author | wenzelm |
Sun, 02 Nov 2014 16:05:43 +0100 | |
changeset 58869 | 963fd2084e8f |
parent 58868 | c5e1cce7ace3 |
child 59005 | 1c54ebc68394 |
permissions | -rw-r--r-- |
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(*<*) |
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theory Documents imports Main begin |
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(*>*) |
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section {* Concrete Syntax \label{sec:concrete-syntax} *} |
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text {* |
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The core concept of Isabelle's framework for concrete syntax is that |
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of \bfindex{mixfix annotations}. Associated with any kind of |
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constant declaration, mixfixes affect both the grammar productions |
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for the parser and output templates for the pretty printer. |
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In full generality, parser and pretty printer configuration is a |
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subtle affair~@{cite "isabelle-isar-ref"}. Your syntax specifications need |
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to interact properly with the existing setup of Isabelle/Pure and |
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Isabelle/HOL\@. To avoid creating ambiguities with existing |
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elements, it is particularly important to give new syntactic |
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constructs the right precedence. |
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Below we introduce a few simple syntax declaration |
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forms that already cover many common situations fairly well. |
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*} |
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subsection {* Infix Annotations *} |
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text {* |
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Syntax annotations may be included wherever constants are declared, |
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such as \isacommand{definition} and \isacommand{primrec} --- and also |
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\isacommand{datatype}, which declares constructor operations. |
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Type-constructors may be annotated as well, although this is less |
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frequently encountered in practice (the infix type @{text "\<times>"} comes |
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to mind). |
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Infix declarations\index{infix annotations} provide a useful special |
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case of mixfixes. The following example of the exclusive-or |
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operation on boolean values illustrates typical infix declarations. |
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*} |
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definition xor :: "bool \<Rightarrow> bool \<Rightarrow> bool" (infixl "[+]" 60) |
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where "A [+] B \<equiv> (A \<and> \<not> B) \<or> (\<not> A \<and> B)" |
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text {* |
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\noindent Now @{text "xor A B"} and @{text "A [+] B"} refer to the |
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same expression internally. Any curried function with at least two |
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arguments may be given infix syntax. For partial applications with |
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fewer than two operands, there is a notation using the prefix~@{text |
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op}. For instance, @{text xor} without arguments is represented as |
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@{text "op [+]"}; together with ordinary function application, this |
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turns @{text "xor A"} into @{text "op [+] A"}. |
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The keyword \isakeyword{infixl} seen above specifies an |
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infix operator that is nested to the \emph{left}: in iterated |
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applications the more complex expression appears on the left-hand |
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side, and @{term "A [+] B [+] C"} stands for @{text "(A [+] B) [+] |
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C"}. Similarly, \isakeyword{infixr} means nesting to the |
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\emph{right}, reading @{term "A [+] B [+] C"} as @{text "A [+] (B |
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[+] C)"}. A \emph{non-oriented} declaration via \isakeyword{infix} |
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would render @{term "A [+] B [+] C"} illegal, but demand explicit |
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parentheses to indicate the intended grouping. |
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The string @{text [source] "[+]"} in our annotation refers to the |
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concrete syntax to represent the operator (a literal token), while |
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the number @{text 60} determines the precedence of the construct: |
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the syntactic priorities of the arguments and result. Isabelle/HOL |
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already uses up many popular combinations of ASCII symbols for its |
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own use, including both @{text "+"} and @{text "++"}. Longer |
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character combinations are more likely to be still available for |
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user extensions, such as our~@{text "[+]"}. |
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Operator precedences have a range of 0--1000. Very low or high |
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priorities are reserved for the meta-logic. HOL syntax mainly uses |
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the range of 10--100: the equality infix @{text "="} is centered at |
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50; logical connectives (like @{text "\<or>"} and @{text "\<and>"}) are |
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below 50; algebraic ones (like @{text "+"} and @{text "*"}) are |
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above 50. User syntax should strive to coexist with common HOL |
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forms, or use the mostly unused range 100--900. |
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*} |
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subsection {* Mathematical Symbols \label{sec:syntax-symbols} *} |
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text {* |
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Concrete syntax based on ASCII characters has inherent limitations. |
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Mathematical notation demands a larger repertoire of glyphs. |
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Several standards of extended character sets have been proposed over |
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decades, but none has become universally available so far. Isabelle |
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has its own notion of \bfindex{symbols} as the smallest entities of |
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source text, without referring to internal encodings. There are |
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three kinds of such ``generalized characters'': |
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\begin{enumerate} |
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\item 7-bit ASCII characters |
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\item named symbols: \verb,\,\verb,<,$ident$\verb,>, |
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\item named control symbols: \verb,\,\verb,<^,$ident$\verb,>, |
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\end{enumerate} |
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Here $ident$ is any sequence of letters. |
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This results in an infinite store of symbols, whose |
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interpretation is left to further front-end tools. For example, the |
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Isabelle document processor (see \S\ref{sec:document-preparation}) |
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display the \verb,\,\verb,<forall>, symbol as~@{text \<forall>}. |
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A list of standard Isabelle symbols is given in |
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@{cite "isabelle-isar-ref"}. You may introduce your own |
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interpretation of further symbols by configuring the appropriate |
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front-end tool accordingly, e.g.\ by defining certain {\LaTeX} |
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macros (see also \S\ref{sec:doc-prep-symbols}). There are also a |
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few predefined control symbols, such as \verb,\,\verb,<^sub>, and |
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\verb,\,\verb,<^sup>, for sub- and superscript of the subsequent |
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printable symbol, respectively. For example, \verb,A\<^sup>\<star>, is |
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output as @{text "A\<^sup>\<star>"}. |
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A number of symbols are considered letters by the Isabelle lexer and |
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can be used as part of identifiers. These are the greek letters |
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@{text "\<alpha>"} (\verb+\+\verb+<alpha>+), @{text "\<beta>"} |
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(\verb+\+\verb+<beta>+), etc. (excluding @{text "\<lambda>"}), |
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special letters like @{text "\<A>"} (\verb+\+\verb+<A>+) and @{text |
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"\<AA>"} (\verb+\+\verb+<AA>+). Moreover the control symbol |
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\verb+\+\verb+<^sub>+ may be used to subscript a single letter or digit |
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in the trailing part of an identifier. This means that the input |
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\medskip |
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{\small\noindent \verb,\,\verb,<forall>\,\verb,<alpha>\<^sub>1.,~\verb,\,\verb,<alpha>\<^sub>1 = \,\verb,<Pi>\<^sub>\<A>,} |
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\medskip |
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\noindent is recognized as the term @{term "\<forall>\<alpha>\<^sub>1. \<alpha>\<^sub>1 = \<Pi>\<^sub>\<A>"} |
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by Isabelle. |
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Replacing our previous definition of @{text xor} by the |
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following specifies an Isabelle symbol for the new operator: |
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*} |
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(*<*) |
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hide_const xor |
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setup {* Sign.add_path "version1" *} |
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(*>*) |
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definition xor :: "bool \<Rightarrow> bool \<Rightarrow> bool" (infixl "\<oplus>" 60) |
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where "A \<oplus> B \<equiv> (A \<and> \<not> B) \<or> (\<not> A \<and> B)" |
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(*<*) |
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setup {* Sign.local_path *} |
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(*>*) |
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text {* |
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It is possible to provide alternative syntax forms |
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through the \bfindex{print mode} concept~@{cite "isabelle-isar-ref"}. By |
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convention, the mode of ``$xsymbols$'' is enabled whenever |
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Proof~General's X-Symbol mode or {\LaTeX} output is active. Now |
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consider the following hybrid declaration of @{text xor}: |
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*} |
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(*<*) |
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replaced generic 'hide' command by more conventional 'hide_class', 'hide_type', 'hide_const', 'hide_fact' -- frees some popular keywords;
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parents:
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hide_const xor |
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setup {* Sign.add_path "version2" *} |
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(*>*) |
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definition xor :: "bool \<Rightarrow> bool \<Rightarrow> bool" (infixl "[+]\<ignore>" 60) |
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where "A [+]\<ignore> B \<equiv> (A \<and> \<not> B) \<or> (\<not> A \<and> B)" |
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notation (xsymbols) xor (infixl "\<oplus>\<ignore>" 60) |
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(*<*) |
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setup {* Sign.local_path *} |
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(*>*) |
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text {*\noindent |
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The \commdx{notation} command associates a mixfix |
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annotation with a known constant. The print mode specification, |
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here @{text "(xsymbols)"}, is optional. |
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We may now write @{text "A [+] B"} or @{text "A \<oplus> B"} in input, while |
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output uses the nicer syntax of $xsymbols$ whenever that print mode is |
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active. Such an arrangement is particularly useful for interactive |
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development, where users may type ASCII text and see mathematical |
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symbols displayed during proofs. *} |
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subsection {* Prefix Annotations *} |
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text {* |
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Prefix syntax annotations\index{prefix annotation} are another form |
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of mixfixes @{cite "isabelle-isar-ref"}, without any template arguments or |
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priorities --- just some literal syntax. The following example |
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associates common symbols with the constructors of a datatype. |
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*} |
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datatype currency = |
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Euro nat ("\<euro>") |
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| Pounds nat ("\<pounds>") |
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| Yen nat ("\<yen>") |
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| Dollar nat ("$") |
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text {* |
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\noindent Here the mixfix annotations on the rightmost column happen |
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to consist of a single Isabelle symbol each: \verb,\,\verb,<euro>,, |
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\verb,\,\verb,<pounds>,, \verb,\,\verb,<yen>,, and \verb,$,. Recall |
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that a constructor like @{text Euro} actually is a function @{typ |
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"nat \<Rightarrow> currency"}. The expression @{text "Euro 10"} will be |
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printed as @{term "\<euro> 10"}; only the head of the application is |
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subject to our concrete syntax. This rather simple form already |
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achieves conformance with notational standards of the European |
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Commission. |
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Prefix syntax works the same way for other commands that introduce new constants, e.g. \isakeyword{primrec}. |
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*} |
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subsection {* Abbreviations \label{sec:abbreviations} *} |
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text{* Mixfix syntax annotations merely decorate particular constant |
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application forms with concrete syntax, for instance replacing |
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@{text "xor A B"} by @{text "A \<oplus> B"}. Occasionally, the relationship |
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between some piece of notation and its internal form is more |
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complicated. Here we need \emph{abbreviations}. |
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Command \commdx{abbreviation} introduces an uninterpreted notational |
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constant as an abbreviation for a complex term. Abbreviations are |
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unfolded upon parsing and re-introduced upon printing. This provides a |
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simple mechanism for syntactic macros. |
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A typical use of abbreviations is to introduce relational notation for |
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membership in a set of pairs, replacing @{text "(x, y) \<in> sim"} by |
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@{text "x \<approx> y"}. We assume that a constant @{text sim } of type |
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@{typ"('a \<times> 'a) set"} has been introduced at this point. *} |
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(*<*)consts sim :: "('a \<times> 'a) set"(*>*) |
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abbreviation sim2 :: "'a \<Rightarrow> 'a \<Rightarrow> bool" (infix "\<approx>" 50) |
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where "x \<approx> y \<equiv> (x, y) \<in> sim" |
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text {* \noindent The given meta-equality is used as a rewrite rule |
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after parsing (replacing \mbox{@{prop"x \<approx> y"}} by @{text"(x,y) \<in> |
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sim"}) and before printing (turning @{text"(x,y) \<in> sim"} back into |
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\mbox{@{prop"x \<approx> y"}}). The name of the dummy constant @{text "sim2"} |
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does not matter, as long as it is unique. |
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Another common application of abbreviations is to |
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provide variant versions of fundamental relational expressions, such |
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as @{text \<noteq>} for negated equalities. The following declaration |
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stems from Isabelle/HOL itself: |
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*} |
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abbreviation not_equal :: "'a \<Rightarrow> 'a \<Rightarrow> bool" (infixl "~=\<ignore>" 50) |
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where "x ~=\<ignore> y \<equiv> \<not> (x = y)" |
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notation (xsymbols) not_equal (infix "\<noteq>\<ignore>" 50) |
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text {* \noindent The notation @{text \<noteq>} is introduced separately to restrict it |
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to the \emph{xsymbols} mode. |
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Abbreviations are appropriate when the defined concept is a |
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simple variation on an existing one. But because of the automatic |
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folding and unfolding of abbreviations, they do not scale up well to |
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large hierarchies of concepts. Abbreviations do not replace |
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definitions. |
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Abbreviations are a simplified form of the general concept of |
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\emph{syntax translations}; even heavier transformations may be |
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written in ML @{cite "isabelle-isar-ref"}. |
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*} |
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section {* Document Preparation \label{sec:document-preparation} *} |
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text {* |
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Isabelle/Isar is centered around the concept of \bfindex{formal |
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proof documents}\index{documents|bold}. The outcome of a formal |
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development effort is meant to be a human-readable record, presented |
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as browsable PDF file or printed on paper. The overall document |
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structure follows traditional mathematical articles, with sections, |
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intermediate explanations, definitions, theorems and proofs. |
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\medskip The Isabelle document preparation system essentially acts |
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as a front-end to {\LaTeX}. After checking specifications and |
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proofs formally, the theory sources are turned into typesetting |
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instructions in a schematic manner. This lets you write authentic |
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reports on theory developments with little effort: many technical |
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consistency checks are handled by the system. |
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Here is an example to illustrate the idea of Isabelle document |
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preparation. |
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*} |
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text_raw {* \begin{quotation} *} |
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text {* |
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The following datatype definition of @{text "'a bintree"} models |
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binary trees with nodes being decorated by elements of type @{typ |
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'a}. |
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*} |
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datatype 'a bintree = |
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Leaf | Branch 'a "'a bintree" "'a bintree" |
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text {* |
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\noindent The datatype induction rule generated here is of the form |
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@{thm [indent = 1, display] bintree.induct [no_vars]} |
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*} |
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text_raw {* \end{quotation} *} |
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text {* |
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\noindent The above document output has been produced as follows: |
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\begin{ttbox} |
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text {\ttlbrace}* |
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The following datatype definition of {\at}{\ttlbrace}text "'a bintree"{\ttrbrace} |
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models binary trees with nodes being decorated by elements |
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of type {\at}{\ttlbrace}typ 'a{\ttrbrace}. |
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*{\ttrbrace} |
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datatype 'a bintree = |
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Leaf | Branch 'a "'a bintree" "'a bintree" |
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\end{ttbox} |
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\begin{ttbox} |
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text {\ttlbrace}* |
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{\ttback}noindent The datatype induction rule generated here is |
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of the form {\at}{\ttlbrace}thm [display] bintree.induct [no_vars]{\ttrbrace} |
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*{\ttrbrace} |
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\end{ttbox}\vspace{-\medskipamount} |
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\noindent Here we have augmented the theory by formal comments |
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(using \isakeyword{text} blocks), the informal parts may again refer |
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to formal entities by means of ``antiquotations'' (such as |
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\texttt{\at}\verb,{text "'a bintree"}, or |
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\texttt{\at}\verb,{typ 'a},), see also \S\ref{sec:doc-prep-text}. |
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*} |
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subsection {* Isabelle Sessions *} |
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text {* |
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In contrast to the highly interactive mode of Isabelle/Isar theory |
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development, the document preparation stage essentially works in |
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batch-mode. An Isabelle \bfindex{session} consists of a collection |
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of source files that may contribute to an output document. Each |
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session is derived from a single parent, usually an object-logic |
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image like \texttt{HOL}. This results in an overall tree structure, |
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which is reflected by the output location in the file system |
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(the root directory is determined by the Isabelle settings variable |
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\verb,ISABELLE_BROWSER_INFO,). |
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\medskip The easiest way to manage Isabelle sessions is via |
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\texttt{isabelle mkroot} (to generate an initial session source |
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setup) and \texttt{isabelle build} (to run sessions as specified in |
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the corresponding \texttt{ROOT} file). These Isabelle tools are |
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described in further detail in the \emph{Isabelle System Manual} |
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@{cite "isabelle-sys"}. |
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For example, a new session \texttt{MySession} (with document |
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preparation) may be produced as follows: |
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\begin{verbatim} |
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isabelle mkroot -d MySession |
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isabelle build -D MySession |
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\end{verbatim} |
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The \texttt{isabelle build} job also informs about the file-system |
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location of the ultimate results. The above dry run should be able |
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to produce some \texttt{document.pdf} (with dummy title, empty table |
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of contents etc.). Any failure at this stage usually indicates |
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technical problems of the {\LaTeX} installation. |
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\medskip The detailed arrangement of the session sources is as |
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follows. |
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\begin{itemize} |
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\item Directory \texttt{MySession} holds the required theory files |
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$T@1$\texttt{.thy}, \dots, $T@n$\texttt{.thy}. |
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\item File \texttt{MySession/ROOT} specifies the session options and |
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content, with declarations for all wanted theories; it is sufficient |
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to specify the terminal nodes of the theory dependency graph. |
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\item Directory \texttt{MySession/document} contains everything |
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required for the {\LaTeX} stage; only \texttt{root.tex} needs to be |
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provided initially. |
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The latter file holds appropriate {\LaTeX} code to commence a |
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document (\verb,\documentclass, etc.), and to include the generated |
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files $T@i$\texttt{.tex} for each theory. Isabelle will generate a |
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file \texttt{session.tex} holding {\LaTeX} commands to include all |
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generated theory output files in topologically sorted order, so |
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\verb,\input{session}, in the body of \texttt{root.tex} does the job |
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in most situations. |
|
12653 | 387 |
|
12645 | 388 |
\end{itemize} |
389 |
||
51057 | 390 |
One may now start to populate the directory \texttt{MySession} and |
391 |
its \texttt{ROOT} file accordingly. The file |
|
12766 | 392 |
\texttt{MySession/document/root.tex} should also be adapted at some |
12685 | 393 |
point; the default version is mostly self-explanatory. Note that |
394 |
\verb,\isabellestyle, enables fine-tuning of the general appearance |
|
395 |
of characters and mathematical symbols (see also |
|
396 |
\S\ref{sec:doc-prep-symbols}). |
|
12653 | 397 |
|
12685 | 398 |
Especially observe the included {\LaTeX} packages \texttt{isabelle} |
399 |
(mandatory), \texttt{isabellesym} (required for mathematical |
|
12743 | 400 |
symbols), and the final \texttt{pdfsetup} (provides sane defaults |
12764 | 401 |
for \texttt{hyperref}, including URL markup). All three are |
12743 | 402 |
distributed with Isabelle. Further packages may be required in |
12764 | 403 |
particular applications, say for unusual mathematical symbols. |
12645 | 404 |
|
12746 | 405 |
\medskip Any additional files for the {\LaTeX} stage go into the |
406 |
\texttt{MySession/document} directory as well. In particular, |
|
12766 | 407 |
adding a file named \texttt{root.bib} causes an automatic run of |
408 |
\texttt{bibtex} to process a bibliographic database; see also |
|
58620 | 409 |
\texttt{isabelle document} @{cite "isabelle-sys"}. |
12645 | 410 |
|
12653 | 411 |
\medskip Any failure of the document preparation phase in an |
12670 | 412 |
Isabelle batch session leaves the generated sources in their target |
12766 | 413 |
location, identified by the accompanying error message. This lets |
414 |
you trace {\LaTeX} problems with the generated files at hand. |
|
12645 | 415 |
*} |
416 |
||
417 |
||
12648 | 418 |
subsection {* Structure Markup *} |
12645 | 419 |
|
12653 | 420 |
text {* |
421 |
The large-scale structure of Isabelle documents follows existing |
|
422 |
{\LaTeX} conventions, with chapters, sections, subsubsections etc. |
|
423 |
The Isar language includes separate \bfindex{markup commands}, which |
|
12681 | 424 |
do not affect the formal meaning of a theory (or proof), but result |
12665 | 425 |
in corresponding {\LaTeX} elements. |
12645 | 426 |
|
427 |
From the Isabelle perspective, each markup command takes a single |
|
12746 | 428 |
$text$ argument (delimited by \verb,",~@{text \<dots>}~\verb,", or |
429 |
\verb,{,\verb,*,~@{text \<dots>}~\verb,*,\verb,},). After stripping any |
|
12645 | 430 |
surrounding white space, the argument is passed to a {\LaTeX} macro |
12766 | 431 |
\verb,\isamarkupXYZ, for command \isakeyword{XYZ}. These macros are |
432 |
defined in \verb,isabelle.sty, according to the meaning given in the |
|
433 |
rightmost column above. |
|
12645 | 434 |
|
435 |
\medskip The following source fragment illustrates structure markup |
|
12653 | 436 |
of a theory. Note that {\LaTeX} labels may be included inside of |
437 |
section headings as well. |
|
12645 | 438 |
|
439 |
\begin{ttbox} |
|
58869 | 440 |
section {\ttlbrace}* Some properties of Foo Bar elements *{\ttrbrace} |
12645 | 441 |
|
15136 | 442 |
theory Foo_Bar |
15141 | 443 |
imports Main |
15136 | 444 |
begin |
12645 | 445 |
|
446 |
subsection {\ttlbrace}* Basic definitions *{\ttrbrace} |
|
447 |
||
27027 | 448 |
definition foo :: \dots |
12648 | 449 |
|
27027 | 450 |
definition bar :: \dots |
12648 | 451 |
|
12645 | 452 |
subsection {\ttlbrace}* Derived rules *{\ttrbrace} |
453 |
||
454 |
lemma fooI: \dots |
|
455 |
lemma fooE: \dots |
|
456 |
||
12648 | 457 |
subsection {\ttlbrace}* Main theorem {\ttback}label{\ttlbrace}sec:main-theorem{\ttrbrace} *{\ttrbrace} |
12645 | 458 |
|
459 |
theorem main: \dots |
|
460 |
||
461 |
end |
|
58869 | 462 |
\end{ttbox} |
12645 | 463 |
*} |
464 |
||
465 |
||
12744 | 466 |
subsection {* Formal Comments and Antiquotations \label{sec:doc-prep-text} *} |
12645 | 467 |
|
468 |
text {* |
|
12744 | 469 |
Isabelle \bfindex{source comments}, which are of the form |
12746 | 470 |
\verb,(,\verb,*,~@{text \<dots>}~\verb,*,\verb,),, essentially act like |
471 |
white space and do not really contribute to the content. They |
|
472 |
mainly serve technical purposes to mark certain oddities in the raw |
|
473 |
input text. In contrast, \bfindex{formal comments} are portions of |
|
474 |
text that are associated with formal Isabelle/Isar commands |
|
12681 | 475 |
(\bfindex{marginal comments}), or as standalone paragraphs within a |
12665 | 476 |
theory or proof context (\bfindex{text blocks}). |
12659 | 477 |
|
478 |
\medskip Marginal comments are part of each command's concrete |
|
58620 | 479 |
syntax @{cite "isabelle-isar-ref"}; the common form is ``\verb,--,~$text$'' |
12746 | 480 |
where $text$ is delimited by \verb,",@{text \<dots>}\verb,", or |
481 |
\verb,{,\verb,*,~@{text \<dots>}~\verb,*,\verb,}, as before. Multiple |
|
12670 | 482 |
marginal comments may be given at the same time. Here is a simple |
483 |
example: |
|
12665 | 484 |
*} |
485 |
||
486 |
lemma "A --> A" |
|
487 |
-- "a triviality of propositional logic" |
|
488 |
-- "(should not really bother)" |
|
489 |
by (rule impI) -- "implicit assumption step involved here" |
|
490 |
||
491 |
text {* |
|
492 |
\noindent The above output has been produced as follows: |
|
12659 | 493 |
|
494 |
\begin{verbatim} |
|
495 |
lemma "A --> A" |
|
496 |
-- "a triviality of propositional logic" |
|
497 |
-- "(should not really bother)" |
|
498 |
by (rule impI) -- "implicit assumption step involved here" |
|
499 |
\end{verbatim} |
|
500 |
||
12670 | 501 |
From the {\LaTeX} viewpoint, ``\verb,--,'' acts like a markup |
502 |
command, associated with the macro \verb,\isamarkupcmt, (taking a |
|
503 |
single argument). |
|
12659 | 504 |
|
12665 | 505 |
\medskip Text blocks are introduced by the commands \bfindex{text} |
506 |
and \bfindex{txt}, for theory and proof contexts, respectively. |
|
507 |
Each takes again a single $text$ argument, which is interpreted as a |
|
508 |
free-form paragraph in {\LaTeX} (surrounded by some additional |
|
12670 | 509 |
vertical space). This behavior may be changed by redefining the |
510 |
{\LaTeX} environments of \verb,isamarkuptext, or |
|
511 |
\verb,isamarkuptxt,, respectively (via \verb,\renewenvironment,) The |
|
512 |
text style of the body is determined by \verb,\isastyletext, and |
|
513 |
\verb,\isastyletxt,; the default setup uses a smaller font within |
|
12746 | 514 |
proofs. This may be changed as follows: |
515 |
||
516 |
\begin{verbatim} |
|
517 |
\renewcommand{\isastyletxt}{\isastyletext} |
|
518 |
\end{verbatim} |
|
12659 | 519 |
|
12766 | 520 |
\medskip The $text$ part of Isabelle markup commands essentially |
521 |
inserts \emph{quoted material} into a formal text, mainly for |
|
522 |
instruction of the reader. An \bfindex{antiquotation} is again a |
|
523 |
formal object embedded into such an informal portion. The |
|
524 |
interpretation of antiquotations is limited to some well-formedness |
|
525 |
checks, with the result being pretty printed to the resulting |
|
526 |
document. Quoted text blocks together with antiquotations provide |
|
527 |
an attractive means of referring to formal entities, with good |
|
528 |
confidence in getting the technical details right (especially syntax |
|
529 |
and types). |
|
12659 | 530 |
|
12665 | 531 |
The general syntax of antiquotations is as follows: |
12659 | 532 |
\texttt{{\at}{\ttlbrace}$name$ $arguments${\ttrbrace}}, or |
533 |
\texttt{{\at}{\ttlbrace}$name$ [$options$] $arguments${\ttrbrace}} |
|
12665 | 534 |
for a comma-separated list of options consisting of a $name$ or |
12766 | 535 |
\texttt{$name$=$value$} each. The syntax of $arguments$ depends on |
536 |
the kind of antiquotation, it generally follows the same conventions |
|
537 |
for types, terms, or theorems as in the formal part of a theory. |
|
12645 | 538 |
|
12766 | 539 |
\medskip This sentence demonstrates quotations and antiquotations: |
540 |
@{term "%x y. x"} is a well-typed term. |
|
12659 | 541 |
|
12764 | 542 |
\medskip\noindent The output above was produced as follows: |
12659 | 543 |
\begin{ttbox} |
544 |
text {\ttlbrace}* |
|
12764 | 545 |
This sentence demonstrates quotations and antiquotations: |
12659 | 546 |
{\at}{\ttlbrace}term "%x y. x"{\ttrbrace} is a well-typed term. |
547 |
*{\ttrbrace} |
|
12766 | 548 |
\end{ttbox}\vspace{-\medskipamount} |
12659 | 549 |
|
12764 | 550 |
The notational change from the ASCII character~\verb,%, to the |
12766 | 551 |
symbol~@{text \<lambda>} reveals that Isabelle printed this term, after |
552 |
parsing and type-checking. Document preparation enables symbolic |
|
553 |
output by default. |
|
12659 | 554 |
|
16523 | 555 |
\medskip The next example includes an option to show the type of all |
556 |
variables. The antiquotation |
|
12766 | 557 |
\texttt{{\at}}\verb,{term [show_types] "%x y. x"}, produces the |
558 |
output @{term [show_types] "%x y. x"}. Type inference has figured |
|
559 |
out the most general typings in the present theory context. Terms |
|
560 |
may acquire different typings due to constraints imposed by their |
|
561 |
environment; within a proof, for example, variables are given the |
|
562 |
same types as they have in the main goal statement. |
|
12659 | 563 |
|
12764 | 564 |
\medskip Several further kinds of antiquotations and options are |
58620 | 565 |
available @{cite "isabelle-isar-ref"}. Here are a few commonly used |
12670 | 566 |
combinations: |
12659 | 567 |
|
568 |
\medskip |
|
12651 | 569 |
|
12659 | 570 |
\begin{tabular}{ll} |
571 |
\texttt{\at}\verb,{typ,~$\tau$\verb,}, & print type $\tau$ \\ |
|
25338 | 572 |
\texttt{\at}\verb,{const,~$c$\verb,}, & check existence of $c$ and print it \\ |
12659 | 573 |
\texttt{\at}\verb,{term,~$t$\verb,}, & print term $t$ \\ |
574 |
\texttt{\at}\verb,{prop,~$\phi$\verb,}, & print proposition $\phi$ \\ |
|
12665 | 575 |
\texttt{\at}\verb,{prop [display],~$\phi$\verb,}, & print large proposition $\phi$ (with linebreaks) \\ |
12659 | 576 |
\texttt{\at}\verb,{prop [source],~$\phi$\verb,}, & check proposition $\phi$, print its input \\ |
577 |
\texttt{\at}\verb,{thm,~$a$\verb,}, & print fact $a$ \\ |
|
578 |
\texttt{\at}\verb,{thm,~$a$~\verb,[no_vars]}, & print fact $a$, fixing schematic variables \\ |
|
12746 | 579 |
\texttt{\at}\verb,{thm [source],~$a$\verb,}, & check availability of fact $a$, print its name \\ |
12659 | 580 |
\texttt{\at}\verb,{text,~$s$\verb,}, & print uninterpreted text $s$ \\ |
581 |
\end{tabular} |
|
582 |
||
583 |
\medskip |
|
584 |
||
12665 | 585 |
Note that \attrdx{no_vars} given above is \emph{not} an |
586 |
antiquotation option, but an attribute of the theorem argument given |
|
587 |
here. This might be useful with a diagnostic command like |
|
588 |
\isakeyword{thm}, too. |
|
12659 | 589 |
|
12665 | 590 |
\medskip The \texttt{\at}\verb,{text, $s$\verb,}, antiquotation is |
12659 | 591 |
particularly interesting. Embedding uninterpreted text within an |
12665 | 592 |
informal body might appear useless at first sight. Here the key |
593 |
virtue is that the string $s$ is processed as Isabelle output, |
|
594 |
interpreting Isabelle symbols appropriately. |
|
12659 | 595 |
|
12665 | 596 |
For example, \texttt{\at}\verb,{text "\<forall>\<exists>"}, produces @{text |
597 |
"\<forall>\<exists>"}, according to the standard interpretation of these symbol |
|
598 |
(cf.\ \S\ref{sec:doc-prep-symbols}). Thus we achieve consistent |
|
12659 | 599 |
mathematical notation in both the formal and informal parts of the |
12766 | 600 |
document very easily, independently of the term language of |
601 |
Isabelle. Manual {\LaTeX} code would leave more control over the |
|
602 |
typesetting, but is also slightly more tedious. |
|
12645 | 603 |
*} |
604 |
||
605 |
||
12674 | 606 |
subsection {* Interpretation of Symbols \label{sec:doc-prep-symbols} *} |
12645 | 607 |
|
608 |
text {* |
|
12665 | 609 |
As has been pointed out before (\S\ref{sec:syntax-symbols}), |
12670 | 610 |
Isabelle symbols are the smallest syntactic entities --- a |
12681 | 611 |
straightforward generalization of ASCII characters. While Isabelle |
12665 | 612 |
does not impose any interpretation of the infinite collection of |
12764 | 613 |
named symbols, {\LaTeX} documents use canonical glyphs for certain |
58620 | 614 |
standard symbols @{cite "isabelle-isar-ref"}. |
12659 | 615 |
|
12766 | 616 |
The {\LaTeX} code produced from Isabelle text follows a simple |
617 |
scheme. You can tune the final appearance by redefining certain |
|
618 |
macros, say in \texttt{root.tex} of the document. |
|
12670 | 619 |
|
620 |
\begin{enumerate} |
|
12659 | 621 |
|
12670 | 622 |
\item 7-bit ASCII characters: letters \texttt{A\dots Z} and |
12746 | 623 |
\texttt{a\dots z} are output directly, digits are passed as an |
12670 | 624 |
argument to the \verb,\isadigit, macro, other characters are |
625 |
replaced by specifically named macros of the form |
|
12665 | 626 |
\verb,\isacharXYZ,. |
12659 | 627 |
|
12766 | 628 |
\item Named symbols: \verb,\,\verb,<XYZ>, is turned into |
629 |
\verb,{\isasymXYZ},; note the additional braces. |
|
12659 | 630 |
|
12766 | 631 |
\item Named control symbols: \verb,\,\verb,<^XYZ>, is turned into |
632 |
\verb,\isactrlXYZ,; subsequent symbols may act as arguments if the |
|
633 |
control macro is defined accordingly. |
|
12670 | 634 |
|
12659 | 635 |
\end{enumerate} |
12665 | 636 |
|
12764 | 637 |
You may occasionally wish to give new {\LaTeX} interpretations of |
638 |
named symbols. This merely requires an appropriate definition of |
|
12766 | 639 |
\verb,\isasymXYZ,, for \verb,\,\verb,<XYZ>, (see |
12746 | 640 |
\texttt{isabelle.sty} for working examples). Control symbols are |
641 |
slightly more difficult to get right, though. |
|
12665 | 642 |
|
643 |
\medskip The \verb,\isabellestyle, macro provides a high-level |
|
644 |
interface to tune the general appearance of individual symbols. For |
|
12670 | 645 |
example, \verb,\isabellestyle{it}, uses the italics text style to |
646 |
mimic the general appearance of the {\LaTeX} math mode; double |
|
12743 | 647 |
quotes are not printed at all. The resulting quality of typesetting |
648 |
is quite good, so this should be the default style for work that |
|
649 |
gets distributed to a broader audience. |
|
12645 | 650 |
*} |
651 |
||
652 |
||
12653 | 653 |
subsection {* Suppressing Output \label{sec:doc-prep-suppress} *} |
12645 | 654 |
|
655 |
text {* |
|
12748 | 656 |
By default, Isabelle's document system generates a {\LaTeX} file for |
657 |
each theory that gets loaded while running the session. The |
|
658 |
generated \texttt{session.tex} will include all of these in order of |
|
659 |
appearance, which in turn gets included by the standard |
|
12743 | 660 |
\texttt{root.tex}. Certainly one may change the order or suppress |
12746 | 661 |
unwanted theories by ignoring \texttt{session.tex} and load |
662 |
individual files directly in \texttt{root.tex}. On the other hand, |
|
663 |
such an arrangement requires additional maintenance whenever the |
|
664 |
collection of theories changes. |
|
12648 | 665 |
|
666 |
Alternatively, one may tune the theory loading process in |
|
51057 | 667 |
\texttt{ROOT} itself: some sequential order of \textbf{theories} |
668 |
sections may enforce a certain traversal of the dependency graph, |
|
669 |
although this could degrade parallel processing. The nodes of each |
|
670 |
sub-graph that is specified here are presented in some topological |
|
671 |
order of their formal dependencies. |
|
672 |
||
673 |
Moreover, the system build option \verb,document=false, allows to |
|
674 |
disable document generation for some theories. Its usage in the |
|
675 |
session \texttt{ROOT} is like this: |
|
12648 | 676 |
|
677 |
\begin{verbatim} |
|
51057 | 678 |
theories [document = false] T |
12648 | 679 |
\end{verbatim} |
12645 | 680 |
|
17183 | 681 |
\medskip Theory output may be suppressed more selectively, either |
682 |
via \bfindex{tagged command regions} or \bfindex{ignored material}. |
|
12648 | 683 |
|
17183 | 684 |
Tagged command regions works by annotating commands with named tags, |
685 |
which correspond to certain {\LaTeX} markup that tells how to treat |
|
686 |
particular parts of a document when doing the actual type-setting. |
|
687 |
By default, certain Isabelle/Isar commands are implicitly marked up |
|
688 |
using the predefined tags ``\emph{theory}'' (for theory begin and |
|
689 |
end), ``\emph{proof}'' (for proof commands), and ``\emph{ML}'' (for |
|
690 |
commands involving ML code). Users may add their own tags using the |
|
691 |
\verb,%,\emph{tag} notation right after a command name. In the |
|
692 |
subsequent example we hide a particularly irrelevant proof: |
|
693 |
*} |
|
12648 | 694 |
|
17183 | 695 |
lemma "x = x" by %invisible (simp) |
12648 | 696 |
|
17183 | 697 |
text {* |
698 |
The original source has been ``\verb,lemma "x = x" by %invisible (simp),''. |
|
699 |
Tags observe the structure of proofs; adjacent commands with the |
|
700 |
same tag are joined into a single region. The Isabelle document |
|
701 |
preparation system allows the user to specify how to interpret a |
|
702 |
tagged region, in order to keep, drop, or fold the corresponding |
|
703 |
parts of the document. See the \emph{Isabelle System Manual} |
|
58620 | 704 |
@{cite "isabelle-sys"} for further details, especially on |
51057 | 705 |
\texttt{isabelle build} and \texttt{isabelle document}. |
12648 | 706 |
|
17183 | 707 |
Ignored material is specified by delimiting the original formal |
708 |
source with special source comments |
|
709 |
\verb,(,\verb,*,\verb,<,\verb,*,\verb,), and |
|
710 |
\verb,(,\verb,*,\verb,>,\verb,*,\verb,),. These parts are stripped |
|
711 |
before the type-setting phase, without affecting the formal checking |
|
712 |
of the theory, of course. For example, we may hide parts of a proof |
|
713 |
that seem unfit for general public inspection. The following |
|
714 |
``fully automatic'' proof is actually a fake: |
|
12651 | 715 |
*} |
716 |
||
717 |
lemma "x \<noteq> (0::int) \<Longrightarrow> 0 < x * x" |
|
14353
79f9fbef9106
Added lemmas to Ring_and_Field with slightly modified simplification rules
paulson
parents:
13439
diff
changeset
|
718 |
by (auto(*<*)simp add: zero_less_mult_iff(*>*)) |
12651 | 719 |
|
720 |
text {* |
|
17183 | 721 |
\noindent The real source of the proof has been as follows: |
12651 | 722 |
|
723 |
\begin{verbatim} |
|
14353
79f9fbef9106
Added lemmas to Ring_and_Field with slightly modified simplification rules
paulson
parents:
13439
diff
changeset
|
724 |
by (auto(*<*)simp add: zero_less_mult_iff(*>*)) |
12659 | 725 |
\end{verbatim} |
726 |
%(* |
|
12651 | 727 |
|
12766 | 728 |
\medskip Suppressing portions of printed text demands care. You |
729 |
should not misrepresent the underlying theory development. It is |
|
730 |
easy to invalidate the visible text by hiding references to |
|
17183 | 731 |
questionable axioms, for example. |
12629 | 732 |
*} |
733 |
||
11647 | 734 |
(*<*) |
735 |
end |
|
736 |
(*>*) |