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-%
-\begin{isabellebody}%
-\def\isabellecontext{Documents}%
-%
-\isadelimtheory
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-\endisadelimtheory
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-\isatagtheory
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-\endisatagtheory
-{\isafoldtheory}%
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-\isadelimtheory
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-\endisadelimtheory
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-\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%
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-\isadelimML
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-\isatagML
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-\endisatagML
-{\isafoldML}%
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-\isadelimML
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-\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
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-\endisadelimML
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-\isatagML
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-\endisatagML
-{\isafoldML}%
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-\isadelimML
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-\endisadelimML
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-\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%
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-\isadelimML
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-\endisadelimML
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-\isatagML
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-\endisatagML
-{\isafoldML}%
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-\isadelimML
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-\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
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-\endisadelimML
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-\isatagML
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-\endisatagML
-{\isafoldML}%
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-\isadelimML
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-\endisadelimML
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-\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: