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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:lex-syntax} *}
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text {*
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The Isabelle/Isar outer syntax provides token classes as presented
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below; most of these coincide with the inner lexical syntax as
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presented in \cite{isabelle-ref}.
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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} *}
|
wenzelm@28752
|
266 |
|
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|
267 |
text {*
|
wenzelm@28752
|
268 |
Wherever explicit propositions (or term fragments) occur in a proof
|
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|
269 |
text, casual binding of schematic term variables may be given
|
wenzelm@28752
|
270 |
specified via patterns of the form ``@{text "(\<IS> p\<^sub>1 \<dots>
|
wenzelm@28752
|
271 |
p\<^sub>n)"}''. This works both for \railqtok{term} and \railqtok{prop}.
|
wenzelm@28752
|
272 |
|
wenzelm@28752
|
273 |
\indexouternonterm{termpat}\indexouternonterm{proppat}
|
wenzelm@28752
|
274 |
\begin{rail}
|
wenzelm@28752
|
275 |
termpat: '(' ('is' term +) ')'
|
wenzelm@28752
|
276 |
;
|
wenzelm@28752
|
277 |
proppat: '(' ('is' prop +) ')'
|
wenzelm@28752
|
278 |
;
|
wenzelm@28752
|
279 |
\end{rail}
|
wenzelm@28752
|
280 |
|
wenzelm@28752
|
281 |
\medskip Declarations of local variables @{text "x :: \<tau>"} and
|
wenzelm@28752
|
282 |
logical propositions @{text "a : \<phi>"} represent different views on
|
wenzelm@28752
|
283 |
the same principle of introducing a local scope. In practice, one
|
wenzelm@28752
|
284 |
may usually omit the typing of \railnonterm{vars} (due to
|
wenzelm@28752
|
285 |
type-inference), and the naming of propositions (due to implicit
|
wenzelm@28752
|
286 |
references of current facts). In any case, Isar proof elements
|
wenzelm@28752
|
287 |
usually admit to introduce multiple such items simultaneously.
|
wenzelm@28752
|
288 |
|
wenzelm@28752
|
289 |
\indexouternonterm{vars}\indexouternonterm{props}
|
wenzelm@28752
|
290 |
\begin{rail}
|
wenzelm@28752
|
291 |
vars: (name+) ('::' type)?
|
wenzelm@28752
|
292 |
;
|
wenzelm@28752
|
293 |
props: thmdecl? (prop proppat? +)
|
wenzelm@28752
|
294 |
;
|
wenzelm@28752
|
295 |
\end{rail}
|
wenzelm@28752
|
296 |
|
wenzelm@28752
|
297 |
The treatment of multiple declarations corresponds to the
|
wenzelm@28752
|
298 |
complementary focus of \railnonterm{vars} versus
|
wenzelm@28752
|
299 |
\railnonterm{props}. In ``@{text "x\<^sub>1 \<dots> x\<^sub>n :: \<tau>"}''
|
wenzelm@28752
|
300 |
the typing refers to all variables, while in @{text "a: \<phi>\<^sub>1 \<dots>
|
wenzelm@28752
|
301 |
\<phi>\<^sub>n"} the naming refers to all propositions collectively.
|
wenzelm@28752
|
302 |
Isar language elements that refer to \railnonterm{vars} or
|
wenzelm@28752
|
303 |
\railnonterm{props} typically admit separate typings or namings via
|
wenzelm@28752
|
304 |
another level of iteration, with explicit @{keyword_ref "and"}
|
wenzelm@28752
|
305 |
separators; e.g.\ see @{command "fix"} and @{command "assume"} in
|
wenzelm@28752
|
306 |
\secref{sec:proof-context}.
|
wenzelm@28752
|
307 |
*}
|
wenzelm@28752
|
308 |
|
wenzelm@28752
|
309 |
|
wenzelm@27037
|
310 |
subsection {* Mixfix annotations *}
|
wenzelm@27037
|
311 |
|
wenzelm@27037
|
312 |
text {*
|
wenzelm@27037
|
313 |
Mixfix annotations specify concrete \emph{inner} syntax of Isabelle
|
wenzelm@27037
|
314 |
types and terms. Some commands such as @{command "types"} (see
|
wenzelm@27037
|
315 |
\secref{sec:types-pure}) admit infixes only, while @{command
|
wenzelm@27037
|
316 |
"consts"} (see \secref{sec:consts}) and @{command "syntax"} (see
|
wenzelm@27037
|
317 |
\secref{sec:syn-trans}) support the full range of general mixfixes
|
wenzelm@27037
|
318 |
and binders.
|
wenzelm@27037
|
319 |
|
wenzelm@27037
|
320 |
\indexouternonterm{infix}\indexouternonterm{mixfix}\indexouternonterm{structmixfix}
|
wenzelm@27037
|
321 |
\begin{rail}
|
wenzelm@28752
|
322 |
infix: '(' ('infix' | 'infixl' | 'infixr') string nat ')'
|
wenzelm@27037
|
323 |
;
|
wenzelm@27037
|
324 |
mixfix: infix | '(' string prios? nat? ')' | '(' 'binder' string prios? nat ')'
|
wenzelm@27037
|
325 |
;
|
wenzelm@27037
|
326 |
structmixfix: mixfix | '(' 'structure' ')'
|
wenzelm@27037
|
327 |
;
|
wenzelm@27037
|
328 |
|
wenzelm@27037
|
329 |
prios: '[' (nat + ',') ']'
|
wenzelm@27037
|
330 |
;
|
wenzelm@27037
|
331 |
\end{rail}
|
wenzelm@27037
|
332 |
|
wenzelm@27037
|
333 |
Here the \railtok{string} specifications refer to the actual mixfix
|
wenzelm@28752
|
334 |
template, which may include literal text, spacing, blocks, and
|
wenzelm@28752
|
335 |
arguments (denoted by ``@{text _}''); the special symbol
|
wenzelm@28752
|
336 |
``@{verbatim "\<index>"}'' (printed as ``@{text "\<index>"}'') represents an index
|
wenzelm@28752
|
337 |
argument that specifies an implicit structure reference (see also
|
wenzelm@28752
|
338 |
\secref{sec:locale}). Infix and binder declarations provide common
|
wenzelm@28752
|
339 |
abbreviations for particular mixfix declarations. So in practice,
|
wenzelm@28752
|
340 |
mixfix templates mostly degenerate to literal text for concrete
|
wenzelm@28752
|
341 |
syntax, such as ``@{verbatim "++"}'' for an infix symbol.
|
wenzelm@28752
|
342 |
|
wenzelm@28752
|
343 |
\medskip In full generality, mixfix declarations work as follows.
|
wenzelm@28752
|
344 |
Suppose a constant @{text "c :: \<tau>\<^sub>1 \<Rightarrow> \<dots> \<tau>\<^sub>n \<Rightarrow> \<tau>"} is
|
wenzelm@28752
|
345 |
annotated by @{text "(mixfix [p\<^sub>1, \<dots>, p\<^sub>n] p)"}, where @{text
|
wenzelm@28752
|
346 |
"mixfix"} is a string @{text "d\<^sub>0 _ d\<^sub>1 _ \<dots> _ d\<^sub>n"} consisting of
|
wenzelm@28752
|
347 |
delimiters that surround argument positions as indicated by
|
wenzelm@28752
|
348 |
underscores.
|
wenzelm@28752
|
349 |
|
wenzelm@28752
|
350 |
Altogether this determines a production for a context-free priority
|
wenzelm@28752
|
351 |
grammar, where for each argument @{text "i"} the syntactic category
|
wenzelm@28752
|
352 |
is determined by @{text "\<tau>\<^sub>i"} (with priority @{text "p\<^sub>i"}), and
|
wenzelm@28752
|
353 |
the result category is determined from @{text "\<tau>"} (with
|
wenzelm@28752
|
354 |
priority @{text "p"}). Priority specifications are optional, with
|
wenzelm@28752
|
355 |
default 0 for arguments and 1000 for the result.
|
wenzelm@28752
|
356 |
|
wenzelm@28752
|
357 |
Since @{text "\<tau>"} may be again a function type, the constant
|
wenzelm@28752
|
358 |
type scheme may have more argument positions than the mixfix
|
wenzelm@28752
|
359 |
pattern. Printing a nested application @{text "c t\<^sub>1 \<dots> t\<^sub>m"} for
|
wenzelm@28752
|
360 |
@{text "m > n"} works by attaching concrete notation only to the
|
wenzelm@28752
|
361 |
innermost part, essentially by printing @{text "(c t\<^sub>1 \<dots> t\<^sub>n) \<dots> t\<^sub>m"}
|
wenzelm@28752
|
362 |
instead. If a term has fewer arguments than specified in the mixfix
|
wenzelm@28752
|
363 |
template, the concrete syntax is ignored.
|
wenzelm@28752
|
364 |
|
wenzelm@28752
|
365 |
\medskip A mixfix template may also contain additional directives
|
wenzelm@28752
|
366 |
for pretty printing, notably spaces, blocks, and breaks. The
|
wenzelm@28752
|
367 |
general template format is a sequence over any of the following
|
wenzelm@28752
|
368 |
entities.
|
wenzelm@28752
|
369 |
|
wenzelm@28752
|
370 |
\begin{itemize}
|
wenzelm@28752
|
371 |
|
wenzelm@28752
|
372 |
\item @{text "\<^bold>d"} is a delimiter, namely a non-empty
|
wenzelm@28752
|
373 |
sequence of characters other than the special characters @{text "'"}
|
wenzelm@28752
|
374 |
(single quote), @{text "_"} (underscore), @{text "\<index>"} (index
|
wenzelm@28752
|
375 |
symbol), @{text "/"} (slash), @{text "("} and @{text ")"}
|
wenzelm@28752
|
376 |
(parentheses).
|
wenzelm@28752
|
377 |
|
wenzelm@28752
|
378 |
A single quote escapes the special meaning of these meta-characters,
|
wenzelm@28752
|
379 |
producing a literal version of the following character, unless that
|
wenzelm@28752
|
380 |
is a blank. A single quote followed by a blank separates
|
wenzelm@28752
|
381 |
delimiters, without affecting printing, but input tokens may have
|
wenzelm@28752
|
382 |
additional white space here.
|
wenzelm@28752
|
383 |
|
wenzelm@28752
|
384 |
\item @{text "_"} is an argument position, which stands for a
|
wenzelm@28752
|
385 |
certain syntactic category in the underlying grammar.
|
wenzelm@28752
|
386 |
|
wenzelm@28752
|
387 |
\item @{text "\<index>"} is an indexed argument position; this is
|
wenzelm@28752
|
388 |
the place where implicit structure arguments can be attached.
|
wenzelm@28752
|
389 |
|
wenzelm@28752
|
390 |
\item @{text "\<^bold>s"} is a non-empty sequence of spaces for
|
wenzelm@28752
|
391 |
printing. This and the following specifications do not affect
|
wenzelm@28752
|
392 |
parsing at all.
|
wenzelm@28752
|
393 |
|
wenzelm@28752
|
394 |
\item @{text "(\<^bold>n"} opens a pretty printing block. The
|
wenzelm@28752
|
395 |
optional number specifies how much indentation to add when a line
|
wenzelm@28752
|
396 |
break occurs within the block. If the parenthesis is not followed
|
wenzelm@28752
|
397 |
by digits, the indentation defaults to 0. A block specified via
|
wenzelm@28752
|
398 |
@{text "(00"} is unbreakable.
|
wenzelm@28752
|
399 |
|
wenzelm@28752
|
400 |
\item @{text ")"} closes a pretty printing block.
|
wenzelm@28752
|
401 |
|
wenzelm@28752
|
402 |
\item @{text "//"} forces a line break.
|
wenzelm@28752
|
403 |
|
wenzelm@28752
|
404 |
\item @{text "/\<^bold>s"} allows a line break. Here @{text
|
wenzelm@28752
|
405 |
"\<^bold>s"} stands for the string of spaces (zero or more) right
|
wenzelm@28752
|
406 |
after the slash. These spaces are printed if the break is
|
wenzelm@28752
|
407 |
\emph{not} taken.
|
wenzelm@28752
|
408 |
|
wenzelm@28752
|
409 |
\end{itemize}
|
wenzelm@28752
|
410 |
|
wenzelm@28752
|
411 |
For example, the template @{text "(_ +/ _)"} specifies an infix
|
wenzelm@28752
|
412 |
operator. There are two argument positions; the delimiter @{text
|
wenzelm@28752
|
413 |
"+"} is preceded by a space and followed by a space or line break;
|
wenzelm@28752
|
414 |
the entire phrase is a pretty printing block.
|
wenzelm@28752
|
415 |
|
wenzelm@28752
|
416 |
The general idea of pretty printing with blocks and breaks is also
|
wenzelm@28752
|
417 |
described in \cite{paulson-ml2}.
|
wenzelm@27037
|
418 |
*}
|
wenzelm@27037
|
419 |
|
wenzelm@27037
|
420 |
|
wenzelm@27037
|
421 |
subsection {* Proof methods \label{sec:syn-meth} *}
|
wenzelm@27037
|
422 |
|
wenzelm@27037
|
423 |
text {*
|
wenzelm@27037
|
424 |
Proof methods are either basic ones, or expressions composed of
|
wenzelm@27037
|
425 |
methods via ``@{verbatim ","}'' (sequential composition),
|
wenzelm@27037
|
426 |
``@{verbatim "|"}'' (alternative choices), ``@{verbatim "?"}''
|
wenzelm@27037
|
427 |
(try), ``@{verbatim "+"}'' (repeat at least once), ``@{verbatim
|
wenzelm@27037
|
428 |
"["}@{text n}@{verbatim "]"}'' (restriction to first @{text n}
|
wenzelm@27037
|
429 |
sub-goals, with default @{text "n = 1"}). In practice, proof
|
wenzelm@27037
|
430 |
methods are usually just a comma separated list of
|
wenzelm@27037
|
431 |
\railqtok{nameref}~\railnonterm{args} specifications. Note that
|
wenzelm@27037
|
432 |
parentheses may be dropped for single method specifications (with no
|
wenzelm@27037
|
433 |
arguments).
|
wenzelm@27037
|
434 |
|
wenzelm@27037
|
435 |
\indexouternonterm{method}
|
wenzelm@27037
|
436 |
\begin{rail}
|
wenzelm@27037
|
437 |
method: (nameref | '(' methods ')') (() | '?' | '+' | '[' nat? ']')
|
wenzelm@27037
|
438 |
;
|
wenzelm@27037
|
439 |
methods: (nameref args | method) + (',' | '|')
|
wenzelm@27037
|
440 |
;
|
wenzelm@27037
|
441 |
\end{rail}
|
wenzelm@27037
|
442 |
|
wenzelm@27037
|
443 |
Proper Isar proof methods do \emph{not} admit arbitrary goal
|
wenzelm@27037
|
444 |
addressing, but refer either to the first sub-goal or all sub-goals
|
wenzelm@27037
|
445 |
uniformly. The goal restriction operator ``@{text "[n]"}''
|
wenzelm@27037
|
446 |
evaluates a method expression within a sandbox consisting of the
|
wenzelm@27037
|
447 |
first @{text n} sub-goals (which need to exist). For example, the
|
wenzelm@27037
|
448 |
method ``@{text "simp_all[3]"}'' simplifies the first three
|
wenzelm@27037
|
449 |
sub-goals, while ``@{text "(rule foo, simp_all)[]"}'' simplifies all
|
wenzelm@27037
|
450 |
new goals that emerge from applying rule @{text "foo"} to the
|
wenzelm@27037
|
451 |
originally first one.
|
wenzelm@27037
|
452 |
|
wenzelm@27037
|
453 |
Improper methods, notably tactic emulations, offer a separate
|
wenzelm@27037
|
454 |
low-level goal addressing scheme as explicit argument to the
|
wenzelm@27037
|
455 |
individual tactic being involved. Here ``@{text "[!]"}'' refers to
|
wenzelm@27037
|
456 |
all goals, and ``@{text "[n-]"}'' to all goals starting from @{text
|
wenzelm@27037
|
457 |
"n"}.
|
wenzelm@27037
|
458 |
|
wenzelm@27037
|
459 |
\indexouternonterm{goalspec}
|
wenzelm@27037
|
460 |
\begin{rail}
|
wenzelm@27037
|
461 |
goalspec: '[' (nat '-' nat | nat '-' | nat | '!' ) ']'
|
wenzelm@27037
|
462 |
;
|
wenzelm@27037
|
463 |
\end{rail}
|
wenzelm@27037
|
464 |
*}
|
wenzelm@27037
|
465 |
|
wenzelm@27037
|
466 |
|
wenzelm@27037
|
467 |
subsection {* Attributes and theorems \label{sec:syn-att} *}
|
wenzelm@27037
|
468 |
|
wenzelm@27037
|
469 |
text {*
|
wenzelm@27037
|
470 |
Attributes (and proof methods, see \secref{sec:syn-meth}) have their
|
wenzelm@27037
|
471 |
own ``semi-inner'' syntax, in the sense that input conforming to
|
wenzelm@27037
|
472 |
\railnonterm{args} below is parsed by the attribute a second time.
|
wenzelm@27037
|
473 |
The attribute argument specifications may be any sequence of atomic
|
wenzelm@27037
|
474 |
entities (identifiers, strings etc.), or properly bracketed argument
|
wenzelm@27037
|
475 |
lists. Below \railqtok{atom} refers to any atomic entity, including
|
wenzelm@27037
|
476 |
any \railtok{keyword} conforming to \railtok{symident}.
|
wenzelm@27037
|
477 |
|
wenzelm@27037
|
478 |
\indexoutertoken{atom}\indexouternonterm{args}\indexouternonterm{attributes}
|
wenzelm@27037
|
479 |
\begin{rail}
|
wenzelm@27037
|
480 |
atom: nameref | typefree | typevar | var | nat | keyword
|
wenzelm@27037
|
481 |
;
|
wenzelm@27037
|
482 |
arg: atom | '(' args ')' | '[' args ']'
|
wenzelm@27037
|
483 |
;
|
wenzelm@27037
|
484 |
args: arg *
|
wenzelm@27037
|
485 |
;
|
wenzelm@27037
|
486 |
attributes: '[' (nameref args * ',') ']'
|
wenzelm@27037
|
487 |
;
|
wenzelm@27037
|
488 |
\end{rail}
|
wenzelm@27037
|
489 |
|
wenzelm@27037
|
490 |
Theorem specifications come in several flavors:
|
wenzelm@27037
|
491 |
\railnonterm{axmdecl} and \railnonterm{thmdecl} usually refer to
|
wenzelm@27037
|
492 |
axioms, assumptions or results of goal statements, while
|
wenzelm@27037
|
493 |
\railnonterm{thmdef} collects lists of existing theorems. Existing
|
wenzelm@27037
|
494 |
theorems are given by \railnonterm{thmref} and
|
wenzelm@27037
|
495 |
\railnonterm{thmrefs}, the former requires an actual singleton
|
wenzelm@27037
|
496 |
result.
|
wenzelm@27037
|
497 |
|
wenzelm@27037
|
498 |
There are three forms of theorem references:
|
wenzelm@27037
|
499 |
\begin{enumerate}
|
wenzelm@27037
|
500 |
|
wenzelm@27037
|
501 |
\item named facts @{text "a"},
|
wenzelm@27037
|
502 |
|
wenzelm@27037
|
503 |
\item selections from named facts @{text "a(i)"} or @{text "a(j - k)"},
|
wenzelm@27037
|
504 |
|
wenzelm@27037
|
505 |
\item literal fact propositions using @{syntax_ref altstring} syntax
|
wenzelm@27037
|
506 |
@{verbatim "`"}@{text "\<phi>"}@{verbatim "`"} (see also method
|
wenzelm@27037
|
507 |
@{method_ref fact} in \secref{sec:pure-meth-att}).
|
wenzelm@27037
|
508 |
|
wenzelm@27037
|
509 |
\end{enumerate}
|
wenzelm@27037
|
510 |
|
wenzelm@27037
|
511 |
Any kind of theorem specification may include lists of attributes
|
wenzelm@27037
|
512 |
both on the left and right hand sides; attributes are applied to any
|
wenzelm@27037
|
513 |
immediately preceding fact. If names are omitted, the theorems are
|
wenzelm@27037
|
514 |
not stored within the theorem database of the theory or proof
|
wenzelm@27037
|
515 |
context, but any given attributes are applied nonetheless.
|
wenzelm@27037
|
516 |
|
wenzelm@27037
|
517 |
An extra pair of brackets around attributes (like ``@{text
|
wenzelm@27037
|
518 |
"[[simproc a]]"}'') abbreviates a theorem reference involving an
|
wenzelm@27037
|
519 |
internal dummy fact, which will be ignored later on. So only the
|
wenzelm@27037
|
520 |
effect of the attribute on the background context will persist.
|
wenzelm@27037
|
521 |
This form of in-place declarations is particularly useful with
|
wenzelm@27037
|
522 |
commands like @{command "declare"} and @{command "using"}.
|
wenzelm@27037
|
523 |
|
wenzelm@27037
|
524 |
\indexouternonterm{axmdecl}\indexouternonterm{thmdecl}
|
wenzelm@27037
|
525 |
\indexouternonterm{thmdef}\indexouternonterm{thmref}
|
wenzelm@27037
|
526 |
\indexouternonterm{thmrefs}\indexouternonterm{selection}
|
wenzelm@27037
|
527 |
\begin{rail}
|
wenzelm@27037
|
528 |
axmdecl: name attributes? ':'
|
wenzelm@27037
|
529 |
;
|
wenzelm@27037
|
530 |
thmdecl: thmbind ':'
|
wenzelm@27037
|
531 |
;
|
wenzelm@27037
|
532 |
thmdef: thmbind '='
|
wenzelm@27037
|
533 |
;
|
wenzelm@27037
|
534 |
thmref: (nameref selection? | altstring) attributes? | '[' attributes ']'
|
wenzelm@27037
|
535 |
;
|
wenzelm@27037
|
536 |
thmrefs: thmref +
|
wenzelm@27037
|
537 |
;
|
wenzelm@27037
|
538 |
|
wenzelm@27037
|
539 |
thmbind: name attributes | name | attributes
|
wenzelm@27037
|
540 |
;
|
wenzelm@27037
|
541 |
selection: '(' ((nat | nat '-' nat?) + ',') ')'
|
wenzelm@27037
|
542 |
;
|
wenzelm@27037
|
543 |
\end{rail}
|
wenzelm@27037
|
544 |
*}
|
wenzelm@27037
|
545 |
|
wenzelm@27037
|
546 |
end
|