author | wenzelm |
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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 three main |
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syntactic categories: \<^emph>\<open>commands\<close> of the top-level Isar engine (covering |
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theory and proof elements), \<^emph>\<open>methods\<close> for general goal refinements |
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(analogous to traditional ``tactics''), and \<^emph>\<open>attributes\<close> for operations on |
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facts (within a certain context). Subsequently we give a reference of basic |
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syntactic entities underlying Isabelle/Isar syntax in a bottom-up manner. |
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Concrete theory and proof language elements will be introduced later on. |
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\<^medskip> |
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In order to get started with writing well-formed Isabelle/Isar documents, |
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the most important aspect to be noted is the difference of \<^emph>\<open>inner\<close> versus |
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\<^emph>\<open>outer\<close> syntax. Inner syntax is that of Isabelle types and terms of the |
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logic, while outer syntax is that of Isabelle/Isar theory sources |
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(specifications and proofs). As a general rule, inner syntax entities may |
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occur only as \<^emph>\<open>atomic entities\<close> within outer syntax. For example, the |
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string \<^verbatim>\<open>"x + y"\<close> and identifier \<^verbatim>\<open>z\<close> are legal term specifications within a |
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theory, while \<^verbatim>\<open>x + y\<close> without quotes is not. |
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Printed theory documents usually omit quotes to gain readability (this is a |
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matter of {\LaTeX} macro setup, say via \<^verbatim>\<open>\isabellestyle\<close>, see also @{cite |
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"isabelle-system"}). Experienced users of Isabelle/Isar may easily |
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reconstruct the lost technical information, while mere readers need not care |
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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> |
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Some common diagnostic commands are retrieved like this (according to usual |
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naming conventions): |
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\<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> |
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The outer lexical syntax consists of three main categories of 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. This helps |
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user-interfaces to determine the overall structure of a theory text, without |
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knowing the full details of command syntax. Internally, there is some |
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additional information about the kind of major keywords, which approximates |
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the command type (theory command, proof command etc.). |
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Keywords override named tokens. For example, the presence of a command |
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called \<^verbatim>\<open>term\<close> inhibits the identifier \<^verbatim>\<open>term\<close>, but the string \<^verbatim>\<open>"term"\<close> can |
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be used instead. By convention, the outer syntax always allows quoted |
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strings in addition to identifiers, wherever a named entity is expected. |
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When tokenizing a given input sequence, the lexer repeatedly takes the |
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longest prefix of the input that forms a valid token. Spaces, tabs, newlines |
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and formfeeds between tokens serve as explicit 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 short_ident} & = & \<open>letter (subscript\<^sup>? quasiletter)\<^sup>*\<close> \\ |
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@{syntax_def long_ident} & = & \<open>short_ident(\<close>\<^verbatim>\<open>.\<close>\<open>short_ident)\<^sup>+\<close> \\ |
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@{syntax_def sym_ident} & = & \<open>sym\<^sup>+ |\<close>~~\<^verbatim>\<open>\\<close>\<^verbatim>\<open><\<close>\<open>short_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 term_var} & = & \<^verbatim>\<open>?\<close>\<open>short_ident |\<close>~~\<^verbatim>\<open>?\<close>\<open>short_ident\<close>\<^verbatim>\<open>.\<close>\<open>nat\<close> \\ |
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@{syntax_def type_ident} & = & \<^verbatim>\<open>'\<close>\<open>short_ident\<close> \\ |
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@{syntax_def type_var} & = & \<^verbatim>\<open>?\<close>\<open>type_ident |\<close>~~\<^verbatim>\<open>?\<close>\<open>type_ident\<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 term_var} or @{syntax_ref type_var} 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 \<open>?x.1\<close> or |
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\<open>?x7.3\<close> or run together as in \<open>?x1\<close>. The latter form is possible if the base |
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name does not end with digits. If the index is 0, it may be dropped |
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altogether: \<open>?x\<close> and \<open>?x0\<close> and \<open>?x.0\<close> all refer to the same unknown, with |
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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>'' (backslash) need to be |
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escaped by a backslash; arbitrary character codes may be specified as |
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``\<^verbatim>\<open>\\<close>\<open>ddd\<close>'', with three decimal digits. Alternative strings according to |
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@{syntax_ref altstring} are analogous, using single back-quotes 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 escapes, but there |
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is no way to escape ``\<^verbatim>\<open>*}\<close>''. Cartouches do not have this limitation. |
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A @{syntax_ref cartouche} consists of arbitrary text, with properly balanced |
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blocks of ``@{verbatim "\<open>"}~\<open>\<dots>\<close>~@{verbatim "\<close>"}''. Note that the rendering |
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of cartouche delimiters is 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 |
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the user-interface might prevent this. Note that this form indicates source |
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comments 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 considered as |
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part of the text (see \secref{sec:comments}). |
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Common mathematical symbols such as \<open>\<forall>\<close> are represented in Isabelle as \<^verbatim>\<open>\<forall>\<close>. |
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There are infinitely many Isabelle symbols like this, although proper |
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presentation is left to front-end tools such as {\LaTeX} or Isabelle/jEdit. |
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A list of predefined Isabelle symbols that work well with these tools is |
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given in \appref{app:symbols}. Note that \<^verbatim>\<open>\<lambda>\<close> does not belong to the |
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\<open>letter\<close> category, since it is already used differently in the Pure term |
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language. |
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\<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, terms, and |
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theorem specifications, which are factored out of the actual Isar language |
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elements to be described later. |
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\<close> |
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subsection \<open>Names\<close> |
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text \<open> |
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Entity @{syntax name} usually refers to any name of types, constants, |
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theorems etc.\ Quoted strings provide an escape for non-identifier names or |
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those ruled out by outer syntax keywords (e.g.\ quoted \<^verbatim>\<open>"let"\<close>). |
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@{rail \<open> |
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@{syntax_def name}: @{syntax short_ident} | @{syntax long_ident} | |
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@{syntax sym_ident} | @{syntax nat} | @{syntax string} |
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; |
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@{syntax_def par_name}: '(' @{syntax name} ')' |
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\<close>} |
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\<close> |
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subsection \<open>Numbers\<close> |
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text \<open> |
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The outer lexical syntax (\secref{sec:outer-lex}) admits natural numbers and |
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floating point numbers. These are combined as @{syntax int} and @{syntax |
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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}, which also |
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includes @{syntax nat}. |
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\<close> |
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subsection \<open>Embedded content\<close> |
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text \<open> |
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Entity @{syntax embedded} refers to content of other languages: cartouches |
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allow arbitrary nesting of sub-languages that respect the recursive |
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balancing of cartouche delimiters. Quoted strings are possible as well, but |
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require escaped quotes when nested. As a shortcut, tokens that appear as |
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plain identifiers in the outer language may be used as inner language |
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content without delimiters. |
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221 |
|
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@{rail \<open> |
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@{syntax_def embedded}: @{syntax cartouche} | @{syntax string} | |
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@{syntax short_ident} | @{syntax long_ident} | @{syntax sym_ident} | |
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@{syntax term_var} | @{syntax type_ident} | @{syntax type_var} | @{syntax nat} |
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\<close>} |
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\<close> |
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228 |
|
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229 |
|
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subsection \<open>Comments \label{sec:comments}\<close> |
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|
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text \<open> |
233 |
Large chunks of plain @{syntax text} are usually given @{syntax verbatim}, |
|
234 |
i.e.\ enclosed in \<^verbatim>\<open>{*\<close>~\<open>\<dots>\<close>~\<^verbatim>\<open>*}\<close>, or as @{syntax cartouche} \<open>\<open>\<dots>\<close>\<close>. For |
|
62969 | 235 |
convenience, any of the smaller text units conforming to @{syntax name} are |
236 |
admitted as well. A marginal @{syntax comment} is of the form \<^verbatim>\<open>--\<close>~@{syntax |
|
237 |
text} or \<^verbatim>\<open>\<comment>\<close>~@{syntax text}. Any number of these may occur within |
|
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Isabelle/Isar commands. |
|
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|
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@{rail \<open> |
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@{syntax_def text}: @{syntax embedded} | @{syntax verbatim} |
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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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|
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||
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subsection \<open>Type classes, sorts and arities\<close> |
27037 | 249 |
|
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text \<open> |
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Classes are specified by plain names. Sorts have a very simple inner syntax, |
252 |
which is either a single class name \<open>c\<close> or a list \<open>{c\<^sub>1, \<dots>, c\<^sub>n}\<close> referring |
|
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to the intersection of these classes. The syntax of type arities is given |
|
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directly at the outer level. |
255 |
||
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@{rail \<open> |
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@{syntax_def classdecl}: @{syntax name} (('<' | '\<subseteq>') (@{syntax name} + ','))? |
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; |
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@{syntax_def sort}: @{syntax embedded} |
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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 | 267 |
|
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text \<open> |
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The actual inner Isabelle syntax, that of types and terms of the logic, is |
270 |
far too sophisticated in order to be modelled explicitly at the outer theory |
|
271 |
level. Basically, any such entity has to be quoted to turn it into a single |
|
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token (the parsing and type-checking is performed internally later). For |
|
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convenience, a slightly more liberal convention is adopted: quotes may be |
|
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omitted for any type or term that is already atomic at the outer level. For |
|
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example, one may just write \<^verbatim>\<open>x\<close> instead of quoted \<^verbatim>\<open>"x"\<close>. Note that |
|
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symbolic identifiers (e.g.\ \<^verbatim>\<open>++\<close> or \<open>\<forall>\<close> are available as well, provided |
|
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these have not been superseded by commands or other keywords already (such |
|
278 |
as \<^verbatim>\<open>=\<close> or \<^verbatim>\<open>+\<close>). |
|
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|
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@{rail \<open> |
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@{syntax_def type}: @{syntax embedded} |
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; |
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@{syntax_def term}: @{syntax embedded} |
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; |
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@{syntax_def prop}: @{syntax embedded} |
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\<close>} |
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|
59853 | 288 |
Positional instantiations are specified as a sequence of terms, or the |
61493 | 289 |
placeholder ``\<open>_\<close>'' (underscore), which means to skip a position. |
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|
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@{rail \<open> |
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@{syntax_def inst}: '_' | @{syntax term} |
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@{syntax_def insts}: (@{syntax inst} *) |
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\<close>} |
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|
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Named instantiations are specified as pairs of assignments \<open>v = t\<close>, which |
298 |
refer to schematic variables in some theorem that is instantiated. Both type |
|
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and terms instantiations are admitted, and distinguished by the usual syntax |
|
300 |
of variable names. |
|
59853 | 301 |
|
302 |
@{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' +) |
|
306 |
; |
|
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variable: @{syntax name} | @{syntax term_var} | @{syntax type_ident} | @{syntax type_var} |
59853 | 308 |
\<close>} |
309 |
||
61662 | 310 |
Type declarations and definitions usually refer to @{syntax typespec} on the |
311 |
left-hand side. This models basic type constructor application at the outer |
|
312 |
syntax level. Note that only plain postfix notation is available here, but |
|
313 |
no infixes. |
|
27037 | 314 |
|
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@{rail \<open> |
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@{syntax_def typespec}: |
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(() | @{syntax type_ident} | '(' ( @{syntax type_ident} + ',' ) ')') @{syntax name} |
27037 | 318 |
; |
42705 | 319 |
@{syntax_def typespec_sorts}: |
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(() | (@{syntax type_ident} ('::' @{syntax sort})?) | |
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'(' ( (@{syntax type_ident} ('::' @{syntax sort})?) + ',' ) ')') @{syntax name} |
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\<close>} |
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\<close> |
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|
325 |
||
58618 | 326 |
subsection \<open>Term patterns and declarations \label{sec:term-decls}\<close> |
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327 |
|
61662 | 328 |
text \<open> |
329 |
Wherever explicit propositions (or term fragments) occur in a proof text, |
|
330 |
casual binding of schematic term variables may be given specified via |
|
61663 | 331 |
patterns of the form ``\<^theory_text>\<open>(is p\<^sub>1 \<dots> p\<^sub>n)\<close>''. This works both for @{syntax |
61662 | 332 |
term} and @{syntax prop}. |
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333 |
|
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@{rail \<open> |
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@{syntax_def term_pat}: '(' (@'is' @{syntax term} +) ')' |
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; |
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@{syntax_def prop_pat}: '(' (@'is' @{syntax prop} +) ')' |
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\<close>} |
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339 |
|
61421 | 340 |
\<^medskip> |
61662 | 341 |
Declarations of local variables \<open>x :: \<tau>\<close> and logical propositions \<open>a : \<phi>\<close> |
342 |
represent different views on the same principle of introducing a local |
|
343 |
scope. In practice, one may usually omit the typing of @{syntax vars} (due |
|
344 |
to type-inference), and the naming of propositions (due to implicit |
|
345 |
references of current facts). In any case, Isar proof elements usually admit |
|
346 |
to introduce multiple such items simultaneously. |
|
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347 |
|
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@{rail \<open> |
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@{syntax_def vars}: (@{syntax name} +) ('::' @{syntax type})? |
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; |
42705 | 351 |
@{syntax_def props}: @{syntax thmdecl}? (@{syntax prop} @{syntax prop_pat}? +) |
61658 | 352 |
; |
353 |
@{syntax_def props'}: (@{syntax prop} @{syntax prop_pat}? +) |
|
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\<close>} |
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355 |
|
61662 | 356 |
The treatment of multiple declarations corresponds to the complementary |
357 |
focus of @{syntax vars} versus @{syntax props}. In ``\<open>x\<^sub>1 \<dots> x\<^sub>n :: \<tau>\<close>'' the |
|
358 |
typing refers to all variables, while in \<open>a: \<phi>\<^sub>1 \<dots> \<phi>\<^sub>n\<close> the naming refers to |
|
359 |
all propositions collectively. Isar language elements that refer to @{syntax |
|
360 |
vars} or @{syntax props} typically admit separate typings or namings via |
|
361 |
another level of iteration, with explicit @{keyword_ref "and"} separators; |
|
362 |
e.g.\ see @{command "fix"} and @{command "assume"} in |
|
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\secref{sec:proof-context}. |
59785 | 364 |
|
365 |
@{rail \<open> |
|
366 |
@{syntax_def "fixes"}: |
|
367 |
((@{syntax name} ('::' @{syntax type})? @{syntax mixfix}? | @{syntax vars}) + @'and') |
|
368 |
; |
|
369 |
@{syntax_def "for_fixes"}: (@'for' @{syntax "fixes"})? |
|
370 |
\<close>} |
|
371 |
||
372 |
The category @{syntax "fixes"} is a richer variant of @{syntax vars}: it |
|
373 |
admits specification of mixfix syntax for the entities that are introduced |
|
61662 | 374 |
into the context. An optional suffix ``@{keyword "for"}~\<open>fixes\<close>'' is |
375 |
admitted in many situations to indicate a so-called ``eigen-context'' of a |
|
376 |
formal element: the result will be exported and thus generalized over the |
|
377 |
given variables. |
|
378 |
\<close> |
|
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379 |
|
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380 |
|
58618 | 381 |
subsection \<open>Attributes and theorems \label{sec:syn-att}\<close> |
27037 | 382 |
|
61662 | 383 |
text \<open> |
384 |
Attributes have their own ``semi-inner'' syntax, in the sense that input |
|
385 |
conforming to @{syntax args} below is parsed by the attribute a second time. |
|
386 |
The attribute argument specifications may be any sequence of atomic entities |
|
387 |
(identifiers, strings etc.), or properly bracketed argument lists. Below |
|
388 |
@{syntax atom} refers to any atomic entity, including any @{syntax keyword} |
|
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conforming to @{syntax sym_ident}. |
27037 | 390 |
|
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391 |
@{rail \<open> |
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@{syntax_def atom}: @{syntax name} | @{syntax type_ident} | |
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@{syntax type_var} | @{syntax term_var} | @{syntax nat} | @{syntax float} | |
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@{syntax keyword} | @{syntax cartouche} |
27037 | 395 |
; |
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arg: @{syntax atom} | '(' @{syntax args} ')' | '[' @{syntax args} ']' |
27037 | 397 |
; |
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@{syntax_def args}: arg * |
27037 | 399 |
; |
62969 | 400 |
@{syntax_def attributes}: '[' (@{syntax name} @{syntax args} * ',') ']' |
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\<close>} |
27037 | 402 |
|
61662 | 403 |
Theorem specifications come in several flavors: @{syntax axmdecl} and |
404 |
@{syntax thmdecl} usually refer to axioms, assumptions or results of goal |
|
405 |
statements, while @{syntax thmdef} collects lists of existing theorems. |
|
62969 | 406 |
Existing theorems are given by @{syntax thm} and @{syntax thms}, the |
61662 | 407 |
former requires an actual singleton result. |
27037 | 408 |
|
409 |
There are three forms of theorem references: |
|
60674 | 410 |
|
61662 | 411 |
\<^enum> named facts \<open>a\<close>, |
27037 | 412 |
|
61662 | 413 |
\<^enum> selections from named facts \<open>a(i)\<close> or \<open>a(j - k)\<close>, |
27037 | 414 |
|
61662 | 415 |
\<^enum> literal fact propositions using token syntax @{syntax_ref altstring} |
416 |
\<^verbatim>\<open>`\<close>\<open>\<phi>\<close>\<^verbatim>\<open>`\<close> or @{syntax_ref cartouche} |
|
417 |
\<open>\<open>\<phi>\<close>\<close> (see also method @{method_ref fact}). |
|
27037 | 418 |
|
61662 | 419 |
Any kind of theorem specification may include lists of attributes both on |
420 |
the left and right hand sides; attributes are applied to any immediately |
|
421 |
preceding fact. If names are omitted, the theorems are not stored within the |
|
422 |
theorem database of the theory or proof context, but any given attributes |
|
423 |
are applied nonetheless. |
|
27037 | 424 |
|
61662 | 425 |
An extra pair of brackets around attributes (like ``\<open>[[simproc a]]\<close>'') |
426 |
abbreviates a theorem reference involving an internal dummy fact, which will |
|
427 |
be ignored later on. So only the effect of the attribute on the background |
|
428 |
context will persist. This form of in-place declarations is particularly |
|
429 |
useful with commands like @{command "declare"} and @{command "using"}. |
|
27037 | 430 |
|
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@{rail \<open> |
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@{syntax_def axmdecl}: @{syntax name} @{syntax attributes}? ':' |
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; |
60631 | 434 |
@{syntax_def thmbind}: |
435 |
@{syntax name} @{syntax attributes} | @{syntax name} | @{syntax attributes} |
|
436 |
; |
|
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@{syntax_def thmdecl}: thmbind ':' |
27037 | 438 |
; |
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@{syntax_def thmdef}: thmbind '=' |
27037 | 440 |
; |
62969 | 441 |
@{syntax_def thm}: |
442 |
(@{syntax name} selection? | @{syntax altstring} | @{syntax cartouche}) |
|
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@{syntax attributes}? | |
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'[' @{syntax attributes} ']' |
27037 | 445 |
; |
62969 | 446 |
@{syntax_def thms}: @{syntax thm} + |
27037 | 447 |
; |
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selection: '(' ((@{syntax nat} | @{syntax nat} '-' @{syntax nat}?) + ',') ')' |
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\<close>} |
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\<close> |
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subsection \<open>Structured specifications\<close> |
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text \<open> |
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Structured specifications use propositions with explicit notation for the |
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``eigen-context'' to describe rule structure: \<open>\<And>x. A x \<Longrightarrow> \<dots> \<Longrightarrow> B x\<close> is |
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expressed as \<^theory_text>\<open>B x if A x and \<dots> for x\<close>. It is also possible to use dummy |
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terms ``\<open>_\<close>'' (underscore) to refer to locally fixed variables anonymously. |
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Multiple specifications are delimited by ``\<open>|\<close>'' to emphasize separate |
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cases: each with its own scope of inferred types for free variables. |
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@{rail \<open> |
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@{syntax_def multi_specs}: (@{syntax structured_spec} + '|') |
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; |
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@{syntax_def structured_spec}: |
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@{syntax thmdecl}? @{syntax prop} @{syntax spec_prems} @{syntax for_fixes} |
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; |
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@{syntax_def spec_prems}: (@'if' ((@{syntax prop}+) + @'and'))? |
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\<close>} |
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\<close> |
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section \<open>Diagnostic commands\<close> |
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text \<open> |
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\begin{matharray}{rcl} |
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@{command_def "print_theory"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
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@{command_def "print_definitions"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
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@{command_def "print_methods"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
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@{command_def "print_attributes"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
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@{command_def "print_theorems"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
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@{command_def "find_theorems"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
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@{command_def "find_consts"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
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@{command_def "thm_deps"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
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@{command_def "unused_thms"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
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@{command_def "print_facts"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
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@{command_def "print_term_bindings"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\ |
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\end{matharray} |
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@{rail \<open> |
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(@@{command print_theory} | |
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@@{command print_definitions} | |
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@@{command print_methods} | |
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@@{command print_attributes} | |
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@@{command print_theorems} | |
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@@{command print_facts}) ('!'?) |
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; |
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@@{command find_theorems} ('(' @{syntax nat}? 'with_dups'? ')')? \<newline> (thm_criterion*) |
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; |
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thm_criterion: ('-'?) ('name' ':' @{syntax name} | 'intro' | 'elim' | 'dest' | |
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'solves' | 'simp' ':' @{syntax term} | @{syntax term}) |
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; |
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@@{command find_consts} (const_criterion*) |
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; |
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const_criterion: ('-'?) |
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('name' ':' @{syntax name} | 'strict' ':' @{syntax type} | @{syntax type}) |
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; |
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@@{command thm_deps} @{syntax thmrefs} |
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; |
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@@{command unused_thms} ((@{syntax name} +) '-' (@{syntax name} * ))? |
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\<close>} |
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||
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These commands print certain parts of the theory and proof context. Note |
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that there are some further ones available, such as for the set of rules |
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declared for simplifications. |
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\<^descr> @{command "print_theory"} prints the main logical content of the |
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background theory; the ``\<open>!\<close>'' option indicates extra verbosity. |
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\<^descr> @{command "print_definitions"} prints dependencies of definitional |
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specifications within the background theory, which may be constants |
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(\secref{sec:term-definitions}, \secref{sec:overloading}) or types |
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(\secref{sec:types-pure}, \secref{sec:hol-typedef}); the ``\<open>!\<close>'' option |
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indicates extra verbosity. |
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\<^descr> @{command "print_methods"} prints all proof methods available in the |
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current theory context; the ``\<open>!\<close>'' option indicates extra verbosity. |
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\<^descr> @{command "print_attributes"} prints all attributes available in the |
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current theory context; the ``\<open>!\<close>'' option indicates extra verbosity. |
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\<^descr> @{command "print_theorems"} prints theorems of the background theory |
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resulting from the last command; the ``\<open>!\<close>'' option indicates extra |
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verbosity. |
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\<^descr> @{command "print_facts"} prints all local facts of the current context, |
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both named and unnamed ones; the ``\<open>!\<close>'' option indicates extra verbosity. |
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\<^descr> @{command "print_term_bindings"} prints all term bindings that are present |
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in the context. |
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\<^descr> @{command "find_theorems"}~\<open>criteria\<close> retrieves facts from the theory or |
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proof context matching all of given search criteria. The criterion \<open>name: p\<close> |
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selects all theorems whose fully qualified name matches pattern \<open>p\<close>, which |
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may contain ``\<open>*\<close>'' wildcards. The criteria \<open>intro\<close>, \<open>elim\<close>, and \<open>dest\<close> |
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select theorems that match the current goal as introduction, elimination or |
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destruction rules, respectively. The criterion \<open>solves\<close> returns all rules |
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that would directly solve the current goal. The criterion \<open>simp: t\<close> selects |
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all rewrite rules whose left-hand side matches the given term. The criterion |
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term \<open>t\<close> selects all theorems that contain the pattern \<open>t\<close> -- as usual, |
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patterns may contain occurrences of the dummy ``\<open>_\<close>'', schematic variables, |
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and type constraints. |
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Criteria can be preceded by ``\<open>-\<close>'' to select theorems that do \<^emph>\<open>not\<close> match. |
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Note that giving the empty list of criteria yields \<^emph>\<open>all\<close> currently known |
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facts. An optional limit for the number of printed facts may be given; the |
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default is 40. By default, duplicates are removed from the search result. |
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Use \<open>with_dups\<close> to display duplicates. |
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\<^descr> @{command "find_consts"}~\<open>criteria\<close> prints all constants whose type meets |
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all of the given criteria. The criterion \<open>strict: ty\<close> is met by any type |
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that matches the type pattern \<open>ty\<close>. Patterns may contain both the dummy type |
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``\<open>_\<close>'' and sort constraints. The criterion \<open>ty\<close> is similar, but it also |
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matches against subtypes. The criterion \<open>name: p\<close> and the prefix ``\<open>-\<close>'' |
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function as described for @{command "find_theorems"}. |
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\<^descr> @{command "thm_deps"}~\<open>a\<^sub>1 \<dots> a\<^sub>n\<close> visualizes dependencies of facts, using |
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Isabelle's graph browser tool (see also @{cite "isabelle-system"}). |
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\<^descr> @{command "unused_thms"}~\<open>A\<^sub>1 \<dots> A\<^sub>m - B\<^sub>1 \<dots> B\<^sub>n\<close> displays all theorems |
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that are proved in theories \<open>B\<^sub>1 \<dots> B\<^sub>n\<close> or their parents but not in \<open>A\<^sub>1 \<dots> |
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A\<^sub>m\<close> or their parents and that are never used. If \<open>n\<close> is \<open>0\<close>, the end of the |
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range of theories defaults to the current theory. If no range is specified, |
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only the unused theorems in the current theory are displayed. |
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\<close> |
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||
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end |