--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/doc-src/TutorialI/document/Documents.tex Thu Jul 26 17:16:02 2012 +0200
@@ -0,0 +1,933 @@
+%
+\begin{isabellebody}%
+\def\isabellecontext{Documents}%
+%
+\isadelimtheory
+%
+\endisadelimtheory
+%
+\isatagtheory
+%
+\endisatagtheory
+{\isafoldtheory}%
+%
+\isadelimtheory
+%
+\endisadelimtheory
+%
+\isamarkupsection{Concrete Syntax \label{sec:concrete-syntax}%
+}
+\isamarkuptrue%
+%
+\begin{isamarkuptext}%
+The core concept of Isabelle's framework for concrete syntax is that
+ of \bfindex{mixfix annotations}. Associated with any kind of
+ constant declaration, mixfixes affect both the grammar productions
+ for the parser and output templates for the pretty printer.
+
+ In full generality, parser and pretty printer configuration is a
+ subtle affair~\cite{isabelle-ref}. Your syntax specifications need
+ to interact properly with the existing setup of Isabelle/Pure and
+ Isabelle/HOL\@. To avoid creating ambiguities with existing
+ elements, it is particularly important to give new syntactic
+ constructs the right precedence.
+
+ Below we introduce a few simple syntax declaration
+ forms that already cover many common situations fairly well.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\isamarkupsubsection{Infix Annotations%
+}
+\isamarkuptrue%
+%
+\begin{isamarkuptext}%
+Syntax annotations may be included wherever constants are declared,
+ 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{{\isaliteral{5C3C74696D65733E}{\isasymtimes}}} comes
+ to mind).
+
+ Infix declarations\index{infix annotations} provide a useful special
+ case of mixfixes. The following example of the exclusive-or
+ operation on boolean values illustrates typical infix declarations.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+\isacommand{definition}\isamarkupfalse%
+\ 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\ {\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\ {\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\ {\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{{\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{{\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{{\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{{\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}%
+\isamarkuptrue%
+%
+\isamarkupsubsection{Mathematical Symbols \label{sec:syntax-symbols}%
+}
+\isamarkuptrue%
+%
+\begin{isamarkuptext}%
+Concrete syntax based on ASCII characters has inherent limitations.
+ Mathematical notation demands a larger repertoire of glyphs.
+ Several standards of extended character sets have been proposed over
+ decades, but none has become universally available so far. Isabelle
+ has its own notion of \bfindex{symbols} as the smallest entities of
+ source text, without referring to internal encodings. There are
+ three kinds of such ``generalized characters'':
+
+ \begin{enumerate}
+
+ \item 7-bit ASCII characters
+
+ \item named symbols: \verb,\,\verb,<,$ident$\verb,>,
+
+ \item named control symbols: \verb,\,\verb,<^,$ident$\verb,>,
+
+ \end{enumerate}
+
+ Here $ident$ is any sequence of letters.
+ This results in an infinite store of symbols, whose
+ 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{{\isaliteral{5C3C666F72616C6C3E}{\isasymforall}}}.
+
+ A list of standard Isabelle symbols is given in
+ \cite{isabelle-isar-ref}. You may introduce your own
+ interpretation of further symbols by configuring the appropriate
+ front-end tool accordingly, e.g.\ by defining certain {\LaTeX}
+ macros (see also \S\ref{sec:doc-prep-symbols}). There are also a
+ 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\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{{\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
+
+ \medskip
+ {\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{{\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
+ following specifies an Isabelle symbol for the new operator:%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\isadelimML
+%
+\endisadelimML
+%
+\isatagML
+%
+\endisatagML
+{\isafoldML}%
+%
+\isadelimML
+%
+\endisadelimML
+\isacommand{definition}\isamarkupfalse%
+\ 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
+%
+\isatagML
+%
+\endisatagML
+{\isafoldML}%
+%
+\isadelimML
+%
+\endisadelimML
+%
+\begin{isamarkuptext}%
+\noindent Proof~General provides several 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.
+
+ More flexible is to provide alternative syntax forms
+ through the \bfindex{print mode} concept~\cite{isabelle-ref}. By
+ convention, the mode of ``$xsymbols$'' is enabled whenever
+ Proof~General's X-Symbol mode or {\LaTeX} output is active. Now
+ consider the following hybrid declaration of \isa{xor}:%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\isadelimML
+%
+\endisadelimML
+%
+\isatagML
+%
+\endisatagML
+{\isafoldML}%
+%
+\isadelimML
+%
+\endisadelimML
+\isacommand{definition}\isamarkupfalse%
+\ 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%
+\ {\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
+%
+\isatagML
+%
+\endisatagML
+{\isafoldML}%
+%
+\isadelimML
+%
+\endisadelimML
+%
+\begin{isamarkuptext}%
+\noindent
+The \commdx{notation} command associates a mixfix
+annotation with a known constant. The print mode specification,
+here \isa{{\isaliteral{28}{\isacharparenleft}}xsymbols{\isaliteral{29}{\isacharparenright}}}, is optional.
+
+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
+symbols displayed during proofs.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\isamarkupsubsection{Prefix Annotations%
+}
+\isamarkuptrue%
+%
+\begin{isamarkuptext}%
+Prefix syntax annotations\index{prefix annotation} are another form
+ of mixfixes \cite{isabelle-ref}, without any template arguments or
+ priorities --- just some literal syntax. The following example
+ associates common symbols with the constructors of a datatype.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+\isacommand{datatype}\isamarkupfalse%
+\ 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\ {\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.
+
+ Prefix syntax works the same way for other commands that introduce new constants, e.g. \isakeyword{primrec}.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\isamarkupsubsection{Abbreviations \label{sec:abbreviations}%
+}
+\isamarkuptrue%
+%
+\begin{isamarkuptext}%
+Mixfix syntax annotations merely decorate particular constant
+application forms with concrete syntax, for instance replacing
+\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}.
+
+Command \commdx{abbreviation} introduces an uninterpreted notational
+constant as an abbreviation for a complex term. Abbreviations are
+unfolded upon parsing and re-introduced upon printing. This provides a
+simple mechanism for syntactic macros.
+
+A typical use of abbreviations is to introduce relational notation for
+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}}\ {\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\ {\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{{\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}} for negated equalities. The following declaration
+stems from Isabelle/HOL itself:%
+\end{isamarkuptext}%
+\isamarkuptrue%
+\isacommand{abbreviation}\isamarkupfalse%
+\ 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%
+\ {\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{{\isaliteral{5C3C6E6F7465713E}{\isasymnoteq}}} is introduced separately to restrict it
+to the \emph{xsymbols} mode.
+
+Abbreviations are appropriate when the defined concept is a
+simple variation on an existing one. But because of the automatic
+folding and unfolding of abbreviations, they do not scale up well to
+large hierarchies of concepts. Abbreviations do not replace
+definitions.
+
+Abbreviations are a simplified form of the general concept of
+\emph{syntax translations}; even heavier transformations may be
+written in ML \cite{isabelle-ref}.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\isamarkupsection{Document Preparation \label{sec:document-preparation}%
+}
+\isamarkuptrue%
+%
+\begin{isamarkuptext}%
+Isabelle/Isar is centered around the concept of \bfindex{formal
+ proof documents}\index{documents|bold}. The outcome of a formal
+ development effort is meant to be a human-readable record, presented
+ as browsable PDF file or printed on paper. The overall document
+ structure follows traditional mathematical articles, with sections,
+ intermediate explanations, definitions, theorems and proofs.
+
+ \medskip The Isabelle document preparation system essentially acts
+ as a front-end to {\LaTeX}. After checking specifications and
+ proofs formally, the theory sources are turned into typesetting
+ instructions in a schematic manner. This lets you write authentic
+ reports on theory developments with little effort: many technical
+ consistency checks are handled by the system.
+
+ Here is an example to illustrate the idea of Isabelle document
+ preparation.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\begin{quotation}
+%
+\begin{isamarkuptext}%
+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%
+\ {\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}%
+\ {\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%
+%
+\end{quotation}
+%
+\begin{isamarkuptext}%
+\noindent The above document output has been produced as follows:
+
+ \begin{ttbox}
+ text {\ttlbrace}*
+ The following datatype definition of {\at}{\ttlbrace}text "'a bintree"{\ttrbrace}
+ models binary trees with nodes being decorated by elements
+ of type {\at}{\ttlbrace}typ 'a{\ttrbrace}.
