%FIXME

 % - examples (!?)

 \chapter{Isar document syntax}

 FIXME shortcut

 FIXME important note: inner versus outer syntax

 \section{Lexical matters}

 \section{Common syntax entities}

 The Isar proof and theory language syntax has been carefully designed with

 orthogonality in mind.  Subsequently, we introduce several basic syntactic

 entities, such as names, terms, theorem specifications, which have been

 factored out of the actual Isar language elements described later.

 Note that some of the basic syntactic entities introduced below act much like

 tokens rather than nonterminals, in particular for the sake of error messages.

 E.g.\ syntax elements such as $\CONSTS$ referring to \railqtoken{name} or

 \railqtoken{type} would really report a missing name or type rather than any

 of the constituent primitive tokens such as \railtoken{ident} or

 \railtoken{string}.

 \subsection{Names}

 Entity \railqtoken{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).  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

 \railqtoken{nameref}.

 \indexoutertoken{name}\indexoutertoken{parname}\indexoutertoken{nameref}

 \begin{rail}

   name: ident | symident | string

   ;

   parname: '(' name ')'

   ;

   nameref: name | longident

   ;

 \end{rail}

 \subsection{Comments}

 Large chunks of plain \railqtoken{text} are usually given

 \railtoken{verbatim}, i.e.\ enclosed in \verb|{*|\dots\verb|*}|.  For

 convenience, any of the smaller text conforming to \railqtoken{nameref} are

 admitted as well.  Almost any of the Isar commands may be annotated by some

 marginal \railnonterm{comment} of the form \texttt{--} \railqtoken{text}.

 Note that this kind of comment is actually part of the language, while source

 level comments \verb|(*|\dots\verb|*)| are already stripped at the lexical

 level.  A few commands such as $\PROOFNAME$ admit additional markup with a

 ``level of interest'': \texttt{\%} followed by an optional number $n$ (default

 $n = 1$) indicates that the respective part of the document becomes $n$ levels

 more boring or obscure; \texttt{\%\%} means that the interest drops by

 $\infty$ --- abandon every hope, who enter here.

 \indexoutertoken{text}\indexouternonterm{comment}\indexouternonterm{interest}

 \begin{rail}

   text: verbatim | nameref

   ;

   comment: '--' text

   ;

   interest: percent nat? | ppercent

   ;

 \end{rail}

 \subsection{Sorts and arities}

 The syntax of sorts and arities is given directly at the outer level.  Note

 that this is in contrast to that types and terms (see \ref{sec:types-terms}).

 \indexouternonterm{sort}\indexouternonterm{arity}\indexouternonterm{simplearity}

 \indexouternonterm{classdecl}

 \begin{rail}

   classdecl: name ('<' (nameref ',' +))?

   ;

   sort: nameref | lbrace (nameref * ',') rbrace

   ;

   arity: ('(' (sort + ',') ')')? sort

   ;

   simplearity: ('(' (sort + ',') ')')? nameref

   ;

 \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 flexible in order to be modeled explicitly at the outer theory level.

 Basically, any such entity has to be quoted at the outer level to turn it into

 a single token, with the actual parsing deferred to some functions for reading

 and type-checking.  For convenience, a more liberal convention is adopted:

 quotes may be omitted for any type or term that is already \emph{atomic} at

 the outer level.  E.g.\ one may write \texttt{x} instead of \texttt{"x"}.

 \indexoutertoken{type}\indexoutertoken{term}\indexoutertoken{prop}

 \begin{rail}

   type: nameref | typefree | typevar

   ;

   term: nameref | var | textvar | nat

   ;

   prop: term

   ;

 \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{Term patterns}

 Assumptions and goal statements usually admit automatic binding of schematic

 text variables by giving (optional) patterns of the form $\IS{p@1 \dots p@n}$.

 There are separate versions available for \railqtoken{term}s and

 \railqtoken{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 +) | 'concl' ('is' prop +) | ('is' prop +) 'concl' ('is' prop +)) ')'

   ;

 \end{rail}

 \subsection{Mixfix annotations}

 Mixfix annotations specify concrete \emph{inner} syntax of Isabelle types and

 terms.  Some commands such as $\TYPES$ admit infixes only, while $\CONSTS$ and

 $\isarkeyword{syntax}$ support the full range of general mixfixes and binders.

 \indexouternonterm{infix}\indexouternonterm{mixfix}

 \begin{rail}

   infix: '(' ('infixl' | 'infixr') string? nat ')'

   ;

   mixfix: infix | '(' string pris? nat? ')' | '(' 'binder' string pris? nat ')'

   ;

   pris: '[' (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, which does not have to be atomic at the outer level

 unlike that of types and terms.  Instead, the attribute argument

 specifications may be any sequence of atomic entities (identifiers, strings

 etc.), or properly bracketed argument lists.  Below \railqtoken{atom} refers

 to any atomic entity, including keywords that conform to \railtoken{symident}.

 \indexoutertoken{atom}\indexouternonterm{args}\indexouternonterm{attributes}

 \begin{rail}

   atom: nameref | typefree | typevar | var | textvar | nat | keyword

   ;

   arg: atom | '(' args ')' | '[' args ']' | lbrace args rbrace

   ;

   args: arg *

   ;

   attributes: '[' (nameref args * ',') ']'

   ;

 \end{rail}

 Theorem specifications come in several flavors: \railnonterm{axmdecl} and

 \railnonterm{thmdecl} usually refer to assumptions or results of goal

 statements, \railnonterm{thmdef} collects lists of existing theorems,

 \railnonterm{thmrefs} refers to any lists of existing theorems.  Any of these

 may include lists of attributes, which are applied to the preceding theorem or

 list of theorems.

 \indexouternonterm{thmdecl}\indexouternonterm{axmdecl}

 \indexouternonterm{thmdef}\indexouternonterm{thmrefs}

 \begin{rail}

   axmdecl: name attributes? ':'

   ;

   thmdecl: thmname ':'

   ;

   thmdef: thmname '='

   ;

   thmrefs: nameref attributes? +

   ;

   thmname: name attributes | name | attributes

   ;

 \end{rail}

 \subsection{Proof methods}\label{sec:syn-meth}

 Proof methods are either basic ones, or expressions composed of methods via

 ``\texttt{,}'' (sequential composition), ``\texttt{|}'' (alternatives),

 ``\texttt{?}'' (try), ``\texttt{*}'' (repeat ${} \ge 0$ times), ``\texttt{+}''

 (repeat ${} > 0$ times).  In practice, proof methods are usually just a comma

 separated list of \railqtoken{nameref}~\railnonterm{args} specifications.

 Thus the syntax is similar to that of attributes, with plain parentheses

 instead of square brackets (see also \S\ref{sec:syn-att}).  Note that

 parentheses may be dropped for single method specifications without arguments.

 \indexouternonterm{method}

 \begin{rail}

   method: (nameref | '(' methods ')') (() | '?' | '*' | '+')

   ;

   methods: (nameref args | method) + (',' | '|')

   ;

 \end{rail}

 %%% Local Variables: 

 %%% mode: latex

 %%% TeX-master: "isar-ref"

 %%% End: