%

\begin{isabellebody}%

\def\isabellecontext{Documents}%

\isamarkupfalse%

%

\isamarkupsection{Concrete syntax \label{sec:concrete-syntax}%

}

\isamarkuptrue%

%

\begin{isamarkuptext}%

Concerning Isabelle's ``inner'' language of simply-typed \isa{{\isasymlambda}}-calculus, the core concept of Isabelle's elaborate infrastructure

  for concrete syntax is that of general \bfindex{mixfix annotations}.

  Associated with any kind of name and type declaration, mixfixes give

  rise both to grammar productions for the parser and output templates

  for the pretty printer.

  In full generality, the whole affair of parser and pretty printer

  configuration is rather subtle.  Any syntax specifications given by

  end-users need to interact properly with the existing setup of

  Isabelle/Pure and Isabelle/HOL; see \cite{isabelle-ref} for further

  details.  It is particularly important to get the precedence of new

  syntactic constructs right, avoiding ambiguities with existing

  elements.

  \medskip Subsequently we introduce a few simple declaration forms

  that already cover the most common situations fairly well.%

\end{isamarkuptext}%

\isamarkuptrue%

%

\isamarkupsubsection{Infix annotations%

}

\isamarkuptrue%

%

\begin{isamarkuptext}%

Syntax annotations may be included wherever constants are declared

  directly or indirectly, including \isacommand{consts},

  \isacommand{constdefs}, or \isacommand{datatype} (for the

  constructor operations).  Type-constructors may be annotated as

  well, although this is less frequently encountered in practice

  (\isa{{\isacharasterisk}} and \isa{{\isacharplus}} types may come to mind).

  Infix declarations\index{infix annotations} provide a useful special

  case of mixfixes, where users need not care about the full details

  of priorities, nesting, spacing, etc.  The subsequent example of the

  exclusive-or operation on boolean values illustrates typical infix

  declarations.%

\end{isamarkuptext}%

\isamarkuptrue%

\isacommand{constdefs}\isanewline

\ \ xor\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}bool\ {\isasymRightarrow}\ bool\ {\isasymRightarrow}\ bool{\isachardoublequote}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequote}{\isacharbrackleft}{\isacharplus}{\isacharbrackright}{\isachardoublequote}\ {\isadigit{6}}{\isadigit{0}}{\isacharparenright}\isanewline

\ \ {\isachardoublequote}A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B\ {\isasymequiv}\ {\isacharparenleft}A\ {\isasymand}\ {\isasymnot}\ B{\isacharparenright}\ {\isasymor}\ {\isacharparenleft}{\isasymnot}\ A\ {\isasymand}\ B{\isacharparenright}{\isachardoublequote}\isamarkupfalse%

%

\begin{isamarkuptext}%

Any curried function with at least two arguments may be associated

  with infix syntax: \isa{xor\ A\ B} and \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B} refer to

  the same expression internally.  In partial applications with less

  than two operands there is a special notation with \isa{op} prefix:

  \isa{xor} without arguments is represented as \isa{op\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}};

  combined with plain prefix application this turns \isa{xor\ A}

  into \isa{op\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ A}.

  \medskip The string \isa{{\isachardoublequote}{\isacharbrackleft}{\isacharplus}{\isacharbrackright}{\isachardoublequote}} in the above declaration

  refers to the bit of concrete syntax to represent the operator,

  while the number \isa{{\isadigit{6}}{\isadigit{0}}} determines the precedence of the whole

  construct.

  As it happens, Isabelle/HOL already spends many popular combinations

  of ASCII symbols for its own use, including both \isa{{\isacharplus}} and

  \isa{{\isacharplus}{\isacharplus}}.  Slightly more awkward combinations like the present

  \isa{{\isacharbrackleft}{\isacharplus}{\isacharbrackright}} tend to be available for user extensions.  The current

  arrangement of inner syntax may be inspected via

  \commdx{print\protect\_syntax}, albeit its output is enormous.

  Operator precedence also needs some special considerations.  The

  admissible range is 0--1000.  Very low or high priorities are

  basically reserved for the meta-logic.  Syntax of Isabelle/HOL

  mainly uses the range of 10--100: the equality infix \isa{{\isacharequal}} is

  centered at 50, logical connectives (like \isa{{\isasymor}} and \isa{{\isasymand}}) are below 50, and algebraic ones (like \isa{{\isacharplus}} and \isa{{\isacharasterisk}}) above 50.  User syntax should strive to coexist with common

  HOL forms, or use the mostly unused range 100--900.

  \medskip The keyword \isakeyword{infixl} specifies an operator that

  is nested to the \emph{left}: in iterated applications the more

  complex expression appears on the left-hand side: \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} refers to nesting to the \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}}.  In contrast,

  a \emph{non-oriented} declaration via \isakeyword{infix} would

  always demand explicit parentheses.

  Many binary operations observe the associative law, so the exact

  grouping does not matter.  Nevertheless, formal statements need be

  given in a particular format, associativity needs to be treated

  explicitly within the logic.  Exclusive-or is happens to be

  associative, as shown below.%

\end{isamarkuptext}%

\isamarkuptrue%

\isacommand{lemma}\ xor{\isacharunderscore}assoc{\isacharcolon}\ {\isachardoublequote}{\isacharparenleft}A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B{\isacharparenright}\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ C\ {\isacharequal}\ A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ {\isacharparenleft}B\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ C{\isacharparenright}{\isachardoublequote}\isanewline

\ \ \isamarkupfalse%

\isacommand{by}\ {\isacharparenleft}auto\ simp\ add{\isacharcolon}\ xor{\isacharunderscore}def{\isacharparenright}\isamarkupfalse%

%

\begin{isamarkuptext}%

Such rules may be used in simplification to regroup nested

  expressions as required.  Note that the system would actually print

  the above statement as \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ C\ {\isacharequal}\ A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ {\isacharparenleft}B\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ C{\isacharparenright}}

  (due to nesting to the left).  We have preferred to give the fully

  parenthesized form in the text for clarity.  Only in rare situations

  one may consider to force parentheses by use of non-oriented infix

  syntax; equality would probably be a typical candidate.%

\end{isamarkuptext}%

\isamarkuptrue%

%

\isamarkupsubsection{Mathematical symbols \label{sec:thy-present-symbols}%

}

\isamarkuptrue%

%

\begin{isamarkuptext}%

Concrete syntax based on plain ASCII characters has its inherent

  limitations.  Rich mathematical notation demands a larger repertoire

  of symbols.  Several standards of extended character sets have been

  proposed over decades, but none has become universally available so

  far, not even Unicode\index{Unicode}.

  Isabelle supports a generic notion of \bfindex{symbols} as the

  smallest entities of source text, without referring to internal

  encodings.  Such ``generalized characters'' may be of one of the

  following three kinds:

  \begin{enumerate}

  \item Traditional 7-bit ASCII characters.

  \item Named symbols: \verb,\,\verb,<,$ident$\verb,>, (or

  \verb,\\,\verb,<,$ident$\verb,>,).

  \item Named control symbols: \verb,\,\verb,<^,$ident$\verb,>, (or

  \verb,\\,\verb,<^,$ident$\verb,>,).

  \end{enumerate}

  Here $ident$ may be any identifier according to the usual Isabelle

  conventions.  This results in an infinite store of symbols, whose

  interpretation is left to further front-end tools.  For example, the

  \verb,\,\verb,<forall>, symbol of Isabelle is really displayed as

  $\forall$ --- both by the user-interface of Proof~General + X-Symbol

  and the Isabelle document processor (see \S\ref{FIXME}).

  A list of standard Isabelle symbols is given in

  \cite[appendix~A]{isabelle-sys}.  Users may introduce their own

  interpretation of further symbols by configuring the appropriate

  front-end tool accordingly, e.g.\ defining appropriate {\LaTeX}

  macros for document preparation.  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.

  \medskip The following version of our \isa{xor} definition uses a

  standard Isabelle symbol to achieve typographically pleasing output.%

\end{isamarkuptext}%

\isamarkuptrue%

\isamarkupfalse%

\isamarkupfalse%

\isacommand{constdefs}\isanewline

\ \ xor\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}bool\ {\isasymRightarrow}\ bool\ {\isasymRightarrow}\ bool{\isachardoublequote}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequote}{\isasymoplus}{\isachardoublequote}\ {\isadigit{6}}{\isadigit{0}}{\isacharparenright}\isanewline

\ \ {\isachardoublequote}A\ {\isasymoplus}\ B\ {\isasymequiv}\ {\isacharparenleft}A\ {\isasymand}\ {\isasymnot}\ B{\isacharparenright}\ {\isasymor}\ {\isacharparenleft}{\isasymnot}\ A\ {\isasymand}\ B{\isacharparenright}{\isachardoublequote}\isamarkupfalse%

\isamarkupfalse%

%

\begin{isamarkuptext}%

The X-Symbol package within Proof~General provides several input

  methods to enter \isa{{\isasymoplus}} in the text.  If all fails one may just

  type \verb,\,\verb,<oplus>, by hand; the display is adapted

  immediately after continuing further input.

  \medskip A slightly more refined scheme is to provide alternative

  syntax via the \bfindex{print mode} concept of Isabelle (see also

  \cite{isabelle-ref}).  By convention, the mode ``$xsymbols$'' is

  enabled whenever X-Symbol is active.  Consider the following hybrid

  declaration of \isa{xor}.%

\end{isamarkuptext}%

\isamarkuptrue%

\isamarkupfalse%

\isamarkupfalse%

\isacommand{constdefs}\isanewline

\ \ 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

\ \ {\isachardoublequote}A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}{\isasymignore}\ B\ {\isasymequiv}\ {\isacharparenleft}A\ {\isasymand}\ {\isasymnot}\ B{\isacharparenright}\ {\isasymor}\ {\isacharparenleft}{\isasymnot}\ A\ {\isasymand}\ B{\isacharparenright}{\isachardoublequote}\isanewline

\isanewline

\isamarkupfalse%

\isacommand{syntax}\ {\isacharparenleft}xsymbols{\isacharparenright}\isanewline

\ \ xor\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}bool\ {\isasymRightarrow}\ bool\ {\isasymRightarrow}\ bool{\isachardoublequote}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequote}{\isasymoplus}{\isasymignore}{\isachardoublequote}\ {\isadigit{6}}{\isadigit{0}}{\isacharparenright}\isamarkupfalse%

\isamarkupfalse%

%

\begin{isamarkuptext}%

Here the \commdx{syntax} command acts like \isakeyword{consts}, but

  without declaring a logical constant, and with an optional print

  mode specification.  Note that the type declaration given here

  merely serves for syntactic purposes, and is not checked for

  consistency with the real constant.

  \medskip Now we may write either \isa{{\isacharbrackleft}{\isacharplus}{\isacharbrackright}} or \isa{{\isasymoplus}} in

  input, while output uses the nicer syntax of $xsymbols$, provided

  that print mode is presently active.  This scheme is particularly

  useful for interactive development, with the user typing plain ASCII

  text, but gaining improved visual feedback from the system (say in

  current goal output).

  \begin{warn}

  Using alternative syntax declarations easily results in varying

  versions of input sources.  Isabelle provides no systematic way to

  convert alternative expressions back and forth.  Print modes only

  affect situations where formal entities are pretty printed by the

  Isabelle process (e.g.\ output of terms and types), but not the

  original theory text.

  \end{warn}

  \medskip The following variant makes the alternative \isa{{\isasymoplus}}

  notation only available for output.  Thus we may enforce input

  sources to refer to plain ASCII only.%

\end{isamarkuptext}%

\isamarkuptrue%

\isacommand{syntax}\ {\isacharparenleft}xsymbols\ \isakeyword{output}{\isacharparenright}\isanewline

\ \ xor\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}bool\ {\isasymRightarrow}\ bool\ {\isasymRightarrow}\ bool{\isachardoublequote}\ \ \ \ {\isacharparenleft}\isakeyword{infixl}\ {\isachardoublequote}{\isasymoplus}{\isasymignore}{\isachardoublequote}\ {\isadigit{6}}{\isadigit{0}}{\isacharparenright}\isamarkupfalse%

%

\isamarkupsubsection{Prefix annotations%

}

\isamarkuptrue%

%

\begin{isamarkuptext}%

Prefix syntax annotations\index{prefix annotation} are just a very

  degenerate of the general mixfix form \cite{isabelle-ref}, without

  any template arguments or priorities --- just some piece of literal

  syntax.

  The following example illustrates this idea idea by associating

  common symbols with the constructors of a currency datatype.%

\end{isamarkuptext}%

\isamarkuptrue%

\isacommand{datatype}\ currency\ {\isacharequal}\isanewline

\ \ \ \ Euro\ nat\ \ \ \ {\isacharparenleft}{\isachardoublequote}{\isasymeuro}{\isachardoublequote}{\isacharparenright}\isanewline

\ \ {\isacharbar}\ Pounds\ nat\ \ {\isacharparenleft}{\isachardoublequote}{\isasympounds}{\isachardoublequote}{\isacharparenright}\isanewline

\ \ {\isacharbar}\ Yen\ nat\ \ \ \ \ {\isacharparenleft}{\isachardoublequote}{\isasymyen}{\isachardoublequote}{\isacharparenright}\isanewline

\ \ {\isacharbar}\ Dollar\ nat\ \ {\isacharparenleft}{\isachardoublequote}{\isachardollar}{\isachardoublequote}{\isacharparenright}\isamarkupfalse%

%

\begin{isamarkuptext}%

Here the degenerate mixfix annotations on the rightmost column

  happen to consist of a single Isabelle symbol each:

  \verb,\,\verb,<euro>,, \verb,\,\verb,<pounds>,,

  \verb,\,\verb,<yen>,, \verb,$,.

  Recall that a constructor like \isa{Euro} actually is a function

  \isa{nat\ {\isasymRightarrow}\ currency}.  An expression like \isa{Euro\ {\isadigit{1}}{\isadigit{0}}} will

  be printed as \isa{{\isasymeuro}\ {\isadigit{1}}{\isadigit{0}}}.  Only the head of the application is

  subject to our concrete syntax; this simple form already achieves

  conformance with notational standards of the European Commission.

  \medskip Certainly, the same idea of prefix syntax also works for

  \isakeyword{consts}, \isakeyword{constdefs} etc.  For example, we

  might introduce a (slightly unrealistic) function to calculate an

  abstract currency value, by cases on the datatype constructors and

  fixed exchange rates.  The funny symbol used here is that of

  \verb,\<currency>,.%

\end{isamarkuptext}%

\isamarkuptrue%

\isacommand{consts}\isanewline

\ \ currency\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}currency\ {\isasymRightarrow}\ nat{\isachardoublequote}\ \ \ \ {\isacharparenleft}{\isachardoublequote}{\isasymcurrency}{\isachardoublequote}{\isacharparenright}\isamarkupfalse%

%

\isamarkupsubsection{Syntax translations \label{sec:def-translations}%

}

\isamarkuptrue%

%

\begin{isamarkuptext}%

FIXME

\index{syntax translations|(}%

\index{translations@\isacommand {translations} (command)|(}

Isabelle offers an additional definitional facility,

\textbf{syntax translations}.

They resemble macros: upon parsing, the defined concept is immediately

replaced by its definition.  This effect is reversed upon printing.  For example,

the symbol \isa{{\isasymnoteq}} is defined via a syntax translation:%

\end{isamarkuptext}%

\isamarkuptrue%

\isacommand{translations}\ {\isachardoublequote}x\ {\isasymnoteq}\ y{\isachardoublequote}\ {\isasymrightleftharpoons}\ {\isachardoublequote}{\isasymnot}{\isacharparenleft}x\ {\isacharequal}\ y{\isacharparenright}{\isachardoublequote}\isamarkupfalse%

%

\begin{isamarkuptext}%

\index{$IsaEqTrans@\isasymrightleftharpoons}

\noindent

Internally, \isa{{\isasymnoteq}} never appears.

In addition to \isa{{\isasymrightleftharpoons}} there are

\isa{{\isasymrightharpoonup}}\index{$IsaEqTrans1@\isasymrightharpoonup}

and \isa{{\isasymleftharpoondown}}\index{$IsaEqTrans2@\isasymleftharpoondown}

for uni-directional translations, which only affect

parsing or printing.  This tutorial will not cover the details of

translations.  We have mentioned the concept merely because it

crops up occasionally; a number of HOL's built-in constructs are defined

via translations.  Translations are preferable to definitions when the new 

concept is a trivial variation on an existing one.  For example, we

don't need to derive new theorems about \isa{{\isasymnoteq}}, since existing theorems

about \isa{{\isacharequal}} still apply.%

\index{syntax translations|)}%

\index{translations@\isacommand {translations} (command)|)}%

\end{isamarkuptext}%

\isamarkuptrue%

%

\isamarkupsection{Document preparation%

}

\isamarkuptrue%

%

\begin{isamarkuptext}%

Isabelle/Isar is centered around a certain notion of \bfindex{formal

  proof documents}\index{documents|bold}: ultimately the result of the

  user's theory development efforts is a human-readable record --- as

  a browsable PDF file or printed on paper.  The overall document

  structure follows traditional mathematical articles, with

  sectioning, explanations, definitions, theorem statements, and

  proofs.

  The Isar proof language \cite{Wenzel-PhD}, which is not covered in

  this book, admits to write formal proof texts that are acceptable

  both to the machine and human readers at the same time.  Thus

  marginal comments and explanations may be kept at a minimum.

  Nevertheless, Isabelle document output is still useful without

  actual Isar proof texts; formal specifications usually deserve their

  own coverage in the text, while unstructured proof scripts may be

  just ignore by readers (or intentionally suppressed from the text).

  \medskip The Isabelle document preparation system essentially acts

  like a formal front-end for {\LaTeX}.  After checking definitions

  and proofs the theory sources are turned into typesetting

  instructions, so the final document is known to observe quite strong

  ``soundness'' properties.  This enables users to write authentic

  reports on formal theory developments with little additional effort,

  the most tedious consistency checks are handled by the system.%

\end{isamarkuptext}%

\isamarkuptrue%

%

\isamarkupsubsection{Isabelle sessions%

}

\isamarkuptrue%

%

\begin{isamarkuptext}%

In contrast to the highly interactive mode of the formal parts of

  Isabelle/Isar theory development, the document preparation stage

  essentially works in batch-mode.  This revolves around the concept

  of a \bfindex{session}, which essentially consists of a collection

  of theory source files that contribute to a single output document.

  Each session is derived from a parent one (usually an object-logic

  image such as \texttt{HOL}); this results in an overall tree

  structure of Isabelle sessions.

  The canonical arrangement of source files of a session called

  \texttt{MySession} is as follows:

  \begin{itemize}

  \item Directory \texttt{MySession} contains the required theory

  files, say $A@1$\texttt{.thy}, \dots, $A@n$\texttt{.thy}.

  \item File \texttt{MySession/ROOT.ML} holds appropriate ML commands

  for loading all wanted theories, usually just

  \texttt{use_thy~"$A@i$"} for any $A@i$ in leaf position of the

  theory dependency graph.

  \item Directory \texttt{MySession/document} contains everything

  required for the {\LaTeX} stage, but 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 $A@i$\texttt{.tex} for each theory.  The

  generated file \texttt{session.tex} holds {\LaTeX} commands to

  include \emph{all} theory output files in topologically sorted

  order.

  \item In addition an \texttt{IsaMakefile} outside of directory

  \texttt{MySession} holds appropriate dependencies and invocations of

  Isabelle tools to control the batch job.  The details are covered in

  \cite{isabelle-sys}; \texttt{isatool usedir} is the most important

  entry point.

  \end{itemize}

  With everything put in its proper place, \texttt{isatool make}

  should be sufficient to process the Isabelle session completely,

  with the generated document appearing in its proper place (within

  \verb,~/isabelle/browser_info,).

  In practive, users may want to have \texttt{isatool mkdir} generate

  an initial working setup without further ado.  For example, an empty

  session \texttt{MySession} derived from \texttt{HOL} may be produced

  as follows:

\begin{verbatim}

  isatool mkdir HOL MySession

  isatool make

\end{verbatim}

  This runs the session with sensible default options, including

  verbose mode to tell the user where the result will appear.  The

  above dry run should produce should produce a single page of output

  (with a dummy title, empty table of contents etc.).  Any failure at

  that stage is likely to indicate some technical problems with your

  {\LaTeX} installation.\footnote{Especially make sure that

  \texttt{pdflatex} is present.}

  \medskip Users may now start to populate the directory

  \texttt{MySession}, and the file \texttt{MySession/ROOT.ML}

  accordingly.  \texttt{MySession/document/root.tex} should be also

  adapted at some point; the generated version is mostly

  self-explanatory.

  Realistic applications may demand additional files in

  \texttt{MySession/document} for the {\LaTeX} stage, such as

  \texttt{root.bib} for the bibliographic database.\footnote{Using

  that particular name of \texttt{root.bib}, the Isabelle document

  processor (actually \texttt{isatool document} \cite{isabelle-sys})

  will be smart enough to invoke \texttt{bibtex} accordingly.}

  \medskip Failure of the document preparation phase in an Isabelle

  batch session leaves the generated sources in there target location

  (as pointed out by the accompanied error message).  In case of

  {\LaTeX} errors, users may trace error messages at the file position

  of the generated text.%

\end{isamarkuptext}%

\isamarkuptrue%

%

\isamarkupsubsection{Structure markup%

}

\isamarkuptrue%

%

\isamarkupsubsubsection{Sections%

}

\isamarkuptrue%

%

\begin{isamarkuptext}%

The large-scale structure of Isabelle documents closely follows

  {\LaTeX} convention, with chapters, sections, subsubsections etc.

  The formal Isar language includes separate structure \bfindex{markup

  commands}, which do not effect the formal content of a theory (or

  proof), but results in corresponding {\LaTeX} elements issued to the

  output.

  There are different markup commands for different formal contexts:

  in header position (just before a \isakeyword{theory} command),

  within the theory body, or within a proof.  Note that the header

  needs to be treated specially, since ordinary theory and proof

  commands may only occur \emph{after} the initial \isakeyword{theory}

  specification.

  \smallskip

  \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,",\dots\verb,", or

  \verb,{,\verb,*,~\dots~\verb,*,\verb,},).  After stripping

  surrounding white space, the argument is passed to a {\LaTeX} macro

  \verb,\isamarkupXXX, for any command \isakeyword{XXX}.  The latter

  are defined in \verb,isabelle.sty, according to the rightmost column

  above.

  \medskip The following source fragment illustrates structure markup

  of a theory.

  \begin{ttbox}

  header {\ttlbrace}* Some properties of Foo Bar elements *{\ttrbrace}

  theory Foo_Bar = Main:

  subsection {\ttlbrace}* Basic definitions *{\ttrbrace}

  consts

    foo :: \dots

    bar :: \dots

  defs \dots

  subsection {\ttlbrace}* Derived rules *{\ttrbrace}

  lemma fooI: \dots

  lemma fooE: \dots

  subsection {\ttlbrace}* Main theorem *{\ttrbrace}

  theorem main: \dots

  end

  \end{ttbox}

  \medskip In realistic applications, users may well want to change

  the meaning of some markup commands, typically via appropriate use

  of \verb,\renewcommand, in \texttt{root.tex}.  The

  \verb,\isamarkupheader, is a good candidate for some adaption, e.g.\

  moving it up in the hierarchy to become \verb,\chapter,.

\begin{verbatim}

  \renewcommand{\isamarkupheader}[1]{\chapter{#1}}

\end{verbatim}

  Certainly, this requires to change the default

  \verb,\documentclass{article}, in \texttt{root.tex} to something

  that supports the notion of chapters in the first place, e.g.\

  \texttt{report} or \texttt{book}.

  \medskip For each generated theory output the {\LaTeX} macro

  \verb,\isabellecontext, holds the name of the formal context.  This

  is particularly useful for document headings or footings, e.g.\ like

  this:

\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} as well.  Moreover,

  the document should have more than 2 pages.%

\end{isamarkuptext}%

\isamarkuptrue%

%

\isamarkupsubsection{Formal comments and antiquotations%

}

\isamarkuptrue%

%

\begin{isamarkuptext}%

Comments of the form \verb,(*,~\dots~\verb,*),%

\end{isamarkuptext}%

\isamarkuptrue%

%

\isamarkupsubsection{Symbols and characters%

}

\isamarkuptrue%

%

\begin{isamarkuptext}%

FIXME \verb,\isabellestyle,%

\end{isamarkuptext}%

\isamarkuptrue%

%

\isamarkupsubsection{Suppressing output%

}

\isamarkuptrue%

%

\begin{isamarkuptext}%

FIXME \verb,no_document,

  FIXME \verb,(,\verb,*,\verb,<,\verb,*,\verb,),

  \verb,(,\verb,*,\verb,>,\verb,*,\verb,),%

\end{isamarkuptext}%

\isamarkuptrue%

\isamarkupfalse%

\end{isabellebody}%

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