+ *{\ttrbrace}
+
+ datatype 'a bintree =
+ Leaf | Branch 'a "'a bintree" "'a bintree"
+ \end{ttbox}
+ \begin{ttbox}
+ text {\ttlbrace}*
+ {\ttback}noindent The datatype induction rule generated here is
+ of the form {\at}{\ttlbrace}thm [display] bintree.induct [no_vars]{\ttrbrace}
+ *{\ttrbrace}
+ \end{ttbox}\vspace{-\medskipamount}
+
+ \noindent Here we have augmented the theory by formal comments
+ (using \isakeyword{text} blocks), the informal parts may again refer
+ to formal entities by means of ``antiquotations'' (such as
+ \texttt{\at}\verb,{text "'a bintree"}, or
+ \texttt{\at}\verb,{typ 'a},), see also \S\ref{sec:doc-prep-text}.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\isamarkupsubsection{Isabelle Sessions%
+}
+\isamarkuptrue%
+%
+\begin{isamarkuptext}%
+In contrast to the highly interactive mode of Isabelle/Isar theory
+ development, the document preparation stage essentially works in
+ batch-mode. An Isabelle \bfindex{session} consists of a collection
+ of source files that may contribute to an output document. Each
+ session is derived from a single parent, usually an object-logic
+ image like \texttt{HOL}. This results in an overall tree structure,
+ which is reflected by the output location in the file system
+ (usually rooted at \verb,~/.isabelle/IsabelleXXXX/browser_info,).
+
+ \medskip The easiest way to manage Isabelle sessions is via
+ \texttt{isabelle mkdir} (generates an initial session source setup)
+ and \texttt{isabelle make} (run sessions controlled by
+ \texttt{IsaMakefile}). For example, a new session
+ \texttt{MySession} derived from \texttt{HOL} may be produced as
+ follows:
+
+\begin{verbatim}
+ isabelle mkdir HOL MySession
+ isabelle make
+\end{verbatim}
+
+ The \texttt{isabelle make} job also informs about the file-system
+ location of the ultimate results. The above dry run should be able
+ to produce some \texttt{document.pdf} (with dummy title, empty table
+ of contents etc.). Any failure at this stage usually indicates
+ technical problems of the {\LaTeX} installation.
+
+ \medskip The detailed arrangement of the session sources is as
+ follows.
+
+ \begin{itemize}
+
+ \item Directory \texttt{MySession} holds the required theory files
+ $T@1$\texttt{.thy}, \dots, $T@n$\texttt{.thy}.
+
+ \item File \texttt{MySession/ROOT.ML} holds appropriate ML commands
+ for loading all wanted theories, usually just
+ ``\texttt{use_thy"$T@i$";}'' for any $T@i$ in leaf position of the
+ dependency graph.
+
+ \item Directory \texttt{MySession/document} contains everything
+ required for the {\LaTeX} stage; only \texttt{root.tex} needs to be
+ provided initially.
+
+ The latter file holds appropriate {\LaTeX} code to commence a
+ document (\verb,\documentclass, etc.), and to include the generated
+ files $T@i$\texttt{.tex} for each theory. Isabelle will generate a
+ file \texttt{session.tex} holding {\LaTeX} commands to include all
+ generated theory output files in topologically sorted order, so
+ \verb,\input{session}, in the body of \texttt{root.tex} does the job
+ in most situations.
+
+ \item \texttt{IsaMakefile} holds appropriate dependencies and
+ invocations of Isabelle tools to control the batch job. In fact,
+ several sessions may be managed by the same \texttt{IsaMakefile}.
+ See the \emph{Isabelle System Manual} \cite{isabelle-sys}
+ for further details, especially on
+ \texttt{isabelle usedir} and \texttt{isabelle make}.
+
+ \end{itemize}
+
+ One may now start to populate the directory \texttt{MySession}, and
+ the file \texttt{MySession/ROOT.ML} accordingly. The file
+ \texttt{MySession/document/root.tex} should also be adapted at some
+ point; the default version is mostly self-explanatory. Note that
+ \verb,\isabellestyle, enables fine-tuning of the general appearance
+ of characters and mathematical symbols (see also
+ \S\ref{sec:doc-prep-symbols}).
+
+ Especially observe the included {\LaTeX} packages \texttt{isabelle}
+ (mandatory), \texttt{isabellesym} (required for mathematical
+ symbols), and the final \texttt{pdfsetup} (provides sane defaults
+ for \texttt{hyperref}, including URL markup). All three are
+ distributed with Isabelle. Further packages may be required in
+ particular applications, say for unusual mathematical symbols.
+
+ \medskip Any additional files for the {\LaTeX} stage go into the
+ \texttt{MySession/document} directory as well. In particular,
+ adding a file named \texttt{root.bib} causes an automatic run of
+ \texttt{bibtex} to process a bibliographic database; see also
+ \texttt{isabelle document} \cite{isabelle-sys}.
+
+ \medskip Any failure of the document preparation phase in an
+ Isabelle batch session leaves the generated sources in their target
+ location, identified by the accompanying error message. This lets
+ you trace {\LaTeX} problems with the generated files at hand.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\isamarkupsubsection{Structure Markup%
+}
+\isamarkuptrue%
+%
+\begin{isamarkuptext}%
+The large-scale structure of Isabelle documents follows existing
+ {\LaTeX} conventions, with chapters, sections, subsubsections etc.
+ The Isar language includes separate \bfindex{markup commands}, which
+ do not affect the formal meaning of a theory (or proof), but result
+ in corresponding {\LaTeX} elements.
+
+ There are separate markup commands depending on the textual context:
+ in header position (just before \isakeyword{theory}), within the
+ theory body, or within a proof. The header needs to be treated
+ specially here, since ordinary theory and proof commands may only
+ occur \emph{after} the initial \isakeyword{theory} specification.
+
+ \medskip
+
+ \begin{tabular}{llll}
+ header & theory & proof & default meaning \\\hline
+ & \commdx{chapter} & & \verb,\chapter, \\
+ \commdx{header} & \commdx{section} & \commdx{sect} & \verb,\section, \\
+ & \commdx{subsection} & \commdx{subsect} & \verb,\subsection, \\
+ & \commdx{subsubsection} & \commdx{subsubsect} & \verb,\subsubsection, \\
+ \end{tabular}
+
+ \medskip
+
+ From the Isabelle perspective, each markup command takes a single
+ $text$ 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
+ rightmost column above.
+
+ \medskip The following source fragment illustrates structure markup
+ of a theory. Note that {\LaTeX} labels may be included inside of
+ section headings as well.
+
+ \begin{ttbox}
+ header {\ttlbrace}* Some properties of Foo Bar elements *{\ttrbrace}
+
+ theory Foo_Bar
+ imports Main
+ begin
+
+ subsection {\ttlbrace}* Basic definitions *{\ttrbrace}
+
+ definition foo :: \dots
+
+ definition bar :: \dots
+
+ subsection {\ttlbrace}* Derived rules *{\ttrbrace}
+
+ lemma fooI: \dots
+ lemma fooE: \dots
+
+ subsection {\ttlbrace}* Main theorem {\ttback}label{\ttlbrace}sec:main-theorem{\ttrbrace} *{\ttrbrace}
+
+ theorem main: \dots
+
+ end
+ \end{ttbox}\vspace{-\medskipamount}
+
+ You may occasionally want to change the meaning of markup commands,
+ say via \verb,\renewcommand, in \texttt{root.tex}. For example,
+ \verb,\isamarkupheader, is a good candidate for some tuning. We
+ could move it up in the hierarchy to become \verb,\chapter,.
+
+\begin{verbatim}
+ \renewcommand{\isamarkupheader}[1]{\chapter{#1}}
+\end{verbatim}
+
+ \noindent Now we must change the document class given in
+ \texttt{root.tex} to something that supports chapters. A suitable
+ command is \verb,\documentclass{report},.
