--- a/doc-src/IsarRef/Thy/document/HOL_Specific.tex Thu Nov 13 22:44:40 2008 +0100
+++ b/doc-src/IsarRef/Thy/document/HOL_Specific.tex Thu Nov 13 22:45:12 2008 +0100
@@ -30,8 +30,8 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{typedecl}\hypertarget{command.HOL.typedecl}{\hyperlink{command.HOL.typedecl}{\mbox{\isa{\isacommand{typedecl}}}}} & : & \isartrans{theory}{theory} \\
- \indexdef{HOL}{command}{typedef}\hypertarget{command.HOL.typedef}{\hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}}} & : & \isartrans{theory}{proof(prove)} \\
+ \indexdef{HOL}{command}{typedecl}\hypertarget{command.HOL.typedecl}{\hyperlink{command.HOL.typedecl}{\mbox{\isa{\isacommand{typedecl}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
+ \indexdef{HOL}{command}{typedef}\hypertarget{command.HOL.typedef}{\hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ proof{\isacharparenleft}prove{\isacharparenright}{\isachardoublequote}} \\
\end{matharray}
\begin{rail}
@@ -48,17 +48,18 @@
;
\end{rail}
- \begin{descr}
+ \begin{description}
- \item [\hyperlink{command.HOL.typedecl}{\mbox{\isa{\isacommand{typedecl}}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t{\isachardoublequote}}] is similar to the original \hyperlink{command.typedecl}{\mbox{\isa{\isacommand{typedecl}}}} of
- Isabelle/Pure (see \secref{sec:types-pure}), but also declares type
- arity \isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}type{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ type{\isacharparenright}\ type{\isachardoublequote}}, making \isa{t} an
- actual HOL type constructor. %FIXME check, update
+ \item \hyperlink{command.HOL.typedecl}{\mbox{\isa{\isacommand{typedecl}}}}~\isa{{\isachardoublequote}{\isacharparenleft}{\isasymalpha}\isactrlsub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlsub n{\isacharparenright}\ t{\isachardoublequote}} is similar
+ to the original \hyperlink{command.typedecl}{\mbox{\isa{\isacommand{typedecl}}}} of Isabelle/Pure (see
+ \secref{sec:types-pure}), but also declares type arity \isa{{\isachardoublequote}t\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}type{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ type{\isacharparenright}\ type{\isachardoublequote}}, making \isa{t} an actual HOL type
+ constructor. %FIXME check, update
- \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}}] sets up a goal stating non-emptiness of the set \isa{A}.
- After finishing the proof, the theory will be augmented by a
- Gordon/HOL-style type definition, which establishes a bijection
- between the representing set \isa{A} and the new type \isa{t}.
+ \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}} sets up
+ a goal stating non-emptiness of the set \isa{A}. After finishing
+ the proof, the theory will be augmented by a Gordon/HOL-style type
+ definition, which establishes a bijection between the representing
+ set \isa{A} and the new type \isa{t}.
Technically, \hyperlink{command.HOL.typedef}{\mbox{\isa{\isacommand{typedef}}}} defines both a type \isa{t} and a set (term constant) of the same name (an alternative base
name may be given in parentheses). The injection from type to set
@@ -80,7 +81,7 @@
declaration suppresses a separate constant definition for the
representing set.
- \end{descr}
+ \end{description}
Note that raw type declarations are rarely used in practice; the
main application is with experimental (or even axiomatic!) theory
@@ -95,7 +96,7 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \hyperlink{attribute.HOL.split-format}{\mbox{\isa{split{\isacharunderscore}format}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isaratt \\
+ \hyperlink{attribute.HOL.split-format}{\mbox{\isa{split{\isacharunderscore}format}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{attribute} \\
\end{matharray}
\begin{rail}
@@ -103,19 +104,19 @@
;
\end{rail}
- \begin{descr}
+ \begin{description}
- \item [\hyperlink{attribute.HOL.split-format}{\mbox{\isa{split{\isacharunderscore}format}}}~\isa{{\isachardoublequote}p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub m\ {\isasymAND}\ {\isasymdots}\ {\isasymAND}\ q\isactrlsub {\isadigit{1}}\ {\isasymdots}\ q\isactrlsub n{\isachardoublequote}}] puts expressions of
- low-level tuple types into canonical form as specified by the
- arguments given; the \isa{i}-th collection of arguments refers to
- occurrences in premise \isa{i} of the rule. The ``\isa{{\isachardoublequote}{\isacharparenleft}complete{\isacharparenright}{\isachardoublequote}}'' option causes \emph{all} arguments in function
- applications to be represented canonically according to their tuple
- type structure.
+ \item \hyperlink{attribute.HOL.split-format}{\mbox{\isa{split{\isacharunderscore}format}}}~\isa{{\isachardoublequote}p\isactrlsub {\isadigit{1}}\ {\isasymdots}\ p\isactrlsub m\ {\isasymAND}\ {\isasymdots}\ {\isasymAND}\ q\isactrlsub {\isadigit{1}}\ {\isasymdots}\ q\isactrlsub n{\isachardoublequote}} puts expressions of low-level tuple types into
+ canonical form as specified by the arguments given; the \isa{i}-th
+ collection of arguments refers to occurrences in premise \isa{i}
+ of the rule. The ``\isa{{\isachardoublequote}{\isacharparenleft}complete{\isacharparenright}{\isachardoublequote}}'' option causes \emph{all}
+ arguments in function applications to be represented canonically
+ according to their tuple type structure.
Note that these operations tend to invent funny names for new local
parameters to be introduced.
- \end{descr}%
+ \end{description}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -204,7 +205,7 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{record}\hypertarget{command.HOL.record}{\hyperlink{command.HOL.record}{\mbox{\isa{\isacommand{record}}}}} & : & \isartrans{theory}{theory} \\
+ \indexdef{HOL}{command}{record}\hypertarget{command.HOL.record}{\hyperlink{command.HOL.record}{\mbox{\isa{\isacommand{record}}}}} & : & \isa{{\isachardoublequote}theory\ {\isasymrightarrow}\ theory{\isachardoublequote}} \\
\end{matharray}
\begin{rail}
@@ -212,10 +213,9 @@
;
\end{rail}
- \begin{descr}
+ \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}},
+ \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.
@@ -236,7 +236,7 @@
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}}.
- \end{descr}%
+ \end{description}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -364,8 +364,8 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{datatype}\hypertarget{command.HOL.datatype}{\hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}}} & : & \isartrans{theory}{theory} \\
- \indexdef{HOL}{command}{rep\_datatype}\hypertarget{command.HOL.rep-datatype}{\hyperlink{command.HOL.rep-datatype}{\mbox{\isa{\isacommand{rep{\isacharunderscore}datatype}}}}} & : & \isartrans{theory}{proof} \\
+ \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}} \\
\end{matharray}
\begin{rail}
@@ -379,16 +379,16 @@
cons: name (type *) mixfix?
\end{rail}
- \begin{descr}
+ \begin{description}
- \item [\hyperlink{command.HOL.datatype}{\mbox{\isa{\isacommand{datatype}}}}] defines inductive datatypes in
+ \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{\isacharunderscore}datatype}}}} represents existing types as
inductive ones, generating the standard infrastructure of derived
concepts (primitive recursion etc.).
- \end{descr}
+ \end{description}
The induction and exhaustion theorems generated provide case names
according to the constructors involved, while parameters are named
@@ -409,10 +409,10 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{primrec}\hypertarget{command.HOL.primrec}{\hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}}} & : & \isarkeep{local{\dsh}theory} \\
- \indexdef{HOL}{command}{fun}\hypertarget{command.HOL.fun}{\hyperlink{command.HOL.fun}{\mbox{\isa{\isacommand{fun}}}}} & : & \isarkeep{local{\dsh}theory} \\
- \indexdef{HOL}{command}{function}\hypertarget{command.HOL.function}{\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}} & : & \isartrans{local{\dsh}theory}{proof(prove)} \\
- \indexdef{HOL}{command}{termination}\hypertarget{command.HOL.termination}{\hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}} & : & \isartrans{local{\dsh}theory}{proof(prove)} \\
+ \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}} \\
\end{matharray}
\begin{rail}
@@ -429,12 +429,12 @@
'termination' ( term )?
\end{rail}
- \begin{descr}
+ \begin{description}
- \item [\hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}}] defines primitive recursive
+ \item \hyperlink{command.HOL.primrec}{\mbox{\isa{\isacommand{primrec}}}} defines primitive recursive
functions over datatypes, see also \cite{isabelle-HOL}.
- \item [\hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}}] defines functions by general
+ \item \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} defines functions by general
wellfounded recursion. A detailed description with examples can be
found in \cite{isabelle-function}. The function is specified by a
set of (possibly conditional) recursive equations with arbitrary
@@ -447,18 +447,17 @@
predicate \isa{{\isachardoublequote}f{\isacharunderscore}dom{\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 proof attempts regarding pattern matching and termination.
- See \cite{isabelle-function} for further details.
+ \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
+ proof attempts regarding pattern matching and termination. See
+ \cite{isabelle-function} for further details.
- \item [\hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}~\isa{f}] commences a
+ \item \hyperlink{command.HOL.termination}{\mbox{\isa{\isacommand{termination}}}}~\isa{f} commences a
termination proof for the previously defined function \isa{f}. If
this is omitted, the command refers to the most recent function
definition. After the proof is closed, the recursive equations and
the induction principle is established.
- \end{descr}
+ \end{description}
%FIXME check
@@ -481,31 +480,31 @@
The \hyperlink{command.HOL.function}{\mbox{\isa{\isacommand{function}}}} command accepts the following
options.
- \begin{descr}
+ \begin{description}
- \item [\isa{sequential}] enables a preprocessor which
- disambiguates overlapping patterns by making them mutually disjoint.
- Earlier equations take precedence over later ones. This allows to
- give the specification in a format very similar to functional
- programming. Note that the resulting simplification and induction
- rules correspond to the transformed specification, not the one given
+ \item \isa{sequential} enables a preprocessor which disambiguates
+ overlapping patterns by making them mutually disjoint. Earlier
+ equations take precedence over later ones. This allows to give the
+ specification in a format very similar to functional programming.
+ Note that the resulting simplification and induction rules
+ correspond to the transformed specification, not the one given
originally. This usually means that each equation given by the user
may result in several theroems. Also note that this automatic
transformation only works for ML-style datatype patterns.
- \item [\isa{domintros}] enables the automated generation of
+ \item \isa{domintros} enables the automated generation of
introduction rules for the domain predicate. While mostly not
needed, they can be helpful in some proofs about partial functions.
- \item [\isa{tailrec}] generates the unconstrained recursive
+ \item \isa{tailrec} generates the unconstrained recursive
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
+ \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}}.
- \end{descr}%
+ \end{description}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -515,9 +514,9 @@
%
\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}}}} & : & \isarmeth \\
- \indexdef{HOL}{method}{relation}\hypertarget{method.HOL.relation}{\hyperlink{method.HOL.relation}{\mbox{\isa{relation}}}} & : & \isarmeth \\
- \indexdef{HOL}{method}{lexicographic\_order}\hypertarget{method.HOL.lexicographic-order}{\hyperlink{method.HOL.lexicographic-order}{\mbox{\isa{lexicographic{\isacharunderscore}order}}}} & : & \isarmeth \\
+ \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}{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} \\
\end{matharray}
\begin{rail}
@@ -527,21 +526,21 @@
;
\end{rail}
- \begin{descr}
+ \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{\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}).
- \item [\hyperlink{method.HOL.relation}{\mbox{\isa{relation}}}~\isa{R}] introduces a termination
+ \item \hyperlink{method.HOL.relation}{\mbox{\isa{relation}}}~\isa{R} introduces a termination
proof using the relation \isa{R}. The resulting proof state will
contain goals expressing that \isa{R} is wellfounded, and that the
arguments of recursive calls decrease with respect to \isa{R}.
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{\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,
@@ -552,7 +551,7 @@
In case of failure, extensive information is printed, which can help
to analyse the situation (cf.\ \cite{isabelle-function}).
- \end{descr}%
+ \end{description}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -564,8 +563,8 @@
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.
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{recdef}\hypertarget{command.HOL.recdef}{\hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}}} & : & \isartrans{theory}{theory} \\
- \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}} & : & \isartrans{theory}{proof(prove)} \\
+ \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}} \\
\end{matharray}
\begin{rail}
@@ -581,9 +580,9 @@
;
\end{rail}
- \begin{descr}
+ \begin{description}
- \item [\hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}}] defines general well-founded
+ \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
TFL to recover from failed proof attempts, returning unfinished
@@ -593,7 +592,7 @@
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{\isacharunderscore}tc}}}}~\isa{{\isachardoublequote}c\ {\isacharparenleft}i{\isacharparenright}{\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}.
@@ -601,15 +600,15 @@
Note that in most cases, \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} is able to finish
its internal proofs without manual intervention.
- \end{descr}
+ \end{description}
\medskip Hints for \hyperlink{command.HOL.recdef}{\mbox{\isa{\isacommand{recdef}}}} may be also declared
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}}}} & : & \isaratt \\
- \indexdef{HOL}{attribute}{recdef\_cong}\hypertarget{attribute.HOL.recdef-cong}{\hyperlink{attribute.HOL.recdef-cong}{\mbox{\isa{recdef{\isacharunderscore}cong}}}} & : & \isaratt \\
- \indexdef{HOL}{attribute}{recdef\_wf}\hypertarget{attribute.HOL.recdef-wf}{\hyperlink{attribute.HOL.recdef-wf}{\mbox{\isa{recdef{\isacharunderscore}wf}}}} & : & \isaratt \\
+ \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} \\
\end{matharray}
\begin{rail}
@@ -647,11 +646,11 @@
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}}}}} & : & \isarkeep{local{\dsh}theory} \\
- \indexdef{HOL}{command}{inductive\_set}\hypertarget{command.HOL.inductive-set}{\hyperlink{command.HOL.inductive-set}{\mbox{\isa{\isacommand{inductive{\isacharunderscore}set}}}}} & : & \isarkeep{local{\dsh}theory} \\
- \indexdef{HOL}{command}{coinductive}\hypertarget{command.HOL.coinductive}{\hyperlink{command.HOL.coinductive}{\mbox{\isa{\isacommand{coinductive}}}}} & : & \isarkeep{local{\dsh}theory} \\
- \indexdef{HOL}{command}{coinductive\_set}\hypertarget{command.HOL.coinductive-set}{\hyperlink{command.HOL.coinductive-set}{\mbox{\isa{\isacommand{coinductive{\isacharunderscore}set}}}}} & : & \isarkeep{local{\dsh}theory} \\
- \indexdef{HOL}{attribute}{mono}\hypertarget{attribute.HOL.mono}{\hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}}} & : & \isaratt \\
+ \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}{attribute}{mono}\hypertarget{attribute.HOL.mono}{\hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}}} & : & \isa{attribute} \\
\end{matharray}
\begin{rail}
@@ -664,9 +663,9 @@
;
\end{rail}
- \begin{descr}
+ \begin{description}
- \item [\hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}} and \hyperlink{command.HOL.coinductive}{\mbox{\isa{\isacommand{coinductive}}}}] define (co)inductive predicates from the
+ \item \hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}} and \hyperlink{command.HOL.coinductive}{\mbox{\isa{\isacommand{coinductive}}}} define (co)inductive predicates from the
introduction rules given in the \hyperlink{keyword.where}{\mbox{\isa{\isakeyword{where}}}} part. The
optional \hyperlink{keyword.for}{\mbox{\isa{\isakeyword{for}}}} part contains a list of parameters of the
(co)inductive predicates that remain fixed throughout the
@@ -676,13 +675,13 @@
\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!
- \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{\isacharunderscore}set}}}} and \hyperlink{command.HOL.coinductive-set}{\mbox{\isa{\isacommand{coinductive{\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
+ \item \hyperlink{attribute.HOL.mono}{\mbox{\isa{mono}}} declares monotonicity rules. These
rule are involved in the automated monotonicity proof of \hyperlink{command.HOL.inductive}{\mbox{\isa{\isacommand{inductive}}}}.
- \end{descr}%
+ \end{description}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -696,14 +695,14 @@
\begin{description}
- \item [\isa{R{\isachardot}intros}] is the list of introduction rules as proven
+ \item \isa{R{\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{\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{\isachardot}induct} or \isa{R{\isachardot}coinduct} is the (co)induction
rule.
\end{description}
@@ -766,8 +765,8 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{HOL}{method}{arith}\hypertarget{method.HOL.arith}{\hyperlink{method.HOL.arith}{\mbox{\isa{arith}}}} & : & \isarmeth \\
- \indexdef{HOL}{attribute}{arith\_split}\hypertarget{attribute.HOL.arith-split}{\hyperlink{attribute.HOL.arith-split}{\mbox{\isa{arith{\isacharunderscore}split}}}} & : & \isaratt \\
+ \indexdef{HOL}{method}{arith}\hypertarget{method.HOL.arith}{\hyperlink{method.HOL.arith}{\mbox{\isa{arith}}}} & : & \isa{method} \\
+ \indexdef{HOL}{attribute}{arith\_split}\hypertarget{attribute.HOL.arith-split}{\hyperlink{attribute.HOL.arith-split}{\mbox{\isa{arith{\isacharunderscore}split}}}} & : & \isa{attribute} \\
\end{matharray}
The \hyperlink{method.HOL.arith}{\mbox{\isa{arith}}} method decides linear arithmetic problems
@@ -811,11 +810,11 @@
search over and over again.
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{sledgehammer}\hypertarget{command.HOL.sledgehammer}{\hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{proof} \\
- \indexdef{HOL}{command}{print\_atps}\hypertarget{command.HOL.print-atps}{\hyperlink{command.HOL.print-atps}{\mbox{\isa{\isacommand{print{\isacharunderscore}atps}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
- \indexdef{HOL}{command}{atp\_info}\hypertarget{command.HOL.atp-info}{\hyperlink{command.HOL.atp-info}{\mbox{\isa{\isacommand{atp{\isacharunderscore}info}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{\cdot} \\
- \indexdef{HOL}{command}{atp\_kill}\hypertarget{command.HOL.atp-kill}{\hyperlink{command.HOL.atp-kill}{\mbox{\isa{\isacommand{atp{\isacharunderscore}kill}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{\cdot} \\
- \indexdef{HOL}{method}{metis}\hypertarget{method.HOL.metis}{\hyperlink{method.HOL.metis}{\mbox{\isa{metis}}}} & : & \isarmeth \\
+ \indexdef{HOL}{command}{sledgehammer}\hypertarget{command.HOL.sledgehammer}{\hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}proof\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{HOL}{command}{print\_atps}\hypertarget{command.HOL.print-atps}{\hyperlink{command.HOL.print-atps}{\mbox{\isa{\isacommand{print{\isacharunderscore}atps}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}context\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{HOL}{command}{atp\_info}\hypertarget{command.HOL.atp-info}{\hyperlink{command.HOL.atp-info}{\mbox{\isa{\isacommand{atp{\isacharunderscore}info}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}any\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{HOL}{command}{atp\_kill}\hypertarget{command.HOL.atp-kill}{\hyperlink{command.HOL.atp-kill}{\mbox{\isa{\isacommand{atp{\isacharunderscore}kill}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isa{{\isachardoublequote}any\ {\isasymrightarrow}{\isachardoublequote}} \\
+ \indexdef{HOL}{method}{metis}\hypertarget{method.HOL.metis}{\hyperlink{method.HOL.metis}{\mbox{\isa{metis}}}} & : & \isa{method} \\
\end{matharray}
\begin{rail}
@@ -826,12 +825,12 @@
;
\end{rail}
- \begin{descr}
+ \begin{description}
- \item [\hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}}~\isa{{\isachardoublequote}prover\isactrlsub {\isadigit{1}}\ {\isasymdots}\ prover\isactrlsub n{\isachardoublequote}}] invokes the specified automated theorem provers on
- the first subgoal. Provers are run in parallel, the first
- successful result is displayed, and the other attempts are
- terminated.
+ \item \hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}}~\isa{{\isachardoublequote}prover\isactrlsub {\isadigit{1}}\ {\isasymdots}\ prover\isactrlsub n{\isachardoublequote}}
+ invokes the specified automated theorem provers on the first
+ subgoal. Provers are run in parallel, the first successful result
+ is displayed, and the other attempts are terminated.
Provers are defined in the theory context, see also \hyperlink{command.HOL.print-atps}{\mbox{\isa{\isacommand{print{\isacharunderscore}atps}}}}. If no provers are given as arguments to \hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}}, the system refers to the default defined as
``ATP provers'' preference by the user interface.
@@ -840,32 +839,32 @@
and the maximum number of independent prover processes (default: 5);
excessive provers are automatically terminated.
- \item [\hyperlink{command.HOL.print-atps}{\mbox{\isa{\isacommand{print{\isacharunderscore}atps}}}}] prints the list of automated
+ \item \hyperlink{command.HOL.print-atps}{\mbox{\isa{\isacommand{print{\isacharunderscore}atps}}}} prints the list of automated
theorem provers available to the \hyperlink{command.HOL.sledgehammer}{\mbox{\isa{\isacommand{sledgehammer}}}}
command.
- \item [\hyperlink{command.HOL.atp-info}{\mbox{\isa{\isacommand{atp{\isacharunderscore}info}}}}] prints information about presently
+ \item \hyperlink{command.HOL.atp-info}{\mbox{\isa{\isacommand{atp{\isacharunderscore}info}}}} prints information about presently
running provers, including elapsed runtime, and the remaining time
until timeout.
- \item [\hyperlink{command.HOL.atp-kill}{\mbox{\isa{\isacommand{atp{\isacharunderscore}kill}}}}] terminates all presently running
+ \item \hyperlink{command.HOL.atp-kill}{\mbox{\isa{\isacommand{atp{\isacharunderscore}kill}}}} terminates all presently running
provers.
- \item [\hyperlink{method.HOL.metis}{\mbox{\isa{metis}}}~\isa{{\isachardoublequote}facts{\isachardoublequote}}] invokes the Metis
- prover with the given facts. Metis is an automated proof tool of
- medium strength, but is fully integrated into Isabelle/HOL, with
- explicit inferences going through the kernel. Thus its results are
+ \item \hyperlink{method.HOL.metis}{\mbox{\isa{metis}}}~\isa{{\isachardoublequote}facts{\isachardoublequote}} invokes the Metis prover
+ with the given facts. Metis is an automated proof tool of medium
+ strength, but is fully integrated into Isabelle/HOL, with explicit
+ inferences going through the kernel. Thus its results are
guaranteed to be ``correct by construction''.
Note that all facts used with Metis need to be specified as explicit
arguments. There are no rule declarations as for other Isabelle
provers, like \hyperlink{method.blast}{\mbox{\isa{blast}}} or \hyperlink{method.fast}{\mbox{\isa{fast}}}.
- \end{descr}%
+ \end{description}%
\end{isamarkuptext}%
\isamarkuptrue%
%
-\isamarkupsection{Unstructured cases analysis and induction \label{sec:hol-induct-tac}%
+\isamarkupsection{Unstructured case analysis and induction \label{sec:hol-induct-tac}%
}
\isamarkuptrue%
%
@@ -875,10 +874,10 @@
\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}} & : & \isarmeth \\
- \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}} & : & \isarmeth \\
- \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}} & : & \isarmeth \\
- \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}} & : & \isartrans{theory}{theory} \\
+ \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}} \\
\end{matharray}
\begin{rail}
@@ -895,11 +894,12 @@
;
\end{rail}
- \begin{descr}
+ \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 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.
+ \item \hyperlink{method.HOL.case-tac}{\mbox{\isa{case{\isacharunderscore}tac}}} and \hyperlink{method.HOL.induct-tac}{\mbox{\isa{induct{\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.
These unstructured tactics feature both goal addressing and dynamic
instantiation. Note that named rule cases are \emph{not} provided
@@ -908,7 +908,7 @@
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{\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
forward manner.
While \hyperlink{method.HOL.ind-cases}{\mbox{\isa{ind{\isacharunderscore}cases}}} is a proof method to apply the
@@ -916,7 +916,7 @@
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
be generalized before applying the resulting rule.
- \end{descr}%
+ \end{description}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -935,12 +935,12 @@
(this actually covers the new-style theory format as well).
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{value}\hypertarget{command.HOL.value}{\hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}}\isa{{\isachardoublequote}\isactrlsup {\isacharasterisk}{\isachardoublequote}} & : & \isarkeep{theory~|~proof} \\
- \indexdef{HOL}{command}{code\_module}\hypertarget{command.HOL.code-module}{\hyperlink{command.HOL.code-module}{\mbox{\isa{\isacommand{code{\isacharunderscore}module}}}}} & : & \isartrans{theory}{theory} \\
- \indexdef{HOL}{command}{code\_library}\hypertarget{command.HOL.code-library}{\hyperlink{command.HOL.code-library}{\mbox{\isa{\isacommand{code{\isacharunderscore}library}}}}} & : & \isartrans{theory}{theory} \\
- \indexdef{HOL}{command}{consts\_code}\hypertarget{command.HOL.consts-code}{\hyperlink{command.HOL.consts-code}{\mbox{\isa{\isacommand{consts{\isacharunderscore}code}}}}} & : & \isartrans{theory}{theory} \\
- \indexdef{HOL}{command}{types\_code}\hypertarget{command.HOL.types-code}{\hyperlink{command.HOL.types-code}{\mbox{\isa{\isacommand{types{\isacharunderscore}code}}}}} & : & \isartrans{theory}{theory} \\
- \indexdef{HOL}{attribute}{code}\hypertarget{attribute.HOL.code}{\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}} & : & \isaratt \\
+ \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}{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}{attribute}{code}\hypertarget{attribute.HOL.code}{\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}} & : & \isa{attribute} \\
\end{matharray}
\begin{rail}
@@ -980,12 +980,12 @@
;
\end{rail}
- \begin{descr}
+ \begin{description}
- \item [\hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}~\isa{t}] evaluates and prints a
- term using the code generator.
+ \item \hyperlink{command.HOL.value}{\mbox{\isa{\isacommand{value}}}}~\isa{t} evaluates and prints a term
+ using the code generator.
- \end{descr}
+ \end{description}
\medskip The other framework generates code from functional programs
(including overloading using type classes) to SML \cite{SML}, OCaml
@@ -997,21 +997,21 @@
introduction on how to use it.
\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}} & : & \isarkeep{theory~|~proof} \\
- \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}} & : & \isarkeep{theory~|~proof} \\
- \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}} & : & \isarkeep{theory~|~proof} \\
- \indexdef{HOL}{command}{code\_datatype}\hypertarget{command.HOL.code-datatype}{\hyperlink{command.HOL.code-datatype}{\mbox{\isa{\isacommand{code{\isacharunderscore}datatype}}}}} & : & \isartrans{theory}{theory} \\
- \indexdef{HOL}{command}{code\_const}\hypertarget{command.HOL.code-const}{\hyperlink{command.HOL.code-const}{\mbox{\isa{\isacommand{code{\isacharunderscore}const}}}}} & : & \isartrans{theory}{theory} \\
- \indexdef{HOL}{command}{code\_type}\hypertarget{command.HOL.code-type}{\hyperlink{command.HOL.code-type}{\mbox{\isa{\isacommand{code{\isacharunderscore}type}}}}} & : & \isartrans{theory}{theory} \\
- \indexdef{HOL}{command}{code\_class}\hypertarget{command.HOL.code-class}{\hyperlink{command.HOL.code-class}{\mbox{\isa{\isacommand{code{\isacharunderscore}class}}}}} & : & \isartrans{theory}{theory} \\
- \indexdef{HOL}{command}{code\_instance}\hypertarget{command.HOL.code-instance}{\hyperlink{command.HOL.code-instance}{\mbox{\isa{\isacommand{code{\isacharunderscore}instance}}}}} & : & \isartrans{theory}{theory} \\
- \indexdef{HOL}{command}{code\_monad}\hypertarget{command.HOL.code-monad}{\hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isacharunderscore}monad}}}}} & : & \isartrans{theory}{theory} \\
- \indexdef{HOL}{command}{code\_reserved}\hypertarget{command.HOL.code-reserved}{\hyperlink{command.HOL.code-reserved}{\mbox{\isa{\isacommand{code{\isacharunderscore}reserved}}}}} & : & \isartrans{theory}{theory} \\
- \indexdef{HOL}{command}{code\_include}\hypertarget{command.HOL.code-include}{\hyperlink{command.HOL.code-include}{\mbox{\isa{\isacommand{code{\isacharunderscore}include}}}}} & : & \isartrans{theory}{theory} \\
- \indexdef{HOL}{command}{code\_modulename}\hypertarget{command.HOL.code-modulename}{\hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isacharunderscore}modulename}}}}} & : & \isartrans{theory}{theory} \\
- \indexdef{HOL}{command}{code\_abort}\hypertarget{command.HOL.code-abort}{\hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isacharunderscore}abort}}}}} & : & \isartrans{theory}{theory} \\
- \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}} & : & \isarkeep{theory~|~proof} \\
- \indexdef{HOL}{attribute}{code}\hypertarget{attribute.HOL.code}{\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}} & : & \isaratt \\
+ \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}{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\_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}{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\_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\_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\_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\_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}{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}\hypertarget{attribute.HOL.code}{\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}} & : & \isa{attribute} \\
\end{matharray}
\begin{rail}
@@ -1082,14 +1082,14 @@
;
\end{rail}
- \begin{descr}
+ \begin{description}
- \item [\hyperlink{command.HOL.export-code}{\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}}] is the canonical interface
- for generating and serializing code: for a given list of constants,
- code is generated for the specified target languages. Abstract code
- is cached incrementally. If no constant is given, the currently
- cached code is serialized. If no serialization instruction is
- given, only abstract code is cached.
+ \item \hyperlink{command.HOL.export-code}{\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}} is the canonical interface for
+ generating and serializing code: for a given list of constants, code
+ is generated for the specified target languages. Abstract code is
+ cached incrementally. If no constant is given, the currently cached
+ code is serialized. If no serialization instruction is given, only
+ abstract code is cached.
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
@@ -1111,71 +1111,70 @@
\emph{Haskell} a module name prefix may be given using the ``\isa{{\isachardoublequote}root{\isacharcolon}{\isachardoublequote}}'' argument; ``\isa{string{\isacharunderscore}classes}'' adds a ``\verb|deriving (Read, Show)|'' clause to each appropriate datatype
declaration.
