharparenleft}a\ {\isacharplus}\ c{\isacharparenright}\ {\isacharequal}\ a\ {\isacharplus}\ {\isacharparenleft}b\ {\isacharplus}\ c{\isacharparenright}%
+b\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2B}{\isacharplus}}\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}b\ {\isaliteral{2B}{\isacharplus}}\ c{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\rulename{add_left_commute}
@@ -115,7 +115,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}Suc{\isacharparenleft}i\ {\isacharplus}\ j{\isacharasterisk}l{\isacharasterisk}k\ {\isacharplus}\ m{\isacharasterisk}n{\isacharparenright}\ {\isacharequal}\ f\ {\isacharparenleft}n{\isacharasterisk}m\ {\isacharplus}\ i\ {\isacharplus}\ k{\isacharasterisk}j{\isacharasterisk}l{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}Suc{\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{2B}{\isacharplus}}\ j{\isaliteral{2A}{\isacharasterisk}}l{\isaliteral{2A}{\isacharasterisk}}k\ {\isaliteral{2B}{\isacharplus}}\ m{\isaliteral{2A}{\isacharasterisk}}n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ f\ {\isaliteral{28}{\isacharparenleft}}n{\isaliteral{2A}{\isacharasterisk}}m\ {\isaliteral{2B}{\isacharplus}}\ i\ {\isaliteral{2B}{\isacharplus}}\ k{\isaliteral{2A}{\isacharasterisk}}j{\isaliteral{2A}{\isacharasterisk}}l{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -124,16 +124,16 @@
%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ Suc\ {\isacharparenleft}i\ {\isacharplus}\ j\ {\isacharasterisk}\ l\ {\isacharasterisk}\ k\ {\isacharplus}\ m\ {\isacharasterisk}\ n{\isacharparenright}\ {\isacharequal}\ f\ {\isacharparenleft}n\ {\isacharasterisk}\ m\ {\isacharplus}\ i\ {\isacharplus}\ k\ {\isacharasterisk}\ j\ {\isacharasterisk}\ l{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ Suc\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{2B}{\isacharplus}}\ j\ {\isaliteral{2A}{\isacharasterisk}}\ l\ {\isaliteral{2A}{\isacharasterisk}}\ k\ {\isaliteral{2B}{\isacharplus}}\ m\ {\isaliteral{2A}{\isacharasterisk}}\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ f\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2A}{\isacharasterisk}}\ m\ {\isaliteral{2B}{\isacharplus}}\ i\ {\isaliteral{2B}{\isacharplus}}\ k\ {\isaliteral{2A}{\isacharasterisk}}\ j\ {\isaliteral{2A}{\isacharasterisk}}\ l{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ add{\isacharunderscore}ac\ mult{\isacharunderscore}ac{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ add{\isaliteral{5F}{\isacharunderscore}}ac\ mult{\isaliteral{5F}{\isacharunderscore}}ac{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ Suc\ {\isacharparenleft}i\ {\isacharplus}\ {\isacharparenleft}m\ {\isacharasterisk}\ n\ {\isacharplus}\ j\ {\isacharasterisk}\ {\isacharparenleft}k\ {\isacharasterisk}\ l{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharequal}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ }f\ {\isacharparenleft}i\ {\isacharplus}\ {\isacharparenleft}m\ {\isacharasterisk}\ n\ {\isacharplus}\ j\ {\isacharasterisk}\ {\isacharparenleft}k\ {\isacharasterisk}\ l{\isacharparenright}{\isacharparenright}{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ Suc\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}m\ {\isaliteral{2A}{\isacharasterisk}}\ n\ {\isaliteral{2B}{\isacharplus}}\ j\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}k\ {\isaliteral{2A}{\isacharasterisk}}\ l{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ }f\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}m\ {\isaliteral{2A}{\isacharasterisk}}\ n\ {\isaliteral{2B}{\isacharplus}}\ j\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}k\ {\isaliteral{2A}{\isacharasterisk}}\ l{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
@@ -148,28 +148,28 @@
%
\begin{isamarkuptext}%
\begin{isabelle}%
-m\ {\isasymle}\ n\ {\isasymLongrightarrow}\ m\ div\ k\ {\isasymle}\ n\ div\ k%
+m\ {\isaliteral{5C3C6C653E}{\isasymle}}\ n\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ m\ div\ k\ {\isaliteral{5C3C6C653E}{\isasymle}}\ n\ div\ k%
\end{isabelle}
\rulename{div_le_mono}
\begin{isabelle}%
-{\isacharparenleft}m\ {\isacharminus}\ n{\isacharparenright}\ {\isacharasterisk}\ k\ {\isacharequal}\ m\ {\isacharasterisk}\ k\ {\isacharminus}\ n\ {\isacharasterisk}\ k%
+{\isaliteral{28}{\isacharparenleft}}m\ {\isaliteral{2D}{\isacharminus}}\ n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ k\ {\isaliteral{3D}{\isacharequal}}\ m\ {\isaliteral{2A}{\isacharasterisk}}\ k\ {\isaliteral{2D}{\isacharminus}}\ n\ {\isaliteral{2A}{\isacharasterisk}}\ k%
\end{isabelle}
\rulename{diff_mult_distrib}
\begin{isabelle}%
-m\ mod\ n\ {\isacharasterisk}\ k\ {\isacharequal}\ m\ {\isacharasterisk}\ k\ mod\ {\isacharparenleft}n\ {\isacharasterisk}\ k{\isacharparenright}%
+m\ mod\ n\ {\isaliteral{2A}{\isacharasterisk}}\ k\ {\isaliteral{3D}{\isacharequal}}\ m\ {\isaliteral{2A}{\isacharasterisk}}\ k\ mod\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2A}{\isacharasterisk}}\ k{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\rulename{mod_mult_distrib}
\begin{isabelle}%
-P\ {\isacharparenleft}a\ {\isacharminus}\ b{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isacharparenleft}a\ {\isacharless}\ b\ {\isasymlongrightarrow}\ P\ {\isadigit{0}}{\isacharparenright}\ {\isasymand}\ {\isacharparenleft}{\isasymforall}d{\isachardot}\ a\ {\isacharequal}\ b\ {\isacharplus}\ d\ {\isasymlongrightarrow}\ P\ d{\isacharparenright}{\isacharparenright}%
+P\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2D}{\isacharminus}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{3C}{\isacharless}}\ b\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ P\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}d{\isaliteral{2E}{\isachardot}}\ a\ {\isaliteral{3D}{\isacharequal}}\ b\ {\isaliteral{2B}{\isacharplus}}\ d\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ P\ d{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\rulename{nat_diff_split}%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}n\ {\isacharminus}\ {\isadigit{1}}{\isacharparenright}\ {\isacharasterisk}\ {\isacharparenleft}n\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}\ {\isacharequal}\ n\ {\isacharasterisk}\ n\ {\isacharminus}\ {\isacharparenleft}{\isadigit{1}}{\isacharcolon}{\isacharcolon}nat{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ n\ {\isaliteral{2A}{\isacharasterisk}}\ n\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -177,15 +177,15 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}clarsimp\ split{\isacharcolon}\ nat{\isacharunderscore}diff{\isacharunderscore}split\ iff\ del{\isacharcolon}\ less{\isacharunderscore}Suc{\isadigit{0}}{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}clarsimp\ split{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{5F}{\isacharunderscore}}diff{\isaliteral{5F}{\isacharunderscore}}split\ iff\ del{\isaliteral{3A}{\isacharcolon}}\ less{\isaliteral{5F}{\isacharunderscore}}Suc{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}\isanewline
\ %
\isamarkupcmt{\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}d{\isachardot}\ {\isasymlbrakk}n\ {\isacharless}\ Suc\ {\isadigit{0}}{\isacharsemicolon}\ n\ {\isacharasterisk}\ n\ {\isacharequal}\ Suc\ d{\isasymrbrakk}\ {\isasymLongrightarrow}\ d\ {\isacharequal}\ {\isadigit{0}}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}d{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}n\ {\isaliteral{3C}{\isacharless}}\ Suc\ {\isadigit{0}}{\isaliteral{3B}{\isacharsemicolon}}\ n\ {\isaliteral{2A}{\isacharasterisk}}\ n\ {\isaliteral{3D}{\isacharequal}}\ Suc\ d{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ d\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}%
\end{isabelle}%
}
\isanewline
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}subgoal{\isacharunderscore}tac\ {\isachardoublequoteopen}n{\isacharequal}{\isadigit{0}}{\isachardoublequoteclose}{\isacharcomma}\ force{\isacharcomma}\ arith{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}subgoal{\isaliteral{5F}{\isacharunderscore}}tac\ {\isaliteral{22}{\isachardoublequoteopen}}n{\isaliteral{3D}{\isacharequal}}{\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{2C}{\isacharcomma}}\ force{\isaliteral{2C}{\isacharcomma}}\ arith{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -198,7 +198,7 @@
\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}n\ {\isacharminus}\ {\isadigit{2}}{\isacharparenright}\ {\isacharasterisk}\ {\isacharparenleft}n\ {\isacharplus}\ {\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ n\ {\isacharasterisk}\ n\ {\isacharminus}\ {\isacharparenleft}{\isadigit{4}}{\isacharcolon}{\isacharcolon}nat{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ n\ {\isaliteral{2A}{\isacharasterisk}}\ n\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{4}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -206,15 +206,15 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}simp\ split{\isacharcolon}\ nat{\isacharunderscore}diff{\isacharunderscore}split{\isacharcomma}\ clarify{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}simp\ split{\isaliteral{3A}{\isacharcolon}}\ nat{\isaliteral{5F}{\isacharunderscore}}diff{\isaliteral{5F}{\isacharunderscore}}split{\isaliteral{2C}{\isacharcomma}}\ clarify{\isaliteral{29}{\isacharparenright}}\isanewline
\ %
\isamarkupcmt{\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}d{\isachardot}\ {\isasymlbrakk}n\ {\isacharless}\ {\isadigit{2}}{\isacharsemicolon}\ n\ {\isacharasterisk}\ n\ {\isacharequal}\ {\isadigit{4}}\ {\isacharplus}\ d{\isasymrbrakk}\ {\isasymLongrightarrow}\ d\ {\isacharequal}\ {\isadigit{0}}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}d{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}n\ {\isaliteral{3C}{\isacharless}}\ {\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\ n\ {\isaliteral{2A}{\isacharasterisk}}\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{4}}\ {\isaliteral{2B}{\isacharplus}}\ d{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ d\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}%
\end{isabelle}%
}
\isanewline
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}subgoal{\isacharunderscore}tac\ {\isachardoublequoteopen}n{\isacharequal}{\isadigit{0}}\ {\isacharbar}\ n{\isacharequal}{\isadigit{1}}{\isachardoublequoteclose}{\isacharcomma}\ force{\isacharcomma}\ arith{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}subgoal{\isaliteral{5F}{\isacharunderscore}}tac\ {\isaliteral{22}{\isachardoublequoteopen}}n{\isaliteral{3D}{\isacharequal}}{\isadigit{0}}\ {\isaliteral{7C}{\isacharbar}}\ n{\isaliteral{3D}{\isacharequal}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}{\isaliteral{2C}{\isacharcomma}}\ force{\isaliteral{2C}{\isacharcomma}}\ arith{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -226,58 +226,58 @@
%
\begin{isamarkuptext}%
\begin{isabelle}%
-m\ mod\ n\ {\isacharequal}\ {\isacharparenleft}if\ m\ {\isacharless}\ n\ then\ m\ else\ {\isacharparenleft}m\ {\isacharminus}\ n{\isacharparenright}\ mod\ n{\isacharparenright}%
+m\ mod\ n\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}if\ m\ {\isaliteral{3C}{\isacharless}}\ n\ then\ m\ else\ {\isaliteral{28}{\isacharparenleft}}m\ {\isaliteral{2D}{\isacharminus}}\ n{\isaliteral{29}{\isacharparenright}}\ mod\ n{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\rulename{mod_if}
\begin{isabelle}%
-a\ div\ b\ {\isacharasterisk}\ b\ {\isacharplus}\ a\ mod\ b\ {\isacharequal}\ a%
+a\ div\ b\ {\isaliteral{2A}{\isacharasterisk}}\ b\ {\isaliteral{2B}{\isacharplus}}\ a\ mod\ b\ {\isaliteral{3D}{\isacharequal}}\ a%
\end{isabelle}
\rulename{mod_div_equality}
\begin{isabelle}%
-a\ {\isacharasterisk}\ b\ div\ c\ {\isacharequal}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ div\ c{\isacharparenright}\ {\isacharplus}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ mod\ c{\isacharparenright}\ div\ c%
+a\ {\isaliteral{2A}{\isacharasterisk}}\ b\ div\ c\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}b\ div\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ a\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}b\ mod\ c{\isaliteral{29}{\isacharparenright}}\ div\ c%
\end{isabelle}
\rulename{div_mult1_eq}
\begin{isabelle}%
-a\ {\isacharasterisk}\ b\ mod\ c\ {\isacharequal}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ mod\ c{\isacharparenright}\ mod\ c%
+a\ {\isaliteral{2A}{\isacharasterisk}}\ b\ mod\ c\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}b\ mod\ c{\isaliteral{29}{\isacharparenright}}\ mod\ c%
\end{isabelle}
\rulename{mod_mult_right_eq}
\begin{isabelle}%
-a\ div\ {\isacharparenleft}b\ {\isacharasterisk}\ c{\isacharparenright}\ {\isacharequal}\ a\ div\ b\ div\ c%
+a\ div\ {\isaliteral{28}{\isacharparenleft}}b\ {\isaliteral{2A}{\isacharasterisk}}\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ a\ div\ b\ div\ c%
\end{isabelle}
\rulename{div_mult2_eq}
\begin{isabelle}%
-a\ mod\ {\isacharparenleft}b\ {\isacharasterisk}\ c{\isacharparenright}\ {\isacharequal}\ b\ {\isacharasterisk}\ {\isacharparenleft}a\ div\ b\ mod\ c{\isacharparenright}\ {\isacharplus}\ a\ mod\ b%
+a\ mod\ {\isaliteral{28}{\isacharparenleft}}b\ {\isaliteral{2A}{\isacharasterisk}}\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ b\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}a\ div\ b\ mod\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ a\ mod\ b%
\end{isabelle}
\rulename{mod_mult2_eq}
\begin{isabelle}%
-c\ {\isasymnoteq}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isasymLongrightarrow}\ c\ {\isacharasterisk}\ a\ div\ {\isacharparenleft}c\ {\isacharasterisk}\ b{\isacharparenright}\ {\isacharequal}\ a\ div\ b%
+c\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ c\ {\isaliteral{2A}{\isacharasterisk}}\ a\ div\ {\isaliteral{28}{\isacharparenleft}}c\ {\isaliteral{2A}{\isacharasterisk}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ a\ div\ b%
\end{isabelle}
\rulename{div_mult_mult1}
\begin{isabelle}%
-a\ div\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}%
+a\ div\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\rulename{div_by_0}
\begin{isabelle}%
-a\ mod\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isacharequal}\ a%
+a\ mod\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ a%
\end{isabelle}
\rulename{mod_by_0}
\begin{isabelle}%
-{\isasymlbrakk}m\ dvd\ n{\isacharsemicolon}\ n\ dvd\ m{\isasymrbrakk}\ {\isasymLongrightarrow}\ m\ {\isacharequal}\ n%
+{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}m\ dvd\ n{\isaliteral{3B}{\isacharsemicolon}}\ n\ dvd\ m{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ m\ {\isaliteral{3D}{\isacharequal}}\ n%
\end{isabelle}
\rulename{dvd_antisym}
\begin{isabelle}%
-{\isasymlbrakk}a\ dvd\ b{\isacharsemicolon}\ a\ dvd\ c{\isasymrbrakk}\ {\isasymLongrightarrow}\ a\ dvd\ b\ {\isacharplus}\ c%
+{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}a\ dvd\ b{\isaliteral{3B}{\isacharsemicolon}}\ a\ dvd\ c{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a\ dvd\ b\ {\isaliteral{2B}{\isacharplus}}\ c%
\end{isabelle}
\rulename{dvd_add}
@@ -291,58 +291,58 @@
\begin{isabelle}%
-{\isadigit{0}}\ {\isacharless}\ b\ {\isasymLongrightarrow}\ {\isadigit{0}}\ {\isasymle}\ a\ mod\ b%
+{\isadigit{0}}\ {\isaliteral{3C}{\isacharless}}\ b\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isadigit{0}}\ {\isaliteral{5C3C6C653E}{\isasymle}}\ a\ mod\ b%
\end{isabelle}
\rulename{pos_mod_sign}
\begin{isabelle}%
-{\isadigit{0}}\ {\isacharless}\ b\ {\isasymLongrightarrow}\ a\ mod\ b\ {\isacharless}\ b%
+{\isadigit{0}}\ {\isaliteral{3C}{\isacharless}}\ b\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a\ mod\ b\ {\isaliteral{3C}{\isacharless}}\ b%
\end{isabelle}
\rulename{pos_mod_bound}
\begin{isabelle}%
-b\ {\isacharless}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ a\ mod\ b\ {\isasymle}\ {\isadigit{0}}%
+b\ {\isaliteral{3C}{\isacharless}}\ {\isadigit{0}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a\ mod\ b\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isadigit{0}}%
\end{isabelle}
\rulename{neg_mod_sign}
\begin{isabelle}%
-b\ {\isacharless}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ b\ {\isacharless}\ a\ mod\ b%
+b\ {\isaliteral{3C}{\isacharless}}\ {\isadigit{0}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ b\ {\isaliteral{3C}{\isacharless}}\ a\ mod\ b%
\end{isabelle}
\rulename{neg_mod_bound}
\begin{isabelle}%
-{\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ div\ c\ {\isacharequal}\ a\ div\ c\ {\isacharplus}\ b\ div\ c\ {\isacharplus}\ {\isacharparenleft}a\ mod\ c\ {\isacharplus}\ b\ mod\ c{\isacharparenright}\ div\ c%
+{\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2B}{\isacharplus}}\ b{\isaliteral{29}{\isacharparenright}}\ div\ c\ {\isaliteral{3D}{\isacharequal}}\ a\ div\ c\ {\isaliteral{2B}{\isacharplus}}\ b\ div\ c\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}a\ mod\ c\ {\isaliteral{2B}{\isacharplus}}\ b\ mod\ c{\isaliteral{29}{\isacharparenright}}\ div\ c%
\end{isabelle}
\rulename{zdiv_zadd1_eq}
\begin{isabelle}%
-{\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ mod\ c\ {\isacharequal}\ {\isacharparenleft}a\ mod\ c\ {\isacharplus}\ b\ mod\ c{\isacharparenright}\ mod\ c%
+{\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2B}{\isacharplus}}\ b{\isaliteral{29}{\isacharparenright}}\ mod\ c\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}a\ mod\ c\ {\isaliteral{2B}{\isacharplus}}\ b\ mod\ c{\isaliteral{29}{\isacharparenright}}\ mod\ c%
\end{isabelle}
\rulename{mod_add_eq}
\begin{isabelle}%
-a\ {\isacharasterisk}\ b\ div\ c\ {\isacharequal}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ div\ c{\isacharparenright}\ {\isacharplus}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ mod\ c{\isacharparenright}\ div\ c%
+a\ {\isaliteral{2A}{\isacharasterisk}}\ b\ div\ c\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}b\ div\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ a\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}b\ mod\ c{\isaliteral{29}{\isacharparenright}}\ div\ c%
\end{isabelle}
\rulename{zdiv_zmult1_eq}
\begin{isabelle}%
-a\ {\isacharasterisk}\ b\ mod\ c\ {\isacharequal}\ a\ {\isacharasterisk}\ {\isacharparenleft}b\ mod\ c{\isacharparenright}\ mod\ c%
+a\ {\isaliteral{2A}{\isacharasterisk}}\ b\ mod\ c\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}b\ mod\ c{\isaliteral{29}{\isacharparenright}}\ mod\ c%
\end{isabelle}
\rulename{zmod_zmult1_eq}
\begin{isabelle}%
-{\isadigit{0}}\ {\isacharless}\ c\ {\isasymLongrightarrow}\ a\ div\ {\isacharparenleft}b\ {\isacharasterisk}\ c{\isacharparenright}\ {\isacharequal}\ a\ div\ b\ div\ c%
+{\isadigit{0}}\ {\isaliteral{3C}{\isacharless}}\ c\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a\ div\ {\isaliteral{28}{\isacharparenleft}}b\ {\isaliteral{2A}{\isacharasterisk}}\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ a\ div\ b\ div\ c%
\end{isabelle}
\rulename{zdiv_zmult2_eq}
\begin{isabelle}%
-{\isadigit{0}}\ {\isacharless}\ c\ {\isasymLongrightarrow}\ a\ mod\ {\isacharparenleft}b\ {\isacharasterisk}\ c{\isacharparenright}\ {\isacharequal}\ b\ {\isacharasterisk}\ {\isacharparenleft}a\ div\ b\ mod\ c{\isacharparenright}\ {\isacharplus}\ a\ mod\ b%
+{\isadigit{0}}\ {\isaliteral{3C}{\isacharless}}\ c\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a\ mod\ {\isaliteral{28}{\isacharparenleft}}b\ {\isaliteral{2A}{\isacharasterisk}}\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ b\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}a\ div\ b\ mod\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ a\ mod\ b%
\end{isabelle}
\rulename{zmod_zmult2_eq}%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}abs\ {\isacharparenleft}x{\isacharplus}y{\isacharparenright}\ {\isasymle}\ abs\ x\ {\isacharplus}\ abs\ {\isacharparenleft}y\ {\isacharcolon}{\isacharcolon}\ int{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}abs\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2B}{\isacharplus}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C653E}{\isasymle}}\ abs\ x\ {\isaliteral{2B}{\isacharplus}}\ abs\ {\isaliteral{28}{\isacharparenleft}}y\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -360,7 +360,7 @@
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}abs\ {\isacharparenleft}{\isadigit{2}}{\isacharasterisk}x{\isacharparenright}\ {\isacharequal}\ {\isadigit{2}}\ {\isacharasterisk}\ abs\ {\isacharparenleft}x\ {\isacharcolon}{\isacharcolon}\ int{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}abs\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}{\isaliteral{2A}{\isacharasterisk}}x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ abs\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -368,7 +368,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ abs{\isacharunderscore}if{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ abs{\isaliteral{5F}{\isacharunderscore}}if{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -380,22 +380,22 @@
Induction rules for the Integers
\begin{isabelle}%
-{\isasymlbrakk}k\ {\isasymle}\ i{\isacharsemicolon}\ P\ k{\isacharsemicolon}\ {\isasymAnd}i{\isachardot}\ {\isasymlbrakk}k\ {\isasymle}\ i{\isacharsemicolon}\ P\ i{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}i\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ i%
+{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}k\ {\isaliteral{5C3C6C653E}{\isasymle}}\ i{\isaliteral{3B}{\isacharsemicolon}}\ P\ k{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}i{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}k\ {\isaliteral{5C3C6C653E}{\isasymle}}\ i{\isaliteral{3B}{\isacharsemicolon}}\ P\ i{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ i%
\end{isabelle}
\rulename{int_ge_induct}
\begin{isabelle}%
-{\isasymlbrakk}k\ {\isacharless}\ i{\isacharsemicolon}\ P\ {\isacharparenleft}k\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}{\isacharsemicolon}\ {\isasymAnd}i{\isachardot}\ {\isasymlbrakk}k\ {\isacharless}\ i{\isacharsemicolon}\ P\ i{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}i\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ i%
+{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}k\ {\isaliteral{3C}{\isacharless}}\ i{\isaliteral{3B}{\isacharsemicolon}}\ P\ {\isaliteral{28}{\isacharparenleft}}k\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}i{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}k\ {\isaliteral{3C}{\isacharless}}\ i{\isaliteral{3B}{\isacharsemicolon}}\ P\ i{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ i%
\end{isabelle}
\rulename{int_gr_induct}
\begin{isabelle}%
-{\isasymlbrakk}i\ {\isasymle}\ k{\isacharsemicolon}\ P\ k{\isacharsemicolon}\ {\isasymAnd}i{\isachardot}\ {\isasymlbrakk}i\ {\isasymle}\ k{\isacharsemicolon}\ P\ i{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}i\ {\isacharminus}\ {\isadigit{1}}{\isacharparenright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ i%
+{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}i\ {\isaliteral{5C3C6C653E}{\isasymle}}\ k{\isaliteral{3B}{\isacharsemicolon}}\ P\ k{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}i{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}i\ {\isaliteral{5C3C6C653E}{\isasymle}}\ k{\isaliteral{3B}{\isacharsemicolon}}\ P\ i{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ i%
\end{isabelle}
\rulename{int_le_induct}
\begin{isabelle}%
-{\isasymlbrakk}i\ {\isacharless}\ k{\isacharsemicolon}\ P\ {\isacharparenleft}k\ {\isacharminus}\ {\isadigit{1}}{\isacharparenright}{\isacharsemicolon}\ {\isasymAnd}i{\isachardot}\ {\isasymlbrakk}i\ {\isacharless}\ k{\isacharsemicolon}\ P\ i{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}i\ {\isacharminus}\ {\isadigit{1}}{\isacharparenright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ i%
+{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}i\ {\isaliteral{3C}{\isacharless}}\ k{\isaliteral{3B}{\isacharsemicolon}}\ P\ {\isaliteral{28}{\isacharparenleft}}k\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}i{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}i\ {\isaliteral{3C}{\isacharless}}\ k{\isaliteral{3B}{\isacharsemicolon}}\ P\ i{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ {\isaliteral{28}{\isacharparenleft}}i\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ i%
\end{isabelle}
\rulename{int_less_induct}%
\end{isamarkuptext}%
@@ -405,50 +405,50 @@
FIELDS
\begin{isabelle}%
-x\ {\isacharless}\ y\ {\isasymLongrightarrow}\ {\isasymexists}z{\isachargreater}x{\isachardot}\ z\ {\isacharless}\ y%
+x\ {\isaliteral{3C}{\isacharless}}\ y\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}z{\isaliteral{3E}{\isachargreater}}x{\isaliteral{2E}{\isachardot}}\ z\ {\isaliteral{3C}{\isacharless}}\ y%
\end{isabelle}
\rulename{dense}
\begin{isabelle}%
-a\ {\isacharasterisk}\ {\isacharparenleft}b\ {\isacharslash}\ c{\isacharparenright}\ {\isacharequal}\ a\ {\isacharasterisk}\ b\ {\isacharslash}\ c%
+a\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}b\ {\isaliteral{2F}{\isacharslash}}\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{2A}{\isacharasterisk}}\ b\ {\isaliteral{2F}{\isacharslash}}\ c%
\end{isabelle}
\rulename{times_divide_eq_right}
\begin{isabelle}%
-b\ {\isacharslash}\ c\ {\isacharasterisk}\ a\ {\isacharequal}\ b\ {\isacharasterisk}\ a\ {\isacharslash}\ c%
+b\ {\isaliteral{2F}{\isacharslash}}\ c\ {\isaliteral{2A}{\isacharasterisk}}\ a\ {\isaliteral{3D}{\isacharequal}}\ b\ {\isaliteral{2A}{\isacharasterisk}}\ a\ {\isaliteral{2F}{\isacharslash}}\ c%
\end{isabelle}
\rulename{times_divide_eq_left}
\begin{isabelle}%
-a\ {\isacharslash}\ {\isacharparenleft}b\ {\isacharslash}\ c{\isacharparenright}\ {\isacharequal}\ a\ {\isacharasterisk}\ c\ {\isacharslash}\ b%
+a\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}b\ {\isaliteral{2F}{\isacharslash}}\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{2A}{\isacharasterisk}}\ c\ {\isaliteral{2F}{\isacharslash}}\ b%
\end{isabelle}
\rulename{divide_divide_eq_right}
\begin{isabelle}%
-a\ {\isacharslash}\ b\ {\isacharslash}\ c\ {\isacharequal}\ a\ {\isacharslash}\ {\isacharparenleft}b\ {\isacharasterisk}\ c{\isacharparenright}%
+a\ {\isaliteral{2F}{\isacharslash}}\ b\ {\isaliteral{2F}{\isacharslash}}\ c\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}b\ {\isaliteral{2A}{\isacharasterisk}}\ c{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\rulename{divide_divide_eq_left}
\begin{isabelle}%
-{\isacharminus}\ {\isacharparenleft}a\ {\isacharslash}\ b{\isacharparenright}\ {\isacharequal}\ {\isacharminus}\ a\ {\isacharslash}\ b%
+{\isaliteral{2D}{\isacharminus}}\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2F}{\isacharslash}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}\ a\ {\isaliteral{2F}{\isacharslash}}\ b%
\end{isabelle}
\rulename{minus_divide_left}
\begin{isabelle}%
-{\isacharminus}\ {\isacharparenleft}a\ {\isacharslash}\ b{\isacharparenright}\ {\isacharequal}\ a\ {\isacharslash}\ {\isacharminus}\ b%
+{\isaliteral{2D}{\isacharminus}}\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2F}{\isacharslash}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{2D}{\isacharminus}}\ b%
\end{isabelle}
\rulename{minus_divide_right}
This last NOT a simprule
\begin{isabelle}%
-{\isacharparenleft}a\ {\isacharplus}\ b{\isacharparenright}\ {\isacharslash}\ c\ {\isacharequal}\ a\ {\isacharslash}\ c\ {\isacharplus}\ b\ {\isacharslash}\ c%
+{\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2B}{\isacharplus}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2F}{\isacharslash}}\ c\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{2F}{\isacharslash}}\ c\ {\isaliteral{2B}{\isacharplus}}\ b\ {\isaliteral{2F}{\isacharslash}}\ c%
\end{isabelle}
\rulename{add_divide_distrib}%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isadigit{3}}{\isacharslash}{\isadigit{4}}\ {\isacharless}\ {\isacharparenleft}{\isadigit{7}}{\isacharslash}{\isadigit{8}}\ {\isacharcolon}{\isacharcolon}\ real{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{3}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}\ {\isaliteral{3C}{\isacharless}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{7}}{\isaliteral{2F}{\isacharslash}}{\isadigit{8}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ real{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -466,7 +466,7 @@
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}P\ {\isacharparenleft}{\isacharparenleft}{\isadigit{3}}{\isacharslash}{\isadigit{4}}{\isacharparenright}\ {\isacharasterisk}\ {\isacharparenleft}{\isadigit{8}}{\isacharslash}{\isadigit{1}}{\isadigit{5}}\ {\isacharcolon}{\isacharcolon}\ real{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}P\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{8}}{\isaliteral{2F}{\isacharslash}}{\isadigit{1}}{\isadigit{5}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ real{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -475,7 +475,7 @@
%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ P\ {\isacharparenleft}{\isadigit{3}}\ {\isacharslash}\ {\isadigit{4}}\ {\isacharasterisk}\ {\isacharparenleft}{\isadigit{8}}\ {\isacharslash}\ {\isadigit{1}}{\isadigit{5}}{\isacharparenright}{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ P\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{8}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{1}}{\isadigit{5}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
@@ -483,7 +483,7 @@
\ simp%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ P\ {\isacharparenleft}{\isadigit{2}}\ {\isacharslash}\ {\isadigit{5}}{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ P\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{5}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
@@ -498,7 +498,7 @@
\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}{\isadigit{3}}{\isacharslash}{\isadigit{4}}{\isacharparenright}\ {\isacharasterisk}\ {\isacharparenleft}{\isadigit{8}}{\isacharslash}{\isadigit{1}}{\isadigit{5}}{\isacharparenright}\ {\isacharless}\ {\isacharparenleft}x\ {\isacharcolon}{\isacharcolon}\ real{\isacharparenright}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{8}}{\isaliteral{2F}{\isacharslash}}{\isadigit{1}}{\isadigit{5}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3C}{\isacharless}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ real{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -507,7 +507,7 @@
%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isadigit{3}}\ {\isacharslash}\ {\isadigit{4}}\ {\isacharasterisk}\ {\isacharparenleft}{\isadigit{8}}\ {\isacharslash}\ {\isadigit{1}}{\isadigit{5}}{\isacharparenright}\ {\isacharless}\ x%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{8}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{1}}{\isadigit{5}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3C}{\isacharless}}\ x%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
@@ -515,7 +515,7 @@
\ simp%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isadigit{2}}\ {\isacharless}\ x\ {\isacharasterisk}\ {\isadigit{5}}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isadigit{2}}\ {\isaliteral{3C}{\isacharless}}\ x\ {\isaliteral{2A}{\isacharasterisk}}\ {\isadigit{5}}%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
@@ -534,17 +534,17 @@
Requires a field, or else an ordered ring
\begin{isabelle}%
-{\isacharparenleft}a\ {\isacharasterisk}\ b\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}a\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isasymor}\ b\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2A}{\isacharasterisk}}\ b\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ b\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\rulename{mult_eq_0_iff}
\begin{isabelle}%
-{\isacharparenleft}a\ {\isacharasterisk}\ c\ {\isacharequal}\ b\ {\isacharasterisk}\ c{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}c\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isasymor}\ a\ {\isacharequal}\ b{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{2A}{\isacharasterisk}}\ c\ {\isaliteral{3D}{\isacharequal}}\ b\ {\isaliteral{2A}{\isacharasterisk}}\ c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}c\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ a\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\rulename{mult_cancel_right}
\begin{isabelle}%
-{\isacharparenleft}c\ {\isacharasterisk}\ a\ {\isacharequal}\ c\ {\isacharasterisk}\ b{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}c\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isasymor}\ a\ {\isacharequal}\ b{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}c\ {\isaliteral{2A}{\isacharasterisk}}\ a\ {\isaliteral{3D}{\isacharequal}}\ c\ {\isaliteral{2A}{\isacharasterisk}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}c\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ a\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\rulename{mult_cancel_left}%
\end{isamarkuptext}%
@@ -554,9 +554,9 @@
effect of show sorts on the above
\begin{isabelle}%
-{\isacharparenleft}{\isacharparenleft}c{\isasymColon}{\isacharprime}a{\isasymColon}ring{\isacharunderscore}no{\isacharunderscore}zero{\isacharunderscore}divisors{\isacharparenright}\ {\isacharasterisk}\ {\isacharparenleft}a{\isasymColon}{\isacharprime}a{\isasymColon}ring{\isacharunderscore}no{\isacharunderscore}zero{\isacharunderscore}divisors{\isacharparenright}\ {\isacharequal}\isanewline
-\isaindent{{\isacharparenleft}}c\ {\isacharasterisk}\ {\isacharparenleft}b{\isasymColon}{\isacharprime}a{\isasymColon}ring{\isacharunderscore}no{\isacharunderscore}zero{\isacharunderscore}divisors{\isacharparenright}{\isacharparenright}\ {\isacharequal}\isanewline
-{\isacharparenleft}c\ {\isacharequal}\ {\isacharparenleft}{\isadigit{0}}{\isasymColon}{\isacharprime}a{\isasymColon}ring{\isacharunderscore}no{\isacharunderscore}zero{\isacharunderscore}divisors{\isacharparenright}\ {\isasymor}\ a\ {\isacharequal}\ b{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}c{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}ring{\isaliteral{5F}{\isacharunderscore}}no{\isaliteral{5F}{\isacharunderscore}}zero{\isaliteral{5F}{\isacharunderscore}}divisors{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}ring{\isaliteral{5F}{\isacharunderscore}}no{\isaliteral{5F}{\isacharunderscore}}zero{\isaliteral{5F}{\isacharunderscore}}divisors{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\isaindent{{\isaliteral{28}{\isacharparenleft}}}c\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}b{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}ring{\isaliteral{5F}{\isacharunderscore}}no{\isaliteral{5F}{\isacharunderscore}}zero{\isaliteral{5F}{\isacharunderscore}}divisors{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+{\isaliteral{28}{\isacharparenleft}}c\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C436F6C6F6E3E}{\isasymColon}}ring{\isaliteral{5F}{\isacharunderscore}}no{\isaliteral{5F}{\isacharunderscore}}zero{\isaliteral{5F}{\isacharunderscore}}divisors{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ a\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\rulename{mult_cancel_left}%
\end{isamarkuptext}%
@@ -566,32 +566,32 @@
absolute value
\begin{isabelle}%
-{\isasymbar}a\ {\isacharasterisk}\ b{\isasymbar}\ {\isacharequal}\ {\isasymbar}a{\isasymbar}\ {\isacharasterisk}\ {\isasymbar}b{\isasymbar}%
+{\isaliteral{5C3C6261723E}{\isasymbar}}a\ {\isaliteral{2A}{\isacharasterisk}}\ b{\isaliteral{5C3C6261723E}{\isasymbar}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6261723E}{\isasymbar}}a{\isaliteral{5C3C6261723E}{\isasymbar}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5C3C6261723E}{\isasymbar}}b{\isaliteral{5C3C6261723E}{\isasymbar}}%
\end{isabelle}
\rulename{abs_mult}
\begin{isabelle}%
-{\isacharparenleft}{\isasymbar}a{\isasymbar}\ {\isasymle}\ b{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}a\ {\isasymle}\ b\ {\isasymand}\ {\isacharminus}\ a\ {\isasymle}\ b{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6261723E}{\isasymbar}}a{\isaliteral{5C3C6261723E}{\isasymbar}}\ {\isaliteral{5C3C6C653E}{\isasymle}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{5C3C6C653E}{\isasymle}}\ b\ {\isaliteral{5C3C616E643E}{\isasymand}}\ {\isaliteral{2D}{\isacharminus}}\ a\ {\isaliteral{5C3C6C653E}{\isasymle}}\ b{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
\rulename{abs_le_iff}
\begin{isabelle}%
-{\isasymbar}a\ {\isacharplus}\ b{\isasymbar}\ {\isasymle}\ {\isasymbar}a{\isasymbar}\ {\isacharplus}\ {\isasymbar}b{\isasymbar}%
+{\isaliteral{5C3C6261723E}{\isasymbar}}a\ {\isaliteral{2B}{\isacharplus}}\ b{\isaliteral{5C3C6261723E}{\isasymbar}}\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{5C3C6261723E}{\isasymbar}}a{\isaliteral{5C3C6261723E}{\isasymbar}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{5C3C6261723E}{\isasymbar}}b{\isaliteral{5C3C6261723E}{\isasymbar}}%
\end{isabelle}
\rulename{abs_triangle_ineq}
\begin{isabelle}%
-a\isactrlbsup m\ {\isacharplus}\ n\isactrlesup \ {\isacharequal}\ a\isactrlbsup m\isactrlesup \ {\isacharasterisk}\ a\isactrlbsup n\isactrlesup %
+a\isaliteral{5C3C5E627375703E}{}\isactrlbsup m\ {\isaliteral{2B}{\isacharplus}}\ n\isaliteral{5C3C5E657375703E}{}\isactrlesup \ {\isaliteral{3D}{\isacharequal}}\ a\isaliteral{5C3C5E627375703E}{}\isactrlbsup m\isaliteral{5C3C5E657375703E}{}\isactrlesup \ {\isaliteral{2A}{\isacharasterisk}}\ a\isaliteral{5C3C5E627375703E}{}\isactrlbsup n\isaliteral{5C3C5E657375703E}{}\isactrlesup %
\end{isabelle}
\rulename{power_add}
\begin{isabelle}%
-a\isactrlbsup m\ {\isacharasterisk}\ n\isactrlesup \ {\isacharequal}\ a\isactrlbsup m\isactrlesup \isactrlbsup n\isactrlesup %
+a\isaliteral{5C3C5E627375703E}{}\isactrlbsup m\ {\isaliteral{2A}{\isacharasterisk}}\ n\isaliteral{5C3C5E657375703E}{}\isactrlesup \ {\isaliteral{3D}{\isacharequal}}\ a\isaliteral{5C3C5E627375703E}{}\isactrlbsup m\isaliteral{5C3C5E657375703E}{}\isactrlesup \isaliteral{5C3C5E627375703E}{}\isactrlbsup n\isaliteral{5C3C5E657375703E}{}\isactrlesup %
\end{isabelle}
\rulename{power_mult}
\begin{isabelle}%
-{\isasymbar}a\isactrlbsup n\isactrlesup {\isasymbar}\ {\isacharequal}\ {\isasymbar}a{\isasymbar}\isactrlbsup n\isactrlesup %
+{\isaliteral{5C3C6261723E}{\isasymbar}}a\isaliteral{5C3C5E627375703E}{}\isactrlbsup n\isaliteral{5C3C5E657375703E}{}\isactrlesup {\isaliteral{5C3C6261723E}{\isasymbar}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6261723E}{\isasymbar}}a{\isaliteral{5C3C6261723E}{\isasymbar}}\isaliteral{5C3C5E627375703E}{}\isactrlbsup n\isaliteral{5C3C5E657375703E}{}\isactrlesup %
\end{isabelle}
\rulename{power_abs}%
\end{isamarkuptext}%
--- a/doc-src/TutorialI/Types/document/Overloading.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Types/document/Overloading.tex Mon Nov 08 14:41:11 2010 +0100
@@ -26,25 +26,25 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-We can introduce a binary infix addition operator \isa{{\isasymotimes}}
+We can introduce a binary infix addition operator \isa{{\isaliteral{5C3C6F74696D65733E}{\isasymotimes}}}
for arbitrary types by means of a type class:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{class}\isamarkupfalse%
-\ plus\ {\isacharequal}\isanewline
-\ \ \isakeyword{fixes}\ plus\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequoteopen}{\isasymoplus}{\isachardoublequoteclose}\ {\isadigit{7}}{\isadigit{0}}{\isacharparenright}%
+\ plus\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \isakeyword{fixes}\ plus\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{22}{\isachardoublequoteclose}}\ {\isaliteral{28}{\isacharparenleft}}\isakeyword{infixl}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6F706C75733E}{\isasymoplus}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{7}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptext}%
\noindent This introduces a new class \isa{plus},
along with a constant \isa{plus} with nice infix syntax.
\isa{plus} is also named \emph{class operation}. The type
-of \isa{plus} carries a class constraint \isa{{\isachardoublequote}{\isacharprime}a\ {\isacharcolon}{\isacharcolon}\ plus{\isachardoublequote}} on its type variable, meaning that only types of class
-\isa{plus} can be instantiated for \isa{{\isachardoublequote}{\isacharprime}a{\isachardoublequote}}.
+of \isa{plus} carries a class constraint \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ plus{\isaliteral{22}{\isachardoublequote}}} on its type variable, meaning that only types of class
+\isa{plus} can be instantiated for \isa{{\isaliteral{22}{\isachardoublequote}}{\isaliteral{27}{\isacharprime}}a{\isaliteral{22}{\isachardoublequote}}}.
To breathe life into \isa{plus} we need to declare a type
to be an \bfindex{instance} of \isa{plus}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{instantiation}\isamarkupfalse%
-\ nat\ {\isacharcolon}{\isacharcolon}\ plus\isanewline
+\ nat\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ plus\isanewline
\isakeyword{begin}%
\begin{isamarkuptext}%
\noindent Command \isacommand{instantiation} opens a local
@@ -53,15 +53,15 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{primrec}\isamarkupfalse%
-\ plus{\isacharunderscore}nat\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ \ \ {\isachardoublequoteopen}{\isacharparenleft}{\isadigit{0}}{\isacharcolon}{\isacharcolon}nat{\isacharparenright}\ {\isasymoplus}\ n\ {\isacharequal}\ n{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}Suc\ m\ {\isasymoplus}\ n\ {\isacharequal}\ Suc\ {\isacharparenleft}m\ {\isasymoplus}\ n{\isacharparenright}{\isachardoublequoteclose}%
+\ plus{\isaliteral{5F}{\isacharunderscore}}nat\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ \ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ n\ {\isaliteral{3D}{\isacharequal}}\ n{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{22}{\isachardoublequoteopen}}Suc\ m\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ n\ {\isaliteral{3D}{\isacharequal}}\ Suc\ {\isaliteral{28}{\isacharparenleft}}m\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ n{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent Note that the name \isa{plus} carries a
-suffix \isa{{\isacharunderscore}nat}; by default, the local name of a class operation
-\isa{f} to be instantiated on type constructor \isa{{\isasymkappa}} is mangled
-as \isa{f{\isacharunderscore}{\isasymkappa}}. In case of uncertainty, these names may be inspected
-using the \hyperlink{command.print-context}{\mbox{\isa{\isacommand{print{\isacharunderscore}context}}}} command or the corresponding
+suffix \isa{{\isaliteral{5F}{\isacharunderscore}}nat}; by default, the local name of a class operation
+\isa{f} to be instantiated on type constructor \isa{{\isaliteral{5C3C6B617070613E}{\isasymkappa}}} is mangled
+as \isa{f{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5C3C6B617070613E}{\isasymkappa}}}. In case of uncertainty, these names may be inspected
+using the \hyperlink{command.print-context}{\mbox{\isa{\isacommand{print{\isaliteral{5F}{\isacharunderscore}}context}}}} command or the corresponding
ProofGeneral button.
Although class \isa{plus} has no axioms, the instantiation must be
@@ -75,7 +75,7 @@
\endisadelimproof
%
\isatagproof
-\isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
@@ -94,12 +94,12 @@
\isacommand{end}\isamarkupfalse%
%
\begin{isamarkuptext}%
-\noindent From now on, terms like \isa{Suc\ {\isacharparenleft}m\ {\isasymoplus}\ {\isadigit{2}}{\isacharparenright}} are
+\noindent From now on, terms like \isa{Suc\ {\isaliteral{28}{\isacharparenleft}}m\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}} are
legal.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{instantiation}\isamarkupfalse%
-\ prod\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}plus{\isacharcomma}\ plus{\isacharparenright}\ plus\isanewline
+\ prod\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{28}{\isacharparenleft}}plus{\isaliteral{2C}{\isacharcomma}}\ plus{\isaliteral{29}{\isacharparenright}}\ plus\isanewline
\isakeyword{begin}%
\begin{isamarkuptext}%
\noindent Here we instantiate the product type \isa{prod} to
@@ -108,8 +108,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{fun}\isamarkupfalse%
-\ plus{\isacharunderscore}prod\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymoplus}\ {\isacharparenleft}w{\isacharcomma}\ z{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}x\ {\isasymoplus}\ w{\isacharcomma}\ y\ {\isasymoplus}\ z{\isacharparenright}{\isachardoublequoteclose}%
+\ plus{\isaliteral{5F}{\isacharunderscore}}prod\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+\ \ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ {\isaliteral{28}{\isacharparenleft}}w{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ w{\isaliteral{2C}{\isacharcomma}}\ y\ {\isaliteral{5C3C6F706C75733E}{\isasymoplus}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent Obviously, overloaded specifications may include
recursion over the syntactic structure of types.%
@@ -122,7 +122,7 @@
\endisadelimproof
%
\isatagproof
-\isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
+\isacommand{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
--- a/doc-src/TutorialI/Types/document/Pairs.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Types/document/Pairs.tex Mon Nov 08 14:41:11 2010 +0100
@@ -36,16 +36,16 @@
%
\begin{isamarkuptext}%
Tuples may be used as patterns in $\lambda$-abstractions,
-for example \isa{{\isasymlambda}{\isacharparenleft}x{\isacharcomma}y{\isacharcomma}z{\isacharparenright}{\isachardot}x{\isacharplus}y{\isacharplus}z} and \isa{{\isasymlambda}{\isacharparenleft}{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}{\isacharcomma}z{\isacharparenright}{\isachardot}x{\isacharplus}y{\isacharplus}z}. In fact,
+for example \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}x{\isaliteral{2B}{\isacharplus}}y{\isaliteral{2B}{\isacharplus}}z} and \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}x{\isaliteral{2B}{\isacharplus}}y{\isaliteral{2B}{\isacharplus}}z}. In fact,
tuple patterns can be used in most variable binding constructs,
and they can be nested. Here are
some typical examples:
\begin{quote}
-\isa{let\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isacharequal}\ f\ z\ in\ {\isacharparenleft}y{\isacharcomma}\ x{\isacharparenright}}\\
-\isa{case\ xs\ of\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymRightarrow}\ {\isadigit{0}}\ {\isacharbar}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isacharhash}\ zs\ {\isasymRightarrow}\ x\ {\isacharplus}\ y}\\
-\isa{{\isasymforall}{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}{\isasymin}A{\isachardot}\ x{\isacharequal}y}\\
-\isa{{\isacharbraceleft}{\isacharparenleft}x{\isacharcomma}y{\isacharcomma}z{\isacharparenright}{\isachardot}\ x{\isacharequal}z{\isacharbraceright}}\\
-\isa{{\isasymUnion}\isactrlbsub {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isasymin}A\isactrlesub \ {\isacharbraceleft}x\ {\isacharplus}\ y{\isacharbraceright}}
+\isa{let\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ f\ z\ in\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}\ x{\isaliteral{29}{\isacharparenright}}}\\
+\isa{case\ xs\ of\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isadigit{0}}\ {\isaliteral{7C}{\isacharbar}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{23}{\isacharhash}}\ zs\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ x\ {\isaliteral{2B}{\isacharplus}}\ y}\\
+\isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C696E3E}{\isasymin}}A{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}y}\\
+\isa{{\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{2C}{\isacharcomma}}z{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}z{\isaliteral{7D}{\isacharbraceright}}}\\
+\isa{{\isaliteral{5C3C556E696F6E3E}{\isasymUnion}}\isaliteral{5C3C5E627375623E}{}\isactrlbsub {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C696E3E}{\isasymin}}A\isaliteral{5C3C5E657375623E}{}\isactrlesub \ {\isaliteral{7B}{\isacharbraceleft}}x\ {\isaliteral{2B}{\isacharplus}}\ y{\isaliteral{7D}{\isacharbraceright}}}
\end{quote}
The intuitive meanings of these expressions should be obvious.
Unfortunately, we need to know in more detail what the notation really stands
@@ -53,15 +53,15 @@
over pairs and tuples is merely a convenient shorthand for a more complex
internal representation. Thus the internal and external form of a term may
differ, which can affect proofs. If you want to avoid this complication,
-stick to \isa{fst} and \isa{snd} and write \isa{{\isasymlambda}p{\isachardot}\ fst\ p\ {\isacharplus}\ snd\ p}
-instead of \isa{{\isasymlambda}{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}{\isachardot}\ x{\isacharplus}y}. These terms are distinct even though they
+stick to \isa{fst} and \isa{snd} and write \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}p{\isaliteral{2E}{\isachardot}}\ fst\ p\ {\isaliteral{2B}{\isacharplus}}\ snd\ p}
+instead of \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{2B}{\isacharplus}}y}. These terms are distinct even though they
denote the same function.
-Internally, \isa{{\isasymlambda}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ t} becomes \isa{split\ {\isacharparenleft}{\isasymlambda}x\ y{\isachardot}\ t{\isacharparenright}}, where
-\cdx{split} is the uncurrying function of type \isa{{\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}c{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}c} defined as
+Internally, \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ t} becomes \isa{split\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}x\ y{\isaliteral{2E}{\isachardot}}\ t{\isaliteral{29}{\isacharparenright}}}, where
+\cdx{split} is the uncurrying function of type \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}c{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}c} defined as
\begin{center}
-\isa{prod{\isacharunderscore}case\ {\isacharequal}\ {\isacharparenleft}{\isasymlambda}c\ p{\isachardot}\ c\ {\isacharparenleft}fst\ p{\isacharparenright}\ {\isacharparenleft}snd\ p{\isacharparenright}{\isacharparenright}}
-\hfill(\isa{split{\isacharunderscore}def})
+\isa{prod{\isaliteral{5F}{\isacharunderscore}}case\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}c\ p{\isaliteral{2E}{\isachardot}}\ c\ {\isaliteral{28}{\isacharparenleft}}fst\ p{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}snd\ p{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}}
+\hfill(\isa{split{\isaliteral{5F}{\isacharunderscore}}def})
\end{center}
Pattern matching in
other variable binding constructs is translated similarly. Thus we need to
@@ -74,11 +74,11 @@
\isamarkuptrue%
%
\begin{isamarkuptext}%
-The most obvious approach is the brute force expansion of \isa{prod{\isacharunderscore}case}:%
+The most obvious approach is the brute force expansion of \isa{prod{\isaliteral{5F}{\isacharunderscore}}case}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}{\isasymlambda}{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}{\isachardot}x{\isacharparenright}\ p\ {\isacharequal}\ fst\ p{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}x{\isaliteral{29}{\isacharparenright}}\ p\ {\isaliteral{3D}{\isacharequal}}\ fst\ p{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -86,7 +86,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-{\isacharparenleft}simp\ add{\isacharcolon}\ split{\isacharunderscore}def{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ split{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -96,25 +96,25 @@
%
\begin{isamarkuptext}%
\noindent
-This works well if rewriting with \isa{split{\isacharunderscore}def} finishes the
+This works well if rewriting with \isa{split{\isaliteral{5F}{\isacharunderscore}}def} finishes the
proof, as it does above. But if it does not, you end up with exactly what
we are trying to avoid: nests of \isa{fst} and \isa{snd}. Thus this
approach is neither elegant nor very practical in large examples, although it
can be effective in small ones.
If we consider why this lemma presents a problem,
-we realize that we need to replace variable~\isa{p} by some pair \isa{{\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}}. Then both sides of the
+we realize that we need to replace variable~\isa{p} by some pair \isa{{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}}. Then both sides of the
equation would simplify to \isa{a} by the simplification rules
-\isa{prod{\isacharunderscore}case\ f\ {\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\ {\isacharequal}\ f\ a\ b} and \isa{fst\ {\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\ {\isacharequal}\ a}.
+\isa{prod{\isaliteral{5F}{\isacharunderscore}}case\ f\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ f\ a\ b} and \isa{fst\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ a}.
To reason about tuple patterns requires some way of
converting a variable of product type into a pair.
-In case of a subterm of the form \isa{prod{\isacharunderscore}case\ f\ p} this is easy: the split
-rule \isa{split{\isacharunderscore}split} replaces \isa{p} by a pair:%
+In case of a subterm of the form \isa{prod{\isaliteral{5F}{\isacharunderscore}}case\ f\ p} this is easy: the split
+rule \isa{split{\isaliteral{5F}{\isacharunderscore}}split} replaces \isa{p} by a pair:%
\index{*split (method)}%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}{\isasymlambda}{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}{\isachardot}y{\isacharparenright}\ p\ {\isacharequal}\ snd\ p{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}y{\isaliteral{29}{\isacharparenright}}\ p\ {\isaliteral{3D}{\isacharequal}}\ snd\ p{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -122,10 +122,10 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}split\ split{\isacharunderscore}split{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}split\ split{\isaliteral{5F}{\isacharunderscore}}split{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymforall}x\ y{\isachardot}\ p\ {\isacharequal}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymlongrightarrow}\ y\ {\isacharequal}\ snd\ p%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x\ y{\isaliteral{2E}{\isachardot}}\ p\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ y\ {\isaliteral{3D}{\isacharequal}}\ snd\ p%
\end{isabelle}
This subgoal is easily proved by simplification. Thus we could have combined
simplification and splitting in one command that proves the goal outright:%
@@ -145,7 +145,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-{\isacharparenleft}simp\ split{\isacharcolon}\ split{\isacharunderscore}split{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp\ split{\isaliteral{3A}{\isacharcolon}}\ split{\isaliteral{5F}{\isacharunderscore}}split{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -158,7 +158,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}let\ {\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isacharequal}\ p\ in\ fst\ p\ {\isacharequal}\ x{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}let\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ p\ in\ fst\ p\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -166,10 +166,10 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp\ only{\isacharcolon}\ Let{\isacharunderscore}def{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp\ only{\isaliteral{3A}{\isacharcolon}}\ Let{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ case\ p\ of\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymRightarrow}\ fst\ p\ {\isacharequal}\ x%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ case\ p\ of\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ fst\ p\ {\isaliteral{3D}{\isacharequal}}\ x%
\end{isabelle}
A paired \isa{let} reduces to a paired $\lambda$-abstraction, which
can be split as above. The same is true for paired set comprehension:%
@@ -183,7 +183,7 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}p\ {\isasymin}\ {\isacharbraceleft}{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}{\isachardot}\ x{\isacharequal}y{\isacharbraceright}\ {\isasymlongrightarrow}\ fst\ p\ {\isacharequal}\ snd\ p{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}p\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}y{\isaliteral{7D}{\isacharbraceright}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ fst\ p\ {\isaliteral{3D}{\isacharequal}}\ snd\ p{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -194,11 +194,11 @@
\ simp%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ prod{\isacharunderscore}case\ op\ {\isacharequal}\ p\ {\isasymlongrightarrow}\ fst\ p\ {\isacharequal}\ snd\ p%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ prod{\isaliteral{5F}{\isacharunderscore}}case\ op\ {\isaliteral{3D}{\isacharequal}}\ p\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ fst\ p\ {\isaliteral{3D}{\isacharequal}}\ snd\ p%
\end{isabelle}
-Again, simplification produces a term suitable for \isa{split{\isacharunderscore}split}
+Again, simplification produces a term suitable for \isa{split{\isaliteral{5F}{\isacharunderscore}}split}
as above. If you are worried about the strange form of the premise:
-\isa{split\ {\isacharparenleft}op\ {\isacharequal}{\isacharparenright}} is short for \isa{{\isasymlambda}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ x\ {\isacharequal}\ y}.
