(* $Id$ *)
theory Outer_Syntax
imports Main
begin
chapter {* Outer syntax *}
text {*
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). Subsequently 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 (specifications and
proofs). As a general rule, inner syntax entities may occur only as
\emph{atomic entities} within outer syntax. For example, the string
@{verbatim "\"x + y\""} and identifier @{verbatim z} are legal term
specifications within a theory, while @{verbatim "x + y"} without
quotes is not.
Printed theory documents usually omit quotes to gain readability
(this is a matter of {\LaTeX} macro setup, say via @{verbatim
"\\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 ``@{verbatim ";"}'' (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 ``@{verbatim "#"}'' until an end-of-command is
clearly recognized from the input syntax, e.g.\ encounter of the
next command keyword.
More 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 @{verbatim "-k ZF"}
(in conjunction with @{verbatim "-l ZF"}, to specify the default
logic image). Note that option @{verbatim "-L"} does both
of this at the same time.
\end{warn}
*}
section {* Lexical matters \label{sec:outer-lex} *}
text {* The Isabelle/Isar outer syntax provides token classes as
presented below; most of these coincide with the inner lexical
syntax as defined in \secref{sec:inner-lex}.
\begin{matharray}{rcl}
@{syntax_def ident} & = & letter\,quasiletter^* \\
@{syntax_def longident} & = & ident (\verb,.,ident)^+ \\
@{syntax_def symident} & = & sym^+ ~|~ \verb,\,\verb,<,ident\verb,>, \\
@{syntax_def nat} & = & digit^+ \\
@{syntax_def var} & = & ident ~|~ \verb,?,ident ~|~ \verb,?,ident\verb,.,nat \\
@{syntax_def typefree} & = & \verb,',ident \\
@{syntax_def typevar} & = & typefree ~|~ \verb,?,typefree ~|~ \verb,?,typefree\verb,.,nat \\
@{syntax_def string} & = & \verb,", ~\dots~ \verb,", \\
@{syntax_def altstring} & = & \backquote ~\dots~ \backquote \\
@{syntax_def verbatim} & = & \verb,{*, ~\dots~ \verb,*,\verb,}, \\[1ex]
letter & = & latin ~|~ \verb,\,\verb,<,latin\verb,>, ~|~ \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,?, ~|~ \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,\<chi>, ~|~ \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 @{syntax string} admits any characters, including
newlines; ``@{verbatim "\""}'' (double-quote) and ``@{verbatim
"\\"}'' (backslash) need to be escaped by a backslash; arbitrary
character codes may be specified as ``@{verbatim "\\"}@{text ddd}'',
with three decimal digits. Alternative strings according to
@{syntax altstring} are analogous, using single back-quotes instead.
The body of @{syntax verbatim} may consist of any text not
containing ``@{verbatim "*"}@{verbatim "}"}''; this allows
convenient inclusion of quotes without further escapes. The greek
letters do \emph{not} include @{verbatim "\<lambda>"}, which is already used
differently in the meta-logic.
Common mathematical symbols such as @{text \<forall>} are represented in
Isabelle as @{verbatim \<forall>}. There are infinitely many Isabelle
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}.
Source comments take the form @{verbatim "(*"}~@{text
"\<dots>"}~@{verbatim "*)"} and may be nested, although user-interface
tools might prevent this. Note that this form indicates source
comments only, which are stripped after lexical analysis of the
input. The Isar syntax also provides proper \emph{document
comments} that are considered as part of the text (see
\secref{sec:comments}).
*}
section {* Common syntax entities *}
text {*
We now introduce several basic syntactic entities, such as names,
terms, and theorem specifications, which are factored out of the
actual Isar language elements to be described later.
*}
subsection {* Names *}
text {*
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.\ quoted @{verbatim "\"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} *}
text {*
Large chunks of plain \railqtok{text} are usually given
\railtok{verbatim}, i.e.\ enclosed in @{verbatim "{"}@{verbatim
"*"}~@{text "\<dots>"}~@{verbatim "*"}@{verbatim "}"}. For convenience,
any of the smaller text units conforming to \railqtok{nameref} are
admitted as well. A marginal \railnonterm{comment} is of the form
@{verbatim "--"} \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 *}
text {*
Classes are specified by plain names. Sorts have a very simple
inner syntax, which is either a single class name @{text c} or a
list @{text "{c\<^sub>1, \<dots>, c\<^sub>n}"} referring to the
intersection of these classes. The syntax of type arities is given
directly at the outer level.
\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} *}
text {*
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 @{verbatim x} instead of quoted @{verbatim "\"x\""}.
Note that symbolic identifiers (e.g.\ @{verbatim "++"} or @{text
"\<forall>"} are available as well, provided these have not been superseded
by commands or other keywords already (such as @{verbatim "="} or
@{verbatim "+"}).
\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 ``@{text _}'' (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 {* Term patterns and declarations \label{sec:term-decls} *}
text {*
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 ``@{text "(\<IS> p\<^sub>1 \<dots>
p\<^sub>n)"}''. This works both for \railqtok{term} and \railqtok{prop}.
\indexouternonterm{termpat}\indexouternonterm{proppat}
\begin{rail}
termpat: '(' ('is' term +) ')'
;
proppat: '(' ('is' prop +) ')'
;
\end{rail}
\medskip Declarations of local variables @{text "x :: \<tau>"} and
logical propositions @{text "a : \<phi>"} represent different views on
the same principle of introducing a local scope. In practice, one
may usually omit the typing of \railnonterm{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 \railnonterm{vars} versus
\railnonterm{props}. In ``@{text "x\<^sub>1 \<dots> x\<^sub>n :: \<tau>"}''
the typing refers to all variables, while in @{text "a: \<phi>\<^sub>1 \<dots>
\<phi>\<^sub>n"} the naming refers to all propositions collectively.
Isar language elements that refer to \railnonterm{vars} or
\railnonterm{props} typically admit separate typings or namings via
another level of iteration, with explicit @{keyword_ref "and"}
separators; e.g.\ see @{command "fix"} and @{command "assume"} in
\secref{sec:proof-context}.
*}
subsection {* Attributes and theorems \label{sec:syn-att} *}
text {* Attributes 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:
\begin{enumerate}
\item named facts @{text "a"},
\item selections from named facts @{text "a(i)"} or @{text "a(j - k)"},
\item literal fact propositions using @{syntax_ref altstring} syntax
@{verbatim "`"}@{text "\<phi>"}@{verbatim "`"} (see also method
@{method_ref fact}).
\end{enumerate}
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.
An extra pair of brackets around attributes (like ``@{text
"[[simproc a]]"}'') abbreviates a theorem reference involving an
internal dummy fact, which will be ignored later on. So only the
effect of the attribute on the background context will persist.
This form of in-place declarations is particularly useful with
commands like @{command "declare"} and @{command "using"}.
\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? | '[' attributes ']'
;
thmrefs: thmref +
;
thmbind: name attributes | name | attributes
;
selection: '(' ((nat | nat '-' nat?) + ',') ')'
;
\end{rail}
*}
end