- \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{\isacharunderscore}thms}}}} prints a list of theorems
representing the corresponding program containing all given
constants; if no constants are given, the currently cached code
theorems are printed.
- \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{\isacharunderscore}deps}}}} visualizes dependencies of
theorems representing the corresponding program containing all given
constants; if no constants are given, the currently cached code
theorems are visualized.
- \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{\isacharunderscore}datatype}}}} specifies a constructor set
for a logical type.
- \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{\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{\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
- with target-specific class names; omitting a
- serialization deletes an existing serialization.
- This applies only to \emph{Haskell}.
+ \item \hyperlink{command.HOL.code-class}{\mbox{\isa{\isacommand{code{\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{\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
``already present'' declaration. This applies only to
\emph{Haskell}.
- \item [\hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isacharunderscore}monad}}}}] provides an auxiliary
- mechanism to generate monadic code for Haskell.
+ \item \hyperlink{command.HOL.code-monad}{\mbox{\isa{\isacommand{code{\isacharunderscore}monad}}}} provides an auxiliary mechanism
+ to generate monadic code for 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{\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-include}{\mbox{\isa{\isacommand{code{\isacharunderscore}include}}}}] adds arbitrary named content
+ \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
will remove an already added ``include''.
- \item [\hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isacharunderscore}modulename}}}}] declares aliasings from
- one module name onto another.
+ \item \hyperlink{command.HOL.code-modulename}{\mbox{\isa{\isacommand{code{\isacharunderscore}modulename}}}} declares aliasings from one
+ module name onto another.
- \item [\hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isacharunderscore}abort}}}}] declares constants which
- are not required to have a definition by means of defining equations;
- if needed these are implemented by program abort instead.
+ \item \hyperlink{command.HOL.code-abort}{\mbox{\isa{\isacommand{code{\isacharunderscore}abort}}}} declares constants which are not
+ required to have a definition by means of defining equations; if
+ needed these are implemented by program abort instead.
- \item [\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}] explicitly selects (or
- with option ``\isa{{\isachardoublequote}del{\isachardoublequote}}'' deselects) a defining equation for
- code generation. Usually packages introducing defining equations
- provide a reasonable default setup for selection.
+ \item \hyperlink{attribute.HOL.code}{\mbox{\isa{code}}} explicitly selects (or with option
+ ``\isa{{\isachardoublequote}del{\isachardoublequote}}'' deselects) a defining equation for code
+ generation. Usually packages introducing defining equations provide
+ a reasonable default setup for selection.
- \item [\hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}\isa{inline}] declares (or with
+ \item \hyperlink{attribute.HOL.code}{\mbox{\isa{code}}}~\isa{inline} declares (or with
option ``\isa{{\isachardoublequote}del{\isachardoublequote}}'' removes) inlining theorems which are
applied as rewrite rules to any defining equation during
preprocessing.
- \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{\isacharunderscore}codesetup}}}} gives an overview on
selected defining equations, code generator datatypes and
preprocessor setup.
- \end{descr}%
+ \end{description}%
\end{isamarkuptext}%
\isamarkuptrue%
%
@@ -1185,8 +1184,8 @@
%
\begin{isamarkuptext}%
\begin{matharray}{rcl}
- \indexdef{HOL}{command}{specification}\hypertarget{command.HOL.specification}{\hyperlink{command.HOL.specification}{\mbox{\isa{\isacommand{specification}}}}} & : & \isartrans{theory}{proof(prove)} \\
- \indexdef{HOL}{command}{ax\_specification}\hypertarget{command.HOL.ax-specification}{\hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}}} & : & \isartrans{theory}{proof(prove)} \\
+ \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}} \\
\end{matharray}
\begin{rail}
@@ -1195,27 +1194,27 @@
decl: ((name ':')? term '(' 'overloaded' ')'?)
\end{rail}
- \begin{descr}
+ \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{{\isachardoublequote}decls\ {\isasymphi}{\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 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 properties given in the first place.
+ \item \hyperlink{command.HOL.ax-specification}{\mbox{\isa{\isacommand{ax{\isacharunderscore}specification}}}}~\isa{{\isachardoublequote}decls\ {\isasymphi}{\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
+ properties given in the first place.
- \item [\isa{decl}] declares a constant to be defined by the
+ \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
the declaration. Overloaded constants should be declared as such.
- \end{descr}
+ \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