+\isa{split\ {\isaliteral{28}{\isacharparenleft}}op\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{29}{\isacharparenright}}} is short for \isa{{\isaliteral{5C3C6C616D6264613E}{\isasymlambda}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3D}{\isacharequal}}\ y}.
The same proof procedure works for%
\end{isamarkuptxt}%
\isamarkuptrue%
@@ -210,7 +210,7 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}p\ {\isasymin}\ {\isacharbraceleft}{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}{\isachardot}\ x{\isacharequal}y{\isacharbraceright}\ {\isasymLongrightarrow}\ fst\ p\ {\isacharequal}\ snd\ p{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}p\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{7B}{\isacharbraceleft}}{\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}{\isaliteral{2E}{\isachardot}}\ x{\isaliteral{3D}{\isacharequal}}y{\isaliteral{7D}{\isacharbraceright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ fst\ p\ {\isaliteral{3D}{\isacharequal}}\ snd\ p{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -219,10 +219,10 @@
%
\begin{isamarkuptxt}%
\noindent
-except that we now have to use \isa{split{\isacharunderscore}split{\isacharunderscore}asm}, because
-\isa{prod{\isacharunderscore}case} occurs in the assumptions.
+except that we now have to use \isa{split{\isaliteral{5F}{\isacharunderscore}}split{\isaliteral{5F}{\isacharunderscore}}asm}, because
+\isa{prod{\isaliteral{5F}{\isacharunderscore}}case} occurs in the assumptions.
-However, splitting \isa{prod{\isacharunderscore}case} is not always a solution, as no \isa{prod{\isacharunderscore}case}
+However, splitting \isa{prod{\isaliteral{5F}{\isacharunderscore}}case} is not always a solution, as no \isa{prod{\isaliteral{5F}{\isacharunderscore}}case}
may be present in the goal. Consider the following function:%
\end{isamarkuptxt}%
\isamarkuptrue%
@@ -234,15 +234,15 @@
%
\endisadelimproof
\isacommand{primrec}\isamarkupfalse%
-\ swap\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymtimes}\ {\isacharprime}a{\isachardoublequoteclose}\ \isakeyword{where}\ {\isachardoublequoteopen}swap\ {\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}y{\isacharcomma}x{\isacharparenright}{\isachardoublequoteclose}%
+\ swap\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}b\ {\isaliteral{5C3C74696D65733E}{\isasymtimes}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}swap\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{2C}{\isacharcomma}}y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}y{\isaliteral{2C}{\isacharcomma}}x{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
Note that the above \isacommand{primrec} definition is admissible
-because \isa{{\isasymtimes}} is a datatype. When we now try to prove%
+because \isa{{\isaliteral{5C3C74696D65733E}{\isasymtimes}}} is a datatype. When we now try to prove%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}swap{\isacharparenleft}swap\ p{\isacharparenright}\ {\isacharequal}\ p{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}swap{\isaliteral{28}{\isacharparenleft}}swap\ p{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ p{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -253,26 +253,26 @@
\noindent
simplification will do nothing, because the defining equation for
\isa{swap} expects a pair. Again, we need to turn \isa{p}
-into a pair first, but this time there is no \isa{prod{\isacharunderscore}case} in sight.
+into a pair first, but this time there is no \isa{prod{\isaliteral{5F}{\isacharunderscore}}case} in sight.
The only thing we can do is to split the term by hand:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}case{\isacharunderscore}tac\ p{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}case{\isaliteral{5F}{\isacharunderscore}}tac\ p{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}a\ b{\isachardot}\ p\ {\isacharequal}\ {\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\ {\isasymLongrightarrow}\ swap\ {\isacharparenleft}swap\ p{\isacharparenright}\ {\isacharequal}\ p%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a\ b{\isaliteral{2E}{\isachardot}}\ p\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ swap\ {\isaliteral{28}{\isacharparenleft}}swap\ p{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ p%
\end{isabelle}
-Again, \methdx{case_tac} is applicable because \isa{{\isasymtimes}} is a datatype.
+Again, \methdx{case_tac} is applicable because \isa{{\isaliteral{5C3C74696D65733E}{\isasymtimes}}} is a datatype.
The subgoal is easily proved by \isa{simp}.
-Splitting by \isa{case{\isacharunderscore}tac} also solves the previous examples and may thus
+Splitting by \isa{case{\isaliteral{5F}{\isacharunderscore}}tac} also solves the previous examples and may thus
appear preferable to the more arcane methods introduced first. However, see
-the warning about \isa{case{\isacharunderscore}tac} in \S\ref{sec:struct-ind-case}.
+the warning about \isa{case{\isaliteral{5F}{\isacharunderscore}}tac} in \S\ref{sec:struct-ind-case}.
-Alternatively, you can split \emph{all} \isa{{\isasymAnd}}-quantified variables
-in a goal with the rewrite rule \isa{split{\isacharunderscore}paired{\isacharunderscore}all}:%
+Alternatively, you can split \emph{all} \isa{{\isaliteral{5C3C416E643E}{\isasymAnd}}}-quantified variables
+in a goal with the rewrite rule \isa{split{\isaliteral{5F}{\isacharunderscore}}paired{\isaliteral{5F}{\isacharunderscore}}all}:%
\end{isamarkuptxt}%
\isamarkuptrue%
%
@@ -283,7 +283,7 @@
%
\endisadelimproof
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymAnd}p\ q{\isachardot}\ swap{\isacharparenleft}swap\ p{\isacharparenright}\ {\isacharequal}\ q\ {\isasymlongrightarrow}\ p\ {\isacharequal}\ q{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C416E643E}{\isasymAnd}}p\ q{\isaliteral{2E}{\isachardot}}\ swap{\isaliteral{28}{\isacharparenleft}}swap\ p{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ q\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ p\ {\isaliteral{3D}{\isacharequal}}\ q{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -291,11 +291,11 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp\ only{\isacharcolon}\ split{\isacharunderscore}paired{\isacharunderscore}all{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp\ only{\isaliteral{3A}{\isacharcolon}}\ split{\isaliteral{5F}{\isacharunderscore}}paired{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\noindent
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}a\ b\ aa\ ba{\isachardot}\ swap\ {\isacharparenleft}swap\ {\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}aa{\isacharcomma}\ ba{\isacharparenright}\ {\isasymlongrightarrow}\ {\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}aa{\isacharcomma}\ ba{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}a\ b\ aa\ ba{\isaliteral{2E}{\isachardot}}\ swap\ {\isaliteral{28}{\isacharparenleft}}swap\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}aa{\isaliteral{2C}{\isacharcomma}}\ ba{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C6C6F6E6772696768746172726F773E}{\isasymlongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}aa{\isaliteral{2C}{\isacharcomma}}\ ba{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
@@ -312,11 +312,11 @@
%
\begin{isamarkuptext}%
\noindent
-Note that we have intentionally included only \isa{split{\isacharunderscore}paired{\isacharunderscore}all}
+Note that we have intentionally included only \isa{split{\isaliteral{5F}{\isacharunderscore}}paired{\isaliteral{5F}{\isacharunderscore}}all}
in the first simplification step, and then we simplify again.
This time the reason was not merely
pedagogical:
-\isa{split{\isacharunderscore}paired{\isacharunderscore}all} may interfere with other functions
+\isa{split{\isaliteral{5F}{\isacharunderscore}}paired{\isaliteral{5F}{\isacharunderscore}}all} may interfere with other functions
of the simplifier.
The following command could fail (here it does not)
where two separate \isa{simp} applications succeed.%
@@ -329,7 +329,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}simp\ add{\isacharcolon}\ split{\isacharunderscore}paired{\isacharunderscore}all{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ split{\isaliteral{5F}{\isacharunderscore}}paired{\isaliteral{5F}{\isacharunderscore}}all{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -339,12 +339,12 @@
%
\begin{isamarkuptext}%
\noindent
-Finally, the simplifier automatically splits all \isa{{\isasymforall}} and
-\isa{{\isasymexists}}-quantified variables:%
+Finally, the simplifier automatically splits all \isa{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}} and
+\isa{{\isaliteral{5C3C6578697374733E}{\isasymexists}}}-quantified variables:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymforall}p{\isachardot}\ {\isasymexists}q{\isachardot}\ swap\ p\ {\isacharequal}\ swap\ q{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}p{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}q{\isaliteral{2E}{\isachardot}}\ swap\ p\ {\isaliteral{3D}{\isacharequal}}\ swap\ q{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -365,12 +365,12 @@
To turn off this automatic splitting, disable the
responsible simplification rules:
\begin{center}
-\isa{{\isacharparenleft}{\isasymforall}x{\isachardot}\ P\ x{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isasymforall}a\ b{\isachardot}\ P\ {\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}{\isacharparenright}}
+\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}x{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}a\ b{\isaliteral{2E}{\isachardot}}\ P\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}}
\hfill
-(\isa{split{\isacharunderscore}paired{\isacharunderscore}All})\\
-\isa{{\isacharparenleft}{\isasymexists}x{\isachardot}\ P\ x{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isasymexists}a\ b{\isachardot}\ P\ {\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}{\isacharparenright}}
+(\isa{split{\isaliteral{5F}{\isacharunderscore}}paired{\isaliteral{5F}{\isacharunderscore}}All})\\
+\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ P\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}a\ b{\isaliteral{2E}{\isachardot}}\ P\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2C}{\isacharcomma}}\ b{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}}
\hfill
-(\isa{split{\isacharunderscore}paired{\isacharunderscore}Ex})
+(\isa{split{\isaliteral{5F}{\isacharunderscore}}paired{\isaliteral{5F}{\isacharunderscore}}Ex})
\end{center}%
\end{isamarkuptext}%
\isamarkuptrue%
--- a/doc-src/TutorialI/Types/document/Records.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Types/document/Records.tex Mon Nov 08 14:41:11 2010 +0100
@@ -57,9 +57,9 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{record}\isamarkupfalse%
-\ point\ {\isacharequal}\isanewline
-\ \ Xcoord\ {\isacharcolon}{\isacharcolon}\ int\isanewline
-\ \ Ycoord\ {\isacharcolon}{\isacharcolon}\ int%
+\ point\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\isanewline
+\ \ Ycoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int%
\begin{isamarkuptext}%
\noindent
Records of type \isa{point} have two fields named \isa{Xcoord}
@@ -68,19 +68,19 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{definition}\isamarkupfalse%
-\ pt{\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ point\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}pt{\isadigit{1}}\ {\isasymequiv}\ {\isacharparenleft}{\isacharbar}\ Xcoord\ {\isacharequal}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isacharcomma}\ Ycoord\ {\isacharequal}\ {\isadigit{2}}{\isadigit{3}}\ {\isacharbar}{\isacharparenright}{\isachardoublequoteclose}%
+\ pt{\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ point\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}pt{\isadigit{1}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{7C}{\isacharbar}}\ Xcoord\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{2}}{\isadigit{3}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
We see above the ASCII notation for record brackets. You can also
- use the symbolic brackets \isa{{\isasymlparr}} and \isa{{\isasymrparr}}. Record type
+ use the symbolic brackets \isa{{\isaliteral{5C3C6C706172723E}{\isasymlparr}}} and \isa{{\isaliteral{5C3C72706172723E}{\isasymrparr}}}. Record type
expressions can be also written directly with individual fields.
The type name above is merely an abbreviation.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{definition}\isamarkupfalse%
-\ pt{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharcolon}\ int{\isacharcomma}\ Ycoord\ {\isacharcolon}{\isacharcolon}\ int{\isasymrparr}{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}pt{\isadigit{2}}\ {\isasymequiv}\ {\isasymlparr}Xcoord\ {\isacharequal}\ {\isacharminus}{\isadigit{4}}{\isadigit{5}}{\isacharcomma}\ Ycoord\ {\isacharequal}\ {\isadigit{9}}{\isadigit{7}}{\isasymrparr}{\isachardoublequoteclose}%
+\ pt{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}pt{\isadigit{2}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{4}}{\isadigit{5}}{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{9}}{\isadigit{7}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
For each field, there is a \emph{selector}\index{selector!record}
function of the same name. For example, if \isa{p} has type \isa{point} then \isa{Xcoord\ p} denotes the value of the \isa{Xcoord} field of~\isa{p}. Expressions involving field selection
@@ -88,7 +88,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}Xcoord\ {\isasymlparr}Xcoord\ {\isacharequal}\ a{\isacharcomma}\ Ycoord\ {\isacharequal}\ b{\isasymrparr}\ {\isacharequal}\ a{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}Xcoord\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -106,13 +106,13 @@
%
\begin{isamarkuptext}%
The \emph{update}\index{update!record} operation is functional. For
- example, \isa{p{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ {\isadigit{0}}{\isasymrparr}} is a record whose \isa{Xcoord}
+ example, \isa{p{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}} is a record whose \isa{Xcoord}
value is zero and whose \isa{Ycoord} value is copied from~\isa{p}. Updates of explicit records are also simplified automatically:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isasymlparr}Xcoord\ {\isacharequal}\ a{\isacharcomma}\ Ycoord\ {\isacharequal}\ b{\isasymrparr}{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ {\isadigit{0}}{\isasymrparr}\ {\isacharequal}\isanewline
-\ \ \ \ \ \ \ \ \ {\isasymlparr}Xcoord\ {\isacharequal}\ {\isadigit{0}}{\isacharcomma}\ Ycoord\ {\isacharequal}\ b{\isasymrparr}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ \ \ \ \ \ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -149,11 +149,11 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ colour\ {\isacharequal}\ Red\ {\isacharbar}\ Green\ {\isacharbar}\ Blue\isanewline
+\ colour\ {\isaliteral{3D}{\isacharequal}}\ Red\ {\isaliteral{7C}{\isacharbar}}\ Green\ {\isaliteral{7C}{\isacharbar}}\ Blue\isanewline
\isanewline
\isacommand{record}\isamarkupfalse%
-\ cpoint\ {\isacharequal}\ point\ {\isacharplus}\isanewline
-\ \ col\ {\isacharcolon}{\isacharcolon}\ colour%
+\ cpoint\ {\isaliteral{3D}{\isacharequal}}\ point\ {\isaliteral{2B}{\isacharplus}}\isanewline
+\ \ col\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ colour%
\begin{isamarkuptext}%
\noindent
The fields of this new type are \isa{Xcoord}, \isa{Ycoord} and
@@ -161,22 +161,22 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{definition}\isamarkupfalse%
-\ cpt{\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ cpoint\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}cpt{\isadigit{1}}\ {\isasymequiv}\ {\isasymlparr}Xcoord\ {\isacharequal}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isacharcomma}\ Ycoord\ {\isacharequal}\ {\isadigit{2}}{\isadigit{3}}{\isacharcomma}\ col\ {\isacharequal}\ Green{\isasymrparr}{\isachardoublequoteclose}%
+\ cpt{\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ cpoint\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}cpt{\isadigit{1}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{2}}{\isadigit{3}}{\isaliteral{2C}{\isacharcomma}}\ col\ {\isaliteral{3D}{\isacharequal}}\ Green{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
We can define generic operations that work on arbitrary
instances of a record scheme, e.g.\ covering \isa{point}, \isa{cpoint}, and any further extensions. Every record structure has an
implicit pseudo-field, \cdx{more}, that keeps the extension as an
explicit value. Its type is declared as completely
- polymorphic:~\isa{{\isacharprime}a}. When a fixed record value is expressed
+ polymorphic:~\isa{{\isaliteral{27}{\isacharprime}}a}. When a fixed record value is expressed
using just its standard fields, the value of \isa{more} is
- implicitly set to \isa{{\isacharparenleft}{\isacharparenright}}, the empty tuple, which has type
+ implicitly set to \isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}}, the empty tuple, which has type
\isa{unit}. Within the record brackets, you can refer to the
- \isa{more} field by writing ``\isa{{\isasymdots}}'' (three dots):%
+ \isa{more} field by writing ``\isa{{\isaliteral{5C3C646F74733E}{\isasymdots}}}'' (three dots):%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}Xcoord\ {\isasymlparr}Xcoord\ {\isacharequal}\ a{\isacharcomma}\ Ycoord\ {\isacharequal}\ b{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ p{\isasymrparr}\ {\isacharequal}\ a{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}Xcoord\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ p{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -193,7 +193,7 @@
\endisadelimproof
%
\begin{isamarkuptext}%
-This lemma applies to any record whose first two fields are \isa{Xcoord} and~\isa{Ycoord}. Note that \isa{{\isasymlparr}Xcoord\ {\isacharequal}\ a{\isacharcomma}\ Ycoord\ {\isacharequal}\ b{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ {\isacharparenleft}{\isacharparenright}{\isasymrparr}} is exactly the same as \isa{{\isasymlparr}Xcoord\ {\isacharequal}\ a{\isacharcomma}\ Ycoord\ {\isacharequal}\ b{\isasymrparr}}. Selectors and updates are always polymorphic wrt.\ the
+This lemma applies to any record whose first two fields are \isa{Xcoord} and~\isa{Ycoord}. Note that \isa{{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}} is exactly the same as \isa{{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}}. Selectors and updates are always polymorphic wrt.\ the
\isa{more} part of a record scheme, its value is just ignored (for
select) or copied (for update).
@@ -202,7 +202,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}point{\isachardot}more\ cpt{\isadigit{1}}\ {\isacharequal}\ {\isasymlparr}col\ {\isacharequal}\ Green{\isasymrparr}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}point{\isaliteral{2E}{\isachardot}}more\ cpt{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}col\ {\isaliteral{3D}{\isacharequal}}\ Green{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -210,7 +210,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ cpt{\isadigit{1}}{\isacharunderscore}def{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ cpt{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -221,7 +221,7 @@
\begin{isamarkuptext}%
\noindent
We see that the colour part attached to this \isa{point} is a
- rudimentary record in its own right, namely \isa{{\isasymlparr}col\ {\isacharequal}\ Green{\isasymrparr}}. In order to select or update \isa{col}, this fragment
+ rudimentary record in its own right, namely \isa{{\isaliteral{5C3C6C706172723E}{\isasymlparr}}col\ {\isaliteral{3D}{\isacharequal}}\ Green{\isaliteral{5C3C72706172723E}{\isasymrparr}}}. In order to select or update \isa{col}, this fragment
needs to be put back into the context of the parent type scheme, say
as \isa{more} part of another \isa{point}.
@@ -231,26 +231,26 @@
\medskip
\begin{tabular}{l}
- \isa{point}~\isa{{\isacharequal}}~\isa{{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharcolon}\ int{\isacharcomma}\ Ycoord\ {\isacharcolon}{\isacharcolon}\ int{\isasymrparr}} \\
- \isa{{\isacharprime}a\ point{\isacharunderscore}scheme}~\isa{{\isacharequal}}~\isa{{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharcolon}\ int{\isacharcomma}\ Ycoord\ {\isacharcolon}{\isacharcolon}\ int{\isacharcomma}\ {\isasymdots}\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a{\isasymrparr}} \\
+ \isa{point}~\isa{{\isaliteral{3D}{\isacharequal}}}~\isa{{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{5C3C72706172723E}{\isasymrparr}}} \\
+ \isa{{\isaliteral{27}{\isacharprime}}a\ point{\isaliteral{5F}{\isacharunderscore}}scheme}~\isa{{\isaliteral{3D}{\isacharequal}}}~\isa{{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{27}{\isacharprime}}a{\isaliteral{5C3C72706172723E}{\isasymrparr}}} \\
\end{tabular}
\medskip
\noindent
Type \isa{point} is for fixed records having exactly the two fields
- \isa{Xcoord} and~\isa{Ycoord}, while the polymorphic type \isa{{\isacharprime}a\ point{\isacharunderscore}scheme} comprises all possible extensions to those two
- fields. Note that \isa{unit\ point{\isacharunderscore}scheme} coincides with \isa{point}, and \isa{{\isasymlparr}col\ {\isacharcolon}{\isacharcolon}\ colour{\isasymrparr}\ point{\isacharunderscore}scheme} with \isa{cpoint}.
+ \isa{Xcoord} and~\isa{Ycoord}, while the polymorphic type \isa{{\isaliteral{27}{\isacharprime}}a\ point{\isaliteral{5F}{\isacharunderscore}}scheme} comprises all possible extensions to those two
+ fields. Note that \isa{unit\ point{\isaliteral{5F}{\isacharunderscore}}scheme} coincides with \isa{point}, and \isa{{\isaliteral{5C3C6C706172723E}{\isasymlparr}}col\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ colour{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ point{\isaliteral{5F}{\isacharunderscore}}scheme} with \isa{cpoint}.
In the following example we define two operations --- methods, if we
regard records as objects --- to get and set any point's \isa{Xcoord} field.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{definition}\isamarkupfalse%
-\ getX\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ point{\isacharunderscore}scheme\ {\isasymRightarrow}\ int{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}getX\ r\ {\isasymequiv}\ Xcoord\ r{\isachardoublequoteclose}\isanewline
+\ getX\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ point{\isaliteral{5F}{\isacharunderscore}}scheme\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}getX\ r\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ Xcoord\ r{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isacommand{definition}\isamarkupfalse%
-\ setX\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ point{\isacharunderscore}scheme\ {\isasymRightarrow}\ int\ {\isasymRightarrow}\ {\isacharprime}a\ point{\isacharunderscore}scheme{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}setX\ r\ a\ {\isasymequiv}\ r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}{\isachardoublequoteclose}%
+\ setX\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ point{\isaliteral{5F}{\isacharunderscore}}scheme\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ point{\isaliteral{5F}{\isacharunderscore}}scheme{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}setX\ r\ a\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
Here is a generic method that modifies a point, incrementing its
\isa{Xcoord} field. The \isa{Ycoord} and \isa{more} fields
@@ -259,16 +259,16 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{definition}\isamarkupfalse%
-\ incX\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ point{\isacharunderscore}scheme\ {\isasymRightarrow}\ {\isacharprime}a\ point{\isacharunderscore}scheme{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}incX\ r\ {\isasymequiv}\isanewline
-\ \ {\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ r\ {\isacharplus}\ {\isadigit{1}}{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ r{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ point{\isachardot}more\ r{\isasymrparr}{\isachardoublequoteclose}%
+\ incX\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{27}{\isacharprime}}a\ point{\isaliteral{5F}{\isacharunderscore}}scheme\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ {\isaliteral{27}{\isacharprime}}a\ point{\isaliteral{5F}{\isacharunderscore}}scheme{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}incX\ r\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\isanewline
+\ \ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ r\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord\ r{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ point{\isaliteral{2E}{\isachardot}}more\ r{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
Generic theorems can be proved about generic methods. This trivial
lemma relates \isa{incX} to \isa{getX} and \isa{setX}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}incX\ r\ {\isacharequal}\ setX\ r\ {\isacharparenleft}getX\ r\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}incX\ r\ {\isaliteral{3D}{\isacharequal}}\ setX\ r\ {\isaliteral{28}{\isacharparenleft}}getX\ r\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -276,7 +276,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ getX{\isacharunderscore}def\ setX{\isacharunderscore}def\ incX{\isacharunderscore}def{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ getX{\isaliteral{5F}{\isacharunderscore}}def\ setX{\isaliteral{5F}{\isacharunderscore}}def\ incX{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -286,9 +286,9 @@
%
\begin{isamarkuptext}%
\begin{warn}
- If you use the symbolic record brackets \isa{{\isasymlparr}} and \isa{{\isasymrparr}},
- then you must also use the symbolic ellipsis, ``\isa{{\isasymdots}}'', rather
- than three consecutive periods, ``\isa{{\isachardot}{\isachardot}{\isachardot}}''. Mixing the ASCII
+ If you use the symbolic record brackets \isa{{\isaliteral{5C3C6C706172723E}{\isasymlparr}}} and \isa{{\isaliteral{5C3C72706172723E}{\isasymrparr}}},
+ then you must also use the symbolic ellipsis, ``\isa{{\isaliteral{5C3C646F74733E}{\isasymdots}}}'', rather
+ than three consecutive periods, ``\isa{{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}}''. Mixing the ASCII
and symbolic versions causes a syntax error. (The two versions are
more distinct on screen than they are on paper.)
\end{warn}%
@@ -307,8 +307,8 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isacharparenleft}{\isasymlparr}Xcoord\ {\isacharequal}\ a{\isacharcomma}\ Ycoord\ {\isacharequal}\ b{\isasymrparr}\ {\isacharequal}\ {\isasymlparr}Xcoord\ {\isacharequal}\ a{\isacharprime}{\isacharcomma}\ Ycoord\ {\isacharequal}\ b{\isacharprime}{\isasymrparr}{\isacharparenright}\ {\isacharequal}\isanewline
-\ \ \ \ {\isacharparenleft}a\ {\isacharequal}\ a{\isacharprime}\ {\isasymand}\ b\ {\isacharequal}\ b{\isacharprime}{\isacharparenright}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
+\ \ \ \ {\isaliteral{28}{\isacharparenleft}}a\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ b\ {\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -326,11 +326,11 @@
%
\begin{isamarkuptext}%
The following equality is similar, but generic, in that \isa{r}
- can be any instance of \isa{{\isacharprime}a\ point{\isacharunderscore}scheme}:%
+ can be any instance of \isa{{\isaliteral{27}{\isacharprime}}a\ point{\isaliteral{5F}{\isacharunderscore}}scheme}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isacharcomma}\ Ycoord\ {\isacharcolon}{\isacharequal}\ b{\isasymrparr}\ {\isacharequal}\ r{\isasymlparr}Ycoord\ {\isacharcolon}{\isacharequal}\ b{\isacharcomma}\ Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\ r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Ycoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{2C}{\isacharcomma}}\ Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -349,7 +349,7 @@
\begin{isamarkuptext}%
\noindent
We see above the syntax for iterated updates. We could equivalently
- have written the left-hand side as \isa{r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}{\isasymlparr}Ycoord\ {\isacharcolon}{\isacharequal}\ b{\isasymrparr}}.
+ have written the left-hand side as \isa{r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Ycoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ b{\isaliteral{5C3C72706172723E}{\isasymrparr}}}.
Record equality is \emph{extensional}:
\index{extensionality!for records} a record is determined entirely
@@ -357,7 +357,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}r\ {\isacharequal}\ {\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ r{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ r{\isasymrparr}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}r\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ r{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord\ r{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -380,7 +380,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}r\ {\isacharequal}\ {\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ r{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ r{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ point{\isachardot}more\ r{\isasymrparr}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}r\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ r{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord\ r{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ point{\isaliteral{2E}{\isachardot}}more\ r{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -403,7 +403,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}\ {\isacharequal}\ r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isacharprime}{\isasymrparr}\ {\isasymLongrightarrow}\ a\ {\isacharequal}\ a{\isacharprime}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\ r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -411,7 +411,7 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ simp{\isacharquery}\isanewline
+\ simp{\isaliteral{3F}{\isacharquery}}\isanewline
\ \ \isacommand{oops}\isamarkupfalse%
%
\endisatagproof
@@ -430,7 +430,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}\ {\isacharequal}\ r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isacharprime}{\isasymrparr}\ {\isasymLongrightarrow}\ a\ {\isacharequal}\ a{\isacharprime}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\ r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -438,10 +438,10 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}drule{\isacharunderscore}tac\ f\ {\isacharequal}\ Xcoord\ \isakeyword{in}\ arg{\isacharunderscore}cong{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}drule{\isaliteral{5F}{\isacharunderscore}}tac\ f\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ \isakeyword{in}\ arg{\isaliteral{5F}{\isacharunderscore}}cong{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ Xcoord\ {\isacharparenleft}r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}{\isacharparenright}\ {\isacharequal}\ Xcoord\ {\isacharparenleft}r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isacharprime}{\isasymrparr}{\isacharparenright}\ {\isasymLongrightarrow}\ a\ {\isacharequal}\ a{\isacharprime}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ Xcoord\ {\isaliteral{28}{\isacharparenleft}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ {\isaliteral{28}{\isacharparenleft}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}%
\end{isabelle}
Now, \isa{simp} will reduce the assumption to the desired
conclusion.%
@@ -464,7 +464,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}\ {\isacharequal}\ r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isacharprime}{\isasymrparr}\ {\isasymLongrightarrow}\ a\ {\isacharequal}\ a{\isacharprime}{\isachardoublequoteclose}%
+\ {\isaliteral{22}{\isachardoublequoteopen}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\ r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -479,13 +479,13 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\ \ \isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}cases\ r{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}cases\ r{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}Xcoord\ Ycoord\ more{\isachardot}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymlbrakk}r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}\ {\isacharequal}\ r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isacharprime}{\isasymrparr}{\isacharsemicolon}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ \ }r\ {\isacharequal}\ {\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ more{\isasymrparr}{\isasymrbrakk}\isanewline
-\isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymLongrightarrow}\ a\ {\isacharequal}\ a{\isacharprime}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}Xcoord\ Ycoord\ more{\isaliteral{2E}{\isachardot}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{5C3C72706172723E}{\isasymrparr}}\ {\isaliteral{3D}{\isacharequal}}\ r{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ \ }r\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ more{\isaliteral{5C3C72706172723E}{\isasymrparr}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\isanewline
+\isaindent{\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ \ \ \ }{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ a\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{27}{\isacharprime}}%
\end{isabelle} Again, \isa{simp} finishes the proof. Because \isa{r} is now represented as
an explicit record construction, the updates can be applied and the
record equality can be replaced by equality of the corresponding
@@ -506,9 +506,9 @@
\begin{isamarkuptext}%
The generic cases method does not admit references to locally bound
parameters of a goal. In longer proof scripts one might have to
- fall back on the primitive \isa{rule{\isacharunderscore}tac} used together with the
+ fall back on the primitive \isa{rule{\isaliteral{5F}{\isacharunderscore}}tac} used together with the
internal field representation rules of records. The above use of
- \isa{{\isacharparenleft}cases\ r{\isacharparenright}} would become \isa{{\isacharparenleft}rule{\isacharunderscore}tac\ r\ {\isacharequal}\ r\ in\ point{\isachardot}cases{\isacharunderscore}scheme{\isacharparenright}}.%
+ \isa{{\isaliteral{28}{\isacharparenleft}}cases\ r{\isaliteral{29}{\isacharparenright}}} would become \isa{{\isaliteral{28}{\isacharparenleft}}rule{\isaliteral{5F}{\isacharunderscore}}tac\ r\ {\isaliteral{3D}{\isacharequal}}\ r\ in\ point{\isaliteral{2E}{\isachardot}}cases{\isaliteral{5F}{\isacharunderscore}}scheme{\isaliteral{29}{\isacharparenright}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -543,37 +543,37 @@
These functions provide useful abbreviations for standard
record expressions involving constructors and selectors. The
definitions, which are \emph{not} unfolded by default, are made
- available by the collective name of \isa{defs} (\isa{point{\isachardot}defs}, \isa{cpoint{\isachardot}defs}, etc.).
+ available by the collective name of \isa{defs} (\isa{point{\isaliteral{2E}{\isachardot}}defs}, \isa{cpoint{\isaliteral{2E}{\isachardot}}defs}, etc.).
For example, here are the versions of those functions generated for
- record \isa{point}. We omit \isa{point{\isachardot}fields}, which happens to
- be the same as \isa{point{\isachardot}make}.
+ record \isa{point}. We omit \isa{point{\isaliteral{2E}{\isachardot}}fields}, which happens to
+ be the same as \isa{point{\isaliteral{2E}{\isachardot}}make}.
\begin{isabelle}%
-point{\isachardot}make\ Xcoord\ Ycoord\ {\isasymequiv}\ {\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord{\isasymrparr}\isasep\isanewline%
-point{\isachardot}extend\ r\ more\ {\isasymequiv}\isanewline
-{\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ r{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ r{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ more{\isasymrparr}\isasep\isanewline%
-point{\isachardot}truncate\ r\ {\isasymequiv}\ {\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ r{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ r{\isasymrparr}%
+point{\isaliteral{2E}{\isachardot}}make\ Xcoord\ Ycoord\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord{\isaliteral{5C3C72706172723E}{\isasymrparr}}\isasep\isanewline%
+point{\isaliteral{2E}{\isachardot}}extend\ r\ more\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\isanewline
+{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ r{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord\ r{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ more{\isaliteral{5C3C72706172723E}{\isasymrparr}}\isasep\isanewline%
+point{\isaliteral{2E}{\isachardot}}truncate\ r\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ r{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord\ r{\isaliteral{5C3C72706172723E}{\isasymrparr}}%
\end{isabelle}
- Contrast those with the corresponding functions for record \isa{cpoint}. Observe \isa{cpoint{\isachardot}fields} in particular.
+ Contrast those with the corresponding functions for record \isa{cpoint}. Observe \isa{cpoint{\isaliteral{2E}{\isachardot}}fields} in particular.
\begin{isabelle}%
-cpoint{\isachardot}make\ Xcoord\ Ycoord\ col\ {\isasymequiv}\isanewline
-{\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord{\isacharcomma}\ col\ {\isacharequal}\ col{\isasymrparr}\isasep\isanewline%
-cpoint{\isachardot}fields\ col\ {\isasymequiv}\ {\isasymlparr}col\ {\isacharequal}\ col{\isasymrparr}\isasep\isanewline%
-cpoint{\isachardot}extend\ r\ more\ {\isasymequiv}\isanewline
-{\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ r{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ r{\isacharcomma}\ col\ {\isacharequal}\ col\ r{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ more{\isasymrparr}\isasep\isanewline%
-cpoint{\isachardot}truncate\ r\ {\isasymequiv}\isanewline
-{\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord\ r{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord\ r{\isacharcomma}\ col\ {\isacharequal}\ col\ r{\isasymrparr}%
+cpoint{\isaliteral{2E}{\isachardot}}make\ Xcoord\ Ycoord\ col\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\isanewline
+{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord{\isaliteral{2C}{\isacharcomma}}\ col\ {\isaliteral{3D}{\isacharequal}}\ col{\isaliteral{5C3C72706172723E}{\isasymrparr}}\isasep\isanewline%
+cpoint{\isaliteral{2E}{\isachardot}}fields\ col\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{5C3C6C706172723E}{\isasymlparr}}col\ {\isaliteral{3D}{\isacharequal}}\ col{\isaliteral{5C3C72706172723E}{\isasymrparr}}\isasep\isanewline%
+cpoint{\isaliteral{2E}{\isachardot}}extend\ r\ more\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\isanewline
+{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ r{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord\ r{\isaliteral{2C}{\isacharcomma}}\ col\ {\isaliteral{3D}{\isacharequal}}\ col\ r{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ {\isaliteral{3D}{\isacharequal}}\ more{\isaliteral{5C3C72706172723E}{\isasymrparr}}\isasep\isanewline%
+cpoint{\isaliteral{2E}{\isachardot}}truncate\ r\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\isanewline
+{\isaliteral{5C3C6C706172723E}{\isasymlparr}}Xcoord\ {\isaliteral{3D}{\isacharequal}}\ Xcoord\ r{\isaliteral{2C}{\isacharcomma}}\ Ycoord\ {\isaliteral{3D}{\isacharequal}}\ Ycoord\ r{\isaliteral{2C}{\isacharcomma}}\ col\ {\isaliteral{3D}{\isacharequal}}\ col\ r{\isaliteral{5C3C72706172723E}{\isasymrparr}}%
\end{isabelle}
To demonstrate these functions, we declare a new coloured point by
- extending an ordinary point. Function \isa{point{\isachardot}extend} augments
+ extending an ordinary point. Function \isa{point{\isaliteral{2E}{\isachardot}}extend} augments
\isa{pt{\isadigit{1}}} with a colour value, which is converted into an
- appropriate record fragment by \isa{cpoint{\isachardot}fields}.%
+ appropriate record fragment by \isa{cpoint{\isaliteral{2E}{\isachardot}}fields}.%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{definition}\isamarkupfalse%
-\ cpt{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ cpoint\ \isakeyword{where}\isanewline
-{\isachardoublequoteopen}cpt{\isadigit{2}}\ {\isasymequiv}\ point{\isachardot}extend\ pt{\isadigit{1}}\ {\isacharparenleft}cpoint{\isachardot}fields\ Green{\isacharparenright}{\isachardoublequoteclose}%
+\ cpt{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ cpoint\ \isakeyword{where}\isanewline
+{\isaliteral{22}{\isachardoublequoteopen}}cpt{\isadigit{2}}\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ point{\isaliteral{2E}{\isachardot}}extend\ pt{\isadigit{1}}\ {\isaliteral{28}{\isacharparenleft}}cpoint{\isaliteral{2E}{\isachardot}}fields\ Green{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
The coloured points \isa{cpt{\isadigit{1}}} and \isa{cpt{\isadigit{2}}} are equal. The
proof is trivial, by unfolding all the definitions. We deliberately
@@ -582,7 +582,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}cpt{\isadigit{1}}\ {\isacharequal}\ cpt{\isadigit{2}}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}cpt{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ cpt{\isadigit{2}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -590,15 +590,15 @@
%
\isatagproof
\isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ cpt{\isadigit{1}}{\isacharunderscore}def\ cpt{\isadigit{2}}{\isacharunderscore}def\ point{\isachardot}defs\ cpoint{\isachardot}defs{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ cpt{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}def\ cpt{\isadigit{2}}{\isaliteral{5F}{\isacharunderscore}}def\ point{\isaliteral{2E}{\isachardot}}defs\ cpoint{\isaliteral{2E}{\isachardot}}defs{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ Xcoord\ pt{\isadigit{1}}\ {\isacharequal}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}\ {\isasymand}\ Ycoord\ pt{\isadigit{1}}\ {\isacharequal}\ {\isadigit{2}}{\isadigit{3}}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ Xcoord\ pt{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}\ {\isaliteral{5C3C616E643E}{\isasymand}}\ Ycoord\ pt{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{2}}{\isadigit{3}}%
\end{isabelle}%
\end{isamarkuptxt}%
\isamarkuptrue%
\ \ \isacommand{apply}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ pt{\isadigit{1}}{\isacharunderscore}def{\isacharparenright}\isanewline
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ pt{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\ \ \isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -614,7 +614,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}point{\isachardot}truncate\ cpt{\isadigit{2}}\ {\isacharequal}\ pt{\isadigit{1}}{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}point{\isaliteral{2E}{\isachardot}}truncate\ cpt{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ pt{\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
\ \ %
@@ -622,7 +622,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ pt{\isadigit{1}}{\isacharunderscore}def\ cpt{\isadigit{2}}{\isacharunderscore}def\ point{\isachardot}defs{\isacharparenright}%
+\ {\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ pt{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}def\ cpt{\isadigit{2}}{\isaliteral{5F}{\isacharunderscore}}def\ point{\isaliteral{2E}{\isachardot}}defs{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
--- a/doc-src/TutorialI/Types/document/Typedefs.tex Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/TutorialI/Types/document/Typedefs.tex Mon Nov 08 14:41:11 2010 +0100
@@ -22,7 +22,7 @@
\begin{isamarkuptext}%
\label{sec:adv-typedef}
For most applications, a combination of predefined types like \isa{bool} and
-\isa{{\isasymRightarrow}} with recursive datatypes and records is quite sufficient. Very
+\isa{{\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}} with recursive datatypes and records is quite sufficient. Very
occasionally you may feel the need for a more advanced type. If you
are certain that your type is not definable by any of the
standard means, then read on.
@@ -46,10 +46,10 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{typedecl}\isamarkupfalse%
-\ my{\isacharunderscore}new{\isacharunderscore}type%
+\ my{\isaliteral{5F}{\isacharunderscore}}new{\isaliteral{5F}{\isacharunderscore}}type%
\begin{isamarkuptext}%
\noindent
-This does not define \isa{my{\isacharunderscore}new{\isacharunderscore}type} at all but merely introduces its
+This does not define \isa{my{\isaliteral{5F}{\isacharunderscore}}new{\isaliteral{5F}{\isacharunderscore}}type} at all but merely introduces its
name. Thus we know nothing about this type, except that it is
non-empty. Such declarations without definitions are
useful if that type can be viewed as a parameter of the theory.
@@ -67,7 +67,7 @@
\isamarkuptrue%
\isacommand{axioms}\isamarkupfalse%
\isanewline
-just{\isacharunderscore}one{\isacharcolon}\ {\isachardoublequoteopen}{\isasymexists}x{\isacharcolon}{\isacharcolon}my{\isacharunderscore}new{\isacharunderscore}type{\isachardot}\ {\isasymforall}y{\isachardot}\ x\ {\isacharequal}\ y{\isachardoublequoteclose}%
+just{\isaliteral{5F}{\isacharunderscore}}one{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}my{\isaliteral{5F}{\isacharunderscore}}new{\isaliteral{5F}{\isacharunderscore}}type{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}y{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
\noindent
However, we strongly discourage this approach, except at explorative stages
@@ -99,7 +99,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{typedef}\isamarkupfalse%
-\ three\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isadigit{0}}{\isacharcolon}{\isacharcolon}nat{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isacharbraceright}{\isachardoublequoteclose}%
+\ three\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7B}{\isacharbraceleft}}{\isadigit{0}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -111,14 +111,14 @@
In order to enforce that the representing set on the right-hand side is
non-empty, this definition actually starts a proof to that effect:
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymexists}x{\isachardot}\ x\ {\isasymin}\ {\isacharbraceleft}{\isadigit{0}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isacharbraceright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6578697374733E}{\isasymexists}}x{\isaliteral{2E}{\isachardot}}\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ {\isaliteral{7B}{\isacharbraceleft}}{\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isaliteral{7D}{\isacharbraceright}}%
\end{isabelle}
Fortunately, this is easy enough to show, even \isa{auto} could do it.
In general, one has to provide a witness, in our case 0:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}rule{\isacharunderscore}tac\ x\ {\isacharequal}\ {\isadigit{0}}\ \isakeyword{in}\ exI{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}rule{\isaliteral{5F}{\isacharunderscore}}tac\ x\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\ \isakeyword{in}\ exI{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{by}\isamarkupfalse%
\ simp%
\endisatagproof
@@ -130,39 +130,39 @@
%
\begin{isamarkuptext}%
This type definition introduces the new type \isa{three} and asserts
-that it is a copy of the set \isa{{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isacharbraceright}}. This assertion
+that it is a copy of the set \isa{{\isaliteral{7B}{\isacharbraceleft}}{\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isaliteral{7D}{\isacharbraceright}}}. This assertion
is expressed via a bijection between the \emph{type} \isa{three} and the
-\emph{set} \isa{{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isacharbraceright}}. To this end, the command declares the following
+\emph{set} \isa{{\isaliteral{7B}{\isacharbraceleft}}{\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isaliteral{7D}{\isacharbraceright}}}. To this end, the command declares the following
constants behind the scenes:
\begin{center}
\begin{tabular}{rcl}
\isa{three} &::& \isa{nat\ set} \\
-\isa{Rep{\isacharunderscore}three} &::& \isa{three\ {\isasymRightarrow}\ nat}\\
-\isa{Abs{\isacharunderscore}three} &::& \isa{nat\ {\isasymRightarrow}\ three}
+\isa{Rep{\isaliteral{5F}{\isacharunderscore}}three} &::& \isa{three\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ nat}\\
+\isa{Abs{\isaliteral{5F}{\isacharunderscore}}three} &::& \isa{nat\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ three}
\end{tabular}
\end{center}
where constant \isa{three} is explicitly defined as the representing set:
\begin{center}
-\isa{three\ {\isasymequiv}\ {\isacharbraceleft}{\isadigit{0}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isacharbraceright}}\hfill(\isa{three{\isacharunderscore}def})
+\isa{three\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ {\isaliteral{7B}{\isacharbraceleft}}{\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isaliteral{7D}{\isacharbraceright}}}\hfill(\isa{three{\isaliteral{5F}{\isacharunderscore}}def})
\end{center}
The situation is best summarized with the help of the following diagram,
where squares denote types and the irregular region denotes a set:
\begin{center}
\includegraphics[scale=.8]{typedef}
\end{center}
-Finally, \isacommand{typedef} asserts that \isa{Rep{\isacharunderscore}three} is
-surjective on the subset \isa{three} and \isa{Abs{\isacharunderscore}three} and \isa{Rep{\isacharunderscore}three} are inverses of each other:
+Finally, \isacommand{typedef} asserts that \isa{Rep{\isaliteral{5F}{\isacharunderscore}}three} is
+surjective on the subset \isa{three} and \isa{Abs{\isaliteral{5F}{\isacharunderscore}}three} and \isa{Rep{\isaliteral{5F}{\isacharunderscore}}three} are inverses of each other:
\begin{center}
\begin{tabular}{@ {}r@ {\qquad\qquad}l@ {}}
-\isa{Rep{\isacharunderscore}three\ x\ {\isasymin}\ three} & (\isa{Rep{\isacharunderscore}three}) \\
-\isa{Abs{\isacharunderscore}three\ {\isacharparenleft}Rep{\isacharunderscore}three\ x{\isacharparenright}\ {\isacharequal}\ x} & (\isa{Rep{\isacharunderscore}three{\isacharunderscore}inverse}) \\
-\isa{y\ {\isasymin}\ three\ {\isasymLongrightarrow}\ Rep{\isacharunderscore}three\ {\isacharparenleft}Abs{\isacharunderscore}three\ y{\isacharparenright}\ {\isacharequal}\ y} & (\isa{Abs{\isacharunderscore}three{\isacharunderscore}inverse})
+\isa{Rep{\isaliteral{5F}{\isacharunderscore}}three\ x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ three} & (\isa{Rep{\isaliteral{5F}{\isacharunderscore}}three}) \\
+\isa{Abs{\isaliteral{5F}{\isacharunderscore}}three\ {\isaliteral{28}{\isacharparenleft}}Rep{\isaliteral{5F}{\isacharunderscore}}three\ x{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ x} & (\isa{Rep{\isaliteral{5F}{\isacharunderscore}}three{\isaliteral{5F}{\isacharunderscore}}inverse}) \\
+\isa{y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ three\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ Rep{\isaliteral{5F}{\isacharunderscore}}three\ {\isaliteral{28}{\isacharparenleft}}Abs{\isaliteral{5F}{\isacharunderscore}}three\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ y} & (\isa{Abs{\isaliteral{5F}{\isacharunderscore}}three{\isaliteral{5F}{\isacharunderscore}}inverse})
\end{tabular}
\end{center}
%
From this example it should be clear what \isacommand{typedef} does
in general given a name (here \isa{three}) and a set
-(here \isa{{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isacharbraceright}}).
+(here \isa{{\isaliteral{7B}{\isacharbraceleft}}{\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isaliteral{7D}{\isacharbraceright}}}).
Our next step is to define the basic functions expected on the new type.
Although this depends on the type at hand, the following strategy works well:
@@ -178,39 +178,39 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{definition}\isamarkupfalse%
-\ A\ {\isacharcolon}{\isacharcolon}\ three\ \isakeyword{where}\ {\isachardoublequoteopen}A\ {\isasymequiv}\ Abs{\isacharunderscore}three\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
+\ A\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ three\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ Abs{\isaliteral{5F}{\isacharunderscore}}three\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isacommand{definition}\isamarkupfalse%
-\ B\ {\isacharcolon}{\isacharcolon}\ three\ \isakeyword{where}\ {\isachardoublequoteopen}B\ {\isasymequiv}\ Abs{\isacharunderscore}three\ {\isadigit{1}}{\isachardoublequoteclose}\isanewline
+\ B\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ three\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}B\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ Abs{\isaliteral{5F}{\isacharunderscore}}three\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
\isacommand{definition}\isamarkupfalse%
-\ C\ {\isacharcolon}{\isacharcolon}\ three\ \isakeyword{where}\ {\isachardoublequoteopen}C\ {\isasymequiv}\ Abs{\isacharunderscore}three\ {\isadigit{2}}{\isachardoublequoteclose}%
+\ C\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ three\ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}C\ {\isaliteral{5C3C65717569763E}{\isasymequiv}}\ Abs{\isaliteral{5F}{\isacharunderscore}}three\ {\isadigit{2}}{\isaliteral{22}{\isachardoublequoteclose}}%
\begin{isamarkuptext}%
So far, everything was easy. But it is clear that reasoning about \isa{three} will be hell if we have to go back to \isa{nat} every time. Thus our
aim must be to raise our level of abstraction by deriving enough theorems
about type \isa{three} to characterize it completely. And those theorems
-should be phrased in terms of \isa{A}, \isa{B} and \isa{C}, not \isa{Abs{\isacharunderscore}three} and \isa{Rep{\isacharunderscore}three}. Because of the simplicity of the example,
+should be phrased in terms of \isa{A}, \isa{B} and \isa{C}, not \isa{Abs{\isaliteral{5F}{\isacharunderscore}}three} and \isa{Rep{\isaliteral{5F}{\isacharunderscore}}three}. Because of the simplicity of the example,
we merely need to prove that \isa{A}, \isa{B} and \isa{C} are distinct
and that they exhaust the type.
In processing our \isacommand{typedef} declaration,
Isabelle proves several helpful lemmas. The first two
-express injectivity of \isa{Rep{\isacharunderscore}three} and \isa{Abs{\isacharunderscore}three}:
+express injectivity of \isa{Rep{\isaliteral{5F}{\isacharunderscore}}three} and \isa{Abs{\isaliteral{5F}{\isacharunderscore}}three}:
\begin{center}
\begin{tabular}{@ {}r@ {\qquad}l@ {}}
-\isa{{\isacharparenleft}Rep{\isacharunderscore}three\ x\ {\isacharequal}\ Rep{\isacharunderscore}three\ y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}x\ {\isacharequal}\ y{\isacharparenright}} & (\isa{Rep{\isacharunderscore}three{\isacharunderscore}inject}) \\
+\isa{{\isaliteral{28}{\isacharparenleft}}Rep{\isaliteral{5F}{\isacharunderscore}}three\ x\ {\isaliteral{3D}{\isacharequal}}\ Rep{\isaliteral{5F}{\isacharunderscore}}three\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{29}{\isacharparenright}}} & (\isa{Rep{\isaliteral{5F}{\isacharunderscore}}three{\isaliteral{5F}{\isacharunderscore}}inject}) \\
\begin{tabular}{@ {}l@ {}}
-\isa{{\isasymlbrakk}x\ {\isasymin}\ three{\isacharsemicolon}\ y\ {\isasymin}\ three\ {\isasymrbrakk}} \\
-\isa{{\isasymLongrightarrow}\ {\isacharparenleft}Abs{\isacharunderscore}three\ x\ {\isacharequal}\ Abs{\isacharunderscore}three\ y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}x\ {\isacharequal}\ y{\isacharparenright}}
-\end{tabular} & (\isa{Abs{\isacharunderscore}three{\isacharunderscore}inject}) \\
+\isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}x\ {\isaliteral{5C3C696E3E}{\isasymin}}\ three{\isaliteral{3B}{\isacharsemicolon}}\ y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ three\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}} \\
+\isa{{\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ {\isaliteral{28}{\isacharparenleft}}Abs{\isaliteral{5F}{\isacharunderscore}}three\ x\ {\isaliteral{3D}{\isacharequal}}\ Abs{\isaliteral{5F}{\isacharunderscore}}three\ y{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3D}{\isacharequal}}\ y{\isaliteral{29}{\isacharparenright}}}
+\end{tabular} & (\isa{Abs{\isaliteral{5F}{\isacharunderscore}}three{\isaliteral{5F}{\isacharunderscore}}inject}) \\
\end{tabular}
\end{center}
-The following ones allow to replace some \isa{x{\isacharcolon}{\isacharcolon}three} by
-\isa{Abs{\isacharunderscore}three{\isacharparenleft}y{\isacharcolon}{\isacharcolon}nat{\isacharparenright}}, and conversely \isa{y} by \isa{Rep{\isacharunderscore}three\ x}:
+The following ones allow to replace some \isa{x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}three} by
+\isa{Abs{\isaliteral{5F}{\isacharunderscore}}three{\isaliteral{28}{\isacharparenleft}}y{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}nat{\isaliteral{29}{\isacharparenright}}}, and conversely \isa{y} by \isa{Rep{\isaliteral{5F}{\isacharunderscore}}three\ x}:
\begin{center}
\begin{tabular}{@ {}r@ {\qquad}l@ {}}
-\isa{{\isasymlbrakk}y\ {\isasymin}\ three{\isacharsemicolon}\ {\isasymAnd}x{\isachardot}\ y\ {\isacharequal}\ Rep{\isacharunderscore}three\ x\ {\isasymLongrightarrow}\ P{\isasymrbrakk}\ {\isasymLongrightarrow}\ P} & (\isa{Rep{\isacharunderscore}three{\isacharunderscore}cases}) \\
-\isa{{\isacharparenleft}{\isasymAnd}y{\isachardot}\ {\isasymlbrakk}x\ {\isacharequal}\ Abs{\isacharunderscore}three\ y{\isacharsemicolon}\ y\ {\isasymin}\ three{\isasymrbrakk}\ {\isasymLongrightarrow}\ P{\isacharparenright}\ {\isasymLongrightarrow}\ P} & (\isa{Abs{\isacharunderscore}three{\isacharunderscore}cases}) \\
-\isa{{\isasymlbrakk}y\ {\isasymin}\ three{\isacharsemicolon}\ {\isasymAnd}x{\isachardot}\ P\ {\isacharparenleft}Rep{\isacharunderscore}three\ x{\isacharparenright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ y} & (\isa{Rep{\isacharunderscore}three{\isacharunderscore}induct}) \\
-\isa{{\isacharparenleft}{\isasymAnd}y{\isachardot}\ y\ {\isasymin}\ three\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}Abs{\isacharunderscore}three\ y{\isacharparenright}{\isacharparenright}\ {\isasymLongrightarrow}\ P\ x} & (\isa{Abs{\isacharunderscore}three{\isacharunderscore}induct}) \\
+\isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ three{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ y\ {\isaliteral{3D}{\isacharequal}}\ Rep{\isaliteral{5F}{\isacharunderscore}}three\ x\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P} & (\isa{Rep{\isaliteral{5F}{\isacharunderscore}}three{\isaliteral{5F}{\isacharunderscore}}cases}) \\
+\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}y{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}x\ {\isaliteral{3D}{\isacharequal}}\ Abs{\isaliteral{5F}{\isacharunderscore}}three\ y{\isaliteral{3B}{\isacharsemicolon}}\ y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ three{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P} & (\isa{Abs{\isaliteral{5F}{\isacharunderscore}}three{\isaliteral{5F}{\isacharunderscore}}cases}) \\
+\isa{{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ three{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}x{\isaliteral{2E}{\isachardot}}\ P\ {\isaliteral{28}{\isacharparenleft}}Rep{\isaliteral{5F}{\isacharunderscore}}three\ x{\isaliteral{29}{\isacharparenright}}{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ y} & (\isa{Rep{\isaliteral{5F}{\isacharunderscore}}three{\isaliteral{5F}{\isacharunderscore}}induct}) \\
+\isa{{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C416E643E}{\isasymAnd}}y{\isaliteral{2E}{\isachardot}}\ y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ three\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ {\isaliteral{28}{\isacharparenleft}}Abs{\isaliteral{5F}{\isacharunderscore}}three\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ x} & (\isa{Abs{\isaliteral{5F}{\isacharunderscore}}three{\isaliteral{5F}{\isacharunderscore}}induct}) \\
\end{tabular}
\end{center}
These theorems are proved for any type definition, with \isa{three}
@@ -218,11 +218,11 @@
Distinctness of \isa{A}, \isa{B} and \isa{C} follows immediately
if we expand their definitions and rewrite with the injectivity
-of \isa{Abs{\isacharunderscore}three}:%
+of \isa{Abs{\isaliteral{5F}{\isacharunderscore}}three}:%
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ {\isachardoublequoteopen}A\ {\isasymnoteq}\ B\ {\isasymand}\ B\ {\isasymnoteq}\ A\ {\isasymand}\ A\ {\isasymnoteq}\ C\ {\isasymand}\ C\ {\isasymnoteq}\ A\ {\isasymand}\ B\ {\isasymnoteq}\ C\ {\isasymand}\ C\ {\isasymnoteq}\ B{\isachardoublequoteclose}\isanewline
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ B\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ A\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ C\ {\isaliteral{5C3C616E643E}{\isasymand}}\ C\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ A\ {\isaliteral{5C3C616E643E}{\isasymand}}\ B\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ C\ {\isaliteral{5C3C616E643E}{\isasymand}}\ C\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ B{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
%
\isadelimproof
%
@@ -230,7 +230,7 @@
%
\isatagproof
\isacommand{by}\isamarkupfalse%
-{\isacharparenleft}simp\ add{\isacharcolon}\ Abs{\isacharunderscore}three{\isacharunderscore}inject\ A{\isacharunderscore}def\ B{\isacharunderscore}def\ C{\isacharunderscore}def\ three{\isacharunderscore}def{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}simp\ add{\isaliteral{3A}{\isacharcolon}}\ Abs{\isaliteral{5F}{\isacharunderscore}}three{\isaliteral{5F}{\isacharunderscore}}inject\ A{\isaliteral{5F}{\isacharunderscore}}def\ B{\isaliteral{5F}{\isacharunderscore}}def\ C{\isaliteral{5F}{\isacharunderscore}}def\ three{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}%
\endisatagproof
{\isafoldproof}%
%
@@ -240,7 +240,7 @@
%
\begin{isamarkuptext}%
\noindent
-Of course we rely on the simplifier to solve goals like \isa{{\isadigit{0}}\ {\isasymnoteq}\ {\isadigit{1}}}.
+Of course we rely on the simplifier to solve goals like \isa{{\isadigit{0}}\ {\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}\ {\isadigit{1}}}.
The fact that \isa{A}, \isa{B} and \isa{C} exhaust type \isa{three} is
best phrased as a case distinction theorem: if you want to prove \isa{P\ x}
@@ -249,7 +249,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{lemma}\isamarkupfalse%
-\ three{\isacharunderscore}cases{\isacharcolon}\ {\isachardoublequoteopen}{\isasymlbrakk}\ P\ A{\isacharsemicolon}\ P\ B{\isacharsemicolon}\ P\ C\ {\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ x{\isachardoublequoteclose}%
+\ three{\isaliteral{5F}{\isacharunderscore}}cases{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}\ P\ A{\isaliteral{3B}{\isacharsemicolon}}\ P\ B{\isaliteral{3B}{\isacharsemicolon}}\ P\ C\ {\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ x{\isaliteral{22}{\isachardoublequoteclose}}%
\isadelimproof
%
\endisadelimproof
@@ -261,17 +261,17 @@
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}induct{\isacharunderscore}tac\ x{\isacharparenright}%
+{\isaliteral{28}{\isacharparenleft}}induct{\isaliteral{5F}{\isacharunderscore}}tac\ x{\isaliteral{29}{\isacharparenright}}%
\begin{isamarkuptxt}%
\begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}y{\isachardot}\ {\isasymlbrakk}P\ A{\isacharsemicolon}\ P\ B{\isacharsemicolon}\ P\ C{\isacharsemicolon}\ y\ {\isasymin}\ three{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}Abs{\isacharunderscore}three\ y{\isacharparenright}%
+\ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C416E643E}{\isasymAnd}}y{\isaliteral{2E}{\isachardot}}\ {\isaliteral{5C3C6C6272616B6B3E}{\isasymlbrakk}}P\ A{\isaliteral{3B}{\isacharsemicolon}}\ P\ B{\isaliteral{3B}{\isacharsemicolon}}\ P\ C{\isaliteral{3B}{\isacharsemicolon}}\ y\ {\isaliteral{5C3C696E3E}{\isasymin}}\ three{\isaliteral{5C3C726272616B6B3E}{\isasymrbrakk}}\ {\isaliteral{5C3C4C6F6E6772696768746172726F773E}{\isasymLongrightarrow}}\ P\ {\isaliteral{28}{\isacharparenleft}}Abs{\isaliteral{5F}{\isacharunderscore}}three\ y{\isaliteral{29}{\isacharparenright}}%
\end{isabelle}
-Simplification with \isa{three{\isacharunderscore}def} leads to the disjunction \isa{y\ {\isacharequal}\ {\isadigit{0}}\ {\isasymor}\ y\ {\isacharequal}\ {\isadigit{1}}\ {\isasymor}\ y\ {\isacharequal}\ {\isadigit{2}}} which \isa{auto} separates into three
+Simplification with \isa{three{\isaliteral{5F}{\isacharunderscore}}def} leads to the disjunction \isa{y\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ y\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}\ {\isaliteral{5C3C6F723E}{\isasymor}}\ y\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{2}}} which \isa{auto} separates into three
subgoals, each of which is easily solved by simplification:%
\end{isamarkuptxt}%
\isamarkuptrue%
\isacommand{apply}\isamarkupfalse%
-{\isacharparenleft}auto\ simp\ add{\isacharcolon}\ three{\isacharunderscore}def\ A{\isacharunderscore}def\ B{\isacharunderscore}def\ C{\isacharunderscore}def{\isacharparenright}\isanewline
+{\isaliteral{28}{\isacharparenleft}}auto\ simp\ add{\isaliteral{3A}{\isacharcolon}}\ three{\isaliteral{5F}{\isacharunderscore}}def\ A{\isaliteral{5F}{\isacharunderscore}}def\ B{\isaliteral{5F}{\isacharunderscore}}def\ C{\isaliteral{5F}{\isacharunderscore}}def{\isaliteral{29}{\isacharparenright}}\isanewline
\isacommand{done}\isamarkupfalse%
%
\endisatagproof
@@ -291,7 +291,7 @@
\end{isamarkuptext}%
\isamarkuptrue%
\isacommand{datatype}\isamarkupfalse%
-\ better{\isacharunderscore}three\ {\isacharequal}\ A\ {\isacharbar}\ B\ {\isacharbar}\ C%
+\ better{\isaliteral{5F}{\isacharunderscore}}three\ {\isaliteral{3D}{\isacharequal}}\ A\ {\isaliteral{7C}{\isacharbar}}\ B\ {\isaliteral{7C}{\isacharbar}}\ C%
\begin{isamarkuptext}%
\noindent
In fact, the \isacommand{datatype} command performs internally more or less
--- a/doc-src/isabelle.sty Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/isabelle.sty Mon Nov 08 14:41:11 2010 +0100
@@ -95,6 +95,9 @@
\def\isacharverbatimclose{\isacharasterisk\isacharbraceright}%
}
+\newcommand{\isaliteral}[2]{#2}
+\newcommand{\isanil}{}
+
% keyword and section markup
@@ -146,9 +149,9 @@
\renewcommand{\isastylescript}{\footnotesize\it}%
\renewcommand{\isacharunderscorekeyword}{\mbox{-}}%
\renewcommand{\isacharbang}{\isamath{!}}%
-\renewcommand{\isachardoublequote}{}%
-\renewcommand{\isachardoublequoteopen}{}%
-\renewcommand{\isachardoublequoteclose}{}%
+\renewcommand{\isachardoublequote}{\isanil}%
+\renewcommand{\isachardoublequoteopen}{\isanil}%
+\renewcommand{\isachardoublequoteclose}{\isanil}%
\renewcommand{\isacharhash}{\isamath{\#}}%
\renewcommand{\isachardollar}{\isamath{\$}}%
\renewcommand{\isacharpercent}{\isamath{\%}}%
--- a/doc-src/isabellesym.sty Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/isabellesym.sty Mon Nov 08 14:41:11 2010 +0100
@@ -1,5 +1,3 @@
-%%
-%%
%%
%% definitions of standard Isabelle symbols
%%
@@ -251,7 +249,7 @@
\newcommand{\isasymsqunion}{\isamath{\sqcup}}
\newcommand{\isasymSqunion}{\isamath{\bigsqcup\,}}
\newcommand{\isasymsqinter}{\isamath{\sqcap}}
-\newcommand{\isasymSqinter}{\isamath{\bigsqcap\,}} %requires amsmath
+\newcommand{\isasymSqinter}{\isamath{\bigsqcap\,}} %requires stmaryrd
\newcommand{\isasymsetminus}{\isamath{\setminus}}
\newcommand{\isasympropto}{\isamath{\propto}}
\newcommand{\isasymuplus}{\isamath{\uplus}}
--- a/doc-src/pdfsetup.sty Mon Nov 08 14:33:54 2010 +0100
+++ b/doc-src/pdfsetup.sty Mon Nov 08 14:41:11 2010 +0100
@@ -13,5 +13,11 @@
\gdef\bold#1{\textbf{\hyperpage{#1}}}
\urlstyle{rm}
+\ifpdf\relax\else\renewcommand{\url}[1]{\nolinkurl{#1}}\fi
-\ifpdf\relax\else\renewcommand{\url}[1]{\nolinkurl{#1}}\fi
+\ifpdf
+\ifnum\pdfminorversion<5\pdfminorversion=5\fi
+\renewcommand{\isaliteral}[2]{%
+\pdfliteral direct{/Span <</ActualText<#1>>> BDC}#2\pdfliteral direct{EMC}}
+\renewcommand{\isanil}{{\color{white}.}}
+\fi
--- a/etc/isar-keywords-ZF.el Mon Nov 08 14:33:54 2010 +0100
+++ b/etc/isar-keywords-ZF.el Mon Nov 08 14:41:11 2010 +0100
@@ -258,6 +258,8 @@
"ProofGeneral\\.restart"
"ProofGeneral\\.undo"
"cannot_undo"
+ "cd"
+ "commit"
"disable_pr"
"enable_pr"
"exit"
@@ -275,9 +277,7 @@
'("ML_command"
"ML_val"
"ProofGeneral\\.pr"
- "cd"
"class_deps"
- "commit"
"display_drafts"
"find_consts"
"find_theorems"
--- a/etc/isar-keywords.el Mon Nov 08 14:33:54 2010 +0100
+++ b/etc/isar-keywords.el Mon Nov 08 14:41:11 2010 +0100
@@ -323,6 +323,8 @@
"ProofGeneral\\.restart"
"ProofGeneral\\.undo"
"cannot_undo"
+ "cd"
+ "commit"
"disable_pr"
"enable_pr"
"exit"
@@ -341,11 +343,9 @@
"ML_val"
"ProofGeneral\\.pr"
"boogie_status"
- "cd"
"class_deps"
"code_deps"
"code_thms"
- "commit"
"display_drafts"
"export_code"
"find_consts"
--- a/lib/texinputs/isabelle.sty Mon Nov 08 14:33:54 2010 +0100
+++ b/lib/texinputs/isabelle.sty Mon Nov 08 14:41:11 2010 +0100
@@ -95,6 +95,9 @@
\def\isacharverbatimclose{\isacharasterisk\isacharbraceright}%
}
+\newcommand{\isaliteral}[2]{#2}
+\newcommand{\isanil}{}
+
% keyword and section markup
@@ -146,9 +149,9 @@
\renewcommand{\isastylescript}{\footnotesize\it}%
\renewcommand{\isacharunderscorekeyword}{\mbox{-}}%
\renewcommand{\isacharbang}{\isamath{!}}%
-\renewcommand{\isachardoublequote}{}%
-\renewcommand{\isachardoublequoteopen}{}%
-\renewcommand{\isachardoublequoteclose}{}%
+\renewcommand{\isachardoublequote}{\isanil}%
+\renewcommand{\isachardoublequoteopen}{\isanil}%
+\renewcommand{\isachardoublequoteclose}{\isanil}%
\renewcommand{\isacharhash}{\isamath{\#}}%
\renewcommand{\isachardollar}{\isamath{\$}}%
\renewcommand{\isacharpercent}{\isamath{\%}}%
--- a/src/Pure/Concurrent/lazy.ML Mon Nov 08 14:33:54 2010 +0100
+++ b/src/Pure/Concurrent/lazy.ML Mon Nov 08 14:41:11 2010 +0100
@@ -2,8 +2,8 @@
Author: Makarius
Lazy evaluation with memoing of results and regular exceptions.
-Parallel version based on futures -- avoids critical or multiple
-evaluation, unless interrupted.
+Parallel version based on (passive) futures, to avoid critical or
+multiple evaluation (unless interrupted).
*)
signature LAZY =
@@ -58,7 +58,7 @@
val res = restore_interrupts (fn () => Exn.capture e ()) ();
val _ = Future.fulfill_result x res;
(*semantic race: some other threads might see the same
- Interrupt, until there is a fresh start*)
+ interrupt, until there is a fresh start*)
val _ =
if Exn.is_interrupt_exn res then
Synchronized.change var (fn _ => Expr e)
--- a/src/Pure/General/markup.ML Mon Nov 08 14:33:54 2010 +0100
+++ b/src/Pure/General/markup.ML Mon Nov 08 14:41:11 2010 +0100
@@ -99,6 +99,10 @@
val command_spanN: string val command_span: string -> T
val ignored_spanN: string val ignored_span: T
val malformed_spanN: string val malformed_span: T
+ val elapsedN: string
+ val cpuN: string
+ val gcN: string
+ val timingN: string val timing: timing -> T
val subgoalsN: string
val proof_stateN: string val proof_state: int -> T
val stateN: string val state: T
@@ -305,6 +309,20 @@
val (malformed_spanN, malformed_span) = markup_elem "malformed_span";
+(* timing *)
+
+val timingN = "timing";
+val elapsedN = "elapsed";
+val cpuN = "cpu";
+val gcN = "gc";
+
+fun timing ({elapsed, cpu, gc, ...}: timing) =
+ (timingN,
+ [(elapsedN, Time.toString elapsed),
+ (cpuN, Time.toString cpu),
+ (gcN, Time.toString gc)]);
+
+
(* toplevel *)
val subgoalsN = "subgoals";
--- a/src/Pure/General/markup.scala Mon Nov 08 14:33:54 2010 +0100
+++ b/src/Pure/General/markup.scala Mon Nov 08 14:41:11 2010 +0100
@@ -11,20 +11,30 @@
{
/* plain values */
- object Int {
- def apply(i: scala.Int): String = i.toString
+ object Int
+ {
+ def apply(x: scala.Int): String = x.toString
def unapply(s: String): Option[scala.Int] =
try { Some(Integer.parseInt(s)) }
catch { case _: NumberFormatException => None }
}
- object Long {
- def apply(i: scala.Long): String = i.toString
+ object Long
+ {
+ def apply(x: scala.Long): String = x.toString
def unapply(s: String): Option[scala.Long] =
try { Some(java.lang.Long.parseLong(s)) }
catch { case _: NumberFormatException => None }
}
+ object Double
+ {
+ def apply(x: scala.Double): String = x.toString
+ def unapply(s: String): Option[scala.Double] =
+ try { Some(java.lang.Double.parseDouble(s)) }
+ catch { case _: NumberFormatException => None }
+ }
+
/* named properties */
@@ -55,6 +65,16 @@
}
}
+ class Double_Property(name: String)
+ {
+ def apply(value: scala.Double): List[(String, String)] = List((name, Double(value)))
+ def unapply(props: List[(String, String)]): Option[Double] =
+ props.find(_._1 == name) match {
+ case None => None
+ case Some((_, value)) => Double.unapply(value)
+ }
+ }
+
/* empty */
@@ -196,6 +216,31 @@
val MALFORMED_SPAN = "malformed_span"
+ /* timing */
+
+ val TIMING = "timing"
+ val ELAPSED = "elapsed"
+ val CPU = "cpu"
+ val GC = "gc"
+
+ object Timing
+ {
+ def apply(timing: isabelle.Timing): Markup =
+ Markup(TIMING, List(
+ (ELAPSED, Double(timing.elapsed)),
+ (CPU, Double(timing.cpu)),
+ (GC, Double(timing.gc))))
+ def unapply(markup: Markup): Option[isabelle.Timing] =
+ markup match {
+ case Markup(TIMING, List(
+ (ELAPSED, Double(elapsed)),
+ (CPU, Double(cpu)),
+ (GC, Double(gc)))) => Some(isabelle.Timing(elapsed, cpu, gc))
+ case _ => None
+ }
+ }
+
+
/* toplevel */
val SUBGOALS = "subgoals"
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Pure/General/timing.ML Mon Nov 08 14:41:11 2010 +0100
@@ -0,0 +1,36 @@
+(* Title: Pure/General/timing.ML
+ Author: Makarius
+
+Basic support for time measurement.
+*)
+
+val seconds = Time.fromReal;
+
+fun start_timing () =
+ let
+ val real_timer = Timer.startRealTimer ();
+ val real_time = Timer.checkRealTimer real_timer;
+ val cpu_timer = Timer.startCPUTimer ();
+ val cpu_times = Timer.checkCPUTimes cpu_timer;
+ in (real_timer, real_time, cpu_timer, cpu_times) end;
+
+type timing = {message: string, elapsed: Time.time, cpu: Time.time, gc: Time.time};
+
+fun end_timing (real_timer, real_time, cpu_timer, cpu_times) : timing =
+ let
+ val real_time2 = Timer.checkRealTimer real_timer;
+ val {nongc = {sys, usr}, gc = {sys = gc_sys, usr = gc_usr}} = cpu_times;
+ val {nongc = {sys = sys2, usr = usr2}, gc = {sys = gc_sys2, usr = gc_usr2}} =
+ Timer.checkCPUTimes cpu_timer;
+
+ open Time;
+ val elapsed = real_time2 - real_time;
+ val gc = gc_usr2 - gc_usr + gc_sys2 - gc_sys;
+ val cpu = usr2 - usr + sys2 - sys + gc;
+
+ val message =
+ (toString elapsed ^ "s elapsed time, " ^
+ toString cpu ^ "s cpu time, " ^
+ toString gc ^ "s GC time") handle Time.Time => "";
+ in {message = message, elapsed = elapsed, cpu = cpu, gc = gc} end;
+
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Pure/General/timing.scala Mon Nov 08 14:41:11 2010 +0100
@@ -0,0 +1,20 @@
+/* Title: Pure/General/timing.scala
+ Author: Makarius
+
+Basic support for time measurement.
+*/
+
+package isabelle
+
+
+sealed case class Timing(val elapsed: Double, cpu: Double, gc: Double)
+{
+ private def print_time(seconds: Double): String =
+ String.format(java.util.Locale.ROOT, "%.3f", seconds.asInstanceOf[AnyRef])
+
+ def message: String =
+ print_time(elapsed) + "s elapsed time, " +
+ print_time(cpu) + "s cpu time, " +
+ print_time(gc) + "s GC time"
+}
+
--- a/src/Pure/IsaMakefile Mon Nov 08 14:33:54 2010 +0100
+++ b/src/Pure/IsaMakefile Mon Nov 08 14:41:11 2010 +0100
@@ -21,6 +21,7 @@
BOOTSTRAP_FILES = \
General/exn.ML \
+ General/timing.ML \
ML-Systems/bash.ML \
ML-Systems/compiler_polyml-5.2.ML \
ML-Systems/compiler_polyml-5.3.ML \
@@ -41,7 +42,6 @@
ML-Systems/smlnj.ML \
ML-Systems/thread_dummy.ML \
ML-Systems/time_limit.ML \
- ML-Systems/timing.ML \
ML-Systems/universal.ML \
ML-Systems/unsynchronized.ML \
ML-Systems/use_context.ML
--- a/src/Pure/Isar/isar_cmd.ML Mon Nov 08 14:33:54 2010 +0100
+++ b/src/Pure/Isar/isar_cmd.ML Mon Nov 08 14:41:11 2010 +0100
@@ -37,8 +37,6 @@
val ml_diag: bool -> Symbol_Pos.text * Position.T -> Toplevel.transition -> Toplevel.transition
val diag_state: unit -> Toplevel.state
val diag_goal: unit -> {context: Proof.context, facts: thm list, goal: thm}
- val cd: Path.T -> Toplevel.transition -> Toplevel.transition
- val pwd: Toplevel.transition -> Toplevel.transition
val display_drafts: Path.T list -> Toplevel.transition -> Toplevel.transition
val print_drafts: Path.T list -> Toplevel.transition -> Toplevel.transition
val print_context: Toplevel.transition -> Toplevel.transition
@@ -289,12 +287,6 @@
val _ = ML_Antiquote.value "Isar.goal" (Scan.succeed "Isar_Cmd.diag_goal ()");
-(* current working directory *)
-
-fun cd path = Toplevel.imperative (fn () => File.cd path);
-val pwd = Toplevel.imperative (fn () => writeln (Path.implode (File.pwd ())));
-
-
(* present draft files *)
fun display_drafts files = Toplevel.imperative (fn () =>
--- a/src/Pure/Isar/isar_syn.ML Mon Nov 08 14:33:54 2010 +0100
+++ b/src/Pure/Isar/isar_syn.ML Mon Nov 08 14:41:11 2010 +0100
@@ -502,7 +502,7 @@
Outer_Syntax.local_theory_to_proof "example_proof"
"example proof body, without any result" Keyword.thy_schematic_goal
(Scan.succeed
- (Specification.schematic_theorem_cmd "" NONE (K I)
+ (Specification.theorem_cmd "" NONE (K I)
Attrib.empty_binding [] (Element.Shows []) false #> Proof.enter_forward));
val _ =
@@ -915,12 +915,13 @@
(** system commands (for interactive mode only) **)
val _ =
- Outer_Syntax.improper_command "cd" "change current working directory" Keyword.diag
- (Parse.path >> (Toplevel.no_timing oo Isar_Cmd.cd));
+ Outer_Syntax.improper_command "cd" "change current working directory" Keyword.control
+ (Parse.path >> (fn path => Toplevel.no_timing o Toplevel.imperative (fn () => File.cd path)));
val _ =
Outer_Syntax.improper_command "pwd" "print current working directory" Keyword.diag
- (Scan.succeed (Toplevel.no_timing o Isar_Cmd.pwd));
+ (Scan.succeed (Toplevel.no_timing o
+ Toplevel.imperative (fn () => writeln (Path.implode (File.pwd ())))));
val _ =
Outer_Syntax.improper_command "use_thy" "use theory file" Keyword.control
@@ -962,7 +963,7 @@
(Scan.succeed (Toplevel.no_timing o Toplevel.imperative (fn () => Toplevel.quiet := false)));
val _ =
- Outer_Syntax.improper_command "commit" "commit current session to ML database" Keyword.diag
+ Outer_Syntax.improper_command "commit" "commit current session to ML database" Keyword.control
(Parse.opt_unit >> K (Toplevel.no_timing o Toplevel.imperative Secure.commit));
val _ =
--- a/src/Pure/Isar/keyword.ML Mon Nov 08 14:33:54 2010 +0100
+++ b/src/Pure/Isar/keyword.ML Mon Nov 08 14:41:11 2010 +0100
@@ -51,6 +51,7 @@
val is_diag: string -> bool
val is_control: string -> bool
val is_regular: string -> bool
+ val is_heading: string -> bool
val is_theory_begin: string -> bool
val is_theory: string -> bool
val is_proof: string -> bool
@@ -192,7 +193,9 @@
val is_diag = command_category [diag];
val is_control = command_category [control];
-fun is_regular name = not (is_diag name orelse is_control name);
+val is_regular = not o command_category [diag, control];
+
+val is_heading = command_category [thy_heading, prf_heading];
val is_theory_begin = command_category [thy_begin];
@@ -211,4 +214,3 @@
end;
-
--- a/src/Pure/ML-Systems/polyml_common.ML Mon Nov 08 14:33:54 2010 +0100
+++ b/src/Pure/ML-Systems/polyml_common.ML Mon Nov 08 14:41:11 2010 +0100
@@ -13,7 +13,7 @@
use "ML-Systems/multithreading.ML";
use "ML-Systems/time_limit.ML";
-use "ML-Systems/timing.ML";
+use "General/timing.ML";
use "ML-Systems/bash.ML";
use "ML-Systems/ml_pretty.ML";
use "ML-Systems/use_context.ML";
--- a/src/Pure/ML-Systems/smlnj.ML Mon Nov 08 14:33:54 2010 +0100
+++ b/src/Pure/ML-Systems/smlnj.ML Mon Nov 08 14:41:11 2010 +0100
@@ -13,7 +13,7 @@
use "ML-Systems/universal.ML";
use "ML-Systems/thread_dummy.ML";
use "ML-Systems/multithreading.ML";
-use "ML-Systems/timing.ML";
+use "General/timing.ML";
use "ML-Systems/bash.ML";
use "ML-Systems/ml_name_space.ML";
use "ML-Systems/ml_pretty.ML";
--- a/src/Pure/ML-Systems/timing.ML Mon Nov 08 14:33:54 2010 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,33 +0,0 @@
-(* Title: Pure/ML-Systems/timing.ML
- Author: Makarius
-
-Basic support for time measurement.
-*)
-
-val seconds = Time.fromReal;
-
-fun start_timing () =
- let
- val real_timer = Timer.startRealTimer ();
- val real_time = Timer.checkRealTimer real_timer;
- val cpu_timer = Timer.startCPUTimer ();
- val cpu_times = Timer.checkCPUTimes cpu_timer;
- in (real_timer, real_time, cpu_timer, cpu_times) end;
-
-fun end_timing (real_timer, real_time, cpu_timer, cpu_times) =
- let
- val real_time2 = Timer.checkRealTimer real_timer;
- val {nongc = {sys, usr}, gc = {sys = gc_sys, usr = gc_usr}} = cpu_times;
- val {nongc = {sys = sys2, usr = usr2}, gc = {sys = gc_sys2, usr = gc_usr2}} =
- Timer.checkCPUTimes cpu_timer;
-
- open Time;
- val elapsed = real_time2 - real_time;
- val gc = gc_usr2 - gc_usr + gc_sys2 - gc_sys;
- val cpu = usr2 - usr + sys2 - sys + gc;
-
- val message =
- (toString elapsed ^ "s elapsed time, " ^ toString cpu ^ "s cpu time, " ^
- toString gc ^ "s GC time") handle Time.Time => "";
- in {message = message, elapsed = elapsed, cpu = cpu, gc = gc} end;
-
--- a/src/Pure/PIDE/document.ML Mon Nov 08 14:33:54 2010 +0100
+++ b/src/Pure/PIDE/document.ML Mon Nov 08 14:41:11 2010 +0100
@@ -119,10 +119,10 @@
(** global state -- document structure and execution process **)
abstype state = State of
- {versions: version Inttab.table, (*version_id -> document content*)
+ {versions: version Inttab.table, (*version_id -> document content*)
commands: Toplevel.transition future Inttab.table, (*command_id -> transition (future parsing)*)
- execs: Toplevel.state option lazy Inttab.table, (*exec_id -> execution process*)
- execution: unit future list} (*global execution process*)
+ execs: (bool * Toplevel.state) lazy Inttab.table, (*exec_id -> execution process*)
+ execution: unit future list} (*global execution process*)
with
fun make_state (versions, commands, execs, execution) =
@@ -134,7 +134,7 @@
val init_state =
make_state (Inttab.make [(no_id, empty_version)],
Inttab.make [(no_id, Future.value Toplevel.empty)],
- Inttab.make [(no_id, Lazy.value (SOME Toplevel.toplevel))],
+ Inttab.make [(no_id, Lazy.value (true, Toplevel.toplevel))],
[]);
@@ -196,6 +196,8 @@
local
+fun timing tr t = Toplevel.status tr (Markup.timing t);
+
fun proof_status tr st =
(case try Toplevel.proof_of st of
SOME prf => Toplevel.status tr (Proof.status_markup prf)
@@ -210,6 +212,15 @@
(fn () => Toplevel.print_state false st) ()))
else ();
+fun run int tr st =
+ (case Toplevel.transition int tr st of
+ SOME (st', NONE) => ([], SOME st')
+ | SOME (_, SOME exn_info) =>
+ (case ML_Compiler.exn_messages (Runtime.EXCURSION_FAIL exn_info) of
+ [] => Exn.interrupt ()
+ | errs => (errs, NONE))
+ | NONE => ([ML_Compiler.exn_message Runtime.TERMINATE], NONE));
+
in
fun run_command thy_name tr st =
@@ -220,28 +231,25 @@
Exn.Result () =>
let
val int = is_some (Toplevel.init_of tr);
- val (errs, result) =
- (case Toplevel.transition int tr st of
- SOME (st', NONE) => ([], SOME st')
- | SOME (_, SOME exn_info) =>
- (case ML_Compiler.exn_messages (Runtime.EXCURSION_FAIL exn_info) of
- [] => Exn.interrupt ()
- | errs => (errs, NONE))
- | NONE => ([ML_Compiler.exn_message Runtime.TERMINATE], NONE));
+ val start = start_timing ();
+ val (errs, result) = run int tr st;
+ val _ = timing tr (end_timing start);
val _ = List.app (Toplevel.error_msg tr) errs;
- val _ =
+ val res =
(case result of
- NONE => Toplevel.status tr Markup.failed
+ NONE => (Toplevel.status tr Markup.failed; (false, st))
| SOME st' =>
(Toplevel.status tr Markup.finished;
proof_status tr st';
- if int then () else async_state tr st'));
- in result end
+ if int then () else async_state tr st';
+ (true, st')));
+ in res end
| Exn.Exn exn =>
if Exn.is_interrupt exn then reraise exn
else
(Toplevel.error_msg tr (ML_Compiler.exn_message exn);
- Toplevel.status tr Markup.failed; NONE));
+ Toplevel.status tr Markup.failed;
+ (false, Toplevel.toplevel)));
end;
@@ -266,11 +274,10 @@
val future_tr = the_command state id;
val exec' =
Lazy.lazy (fn () =>
- (case Lazy.force exec of
- NONE => NONE
- | SOME st =>
- let val exec_tr = Toplevel.put_id (print_id exec_id') (Future.join future_tr)
- in run_command name exec_tr st end));
+ let
+ val st = #2 (Lazy.force exec);
+ val exec_tr = Toplevel.put_id (print_id exec_id') (Future.join future_tr);
+ in run_command name exec_tr st end);
val state' = define_exec exec_id' exec' state;
in (exec_id', (id, exec_id') :: updates, state') end;
--- a/src/Pure/Thy/latex.ML Mon Nov 08 14:33:54 2010 +0100
+++ b/src/Pure/Thy/latex.ML Mon Nov 08 14:41:11 2010 +0100
@@ -30,47 +30,64 @@
structure Latex: LATEX =
struct
+(* literal text *)
+
+local
+ val hex = Int.fmt StringCvt.HEX;
+ fun hex_byte c = hex (ord c div 16) ^ hex (ord c mod 16);
+in
+
+fun literal txt = "\\isaliteral{" ^ translate_string hex_byte txt ^ "}";
+fun enclose_literal txt arg = enclose "{" "}" (literal txt ^ arg);
+
+end;
+
(* symbol output *)
local
-val output_chr = fn
- " " => "\\ " |
- "\n" => "\\isanewline\n" |
- "!" => "{\\isacharbang}" |
- "\"" => "{\\isachardoublequote}" |
- "#" => "{\\isacharhash}" |
- "$" => "{\\isachardollar}" |
- "%" => "{\\isacharpercent}" |
- "&" => "{\\isacharampersand}" |
- "'" => "{\\isacharprime}" |
- "(" => "{\\isacharparenleft}" |
- ")" => "{\\isacharparenright}" |
- "*" => "{\\isacharasterisk}" |
- "+" => "{\\isacharplus}" |
- "," => "{\\isacharcomma}" |
- "-" => "{\\isacharminus}" |
- "." => "{\\isachardot}" |
- "/" => "{\\isacharslash}" |
- ":" => "{\\isacharcolon}" |
- ";" => "{\\isacharsemicolon}" |
- "<" => "{\\isacharless}" |
- "=" => "{\\isacharequal}" |
- ">" => "{\\isachargreater}" |
- "?" => "{\\isacharquery}" |
- "@" => "{\\isacharat}" |
- "[" => "{\\isacharbrackleft}" |
- "\\" => "{\\isacharbackslash}" |
- "]" => "{\\isacharbrackright}" |
- "^" => "{\\isacharcircum}" |
- "_" => "{\\isacharunderscore}" |
- "`" => "{\\isacharbackquote}" |
- "{" => "{\\isacharbraceleft}" |
- "|" => "{\\isacharbar}" |
- "}" => "{\\isacharbraceright}" |
- "~" => "{\\isachartilde}" |
- c => if Symbol.is_ascii_digit c then enclose "{\\isadigit{" "}}" c else c;
+val char_table =
+ Symtab.make
+ [("!", "{\\isacharbang}"),
+ ("\"", "{\\isachardoublequote}"),
+ ("#", "{\\isacharhash}"),
+ ("$", "{\\isachardollar}"),
+ ("%", "{\\isacharpercent}"),
+ ("&", "{\\isacharampersand}"),
+ ("'", "{\\isacharprime}"),
+ ("(", "{\\isacharparenleft}"),
+ (")", "{\\isacharparenright}"),
+ ("*", "{\\isacharasterisk}"),
+ ("+", "{\\isacharplus}"),
+ (",", "{\\isacharcomma}"),
+ ("-", "{\\isacharminus}"),
+ (".", "{\\isachardot}"),
+ ("/", "{\\isacharslash}"),
+ (":", "{\\isacharcolon}"),
+ (";", "{\\isacharsemicolon}"),
+ ("<", "{\\isacharless}"),
+ ("=", "{\\isacharequal}"),
+ (">", "{\\isachargreater}"),
+ ("?", "{\\isacharquery}"),
+ ("@", "{\\isacharat}"),
+ ("[", "{\\isacharbrackleft}"),
+ ("\\", "{\\isacharbackslash}"),
+ ("]", "{\\isacharbrackright}"),
+ ("^", "{\\isacharcircum}"),
+ ("_", "{\\isacharunderscore}"),
+ ("`", "{\\isacharbackquote}"),
+ ("{", "{\\isacharbraceleft}"),
+ ("|", "{\\isacharbar}"),
+ ("}", "{\\isacharbraceright}"),
+ ("~", "{\\isachartilde}")];
+
+fun output_chr " " = "\\ "
+ | output_chr "\n" = "\\isanewline\n"
+ | output_chr c =
+ (case Symtab.lookup char_table c of
+ SOME s => enclose_literal c s
+ | NONE => if Symbol.is_ascii_digit c then enclose "{\\isadigit{" "}}" c else c);
val output_chrs = translate_string output_chr;
@@ -78,8 +95,12 @@
(case Symbol.decode sym of
Symbol.Char s => output_chr s
| Symbol.UTF8 s => s
- | Symbol.Sym s => if known_sym s then enclose "{\\isasym" "}" s else output_chrs sym
- | Symbol.Ctrl s => if known_ctrl s then enclose "\\isactrl" " " s else output_chrs sym
+ | Symbol.Sym s =>
+ if known_sym s then enclose_literal sym (enclose "{\\isasym" "}" s)
+ else output_chrs sym
+ | Symbol.Ctrl s =>
+ if known_ctrl s then literal sym ^ "{}" ^ enclose "\\isactrl" " " s
+ else output_chrs sym
| Symbol.Raw s => s);
in
@@ -91,9 +112,10 @@
val output_syms_antiq =
(fn Antiquote.Text ss => output_symbols (map Symbol_Pos.symbol ss)
| Antiquote.Antiq (ss, _) =>
- enclose "%\n\\isaantiq\n" "%\n\\endisaantiq\n" (output_symbols (map Symbol_Pos.symbol ss))
- | Antiquote.Open _ => "{\\isaantiqopen}"
- | Antiquote.Close _ => "{\\isaantiqclose}");
+ enclose "%\n\\isaantiq\n" "{}%\n\\endisaantiq\n"
+ (output_symbols (map Symbol_Pos.symbol ss))
+ | Antiquote.Open _ => enclose_literal "\\<lbrace>" "{\\isaantiqopen}"
+ | Antiquote.Close _ => enclose_literal "\\<rbrace>" "{\\isaantiqclose}");
end;
@@ -110,15 +132,23 @@
else if Token.is_kind Token.Keyword tok andalso Syntax.is_ascii_identifier s then
"\\isakeyword{" ^ output_syms s ^ "}"
else if Token.is_kind Token.String tok then
- enclose "{\\isachardoublequoteopen}" "{\\isachardoublequoteclose}" (output_syms s)
+ output_syms s |> enclose
+ (enclose_literal "\"" "{\\isachardoublequoteopen}")
+ (enclose_literal "\"" "{\\isachardoublequoteclose}")
else if Token.is_kind Token.AltString tok then
- enclose "{\\isacharbackquoteopen}" "{\\isacharbackquoteclose}" (output_syms s)
+ output_syms s |> enclose
+ (enclose_literal "`" "{\\isacharbackquoteopen}")
+ (enclose_literal "`" "{\\isacharbackquoteclose}")
else if Token.is_kind Token.Verbatim tok then
let
val (txt, pos) = Token.source_position_of tok;
val ants = Antiquote.read (Symbol_Pos.explode (txt, pos), pos);
val out = implode (map output_syms_antiq ants);
- in enclose "{\\isacharverbatimopen}" "{\\isacharverbatimclose}" out end
+ in
+ out |> enclose
+ (enclose_literal "{*" "{\\isacharverbatimopen}")
+ (enclose_literal "*}" "{\\isacharverbatimclose}")
+ end
else output_syms s
end;
--- a/src/Pure/build-jars Mon Nov 08 14:33:54 2010 +0100
+++ b/src/Pure/build-jars Mon Nov 08 14:41:11 2010 +0100
@@ -26,6 +26,7 @@
Concurrent/simple_thread.scala
Concurrent/volatile.scala
General/exn.scala
+ General/timing.scala
General/linear_set.scala
General/markup.scala
General/position.scala