+
+ \medskip The {\LaTeX} macro \verb,\isabellecontext, is maintained to
+ hold the name of the current theory context. This is particularly
+ useful for document headings:
+
+\begin{verbatim}
+ \renewcommand{\isamarkupheader}[1]
+ {\chapter{#1}\markright{THEORY~\isabellecontext}}
+\end{verbatim}
+
+ \noindent Make sure to include something like
+ \verb,\pagestyle{headings}, in \texttt{root.tex}; the document
+ should have more than two pages to show the effect.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\isamarkupsubsection{Formal Comments and Antiquotations \label{sec:doc-prep-text}%
+}
+\isamarkuptrue%
+%
+\begin{isamarkuptext}%
+Isabelle \bfindex{source comments}, which are of the form
+ \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
+ text that are associated with formal Isabelle/Isar commands
+ (\bfindex{marginal comments}), or as standalone paragraphs within a
+ theory or proof context (\bfindex{text blocks}).
+
+ \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{{\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%
+\ {\isaliteral{22}{\isachardoublequoteopen}}A\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ A{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
+\ \ %
+\isamarkupcmt{a triviality of propositional logic%
+}
+\isanewline
+\ \ %
+\isamarkupcmt{(should not really bother)%
+}
+\isanewline
+%
+\isadelimproof
+\ \ %
+\endisadelimproof
+%
+\isatagproof
+\isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}rule\ impI{\isaliteral{29}{\isacharparenright}}\ %
+\isamarkupcmt{implicit assumption step involved here%
+}
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\begin{isamarkuptext}%
+\noindent The above output has been produced as follows:
+
+\begin{verbatim}
+ lemma "A --> A"
+ -- "a triviality of propositional logic"
+ -- "(should not really bother)"
+ by (rule impI) -- "implicit assumption step involved here"
+\end{verbatim}
+
+ From the {\LaTeX} viewpoint, ``\verb,--,'' acts like a markup
+ command, associated with the macro \verb,\isamarkupcmt, (taking a
+ single argument).
+
+ \medskip Text blocks are introduced by the commands \bfindex{text}
+ and \bfindex{txt}, for theory and proof contexts, respectively.
+ Each takes again a single $text$ argument, which is interpreted as a
+ free-form paragraph in {\LaTeX} (surrounded by some additional
+ vertical space). This behavior may be changed by redefining the
+ {\LaTeX} environments of \verb,isamarkuptext, or
+ \verb,isamarkuptxt,, respectively (via \verb,\renewenvironment,) The
+ text style of the body is determined by \verb,\isastyletext, and
+ \verb,\isastyletxt,; the default setup uses a smaller font within
+ proofs. This may be changed as follows:
+
+\begin{verbatim}
+ \renewcommand{\isastyletxt}{\isastyletext}
+\end{verbatim}
+
+ \medskip The $text$ part of Isabelle markup commands essentially
+ inserts \emph{quoted material} into a formal text, mainly for
+ instruction of the reader. An \bfindex{antiquotation} is again a
+ formal object embedded into such an informal portion. The
+ interpretation of antiquotations is limited to some well-formedness
+ checks, with the result being pretty printed to the resulting
+ document. Quoted text blocks together with antiquotations provide
+ an attractive means of referring to formal entities, with good
+ confidence in getting the technical details right (especially syntax
+ and types).
+
+ The general syntax of antiquotations is as follows:
+ \texttt{{\at}{\ttlbrace}$name$ $arguments${\ttrbrace}}, or
+ \texttt{{\at}{\ttlbrace}$name$ [$options$] $arguments${\ttrbrace}}
+ for a comma-separated list of options consisting of a $name$ or
+ \texttt{$name$=$value$} each. The syntax of $arguments$ depends on
+ the kind of antiquotation, it generally follows the same conventions
+ for types, terms, or theorems as in the formal part of a theory.
+
+ \medskip This sentence demonstrates quotations and antiquotations:
+ \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}
+text {\ttlbrace}*
+ This sentence demonstrates quotations and antiquotations:
+ {\at}{\ttlbrace}term "%x y. x"{\ttrbrace} is a well-typed term.
+*{\ttrbrace}
+ \end{ttbox}\vspace{-\medskipamount}
+
+ The notational change from the ASCII character~\verb,%, to the
+ 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{{\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
+ same types as they have in the main goal statement.
+
+ \medskip Several further kinds of antiquotations and options are
+ available \cite{isabelle-isar-ref}. Here are a few commonly used
+ combinations:
+
+ \medskip
+
+ \begin{tabular}{ll}
+ \texttt{\at}\verb,{typ,~$\tau$\verb,}, & print type $\tau$ \\
+ \texttt{\at}\verb,{const,~$c$\verb,}, & check existence of $c$ and print it \\
+ \texttt{\at}\verb,{term,~$t$\verb,}, & print term $t$ \\
+ \texttt{\at}\verb,{prop,~$\phi$\verb,}, & print proposition $\phi$ \\
+ \texttt{\at}\verb,{prop [display],~$\phi$\verb,}, & print large proposition $\phi$ (with linebreaks) \\
+ \texttt{\at}\verb,{prop [source],~$\phi$\verb,}, & check proposition $\phi$, print its input \\
+ \texttt{\at}\verb,{thm,~$a$\verb,}, & print fact $a$ \\
+ \texttt{\at}\verb,{thm,~$a$~\verb,[no_vars]}, & print fact $a$, fixing schematic variables \\
+ \texttt{\at}\verb,{thm [source],~$a$\verb,}, & check availability of fact $a$, print its name \\
+ \texttt{\at}\verb,{text,~$s$\verb,}, & print uninterpreted text $s$ \\
+ \end{tabular}
+
+ \medskip
+
+ Note that \attrdx{no_vars} given above is \emph{not} an
+ antiquotation option, but an attribute of the theorem argument given
+ here. This might be useful with a diagnostic command like
+ \isakeyword{thm}, too.
+
+ \medskip The \texttt{\at}\verb,{text, $s$\verb,}, antiquotation is
+ particularly interesting. Embedding uninterpreted text within an
+ informal body might appear useless at first sight. Here the key
+ 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{{\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
+ Isabelle. Manual {\LaTeX} code would leave more control over the
+ typesetting, but is also slightly more tedious.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\isamarkupsubsection{Interpretation of Symbols \label{sec:doc-prep-symbols}%
+}
+\isamarkuptrue%
+%
+\begin{isamarkuptext}%
+As has been pointed out before (\S\ref{sec:syntax-symbols}),
+ Isabelle symbols are the smallest syntactic entities --- a
+ straightforward generalization of ASCII characters. While Isabelle
+ does not impose any interpretation of the infinite collection of
+ named symbols, {\LaTeX} documents use canonical glyphs for certain
+ standard symbols \cite{isabelle-isar-ref}.
+
+ The {\LaTeX} code produced from Isabelle text follows a simple
+ scheme. You can tune the final appearance by redefining certain
+ macros, say in \texttt{root.tex} of the document.
+
+ \begin{enumerate}
+
+ \item 7-bit ASCII characters: letters \texttt{A\dots Z} and
+ \texttt{a\dots z} are output directly, digits are passed as an
+ argument to the \verb,\isadigit, macro, other characters are
+ replaced by specifically named macros of the form
+ \verb,\isacharXYZ,.
+
+ \item Named symbols: \verb,\,\verb,<XYZ>, is turned into
+ \verb,{\isasymXYZ},; note the additional braces.
+
+ \item Named control symbols: \verb,\,\verb,<^XYZ>, is turned into
+ \verb,\isactrlXYZ,; subsequent symbols may act as arguments if the
+ control macro is defined accordingly.
+
+ \end{enumerate}
+
+ You may occasionally wish to give new {\LaTeX} interpretations of
+ named symbols. This merely requires an appropriate definition of
+ \verb,\isasymXYZ,, for \verb,\,\verb,<XYZ>, (see
+ \texttt{isabelle.sty} for working examples). Control symbols are
+ slightly more difficult to get right, though.
+
+ \medskip The \verb,\isabellestyle, macro provides a high-level
+ interface to tune the general appearance of individual symbols. For
+ example, \verb,\isabellestyle{it}, uses the italics text style to
+ mimic the general appearance of the {\LaTeX} math mode; double
+ quotes are not printed at all. The resulting quality of typesetting
+ is quite good, so this should be the default style for work that
+ gets distributed to a broader audience.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\isamarkupsubsection{Suppressing Output \label{sec:doc-prep-suppress}%
+}
+\isamarkuptrue%
+%
+\begin{isamarkuptext}%
+By default, Isabelle's document system generates a {\LaTeX} file for
+ each theory that gets loaded while running the session. The
+ generated \texttt{session.tex} will include all of these in order of
+ appearance, which in turn gets included by the standard
+ \texttt{root.tex}. Certainly one may change the order or suppress
+ unwanted theories by ignoring \texttt{session.tex} and load
+ individual files directly in \texttt{root.tex}. On the other hand,
+ such an arrangement requires additional maintenance whenever the
+ collection of theories changes.
