doc-src/IsarRef/syntax.tex

complete_split_rule: all Vars;
tuned;

+
−
+
−\chapter{Syntax primitives}
+
−
+
−The rather generic framework of Isabelle/Isar syntax emerges from three main
+
−syntactic categories: \emph{commands} of the top-level Isar engine (covering
+
−theory and proof elements), \emph{methods} for general goal refinements
+
−(analogous to traditional ``tactics''), and \emph{attributes} for operations
+
−on facts (within a certain context).  Here we give a reference of basic
+
−syntactic entities underlying Isabelle/Isar syntax in a bottom-up manner.
+
−Concrete theory and proof language elements will be introduced later on.
+
−
+
−\medskip
+
−
+
−In order to get started with writing well-formed Isabelle/Isar documents, the
+
−most important aspect to be noted is the difference of \emph{inner} versus
+
−\emph{outer} syntax.  Inner syntax is that of Isabelle types and terms of the
+
−logic, while outer syntax is that of Isabelle/Isar theory sources (including
+
−proofs).  As a general rule, inner syntax entities may occur only as
+
−\emph{atomic entities} within outer syntax.  For example, the string
+
−\texttt{"x + y"} and identifier \texttt{z} are legal term specifications
+
−within a theory, while \texttt{x + y} is not.
+
−
+
−\begin{warn}
+
−  Old-style Isabelle theories used to fake parts of the inner syntax of types,
+
−  with rather complicated rules when quotes may be omitted.  Despite the minor
+
−  drawback of requiring quotes more often, the syntax of Isabelle/Isar is
+
−  somewhat simpler and more robust in that respect.
+
−\end{warn}
+
−
+
−Printed theory documents usually omit quotes to gain readability (this is a
+
−matter of {\LaTeX} macro setup, say via \verb,\isabellestyle,, see also
+
−\cite{isabelle-sys}).  Experienced users of Isabelle/Isar may easily
+
−reconstruct the lost technical information, while mere readers need not care
+
−about quotes at all.
+
−
+
−\medskip
+
−
+
−Isabelle/Isar input may contain any number of input termination characters
+
−``\texttt{;}'' (semicolon) to separate commands explicitly.  This is
+
−particularly useful in interactive shell sessions to make clear where the
+
−current command is intended to end.  Otherwise, the interpreter loop will
+
−continue to issue a secondary prompt ``\verb,#,'' until an end-of-command is
+
−clearly recognized from the input syntax, e.g.\ encounter of the next command
+
−keyword.
+
−
+
−Advanced interfaces such as Proof~General \cite{proofgeneral} do not require
+
−explicit semicolons, the amount of input text is determined automatically by
+
−inspecting the present content of the Emacs text buffer.  In the printed
+
−presentation of Isabelle/Isar documents semicolons are omitted altogether for
+
−readability.
+
−
+
−\begin{warn}
+
−  Proof~General requires certain syntax classification tables in order to
+
−  achieve properly synchronized interaction with the Isabelle/Isar process.
+
−  These tables need to be consistent with the Isabelle version and particular
+
−  logic image to be used in a running session (common object-logics may well
+
−  change the outer syntax).  The standard setup should work correctly with any
+
−  of the ``official'' logic images derived from Isabelle/HOL (including HOLCF
+
−  etc.).  Users of alternative logics may need to tell Proof~General
+
−  explicitly, e.g.\ by giving an option \verb,-k ZF, (in conjunction with
+
−  \verb,-l ZF, to specify the default logic image).
+
−\end{warn}
+
−
+
−\section{Lexical matters}\label{sec:lex-syntax}
+
−
+
−The Isabelle/Isar outer syntax provides token classes as presented below; most
+
−of these coincide with the inner lexical syntax as presented in
+
−\cite{isabelle-ref}.
+
−
+
−\indexoutertoken{ident}\indexoutertoken{longident}\indexoutertoken{symident}
+
−\indexoutertoken{nat}\indexoutertoken{var}\indexoutertoken{typefree}
+
−\indexoutertoken{typevar}\indexoutertoken{string}\indexoutertoken{altstring}
+
−\indexoutertoken{verbatim}
+
−\begin{matharray}{rcl}
+
−  ident & = & letter\,quasiletter^* \\
+
−  longident & = & ident (\verb,.,ident)^+ \\
+
−  symident & = & sym^+ ~|~ \verb,\<,ident\verb,>, \\
+
−  nat & = & digit^+ \\
+
−  var & = & ident ~|~ \verb,?,ident ~|~ \verb,?,ident\verb,.,nat \\
+
−  typefree & = & \verb,',ident \\
+
−  typevar & = & typefree ~|~ \verb,?,typefree ~|~ \verb,?,typefree\verb,.,nat \\
+
−  string & = & \verb,", ~\dots~ \verb,", \\
+
−  altstring & = & \backquote ~\dots~ \backquote \\
+
−  verbatim & = & \verb,{*, ~\dots~ \verb,*}, \\[1ex]
+
−
+
−  letter & = & latin ~|~ \verb,\<,latin\verb,>, ~|~ \verb,\<,latin\,latin\verb,>, ~|~ greek ~|~ \\
+
−         &   & \verb,\<^isub>, ~|~ \verb,\<^isup>, \\
+
−  quasiletter & = & letter ~|~ digit ~|~ \verb,_, ~|~ \verb,', \\
+
−  latin & = & \verb,a, ~|~ \dots ~|~ \verb,z, ~|~ \verb,A, ~|~ \dots ~|~ \verb,Z, \\
+
−  digit & = & \verb,0, ~|~ \dots ~|~ \verb,9, \\
+
−  sym & = & \verb,!, ~|~ \verb,#, ~|~ \verb,$, ~|~ \verb,%, ~|~ \verb,&, ~|~  %$
+
−   \verb,*, ~|~ \verb,+, ~|~ \verb,-, ~|~ \verb,/, ~|~ \verb,:, ~|~ \\
+
−  & & \verb,<, ~|~ \verb,=, ~|~ \verb,>, ~|~ \verb,?, ~|~ \texttt{\at} ~|~
+
−  \verb,^, ~|~ \verb,_, ~|~ \verb,|, ~|~ \verb,~, \\
+
−greek & = & \verb,\<alpha>, ~|~ \verb,\<beta>, ~|~ \verb,\<gamma>, ~|~ \verb,\<delta>, ~| \\
+
−      &   & \verb,\<epsilon>, ~|~ \verb,\<zeta>, ~|~ \verb,\<eta>, ~|~ \verb,\<theta>, ~| \\
+
−      &   & \verb,\<iota>, ~|~ \verb,\<kappa>, ~|~ \verb,\<mu>, ~|~ \verb,\<nu>, ~| \\
+
−      &   & \verb,\<xi>, ~|~ \verb,\<pi>, ~|~ \verb,\<rho>, ~|~ \verb,\<sigma>, ~| \\
+
−      &   & \verb,\<tau>, ~|~ \verb,\<upsilon>, ~|~ \verb,\<phi>, ~|~ \verb,\<psi>, ~| \\
+
−      &   & \verb,\<omega>, ~|~ \verb,\<Gamma>, ~|~ \verb,\<Delta>, ~|~ \verb,\<Theta>, ~| \\
+
−      &   & \verb,\<Lambda>, ~|~ \verb,\<Xi>, ~|~ \verb,\<Pi>, ~|~ \verb,\<Sigma>, ~| \\
+
−      &   & \verb,\<Upsilon>, ~|~ \verb,\<Phi>, ~|~ \verb,\<Psi>, ~|~ \verb,\<Omega>, \\
+
−\end{matharray}
+
−
+
−The syntax of $string$ admits any characters, including newlines; ``\verb|"|''
+
−(double-quote) and ``\verb|\|'' (backslash) need to be escaped by a backslash.
+
−Alternative strings according to $altstring$ are analogous, using single
+
−back-quotes instead.  The body of $verbatim$ may consist of any text not
+
−containing ``\verb|*}|''; this allows convenient inclusion of quotes without
+
−further escapes.  The greek letters do \emph{not} include \verb,\<lambda>,,
+
−which is already used differently in the meta-logic.
+
−
+
−Common mathematical symbols such as $\forall$ are represented in Isabelle as
+
−\verb,\<forall>,.  There are infinitely many legal symbols like this, although
+
−proper presentation is left to front-end tools such as {\LaTeX} or
+
−Proof~General with the X-Symbol package.  A list of standard Isabelle symbols
+
−that work well with these tools is given in \cite[appendix~A]{isabelle-sys}.
+
−
+
−Comments take the form \texttt{(*~\dots~*)} and may be nested, although
+
−user-interface tools may prevent this.  Note that \texttt{(*~\dots~*)}
+
−indicate source comments only, which are stripped after lexical analysis of
+
−the input.  The Isar document syntax also provides formal comments that are
+
−considered as part of the text (see \S\ref{sec:comments}).
+
−
+
−\begin{warn}
+
−  Proof~General does not handle nested comments properly; it is also unable to
+
−  keep \verb,(*,\,/\,\verb,{*, and \verb,*),\,/\,\verb,*}, apart, despite
+
−  their rather different meaning.  These are inherent problems of Emacs
+
−  legacy.  Users should not be overly aggressive about nesting or alternating
+
−  these delimiters.
+
−\end{warn}
+
−
+
−
+
−\section{Common syntax entities}
+
−
+
−Subsequently, we introduce several basic syntactic entities, such as names,
+
−terms, and theorem specifications, which have been factored out of the actual
+
−Isar language elements to be described later.
+
−
+
−Note that some of the basic syntactic entities introduced below (e.g.\
+
−\railqtok{name}) act much like tokens rather than plain nonterminals (e.g.\
+
−\railnonterm{sort}), especially for the sake of error messages.  E.g.\ syntax
+
−elements like $\CONSTS$ referring to \railqtok{name} or \railqtok{type} would
+
−really report a missing name or type rather than any of the constituent
+
−primitive tokens such as \railtok{ident} or \railtok{string}.
+
−
+
−
+
−\subsection{Names}
+
−
+
−Entity \railqtok{name} usually refers to any name of types, constants,
+
−theorems etc.\ that are to be \emph{declared} or \emph{defined} (so qualified
+
−identifiers are excluded here).  Quoted strings provide an escape for
+
−non-identifier names or those ruled out by outer syntax keywords (e.g.\
+
−\verb|"let"|).  Already existing objects are usually referenced by
+
−\railqtok{nameref}.
+
−
+
−\indexoutertoken{name}\indexoutertoken{parname}\indexoutertoken{nameref}
+
−\indexoutertoken{int}
+
−\begin{rail}
+
−  name: ident | symident | string | nat
+
−  ;
+
−  parname: '(' name ')'
+
−  ;
+
−  nameref: name | longident
+
−  ;
+
−  int: nat | '-' nat
+
−  ;
+
−\end{rail}
+
−
+
−
+
−\subsection{Comments}\label{sec:comments}
+
−
+
−Large chunks of plain \railqtok{text} are usually given \railtok{verbatim},
+
−i.e.\ enclosed in \verb|{*|~\dots~\verb|*}|.  For convenience, any of the
+
−smaller text units conforming to \railqtok{nameref} are admitted as well.  A
+
−marginal \railnonterm{comment} is of the form \texttt{--} \railqtok{text}.
+
−Any number of these may occur within Isabelle/Isar commands.
+
−
+
−\indexoutertoken{text}\indexouternonterm{comment}
+
−\begin{rail}
+
−  text: verbatim | nameref
+
−  ;
+
−  comment: '--' text
+
−  ;
+
−\end{rail}
+
−
+
−
+
−\subsection{Type classes, sorts and arities}
+
−
+
−Classes are specified by plain names.  Sorts have a very simple inner syntax,
+
−which is either a single class name $c$ or a list $\{c@1, \dots, c@n\}$
+
−referring to the intersection of these classes.  The syntax of type arities is
+
−given directly at the outer level.
+
−
+
−\railalias{subseteq}{\isasymsubseteq}
+
−\railterm{subseteq}
+
−
+
−\indexouternonterm{sort}\indexouternonterm{arity}
+
−\indexouternonterm{classdecl}
+
−\begin{rail}
+
−  classdecl: name (('<' | subseteq) (nameref + ','))?
+
−  ;
+
−  sort: nameref
+
−  ;
+
−  arity: ('(' (sort + ',') ')')? sort
+
−  ;
+
−\end{rail}
+
−
+
−
+
−\subsection{Types and terms}\label{sec:types-terms}
+
−
+
−The actual inner Isabelle syntax, that of types and terms of the logic, is far
+
−too sophisticated in order to be modelled explicitly at the outer theory
+
−level.  Basically, any such entity has to be quoted to turn it into a single
+
−token (the parsing and type-checking is performed internally later).  For
+
−convenience, a slightly more liberal convention is adopted: quotes may be
+
−omitted for any type or term that is already atomic at the outer level.  For
+
−example, one may just write \texttt{x} instead of \texttt{"x"}.  Note that
+
−symbolic identifiers (e.g.\ \texttt{++} or $\forall$) are available as well,
+
−provided these have not been superseded by commands or other keywords already
+
−(e.g.\ \texttt{=} or \texttt{+}).
+
−
+
−\indexoutertoken{type}\indexoutertoken{term}\indexoutertoken{prop}
+
−\begin{rail}
+
−  type: nameref | typefree | typevar
+
−  ;
+
−  term: nameref | var
+
−  ;
+
−  prop: term
+
−  ;
+
−\end{rail}
+
−
+
−Positional instantiations are indicated by giving a sequence of terms, or the
+
−placeholder ``$\_$'' (underscore), which means to skip a position.
+
−
+
−\indexoutertoken{inst}\indexoutertoken{insts}
+
−\begin{rail}
+
−  inst: underscore | term
+
−  ;
+
−  insts: (inst *)
+
−  ;
+
−\end{rail}
+
−
+
−Type declarations and definitions usually refer to \railnonterm{typespec} on
+
−the left-hand side.  This models basic type constructor application at the
+
−outer syntax level.  Note that only plain postfix notation is available here,
+
−but no infixes.
+
−
+
−\indexouternonterm{typespec}
+
−\begin{rail}
+
−  typespec: (() | typefree | '(' ( typefree + ',' ) ')') name
+
−  ;
+
−\end{rail}
+
−
+
−
+
−\subsection{Mixfix annotations}
+
−
+
−Mixfix annotations specify concrete \emph{inner} syntax of Isabelle types and
+
−terms.  Some commands such as $\TYPES$ (see \S\ref{sec:types-pure}) admit
+
−infixes only, while $\CONSTS$ (see \S\ref{sec:consts}) and
+
−$\isarkeyword{syntax}$ (see \S\ref{sec:syn-trans}) support the full range of
+
−general mixfixes and binders.
+
−
+
−\indexouternonterm{infix}\indexouternonterm{mixfix}\indexouternonterm{structmixfix}
+
−\begin{rail}
+
−  infix: '(' ('infix' | 'infixl' | 'infixr') string? nat ')'
+
−  ;
+
−  mixfix: infix | '(' string prios? nat? ')' | '(' 'binder' string prios? nat ')'
+
−  ;
+
−  structmixfix: mixfix | '(' 'structure' ')'
+
−  ;
+
−
+
−  prios: '[' (nat + ',') ']'
+
−  ;
+
−\end{rail}
+
−
+
−Here the \railtok{string} specifications refer to the actual mixfix template
+
−(see also \cite{isabelle-ref}), which may include literal text, spacing,
+
−blocks, and arguments (denoted by ``$_$''); the special symbol \verb,\<index>,
+
−(printed as ``\i'') represents an index argument that specifies an implicit
+
−structure reference (see also \S\ref{sec:locale}).  Infix and binder
+
−declarations provide common abbreviations for particular mixfix declarations.
+
−So in practice, mixfix templates mostly degenerate to literal text for
+
−concrete syntax, such as ``\verb,++,'' for an infix symbol, or ``\verb,++,\i''
+
−for an infix of an implicit structure.
+
−
+
−
+
−
+
−\subsection{Proof methods}\label{sec:syn-meth}
+
−
+
−Proof methods are either basic ones, or expressions composed of
+
−methods via ``\texttt{,}'' (sequential composition), ``\texttt{|}''
+
−(alternative choices), ``\texttt{?}'' (try), ``\texttt{+}'' (repeat at
+
−least once), ``\texttt{[$n$]}'' (restriction to first $n$ sub-goals,
+
−default $n = 1$).  In practice, proof methods are usually just a comma
+
−separated list of \railqtok{nameref}~\railnonterm{args}
+
−specifications.  Note that parentheses may be dropped for single
+
−method specifications (with no arguments).
+
−
+
−\indexouternonterm{method}
+
−\begin{rail}
+
−  method: (nameref | '(' methods ')') (() | '?' | '+' | '[' nat? ']')
+
−  ;
+
−  methods: (nameref args | method) + (',' | '|')
+
−  ;
+
−\end{rail}
+
−
+
−Proper Isar proof methods do \emph{not} admit arbitrary goal
+
−addressing, but refer either to the first sub-goal or all sub-goals
+
−uniformly.  The goal restriction operator ``\texttt{[$n$]}'' evaluates
+
−a method expression within a sandbox consisting of the first $n$
+
−sub-goals (which need to exist).  For example,
+
−$simp_all\mbox{\tt[}3\mbox{\tt]}$ simplifies the first three
+
−sub-goals, while $(rule~foo, simp_all)\mbox{\tt[]}$ simplifies all new
+
−goals that emerge from applying rule $foo$ to the originally first
+
−one.
+
−
+
−Improper methods, notably tactic emulations, offer a separate
+
−low-level goal addressing scheme as explicit argument to the
+
−individual tactic being involved.  Here $[!]$ refers to all goals, and
+
−$[n-]$ to all goals starting from $n$,
+
−
+
−\indexouternonterm{goalspec}
+
−\begin{rail}
+
−  goalspec: '[' (nat '-' nat | nat '-' | nat | '!' ) ']'
+
−  ;
+
−\end{rail}
+
−
+
−
+
−\subsection{Attributes and theorems}\label{sec:syn-att}
+
−
+
−Attributes (and proof methods, see \S\ref{sec:syn-meth}) have their own
+
−``semi-inner'' syntax, in the sense that input conforming to
+
−\railnonterm{args} below is parsed by the attribute a second time.  The
+
−attribute argument specifications may be any sequence of atomic entities
+
−(identifiers, strings etc.), or properly bracketed argument lists.  Below
+
−\railqtok{atom} refers to any atomic entity, including any \railtok{keyword}
+
−conforming to \railtok{symident}.
+
−
+
−\indexoutertoken{atom}\indexouternonterm{args}\indexouternonterm{attributes}
+
−\begin{rail}
+
−  atom: nameref | typefree | typevar | var | nat | keyword
+
−  ;
+
−  arg: atom | '(' args ')' | '[' args ']'
+
−  ;
+
−  args: arg *
+
−  ;
+
−  attributes: '[' (nameref args * ',') ']'
+
−  ;
+
−\end{rail}
+
−
+
−Theorem specifications come in several flavors: \railnonterm{axmdecl} and
+
−\railnonterm{thmdecl} usually refer to axioms, assumptions or results of goal
+
−statements, while \railnonterm{thmdef} collects lists of existing theorems.
+
−Existing theorems are given by \railnonterm{thmref} and \railnonterm{thmrefs},
+
−the former requires an actual singleton result.  There are three forms of
+
−theorem references: (1) named facts $a$, (2) selections from named facts $a(i,
+
−j - k)$, or (3) literal fact propositions using $altstring$ syntax
+
−$\backquote\phi\backquote$, (see also method $fact$ in
+
−\S\ref{sec:pure-meth-att}).
+
−
+
−Any kind of theorem specification may include lists of attributes both on the
+
−left and right hand sides; attributes are applied to any immediately preceding
+
−fact.  If names are omitted, the theorems are not stored within the theorem
+
−database of the theory or proof context, but any given attributes are applied
+
−nonetheless.
+
−
+
−\indexouternonterm{axmdecl}\indexouternonterm{thmdecl}
+
−\indexouternonterm{thmdef}\indexouternonterm{thmref}
+
−\indexouternonterm{thmrefs}\indexouternonterm{selection}
+
−\begin{rail}
+
−  axmdecl: name attributes? ':'
+
−  ;
+
−  thmdecl: thmbind ':'
+
−  ;
+
−  thmdef: thmbind '='
+
−  ;
+
−  thmref: (nameref selection? | altstring) attributes?
+
−  ;
+
−  thmrefs: thmref +
+
−  ;
+
−
+
−  thmbind: name attributes | name | attributes
+
−  ;
+
−  selection: '(' ((nat | nat '-' nat?) + ',') ')'
+
−  ;
+
−\end{rail}
+
−
+
−
+
−\subsection{Term patterns and declarations}\label{sec:term-decls}
+
−
+
−Wherever explicit propositions (or term fragments) occur in a proof text,
+
−casual binding of schematic term variables may be given specified via patterns
+
−of the form ``$\ISS{p@1\;\dots}{p@n}$''.  There are separate versions
+
−available for \railqtok{term}s and \railqtok{prop}s.  The latter provides a
+
−$\CONCLNAME$ part with patterns referring the (atomic) conclusion of a rule.
+
−
+
−\indexouternonterm{termpat}\indexouternonterm{proppat}
+
−\begin{rail}
+
−  termpat: '(' ('is' term +) ')'
+
−  ;
+
−  proppat: '(' ('is' prop +) ')'
+
−  ;
+
−\end{rail}
+
−
+
−Declarations of local variables $x :: \tau$ and logical propositions $a :
+
−\phi$ represent different views on the same principle of introducing a local
+
−scope.  In practice, one may usually omit the typing of $vars$ (due to
+
−type-inference), and the naming of propositions (due to implicit references of
+
−current facts).  In any case, Isar proof elements usually admit to introduce
+
−multiple such items simultaneously.
+
−
+
−\indexouternonterm{vars}\indexouternonterm{props}
+
−\begin{rail}
+
−  vars: (name+) ('::' type)?
+
−  ;
+
−  props: thmdecl? (prop proppat? +)
+
−  ;
+
−\end{rail}
+
−
+
−The treatment of multiple declarations corresponds to the complementary focus
+
−of $vars$ versus $props$: in ``$x@1~\dots~x@n :: \tau$'' the typing refers to
+
−all variables, while in $a\colon \phi@1~\dots~\phi@n$ the naming refers to all
+
−propositions collectively.  Isar language elements that refer to $vars$ or
+
−$props$ typically admit separate typings or namings via another level of
+
−iteration, with explicit $\AND$ separators; e.g.\ see $\FIXNAME$ and
+
−$\ASSUMENAME$ in \S\ref{sec:proof-context}.
+
−
+
−
+
−\subsection{Antiquotations}\label{sec:antiq}
+
−
+
−\begin{matharray}{rcl}
+
−  thm & : & \isarantiq \\
+
−  prop & : & \isarantiq \\
+
−  term & : & \isarantiq \\
+
−  const & : & \isarantiq \\
+
−  typeof & : & \isarantiq \\
+
−  typ & : & \isarantiq \\
+
−  thm_style & : & \isarantiq \\
+
−  term_style & : & \isarantiq \\
+
−  text & : & \isarantiq \\
+
−  goals & : & \isarantiq \\
+
−  subgoals & : & \isarantiq \\
+
−  prf & : & \isarantiq \\
+
−  full_prf & : & \isarantiq \\
+
−  ML & : & \isarantiq \\
+
−  ML_type & : & \isarantiq \\
+
−  ML_struct & : & \isarantiq \\
+
−\end{matharray}
+
−
+
−The text body of formal comments (see also \S\ref{sec:comments}) may contain
+
−antiquotations of logical entities, such as theorems, terms and types, which
+
−are to be presented in the final output produced by the Isabelle document
+
−preparation system (see also \S\ref{sec:document-prep}).
+
−
+
−Thus embedding of
+
−``\texttt{{\at}{\ttlbrace}term~[show_types]~"f(x)~=~a~+~x"{\ttrbrace}}''
+
−within a text block would cause
+
−\isa{(f{\isasymColon}'a~{\isasymRightarrow}~'a)~(x{\isasymColon}'a)~=~(a{\isasymColon}'a)~+~x}
+
−to appear in the final {\LaTeX} document.  Also note that theorem
+
−antiquotations may involve attributes as well.  For example,
+
−\texttt{{\at}{\ttlbrace}thm~sym~[no_vars]{\ttrbrace}} would print the
+
−statement where all schematic variables have been replaced by fixed ones,
+
−which are easier to read.
+
−
+
−\indexisarant{thm}\indexisarant{prop}\indexisarant{term}\indexisarant{const}
+
−\indexisarant{typeof}\indexisarant{typ}\indexisarant{thm-style}
+
−\indexisarant{term-style}\indexisarant{text}\indexisarant{goals}
+
−\indexisarant{subgoals}\indexisarant{prf}\indexisarant{full-prf}\indexisarant{ML}
+
−\indexisarant{ML-type}\indexisarant{ML-struct}
+
−
+
−\begin{rail}
+
−  atsign lbrace antiquotation rbrace
+
−  ;
+
−
+
−  antiquotation:
+
−    'thm' options thmrefs |
+
−    'prop' options prop |
+
−    'term' options term |
+
−    'const' options term |
+
−    'typeof' options term |
+
−    'typ' options type |
+
−    'thm\_style' options name thmref |
+
−    'term\_style' options name term |
+
−    'text' options name |
+
−    'goals' options |
+
−    'subgoals' options |
+
−    'prf' options thmrefs |
+
−    'full\_prf' options thmrefs |
+
−    'ML' options name |
+
−    'ML\_type' options name |
+
−    'ML\_struct' options name
+
−  ;
+
−  options: '[' (option * ',') ']'
+
−  ;
+
−  option: name | name '=' name
+
−  ;
+
−\end{rail}
+
−
+
−Note that the syntax of antiquotations may \emph{not} include source comments
+
−\texttt{(*~\dots~*)} or verbatim text \verb|{*|~\dots~\verb|*}|.
+
−
+
−\begin{descr}
+
−
+
−\item [$\at\{thm~\vec a\}$] prints theorems $\vec a$. Note that attribute
+
−  specifications may be included as well (see also \S\ref{sec:syn-att}); the
+
−  $no_vars$ operation (see \S\ref{sec:misc-meth-att}) would be particularly
+
−  useful to suppress printing of schematic variables.
+
−
+
−\item [$\at\{prop~\phi\}$] prints a well-typed proposition $\phi$.
+
−
+
−\item [$\at\{term~t\}$] prints a well-typed term $t$.
+
−
+
−\item [$\at\{const~c\}$] prints a well-defined constant $c$.
+
−
+
−\item [$\at\{typeof~t\}$] prints the type of a well-typed term $t$.
+
−
+
−\item [$\at\{typ~\tau\}$] prints a well-formed type $\tau$.
+
−  
+
−\item [$\at\{thm_style~s~a\}$] prints theorem $a$, previously applying a style
+
−  $s$ to it (see below).
+
−  
+
−\item [$\at\{term_style~s~t\}$] prints a well-typed term $t$ after applying a
+
−  style $s$ to it (see below).
+
−
+
−\item [$\at\{text~s\}$] prints uninterpreted source text $s$.  This is
+
−  particularly useful to print portions of text according to the Isabelle
+
−  {\LaTeX} output style, without demanding well-formedness (e.g.\ small pieces
+
−  of terms that should not be parsed or type-checked yet).
+
−
+
−\item [$\at\{goals\}$] prints the current \emph{dynamic} goal state.  This is
+
−  mainly for support of tactic-emulation scripts within Isar --- presentation
+
−  of goal states does not conform to actual human-readable proof documents.
+
−  Please do not include goal states into document output unless you really
+
−  know what you are doing!
+
−  
+
−\item [$\at\{subgoals\}$] is similar to $goals$, but does not print the main
+
−  goal.
+
−  
+
−\item [$\at\{prf~\vec a\}$] prints the (compact) proof terms corresponding to
+
−  the theorems $\vec a$. Note that this requires proof terms to be switched on
+
−  for the current object logic (see the ``Proof terms'' section of the
+
−  Isabelle reference manual for information on how to do this).
+
−  
+
−\item [$\at\{full_prf~\vec a\}$] is like $\at\{prf~\vec a\}$, but displays the
+
−  full proof terms, i.e.\ also displays information omitted in the compact
+
−  proof term, which is denoted by ``$_$'' placeholders there.
+
−  
+
−\item [$\at\{ML~s\}$, $\at\{ML_type~s\}$, and $\at\{ML_struct~s\}$] check text
+
−  $s$ as ML value, type, and structure, respectively.  If successful, the
+
−  source is displayed verbatim.
+
−
+
−\end{descr}
+
−
+
−\medskip
+
−
+
−The following standard styles for use with $thm_style$ and $term_style$ are
+
−available:
+
−
+
−\begin{descr}
+
−  
+
−\item [$lhs$] extracts the first argument of any application form with at
+
−  least two arguments -- typically meta-level or object-level equality, or any
+
−  other binary relation.
+
−  
+
−\item [$rhs$] is like $lhs$, but extracts the second argument.
+
−  
+
−\item [$concl$] extracts the conclusion $C$ from a nested meta-level
+
−  implication $A@1 \Imp \cdots A@n \Imp C$.
+
−  
+
−\item [$prem1$, \dots, $prem9$] extract premise number $1$, \dots, $9$,
+
−  respectively, from a nested meta-level implication $A@1 \Imp \cdots A@n \Imp
+
−  C$.
+
−
+
−\end{descr}
+
−
+
−\medskip
+
−
+
−The following options are available to tune the output.  Note that most of
+
−these coincide with ML flags of the same names (see also \cite{isabelle-ref}).
+
−\begin{descr}
+
−\item[$show_types = bool$ and $show_sorts = bool$] control printing of
+
−  explicit type and sort constraints.
+
−\item[$show_structs = bool$] controls printing of implicit structures.
+
−\item[$long_names = bool$] forces names of types and constants etc.\ to be
+
−  printed in their fully qualified internal form.
+
−\item[$short_names = bool$] forces names of types and constants etc.\ to be
+
−  printed unqualified.  Note that internalizing the output again in the
+
−  current context may well yield a different result.
+
−\item[$unique_names = bool$] determines whether the printed version of
+
−  qualified names should be made sufficiently long to avoid overlap with names
+
−  declared further back.  Set to $false$ for more concise output.
+
−\item[$eta_contract = bool$] prints terms in $\eta$-contracted form.
+
−\item[$display = bool$] indicates if the text is to be output as multi-line
+
−  ``display material'', rather than a small piece of text without line breaks
+
−  (which is the default).
+
−\item[$breaks = bool$] controls line breaks in non-display material.
+
−\item[$quotes = bool$] indicates if the output should be enclosed in double
+
−  quotes.
+
−\item[$mode = name$] adds $name$ to the print mode to be used for presentation
+
−  (see also \cite{isabelle-ref}).  Note that the standard setup for {\LaTeX}
+
−  output is already present by default, including the modes ``$latex$'',
+
−  ``$xsymbols$'', ``$symbols$''.
+
−\item[$margin = nat$ and $indent = nat$] change the margin or indentation for
+
−  pretty printing of display material.
+
−\item[$source = bool$] prints the source text of the antiquotation arguments,
+
−  rather than the actual value.  Note that this does not affect
+
−  well-formedness checks of $thm$, $term$, etc. (only the $text$ antiquotation
+
−  admits arbitrary output).
+
−\item[$goals_limit = nat$] determines the maximum number of goals to be
+
−  printed.
+
−\item[$locale = name$] specifies an alternative context used for evaluating
+
−  and printing the subsequent argument.
+
−\end{descr}
+
−
+
−For boolean flags, ``$name = true$'' may be abbreviated as ``$name$''.  All of
+
−the above flags are disabled by default, unless changed from ML.
+
−
+
−\medskip Note that antiquotations do not only spare the author from tedious
+
−typing of logical entities, but also achieve some degree of
+
−consistency-checking of informal explanations with formal developments:
+
−well-formedness of terms and types with respect to the current theory or proof
+
−context is ensured here.
+
−
+
−
+
−\subsection{Tagged commands}\label{sec:tags}
+
−
+
−Each Isabelle/Isar command may be decorated by presentation tags:
+
−
+
−\indexouternonterm{tags}
+
−\begin{rail}
+
−  tags: ( tag * )
+
−  ;
+
−  tag: '\%' (ident | string)
+
−\end{rail}
+
−
+
−The tags $theory$, $proof$, $ML$ are already pre-declared for certain classes
+
−of commands:
+
−
+
−\medskip
+
−
+
−\begin{tabular}{ll}
+
−  $theory$ & theory begin and end \\
+
−  $proof$ & all proof commands \\
+
−  $ML$ & all commands involving ML code \\
+
−\end{tabular}
+
−
+
−\medskip The Isabelle document preparation system (see also
+
−\cite{isabelle-sys}) allows tagged command regions to be presented
+
−specifically, e.g.\ to fold proof texts, or drop parts of the text completely.
+
−
+
−For example ``$\BYNAME~\%invisible~(auto)$'' would cause that piece of proof
+
−to be treated as $invisible$ instead of $proof$ (the default), which may be
+
−either show or hidden depending on the document setup.  In contrast,
+
−``$\BYNAME~\%visible~(auto)$'' would force this text to be shown invariably.
+
−
+
−Explicit tag specifications within a proof apply to all subsequent commands of
+
−the same level of nesting.  For example,
+
−``$\PROOFNAME~\%visible~\dots\QEDNAME$'' would force the whole sub-proof to be
+
−typeset as $visible$ (unless some of its parts are tagged differently).
+
−
+
−%%% Local Variables:
+
−%%% mode: latex
+
−%%% TeX-master: "isar-ref"
+
−%%% End: