author | wenzelm |
Thu, 05 Nov 2015 00:02:30 +0100 | |
changeset 61579 | 634cd44bb1d3 |
parent 61503 | 28e788ca2c5d |
child 61656 | cfabbc083977 |
permissions | -rw-r--r-- |
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theory Outer_Syntax |
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imports Base Main |
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begin |
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chapter \<open>Outer syntax --- the theory language \label{ch:outer-syntax}\<close> |
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text \<open> |
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The rather generic framework of Isabelle/Isar syntax emerges from |
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three main syntactic categories: \<^emph>\<open>commands\<close> of the top-level |
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Isar engine (covering theory and proof elements), \<^emph>\<open>methods\<close> for |
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general goal refinements (analogous to traditional ``tactics''), and |
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\<^emph>\<open>attributes\<close> for operations on facts (within a certain |
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context). Subsequently we give a reference of basic syntactic |
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entities underlying Isabelle/Isar syntax in a bottom-up manner. |
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Concrete theory and proof language elements will be introduced later |
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on. |
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\<^medskip> |
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In order to get started with writing well-formed |
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Isabelle/Isar documents, the most important aspect to be noted is |
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the difference of \<^emph>\<open>inner\<close> versus \<^emph>\<open>outer\<close> syntax. Inner |
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syntax is that of Isabelle types and terms of the logic, while outer |
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syntax is that of Isabelle/Isar theory sources (specifications and |
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proofs). As a general rule, inner syntax entities may occur only as |
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\<^emph>\<open>atomic entities\<close> within outer syntax. For example, the string |
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\<^verbatim>\<open>"x + y"\<close> and identifier \<^verbatim>\<open>z\<close> are legal term |
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specifications within a theory, while \<^verbatim>\<open>x + y\<close> without |
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quotes is not. |
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Printed theory documents usually omit quotes to gain readability |
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(this is a matter of {\LaTeX} macro setup, say via \<^verbatim>\<open>\isabellestyle\<close>, |
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see also @{cite "isabelle-system"}). Experienced |
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users of Isabelle/Isar may easily reconstruct the lost technical |
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information, while mere readers need not care about quotes at all. |
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\<close> |
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section \<open>Commands\<close> |
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text \<open> |
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\begin{matharray}{rcl} |
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@{command_def "print_commands"}\<open>\<^sup>*\<close> & : & \<open>any \<rightarrow>\<close> \\ |
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@{command_def "help"}\<open>\<^sup>*\<close> & : & \<open>any \<rightarrow>\<close> \\ |
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\end{matharray} |
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@{rail \<open> |
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@@{command help} (@{syntax name} * ) |
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\<close>} |
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\<^descr> @{command "print_commands"} prints all outer syntax keywords |
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and commands. |
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\<^descr> @{command "help"}~\<open>pats\<close> retrieves outer syntax |
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commands according to the specified name patterns. |
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\<close> |
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subsubsection \<open>Examples\<close> |
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text \<open>Some common diagnostic commands are retrieved like this |
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(according to usual naming conventions):\<close> |
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help "print" |
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help "find" |
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section \<open>Lexical matters \label{sec:outer-lex}\<close> |
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text \<open>The outer lexical syntax consists of three main categories of |
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syntax tokens: |
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\<^enum> \<^emph>\<open>major keywords\<close> --- the command names that are available |
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in the present logic session; |
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\<^enum> \<^emph>\<open>minor keywords\<close> --- additional literal tokens required |
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by the syntax of commands; |
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\<^enum> \<^emph>\<open>named tokens\<close> --- various categories of identifiers etc. |
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Major keywords and minor keywords are guaranteed to be disjoint. |
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This helps user-interfaces to determine the overall structure of a |
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theory text, without knowing the full details of command syntax. |
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Internally, there is some additional information about the kind of |
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major keywords, which approximates the command type (theory command, |
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proof command etc.). |
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Keywords override named tokens. For example, the presence of a |
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command called \<^verbatim>\<open>term\<close> inhibits the identifier \<^verbatim>\<open>term\<close>, but the |
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string \<^verbatim>\<open>"term"\<close> can be used instead. |
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By convention, the outer syntax always allows quoted strings in |
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addition to identifiers, wherever a named entity is expected. |
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When tokenizing a given input sequence, the lexer repeatedly takes |
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the longest prefix of the input that forms a valid token. Spaces, |
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tabs, newlines and formfeeds between tokens serve as explicit |
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separators. |
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\<^medskip> |
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The categories for named tokens are defined once and for all as follows. |
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\begin{center} |
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\begin{supertabular}{rcl} |
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@{syntax_def ident} & = & \<open>letter (subscript\<^sup>? quasiletter)\<^sup>*\<close> \\ |
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@{syntax_def longident} & = & \<open>ident(\<close>\<^verbatim>\<open>.\<close>\<open>ident)\<^sup>+\<close> \\ |
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@{syntax_def symident} & = & \<open>sym\<^sup>+ |\<close>~~\<^verbatim>\<open>\\<close>\<^verbatim>\<open><\<close>\<open>ident\<close>\<^verbatim>\<open>>\<close> \\ |
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@{syntax_def nat} & = & \<open>digit\<^sup>+\<close> \\ |
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@{syntax_def float} & = & @{syntax_ref nat}\<^verbatim>\<open>.\<close>@{syntax_ref nat}~~\<open>|\<close>~~\<^verbatim>\<open>-\<close>@{syntax_ref nat}\<^verbatim>\<open>.\<close>@{syntax_ref nat} \\ |
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@{syntax_def var} & = & \<^verbatim>\<open>?\<close>\<open>ident |\<close>~~\<^verbatim>\<open>?\<close>\<open>ident\<close>\<^verbatim>\<open>.\<close>\<open>nat\<close> \\ |
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@{syntax_def typefree} & = & \<^verbatim>\<open>'\<close>\<open>ident\<close> \\ |
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@{syntax_def typevar} & = & \<^verbatim>\<open>?\<close>\<open>typefree |\<close>~~\<^verbatim>\<open>?\<close>\<open>typefree\<close>\<^verbatim>\<open>.\<close>\<open>nat\<close> \\ |
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@{syntax_def string} & = & \<^verbatim>\<open>"\<close> \<open>\<dots>\<close> \<^verbatim>\<open>"\<close> \\ |
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@{syntax_def altstring} & = & \<^verbatim>\<open>`\<close> \<open>\<dots>\<close> \<^verbatim>\<open>`\<close> \\ |
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@{syntax_def cartouche} & = & @{verbatim "\<open>"} \<open>\<dots>\<close> @{verbatim "\<close>"} \\ |
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@{syntax_def verbatim} & = & \<^verbatim>\<open>{*\<close> \<open>\<dots>\<close> \<^verbatim>\<open>*}\<close> \\[1ex] |
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\<open>letter\<close> & = & \<open>latin |\<close>~~\<^verbatim>\<open>\\<close>\<^verbatim>\<open><\<close>\<open>latin\<close>\<^verbatim>\<open>>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\\<close>\<^verbatim>\<open><\<close>\<open>latin latin\<close>\<^verbatim>\<open>>\<close>~~\<open>| greek |\<close> \\ |
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\<open>subscript\<close> & = & \<^verbatim>\<open>\<^sub>\<close> \\ |
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\<open>quasiletter\<close> & = & \<open>letter | digit |\<close>~~\<^verbatim>\<open>_\<close>~~\<open>|\<close>~~\<^verbatim>\<open>'\<close> \\ |
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\<open>latin\<close> & = & \<^verbatim>\<open>a\<close>~~\<open>| \<dots> |\<close>~~\<^verbatim>\<open>z\<close>~~\<open>|\<close>~~\<^verbatim>\<open>A\<close>~~\<open>| \<dots> |\<close>~~\<^verbatim>\<open>Z\<close> \\ |
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\<open>digit\<close> & = & \<^verbatim>\<open>0\<close>~~\<open>| \<dots> |\<close>~~\<^verbatim>\<open>9\<close> \\ |
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\<open>sym\<close> & = & \<^verbatim>\<open>!\<close>~~\<open>|\<close>~~\<^verbatim>\<open>#\<close>~~\<open>|\<close>~~\<^verbatim>\<open>$\<close>~~\<open>|\<close>~~\<^verbatim>\<open>%\<close>~~\<open>|\<close>~~\<^verbatim>\<open>&\<close>~~\<open>|\<close>~~\<^verbatim>\<open>*\<close>~~\<open>|\<close>~~\<^verbatim>\<open>+\<close>~~\<open>|\<close>~~\<^verbatim>\<open>-\<close>~~\<open>|\<close>~~\<^verbatim>\<open>/\<close>~~\<open>|\<close> \\ |
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& & \<^verbatim>\<open><\<close>~~\<open>|\<close>~~\<^verbatim>\<open>=\<close>~~\<open>|\<close>~~\<^verbatim>\<open>>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>?\<close>~~\<open>|\<close>~~\<^verbatim>\<open>@\<close>~~\<open>|\<close>~~\<^verbatim>\<open>^\<close>~~\<open>|\<close>~~\<^verbatim>\<open>_\<close>~~\<open>|\<close>~~\<^verbatim>\<open>|\<close>~~\<open>|\<close>~~\<^verbatim>\<open>~\<close> \\ |
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\<open>greek\<close> & = & \<^verbatim>\<open>\<alpha>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<beta>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<gamma>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<delta>\<close>~~\<open>|\<close> \\ |
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& & \<^verbatim>\<open>\<epsilon>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<zeta>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<eta>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<theta>\<close>~~\<open>|\<close> \\ |
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& & \<^verbatim>\<open>\<iota>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<kappa>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<mu>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<nu>\<close>~~\<open>|\<close> \\ |
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& & \<^verbatim>\<open>\<xi>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<pi>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<rho>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<sigma>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<tau>\<close>~~\<open>|\<close> \\ |
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& & \<^verbatim>\<open>\<upsilon>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<phi>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<chi>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<psi>\<close>~~\<open>|\<close> \\ |
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& & \<^verbatim>\<open>\<omega>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Gamma>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Delta>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Theta>\<close>~~\<open>|\<close> \\ |
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& & \<^verbatim>\<open>\<Lambda>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Xi>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Pi>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Sigma>\<close>~~\<open>|\<close> \\ |
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& & \<^verbatim>\<open>\<Upsilon>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Phi>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Psi>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Omega>\<close> \\ |
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\end{supertabular} |
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\end{center} |
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A @{syntax_ref var} or @{syntax_ref typevar} describes an unknown, |
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which is internally a pair of base name and index (ML type @{ML_type |
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indexname}). These components are either separated by a dot as in |
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\<open>?x.1\<close> or \<open>?x7.3\<close> or run together as in \<open>?x1\<close>. The latter form is possible |
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if the base name does not end with digits. If the index is 0, it may be |
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dropped altogether: \<open>?x\<close> and \<open>?x0\<close> and \<open>?x.0\<close> all refer to the |
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same unknown, with basename \<open>x\<close> and index 0. |
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The syntax of @{syntax_ref string} admits any characters, including |
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newlines; ``\<^verbatim>\<open>"\<close>'' (double-quote) and ``\<^verbatim>\<open>\\<close>'' |
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(backslash) need to be escaped by a backslash; arbitrary |
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character codes may be specified as ``\<^verbatim>\<open>\\<close>\<open>ddd\<close>'', |
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with three decimal digits. Alternative strings according to |
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@{syntax_ref altstring} are analogous, using single back-quotes |
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instead. |
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The body of @{syntax_ref verbatim} may consist of any text not containing |
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``\<^verbatim>\<open>*}\<close>''; this allows to include quotes without further |
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escapes, but there is no way to escape ``\<^verbatim>\<open>*}\<close>''. Cartouches |
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do not have this limitation. |
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A @{syntax_ref cartouche} consists of arbitrary text, with properly |
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balanced blocks of ``@{verbatim "\<open>"}~\<open>\<dots>\<close>~@{verbatim |
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"\<close>"}''. Note that the rendering of cartouche delimiters is |
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usually like this: ``\<open>\<open> \<dots> \<close>\<close>''. |
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Source comments take the form \<^verbatim>\<open>(*\<close>~\<open>\<dots>\<close>~\<^verbatim>\<open>*)\<close> and may be nested, although the user-interface |
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might prevent this. Note that this form indicates source comments |
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only, which are stripped after lexical analysis of the input. The |
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Isar syntax also provides proper \<^emph>\<open>document comments\<close> that are |
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considered as part of the text (see \secref{sec:comments}). |
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Common mathematical symbols such as \<open>\<forall>\<close> are represented in |
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Isabelle as \<^verbatim>\<open>\<forall>\<close>. There are infinitely many Isabelle |
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symbols like this, although proper presentation is left to front-end |
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tools such as {\LaTeX} or Isabelle/jEdit. A list of |
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predefined Isabelle symbols that work well with these tools is given |
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in \appref{app:symbols}. Note that \<^verbatim>\<open>\<lambda>\<close> does not belong |
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to the \<open>letter\<close> category, since it is already used differently |
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in the Pure term language.\<close> |
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section \<open>Common syntax entities\<close> |
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text \<open> |
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We now introduce several basic syntactic entities, such as names, |
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terms, and theorem specifications, which are factored out of the |
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actual Isar language elements to be described later. |
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\<close> |
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subsection \<open>Names\<close> |
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text \<open>Entity @{syntax name} usually refers to any name of types, |
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constants, theorems etc.\ that are to be \<^emph>\<open>declared\<close> or |
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\<^emph>\<open>defined\<close> (so qualified identifiers are excluded here). Quoted |
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strings provide an escape for non-identifier names or those ruled |
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out by outer syntax keywords (e.g.\ quoted \<^verbatim>\<open>"let"\<close>). |
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Already existing objects are usually referenced by @{syntax |
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nameref}. |
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@{rail \<open> |
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@{syntax_def name}: @{syntax ident} | @{syntax symident} | |
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@{syntax string} | @{syntax nat} |
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; |
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@{syntax_def par_name}: '(' @{syntax name} ')' |
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; |
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@{syntax_def nameref}: @{syntax name} | @{syntax longident} |
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\<close>} |
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\<close> |
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subsection \<open>Numbers\<close> |
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text \<open>The outer lexical syntax (\secref{sec:outer-lex}) admits |
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natural numbers and floating point numbers. These are combined as |
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@{syntax int} and @{syntax real} as follows. |
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@{rail \<open> |
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@{syntax_def int}: @{syntax nat} | '-' @{syntax nat} |
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; |
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@{syntax_def real}: @{syntax float} | @{syntax int} |
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\<close>} |
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Note that there is an overlap with the category @{syntax name}, |
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which also includes @{syntax nat}. |
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\<close> |
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subsection \<open>Comments \label{sec:comments}\<close> |
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text \<open> |
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Large chunks of plain @{syntax text} are usually given @{syntax verbatim}, |
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i.e.\ enclosed in \<^verbatim>\<open>{*\<close>~\<open>\<dots>\<close>~\<^verbatim>\<open>*}\<close>, or as @{syntax cartouche} \<open>\<open>\<dots>\<close>\<close>. For |
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convenience, any of the smaller text units conforming to @{syntax nameref} |
|
230 |
are admitted as well. A marginal @{syntax comment} is of the form |
|
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\<^verbatim>\<open>--\<close>~@{syntax text} or \<^verbatim>\<open>\<comment>\<close>~@{syntax text}. Any number of these may occur |
|
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within Isabelle/Isar commands. |
|
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|
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@{rail \<open> |
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@{syntax_def text}: @{syntax verbatim} | @{syntax cartouche} | @{syntax nameref} |
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; |
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@{syntax_def comment}: ('--' | @'\<comment>') @{syntax text} |
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\<close>} |
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\<close> |
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|
241 |
||
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subsection \<open>Type classes, sorts and arities\<close> |
27037 | 243 |
|
58618 | 244 |
text \<open> |
27037 | 245 |
Classes are specified by plain names. Sorts have a very simple |
61493 | 246 |
inner syntax, which is either a single class name \<open>c\<close> or a |
247 |
list \<open>{c\<^sub>1, \<dots>, c\<^sub>n}\<close> referring to the |
|
27037 | 248 |
intersection of these classes. The syntax of type arities is given |
249 |
directly at the outer level. |
|
250 |
||
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@{rail \<open> |
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@{syntax_def classdecl}: @{syntax name} (('<' | '\<subseteq>') (@{syntax nameref} + ','))? |
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; |
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@{syntax_def sort}: @{syntax nameref} |
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; |
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@{syntax_def arity}: ('(' (@{syntax sort} + ',') ')')? @{syntax sort} |
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\<close>} |
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\<close> |
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|
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||
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subsection \<open>Types and terms \label{sec:types-terms}\<close> |
27037 | 262 |
|
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text \<open> |
27037 | 264 |
The actual inner Isabelle syntax, that of types and terms of the |
265 |
logic, is far too sophisticated in order to be modelled explicitly |
|
266 |
at the outer theory level. Basically, any such entity has to be |
|
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quoted to turn it into a single token (the parsing and type-checking |
|
268 |
is performed internally later). For convenience, a slightly more |
|
269 |
liberal convention is adopted: quotes may be omitted for any type or |
|
270 |
term that is already atomic at the outer level. For example, one |
|
61503 | 271 |
may just write \<^verbatim>\<open>x\<close> instead of quoted \<^verbatim>\<open>"x"\<close>. |
272 |
Note that symbolic identifiers (e.g.\ \<^verbatim>\<open>++\<close> or \<open>\<forall>\<close> are available as well, |
|
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provided these have not been superseded |
|
274 |
by commands or other keywords already (such as \<^verbatim>\<open>=\<close> or |
|
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\<^verbatim>\<open>+\<close>). |
|
27037 | 276 |
|
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@{rail \<open> |
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@{syntax_def type}: @{syntax nameref} | @{syntax typefree} | |
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@{syntax typevar} |
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; |
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@{syntax_def term}: @{syntax nameref} | @{syntax var} |
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; |
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@{syntax_def prop}: @{syntax term} |
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\<close>} |
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|
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Positional instantiations are specified as a sequence of terms, or the |
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placeholder ``\<open>_\<close>'' (underscore), which means to skip a position. |
27037 | 288 |
|
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@{rail \<open> |
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@{syntax_def inst}: '_' | @{syntax term} |
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; |
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@{syntax_def insts}: (@{syntax inst} *) |
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\<close>} |
27037 | 294 |
|
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Named instantiations are specified as pairs of assignments \<open>v = |
296 |
t\<close>, which refer to schematic variables in some theorem that is |
|
59853 | 297 |
instantiated. Both type and terms instantiations are admitted, and |
298 |
distinguished by the usual syntax of variable names. |
|
299 |
||
300 |
@{rail \<open> |
|
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@{syntax_def named_inst}: variable '=' (type | term) |
|
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; |
|
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@{syntax_def named_insts}: (named_inst @'and' +) |
|
304 |
; |
|
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variable: @{syntax name} | @{syntax var} | @{syntax typefree} | @{syntax typevar} |
|
306 |
\<close>} |
|
307 |
||
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Type declarations and definitions usually refer to @{syntax |
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typespec} on the left-hand side. This models basic type constructor |
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application at the outer syntax level. Note that only plain postfix |
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notation is available here, but no infixes. |
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|
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@{rail \<open> |
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@{syntax_def typespec}: |
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(() | @{syntax typefree} | '(' ( @{syntax typefree} + ',' ) ')') @{syntax name} |
27037 | 316 |
; |
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@{syntax_def typespec_sorts}: |
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(() | (@{syntax typefree} ('::' @{syntax sort})?) | |
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'(' ( (@{syntax typefree} ('::' @{syntax sort})?) + ',' ) ')') @{syntax name} |
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\<close>} |
58618 | 321 |
\<close> |
27037 | 322 |
|
323 |
||
58618 | 324 |
subsection \<open>Term patterns and declarations \label{sec:term-decls}\<close> |
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325 |
|
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text \<open>Wherever explicit propositions (or term fragments) occur in a |
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proof text, casual binding of schematic term variables may be given |
61493 | 328 |
specified via patterns of the form ``\<open>(\<IS> p\<^sub>1 \<dots> p\<^sub>n)\<close>''. |
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This works both for @{syntax term} and @{syntax prop}. |
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330 |
|
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@{rail \<open> |
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@{syntax_def term_pat}: '(' (@'is' @{syntax term} +) ')' |
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; |
42705 | 334 |
@{syntax_def prop_pat}: '(' (@'is' @{syntax prop} +) ')' |
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\<close>} |
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336 |
|
61421 | 337 |
\<^medskip> |
61493 | 338 |
Declarations of local variables \<open>x :: \<tau>\<close> and |
339 |
logical propositions \<open>a : \<phi>\<close> represent different views on |
|
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the same principle of introducing a local scope. In practice, one |
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may usually omit the typing of @{syntax vars} (due to |
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type-inference), and the naming of propositions (due to implicit |
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references of current facts). In any case, Isar proof elements |
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usually admit to introduce multiple such items simultaneously. |
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345 |
|
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346 |
@{rail \<open> |
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@{syntax_def vars}: (@{syntax name} +) ('::' @{syntax type})? |
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; |
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@{syntax_def props}: @{syntax thmdecl}? (@{syntax prop} @{syntax prop_pat}? +) |
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350 |
\<close>} |
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351 |
|
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352 |
The treatment of multiple declarations corresponds to the |
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353 |
complementary focus of @{syntax vars} versus @{syntax props}. In |
61493 | 354 |
``\<open>x\<^sub>1 \<dots> x\<^sub>n :: \<tau>\<close>'' the typing refers to all variables, while |
355 |
in \<open>a: \<phi>\<^sub>1 \<dots> \<phi>\<^sub>n\<close> the naming refers to all propositions |
|
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collectively. Isar language elements that refer to @{syntax vars} |
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or @{syntax props} typically admit separate typings or namings via |
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another level of iteration, with explicit @{keyword_ref "and"} |
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separators; e.g.\ see @{command "fix"} and @{command "assume"} in |
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\secref{sec:proof-context}. |
59785 | 361 |
|
362 |
@{rail \<open> |
|
363 |
@{syntax_def "fixes"}: |
|
364 |
((@{syntax name} ('::' @{syntax type})? @{syntax mixfix}? | @{syntax vars}) + @'and') |
|
365 |
; |
|
366 |
@{syntax_def "for_fixes"}: (@'for' @{syntax "fixes"})? |
|
367 |
\<close>} |
|
368 |
||
369 |
The category @{syntax "fixes"} is a richer variant of @{syntax vars}: it |
|
370 |
admits specification of mixfix syntax for the entities that are introduced |
|
61493 | 371 |
into the context. An optional suffix ``@{keyword "for"}~\<open>fixes\<close>'' |
59785 | 372 |
is admitted in many situations to indicate a so-called ``eigen-context'' |
373 |
of a formal element: the result will be exported and thus generalized over |
|
374 |
the given variables.\<close> |
|
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375 |
|
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376 |
|
58618 | 377 |
subsection \<open>Attributes and theorems \label{sec:syn-att}\<close> |
27037 | 378 |
|
58618 | 379 |
text \<open>Attributes have their own ``semi-inner'' syntax, in the sense |
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that input conforming to @{syntax args} below is parsed by the |
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381 |
attribute a second time. The attribute argument specifications may |
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be any sequence of atomic entities (identifiers, strings etc.), or |
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properly bracketed argument lists. Below @{syntax atom} refers to |
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any atomic entity, including any @{syntax keyword} conforming to |
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@{syntax symident}. |
27037 | 386 |
|
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387 |
@{rail \<open> |
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@{syntax_def atom}: @{syntax nameref} | @{syntax typefree} | |
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@{syntax typevar} | @{syntax var} | @{syntax nat} | @{syntax float} | |
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390 |
@{syntax keyword} | @{syntax cartouche} |
27037 | 391 |
; |
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arg: @{syntax atom} | '(' @{syntax args} ')' | '[' @{syntax args} ']' |
27037 | 393 |
; |
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@{syntax_def args}: arg * |
27037 | 395 |
; |
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396 |
@{syntax_def attributes}: '[' (@{syntax nameref} @{syntax args} * ',') ']' |
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\<close>} |
27037 | 398 |
|
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399 |
Theorem specifications come in several flavors: @{syntax axmdecl} |
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and @{syntax thmdecl} usually refer to axioms, assumptions or |
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results of goal statements, while @{syntax thmdef} collects lists of |
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existing theorems. Existing theorems are given by @{syntax thmref} |
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403 |
and @{syntax thmrefs}, the former requires an actual singleton |
27037 | 404 |
result. |
405 |
||
406 |
There are three forms of theorem references: |
|
60674 | 407 |
|
61493 | 408 |
\<^enum> named facts \<open>a\<close>, |
27037 | 409 |
|
61493 | 410 |
\<^enum> selections from named facts \<open>a(i)\<close> or \<open>a(j - k)\<close>, |
27037 | 411 |
|
61421 | 412 |
\<^enum> literal fact propositions using token syntax @{syntax_ref altstring} |
61503 | 413 |
\<^verbatim>\<open>`\<close>\<open>\<phi>\<close>\<^verbatim>\<open>`\<close> or @{syntax_ref cartouche} |
61493 | 414 |
\<open>\<open>\<phi>\<close>\<close> (see also method @{method_ref fact}). |
27037 | 415 |
|
416 |
||
417 |
Any kind of theorem specification may include lists of attributes |
|
418 |
both on the left and right hand sides; attributes are applied to any |
|
419 |
immediately preceding fact. If names are omitted, the theorems are |
|
420 |
not stored within the theorem database of the theory or proof |
|
421 |
context, but any given attributes are applied nonetheless. |
|
422 |
||
61493 | 423 |
An extra pair of brackets around attributes (like ``\<open>[[simproc a]]\<close>'') abbreviates a theorem reference involving an |
27037 | 424 |
internal dummy fact, which will be ignored later on. So only the |
425 |
effect of the attribute on the background context will persist. |
|
426 |
This form of in-place declarations is particularly useful with |
|
427 |
commands like @{command "declare"} and @{command "using"}. |
|
428 |
||
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429 |
@{rail \<open> |
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@{syntax_def axmdecl}: @{syntax name} @{syntax attributes}? ':' |
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431 |
; |
60631 | 432 |
@{syntax_def thmbind}: |
433 |
@{syntax name} @{syntax attributes} | @{syntax name} | @{syntax attributes} |
|
434 |
; |
|
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435 |
@{syntax_def thmdecl}: thmbind ':' |
27037 | 436 |
; |
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@{syntax_def thmdef}: thmbind '=' |
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; |
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@{syntax_def thmref}: |
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(@{syntax nameref} selection? | @{syntax altstring} | @{syntax cartouche}) |
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@{syntax attributes}? | |
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'[' @{syntax attributes} ']' |
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; |
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@{syntax_def thmrefs}: @{syntax thmref} + |
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; |
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selection: '(' ((@{syntax nat} | @{syntax nat} '-' @{syntax nat}?) + ',') ')' |
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\<close>} |
58618 | 448 |
\<close> |
27037 | 449 |
|
60674 | 450 |
|
451 |
section \<open>Diagnostic commands\<close> |
|
452 |
||
453 |
text \<open> |
|
454 |
\begin{matharray}{rcl} |
|
61493 | 455 |
@{command_def "print_theory"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
456 |
@{command_def "print_definitions"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
|
457 |
@{command_def "print_methods"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
|
458 |
@{command_def "print_attributes"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
|
459 |
@{command_def "print_theorems"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
|
460 |
@{command_def "find_theorems"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
|
461 |
@{command_def "find_consts"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
|
462 |
@{command_def "thm_deps"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
|
463 |
@{command_def "unused_thms"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
|
464 |
@{command_def "print_facts"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
|
465 |
@{command_def "print_term_bindings"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
|
60674 | 466 |
\end{matharray} |
467 |
||
468 |
@{rail \<open> |
|
469 |
(@@{command print_theory} | |
|
61252 | 470 |
@@{command print_definitions} | |
60674 | 471 |
@@{command print_methods} | |
472 |
@@{command print_attributes} | |
|
473 |
@@{command print_theorems} | |
|
474 |
@@{command print_facts}) ('!'?) |
|
475 |
; |
|
476 |
@@{command find_theorems} ('(' @{syntax nat}? 'with_dups'? ')')? \<newline> (thm_criterion*) |
|
477 |
; |
|
478 |
thm_criterion: ('-'?) ('name' ':' @{syntax nameref} | 'intro' | 'elim' | 'dest' | |
|
479 |
'solves' | 'simp' ':' @{syntax term} | @{syntax term}) |
|
480 |
; |
|
481 |
@@{command find_consts} (const_criterion*) |
|
482 |
; |
|
483 |
const_criterion: ('-'?) |
|
484 |
('name' ':' @{syntax nameref} | 'strict' ':' @{syntax type} | @{syntax type}) |
|
485 |
; |
|
486 |
@@{command thm_deps} @{syntax thmrefs} |
|
487 |
; |
|
488 |
@@{command unused_thms} ((@{syntax name} +) '-' (@{syntax name} * ))? |
|
489 |
\<close>} |
|
490 |
||
491 |
These commands print certain parts of the theory and proof context. |
|
492 |
Note that there are some further ones available, such as for the set |
|
493 |
of rules declared for simplifications. |
|
494 |
||
61439 | 495 |
\<^descr> @{command "print_theory"} prints the main logical content of the |
61493 | 496 |
background theory; the ``\<open>!\<close>'' option indicates extra verbosity. |
60674 | 497 |
|
61439 | 498 |
\<^descr> @{command "print_definitions"} prints dependencies of definitional |
61252 | 499 |
specifications within the background theory, which may be constants |
500 |
\secref{sec:consts} or types (\secref{sec:types-pure}, |
|
61493 | 501 |
\secref{sec:hol-typedef}); the ``\<open>!\<close>'' option indicates extra |
61252 | 502 |
verbosity. |
503 |
||
61439 | 504 |
\<^descr> @{command "print_methods"} prints all proof methods available in the |
61493 | 505 |
current theory context; the ``\<open>!\<close>'' option indicates extra |
60674 | 506 |
verbosity. |
507 |
||
61439 | 508 |
\<^descr> @{command "print_attributes"} prints all attributes available in the |
61493 | 509 |
current theory context; the ``\<open>!\<close>'' option indicates extra |
60674 | 510 |
verbosity. |
511 |
||
61439 | 512 |
\<^descr> @{command "print_theorems"} prints theorems of the background theory |
61493 | 513 |
resulting from the last command; the ``\<open>!\<close>'' option indicates |
60674 | 514 |
extra verbosity. |
515 |
||
61439 | 516 |
\<^descr> @{command "print_facts"} prints all local facts of the current |
61493 | 517 |
context, both named and unnamed ones; the ``\<open>!\<close>'' option indicates |
60674 | 518 |
extra verbosity. |
519 |
||
61439 | 520 |
\<^descr> @{command "print_term_bindings"} prints all term bindings that |
60674 | 521 |
are present in the context. |
522 |
||
61493 | 523 |
\<^descr> @{command "find_theorems"}~\<open>criteria\<close> retrieves facts |
60674 | 524 |
from the theory or proof context matching all of given search |
61493 | 525 |
criteria. The criterion \<open>name: p\<close> selects all theorems |
526 |
whose fully qualified name matches pattern \<open>p\<close>, which may |
|
527 |
contain ``\<open>*\<close>'' wildcards. The criteria \<open>intro\<close>, |
|
528 |
\<open>elim\<close>, and \<open>dest\<close> select theorems that match the |
|
60674 | 529 |
current goal as introduction, elimination or destruction rules, |
61493 | 530 |
respectively. The criterion \<open>solves\<close> returns all rules |
60674 | 531 |
that would directly solve the current goal. The criterion |
61493 | 532 |
\<open>simp: t\<close> selects all rewrite rules whose left-hand side |
533 |
matches the given term. The criterion term \<open>t\<close> selects all |
|
534 |
theorems that contain the pattern \<open>t\<close> -- as usual, patterns |
|
535 |
may contain occurrences of the dummy ``\<open>_\<close>'', schematic |
|
60674 | 536 |
variables, and type constraints. |
537 |
||
61493 | 538 |
Criteria can be preceded by ``\<open>-\<close>'' to select theorems that |
61477 | 539 |
do \<^emph>\<open>not\<close> match. Note that giving the empty list of criteria |
540 |
yields \<^emph>\<open>all\<close> currently known facts. An optional limit for the |
|
60674 | 541 |
number of printed facts may be given; the default is 40. By |
542 |
default, duplicates are removed from the search result. Use |
|
61493 | 543 |
\<open>with_dups\<close> to display duplicates. |
60674 | 544 |
|
61493 | 545 |
\<^descr> @{command "find_consts"}~\<open>criteria\<close> prints all constants |
546 |
whose type meets all of the given criteria. The criterion \<open>strict: ty\<close> is met by any type that matches the type pattern |
|
547 |
\<open>ty\<close>. Patterns may contain both the dummy type ``\<open>_\<close>'' |
|
548 |
and sort constraints. The criterion \<open>ty\<close> is similar, but it |
|
549 |
also matches against subtypes. The criterion \<open>name: p\<close> and |
|
550 |
the prefix ``\<open>-\<close>'' function as described for @{command |
|
60674 | 551 |
"find_theorems"}. |
552 |
||
61493 | 553 |
\<^descr> @{command "thm_deps"}~\<open>a\<^sub>1 \<dots> a\<^sub>n\<close> |
60674 | 554 |
visualizes dependencies of facts, using Isabelle's graph browser |
555 |
tool (see also @{cite "isabelle-system"}). |
|
556 |
||
61493 | 557 |
\<^descr> @{command "unused_thms"}~\<open>A\<^sub>1 \<dots> A\<^sub>m - B\<^sub>1 \<dots> B\<^sub>n\<close> |
558 |
displays all theorems that are proved in theories \<open>B\<^sub>1 \<dots> B\<^sub>n\<close> |
|
559 |
or their parents but not in \<open>A\<^sub>1 \<dots> A\<^sub>m\<close> or their parents and |
|
60674 | 560 |
that are never used. |
61493 | 561 |
If \<open>n\<close> is \<open>0\<close>, the end of the range of theories |
60674 | 562 |
defaults to the current theory. If no range is specified, |
563 |
only the unused theorems in the current theory are displayed. |
|
564 |
\<close> |
|
565 |
||
27037 | 566 |
end |