+
+ Alternatively, one may tune the theory loading process in
+ \texttt{ROOT.ML} itself: traversal of the theory dependency graph
+ may be fine-tuned by adding \verb,use_thy, invocations, although
+ topological sorting still has to be observed. Moreover, the ML
+ operator \verb,no_document, temporarily disables document generation
+ while executing a theory loader command. Its usage is like this:
+
+\begin{verbatim}
+ no_document use_thy "T";
+\end{verbatim}
+
+ \medskip Theory output may be suppressed more selectively, either
+ via \bfindex{tagged command regions} or \bfindex{ignored material}.
+
+ Tagged command regions works by annotating commands with named tags,
+ which correspond to certain {\LaTeX} markup that tells how to treat
+ particular parts of a document when doing the actual type-setting.
+ By default, certain Isabelle/Isar commands are implicitly marked up
+ using the predefined tags ``\emph{theory}'' (for theory begin and
+ end), ``\emph{proof}'' (for proof commands), and ``\emph{ML}'' (for
+ commands involving ML code). Users may add their own tags using the
+ \verb,%,\emph{tag} notation right after a command name. In the
+ subsequent example we hide a particularly irrelevant proof:%
+\end{isamarkuptext}%
+\isamarkuptrue%
+\isacommand{lemma}\isamarkupfalse%
+\ {\isaliteral{22}{\isachardoublequoteopen}}x\ {\isaliteral{3D}{\isacharequal}}\ x{\isaliteral{22}{\isachardoublequoteclose}}%
+\isadeliminvisible
+\ %
+\endisadeliminvisible
+%
+\isataginvisible
+\isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}simp{\isaliteral{29}{\isacharparenright}}%
+\endisataginvisible
+{\isafoldinvisible}%
+%
+\isadeliminvisible
+%
+\endisadeliminvisible
+%
+\begin{isamarkuptext}%
+The original source has been ``\verb,lemma "x = x" by %invisible (simp),''.
+ Tags observe the structure of proofs; adjacent commands with the
+ same tag are joined into a single region. The Isabelle document
+ preparation system allows the user to specify how to interpret a
+ tagged region, in order to keep, drop, or fold the corresponding
+ parts of the document. See the \emph{Isabelle System Manual}
+ \cite{isabelle-sys} for further details, especially on
+ \texttt{isabelle usedir} and \texttt{isabelle document}.
+
+ Ignored material is specified by delimiting the original formal
+ source with special source comments
+ \verb,(,\verb,*,\verb,<,\verb,*,\verb,), and
+ \verb,(,\verb,*,\verb,>,\verb,*,\verb,),. These parts are stripped
+ before the type-setting phase, without affecting the formal checking
+ of the theory, of course. For example, we may hide parts of a proof
+ that seem unfit for general public inspection. The following
+ ``fully automatic'' proof is actually a fake:%
+\end{isamarkuptext}%
+\isamarkuptrue%
+\isacommand{lemma}\isamarkupfalse%
+\ {\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
+\ \ %
+\endisadelimproof
+%
+\isatagproof
+\isacommand{by}\isamarkupfalse%
+\ {\isaliteral{28}{\isacharparenleft}}auto{\isaliteral{29}{\isacharparenright}}%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\begin{isamarkuptext}%
+\noindent The real source of the proof has been as follows:
+
+\begin{verbatim}
+ by (auto(*<*)simp add: zero_less_mult_iff(*>*))
+\end{verbatim}
+%(*
+
+ \medskip Suppressing portions of printed text demands care. You
+ should not misrepresent the underlying theory development. It is
+ easy to invalidate the visible text by hiding references to
+ questionable axioms, for example.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\isadelimtheory
+%
+\endisadelimtheory
+%
+\isatagtheory
+%
+\endisatagtheory
+{\isafoldtheory}%
+%
+\isadelimtheory
+%
+\endisadelimtheory
+\end{isabellebody}%
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "root"
+%%% End: