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(* $Id$ *)
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theory Outer_Syntax
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imports Main
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begin
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chapter {* 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 Proof~General \cite{proofgeneral}
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do not require explicit semicolons, the amount of input text is
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determined automatically by inspecting the present content of the
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Emacs text 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 {* 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 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 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 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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& & @{verbatim "\<^isub>"}@{text " | "}@{verbatim "\<^isup>"} \\
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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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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} or Proof~General with the X-Symbol package.
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A list of standard Isabelle symbols that work well with these tools
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is given in \appref{app:symbols}. Note that @{verbatim "\<lambda>"} does
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not belong to the @{text letter} category, since it is already used
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differently in the Pure term language.
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*}
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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 {*
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Entity \railqtok{name} usually refers to any name of types,
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constants, theorems etc.\ that are to be \emph{declared} or
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\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
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\railqtok{nameref}.
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\indexoutertoken{name}\indexoutertoken{parname}\indexoutertoken{nameref}
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\indexoutertoken{int}
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\begin{rail}
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name: ident | symident | string | nat
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;
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parname: '(' name ')'
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;
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nameref: name | longident
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;
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int: nat | '-' nat
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;
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\end{rail}
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*}
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subsection {* Comments \label{sec:comments} *}
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text {*
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Large chunks of plain \railqtok{text} are usually given
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\railtok{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 \railqtok{nameref} are
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admitted as well. A marginal \railnonterm{comment} is of the form
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@{verbatim "--"} \railqtok{text}. Any number of these may occur
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within Isabelle/Isar commands.
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\indexoutertoken{text}\indexouternonterm{comment}
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\begin{rail}
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text: verbatim | nameref
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;
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comment: '--' text
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;
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\end{rail}
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*}
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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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\indexouternonterm{sort}\indexouternonterm{arity}
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\indexouternonterm{classdecl}
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\begin{rail}
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classdecl: name (('<' | subseteq) (nameref + ','))?
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;
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sort: nameref
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;
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arity: ('(' (sort + ',') ')')? sort
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;
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\end{rail}
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*}
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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
|
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|
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logic, is far too sophisticated in order to be modelled explicitly
|
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|
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at the outer theory level. Basically, any such entity has to be
|
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|
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quoted to turn it into a single token (the parsing and type-checking
|
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|
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is performed internally later). For convenience, a slightly more
|
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|
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liberal convention is adopted: quotes may be omitted for any type or
|
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|
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term that is already atomic at the outer level. For example, one
|
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|
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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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|
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"\<forall>"} are available as well, provided these have not been superseded
|
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|
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by commands or other keywords already (such as @{verbatim "="} or
|
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@{verbatim "+"}).
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\indexoutertoken{type}\indexoutertoken{term}\indexoutertoken{prop}
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\begin{rail}
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type: nameref | typefree | typevar
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;
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term: nameref | var
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|
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;
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|
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prop: term
|
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|
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;
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|
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\end{rail}
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|
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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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|
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terms, or the placeholder ``@{text _}'' (underscore), which means to
|
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|
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skip a position.
|
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|
287 |
|
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|
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\indexoutertoken{inst}\indexoutertoken{insts}
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|
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\begin{rail}
|
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|
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inst: underscore | term
|
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|
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;
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|
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insts: (inst *)
|
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|
293 |
;
|
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|
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\end{rail}
|
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|
295 |
|
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|
296 |
Type declarations and definitions usually refer to
|
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|
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\railnonterm{typespec} on the left-hand side. This models basic
|
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|
298 |
type constructor application at the outer syntax level. Note that
|
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|
299 |
only plain postfix notation is available here, but no infixes.
|
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|
300 |
|
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|
301 |
\indexouternonterm{typespec}
|
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|
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\begin{rail}
|
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|
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typespec: (() | typefree | '(' ( typefree + ',' ) ')') name
|
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|
304 |
;
|
wenzelm@27037
|
305 |
\end{rail}
|
wenzelm@27037
|
306 |
*}
|
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|
307 |
|
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|
308 |
|
wenzelm@28754
|
309 |
subsection {* Term patterns and declarations \label{sec:term-decls} *}
|
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|
310 |
|
wenzelm@28754
|
311 |
text {*
|
wenzelm@28754
|
312 |
Wherever explicit propositions (or term fragments) occur in a proof
|
wenzelm@28754
|
313 |
text, casual binding of schematic term variables may be given
|
wenzelm@28754
|
314 |
specified via patterns of the form ``@{text "(\<IS> p\<^sub>1 \<dots>
|
wenzelm@28754
|
315 |
p\<^sub>n)"}''. This works both for \railqtok{term} and \railqtok{prop}.
|
wenzelm@28754
|
316 |
|
wenzelm@28754
|
317 |
\indexouternonterm{termpat}\indexouternonterm{proppat}
|
wenzelm@28754
|
318 |
\begin{rail}
|
wenzelm@28754
|
319 |
termpat: '(' ('is' term +) ')'
|
wenzelm@28754
|
320 |
;
|
wenzelm@28754
|
321 |
proppat: '(' ('is' prop +) ')'
|
wenzelm@28754
|
322 |
;
|
wenzelm@28754
|
323 |
\end{rail}
|
wenzelm@28754
|
324 |
|
wenzelm@28754
|
325 |
\medskip Declarations of local variables @{text "x :: \<tau>"} and
|
wenzelm@28754
|
326 |
logical propositions @{text "a : \<phi>"} represent different views on
|
wenzelm@28754
|
327 |
the same principle of introducing a local scope. In practice, one
|
wenzelm@28754
|
328 |
may usually omit the typing of \railnonterm{vars} (due to
|
wenzelm@28754
|
329 |
type-inference), and the naming of propositions (due to implicit
|
wenzelm@28754
|
330 |
references of current facts). In any case, Isar proof elements
|
wenzelm@28754
|
331 |
usually admit to introduce multiple such items simultaneously.
|
wenzelm@28754
|
332 |
|
wenzelm@28754
|
333 |
\indexouternonterm{vars}\indexouternonterm{props}
|
wenzelm@28754
|
334 |
\begin{rail}
|
wenzelm@28754
|
335 |
vars: (name+) ('::' type)?
|
wenzelm@28754
|
336 |
;
|
wenzelm@28754
|
337 |
props: thmdecl? (prop proppat? +)
|
wenzelm@28754
|
338 |
;
|
wenzelm@28754
|
339 |
\end{rail}
|
wenzelm@28754
|
340 |
|
wenzelm@28754
|
341 |
The treatment of multiple declarations corresponds to the
|
wenzelm@28754
|
342 |
complementary focus of \railnonterm{vars} versus
|
wenzelm@28754
|
343 |
\railnonterm{props}. In ``@{text "x\<^sub>1 \<dots> x\<^sub>n :: \<tau>"}''
|
wenzelm@28754
|
344 |
the typing refers to all variables, while in @{text "a: \<phi>\<^sub>1 \<dots>
|
wenzelm@28754
|
345 |
\<phi>\<^sub>n"} the naming refers to all propositions collectively.
|
wenzelm@28754
|
346 |
Isar language elements that refer to \railnonterm{vars} or
|
wenzelm@28754
|
347 |
\railnonterm{props} typically admit separate typings or namings via
|
wenzelm@28754
|
348 |
another level of iteration, with explicit @{keyword_ref "and"}
|
wenzelm@28754
|
349 |
separators; e.g.\ see @{command "fix"} and @{command "assume"} in
|
wenzelm@28754
|
350 |
\secref{sec:proof-context}.
|
wenzelm@28754
|
351 |
*}
|
wenzelm@28754
|
352 |
|
wenzelm@28754
|
353 |
|
wenzelm@27037
|
354 |
subsection {* Attributes and theorems \label{sec:syn-att} *}
|
wenzelm@27037
|
355 |
|
wenzelm@28754
|
356 |
text {* Attributes have their own ``semi-inner'' syntax, in the sense
|
wenzelm@28754
|
357 |
that input conforming to \railnonterm{args} below is parsed by the
|
wenzelm@28754
|
358 |
attribute a second time. The attribute argument specifications may
|
wenzelm@28754
|
359 |
be any sequence of atomic entities (identifiers, strings etc.), or
|
wenzelm@28754
|
360 |
properly bracketed argument lists. Below \railqtok{atom} refers to
|
wenzelm@28754
|
361 |
any atomic entity, including any \railtok{keyword} conforming to
|
wenzelm@28754
|
362 |
\railtok{symident}.
|
wenzelm@27037
|
363 |
|
wenzelm@27037
|
364 |
\indexoutertoken{atom}\indexouternonterm{args}\indexouternonterm{attributes}
|
wenzelm@27037
|
365 |
\begin{rail}
|
wenzelm@27037
|
366 |
atom: nameref | typefree | typevar | var | nat | keyword
|
wenzelm@27037
|
367 |
;
|
wenzelm@27037
|
368 |
arg: atom | '(' args ')' | '[' args ']'
|
wenzelm@27037
|
369 |
;
|
wenzelm@27037
|
370 |
args: arg *
|
wenzelm@27037
|
371 |
;
|
wenzelm@27037
|
372 |
attributes: '[' (nameref args * ',') ']'
|
wenzelm@27037
|
373 |
;
|
wenzelm@27037
|
374 |
\end{rail}
|
wenzelm@27037
|
375 |
|
wenzelm@27037
|
376 |
Theorem specifications come in several flavors:
|
wenzelm@27037
|
377 |
\railnonterm{axmdecl} and \railnonterm{thmdecl} usually refer to
|
wenzelm@27037
|
378 |
axioms, assumptions or results of goal statements, while
|
wenzelm@27037
|
379 |
\railnonterm{thmdef} collects lists of existing theorems. Existing
|
wenzelm@27037
|
380 |
theorems are given by \railnonterm{thmref} and
|
wenzelm@27037
|
381 |
\railnonterm{thmrefs}, the former requires an actual singleton
|
wenzelm@27037
|
382 |
result.
|
wenzelm@27037
|
383 |
|
wenzelm@27037
|
384 |
There are three forms of theorem references:
|
wenzelm@27037
|
385 |
\begin{enumerate}
|
wenzelm@27037
|
386 |
|
wenzelm@27037
|
387 |
\item named facts @{text "a"},
|
wenzelm@27037
|
388 |
|
wenzelm@27037
|
389 |
\item selections from named facts @{text "a(i)"} or @{text "a(j - k)"},
|
wenzelm@27037
|
390 |
|
wenzelm@27037
|
391 |
\item literal fact propositions using @{syntax_ref altstring} syntax
|
wenzelm@27037
|
392 |
@{verbatim "`"}@{text "\<phi>"}@{verbatim "`"} (see also method
|
wenzelm@28754
|
393 |
@{method_ref fact}).
|
wenzelm@27037
|
394 |
|
wenzelm@27037
|
395 |
\end{enumerate}
|
wenzelm@27037
|
396 |
|
wenzelm@27037
|
397 |
Any kind of theorem specification may include lists of attributes
|
wenzelm@27037
|
398 |
both on the left and right hand sides; attributes are applied to any
|
wenzelm@27037
|
399 |
immediately preceding fact. If names are omitted, the theorems are
|
wenzelm@27037
|
400 |
not stored within the theorem database of the theory or proof
|
wenzelm@27037
|
401 |
context, but any given attributes are applied nonetheless.
|
wenzelm@27037
|
402 |
|
wenzelm@27037
|
403 |
An extra pair of brackets around attributes (like ``@{text
|
wenzelm@27037
|
404 |
"[[simproc a]]"}'') abbreviates a theorem reference involving an
|
wenzelm@27037
|
405 |
internal dummy fact, which will be ignored later on. So only the
|
wenzelm@27037
|
406 |
effect of the attribute on the background context will persist.
|
wenzelm@27037
|
407 |
This form of in-place declarations is particularly useful with
|
wenzelm@27037
|
408 |
commands like @{command "declare"} and @{command "using"}.
|
wenzelm@27037
|
409 |
|
wenzelm@27037
|
410 |
\indexouternonterm{axmdecl}\indexouternonterm{thmdecl}
|
wenzelm@27037
|
411 |
\indexouternonterm{thmdef}\indexouternonterm{thmref}
|
wenzelm@27037
|
412 |
\indexouternonterm{thmrefs}\indexouternonterm{selection}
|
wenzelm@27037
|
413 |
\begin{rail}
|
wenzelm@27037
|
414 |
axmdecl: name attributes? ':'
|
wenzelm@27037
|
415 |
;
|
wenzelm@27037
|
416 |
thmdecl: thmbind ':'
|
wenzelm@27037
|
417 |
;
|
wenzelm@27037
|
418 |
thmdef: thmbind '='
|
wenzelm@27037
|
419 |
;
|
wenzelm@27037
|
420 |
thmref: (nameref selection? | altstring) attributes? | '[' attributes ']'
|
wenzelm@27037
|
421 |
;
|
wenzelm@27037
|
422 |
thmrefs: thmref +
|
wenzelm@27037
|
423 |
;
|
wenzelm@27037
|
424 |
|
wenzelm@27037
|
425 |
thmbind: name attributes | name | attributes
|
wenzelm@27037
|
426 |
;
|
wenzelm@27037
|
427 |
selection: '(' ((nat | nat '-' nat?) + ',') ')'
|
wenzelm@27037
|
428 |
;
|
wenzelm@27037
|
429 |
\end{rail}
|
wenzelm@27037
|
430 |
*}
|
wenzelm@27037
|
431 |
|
wenzelm@27037
|
432 |
end
|