doc-src/IsarRef/Thy/Outer_Syntax.thy
author wenzelm
Tue May 03 15:07:36 2011 +0200 (2011-05-03)
changeset 42651 e3fdb7c96be5
parent 42596 6c621a9d612a
child 42705 528a2ba8fa74
permissions -rw-r--r--
formal Base theory;
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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 *}
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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 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 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 predefined Isabelle symbols that work well with these
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  tools is given in \appref{app:symbols}.  Note that @{verbatim "\<lambda>"}
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  does not belong to the @{text letter} category, since it is already
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  used 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 {* Entity @{syntax 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 @{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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*}
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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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*}
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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.
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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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*}
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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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*}
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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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  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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  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.
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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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  @{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 typespecsorts}:
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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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*}
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subsection {* Term patterns and declarations \label{sec:term-decls} *}
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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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  @{rail "
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    @{syntax_def termpat}: '(' (@'is' @{syntax term} +) ')'
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    ;
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    @{syntax_def proppat}: '(' (@'is' @{syntax prop} +) ')'
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  "}
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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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  @{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 proppat}? +)
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  "}
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  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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subsection {* Attributes and theorems \label{sec:syn-att} *}
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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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  @{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}
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    ;
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    arg: @{syntax atom} | '(' @{syntax args} ')' | '[' @{syntax args} ']'
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    ;
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    @{syntax_def args}: arg *
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    ;
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    @{syntax_def attributes}: '[' (@{syntax nameref} @{syntax args} * ',') ']'
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  "}
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  Theorem specifications come in several flavors: @{syntax axmdecl}
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  and @{syntax thmdecl} usually refer to axioms, assumptions or
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  results of goal statements, while @{syntax thmdef} collects lists of
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  existing theorems.  Existing theorems are given by @{syntax thmref}
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  and @{syntax thmrefs}, the former requires an actual singleton
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  result.
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  There are three forms of theorem references:
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  \begin{enumerate}
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  \item named facts @{text "a"},
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  \item selections from named facts @{text "a(i)"} or @{text "a(j - k)"},
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  \item literal fact propositions using @{syntax_ref altstring} syntax
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  @{verbatim "`"}@{text "\<phi>"}@{verbatim "`"} (see also method
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  @{method_ref fact}).
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  \end{enumerate}
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  Any kind of theorem specification may include lists of attributes
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  both on the left and right hand sides; attributes are applied to any
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  immediately preceding fact.  If names are omitted, the theorems are
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  not stored within the theorem database of the theory or proof
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  context, but any given attributes are applied nonetheless.
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  An extra pair of brackets around attributes (like ``@{text
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  "[[simproc a]]"}'') abbreviates a theorem reference involving an
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  internal dummy fact, which will be ignored later on.  So only the
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  effect of the attribute on the background context will persist.
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  This form of in-place declarations is particularly useful with
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  commands like @{command "declare"} and @{command "using"}.
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  @{rail "
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    @{syntax_def axmdecl}: @{syntax name} @{syntax attributes}? ':'
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    ;
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    @{syntax_def thmdecl}: thmbind ':'
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    ;
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    @{syntax_def thmdef}: thmbind '='
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    ;
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    @{syntax_def thmref}:
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      (@{syntax nameref} selection? | @{syntax altstring}) @{syntax attributes}? |
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      '[' @{syntax attributes} ']'
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    ;
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    @{syntax_def thmrefs}: @{syntax thmref} +
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    ;
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    thmbind: @{syntax name} @{syntax attributes} | @{syntax name} | @{syntax attributes}
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    ;
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    selection: '(' ((@{syntax nat} | @{syntax nat} '-' @{syntax nat}?) + ',') ')'
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  "}
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*}
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end