doc-src/TutorialI/Documents/document/Documents.tex

 \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.
+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 constant
+  declaration, mixfixes affect both the 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
+  configuration is rather subtle, see \cite{isabelle-ref} for further
+  details.  Any syntax specifications given by end-users need to
+  interact properly with the existing setup of Isabelle/Pure and
+  Isabelle/HOL.  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}%

 
   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.%
+  declarations arising in practice.%
 \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
+\noindent Now \isa{xor\ A\ B} and \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B} refer to the
+  same expression internally.  Any curried function with at least two
+  arguments may be associated with infix syntax.  For 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}}; together 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 annotation
   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.
+  while the number \isa{{\isadigit{6}}{\isadigit{0}}} determines the precedence of the
+  construct (i.e.\ the syntactic priorities of the arguments and
+  result).
 
   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

   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.%
+  \isakeyword{infixr} specifies 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 have rendered \isa{A\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ B\ {\isacharbrackleft}{\isacharplus}{\isacharbrackright}\ C} illegal, but demand
+  explicit parentheses about the intended grouping.%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
 \isamarkupsubsection{Mathematical Symbols%
 }

 \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:
+  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.
+
+  There are three kinds of such ``generalized characters'' available:
 
   \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,>,).
+  \item 7-bit ASCII characters
+
+  \item named symbols: \verb,\,\verb,<,$ident$\verb,>,
+
+  \item named control symbols: \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{sec:document-prep}).
+  interpretation is left to further front-end tools.  For example,
+  both by the user-interface of Proof~General + X-Symbol and the
+  Isabelle document processor (see \S\ref{sec:document-preparation})
+  display the \verb,\,\verb,<forall>, symbol really as ``$\forall$''.
 
   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
+  front-end tool accordingly, e.g.\ by defining certain {\LaTeX}
+  macros (see also \S\ref{sec:doc-prep-symbols}).  There are also a
+  few predefined control symbols, such as \verb,\,\verb,<^sub>, and
   \verb,\,\verb,<^sup>, for sub- and superscript of the subsequent
-  (printable) symbol, respectively.
+  (printable) symbol, respectively.  For example, \verb,A\<^sup>\<star>, is
+  shown as ``\isa{A\isactrlsup {\isasymstar}}''.
 
   \medskip The following version of our \isa{xor} definition uses a
   standard Isabelle symbol to achieve typographically pleasing output.%
 \end{isamarkuptext}%
 \isamarkuptrue%

 \ \ 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.
+\noindent 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 will be
+  adapted immediately after continuing 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}.%
+  \cite{isabelle-ref}).  By convention, the mode of ``$xsymbols$'' is
+  enabled whenever Proof~General's X-Symbol mode (or {\LaTeX} output)
+  is active.  Consider the following hybrid declaration of \isa{xor}.%
 \end{isamarkuptext}%
 \isamarkuptrue%
 \isamarkupfalse%
 \isamarkupfalse%
 \isacommand{constdefs}\isanewline

 \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
+The \commdx{syntax} command introduced here acts like
+  \isakeyword{consts}, but without declaring a logical constant; an
+  optional print mode specification may be given, too.  Note that the
+  type declaration given here merely serves for syntactic purposes,
+  and is not checked for consistency with the real constant.
+
+  \medskip We may now 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).
+  that print mode is presently active.  Such an arrangement is
+  particularly useful for interactive development, where users may
+  type plain ASCII text, but gain 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.
+  Alternative syntax declarations are apt to result in varying
+  occurrences of concrete syntax in the input sources.  Isabelle
+  provides no systematic way to convert alternative syntax 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.%
+  sources to refer to plain ASCII only, but effectively disable
+  cut-and-paste from output as well.%
 \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.%
+Prefix syntax annotations\index{prefix annotation} are just another
+  degenerate form of general mixfixes \cite{isabelle-ref}, without any
+  template arguments or priorities --- just some bits of literal
+  syntax.  The following example illustrates this idea idea by
+  associating common symbols with the constructors of a 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}%
-\noindent 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>,, and \verb,$,.
-
-  Recall that a constructor like \isa{Euro} actually is a function
-  \isa{nat\ {\isasymRightarrow}\ currency}.  An expression like \isa{Euro\ {\isadigit{1}}{\isadigit{0}}} will
-  be printed as \isa{{\isasymeuro}\ {\isadigit{1}}{\isadigit{0}}}; only the head of the application is
+\noindent Here the mixfix annotations on the rightmost column happen
+  to consist of a single Isabelle symbol each: \verb,\,\verb,<euro>,,
+  \verb,\,\verb,<pounds>,, \verb,\,\verb,<yen>,, and \verb,$,.  Recall
+  that a constructor like \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.  The slightly

 \isacommand{syntax}\isanewline
 \ \ currency\ {\isacharcolon}{\isacharcolon}\ type\ \ \ \ {\isacharparenleft}{\isachardoublequote}{\isasymcurrency}{\isachardoublequote}{\isacharparenright}\isamarkupfalse%
 %
 \begin{isamarkuptext}%
 \noindent Here \isa{type} refers to the builtin syntactic category
-  of Isabelle types.  We could now write down funny things like \isa{{\isasymeuro}\ {\isacharcolon}{\isacharcolon}\ nat\ {\isasymRightarrow}\ {\isasymcurrency}}, for example.%
+  of Isabelle types.  We may now write down funny things like \isa{{\isasymeuro}\ {\isacharcolon}{\isacharcolon}\ nat\ {\isasymRightarrow}\ {\isasymcurrency}}, for example.%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
 \isamarkupsubsection{Syntax Translations \label{sec:syntax-translations}%
 }
 \isamarkuptrue%
 %
 \begin{isamarkuptext}%
-Mixfix syntax annotations work well for those situations, where a
-  constant application forms needs to be decorated by concrete syntax.
-  Just reconsider \isa{xor\ A\ B} versus \isa{A\ {\isasymoplus}\ B} covered
-  before.  Occasionally, the relationship between some piece of
-  notation and its internal form is slightly more involved.
-
+Mixfix syntax annotations work well for those situations where a
+  particular constant application forms need to be decorated by
+  concrete syntax; just reconsider \isa{xor\ A\ B} versus \isa{A\ {\isasymoplus}\ B} covered before.  Occasionally, the relationship between some
+  piece of notation and its internal form is slightly more involved.
   Here the concept of \bfindex{syntax translations} enters the scene.
+
   Using the raw \isakeyword{syntax}\index{syntax (command)} command we
-  introduce uninterpreted notational elements, while
-  \commdx{translations} relates the input forms with certain logical
-  expressions.  This essentially provides a simple mechanism for for
-  syntactic macros; even heavier transformations may be programmed in
-  ML \cite{isabelle-ref}.
-
-  \medskip A typical example of syntax translations is to decorate an
-  relational expression (i.e.\ set membership of tuples) with nice
-  symbolic notation, such as \isa{{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ sim} versus \isa{x\ {\isasymapprox}\ y}.%
+  may introduce uninterpreted notational elements, while
+  \commdx{translations} relates the input forms with more complex
+  logical expressions.  This essentially provides a simple mechanism
+  for for syntactic macros; even heavier transformations may be
+  programmed in ML \cite{isabelle-ref}.
+
+  \medskip A typical example of syntax translations is to decorate
+  relational expressions (set membership of tuples) with nice symbolic
+  notation, such as \isa{{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ sim} versus \isa{x\ {\isasymapprox}\ y}.%
 \end{isamarkuptext}%
 \isamarkuptrue%
 \isacommand{consts}\isanewline
 \ \ sim\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ set{\isachardoublequote}\isanewline
 \isanewline

 \isacommand{translations}\isanewline
 \ \ {\isachardoublequote}x\ {\isasymapprox}\ y{\isachardoublequote}\ {\isasymrightleftharpoons}\ {\isachardoublequote}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ sim{\isachardoublequote}\isamarkupfalse%
 %
 \begin{isamarkuptext}%
 \noindent Here the name of the dummy constant \isa{{\isacharunderscore}sim} does
-  not really matter, as long as it is not used otherwise.  Prefixing
+  not really matter, as long as it is not used elsewhere.  Prefixing
   an underscore is a common convention.  The \isakeyword{translations}
   declaration already uses concrete syntax on the left-hand side;
   internally we relate a raw application \isa{{\isacharunderscore}sim\ x\ y} with
   \isa{{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ sim}.
 
-  \medskip Another useful application of syntax translations is to
+  \medskip Another common application of syntax translations is to
   provide variant versions of fundamental relational expressions, such
   as \isa{{\isasymnoteq}} for negated equalities.  The following declaration
   stems from Isabelle/HOL itself:%
 \end{isamarkuptext}%
 \isamarkuptrue%

 \isamarkupfalse%
 \isacommand{translations}\ {\isachardoublequote}x\ {\isasymnoteq}{\isasymignore}\ y{\isachardoublequote}\ {\isasymrightleftharpoons}\ {\isachardoublequote}{\isasymnot}\ {\isacharparenleft}x\ {\isacharequal}\ y{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
 %
 \begin{isamarkuptext}%
 \noindent Normally one would introduce derived concepts like this
-  within the logic, using \isakeyword{consts} and \isakeyword{defs}
-  instead of \isakeyword{syntax} and \isakeyword{translations}.  The
+  within the logic, using \isakeyword{consts} + \isakeyword{defs}
+  instead of \isakeyword{syntax} + \isakeyword{translations}.  The
   present formulation has the virtue that expressions are immediately
   replaced by its ``definition'' upon parsing; the effect is reversed
   upon printing.  Internally, \isa{{\isasymnoteq}} never appears.
 
   Simulating definitions via translations is adequate for very basic
-  variations of fundamental logical concepts, when the new
-  representation is a trivial variation on an existing one.  On the
-  other hand, syntax translations do not scale up well to large
-  hierarchies of concepts built on each other.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsection{Document Preparation \label{sec:document-prep}%
-}
-\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.
+  logical concepts, where a new representation is a trivial variation
+  on an existing one.  On the other hand, syntax translations do not
+  scale up well to large hierarchies of concepts built on each other.%
+\end{isamarkuptext}%
+\isamarkuptrue%
+%
+\isamarkupsection{Document Preparation \label{sec:document-preparation}%
+}
+\isamarkuptrue%
+%
+\begin{isamarkuptext}%
+Isabelle/Isar is centered around the concept of \bfindex{formal
+  proof documents}\index{documents|bold}.  Ultimately the result of
+  the user's theory development efforts is meant to be a
+  human-readable record, presented as a browsable PDF file or printed
+  on paper.  The overall document structure follows traditional
+  mathematical articles, with sectioning, intermediate 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).
+  marginal comments and explanations may be kept at a minimum.  Even
+  without proper coverage of human-readable proofs, Isabelle document
+  is very useful to produce formally derived texts (elaborating on the
+  specifications etc.).  Unstructured proof scripts given here may be
+  just ignored by readers, or intentionally suppressed from the text
+  by the writer (see also \S\ref{sec:doc-prep-suppress}).
 
   \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.%
+  like a formal front-end to {\LaTeX}.  After checking specifications
+  and proofs, the theory sources are turned into typesetting
+  instructions in a well-defined manner.  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:
+In contrast to the highly interactive mode of Isabelle/Isar theory
+  development, the document preparation stage essentially works in
+  batch-mode.  An Isabelle \bfindex{session} essentially consists of a
+  collection of theory source files that contribute to a single output
+  document eventually.  Session is derived from a single parent each
+  (usually an object-logic image like \texttt{HOL}), resulting in an
+  overall tree structure that is reflected in the output location
+  within the file system (usually rooted at
+  \verb,~/isabelle/browser_info,).
+
+  Here is the canonical arrangement of sources of a session called
+  \texttt{MySession}:
 
   \begin{itemize}
 
   \item Directory \texttt{MySession} contains the required theory
-  files, say $A@1$\texttt{.thy}, \dots, $A@n$\texttt{.thy}.
+  files ($A@1$\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
+  ``\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
+  required for the {\LaTeX} stage; only \texttt{root.tex} needs to be
+  provided initially.
+
+  The latter file holds appropriate {\LaTeX} code to commence a
+  document (\verb,\documentclass, etc.), and to include the generated
+  files $A@i$\texttt{.tex} for each theory.  The generated
+  \texttt{session.tex} will hold {\LaTeX} commands to include all
+  theory output files in topologically sorted order, so
+  \verb,\input{session}, in \texttt{root.tex} will do it in most
+  situations.
+
+  \item In addition, \texttt{IsaMakefile} outside of the 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.
+  Isabelle tools to control the batch job.  In fact, several sessions
+  may be controlled by the same \texttt{IsaMakefile}.  See also
+  \cite{isabelle-sys} for further details, especially on
+  \texttt{isatool usedir} and \texttt{isatool make}.
 
   \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 practice, 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:
+  with the generated document appearing in its proper place.
+
+  \medskip In practice, 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
+  This processes the session with sensible default options, including
+  verbose mode to tell the user where the ultimate results will
+  appear.  The above dry run should produce should already be able to
+  produce a single page of output (with a dummy title, empty table of
+  contents etc.).  Any failure at that stage is likely to indicate
+  technical problems with the user's {\LaTeX}
+  installation.\footnote{Especially make sure that \texttt{pdflatex}
+  is present; if all fails one may fall back on DVI output by changing
+  \texttt{usedir} options \cite{isabelle-sys}.}
+
+  \medskip One 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.  The default versions includes the
-  \texttt{isabelle} (mandatory) and \texttt{isabellesym} (required for
-  mathematical symbols); further packages may required, e.g.\ for
-  unusual Isabelle symbols.
-
-  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.%
+  adapted at some point; the default version is mostly
+  self-explanatory.
+
+  Especially note the standard inclusion of {\LaTeX} packages
+  \texttt{isabelle} (mandatory), and \texttt{isabellesym} (required
+  for mathematical symbols), and the final \texttt{pdfsetup} (provides
+  handsome defaults for \texttt{hyperref}, including URL markup).
+  Further {\LaTeX} packages further packages may required in
+  particular applications, e.g.\ for unusual Isabelle symbols.
+
+  \medskip Further auxiliary files for the {\LaTeX} stage should be
+  included in the \texttt{MySession/document} directory, e.g.\
+  additional {\TeX} sources or graphics.  In particular, adding
+  \texttt{root.bib} here (with that specific name) causes an automatic
+  run of \texttt{bibtex} to process a bibliographic database; see for
+  further commodities \texttt{isatool document} covered in
+  \cite{isabelle-sys}.
+
+  \medskip Any 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}
+\begin{isamarkuptext}%
+The large-scale structure of Isabelle documents follows existing
+  {\LaTeX} conventions, with chapters, sections, subsubsections etc.
+  The Isar language includes separate \bfindex{markup commands}, which
+  do not effect the formal content of a theory (or proof), but result
+  in corresponding {\LaTeX} elements issued to the output.
+
+  There are separate 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}

 
   \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
+  \verb,{,\verb,*,~\dots~\verb,*,\verb,},).  After stripping any
   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.
+  \verb,\isamarkupXYZ, for any command \isakeyword{XYZ}.  These macros
+  are defined in \verb,isabelle.sty, according to the meaning given in
+  the rightmost column above.
 
   \medskip The following source fragment illustrates structure markup
-  of a theory.  Note that {\LaTeX} labels may well be included inside
-  of section headings as well.
+  of a theory.  Note that {\LaTeX} labels may be included inside of
+  section headings as well.
 
   \begin{ttbox}
   header {\ttlbrace}* Some properties of Foo Bar elements *{\ttrbrace}
 
   theory Foo_Bar = Main:

   theorem main: \dots
 
   end
   \end{ttbox}
 
-  Users may occasionally 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,.
+  Users may occasionally want to change the meaning of markup
+  commands, say via \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
+  \noindent 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.\
   \verb,\documentclass{report},.
 
   \medskip The {\LaTeX} macro \verb,\isabellecontext, is maintained to
   hold the name of the current theory context.  This is particularly
-  useful for document headings or footings, e.g.\ like this:
+  useful for document headings:
 
 \begin{verbatim}
-  \renewcommand{\isamarkupheader}[1]%
+  \renewcommand{\isamarkupheader}[1]
   {\chapter{#1}\markright{THEORY~\isabellecontext}}
 \end{verbatim}
 
   \noindent Make sure to include something like
   \verb,\pagestyle{headings}, in \texttt{root.tex}; the document

 
   FIXME%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
-\isamarkupsubsection{Symbols and Characters%
+\isamarkupsubsection{Symbols and Characters \label{sec:doc-prep-symbols}%
 }
 \isamarkuptrue%
 %
 \begin{isamarkuptext}%
 FIXME \verb,\isabellestyle,%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %
-\isamarkupsubsection{Suppressing Output%
+\isamarkupsubsection{Suppressing Output \label{sec:doc-prep-suppress}%
 }
 \isamarkuptrue%
 %
 \begin{isamarkuptext}%
 By default Isabelle's document system generates a {\LaTeX} source
   file for each theory that happens to get loaded during the session.
-  The generated \texttt{session.tex} file will include all of these in
+  The generated \texttt{session.tex} will include all of these in
   order of appearance, which in turn gets included by the standard
-  \texttt{root.tex} file.  Certainly one may change the order of
-  appearance or suppress unwanted theories by ignoring
-  \texttt{session.tex} and include individual files in
-  \texttt{root.tex} by hand.  On the other hand, such an arrangement
-  requires additional efforts for maintenance.
+  \texttt{root.tex}.  Certainly one may change the order of appearance
+  or suppress unwanted theories by ignoring \texttt{session.tex} and
+  include individual files in \texttt{root.tex} by hand.  On the other
+  hand, such an arrangement requires additional maintenance chores
+  whenever the collection of theories changes.
 
   Alternatively, one may tune the theory loading process in
-  \texttt{ROOT.ML}: traversal of the theory dependency graph may be
-  fine-tuned by adding further \verb,use_thy, invocations, although
-  topological sorting needs to be preserved.  Moreover, the ML
-  operator \verb,no_document, temporarily disables document generation
-  while executing a theory loader command; the usage is like this:
+  \texttt{ROOT.ML} itself: traversal of the theory dependency graph
+  may be fine-tuned by adding further \verb,use_thy, invocations,
+  although topological sorting still has to be observed.  Moreover,
+  the ML operator \verb,no_document, temporarily disables document
+  generation while executing a theory loader command; its usage is
+  like this:
 
 \begin{verbatim}
-  no_document use_thy "Aux";
+  no_document use_thy "A";
 \end{verbatim}
 
-  Theory output may be also suppressed \emph{partially} as well.
-  Typical applications include research papers or slides based on
-  formal developments --- these usually do not show the full formal
-  content.  The special source comments
+  \medskip Theory output may be also suppressed in smaller portions as
+  well.  For example, research papers or slides usually do not include
+  the formal content in full.  In order to delimit \bfindex{ignored
+  material} special source comments
   \verb,(,\verb,*,\verb,<,\verb,*,\verb,), and
-  \verb,(,\verb,*,\verb,>,\verb,*,\verb,), are interpreted by the
-  document generator as open and close parenthesis for
-  \bfindex{ignored material}.  Any text inside of (potentially nested)
-  \verb,(,\verb,*,\verb,<,\verb,*,\verb,),~\dots~\verb,(,\verb,*,\verb,>,\verb,*,\verb,),
-  parentheses is just ignored from the output --- after correct formal
-  checking.
+  \verb,(,\verb,*,\verb,>,\verb,*,\verb,), may be included in the
+  text.  Only the document preparation system is affected, the formal
+  checking the theory is performed as before.
 
   In the following example we suppress the slightly formalistic
-  \isakeyword{theory} and \isakeyword{end} part of a theory text.
+  \isakeyword{theory} + \isakeyword{end} surroundings a theory.
 
   \medskip
 
   \begin{tabular}{l}
   \verb,(,\verb,*,\verb,<,\verb,*,\verb,), \\

   \verb,(,\verb,*,\verb,>,\verb,*,\verb,), \\
   \end{tabular}
 
   \medskip
 
-  Text may be suppressed at a very fine grain; thus we may even drop
-  vital parts of the formal text, preventing that things have been
-  simpler than in reality.  For example, the following ``fully
-  automatic'' proof is actually a fake:%
+  Text may be suppressed in a fine grained manner.  For example, we
+  may even drop vital parts of a formal proof, pretending that things
+  have been simpler than in reality.  For example, the following
+  ``fully automatic'' proof is actually a fake:%
 \end{isamarkuptext}%
 \isamarkuptrue%
 \isacommand{lemma}\ {\isachardoublequote}x\ {\isasymnoteq}\ {\isacharparenleft}{\isadigit{0}}{\isacharcolon}{\isacharcolon}int{\isacharparenright}\ {\isasymLongrightarrow}\ {\isadigit{0}}\ {\isacharless}\ x\ {\isacharasterisk}\ x{\isachardoublequote}\isanewline
 \ \ \isamarkupfalse%
 \isacommand{by}\ {\isacharparenleft}auto{\isacharparenright}\isamarkupfalse%

 
 \begin{verbatim}
   by (auto(*<*)simp add: int_less_le(*>*))
 \end{verbatim} %(*
 
-  \medskip Ignoring portions of printed text generally demands some
-  care by the user.  First of all, the writer is responsible not to
-  obfuscate the underlying formal development in an unduly manner.  It
-  is fairly easy to scramble the remaining visible text by referring
-  to questionable formal items (strange definitions, arbitrary axioms
-  etc.) that have been hidden from sight.
-  
+  \medskip Ignoring portions of printed does demand some care by the
+  user.  First of all, the writer is responsible not to obfuscate the
+  underlying formal development in an unduly manner.  It is fairly
+  easy to invalidate the remaining visible text, e.g.\ by referencing
+  questionable formal items (strange definitions, arbitrary axioms
+  etc.) that have been hidden from sight beforehand.
+
   Some minor technical subtleties of the
-  \verb,(,\verb,*,\verb,<,\verb,*,\verb,),~\verb,(,\verb,*,\verb,>,\verb,*,\verb,),
-  elements need to be observed as well, as the system performs little
-  sanity checks here.  Arguments of markup commands and formal
+  \verb,(,\verb,*,\verb,<,\verb,*,\verb,),-\verb,(,\verb,*,\verb,>,\verb,*,\verb,),
+  elements need to be kept in mind as well, since the system performs
+  little sanity checks here.  Arguments of markup commands and formal
   comments must not be hidden, otherwise presentation fails.  Open and
   close parentheses need to be inserted carefully; it is fairly easy
-  to hide just the wrong parts, especially after rearranging the
-  sources.
+  to hide the wrong parts, especially after rearranging the sources.
 
   \medskip Authentic reports of formal theories, say as part of a
-  library, should usually refrain from suppressing parts of the text
+  library, usually should refrain from suppressing parts of the text
   at all.  Other users may need the full information for their own
-  derivative work.  If a particular formalization works out as too
-  ugly for general public coverage, it is often better to think of a
-  better way in the first place.%
+  derivative work.  If a particular formalization appears inadequate
+  for general public coverage, it is often more appropriate to think
+  of a better way in the first place.%
 \end{isamarkuptext}%
 \isamarkuptrue%
 \isamarkupfalse%
 \end{isabellebody}%
 %%% Local Variables: