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}\isanewline
136 \begin{isamarkuptext}%
137 \noindent The X-Symbol package within Proof~General provides several
138 input methods to enter \isa{{\isasymoplus}} in the text. If all fails one may
139 just type a named entity \verb,\,\verb,<oplus>, by hand; the
140 corresponding symbol will be displayed after further input.
142 \medskip More flexible is to provide alternative syntax forms
143 through the \bfindex{print mode} concept~\cite{isabelle-ref}. By
144 convention, the mode of ``$xsymbols$'' is enabled whenever
145 Proof~General's X-Symbol mode or {\LaTeX} output is active. Now
146 consider the following hybrid declaration of \isa{xor}:%
151 \isacommand{constdefs}\isanewline
152 \ \ 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
153 \ \ {\isachardoublequote}A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}{\isasymignore}\ B\ {\isasymequiv}\ {\isacharparenleft}A\ {\isasymand}\ {\isasymnot}\ B{\isacharparenright}\ {\isasymor}\ {\isacharparenleft}{\isasymnot}\ A\ {\isasymand}\ B{\isacharparenright}{\isachardoublequote}\isanewline
156 \isacommand{syntax}\ {\isacharparenleft}xsymbols{\isacharparenright}\isanewline
157 \ \ xor\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}bool\ {\isasymRightarrow}\ bool\ {\isasymRightarrow}\ bool{\isachardoublequote}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequote}{\isasymoplus}{\isasymignore}{\isachardoublequote}\ {\isadigit{6}}{\isadigit{0}}{\isacharparenright}\isanewline
161 \begin{isamarkuptext}%
162 The \commdx{syntax} command introduced here acts like
163 \isakeyword{consts}, but without declaring a logical constant. The
164 print mode specification of \isakeyword{syntax}, here \isa{{\isacharparenleft}xsymbols{\isacharparenright}}, is optional. Also note that its type merely serves
165 for syntactic purposes, and is \emph{not} checked for consistency
166 with the real constant.
168 \medskip We may now write \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B} or \isa{A\ {\isasymoplus}\ B} in
169 input, while output uses the nicer syntax of $xsymbols$ whenever
170 that print mode is active. Such an arrangement is particularly
171 useful for interactive development, where users may type ASCII text
172 and see mathematical symbols displayed during proofs.%
176 \isamarkupsubsection{Prefix Annotations%
180 \begin{isamarkuptext}%
181 Prefix syntax annotations\index{prefix annotation} are another form
182 of mixfixes \cite{isabelle-ref}, without any template arguments or
183 priorities --- just some literal syntax. The following example
184 associates common symbols with the constructors of a datatype.%
187 \isacommand{datatype}\ currency\ {\isacharequal}\isanewline
188 \ \ \ \ Euro\ nat\ \ \ \ {\isacharparenleft}{\isachardoublequote}{\isasymeuro}{\isachardoublequote}{\isacharparenright}\isanewline
189 \ \ {\isacharbar}\ Pounds\ nat\ \ {\isacharparenleft}{\isachardoublequote}{\isasympounds}{\isachardoublequote}{\isacharparenright}\isanewline
190 \ \ {\isacharbar}\ Yen\ nat\ \ \ \ \ {\isacharparenleft}{\isachardoublequote}{\isasymyen}{\isachardoublequote}{\isacharparenright}\isanewline
191 \ \ {\isacharbar}\ Dollar\ nat\ \ {\isacharparenleft}{\isachardoublequote}{\isachardollar}{\isachardoublequote}{\isacharparenright}\isamarkupfalse%
193 \begin{isamarkuptext}%
194 \noindent Here the mixfix annotations on the rightmost column happen
195 to consist of a single Isabelle symbol each: \verb,\,\verb,<euro>,,
196 \verb,\,\verb,<pounds>,, \verb,\,\verb,<yen>,, and \verb,$,. Recall
197 that a constructor like \isa{Euro} actually is a function \isa{nat\ {\isasymRightarrow}\ currency}. The expression \isa{Euro\ {\isadigit{1}}{\isadigit{0}}} will be
198 printed as \isa{{\isasymeuro}\ {\isadigit{1}}{\isadigit{0}}}; only the head of the application is
199 subject to our concrete syntax. This rather simple form already
200 achieves conformance with notational standards of the European
203 Prefix syntax works the same way for \isakeyword{consts} or
204 \isakeyword{constdefs}.%
208 \isamarkupsubsection{Syntax Translations \label{sec:syntax-translations}%
212 \begin{isamarkuptext}%
213 Mixfix syntax annotations merely decorate particular constant
214 application forms with concrete syntax, for instance replacing \
215 \isa{xor\ A\ B} by \isa{A\ {\isasymoplus}\ B}. Occasionally, the
216 relationship between some piece of notation and its internal form is
217 more complicated. Here we need \bfindex{syntax translations}.
219 Using the \isakeyword{syntax}\index{syntax (command)}, command we
220 introduce uninterpreted notational elements. Then
221 \commdx{translations} relate input forms to complex logical
222 expressions. This provides a simple mechanism for syntactic macros;
223 even heavier transformations may be written in ML
226 \medskip A typical use of syntax translations is to introduce
227 relational notation for membership in a set of pair, replacing \
228 \isa{{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ sim} by \isa{x\ {\isasymapprox}\ y}.%
231 \isacommand{consts}\isanewline
232 \ \ sim\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set{\isachardoublequote}\isanewline
235 \isacommand{syntax}\isanewline
236 \ \ {\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
238 \isacommand{translations}\isanewline
239 \ \ {\isachardoublequote}x\ {\isasymapprox}\ y{\isachardoublequote}\ {\isasymrightleftharpoons}\ {\isachardoublequote}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ sim{\isachardoublequote}\isamarkupfalse%
241 \begin{isamarkuptext}%
242 \noindent Here the name of the dummy constant \isa{{\isacharunderscore}sim} does
243 not matter, as long as it is not used elsewhere. Prefixing an
244 underscore is a common convention. The \isakeyword{translations}
245 declaration already uses concrete syntax on the left-hand side;
246 internally we relate a raw application \isa{{\isacharunderscore}sim\ x\ y} with
247 \isa{{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ sim}.
249 \medskip Another common application of syntax translations is to
250 provide variant versions of fundamental relational expressions, such
251 as \isa{{\isasymnoteq}} for negated equalities. The following declaration
252 stems from Isabelle/HOL itself:%
255 \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
257 \isacommand{translations}\ {\isachardoublequote}x\ {\isasymnoteq}{\isasymignore}\ y{\isachardoublequote}\ {\isasymrightleftharpoons}\ {\isachardoublequote}{\isasymnot}\ {\isacharparenleft}x\ {\isacharequal}\ y{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
259 \begin{isamarkuptext}%
260 \noindent Normally one would introduce derived concepts like this
261 within the logic, using \isakeyword{consts} + \isakeyword{defs}
262 instead of \isakeyword{syntax} + \isakeyword{translations}. The
263 present formulation has the virtue that expressions are immediately
264 replaced by the ``definition'' upon parsing; the effect is reversed
267 This sort of translation is appropriate when the defined concept is
268 a trivial variation on an existing one. On the other hand, syntax
269 translations do not scale up well to large hierarchies of concepts.
270 Translations do not replace definitions!%
274 \isamarkupsection{Document Preparation \label{sec:document-preparation}%
278 \begin{isamarkuptext}%
279 Isabelle/Isar is centered around the concept of \bfindex{formal
280 proof documents}\index{documents|bold}. The outcome of a formal
281 development effort is meant to be a human-readable record, presented
282 as browsable PDF file or printed on paper. The overall document
283 structure follows traditional mathematical articles, with sections,
284 intermediate explanations, definitions, theorems and proofs.
286 \medskip The Isabelle document preparation system essentially acts
287 as a front-end to {\LaTeX}. After checking specifications and
288 proofs formally, the theory sources are turned into typesetting
289 instructions in a schematic manner. This lets you write authentic
290 reports on theory developments with little effort: many technical
291 consistency checks are handled by the system.
293 Here is an example to illustrate the idea of Isabelle document
300 \begin{isamarkuptext}%
301 The following datatype definition of \isa{{\isacharprime}a\ bintree} models
302 binary trees with nodes being decorated by elements of type \isa{{\isacharprime}a}.%
305 \isacommand{datatype}\ {\isacharprime}a\ bintree\ {\isacharequal}\isanewline
306 \ \ \ \ \ Leaf\ {\isacharbar}\ Branch\ {\isacharprime}a\ \ {\isachardoublequote}{\isacharprime}a\ bintree{\isachardoublequote}\ \ {\isachardoublequote}{\isacharprime}a\ bintree{\isachardoublequote}\isamarkupfalse%
308 \begin{isamarkuptext}%
309 \noindent The datatype induction rule generated here is of the form
311 \ {\isasymlbrakk}P\ Leaf{\isacharsemicolon}\isanewline
312 \isaindent{\ \ \ \ }{\isasymAnd}a\ bintree{\isadigit{1}}\ bintree{\isadigit{2}}{\isachardot}\isanewline
313 \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
314 \isaindent{\ }{\isasymLongrightarrow}\ P\ bintree%
321 \begin{isamarkuptext}%
322 \noindent The above document output has been produced as follows:
326 The following datatype definition of {\at}{\ttlbrace}text "'a bintree"{\ttrbrace}
327 models binary trees with nodes being decorated by elements
328 of type {\at}{\ttlbrace}typ 'a{\ttrbrace}.
331 datatype 'a bintree =
332 Leaf | Branch 'a "'a bintree" "'a bintree"
336 {\ttback}noindent The datatype induction rule generated here is
337 of the form {\at}{\ttlbrace}thm [display] bintree.induct [no_vars]{\ttrbrace}
339 \end{ttbox}\vspace{-\medskipamount}
341 \noindent Here we have augmented the theory by formal comments
342 (using \isakeyword{text} blocks), the informal parts may again refer
343 to formal entities by means of ``antiquotations'' (such as
344 \texttt{\at}\verb,{text "'a bintree"}, or
345 \texttt{\at}\verb,{typ 'a},), see also \S\ref{sec:doc-prep-text}.%
349 \isamarkupsubsection{Isabelle Sessions%
353 \begin{isamarkuptext}%
354 In contrast to the highly interactive mode of Isabelle/Isar theory
355 development, the document preparation stage essentially works in
356 batch-mode. An Isabelle \bfindex{session} consists of a collection
357 of source files that may contribute to an output document. Each
358 session is derived from a single parent, usually an object-logic
359 image like \texttt{HOL}. This results in an overall tree structure,
360 which is reflected by the output location in the file system
361 (usually rooted at \verb,~/isabelle/browser_info,).
363 \medskip The easiest way to manage Isabelle sessions is via
364 \texttt{isatool mkdir} (generates an initial session source setup)
365 and \texttt{isatool make} (run sessions controlled by
366 \texttt{IsaMakefile}). For example, a new session
367 \texttt{MySession} derived from \texttt{HOL} may be produced as
371 isatool mkdir HOL MySession
375 The \texttt{isatool make} job also informs about the file-system
376 location of the ultimate results. The above dry run should be able
377 to produce some \texttt{document.pdf} (with dummy title, empty table
378 of contents etc.). Any failure at this stage usually indicates
379 technical problems of the {\LaTeX} installation.\footnote{Especially
380 make sure that \texttt{pdflatex} is present; if in doubt one may
381 fall back on DVI output by changing \texttt{usedir} options in
382 \texttt{IsaMakefile} \cite{isabelle-sys}.}
384 \medskip The detailed arrangement of the session sources is as
389 \item Directory \texttt{MySession} holds the required theory files
390 $T@1$\texttt{.thy}, \dots, $T@n$\texttt{.thy}.
392 \item File \texttt{MySession/ROOT.ML} holds appropriate ML commands
393 for loading all wanted theories, usually just
394 ``\texttt{use_thy"$T@i$";}'' for any $T@i$ in leaf position of the
397 \item Directory \texttt{MySession/document} contains everything
398 required for the {\LaTeX} stage; only \texttt{root.tex} needs to be
401 The latter file holds appropriate {\LaTeX} code to commence a
402 document (\verb,\documentclass, etc.), and to include the generated
403 files $T@i$\texttt{.tex} for each theory. Isabelle will generate a
404 file \texttt{session.tex} holding {\LaTeX} commands to include all
405 generated theory output files in topologically sorted order, so
406 \verb,\input{session}, in the body of \texttt{root.tex} does the job
409 \item \texttt{IsaMakefile} holds appropriate dependencies and
410 invocations of Isabelle tools to control the batch job. In fact,
411 several sessions may be managed by the same \texttt{IsaMakefile}.
412 See the \emph{Isabelle System Manual} \cite{isabelle-sys}
413 for further details, especially on
414 \texttt{isatool usedir} and \texttt{isatool make}.
418 One may now start to populate the directory \texttt{MySession}, and
419 the file \texttt{MySession/ROOT.ML} accordingly. The file
420 \texttt{MySession/document/root.tex} should also be adapted at some
421 point; the default version is mostly self-explanatory. Note that
422 \verb,\isabellestyle, enables fine-tuning of the general appearance
423 of characters and mathematical symbols (see also
424 \S\ref{sec:doc-prep-symbols}).
426 Especially observe the included {\LaTeX} packages \texttt{isabelle}
427 (mandatory), \texttt{isabellesym} (required for mathematical
428 symbols), and the final \texttt{pdfsetup} (provides sane defaults
429 for \texttt{hyperref}, including URL markup). All three are
430 distributed with Isabelle. Further packages may be required in
431 particular applications, say for unusual mathematical symbols.
433 \medskip Any additional files for the {\LaTeX} stage go into the
434 \texttt{MySession/document} directory as well. In particular,
435 adding a file named \texttt{root.bib} causes an automatic run of
436 \texttt{bibtex} to process a bibliographic database; see also
437 \texttt{isatool document} \cite{isabelle-sys}.
439 \medskip Any failure of the document preparation phase in an
440 Isabelle batch session leaves the generated sources in their target
441 location, identified by the accompanying error message. This lets
442 you trace {\LaTeX} problems with the generated files at hand.%
446 \isamarkupsubsection{Structure Markup%
450 \begin{isamarkuptext}%
451 The large-scale structure of Isabelle documents follows existing
452 {\LaTeX} conventions, with chapters, sections, subsubsections etc.
453 The Isar language includes separate \bfindex{markup commands}, which
454 do not affect the formal meaning of a theory (or proof), but result
455 in corresponding {\LaTeX} elements.
457 There are separate markup commands depending on the textual context:
458 in header position (just before \isakeyword{theory}), within the
459 theory body, or within a proof. The header needs to be treated
460 specially here, since ordinary theory and proof commands may only
461 occur \emph{after} the initial \isakeyword{theory} specification.
465 \begin{tabular}{llll}
466 header & theory & proof & default meaning \\\hline
467 & \commdx{chapter} & & \verb,\chapter, \\
468 \commdx{header} & \commdx{section} & \commdx{sect} & \verb,\section, \\
469 & \commdx{subsection} & \commdx{subsect} & \verb,\subsection, \\
470 & \commdx{subsubsection} & \commdx{subsubsect} & \verb,\subsubsection, \\
475 From the Isabelle perspective, each markup command takes a single
476 $text$ argument (delimited by \verb,",~\isa{{\isasymdots}}~\verb,", or
477 \verb,{,\verb,*,~\isa{{\isasymdots}}~\verb,*,\verb,},). After stripping any
478 surrounding white space, the argument is passed to a {\LaTeX} macro
479 \verb,\isamarkupXYZ, for command \isakeyword{XYZ}. These macros are
480 defined in \verb,isabelle.sty, according to the meaning given in the
481 rightmost column above.
483 \medskip The following source fragment illustrates structure markup
484 of a theory. Note that {\LaTeX} labels may be included inside of
485 section headings as well.
488 header {\ttlbrace}* Some properties of Foo Bar elements *{\ttrbrace}
490 theory Foo_Bar = Main:
492 subsection {\ttlbrace}* Basic definitions *{\ttrbrace}
500 subsection {\ttlbrace}* Derived rules *{\ttrbrace}
505 subsection {\ttlbrace}* Main theorem {\ttback}label{\ttlbrace}sec:main-theorem{\ttrbrace} *{\ttrbrace}
510 \end{ttbox}\vspace{-\medskipamount}
512 You may occasionally want to change the meaning of markup commands,
513 say via \verb,\renewcommand, in \texttt{root.tex}. For example,
514 \verb,\isamarkupheader, is a good candidate for some tuning. We
515 could move it up in the hierarchy to become \verb,\chapter,.
518 \renewcommand{\isamarkupheader}[1]{\chapter{#1}}
521 \noindent Now we must change the document class given in
522 \texttt{root.tex} to something that supports chapters. A suitable
523 command is \verb,\documentclass{report},.
525 \medskip The {\LaTeX} macro \verb,\isabellecontext, is maintained to
526 hold the name of the current theory context. This is particularly
527 useful for document headings:
530 \renewcommand{\isamarkupheader}[1]
531 {\chapter{#1}\markright{THEORY~\isabellecontext}}
534 \noindent Make sure to include something like
535 \verb,\pagestyle{headings}, in \texttt{root.tex}; the document
536 should have more than two pages to show the effect.%
540 \isamarkupsubsection{Formal Comments and Antiquotations \label{sec:doc-prep-text}%
544 \begin{isamarkuptext}%
545 Isabelle \bfindex{source comments}, which are of the form
546 \verb,(,\verb,*,~\isa{{\isasymdots}}~\verb,*,\verb,),, essentially act like
547 white space and do not really contribute to the content. They
548 mainly serve technical purposes to mark certain oddities in the raw
549 input text. In contrast, \bfindex{formal comments} are portions of
550 text that are associated with formal Isabelle/Isar commands
551 (\bfindex{marginal comments}), or as standalone paragraphs within a
552 theory or proof context (\bfindex{text blocks}).
554 \medskip Marginal comments are part of each command's concrete
555 syntax \cite{isabelle-ref}; the common form is ``\verb,--,~$text$''
556 where $text$ is delimited by \verb,",\isa{{\isasymdots}}\verb,", or
557 \verb,{,\verb,*,~\isa{{\isasymdots}}~\verb,*,\verb,}, as before. Multiple
558 marginal comments may be given at the same time. Here is a simple
562 \isacommand{lemma}\ {\isachardoublequote}A\ {\isacharminus}{\isacharminus}{\isachargreater}\ A{\isachardoublequote}\isanewline
564 \isamarkupcmt{a triviality of propositional logic%
568 \isamarkupcmt{(should not really bother)%
572 \isacommand{by}\ {\isacharparenleft}rule\ impI{\isacharparenright}\ %
573 \isamarkupcmt{implicit assumption step involved here%
577 \begin{isamarkuptext}%
578 \noindent The above output has been produced as follows:
582 -- "a triviality of propositional logic"
583 -- "(should not really bother)"
584 by (rule impI) -- "implicit assumption step involved here"
587 From the {\LaTeX} viewpoint, ``\verb,--,'' acts like a markup
588 command, associated with the macro \verb,\isamarkupcmt, (taking a
591 \medskip Text blocks are introduced by the commands \bfindex{text}
592 and \bfindex{txt}, for theory and proof contexts, respectively.
593 Each takes again a single $text$ argument, which is interpreted as a
594 free-form paragraph in {\LaTeX} (surrounded by some additional
595 vertical space). This behavior may be changed by redefining the
596 {\LaTeX} environments of \verb,isamarkuptext, or
597 \verb,isamarkuptxt,, respectively (via \verb,\renewenvironment,) The
598 text style of the body is determined by \verb,\isastyletext, and
599 \verb,\isastyletxt,; the default setup uses a smaller font within
600 proofs. This may be changed as follows:
603 \renewcommand{\isastyletxt}{\isastyletext}
606 \medskip The $text$ part of Isabelle markup commands essentially
607 inserts \emph{quoted material} into a formal text, mainly for
608 instruction of the reader. An \bfindex{antiquotation} is again a
609 formal object embedded into such an informal portion. The
610 interpretation of antiquotations is limited to some well-formedness
611 checks, with the result being pretty printed to the resulting
612 document. Quoted text blocks together with antiquotations provide
613 an attractive means of referring to formal entities, with good
614 confidence in getting the technical details right (especially syntax
617 The general syntax of antiquotations is as follows:
618 \texttt{{\at}{\ttlbrace}$name$ $arguments${\ttrbrace}}, or
619 \texttt{{\at}{\ttlbrace}$name$ [$options$] $arguments${\ttrbrace}}
620 for a comma-separated list of options consisting of a $name$ or
621 \texttt{$name$=$value$} each. The syntax of $arguments$ depends on
622 the kind of antiquotation, it generally follows the same conventions
623 for types, terms, or theorems as in the formal part of a theory.
625 \medskip This sentence demonstrates quotations and antiquotations:
626 \isa{{\isasymlambda}x\ y{\isachardot}\ x} is a well-typed term.
628 \medskip\noindent The output above was produced as follows:
631 This sentence demonstrates quotations and antiquotations:
632 {\at}{\ttlbrace}term "%x y. x"{\ttrbrace} is a well-typed term.
634 \end{ttbox}\vspace{-\medskipamount}
636 The notational change from the ASCII character~\verb,%, to the
637 symbol~\isa{{\isasymlambda}} reveals that Isabelle printed this term, after
638 parsing and type-checking. Document preparation enables symbolic
641 \medskip The next example includes an option to modify Isabelle's
642 \verb,show_types, flag. The antiquotation
643 \texttt{{\at}}\verb,{term [show_types] "%x y. x"}, produces the
644 output \isa{{\isasymlambda}{\isacharparenleft}x{\isasymColon}{\isacharprime}a{\isacharparenright}\ y{\isasymColon}{\isacharprime}b{\isachardot}\ x}. Type inference has figured
645 out the most general typings in the present theory context. Terms
646 may acquire different typings due to constraints imposed by their
647 environment; within a proof, for example, variables are given the
648 same types as they have in the main goal statement.
650 \medskip Several further kinds of antiquotations and options are
651 available \cite{isabelle-sys}. Here are a few commonly used
657 \texttt{\at}\verb,{typ,~$\tau$\verb,}, & print type $\tau$ \\
658 \texttt{\at}\verb,{term,~$t$\verb,}, & print term $t$ \\
659 \texttt{\at}\verb,{prop,~$\phi$\verb,}, & print proposition $\phi$ \\
660 \texttt{\at}\verb,{prop [display],~$\phi$\verb,}, & print large proposition $\phi$ (with linebreaks) \\
661 \texttt{\at}\verb,{prop [source],~$\phi$\verb,}, & check proposition $\phi$, print its input \\
662 \texttt{\at}\verb,{thm,~$a$\verb,}, & print fact $a$ \\
663 \texttt{\at}\verb,{thm,~$a$~\verb,[no_vars]}, & print fact $a$, fixing schematic variables \\
664 \texttt{\at}\verb,{thm [source],~$a$\verb,}, & check availability of fact $a$, print its name \\
665 \texttt{\at}\verb,{text,~$s$\verb,}, & print uninterpreted text $s$ \\
670 Note that \attrdx{no_vars} given above is \emph{not} an
671 antiquotation option, but an attribute of the theorem argument given
672 here. This might be useful with a diagnostic command like
673 \isakeyword{thm}, too.
675 \medskip The \texttt{\at}\verb,{text, $s$\verb,}, antiquotation is
676 particularly interesting. Embedding uninterpreted text within an
677 informal body might appear useless at first sight. Here the key
678 virtue is that the string $s$ is processed as Isabelle output,
679 interpreting Isabelle symbols appropriately.
681 For example, \texttt{\at}\verb,{text "\<forall>\<exists>"}, produces \isa{{\isasymforall}{\isasymexists}}, according to the standard interpretation of these symbol
682 (cf.\ \S\ref{sec:doc-prep-symbols}). Thus we achieve consistent
683 mathematical notation in both the formal and informal parts of the
684 document very easily, independently of the term language of
685 Isabelle. Manual {\LaTeX} code would leave more control over the
686 typesetting, but is also slightly more tedious.%
690 \isamarkupsubsection{Interpretation of Symbols \label{sec:doc-prep-symbols}%
694 \begin{isamarkuptext}%
695 As has been pointed out before (\S\ref{sec:syntax-symbols}),
696 Isabelle symbols are the smallest syntactic entities --- a
697 straightforward generalization of ASCII characters. While Isabelle
698 does not impose any interpretation of the infinite collection of
699 named symbols, {\LaTeX} documents use canonical glyphs for certain
700 standard symbols \cite[appendix~A]{isabelle-sys}.
702 The {\LaTeX} code produced from Isabelle text follows a simple
703 scheme. You can tune the final appearance by redefining certain
704 macros, say in \texttt{root.tex} of the document.
708 \item 7-bit ASCII characters: letters \texttt{A\dots Z} and
709 \texttt{a\dots z} are output directly, digits are passed as an
710 argument to the \verb,\isadigit, macro, other characters are
711 replaced by specifically named macros of the form
714 \item Named symbols: \verb,\,\verb,<XYZ>, is turned into
715 \verb,{\isasymXYZ},; note the additional braces.
717 \item Named control symbols: \verb,\,\verb,<^XYZ>, is turned into
718 \verb,\isactrlXYZ,; subsequent symbols may act as arguments if the
719 control macro is defined accordingly.
723 You may occasionally wish to give new {\LaTeX} interpretations of
724 named symbols. This merely requires an appropriate definition of
725 \verb,\isasymXYZ,, for \verb,\,\verb,<XYZ>, (see
726 \texttt{isabelle.sty} for working examples). Control symbols are
727 slightly more difficult to get right, though.
729 \medskip The \verb,\isabellestyle, macro provides a high-level
730 interface to tune the general appearance of individual symbols. For
731 example, \verb,\isabellestyle{it}, uses the italics text style to
732 mimic the general appearance of the {\LaTeX} math mode; double
733 quotes are not printed at all. The resulting quality of typesetting
734 is quite good, so this should be the default style for work that
735 gets distributed to a broader audience.%
739 \isamarkupsubsection{Suppressing Output \label{sec:doc-prep-suppress}%
743 \begin{isamarkuptext}%
744 By default, Isabelle's document system generates a {\LaTeX} file for
745 each theory that gets loaded while running the session. The
746 generated \texttt{session.tex} will include all of these in order of
747 appearance, which in turn gets included by the standard
748 \texttt{root.tex}. Certainly one may change the order or suppress
749 unwanted theories by ignoring \texttt{session.tex} and load
750 individual files directly in \texttt{root.tex}. On the other hand,
751 such an arrangement requires additional maintenance whenever the
752 collection of theories changes.
754 Alternatively, one may tune the theory loading process in
755 \texttt{ROOT.ML} itself: traversal of the theory dependency graph
756 may be fine-tuned by adding \verb,use_thy, invocations, although
757 topological sorting still has to be observed. Moreover, the ML
758 operator \verb,no_document, temporarily disables document generation
759 while executing a theory loader command. Its usage is like this:
762 no_document use_thy "T";
765 \medskip Theory output may be suppressed more selectively. Research
766 articles and slides usually do not include the formal content in
767 full. Delimiting \bfindex{ignored material} by the special source
768 comments \verb,(,\verb,*,\verb,<,\verb,*,\verb,), and
769 \verb,(,\verb,*,\verb,>,\verb,*,\verb,), tells the document
770 preparation system to suppress these parts; the formal checking of
771 the theory is unchanged, of course.
773 In this example, we hide a theory's \isakeyword{theory} and
774 \isakeyword{end} brackets:
779 \verb,(,\verb,*,\verb,<,\verb,*,\verb,), \\
780 \texttt{theory T = Main:} \\
781 \verb,(,\verb,*,\verb,>,\verb,*,\verb,), \\
783 \verb,(,\verb,*,\verb,<,\verb,*,\verb,), \\
785 \verb,(,\verb,*,\verb,>,\verb,*,\verb,), \\
790 Text may be suppressed in a fine-grained manner. We may even hide
791 vital parts of a proof, pretending that things have been simpler
792 than they really were. For example, this ``fully automatic'' proof
796 \isacommand{lemma}\ {\isachardoublequote}x\ {\isasymnoteq}\ {\isacharparenleft}{\isadigit{0}}{\isacharcolon}{\isacharcolon}int{\isacharparenright}\ {\isasymLongrightarrow}\ {\isadigit{0}}\ {\isacharless}\ x\ {\isacharasterisk}\ x{\isachardoublequote}\isanewline
798 \isacommand{by}\ {\isacharparenleft}auto{\isacharparenright}\isamarkupfalse%
800 \begin{isamarkuptext}%
801 \noindent Here the real source of the proof has been as follows:
804 by (auto(*<*)simp add: int_less_le(*>*))
808 \medskip Suppressing portions of printed text demands care. You
809 should not misrepresent the underlying theory development. It is
810 easy to invalidate the visible text by hiding references to
813 Authentic reports of Isabelle/Isar theories, say as part of a
814 library, should suppress nothing. Other users may need the full
815 information for their own derivative work. If a particular
816 formalization appears inadequate for general public coverage, it is
817 often more appropriate to think of a better way in the first place.
819 \medskip Some technical subtleties of the
820 \verb,(,\verb,*,\verb,<,\verb,*,\verb,),~\verb,(,\verb,*,\verb,>,\verb,*,\verb,),
821 elements need to be kept in mind, too --- the system performs few
822 sanity checks here. Arguments of markup commands and formal
823 comments must not be hidden, otherwise presentation fails. Open and
824 close parentheses need to be inserted carefully; it is easy to hide
825 the wrong parts, especially after rearranging the theory text.%
832 %%% TeX-master: "root"