(* $Id$ *)
theory "syntax"
imports Pure
begin
chapter {* Syntax primitives *}
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:lex-syntax} *}
text {*
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}.
\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 document syntax also provides formal 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 {* Mixfix annotations *}
text {*
Mixfix annotations specify concrete \emph{inner} syntax of Isabelle
types and terms. Some commands such as @{command "types"} (see
\secref{sec:types-pure}) admit infixes only, while @{command
"consts"} (see \secref{sec:consts}) and @{command "syntax"} (see
\secref{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 ``@{text _}''); the
special symbol ``@{verbatim "\<index>"}'' (printed as ``@{text "\<index>"}'')
represents an index argument that specifies an implicit structure
reference (see also \secref{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 ``@{verbatim "++"}'' for
an infix symbol, or ``@{verbatim "++"}@{text "\<index>"}'' for an infix of
an implicit structure.
*}
subsection {* Proof methods \label{sec:syn-meth} *}
text {*
Proof methods are either basic ones, or expressions composed of
methods via ``@{verbatim ","}'' (sequential composition),
``@{verbatim "|"}'' (alternative choices), ``@{verbatim "?"}''
(try), ``@{verbatim "+"}'' (repeat at least once), ``@{verbatim
"["}@{text n}@{verbatim "]"}'' (restriction to first @{text n}
sub-goals, with default @{text "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 ``@{text "[n]"}''
evaluates a method expression within a sandbox consisting of the
first @{text n} sub-goals (which need to exist). For example, the
method ``@{text "simp_all[3]"}'' simplifies the first three
sub-goals, while ``@{text "(rule foo, simp_all)[]"}'' simplifies all
new goals that emerge from applying rule @{text "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 ``@{text "[!]"}'' refers to
all goals, and ``@{text "[n-]"}'' to all goals starting from @{text
"n"}.
\indexouternonterm{goalspec}
\begin{rail}
goalspec: '[' (nat '-' nat | nat '-' | nat | '!' ) ']'
;
\end{rail}
*}
subsection {* Attributes and theorems \label{sec:syn-att} *}
text {*
Attributes (and proof methods, see \secref{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:
\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} in \secref{sec:pure-meth-att}).
\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}
*}
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 {* Antiquotations \label{sec:antiq} *}
text {*
\begin{matharray}{rcl}
@{antiquotation_def "theory"} & : & \isarantiq \\
@{antiquotation_def "thm"} & : & \isarantiq \\
@{antiquotation_def "prop"} & : & \isarantiq \\
@{antiquotation_def "term"} & : & \isarantiq \\
@{antiquotation_def const} & : & \isarantiq \\
@{antiquotation_def abbrev} & : & \isarantiq \\
@{antiquotation_def typeof} & : & \isarantiq \\
@{antiquotation_def typ} & : & \isarantiq \\
@{antiquotation_def thm_style} & : & \isarantiq \\
@{antiquotation_def term_style} & : & \isarantiq \\
@{antiquotation_def "text"} & : & \isarantiq \\
@{antiquotation_def goals} & : & \isarantiq \\
@{antiquotation_def subgoals} & : & \isarantiq \\
@{antiquotation_def prf} & : & \isarantiq \\
@{antiquotation_def full_prf} & : & \isarantiq \\
@{antiquotation_def ML} & : & \isarantiq \\
@{antiquotation_def ML_type} & : & \isarantiq \\
@{antiquotation_def ML_struct} & : & \isarantiq \\
\end{matharray}
The text body of formal comments (see also \secref{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
\secref{sec:document-prep}).
Thus embedding of ``@{text "@{term [show_types] \"f x = a + x\"}"}''
within a text block would cause
\isa{{\isacharparenleft}f{\isasymColon}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}\ {\isacharparenleft}x{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}a{\isasymColon}{\isacharprime}a{\isacharparenright}\ {\isacharplus}\ x} to appear in the final {\LaTeX} document. Also note that theorem
antiquotations may involve attributes as well. For example,
@{text "@{thm sym [no_vars]}"} would print the theorem's
statement where all schematic variables have been replaced by fixed
ones, which are easier to read.
\begin{rail}
atsign lbrace antiquotation rbrace
;
antiquotation:
'theory' options name |
'thm' options thmrefs |
'prop' options prop |
'term' options term |
'const' options term |
'abbrev' 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 @{verbatim "(*"}~@{text "\<dots>"}~@{verbatim "*)"} or verbatim
text @{verbatim "{"}@{verbatim "*"}~@{text "\<dots>"}~@{verbatim
"*"}@{verbatim "}"}.
\begin{descr}
\item [@{text "@{theory A}"}] prints the name @{text "A"}, which is
guaranteed to refer to a valid ancestor theory in the current
context.
\item [@{text "@{thm a\<^sub>1 \<dots> a\<^sub>n}"}] prints theorems
@{text "a\<^sub>1 \<dots> a\<^sub>n"}. Note that attribute specifications
may be included as well (see also \secref{sec:syn-att}); the
@{attribute_ref no_vars} rule (see \secref{sec:misc-meth-att}) would
be particularly useful to suppress printing of schematic variables.
\item [@{text "@{prop \<phi>}"}] prints a well-typed proposition @{text
"\<phi>"}.
\item [@{text "@{term t}"}] prints a well-typed term @{text "t"}.
\item [@{text "@{const c}"}] prints a logical or syntactic constant
@{text "c"}.
\item [@{text "@{abbrev c x\<^sub>1 \<dots> x\<^sub>n}"}] prints a constant
abbreviation @{text "c x\<^sub>1 \<dots> x\<^sub>n \<equiv> rhs"} as defined in
the current context.
\item [@{text "@{typeof t}"}] prints the type of a well-typed term
@{text "t"}.
\item [@{text "@{typ \<tau>}"}] prints a well-formed type @{text "\<tau>"}.
\item [@{text "@{thm_style s a}"}] prints theorem @{text a},
previously applying a style @{text s} to it (see below).
\item [@{text "@{term_style s t}"}] prints a well-typed term @{text
t} after applying a style @{text s} to it (see below).
\item [@{text "@{text s}"}] prints uninterpreted source text @{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 [@{text "@{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 [@{text "@{subgoals}"}] is similar to @{text "@{goals}"}, but
does not print the main goal.
\item [@{text "@{prf a\<^sub>1 \<dots> a\<^sub>n}"}] prints the (compact)
proof terms corresponding to the theorems @{text "a\<^sub>1 \<dots>
a\<^sub>n"}. 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 [@{text "@{full_prf a\<^sub>1 \<dots> a\<^sub>n}"}] is like @{text
"@{prf a\<^sub>1 \<dots> a\<^sub>n}"}, but displays the full proof terms,
i.e.\ also displays information omitted in the compact proof term,
which is denoted by ``@{text _}'' placeholders there.
\item [@{text "@{ML s}"}, @{text "@{ML_type s}"}, and @{text
"@{ML_struct s}"}] check text @{text s} as ML value, type, and
structure, respectively. The source is displayed verbatim.
\end{descr}
\medskip The following standard styles for use with @{text
thm_style} and @{text term_style} are available:
\begin{descr}
\item [@{text 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 [@{text rhs}] is like @{text lhs}, but extracts the second
argument.
\item [@{text "concl"}] extracts the conclusion @{text C} from a rule
in Horn-clause normal form @{text "A\<^sub>1 \<Longrightarrow> \<dots> A\<^sub>n \<Longrightarrow> C"}.
\item [@{text "prem1"}, \dots, @{text "prem9"}] extract premise
number @{text "1, \<dots>, 9"}, respectively, from from a rule in
Horn-clause normal form @{text "A\<^sub>1 \<Longrightarrow> \<dots> A\<^sub>n \<Longrightarrow> 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[@{text "show_types = bool"} and @{text "show_sorts = bool"}]
control printing of explicit type and sort constraints.
\item[@{text "show_structs = bool"}] controls printing of implicit
structures.
\item[@{text "long_names = bool"}] forces names of types and
constants etc.\ to be printed in their fully qualified internal
form.
\item[@{text "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[@{text "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 @{text false} for
more concise output.
\item[@{text "eta_contract = bool"}] prints terms in @{text
\<eta>}-contracted form.
\item[@{text "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[@{text "break = bool"}] controls line breaks in non-display
material.
\item[@{text "quotes = bool"}] indicates if the output should be
enclosed in double quotes.
\item[@{text "mode = name"}] adds @{text 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 @{text latex} and @{text xsymbols}.
\item[@{text "margin = nat"} and @{text "indent = nat"}] change the
margin or indentation for pretty printing of display material.
\item[@{text "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 @{antiquotation
"thm"}, @{antiquotation "term"}, etc. (only the @{antiquotation
"text"} antiquotation admits arbitrary output).
\item[@{text "goals_limit = nat"}] determines the maximum number of
goals to be printed.
\item[@{text "locale = name"}] specifies an alternative locale
context used for evaluating and printing the subsequent argument.
\end{descr}
For boolean flags, ``@{text "name = true"}'' may be abbreviated as
``@{text 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} *}
text {*
Each Isabelle/Isar command may be decorated by presentation tags:
\indexouternonterm{tags}
\begin{rail}
tags: ( tag * )
;
tag: '\%' (ident | string)
\end{rail}
The tags @{text "theory"}, @{text "proof"}, @{text "ML"} are already
pre-declared for certain classes of commands:
\medskip
\begin{tabular}{ll}
@{text "theory"} & theory begin/end \\
@{text "proof"} & all proof commands \\
@{text "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 ``@{command "by"}~@{text "%invisible auto"}'' would
cause that piece of proof to be treated as @{text invisible} instead
of @{text "proof"} (the default), which may be either show or hidden
depending on the document setup. In contrast, ``@{command
"by"}~@{text "%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, ``@{command
"proof"}~@{text "%visible \<dots>"}~@{command "qed"}'' would force the
whole sub-proof to be typeset as @{text visible} (unless some of its
parts are tagged differently).
*}
end