author | wenzelm |
Sat, 18 Jan 2014 19:15:12 +0100 | |
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parent 53059 | f4811f3628dc |
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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 {* Outer syntax --- the theory language \label{ch:outer-syntax} *} |
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text {* |
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The rather generic framework of Isabelle/Isar syntax emerges from |
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three main syntactic categories: \emph{commands} of the top-level |
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Isar engine (covering theory and proof elements), \emph{methods} for |
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general goal refinements (analogous to traditional ``tactics''), and |
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\emph{attributes} 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 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{inner} versus \emph{outer} 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{atomic entities} within outer syntax. For example, the string |
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@{verbatim "\"x + y\""} and identifier @{verbatim z} are legal term |
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specifications within a theory, while @{verbatim "x + y"} 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 |
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"\\isabellestyle"}, see also \cite{isabelle-sys}). 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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\medskip Isabelle/Isar input may contain any number of input |
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termination characters ``@{verbatim ";"}'' (semicolon) to separate |
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commands explicitly. This is particularly useful in interactive |
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shell sessions to make clear where the current command is intended |
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to end. Otherwise, the interpreter loop will continue to issue a |
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secondary prompt ``@{verbatim "#"}'' until an end-of-command is |
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clearly recognized from the input syntax, e.g.\ encounter of the |
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next command keyword. |
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More advanced interfaces such as Isabelle/jEdit \cite{Wenzel:2012} |
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and Proof~General \cite{proofgeneral} do not require explicit |
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semicolons: command spans are determined by inspecting the content |
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of the editor buffer. In the printed presentation of Isabelle/Isar |
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documents semicolons are omitted altogether for readability. |
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\begin{warn} |
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Proof~General requires certain syntax classification tables in |
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order to achieve properly synchronized interaction with the |
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Isabelle/Isar process. These tables need to be consistent with |
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the Isabelle version and particular logic image to be used in a |
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running session (common object-logics may well change the outer |
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syntax). The standard setup should work correctly with any of the |
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``official'' logic images derived from Isabelle/HOL (including |
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HOLCF etc.). Users of alternative logics may need to tell |
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Proof~General explicitly, e.g.\ by giving an option @{verbatim "-k ZF"} |
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(in conjunction with @{verbatim "-l ZF"}, to specify the default |
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logic image). Note that option @{verbatim "-L"} does both |
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of this at the same time. |
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\end{warn} |
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*} |
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section {* Commands *} |
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text {* |
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\begin{matharray}{rcl} |
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@{command_def "print_commands"}@{text "\<^sup>*"} & : & @{text "any \<rightarrow>"} \\ |
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@{command_def "help"}@{text "\<^sup>*"} & : & @{text "any \<rightarrow>"} \\ |
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\end{matharray} |
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@{rail " |
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@@{command help} (@{syntax name} * ) |
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"} |
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\begin{description} |
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\item @{command "print_commands"} prints all outer syntax keywords |
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and commands. |
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\item @{command "help"}~@{text "pats"} retrieves outer syntax |
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commands according to the specified name patterns. |
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\end{description} |
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*} |
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subsubsection {* Examples *} |
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text {* Some common diagnostic commands are retrieved like this |
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(according to usual naming conventions): *} |
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help "print" |
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help "find" |
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section {* Lexical matters \label{sec:outer-lex} *} |
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text {* The outer lexical syntax consists of three main categories of |
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syntax tokens: |
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\begin{enumerate} |
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\item \emph{major keywords} --- the command names that are available |
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in the present logic session; |
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\item \emph{minor keywords} --- additional literal tokens required |
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by the syntax of commands; |
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\item \emph{named tokens} --- various categories of identifiers etc. |
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\end{enumerate} |
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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 term} inhibits the identifier @{verbatim |
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term}, but the string @{verbatim "\"term\""} 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 The categories for named tokens are defined once and for |
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all as follows. |
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\begin{center} |
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\begin{supertabular}{rcl} |
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@{syntax_def ident} & = & @{text "letter (subscript\<^sup>? quasiletter)\<^sup>*"} \\ |
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@{syntax_def longident} & = & @{text "ident("}@{verbatim "."}@{text "ident)\<^sup>+"} \\ |
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@{syntax_def symident} & = & @{text "sym\<^sup>+ | "}@{verbatim "\\"}@{verbatim "<"}@{text ident}@{verbatim ">"} \\ |
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@{syntax_def nat} & = & @{text "digit\<^sup>+"} \\ |
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@{syntax_def float} & = & @{syntax_ref nat}@{verbatim "."}@{syntax_ref nat}@{text " | "}@{verbatim "-"}@{syntax_ref nat}@{verbatim "."}@{syntax_ref nat} \\ |
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@{syntax_def var} & = & @{verbatim "?"}@{text "ident | "}@{verbatim "?"}@{text ident}@{verbatim "."}@{text nat} \\ |
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@{syntax_def typefree} & = & @{verbatim "'"}@{text ident} \\ |
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@{syntax_def typevar} & = & @{verbatim "?"}@{text "typefree | "}@{verbatim "?"}@{text typefree}@{verbatim "."}@{text nat} \\ |
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@{syntax_def string} & = & @{verbatim "\""} @{text "\<dots>"} @{verbatim "\""} \\ |
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@{syntax_def altstring} & = & @{verbatim "`"} @{text "\<dots>"} @{verbatim "`"} \\ |
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@{syntax_def cartouche} & = & @{verbatim "\<open>"} @{text "\<dots>"} @{verbatim "\<close>"} \\ |
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@{syntax_def verbatim} & = & @{verbatim "{*"} @{text "\<dots>"} @{verbatim "*"}@{verbatim "}"} \\[1ex] |
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@{text letter} & = & @{text "latin | "}@{verbatim "\\"}@{verbatim "<"}@{text latin}@{verbatim ">"}@{text " | "}@{verbatim "\\"}@{verbatim "<"}@{text "latin latin"}@{verbatim ">"}@{text " | greek |"} \\ |
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@{text subscript} & = & @{verbatim "\<^sub>"} \\ |
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@{text quasiletter} & = & @{text "letter | digit | "}@{verbatim "_"}@{text " | "}@{verbatim "'"} \\ |
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@{text latin} & = & @{verbatim a}@{text " | \<dots> | "}@{verbatim z}@{text " | "}@{verbatim A}@{text " | \<dots> | "}@{verbatim Z} \\ |
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@{text digit} & = & @{verbatim "0"}@{text " | \<dots> | "}@{verbatim "9"} \\ |
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@{text sym} & = & @{verbatim "!"}@{text " | "}@{verbatim "#"}@{text " | "}@{verbatim "$"}@{text " | "}@{verbatim "%"}@{text " | "}@{verbatim "&"}@{text " | "}@{verbatim "*"}@{text " | "}@{verbatim "+"}@{text " | "}@{verbatim "-"}@{text " | "}@{verbatim "/"}@{text " |"} \\ |
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& & @{verbatim "<"}@{text " | "}@{verbatim "="}@{text " | "}@{verbatim ">"}@{text " | "}@{verbatim "?"}@{text " | "}@{verbatim "@"}@{text " | "}@{verbatim "^"}@{text " | "}@{verbatim "_"}@{text " | "}@{verbatim "|"}@{text " | "}@{verbatim "~"} \\ |
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@{text greek} & = & @{verbatim "\<alpha>"}@{text " | "}@{verbatim "\<beta>"}@{text " | "}@{verbatim "\<gamma>"}@{text " | "}@{verbatim "\<delta>"}@{text " |"} \\ |
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& & @{verbatim "\<epsilon>"}@{text " | "}@{verbatim "\<zeta>"}@{text " | "}@{verbatim "\<eta>"}@{text " | "}@{verbatim "\<theta>"}@{text " |"} \\ |
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& & @{verbatim "\<iota>"}@{text " | "}@{verbatim "\<kappa>"}@{text " | "}@{verbatim "\<mu>"}@{text " | "}@{verbatim "\<nu>"}@{text " |"} \\ |
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& & @{verbatim "\<xi>"}@{text " | "}@{verbatim "\<pi>"}@{text " | "}@{verbatim "\<rho>"}@{text " | "}@{verbatim "\<sigma>"}@{text " | "}@{verbatim "\<tau>"}@{text " |"} \\ |
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& & @{verbatim "\<upsilon>"}@{text " | "}@{verbatim "\<phi>"}@{text " | "}@{verbatim "\<chi>"}@{text " | "}@{verbatim "\<psi>"}@{text " |"} \\ |
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& & @{verbatim "\<omega>"}@{text " | "}@{verbatim "\<Gamma>"}@{text " | "}@{verbatim "\<Delta>"}@{text " | "}@{verbatim "\<Theta>"}@{text " |"} \\ |
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& & @{verbatim "\<Lambda>"}@{text " | "}@{verbatim "\<Xi>"}@{text " | "}@{verbatim "\<Pi>"}@{text " | "}@{verbatim "\<Sigma>"}@{text " |"} \\ |
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& & @{verbatim "\<Upsilon>"}@{text " | "}@{verbatim "\<Phi>"}@{text " | "}@{verbatim "\<Psi>"}@{text " | "}@{verbatim "\<Omega>"} \\ |
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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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@{text "?x.1"} or @{text "?x7.3"} or run together as in @{text |
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"?x1"}. The latter form is possible if the base name does not end |
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with digits. If the index is 0, it may be dropped altogether: |
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@{text "?x"} and @{text "?x0"} and @{text "?x.0"} all refer to the |
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same unknown, with basename @{text "x"} and index 0. |
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The syntax of @{syntax_ref string} admits any characters, including |
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newlines; ``@{verbatim "\""}'' (double-quote) and ``@{verbatim |
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"\\"}'' (backslash) need to be escaped by a backslash; arbitrary |
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character codes may be specified as ``@{verbatim "\\"}@{text ddd}'', |
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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 |
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containing ``@{verbatim "*"}@{verbatim "}"}''; this allows |
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convenient inclusion of quotes without further escapes. There is no |
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way to escape ``@{verbatim "*"}@{verbatim "}"}''. If the quoted |
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text is {\LaTeX} source, one may usually add some blank or comment |
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to avoid the critical character sequence. |
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A @{syntax_ref cartouche} consists of arbitrary text, with properly |
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balanced blocks of ``@{verbatim "\<open>"}~@{text "\<dots>"}~@{verbatim |
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"\<close>"}''. Note that the rendering of cartouche delimiters is |
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usually like this: ``@{text "\<open> \<dots> \<close>"}''. |
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Source comments take the form @{verbatim "(*"}~@{text |
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"\<dots>"}~@{verbatim "*)"} 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{document comments} 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 @{text \<forall>} are represented in |
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Isabelle as @{verbatim \<forall>}. 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}, Proof~General, 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 "\<lambda>"} does not belong |
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to the @{text letter} category, since it is already used differently |
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in the Pure term language. *} |
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section {* Common syntax entities *} |
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text {* |
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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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*} |
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subsection {* Names *} |
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text {* Entity @{syntax name} usually refers to any name of types, |
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constants, theorems etc.\ that are to be \emph{declared} or |
230 |
\emph{defined} (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 "\"let\""}). |
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Already existing objects are usually referenced by @{syntax |
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nameref}. |
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@{rail " |
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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 parname}: '(' @{syntax name} ')' |
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; |
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@{syntax_def nameref}: @{syntax name} | @{syntax longident} |
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"} |
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*} |
245 |
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subsection {* Numbers *} |
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text {* 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 " |
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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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"} |
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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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*} |
262 |
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subsection {* Comments \label{sec:comments} *} |
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text {* Large chunks of plain @{syntax text} are usually given |
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@{syntax verbatim}, i.e.\ enclosed in @{verbatim "{"}@{verbatim |
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"*"}~@{text "\<dots>"}~@{verbatim "*"}@{verbatim "}"}. For convenience, |
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any of the smaller text units conforming to @{syntax nameref} are |
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admitted as well. A marginal @{syntax comment} is of the form |
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@{verbatim "--"}~@{syntax text}. Any number of these may occur |
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within Isabelle/Isar commands. |
273 |
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@{rail " |
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@{syntax_def text}: @{syntax verbatim} | @{syntax nameref} |
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; |
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@{syntax_def comment}: '--' @{syntax text} |
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"} |
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*} |
280 |
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subsection {* Type classes, sorts and arities *} |
|
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text {* |
|
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Classes are specified by plain names. Sorts have a very simple |
|
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inner syntax, which is either a single class name @{text c} or a |
|
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list @{text "{c\<^sub>1, \<dots>, c\<^sub>n}"} referring to the |
|
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intersection of these classes. The syntax of type arities is given |
|
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directly at the outer level. |
|
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@{rail " |
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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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"} |
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*} |
299 |
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subsection {* Types and terms \label{sec:types-terms} *} |
|
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text {* |
|
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The actual inner Isabelle syntax, that of types and terms of the |
|
305 |
logic, is far too sophisticated in order to be modelled explicitly |
|
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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 |
|
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is performed internally later). For convenience, a slightly more |
|
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liberal convention is adopted: quotes may be omitted for any type or |
|
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term that is already atomic at the outer level. For example, one |
|
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may just write @{verbatim x} instead of quoted @{verbatim "\"x\""}. |
|
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Note that symbolic identifiers (e.g.\ @{verbatim "++"} or @{text |
|
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"\<forall>"} are available as well, provided these have not been superseded |
|
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by commands or other keywords already (such as @{verbatim "="} or |
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@{verbatim "+"}). |
|
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@{rail " |
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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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"} |
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|
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Positional instantiations are indicated by giving a sequence of |
|
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terms, or the placeholder ``@{text _}'' (underscore), which means to |
|
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skip a position. |
|
329 |
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@{rail " |
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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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"} |
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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 " |
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@{syntax_def typespec}: |
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(() | @{syntax typefree} | '(' ( @{syntax typefree} + ',' ) ')') @{syntax name} |
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; |
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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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"} |
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*} |
350 |
||
351 |
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subsection {* Term patterns and declarations \label{sec:term-decls} *} |
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353 |
|
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text {* Wherever explicit propositions (or term fragments) occur in a |
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proof text, casual binding of schematic term variables may be given |
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specified via patterns of the form ``@{text "(\<IS> p\<^sub>1 \<dots> p\<^sub>n)"}''. |
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This works both for @{syntax term} and @{syntax prop}. |
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358 |
|
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@{rail " |
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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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"} |
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364 |
|
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\medskip Declarations of local variables @{text "x :: \<tau>"} and |
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logical propositions @{text "a : \<phi>"} 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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372 |
|
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@{rail " |
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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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"} |
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378 |
|
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379 |
The treatment of multiple declarations corresponds to the |
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complementary focus of @{syntax vars} versus @{syntax props}. In |
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``@{text "x\<^sub>1 \<dots> x\<^sub>n :: \<tau>"}'' the typing refers to all variables, while |
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in @{text "a: \<phi>\<^sub>1 \<dots> \<phi>\<^sub>n"} 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}. |
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*} |
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389 |
|
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390 |
|
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subsection {* Attributes and theorems \label{sec:syn-att} *} |
392 |
||
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text {* 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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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}. |
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|
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401 |
@{rail " |
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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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@{syntax keyword} |
27037 | 405 |
; |
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arg: @{syntax atom} | '(' @{syntax args} ')' | '[' @{syntax args} ']' |
27037 | 407 |
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408 |
@{syntax_def args}: arg * |
27037 | 409 |
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410 |
@{syntax_def attributes}: '[' (@{syntax nameref} @{syntax args} * ',') ']' |
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411 |
"} |
27037 | 412 |
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413 |
Theorem specifications come in several flavors: @{syntax axmdecl} |
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414 |
and @{syntax thmdecl} usually refer to axioms, assumptions or |
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415 |
results of goal statements, while @{syntax thmdef} collects lists of |
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416 |
existing theorems. Existing theorems are given by @{syntax thmref} |
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417 |
and @{syntax thmrefs}, the former requires an actual singleton |
27037 | 418 |
result. |
419 |
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420 |
There are three forms of theorem references: |
|
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\begin{enumerate} |
|
422 |
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423 |
\item named facts @{text "a"}, |
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424 |
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\item selections from named facts @{text "a(i)"} or @{text "a(j - k)"}, |
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426 |
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\item literal fact propositions using @{syntax_ref altstring} syntax |
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428 |
@{verbatim "`"}@{text "\<phi>"}@{verbatim "`"} (see also method |
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@{method_ref fact}). |
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431 |
\end{enumerate} |
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432 |
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433 |
Any kind of theorem specification may include lists of attributes |
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434 |
both on the left and right hand sides; attributes are applied to any |
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435 |
immediately preceding fact. If names are omitted, the theorems are |
|
436 |
not stored within the theorem database of the theory or proof |
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437 |
context, but any given attributes are applied nonetheless. |
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438 |
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439 |
An extra pair of brackets around attributes (like ``@{text |
|
440 |
"[[simproc a]]"}'') abbreviates a theorem reference involving an |
|
441 |
internal dummy fact, which will be ignored later on. So only the |
|
442 |
effect of the attribute on the background context will persist. |
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443 |
This form of in-place declarations is particularly useful with |
|
444 |
commands like @{command "declare"} and @{command "using"}. |
|
445 |
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446 |
@{rail " |
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@{syntax_def axmdecl}: @{syntax name} @{syntax attributes}? ':' |
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448 |
; |
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@{syntax_def thmdecl}: thmbind ':' |
27037 | 450 |
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451 |
@{syntax_def thmdef}: thmbind '=' |
27037 | 452 |
; |
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453 |
@{syntax_def thmref}: |
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454 |
(@{syntax nameref} selection? | @{syntax altstring}) @{syntax attributes}? | |
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455 |
'[' @{syntax attributes} ']' |
27037 | 456 |
; |
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457 |
@{syntax_def thmrefs}: @{syntax thmref} + |
27037 | 458 |
; |
459 |
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460 |
thmbind: @{syntax name} @{syntax attributes} | @{syntax name} | @{syntax attributes} |
27037 | 461 |
; |
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selection: '(' ((@{syntax nat} | @{syntax nat} '-' @{syntax nat}?) + ',') ')' |
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463 |
"} |
27037 | 464 |
*} |
465 |
||
466 |
end |