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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 Isabelle/Isar outer syntax provides token classes as
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presented below; most of these coincide with the inner lexical
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syntax as defined in \secref{sec:inner-lex}.
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\begin{matharray}{rcl}
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@{syntax_def ident} & = & letter\,quasiletter^* \\
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@{syntax_def longident} & = & ident (\verb,.,ident)^+ \\
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@{syntax_def symident} & = & sym^+ ~|~ \verb,\,\verb,<,ident\verb,>, \\
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@{syntax_def nat} & = & digit^+ \\
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@{syntax_def var} & = & ident ~|~ \verb,?,ident ~|~ \verb,?,ident\verb,.,nat \\
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@{syntax_def typefree} & = & \verb,',ident \\
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@{syntax_def typevar} & = & typefree ~|~ \verb,?,typefree ~|~ \verb,?,typefree\verb,.,nat \\
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@{syntax_def string} & = & \verb,", ~\dots~ \verb,", \\
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@{syntax_def altstring} & = & \backquote ~\dots~ \backquote \\
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@{syntax_def verbatim} & = & \verb,{*, ~\dots~ \verb,*,\verb,}, \\[1ex]
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letter & = & latin ~|~ \verb,\,\verb,<,latin\verb,>, ~|~ \verb,\,\verb,<,latin\,latin\verb,>, ~|~ greek ~|~ \\
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& & \verb,\<^isub>, ~|~ \verb,\<^isup>, \\
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quasiletter & = & letter ~|~ digit ~|~ \verb,_, ~|~ \verb,', \\
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latin & = & \verb,a, ~|~ \dots ~|~ \verb,z, ~|~ \verb,A, ~|~ \dots ~|~ \verb,Z, \\
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digit & = & \verb,0, ~|~ \dots ~|~ \verb,9, \\
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sym & = & \verb,!, ~|~ \verb,#, ~|~ \verb,$, ~|~ \verb,%, ~|~ \verb,&, ~|~
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\verb,*, ~|~ \verb,+, ~|~ \verb,-, ~|~ \verb,/, ~|~ \\
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& & \verb,<, ~|~ \verb,=, ~|~ \verb,>, ~|~ \verb,?, ~|~ \texttt{\at} ~|~
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\verb,^, ~|~ \verb,_, ~|~ \verb,|, ~|~ \verb,~, \\
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greek & = & \verb,\<alpha>, ~|~ \verb,\<beta>, ~|~ \verb,\<gamma>, ~|~ \verb,\<delta>, ~| \\
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& & \verb,\<epsilon>, ~|~ \verb,\<zeta>, ~|~ \verb,\<eta>, ~|~ \verb,\<theta>, ~| \\
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& & \verb,\<iota>, ~|~ \verb,\<kappa>, ~|~ \verb,\<mu>, ~|~ \verb,\<nu>, ~| \\
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& & \verb,\<xi>, ~|~ \verb,\<pi>, ~|~ \verb,\<rho>, ~|~ \verb,\<sigma>, ~|~ \verb,\<tau>, ~| \\
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& & \verb,\<upsilon>, ~|~ \verb,\<phi>, ~|~ \verb,\<chi>, ~|~ \verb,\<psi>, ~| \\
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& & \verb,\<omega>, ~|~ \verb,\<Gamma>, ~|~ \verb,\<Delta>, ~|~ \verb,\<Theta>, ~| \\
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& & \verb,\<Lambda>, ~|~ \verb,\<Xi>, ~|~ \verb,\<Pi>, ~|~ \verb,\<Sigma>, ~| \\
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& & \verb,\<Upsilon>, ~|~ \verb,\<Phi>, ~|~ \verb,\<Psi>, ~|~ \verb,\<Omega>, \\
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\end{matharray}
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The syntax of @{syntax 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 altstring} are analogous, using single back-quotes instead.
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The body of @{syntax 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. The greek
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letters do \emph{not} include @{verbatim "\<lambda>"}, which is already used
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differently in the meta-logic.
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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 \cite[appendix~A]{isabelle-sys}.
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Source comments take the form @{verbatim "(*"}~@{text
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"\<dots>"}~@{verbatim "*)"} and may be nested, although user-interface
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tools might prevent this. Note that this form indicates source
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comments only, which are stripped after lexical analysis of the
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input. The Isar syntax also provides proper \emph{document
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comments} that are considered as part of the text (see
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\secref{sec:comments}).
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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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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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\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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prop: term
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;
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\end{rail}
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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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\indexoutertoken{inst}\indexoutertoken{insts}
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\begin{rail}
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inst: underscore | term
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;
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insts: (inst *)
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;
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\end{rail}
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Type declarations and definitions usually refer to
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\railnonterm{typespec} on the left-hand side. This models basic
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type constructor application at the outer syntax level. Note that
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only plain postfix notation is available here, but no infixes.
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\indexouternonterm{typespec}
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\begin{rail}
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typespec: (() | typefree | '(' ( typefree + ',' ) ')') name
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;
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\end{rail}
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*}
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subsection {* Term patterns and declarations \label{sec:term-decls} *}
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text {*
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Wherever explicit propositions (or term fragments) occur in a proof
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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>
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p\<^sub>n)"}''. This works both for \railqtok{term} and \railqtok{prop}.
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\indexouternonterm{termpat}\indexouternonterm{proppat}
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\begin{rail}
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termpat: '(' ('is' term +) ')'
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;
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proppat: '(' ('is' prop +) ')'
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;
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\end{rail}
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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 \railnonterm{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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\indexouternonterm{vars}\indexouternonterm{props}
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\begin{rail}
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vars: (name+) ('::' type)?
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;
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props: thmdecl? (prop proppat? +)
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;
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\end{rail}
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The treatment of multiple declarations corresponds to the
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complementary focus of \railnonterm{vars} versus
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\railnonterm{props}. In ``@{text "x\<^sub>1 \<dots> x\<^sub>n :: \<tau>"}''
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the typing refers to all variables, while in @{text "a: \<phi>\<^sub>1 \<dots>
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\<phi>\<^sub>n"} the naming refers to all propositions collectively.
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Isar language elements that refer to \railnonterm{vars} or
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\railnonterm{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 \railnonterm{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 \railqtok{atom} refers to
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any atomic entity, including any \railtok{keyword} conforming to
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\railtok{symident}.
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\indexoutertoken{atom}\indexouternonterm{args}\indexouternonterm{attributes}
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\begin{rail}
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atom: nameref | typefree | typevar | var | nat | keyword
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;
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arg: atom | '(' args ')' | '[' args ']'
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;
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args: arg *
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;
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attributes: '[' (nameref args * ',') ']'
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;
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\end{rail}
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Theorem specifications come in several flavors:
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\railnonterm{axmdecl} and \railnonterm{thmdecl} usually refer to
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axioms, assumptions or results of goal statements, while
|
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\railnonterm{thmdef} collects lists of existing theorems. Existing
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theorems are given by \railnonterm{thmref} and
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\railnonterm{thmrefs}, the former requires an actual singleton
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result.
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|
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|
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|
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There are three forms of theorem references:
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\begin{enumerate}
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|
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\item named facts @{text "a"},
|
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|
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\item selections from named facts @{text "a(i)"} or @{text "a(j - k)"},
|
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|
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|
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|
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\item literal fact propositions using @{syntax_ref altstring} syntax
|
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|
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@{verbatim "`"}@{text "\<phi>"}@{verbatim "`"} (see also method
|
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|
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@{method_ref fact}).
|
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|
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|
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|
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\end{enumerate}
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|
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|
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|
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Any kind of theorem specification may include lists of attributes
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|
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both on the left and right hand sides; attributes are applied to any
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|
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immediately preceding fact. If names are omitted, the theorems are
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|
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not stored within the theorem database of the theory or proof
|
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|
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context, but any given attributes are applied nonetheless.
|
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|
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|
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|
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An extra pair of brackets around attributes (like ``@{text
|
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|
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"[[simproc a]]"}'') abbreviates a theorem reference involving an
|
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|
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internal dummy fact, which will be ignored later on. So only the
|
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|
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effect of the attribute on the background context will persist.
|
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|
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This form of in-place declarations is particularly useful with
|
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|
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commands like @{command "declare"} and @{command "using"}.
|
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|
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|
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|
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\indexouternonterm{axmdecl}\indexouternonterm{thmdecl}
|
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|
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\indexouternonterm{thmdef}\indexouternonterm{thmref}
|
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|
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\indexouternonterm{thmrefs}\indexouternonterm{selection}
|
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|
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\begin{rail}
|
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|
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axmdecl: name attributes? ':'
|
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|
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;
|
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|
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thmdecl: thmbind ':'
|
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|
372 |
;
|
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|
373 |
thmdef: thmbind '='
|
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|
374 |
;
|
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|
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thmref: (nameref selection? | altstring) attributes? | '[' attributes ']'
|
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|
376 |
;
|
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|
377 |
thmrefs: thmref +
|
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|
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;
|
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|
379 |
|
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|
380 |
thmbind: name attributes | name | attributes
|
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|
381 |
;
|
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|
382 |
selection: '(' ((nat | nat '-' nat?) + ',') ')'
|
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|
383 |
;
|
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|
384 |
\end{rail}
|
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|
385 |
*}
|
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|
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|
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|
387 |
end
|