(*<*)
theory Documents imports Main begin
(*>*)
section {* Concrete Syntax \label{sec:concrete-syntax} *}
text {*
The core concept of Isabelle's framework for concrete syntax is that
of \bfindex{mixfix annotations}. Associated with any kind of
constant declaration, mixfixes affect both the grammar productions
for the parser and output templates for the pretty printer.
In full generality, parser and pretty printer configuration is a
subtle affair~\cite{isabelle-ref}. Your syntax specifications need
to interact properly with the existing setup of Isabelle/Pure and
Isabelle/HOL\@. To avoid creating ambiguities with existing
elements, it is particularly important to give new syntactic
constructs the right precedence.
Below we introduce a few simple syntax declaration
forms that already cover many common situations fairly well.
*}
subsection {* Infix Annotations *}
text {*
Syntax annotations may be included wherever constants are declared,
such as \isacommand{definition} and \isacommand{primrec} --- and also
\isacommand{datatype}, which declares constructor operations.
Type-constructors may be annotated as well, although this is less
frequently encountered in practice (the infix type @{text "\<times>"} comes
to mind).
Infix declarations\index{infix annotations} provide a useful special
case of mixfixes. The following example of the exclusive-or
operation on boolean values illustrates typical infix declarations.
*}
definition xor :: "bool \<Rightarrow> bool \<Rightarrow> bool" (infixl "[+]" 60)
where "A [+] B \<equiv> (A \<and> \<not> B) \<or> (\<not> A \<and> B)"
text {*
\noindent Now @{text "xor A B"} and @{text "A [+] B"} refer to the
same expression internally. Any curried function with at least two
arguments may be given infix syntax. For partial applications with
fewer than two operands, there is a notation using the prefix~@{text
op}. For instance, @{text xor} without arguments is represented as
@{text "op [+]"}; together with ordinary function application, this
turns @{text "xor A"} into @{text "op [+] A"}.
The keyword \isakeyword{infixl} seen above specifies an
infix operator that is nested to the \emph{left}: in iterated
applications the more complex expression appears on the left-hand
side, and @{term "A [+] B [+] C"} stands for @{text "(A [+] B) [+]
C"}. Similarly, \isakeyword{infixr} means nesting to the
\emph{right}, reading @{term "A [+] B [+] C"} as @{text "A [+] (B
[+] C)"}. A \emph{non-oriented} declaration via \isakeyword{infix}
would render @{term "A [+] B [+] C"} illegal, but demand explicit
parentheses to indicate the intended grouping.
The string @{text [source] "[+]"} in our annotation refers to the
concrete syntax to represent the operator (a literal token), while
the number @{text 60} determines the precedence of the construct:
the syntactic priorities of the arguments and result. Isabelle/HOL
already uses up many popular combinations of ASCII symbols for its
own use, including both @{text "+"} and @{text "++"}. Longer
character combinations are more likely to be still available for
user extensions, such as our~@{text "[+]"}.
Operator precedences have a range of 0--1000. Very low or high
priorities are reserved for the meta-logic. HOL syntax mainly uses
the range of 10--100: the equality infix @{text "="} is centered at
50; logical connectives (like @{text "\<or>"} and @{text "\<and>"}) are
below 50; algebraic ones (like @{text "+"} and @{text "*"}) are
above 50. User syntax should strive to coexist with common HOL
forms, or use the mostly unused range 100--900.
*}
subsection {* Mathematical Symbols \label{sec:syntax-symbols} *}
text {*
Concrete syntax based on ASCII characters has inherent limitations.
Mathematical notation demands a larger repertoire of glyphs.
Several standards of extended character sets have been proposed over
decades, but none has become universally available so far. Isabelle
has its own notion of \bfindex{symbols} as the smallest entities of
source text, without referring to internal encodings. There are
three kinds of such ``generalized characters'':
\begin{enumerate}
\item 7-bit ASCII characters
\item named symbols: \verb,\,\verb,<,$ident$\verb,>,
\item named control symbols: \verb,\,\verb,<^,$ident$\verb,>,
\end{enumerate}
Here $ident$ is any sequence of letters.
This results in an infinite store of symbols, whose
interpretation is left to further front-end tools. For example, the
user-interface of Proof~General + X-Symbol and the Isabelle document
processor (see \S\ref{sec:document-preparation}) display the
\verb,\,\verb,<forall>, symbol as~@{text \<forall>}.
A list of standard Isabelle symbols is given in
\cite{isabelle-isar-ref}. You may introduce your own
interpretation of further symbols by configuring the appropriate
front-end tool accordingly, e.g.\ by defining certain {\LaTeX}
macros (see also \S\ref{sec:doc-prep-symbols}). There are also a
few predefined control symbols, such as \verb,\,\verb,<^sub>, and
\verb,\,\verb,<^sup>, for sub- and superscript of the subsequent
printable symbol, respectively. For example, \verb,A\<^sup>\<star>, is
output as @{text "A\<^sup>\<star>"}.
A number of symbols are considered letters by the Isabelle lexer and
can be used as part of identifiers. These are the greek letters
@{text "\<alpha>"} (\verb+\+\verb+<alpha>+), @{text "\<beta>"}
(\verb+\+\verb+<beta>+), etc. (excluding @{text "\<lambda>"}),
special letters like @{text "\<A>"} (\verb+\+\verb+<A>+) and @{text
"\<AA>"} (\verb+\+\verb+<AA>+), and the control symbols
\verb+\+\verb+<^isub>+ and \verb+\+\verb+<^isup>+ for single letter
sub and super scripts. This means that the input
\medskip
{\small\noindent \verb,\,\verb,<forall>\,\verb,<alpha>\<^isub>1.,~\verb,\,\verb,<alpha>\<^isub>1 = \,\verb,<Pi>\<^isup>\<A>,}
\medskip
\noindent is recognized as the term @{term "\<forall>\<alpha>\<^isub>1. \<alpha>\<^isub>1 = \<Pi>\<^isup>\<A>"}
by Isabelle. Note that @{text "\<Pi>\<^isup>\<A>"} is a single
syntactic entity, not an exponentiation.
Replacing our previous definition of @{text xor} by the
following specifies an Isabelle symbol for the new operator:
*}
(*<*)
hide_const xor
setup {* Sign.add_path "version1" *}
(*>*)
definition xor :: "bool \<Rightarrow> bool \<Rightarrow> bool" (infixl "\<oplus>" 60)
where "A \<oplus> B \<equiv> (A \<and> \<not> B) \<or> (\<not> A \<and> B)"
(*<*)
setup {* Sign.local_path *}
(*>*)
text {*
\noindent The X-Symbol package within Proof~General provides several
input methods to enter @{text \<oplus>} in the text. If all fails one may
just type a named entity \verb,\,\verb,<oplus>, by hand; the
corresponding symbol will be displayed after further input.
More flexible is to provide alternative syntax forms
through the \bfindex{print mode} concept~\cite{isabelle-ref}. By
convention, the mode of ``$xsymbols$'' is enabled whenever
Proof~General's X-Symbol mode or {\LaTeX} output is active. Now
consider the following hybrid declaration of @{text xor}:
*}
(*<*)
hide_const xor
setup {* Sign.add_path "version2" *}
(*>*)
definition xor :: "bool \<Rightarrow> bool \<Rightarrow> bool" (infixl "[+]\<ignore>" 60)
where "A [+]\<ignore> B \<equiv> (A \<and> \<not> B) \<or> (\<not> A \<and> B)"
notation (xsymbols) xor (infixl "\<oplus>\<ignore>" 60)
(*<*)
setup {* Sign.local_path *}
(*>*)
text {*\noindent
The \commdx{notation} command associates a mixfix
annotation with a known constant. The print mode specification,
here @{text "(xsymbols)"}, is optional.
We may now write @{text "A [+] B"} or @{text "A \<oplus> B"} in input, while
output uses the nicer syntax of $xsymbols$ whenever that print mode is
active. Such an arrangement is particularly useful for interactive
development, where users may type ASCII text and see mathematical
symbols displayed during proofs. *}
subsection {* Prefix Annotations *}
text {*
Prefix syntax annotations\index{prefix annotation} are another form
of mixfixes \cite{isabelle-ref}, without any template arguments or
priorities --- just some literal syntax. The following example
associates common symbols with the constructors of a datatype.
*}
datatype currency =
Euro nat ("\<euro>")
| Pounds nat ("\<pounds>")
| Yen nat ("\<yen>")
| Dollar nat ("$")
text {*
\noindent Here the mixfix annotations on the rightmost column happen
to consist of a single Isabelle symbol each: \verb,\,\verb,<euro>,,
\verb,\,\verb,<pounds>,, \verb,\,\verb,<yen>,, and \verb,$,. Recall
that a constructor like @{text Euro} actually is a function @{typ
"nat \<Rightarrow> currency"}. The expression @{text "Euro 10"} will be
printed as @{term "\<euro> 10"}; only the head of the application is
subject to our concrete syntax. This rather simple form already
achieves conformance with notational standards of the European
Commission.
Prefix syntax works the same way for other commands that introduce new constants, e.g. \isakeyword{primrec}.
*}
subsection {* Abbreviations \label{sec:abbreviations} *}
text{* Mixfix syntax annotations merely decorate particular constant
application forms with concrete syntax, for instance replacing
@{text "xor A B"} by @{text "A \<oplus> B"}. Occasionally, the relationship
between some piece of notation and its internal form is more
complicated. Here we need \emph{abbreviations}.
Command \commdx{abbreviation} introduces an uninterpreted notational
constant as an abbreviation for a complex term. Abbreviations are
unfolded upon parsing and re-introduced upon printing. This provides a
simple mechanism for syntactic macros.
A typical use of abbreviations is to introduce relational notation for
membership in a set of pairs, replacing @{text "(x, y) \<in> sim"} by
@{text "x \<approx> y"}. We assume that a constant @{text sim } of type
@{typ"('a \<times> 'a) set"} has been introduced at this point. *}
(*<*)consts sim :: "('a \<times> 'a) set"(*>*)
abbreviation sim2 :: "'a \<Rightarrow> 'a \<Rightarrow> bool" (infix "\<approx>" 50)
where "x \<approx> y \<equiv> (x, y) \<in> sim"
text {* \noindent The given meta-equality is used as a rewrite rule
after parsing (replacing \mbox{@{prop"x \<approx> y"}} by @{text"(x,y) \<in>
sim"}) and before printing (turning @{text"(x,y) \<in> sim"} back into
\mbox{@{prop"x \<approx> y"}}). The name of the dummy constant @{text "sim2"}
does not matter, as long as it is unique.
Another common application of abbreviations is to
provide variant versions of fundamental relational expressions, such
as @{text \<noteq>} for negated equalities. The following declaration
stems from Isabelle/HOL itself:
*}
abbreviation not_equal :: "'a \<Rightarrow> 'a \<Rightarrow> bool" (infixl "~=\<ignore>" 50)
where "x ~=\<ignore> y \<equiv> \<not> (x = y)"
notation (xsymbols) not_equal (infix "\<noteq>\<ignore>" 50)
text {* \noindent The notation @{text \<noteq>} is introduced separately to restrict it
to the \emph{xsymbols} mode.
Abbreviations are appropriate when the defined concept is a
simple variation on an existing one. But because of the automatic
folding and unfolding of abbreviations, they do not scale up well to
large hierarchies of concepts. Abbreviations do not replace
definitions.
Abbreviations are a simplified form of the general concept of
\emph{syntax translations}; even heavier transformations may be
written in ML \cite{isabelle-ref}.
*}
section {* Document Preparation \label{sec:document-preparation} *}
text {*
Isabelle/Isar is centered around the concept of \bfindex{formal
proof documents}\index{documents|bold}. The outcome of a formal
development effort is meant to be a human-readable record, presented
as browsable PDF file or printed on paper. The overall document
structure follows traditional mathematical articles, with sections,
intermediate explanations, definitions, theorems and proofs.
\medskip The Isabelle document preparation system essentially acts
as a front-end to {\LaTeX}. After checking specifications and
proofs formally, the theory sources are turned into typesetting
instructions in a schematic manner. This lets you write authentic
reports on theory developments with little effort: many technical
consistency checks are handled by the system.
Here is an example to illustrate the idea of Isabelle document
preparation.
*}
text_raw {* \begin{quotation} *}
text {*
The following datatype definition of @{text "'a bintree"} models
binary trees with nodes being decorated by elements of type @{typ
'a}.
*}
datatype 'a bintree =
Leaf | Branch 'a "'a bintree" "'a bintree"
text {*
\noindent The datatype induction rule generated here is of the form
@{thm [indent = 1, display] bintree.induct [no_vars]}
*}
text_raw {* \end{quotation} *}
text {*
\noindent The above document output has been produced as follows:
\begin{ttbox}
text {\ttlbrace}*
The following datatype definition of {\at}{\ttlbrace}text "'a bintree"{\ttrbrace}
models binary trees with nodes being decorated by elements
of type {\at}{\ttlbrace}typ 'a{\ttrbrace}.
*{\ttrbrace}
datatype 'a bintree =
Leaf | Branch 'a "'a bintree" "'a bintree"
\end{ttbox}
\begin{ttbox}
text {\ttlbrace}*
{\ttback}noindent The datatype induction rule generated here is
of the form {\at}{\ttlbrace}thm [display] bintree.induct [no_vars]{\ttrbrace}
*{\ttrbrace}
\end{ttbox}\vspace{-\medskipamount}
\noindent Here we have augmented the theory by formal comments
(using \isakeyword{text} blocks), the informal parts may again refer
to formal entities by means of ``antiquotations'' (such as
\texttt{\at}\verb,{text "'a bintree"}, or
\texttt{\at}\verb,{typ 'a},), see also \S\ref{sec:doc-prep-text}.
*}
subsection {* Isabelle Sessions *}
text {*
In contrast to the highly interactive mode of Isabelle/Isar theory
development, the document preparation stage essentially works in
batch-mode. An Isabelle \bfindex{session} consists of a collection
of source files that may contribute to an output document. Each
session is derived from a single parent, usually an object-logic
image like \texttt{HOL}. This results in an overall tree structure,
which is reflected by the output location in the file system
(usually rooted at \verb,~/.isabelle/IsabelleXXXX/browser_info,).
\medskip The easiest way to manage Isabelle sessions is via
\texttt{isabelle mkdir} (generates an initial session source setup)
and \texttt{isabelle make} (run sessions controlled by
\texttt{IsaMakefile}). For example, a new session
\texttt{MySession} derived from \texttt{HOL} may be produced as
follows:
\begin{verbatim}
isabelle mkdir HOL MySession
isabelle make
\end{verbatim}
The \texttt{isabelle make} job also informs about the file-system
location of the ultimate results. The above dry run should be able
to produce some \texttt{document.pdf} (with dummy title, empty table
of contents etc.). Any failure at this stage usually indicates
technical problems of the {\LaTeX} installation.
\medskip The detailed arrangement of the session sources is as
follows.
\begin{itemize}
\item Directory \texttt{MySession} holds the required theory files
$T@1$\texttt{.thy}, \dots, $T@n$\texttt{.thy}.
\item File \texttt{MySession/ROOT.ML} holds appropriate ML commands
for loading all wanted theories, usually just
``\texttt{use_thy"$T@i$";}'' for any $T@i$ in leaf position of the
dependency graph.
\item Directory \texttt{MySession/document} contains everything
required for the {\LaTeX} stage; only \texttt{root.tex} needs to be
provided initially.
The latter file holds appropriate {\LaTeX} code to commence a
document (\verb,\documentclass, etc.), and to include the generated
files $T@i$\texttt{.tex} for each theory. Isabelle will generate a
file \texttt{session.tex} holding {\LaTeX} commands to include all
generated theory output files in topologically sorted order, so
\verb,\input{session}, in the body of \texttt{root.tex} does the job
in most situations.
\item \texttt{IsaMakefile} holds appropriate dependencies and
invocations of Isabelle tools to control the batch job. In fact,
several sessions may be managed by the same \texttt{IsaMakefile}.
See the \emph{Isabelle System Manual} \cite{isabelle-sys}
for further details, especially on
\texttt{isabelle usedir} and \texttt{isabelle make}.
\end{itemize}
One may now start to populate the directory \texttt{MySession}, and
the file \texttt{MySession/ROOT.ML} accordingly. The file
\texttt{MySession/document/root.tex} should also be adapted at some
point; the default version is mostly self-explanatory. Note that
\verb,\isabellestyle, enables fine-tuning of the general appearance
of characters and mathematical symbols (see also
\S\ref{sec:doc-prep-symbols}).
Especially observe the included {\LaTeX} packages \texttt{isabelle}
(mandatory), \texttt{isabellesym} (required for mathematical
symbols), and the final \texttt{pdfsetup} (provides sane defaults
for \texttt{hyperref}, including URL markup). All three are
distributed with Isabelle. Further packages may be required in
particular applications, say for unusual mathematical symbols.
\medskip Any additional files for the {\LaTeX} stage go into the
\texttt{MySession/document} directory as well. In particular,
adding a file named \texttt{root.bib} causes an automatic run of
\texttt{bibtex} to process a bibliographic database; see also
\texttt{isabelle document} \cite{isabelle-sys}.
\medskip Any failure of the document preparation phase in an
Isabelle batch session leaves the generated sources in their target
location, identified by the accompanying error message. This lets
you trace {\LaTeX} problems with the generated files at hand.
*}
subsection {* Structure Markup *}
text {*
The large-scale structure of Isabelle documents follows existing
{\LaTeX} conventions, with chapters, sections, subsubsections etc.
The Isar language includes separate \bfindex{markup commands}, which
do not affect the formal meaning of a theory (or proof), but result
in corresponding {\LaTeX} elements.
There are separate markup commands depending on the textual context:
in header position (just before \isakeyword{theory}), within the
theory body, or within a proof. The header needs to be treated
specially here, since ordinary theory and proof commands may only
occur \emph{after} the initial \isakeyword{theory} specification.
\medskip
\begin{tabular}{llll}
header & theory & proof & default meaning \\\hline
& \commdx{chapter} & & \verb,\chapter, \\
\commdx{header} & \commdx{section} & \commdx{sect} & \verb,\section, \\
& \commdx{subsection} & \commdx{subsect} & \verb,\subsection, \\
& \commdx{subsubsection} & \commdx{subsubsect} & \verb,\subsubsection, \\
\end{tabular}
\medskip
From the Isabelle perspective, each markup command takes a single
$text$ argument (delimited by \verb,",~@{text \<dots>}~\verb,", or
\verb,{,\verb,*,~@{text \<dots>}~\verb,*,\verb,},). After stripping any
surrounding white space, the argument is passed to a {\LaTeX} macro
\verb,\isamarkupXYZ, for command \isakeyword{XYZ}. These macros are
defined in \verb,isabelle.sty, according to the meaning given in the
rightmost column above.
\medskip The following source fragment illustrates structure markup
of a theory. Note that {\LaTeX} labels may be included inside of
section headings as well.
\begin{ttbox}
header {\ttlbrace}* Some properties of Foo Bar elements *{\ttrbrace}
theory Foo_Bar
imports Main
begin
subsection {\ttlbrace}* Basic definitions *{\ttrbrace}
definition foo :: \dots
definition bar :: \dots
subsection {\ttlbrace}* Derived rules *{\ttrbrace}
lemma fooI: \dots
lemma fooE: \dots
subsection {\ttlbrace}* Main theorem {\ttback}label{\ttlbrace}sec:main-theorem{\ttrbrace} *{\ttrbrace}
theorem main: \dots
end
\end{ttbox}\vspace{-\medskipamount}
You may occasionally want to change the meaning of markup commands,
say via \verb,\renewcommand, in \texttt{root.tex}. For example,
\verb,\isamarkupheader, is a good candidate for some tuning. We
could move it up in the hierarchy to become \verb,\chapter,.
\begin{verbatim}
\renewcommand{\isamarkupheader}[1]{\chapter{#1}}
\end{verbatim}
\noindent Now we must change the document class given in
\texttt{root.tex} to something that supports chapters. A suitable
command is \verb,\documentclass{report},.
\medskip The {\LaTeX} macro \verb,\isabellecontext, is maintained to
hold the name of the current theory context. This is particularly
useful for document headings:
\begin{verbatim}
\renewcommand{\isamarkupheader}[1]
{\chapter{#1}\markright{THEORY~\isabellecontext}}
\end{verbatim}
\noindent Make sure to include something like
\verb,\pagestyle{headings}, in \texttt{root.tex}; the document
should have more than two pages to show the effect.
*}
subsection {* Formal Comments and Antiquotations \label{sec:doc-prep-text} *}
text {*
Isabelle \bfindex{source comments}, which are of the form
\verb,(,\verb,*,~@{text \<dots>}~\verb,*,\verb,),, essentially act like
white space and do not really contribute to the content. They
mainly serve technical purposes to mark certain oddities in the raw
input text. In contrast, \bfindex{formal comments} are portions of
text that are associated with formal Isabelle/Isar commands
(\bfindex{marginal comments}), or as standalone paragraphs within a
theory or proof context (\bfindex{text blocks}).
\medskip Marginal comments are part of each command's concrete
syntax \cite{isabelle-ref}; the common form is ``\verb,--,~$text$''
where $text$ is delimited by \verb,",@{text \<dots>}\verb,", or
\verb,{,\verb,*,~@{text \<dots>}~\verb,*,\verb,}, as before. Multiple
marginal comments may be given at the same time. Here is a simple
example:
*}
lemma "A --> A"
-- "a triviality of propositional logic"
-- "(should not really bother)"
by (rule impI) -- "implicit assumption step involved here"
text {*
\noindent The above output has been produced as follows:
\begin{verbatim}
lemma "A --> A"
-- "a triviality of propositional logic"
-- "(should not really bother)"
by (rule impI) -- "implicit assumption step involved here"
\end{verbatim}
From the {\LaTeX} viewpoint, ``\verb,--,'' acts like a markup
command, associated with the macro \verb,\isamarkupcmt, (taking a
single argument).
\medskip Text blocks are introduced by the commands \bfindex{text}
and \bfindex{txt}, for theory and proof contexts, respectively.
Each takes again a single $text$ argument, which is interpreted as a
free-form paragraph in {\LaTeX} (surrounded by some additional
vertical space). This behavior may be changed by redefining the
{\LaTeX} environments of \verb,isamarkuptext, or
\verb,isamarkuptxt,, respectively (via \verb,\renewenvironment,) The
text style of the body is determined by \verb,\isastyletext, and
\verb,\isastyletxt,; the default setup uses a smaller font within
proofs. This may be changed as follows:
\begin{verbatim}
\renewcommand{\isastyletxt}{\isastyletext}
\end{verbatim}
\medskip The $text$ part of Isabelle markup commands essentially
inserts \emph{quoted material} into a formal text, mainly for
instruction of the reader. An \bfindex{antiquotation} is again a
formal object embedded into such an informal portion. The
interpretation of antiquotations is limited to some well-formedness
checks, with the result being pretty printed to the resulting
document. Quoted text blocks together with antiquotations provide
an attractive means of referring to formal entities, with good
confidence in getting the technical details right (especially syntax
and types).
The general syntax of antiquotations is as follows:
\texttt{{\at}{\ttlbrace}$name$ $arguments${\ttrbrace}}, or
\texttt{{\at}{\ttlbrace}$name$ [$options$] $arguments${\ttrbrace}}
for a comma-separated list of options consisting of a $name$ or
\texttt{$name$=$value$} each. The syntax of $arguments$ depends on
the kind of antiquotation, it generally follows the same conventions
for types, terms, or theorems as in the formal part of a theory.
\medskip This sentence demonstrates quotations and antiquotations:
@{term "%x y. x"} is a well-typed term.
\medskip\noindent The output above was produced as follows:
\begin{ttbox}
text {\ttlbrace}*
This sentence demonstrates quotations and antiquotations:
{\at}{\ttlbrace}term "%x y. x"{\ttrbrace} is a well-typed term.
*{\ttrbrace}
\end{ttbox}\vspace{-\medskipamount}
The notational change from the ASCII character~\verb,%, to the
symbol~@{text \<lambda>} reveals that Isabelle printed this term, after
parsing and type-checking. Document preparation enables symbolic
output by default.
\medskip The next example includes an option to show the type of all
variables. The antiquotation
\texttt{{\at}}\verb,{term [show_types] "%x y. x"}, produces the
output @{term [show_types] "%x y. x"}. Type inference has figured
out the most general typings in the present theory context. Terms
may acquire different typings due to constraints imposed by their
environment; within a proof, for example, variables are given the
same types as they have in the main goal statement.
\medskip Several further kinds of antiquotations and options are
available \cite{isabelle-isar-ref}. Here are a few commonly used
combinations:
\medskip
\begin{tabular}{ll}
\texttt{\at}\verb,{typ,~$\tau$\verb,}, & print type $\tau$ \\
\texttt{\at}\verb,{const,~$c$\verb,}, & check existence of $c$ and print it \\
\texttt{\at}\verb,{term,~$t$\verb,}, & print term $t$ \\
\texttt{\at}\verb,{prop,~$\phi$\verb,}, & print proposition $\phi$ \\
\texttt{\at}\verb,{prop [display],~$\phi$\verb,}, & print large proposition $\phi$ (with linebreaks) \\
\texttt{\at}\verb,{prop [source],~$\phi$\verb,}, & check proposition $\phi$, print its input \\
\texttt{\at}\verb,{thm,~$a$\verb,}, & print fact $a$ \\
\texttt{\at}\verb,{thm,~$a$~\verb,[no_vars]}, & print fact $a$, fixing schematic variables \\
\texttt{\at}\verb,{thm [source],~$a$\verb,}, & check availability of fact $a$, print its name \\
\texttt{\at}\verb,{text,~$s$\verb,}, & print uninterpreted text $s$ \\
\end{tabular}
\medskip
Note that \attrdx{no_vars} given above is \emph{not} an
antiquotation option, but an attribute of the theorem argument given
here. This might be useful with a diagnostic command like
\isakeyword{thm}, too.
\medskip The \texttt{\at}\verb,{text, $s$\verb,}, antiquotation is
particularly interesting. Embedding uninterpreted text within an
informal body might appear useless at first sight. Here the key
virtue is that the string $s$ is processed as Isabelle output,
interpreting Isabelle symbols appropriately.
For example, \texttt{\at}\verb,{text "\<forall>\<exists>"}, produces @{text
"\<forall>\<exists>"}, according to the standard interpretation of these symbol
(cf.\ \S\ref{sec:doc-prep-symbols}). Thus we achieve consistent
mathematical notation in both the formal and informal parts of the
document very easily, independently of the term language of
Isabelle. Manual {\LaTeX} code would leave more control over the
typesetting, but is also slightly more tedious.
*}
subsection {* Interpretation of Symbols \label{sec:doc-prep-symbols} *}
text {*
As has been pointed out before (\S\ref{sec:syntax-symbols}),
Isabelle symbols are the smallest syntactic entities --- a
straightforward generalization of ASCII characters. While Isabelle
does not impose any interpretation of the infinite collection of
named symbols, {\LaTeX} documents use canonical glyphs for certain
standard symbols \cite{isabelle-isar-ref}.
The {\LaTeX} code produced from Isabelle text follows a simple
scheme. You can tune the final appearance by redefining certain
macros, say in \texttt{root.tex} of the document.
\begin{enumerate}
\item 7-bit ASCII characters: letters \texttt{A\dots Z} and
\texttt{a\dots z} are output directly, digits are passed as an
argument to the \verb,\isadigit, macro, other characters are
replaced by specifically named macros of the form
\verb,\isacharXYZ,.
\item Named symbols: \verb,\,\verb,<XYZ>, is turned into
\verb,{\isasymXYZ},; note the additional braces.
\item Named control symbols: \verb,\,\verb,<^XYZ>, is turned into
\verb,\isactrlXYZ,; subsequent symbols may act as arguments if the
control macro is defined accordingly.
\end{enumerate}
You may occasionally wish to give new {\LaTeX} interpretations of
named symbols. This merely requires an appropriate definition of
\verb,\isasymXYZ,, for \verb,\,\verb,<XYZ>, (see
\texttt{isabelle.sty} for working examples). Control symbols are
slightly more difficult to get right, though.
\medskip The \verb,\isabellestyle, macro provides a high-level
interface to tune the general appearance of individual symbols. For
example, \verb,\isabellestyle{it}, uses the italics text style to
mimic the general appearance of the {\LaTeX} math mode; double
quotes are not printed at all. The resulting quality of typesetting
is quite good, so this should be the default style for work that
gets distributed to a broader audience.
*}
subsection {* Suppressing Output \label{sec:doc-prep-suppress} *}
text {*
By default, Isabelle's document system generates a {\LaTeX} file for
each theory that gets loaded while running the session. The
generated \texttt{session.tex} will include all of these in order of
appearance, which in turn gets included by the standard
\texttt{root.tex}. Certainly one may change the order or suppress
unwanted theories by ignoring \texttt{session.tex} and load
individual files directly in \texttt{root.tex}. On the other hand,
such an arrangement requires additional maintenance whenever the
collection of theories changes.
Alternatively, one may tune the theory loading process in
\texttt{ROOT.ML} itself: traversal of the theory dependency graph
may be fine-tuned by adding \verb,use_thy, invocations, although
topological sorting still has to be observed. Moreover, the ML
operator \verb,no_document, temporarily disables document generation
while executing a theory loader command. Its usage is like this:
\begin{verbatim}
no_document use_thy "T";
\end{verbatim}
\medskip Theory output may be suppressed more selectively, either
via \bfindex{tagged command regions} or \bfindex{ignored material}.
Tagged command regions works by annotating commands with named tags,
which correspond to certain {\LaTeX} markup that tells how to treat
particular parts of a document when doing the actual type-setting.
By default, certain Isabelle/Isar commands are implicitly marked up
using the predefined tags ``\emph{theory}'' (for theory begin and
end), ``\emph{proof}'' (for proof commands), and ``\emph{ML}'' (for
commands involving ML code). Users may add their own tags using the
\verb,%,\emph{tag} notation right after a command name. In the
subsequent example we hide a particularly irrelevant proof:
*}
lemma "x = x" by %invisible (simp)
text {*
The original source has been ``\verb,lemma "x = x" by %invisible (simp),''.
Tags observe the structure of proofs; adjacent commands with the
same tag are joined into a single region. The Isabelle document
preparation system allows the user to specify how to interpret a
tagged region, in order to keep, drop, or fold the corresponding
parts of the document. See the \emph{Isabelle System Manual}
\cite{isabelle-sys} for further details, especially on
\texttt{isabelle usedir} and \texttt{isabelle document}.
Ignored material is specified by delimiting the original formal
source with special source comments
\verb,(,\verb,*,\verb,<,\verb,*,\verb,), and
\verb,(,\verb,*,\verb,>,\verb,*,\verb,),. These parts are stripped
before the type-setting phase, without affecting the formal checking
of the theory, of course. For example, we may hide parts of a proof
that seem unfit for general public inspection. The following
``fully automatic'' proof is actually a fake:
*}
lemma "x \<noteq> (0::int) \<Longrightarrow> 0 < x * x"
by (auto(*<*)simp add: zero_less_mult_iff(*>*))
text {*
\noindent The real source of the proof has been as follows:
\begin{verbatim}
by (auto(*<*)simp add: zero_less_mult_iff(*>*))
\end{verbatim}
%(*
\medskip Suppressing portions of printed text demands care. You
should not misrepresent the underlying theory development. It is
easy to invalidate the visible text by hiding references to
questionable axioms, for example.
*}
(*<*)
end
(*>*)