3 \def\isabellecontext{Documents}%
6 \isamarkupsection{Concrete Syntax \label{sec:concrete-syntax}%
10 \begin{isamarkuptext}%
11 The core concept of Isabelle's framework for concrete syntax is that
12 of \bfindex{mixfix annotations}. Associated with any kind of
13 constant declaration, mixfixes affect both the grammar productions
14 for the parser and output templates for the pretty printer.
16 In full generality, parser and pretty printer configuration is a
17 subtle affair \cite{isabelle-ref}. Your syntax specifications need
18 to interact properly with the existing setup of Isabelle/Pure and
19 Isabelle/HOL\@. To avoid creating ambiguities with existing
20 elements, it is particularly important to give new syntactic
21 constructs the right precedence.
23 \medskip Subsequently we introduce a few simple syntax declaration
24 forms that already cover many common situations fairly well.%
28 \isamarkupsubsection{Infix Annotations%
32 \begin{isamarkuptext}%
33 Syntax annotations may be included wherever constants are declared,
34 such as \isacommand{consts} and \isacommand{constdefs} --- and also
35 \isacommand{datatype}, which declares constructor operations.
36 Type-constructors may be annotated as well, although this is less
37 frequently encountered in practice (the infix type \isa{{\isasymtimes}} comes
40 Infix declarations\index{infix annotations} provide a useful special
41 case of mixfixes. The following example of the exclusive-or
42 operation on boolean values illustrates typical infix declarations.%
45 \isacommand{constdefs}\isanewline
46 \ \ xor\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}bool\ {\isasymRightarrow}\ bool\ {\isasymRightarrow}\ bool{\isachardoublequote}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequote}{\isacharbrackleft}{\isacharplus}{\isacharbrackright}{\isachardoublequote}\ {\isadigit{6}}{\isadigit{0}}{\isacharparenright}\isanewline
47 \ \ {\isachardoublequote}A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B\ {\isasymequiv}\ {\isacharparenleft}A\ {\isasymand}\ {\isasymnot}\ B{\isacharparenright}\ {\isasymor}\ {\isacharparenleft}{\isasymnot}\ A\ {\isasymand}\ B{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
49 \begin{isamarkuptext}%
50 \noindent Now \isa{xor\ A\ B} and \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B} refer to the
51 same expression internally. Any curried function with at least two
52 arguments may be given infix syntax. For partial applications with
53 fewer than two operands, there is a notation using the prefix~\isa{op}. For instance, \isa{xor} without arguments is represented as
54 \isa{op\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}}; together with ordinary function application, this
55 turns \isa{xor\ A} into \isa{op\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ A}.
57 \medskip The keyword \isakeyword{infixl} seen above specifies an
58 infix operator that is nested to the \emph{left}: in iterated
59 applications the more complex expression appears on the left-hand
60 side, and \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ C} stands for \isa{{\isacharparenleft}A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B{\isacharparenright}\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ C}. Similarly, \isakeyword{infixr} means nesting to the
61 \emph{right}, reading \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ C} as \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ {\isacharparenleft}B\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ C{\isacharparenright}}. A \emph{non-oriented} declaration via \isakeyword{infix}
62 would render \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ C} illegal, but demand explicit
63 parentheses to indicate the intended grouping.
65 The string \isa{{\isachardoublequote}{\isacharbrackleft}{\isacharplus}{\isacharbrackright}{\isachardoublequote}} in our annotation refers to the
66 concrete syntax to represent the operator (a literal token), while
67 the number \isa{{\isadigit{6}}{\isadigit{0}}} determines the precedence of the construct:
68 the syntactic priorities of the arguments and result. Isabelle/HOL
69 already uses up many popular combinations of ASCII symbols for its
70 own use, including both \isa{{\isacharplus}} and \isa{{\isacharplus}{\isacharplus}}. Longer
71 character combinations are more likely to be still available for
72 user extensions, such as our~\isa{{\isacharbrackleft}{\isacharplus}{\isacharbrackright}}.
74 Operator precedences have a range of 0--1000. Very low or high
75 priorities are reserved for the meta-logic. HOL syntax mainly uses
76 the range of 10--100: the equality infix \isa{{\isacharequal}} is centered at
77 50; logical connectives (like \isa{{\isasymor}} and \isa{{\isasymand}}) are
78 below 50; algebraic ones (like \isa{{\isacharplus}} and \isa{{\isacharasterisk}}) are
79 above 50. User syntax should strive to coexist with common HOL
80 forms, or use the mostly unused range 100--900.%
84 \isamarkupsubsection{Mathematical Symbols \label{sec:syntax-symbols}%
88 \begin{isamarkuptext}%
89 Concrete syntax based on ASCII characters has inherent limitations.
90 Mathematical notation demands a larger repertoire of glyphs.
91 Several standards of extended character sets have been proposed over
92 decades, but none has become universally available so far. Isabelle
93 has its own notion of \bfindex{symbols} as the smallest entities of
94 source text, without referring to internal encodings. There are
95 three kinds of such ``generalized characters'':
99 \item 7-bit ASCII characters
101 \item named symbols: \verb,\,\verb,<,$ident$\verb,>,
103 \item named control symbols: \verb,\,\verb,<^,$ident$\verb,>,
107 Here $ident$ may be any identifier according to the usual Isabelle
108 conventions. This results in an infinite store of symbols, whose
109 interpretation is left to further front-end tools. For example, the
110 user-interface of Proof~General + X-Symbol and the Isabelle document
111 processor (see \S\ref{sec:document-preparation}) display the
112 \verb,\,\verb,<forall>, symbol as~\isa{{\isasymforall}}.
114 A list of standard Isabelle symbols is given in
115 \cite[appendix~A]{isabelle-sys}. You may introduce your own
116 interpretation of further symbols by configuring the appropriate
117 front-end tool accordingly, e.g.\ by defining certain {\LaTeX}
118 macros (see also \S\ref{sec:doc-prep-symbols}). There are also a
119 few predefined control symbols, such as \verb,\,\verb,<^sub>, and
120 \verb,\,\verb,<^sup>, for sub- and superscript of the subsequent
121 printable symbol, respectively. For example, \verb,A\<^sup>\<star>, is
122 output as \isa{A\isactrlsup {\isasymstar}}.
124 \medskip Replacing our definition of \isa{xor} by the following
125 specifies an Isabelle symbol for the new operator:%
130 \isacommand{constdefs}\isanewline
131 \ \ xor\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}bool\ {\isasymRightarrow}\ bool\ {\isasymRightarrow}\ bool{\isachardoublequote}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequote}{\isasymoplus}{\isachardoublequote}\ {\isadigit{6}}{\isadigit{0}}{\isacharparenright}\isanewline
132 \ \ {\isachardoublequote}A\ {\isasymoplus}\ B\ {\isasymequiv}\ {\isacharparenleft}A\ {\isasymand}\ {\isasymnot}\ B{\isacharparenright}\ {\isasymor}\ {\isacharparenleft}{\isasymnot}\ A\ {\isasymand}\ B{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
135 \begin{isamarkuptext}%
136 \noindent The X-Symbol package within Proof~General provides several
137 input methods to enter \isa{{\isasymoplus}} in the text. If all fails one may
138 just type a named entity \verb,\,\verb,<oplus>, by hand; the
139 corresponding symbol will be displayed after further input.
141 \medskip More flexible is to provide alternative syntax forms
142 through the \bfindex{print mode} concept~\cite{isabelle-ref}. By
143 convention, the mode of ``$xsymbols$'' is enabled whenever
144 Proof~General's X-Symbol mode or {\LaTeX} output is active. Now
145 consider the following hybrid declaration of \isa{xor}:%
150 \isacommand{constdefs}\isanewline
151 \ \ xor\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}bool\ {\isasymRightarrow}\ bool\ {\isasymRightarrow}\ bool{\isachardoublequote}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequote}{\isacharbrackleft}{\isacharplus}{\isacharbrackright}{\isasymignore}{\isachardoublequote}\ {\isadigit{6}}{\isadigit{0}}{\isacharparenright}\isanewline
152 \ \ {\isachardoublequote}A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}{\isasymignore}\ B\ {\isasymequiv}\ {\isacharparenleft}A\ {\isasymand}\ {\isasymnot}\ B{\isacharparenright}\ {\isasymor}\ {\isacharparenleft}{\isasymnot}\ A\ {\isasymand}\ B{\isacharparenright}{\isachardoublequote}\isanewline
155 \isacommand{syntax}\ {\isacharparenleft}xsymbols{\isacharparenright}\isanewline
156 \ \ xor\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}bool\ {\isasymRightarrow}\ bool\ {\isasymRightarrow}\ bool{\isachardoublequote}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequote}{\isasymoplus}{\isasymignore}{\isachardoublequote}\ {\isadigit{6}}{\isadigit{0}}{\isacharparenright}\isamarkupfalse%
159 \begin{isamarkuptext}%
160 The \commdx{syntax} command introduced here acts like
161 \isakeyword{consts}, but without declaring a logical constant. The
162 print mode specification of \isakeyword{syntax}, here \isa{{\isacharparenleft}xsymbols{\isacharparenright}}, is optional. Also note that its type merely serves
163 for syntactic purposes, and is \emph{not} checked for consistency
164 with the real constant.
166 \medskip We may now write \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B} or \isa{A\ {\isasymoplus}\ B} in
167 input, while output uses the nicer syntax of $xsymbols$ whenever
168 that print mode is active. Such an arrangement is particularly
169 useful for interactive development, where users may type ASCII text
170 and see mathematical symbols displayed during proofs.%
174 \isamarkupsubsection{Prefix Annotations%
178 \begin{isamarkuptext}%
179 Prefix syntax annotations\index{prefix annotation} are another form
180 of mixfixes \cite{isabelle-ref}, without any template arguments or
181 priorities --- just some literal syntax. The following example
182 associates common symbols with the constructors of a datatype.%
185 \isacommand{datatype}\ currency\ {\isacharequal}\isanewline
186 \ \ \ \ Euro\ nat\ \ \ \ {\isacharparenleft}{\isachardoublequote}{\isasymeuro}{\isachardoublequote}{\isacharparenright}\isanewline
187 \ \ {\isacharbar}\ Pounds\ nat\ \ {\isacharparenleft}{\isachardoublequote}{\isasympounds}{\isachardoublequote}{\isacharparenright}\isanewline
188 \ \ {\isacharbar}\ Yen\ nat\ \ \ \ \ {\isacharparenleft}{\isachardoublequote}{\isasymyen}{\isachardoublequote}{\isacharparenright}\isanewline
189 \ \ {\isacharbar}\ Dollar\ nat\ \ {\isacharparenleft}{\isachardoublequote}{\isachardollar}{\isachardoublequote}{\isacharparenright}\isamarkupfalse%
191 \begin{isamarkuptext}%
192 \noindent Here the mixfix annotations on the rightmost column happen
193 to consist of a single Isabelle symbol each: \verb,\,\verb,<euro>,,
194 \verb,\,\verb,<pounds>,, \verb,\,\verb,<yen>,, and \verb,$,. Recall
195 that a constructor like \isa{Euro} actually is a function \isa{nat\ {\isasymRightarrow}\ currency}. The expression \isa{Euro\ {\isadigit{1}}{\isadigit{0}}} will be
196 printed as \isa{{\isasymeuro}\ {\isadigit{1}}{\isadigit{0}}}; only the head of the application is
197 subject to our concrete syntax. This rather simple form already
198 achieves conformance with notational standards of the European
201 Prefix syntax works the same way for \isakeyword{consts} or
202 \isakeyword{constdefs}.%
206 \isamarkupsubsection{Syntax Translations \label{sec:syntax-translations}%
210 \begin{isamarkuptext}%
211 Mixfix syntax annotations merely decorate particular constant
212 application forms with concrete syntax, for instance replacing \
213 \isa{xor\ A\ B} by \isa{A\ {\isasymoplus}\ B}. Occasionally, the
214 relationship between some piece of notation and its internal form is
215 more complicated. Here we need \bfindex{syntax translations}.
217 Using the \isakeyword{syntax}\index{syntax (command)}, command we
218 introduce uninterpreted notational elements. Then
219 \commdx{translations} relate input forms to complex logical
220 expressions. This provides a simple mechanism for syntactic macros;
221 even heavier transformations may be written in ML
224 \medskip A typical use of syntax translations is to introduce
225 relational notation for membership in a set of pair, replacing \
226 \isa{{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ sim} by \isa{x\ {\isasymapprox}\ y}.%
229 \isacommand{consts}\isanewline
230 \ \ sim\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set{\isachardoublequote}\isanewline
233 \isacommand{syntax}\isanewline
234 \ \ {\isachardoublequote}{\isacharunderscore}sim{\isachardoublequote}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ bool{\isachardoublequote}\ \ \ \ {\isacharparenleft}\isakeyword{infix}\ {\isachardoublequote}{\isasymapprox}{\isachardoublequote}\ {\isadigit{5}}{\isadigit{0}}{\isacharparenright}\isanewline
236 \isacommand{translations}\isanewline
237 \ \ {\isachardoublequote}x\ {\isasymapprox}\ y{\isachardoublequote}\ {\isasymrightleftharpoons}\ {\isachardoublequote}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ sim{\isachardoublequote}\isamarkupfalse%
239 \begin{isamarkuptext}%
240 \noindent Here the name of the dummy constant \isa{{\isacharunderscore}sim} does
241 not matter, as long as it is not used elsewhere. Prefixing an
242 underscore is a common convention. The \isakeyword{translations}
243 declaration already uses concrete syntax on the left-hand side;
244 internally we relate a raw application \isa{{\isacharunderscore}sim\ x\ y} with
245 \isa{{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ sim}.
247 \medskip Another common application of syntax translations is to
248 provide variant versions of fundamental relational expressions, such
249 as \isa{{\isasymnoteq}} for negated equalities. The following declaration
250 stems from Isabelle/HOL itself:%
253 \isacommand{syntax}\ {\isachardoublequote}{\isacharunderscore}not{\isacharunderscore}equal{\isachardoublequote}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ bool{\isachardoublequote}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequote}{\isasymnoteq}{\isasymignore}{\isachardoublequote}\ {\isadigit{5}}{\isadigit{0}}{\isacharparenright}\isanewline
255 \isacommand{translations}\ {\isachardoublequote}x\ {\isasymnoteq}{\isasymignore}\ y{\isachardoublequote}\ {\isasymrightleftharpoons}\ {\isachardoublequote}{\isasymnot}\ {\isacharparenleft}x\ {\isacharequal}\ y{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
257 \begin{isamarkuptext}%
258 \noindent Normally one would introduce derived concepts like this
259 within the logic, using \isakeyword{consts} + \isakeyword{defs}
260 instead of \isakeyword{syntax} + \isakeyword{translations}. The
261 present formulation has the virtue that expressions are immediately
262 replaced by the ``definition'' upon parsing; the effect is reversed
265 This sort of translation is appropriate when the defined concept is
266 a trivial variation on an existing one. On the other hand, syntax
267 translations do not scale up well to large hierarchies of concepts.
268 Translations do not replace definitions!%
272 \isamarkupsection{Document Preparation \label{sec:document-preparation}%
276 \begin{isamarkuptext}%
277 Isabelle/Isar is centered around the concept of \bfindex{formal
278 proof documents}\index{documents|bold}. The outcome of a formal
279 development effort is meant to be a human-readable record, presented
280 as browsable PDF file or printed on paper. The overall document
281 structure follows traditional mathematical articles, with sections,
282 intermediate explanations, definitions, theorems and proofs.
284 \medskip The Isabelle document preparation system essentially acts
285 as a front-end to {\LaTeX}. After checking specifications and
286 proofs formally, the theory sources are turned into typesetting
287 instructions in a schematic manner. This lets you write authentic
288 reports on theory developments with little effort: many technical
289 consistency checks are handled by the system.
291 Here is an example to illustrate the idea of Isabelle document
298 \begin{isamarkuptext}%
299 The following datatype definition of \isa{{\isacharprime}a\ bintree} models
300 binary trees with nodes being decorated by elements of type \isa{{\isacharprime}a}.%
303 \isacommand{datatype}\ {\isacharprime}a\ bintree\ {\isacharequal}\isanewline
304 \ \ \ \ \ Leaf\ {\isacharbar}\ Branch\ {\isacharprime}a\ \ {\isachardoublequote}{\isacharprime}a\ bintree{\isachardoublequote}\ \ {\isachardoublequote}{\isacharprime}a\ bintree{\isachardoublequote}\isamarkupfalse%
306 \begin{isamarkuptext}%
307 \noindent The datatype induction rule generated here is of the form
309 \ {\isasymlbrakk}P\ Leaf{\isacharsemicolon}\isanewline
310 \isaindent{\ \ \ \ }{\isasymAnd}a\ bintree{\isadigit{1}}\ bintree{\isadigit{2}}{\isachardot}\isanewline
311 \isaindent{\ \ \ \ \ \ \ }{\isasymlbrakk}P\ bintree{\isadigit{1}}{\isacharsemicolon}\ P\ bintree{\isadigit{2}}{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}Branch\ a\ bintree{\isadigit{1}}\ bintree{\isadigit{2}}{\isacharparenright}{\isasymrbrakk}\isanewline
312 \isaindent{\ }{\isasymLongrightarrow}\ P\ bintree%
319 \begin{isamarkuptext}%
320 \noindent The above document output has been produced as follows:
324 The following datatype definition of {\at}{\ttlbrace}text "'a bintree"{\ttrbrace}
325 models binary trees with nodes being decorated by elements
326 of type {\at}{\ttlbrace}typ 'a{\ttrbrace}.
329 datatype 'a bintree =
330 Leaf | Branch 'a "'a bintree" "'a bintree"
334 {\ttback}noindent The datatype induction rule generated here is
335 of the form {\at}{\ttlbrace}thm [display] bintree.induct [no_vars]{\ttrbrace}
337 \end{ttbox}\vspace{-\medskipamount}
339 \noindent Here we have augmented the theory by formal comments
340 (using \isakeyword{text} blocks), the informal parts may again refer
341 to formal entities by means of ``antiquotations'' (such as
342 \texttt{\at}\verb,{text "'a bintree"}, or
343 \texttt{\at}\verb,{typ 'a},), see also \S\ref{sec:doc-prep-text}.%
347 \isamarkupsubsection{Isabelle Sessions%
351 \begin{isamarkuptext}%
352 In contrast to the highly interactive mode of Isabelle/Isar theory
353 development, the document preparation stage essentially works in
354 batch-mode. An Isabelle \bfindex{session} consists of a collection
355 of source files that may contribute to an output document. Each
356 session is derived from a single parent, usually an object-logic
357 image like \texttt{HOL}. This results in an overall tree structure,
358 which is reflected by the output location in the file system
359 (usually rooted at \verb,~/isabelle/browser_info,).
361 \medskip The easiest way to manage Isabelle sessions is via
362 \texttt{isatool mkdir} (generates an initial session source setup)
363 and \texttt{isatool make} (run sessions controlled by
364 \texttt{IsaMakefile}). For example, a new session
365 \texttt{MySession} derived from \texttt{HOL} may be produced as
369 isatool mkdir HOL MySession
373 The \texttt{isatool make} job also informs about the file-system
374 location of the ultimate results. The above dry run should be able
375 to produce some \texttt{document.pdf} (with dummy title, empty table
376 of contents etc.). Any failure at this stage usually indicates
377 technical problems of the {\LaTeX} installation.\footnote{Especially
378 make sure that \texttt{pdflatex} is present; if in doubt one may
379 fall back on DVI output by changing \texttt{usedir} options in
380 \texttt{IsaMakefile} \cite{isabelle-sys}.}
382 \medskip The detailed arrangement of the session sources is as
387 \item Directory \texttt{MySession} holds the required theory files
388 $T@1$\texttt{.thy}, \dots, $T@n$\texttt{.thy}.
390 \item File \texttt{MySession/ROOT.ML} holds appropriate ML commands
391 for loading all wanted theories, usually just
392 ``\texttt{use_thy"$T@i$";}'' for any $T@i$ in leaf position of the
395 \item Directory \texttt{MySession/document} contains everything
396 required for the {\LaTeX} stage; only \texttt{root.tex} needs to be
399 The latter file holds appropriate {\LaTeX} code to commence a
400 document (\verb,\documentclass, etc.), and to include the generated
401 files $T@i$\texttt{.tex} for each theory. Isabelle will generate a
402 file \texttt{session.tex} holding {\LaTeX} commands to include all
403 generated theory output files in topologically sorted order, so
404 \verb,\input{session}, in the body of \texttt{root.tex} does the job
407 \item \texttt{IsaMakefile} holds appropriate dependencies and
408 invocations of Isabelle tools to control the batch job. In fact,
409 several sessions may be managed by the same \texttt{IsaMakefile}.
410 See the \emph{Isabelle System Manual} \cite{isabelle-sys}
411 for further details, especially on
412 \texttt{isatool usedir} and \texttt{isatool make}.
416 One may now start to populate the directory \texttt{MySession}, and
417 the file \texttt{MySession/ROOT.ML} accordingly. The file
418 \texttt{MySession/document/root.tex} should also be adapted at some
419 point; the default version is mostly self-explanatory. Note that
420 \verb,\isabellestyle, enables fine-tuning of the general appearance
421 of characters and mathematical symbols (see also
422 \S\ref{sec:doc-prep-symbols}).
424 Especially observe the included {\LaTeX} packages \texttt{isabelle}
425 (mandatory), \texttt{isabellesym} (required for mathematical
426 symbols), and the final \texttt{pdfsetup} (provides sane defaults
427 for \texttt{hyperref}, including URL markup). All three are
428 distributed with Isabelle. Further packages may be required in
429 particular applications, say for unusual mathematical symbols.
431 \medskip Any additional files for the {\LaTeX} stage go into the
432 \texttt{MySession/document} directory as well. In particular,
433 adding a file named \texttt{root.bib} causes an automatic run of
434 \texttt{bibtex} to process a bibliographic database; see also
435 \texttt{isatool document} \cite{isabelle-sys}.
437 \medskip Any failure of the document preparation phase in an
438 Isabelle batch session leaves the generated sources in their target
439 location, identified by the accompanying error message. This lets
440 you trace {\LaTeX} problems with the generated files at hand.%
444 \isamarkupsubsection{Structure Markup%
448 \begin{isamarkuptext}%
449 The large-scale structure of Isabelle documents follows existing
450 {\LaTeX} conventions, with chapters, sections, subsubsections etc.
451 The Isar language includes separate \bfindex{markup commands}, which
452 do not affect the formal meaning of a theory (or proof), but result
453 in corresponding {\LaTeX} elements.
455 There are separate markup commands depending on the textual context:
456 in header position (just before \isakeyword{theory}), within the
457 theory body, or within a proof. The header needs to be treated
458 specially here, since ordinary theory and proof commands may only
459 occur \emph{after} the initial \isakeyword{theory} specification.
463 \begin{tabular}{llll}
464 header & theory & proof & default meaning \\\hline
465 & \commdx{chapter} & & \verb,\chapter, \\
466 \commdx{header} & \commdx{section} & \commdx{sect} & \verb,\section, \\
467 & \commdx{subsection} & \commdx{subsect} & \verb,\subsection, \\
468 & \commdx{subsubsection} & \commdx{subsubsect} & \verb,\subsubsection, \\
473 From the Isabelle perspective, each markup command takes a single
474 $text$ argument (delimited by \verb,",~\isa{{\isasymdots}}~\verb,", or
475 \verb,{,\verb,*,~\isa{{\isasymdots}}~\verb,*,\verb,},). After stripping any
476 surrounding white space, the argument is passed to a {\LaTeX} macro
477 \verb,\isamarkupXYZ, for command \isakeyword{XYZ}. These macros are
478 defined in \verb,isabelle.sty, according to the meaning given in the
479 rightmost column above.
481 \medskip The following source fragment illustrates structure markup
482 of a theory. Note that {\LaTeX} labels may be included inside of
483 section headings as well.
486 header {\ttlbrace}* Some properties of Foo Bar elements *{\ttrbrace}
488 theory Foo_Bar = Main:
490 subsection {\ttlbrace}* Basic definitions *{\ttrbrace}
498 subsection {\ttlbrace}* Derived rules *{\ttrbrace}
503 subsection {\ttlbrace}* Main theorem {\ttback}label{\ttlbrace}sec:main-theorem{\ttrbrace} *{\ttrbrace}
508 \end{ttbox}\vspace{-\medskipamount}
510 You may occasionally want to change the meaning of markup commands,
511 say via \verb,\renewcommand, in \texttt{root.tex}. For example,
512 \verb,\isamarkupheader, is a good candidate for some tuning. We
513 could move it up in the hierarchy to become \verb,\chapter,.
516 \renewcommand{\isamarkupheader}[1]{\chapter{#1}}
519 \noindent Now we must change the document class given in
520 \texttt{root.tex} to something that supports chapters. A suitable
521 command is \verb,\documentclass{report},.
523 \medskip The {\LaTeX} macro \verb,\isabellecontext, is maintained to
524 hold the name of the current theory context. This is particularly
525 useful for document headings:
528 \renewcommand{\isamarkupheader}[1]
529 {\chapter{#1}\markright{THEORY~\isabellecontext}}
532 \noindent Make sure to include something like
533 \verb,\pagestyle{headings}, in \texttt{root.tex}; the document
534 should have more than two pages to show the effect.%
538 \isamarkupsubsection{Formal Comments and Antiquotations \label{sec:doc-prep-text}%
542 \begin{isamarkuptext}%
543 Isabelle \bfindex{source comments}, which are of the form
544 \verb,(,\verb,*,~\isa{{\isasymdots}}~\verb,*,\verb,),, essentially act like
545 white space and do not really contribute to the content. They
546 mainly serve technical purposes to mark certain oddities in the raw
547 input text. In contrast, \bfindex{formal comments} are portions of
548 text that are associated with formal Isabelle/Isar commands
549 (\bfindex{marginal comments}), or as standalone paragraphs within a
550 theory or proof context (\bfindex{text blocks}).
552 \medskip Marginal comments are part of each command's concrete
553 syntax \cite{isabelle-ref}; the common form is ``\verb,--,~$text$''
554 where $text$ is delimited by \verb,",\isa{{\isasymdots}}\verb,", or
555 \verb,{,\verb,*,~\isa{{\isasymdots}}~\verb,*,\verb,}, as before. Multiple
556 marginal comments may be given at the same time. Here is a simple
560 \isacommand{lemma}\ {\isachardoublequote}A\ {\isacharminus}{\isacharminus}{\isachargreater}\ A{\isachardoublequote}\isanewline
562 \isamarkupcmt{a triviality of propositional logic%
566 \isamarkupcmt{(should not really bother)%
570 \isacommand{by}\ {\isacharparenleft}rule\ impI{\isacharparenright}\ %
571 \isamarkupcmt{implicit assumption step involved here%
575 \begin{isamarkuptext}%
576 \noindent The above output has been produced as follows:
580 -- "a triviality of propositional logic"
581 -- "(should not really bother)"
582 by (rule impI) -- "implicit assumption step involved here"
585 From the {\LaTeX} viewpoint, ``\verb,--,'' acts like a markup
586 command, associated with the macro \verb,\isamarkupcmt, (taking a
589 \medskip Text blocks are introduced by the commands \bfindex{text}
590 and \bfindex{txt}, for theory and proof contexts, respectively.
591 Each takes again a single $text$ argument, which is interpreted as a
592 free-form paragraph in {\LaTeX} (surrounded by some additional
593 vertical space). This behavior may be changed by redefining the
594 {\LaTeX} environments of \verb,isamarkuptext, or
595 \verb,isamarkuptxt,, respectively (via \verb,\renewenvironment,) The
596 text style of the body is determined by \verb,\isastyletext, and
597 \verb,\isastyletxt,; the default setup uses a smaller font within
598 proofs. This may be changed as follows:
601 \renewcommand{\isastyletxt}{\isastyletext}
604 \medskip The $text$ part of Isabelle markup commands essentially
605 inserts \emph{quoted material} into a formal text, mainly for
606 instruction of the reader. An \bfindex{antiquotation} is again a
607 formal object embedded into such an informal portion. The
608 interpretation of antiquotations is limited to some well-formedness
609 checks, with the result being pretty printed to the resulting
610 document. Quoted text blocks together with antiquotations provide
611 an attractive means of referring to formal entities, with good
612 confidence in getting the technical details right (especially syntax
615 The general syntax of antiquotations is as follows:
616 \texttt{{\at}{\ttlbrace}$name$ $arguments${\ttrbrace}}, or
617 \texttt{{\at}{\ttlbrace}$name$ [$options$] $arguments${\ttrbrace}}
618 for a comma-separated list of options consisting of a $name$ or
619 \texttt{$name$=$value$} each. The syntax of $arguments$ depends on
620 the kind of antiquotation, it generally follows the same conventions
621 for types, terms, or theorems as in the formal part of a theory.
623 \medskip This sentence demonstrates quotations and antiquotations:
624 \isa{{\isasymlambda}x\ y{\isachardot}\ x} is a well-typed term.
626 \medskip\noindent The output above was produced as follows:
629 This sentence demonstrates quotations and antiquotations:
630 {\at}{\ttlbrace}term "%x y. x"{\ttrbrace} is a well-typed term.
632 \end{ttbox}\vspace{-\medskipamount}
634 The notational change from the ASCII character~\verb,%, to the
635 symbol~\isa{{\isasymlambda}} reveals that Isabelle printed this term, after
636 parsing and type-checking. Document preparation enables symbolic
639 \medskip The next example includes an option to modify Isabelle's
640 \verb,show_types, flag. The antiquotation
641 \texttt{{\at}}\verb,{term [show_types] "%x y. x"}, produces the
642 output \isa{{\isasymlambda}{\isacharparenleft}x{\isasymColon}{\isacharprime}a{\isacharparenright}\ y{\isasymColon}{\isacharprime}b{\isachardot}\ x}. Type inference has figured
643 out the most general typings in the present theory context. Terms
644 may acquire different typings due to constraints imposed by their
645 environment; within a proof, for example, variables are given the
646 same types as they have in the main goal statement.
648 \medskip Several further kinds of antiquotations and options are
649 available \cite{isabelle-sys}. Here are a few commonly used
655 \texttt{\at}\verb,{typ,~$\tau$\verb,}, & print type $\tau$ \\
656 \texttt{\at}\verb,{term,~$t$\verb,}, & print term $t$ \\
657 \texttt{\at}\verb,{prop,~$\phi$\verb,}, & print proposition $\phi$ \\
658 \texttt{\at}\verb,{prop [display],~$\phi$\verb,}, & print large proposition $\phi$ (with linebreaks) \\
659 \texttt{\at}\verb,{prop [source],~$\phi$\verb,}, & check proposition $\phi$, print its input \\
660 \texttt{\at}\verb,{thm,~$a$\verb,}, & print fact $a$ \\
661 \texttt{\at}\verb,{thm,~$a$~\verb,[no_vars]}, & print fact $a$, fixing schematic variables \\
662 \texttt{\at}\verb,{thm [source],~$a$\verb,}, & check availability of fact $a$, print its name \\
663 \texttt{\at}\verb,{text,~$s$\verb,}, & print uninterpreted text $s$ \\
668 Note that \attrdx{no_vars} given above is \emph{not} an
669 antiquotation option, but an attribute of the theorem argument given
670 here. This might be useful with a diagnostic command like
671 \isakeyword{thm}, too.
673 \medskip The \texttt{\at}\verb,{text, $s$\verb,}, antiquotation is
674 particularly interesting. Embedding uninterpreted text within an
675 informal body might appear useless at first sight. Here the key
676 virtue is that the string $s$ is processed as Isabelle output,
677 interpreting Isabelle symbols appropriately.
679 For example, \texttt{\at}\verb,{text "\<forall>\<exists>"}, produces \isa{{\isasymforall}{\isasymexists}}, according to the standard interpretation of these symbol
680 (cf.\ \S\ref{sec:doc-prep-symbols}). Thus we achieve consistent
681 mathematical notation in both the formal and informal parts of the
682 document very easily, independently of the term language of
683 Isabelle. Manual {\LaTeX} code would leave more control over the
684 typesetting, but is also slightly more tedious.%
688 \isamarkupsubsection{Interpretation of Symbols \label{sec:doc-prep-symbols}%
692 \begin{isamarkuptext}%
693 As has been pointed out before (\S\ref{sec:syntax-symbols}),
694 Isabelle symbols are the smallest syntactic entities --- a
695 straightforward generalization of ASCII characters. While Isabelle
696 does not impose any interpretation of the infinite collection of
697 named symbols, {\LaTeX} documents use canonical glyphs for certain
698 standard symbols \cite[appendix~A]{isabelle-sys}.
700 The {\LaTeX} code produced from Isabelle text follows a simple
701 scheme. You can tune the final appearance by redefining certain
702 macros, say in \texttt{root.tex} of the document.
706 \item 7-bit ASCII characters: letters \texttt{A\dots Z} and
707 \texttt{a\dots z} are output directly, digits are passed as an
708 argument to the \verb,\isadigit, macro, other characters are
709 replaced by specifically named macros of the form
712 \item Named symbols: \verb,\,\verb,<XYZ>, is turned into
713 \verb,{\isasymXYZ},; note the additional braces.
715 \item Named control symbols: \verb,\,\verb,<^XYZ>, is turned into
716 \verb,\isactrlXYZ,; subsequent symbols may act as arguments if the
717 control macro is defined accordingly.
721 You may occasionally wish to give new {\LaTeX} interpretations of
722 named symbols. This merely requires an appropriate definition of
723 \verb,\isasymXYZ,, for \verb,\,\verb,<XYZ>, (see
724 \texttt{isabelle.sty} for working examples). Control symbols are
725 slightly more difficult to get right, though.
727 \medskip The \verb,\isabellestyle, macro provides a high-level
728 interface to tune the general appearance of individual symbols. For
729 example, \verb,\isabellestyle{it}, uses the italics text style to
730 mimic the general appearance of the {\LaTeX} math mode; double
731 quotes are not printed at all. The resulting quality of typesetting
732 is quite good, so this should be the default style for work that
733 gets distributed to a broader audience.%
737 \isamarkupsubsection{Suppressing Output \label{sec:doc-prep-suppress}%
741 \begin{isamarkuptext}%
742 By default, Isabelle's document system generates a {\LaTeX} file for
743 each theory that gets loaded while running the session. The
744 generated \texttt{session.tex} will include all of these in order of
745 appearance, which in turn gets included by the standard
746 \texttt{root.tex}. Certainly one may change the order or suppress
747 unwanted theories by ignoring \texttt{session.tex} and load
748 individual files directly in \texttt{root.tex}. On the other hand,
749 such an arrangement requires additional maintenance whenever the
750 collection of theories changes.
752 Alternatively, one may tune the theory loading process in
753 \texttt{ROOT.ML} itself: traversal of the theory dependency graph
754 may be fine-tuned by adding \verb,use_thy, invocations, although
755 topological sorting still has to be observed. Moreover, the ML
756 operator \verb,no_document, temporarily disables document generation
757 while executing a theory loader command. Its usage is like this:
760 no_document use_thy "T";
763 \medskip Theory output may be suppressed more selectively. Research
764 articles and slides usually do not include the formal content in
765 full. Delimiting \bfindex{ignored material} by the special source
766 comments \verb,(,\verb,*,\verb,<,\verb,*,\verb,), and
767 \verb,(,\verb,*,\verb,>,\verb,*,\verb,), tells the document
768 preparation system to suppress these parts; the formal checking of
769 the theory is unchanged, of course.
771 In this example, we hide a theory's \isakeyword{theory} and
772 \isakeyword{end} brackets:
777 \verb,(,\verb,*,\verb,<,\verb,*,\verb,), \\
778 \texttt{theory T = Main:} \\
779 \verb,(,\verb,*,\verb,>,\verb,*,\verb,), \\
781 \verb,(,\verb,*,\verb,<,\verb,*,\verb,), \\
783 \verb,(,\verb,*,\verb,>,\verb,*,\verb,), \\
788 Text may be suppressed in a fine-grained manner. We may even hide
789 vital parts of a proof, pretending that things have been simpler
790 than they really were. For example, this ``fully automatic'' proof
794 \isacommand{lemma}\ {\isachardoublequote}x\ {\isasymnoteq}\ {\isacharparenleft}{\isadigit{0}}{\isacharcolon}{\isacharcolon}int{\isacharparenright}\ {\isasymLongrightarrow}\ {\isadigit{0}}\ {\isacharless}\ x\ {\isacharasterisk}\ x{\isachardoublequote}\isanewline
796 \isacommand{by}\ {\isacharparenleft}auto{\isacharparenright}\isamarkupfalse%
798 \begin{isamarkuptext}%
799 \noindent Here the real source of the proof has been as follows:
802 by (auto(*<*)simp add: int_less_le(*>*))
806 \medskip Suppressing portions of printed text demands care. You
807 should not misrepresent the underlying theory development. It is
808 easy to invalidate the visible text by hiding references to
811 Authentic reports of Isabelle/Isar theories, say as part of a
812 library, should suppress nothing. Other users may need the full
813 information for their own derivative work. If a particular
814 formalization appears inadequate for general public coverage, it is
815 often more appropriate to think of a better way in the first place.
817 \medskip Some technical subtleties of the
818 \verb,(,\verb,*,\verb,<,\verb,*,\verb,),~\verb,(,\verb,*,\verb,>,\verb,*,\verb,),
819 elements need to be kept in mind, too --- the system performs few
820 sanity checks here. Arguments of markup commands and formal
821 comments must not be hidden, otherwise presentation fails. Open and
822 close parentheses need to be inserted carefully; it is easy to hide
823 the wrong parts, especially after rearranging the theory text.%
830 %%% TeX-master: "root"