vdm

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+%%% ====================================================================
+%%%  @LaTeX-style-file{
+%%%     author          = "Mario Wolczko",
+%%%     version         = "4.00",
+%%%     date            = "14 October 1994",
+%%%     filename        = "vdm.sty",
+%%%     address         = "FORMERLY AT
+%%%                        Dept of Computer Science
+%%%                        The University of Manchester
+%%%                        Oxford Road
+%%%                        Manchester M13 9PL
+%%%                        UK",
+%%%     codetable       = "ISO/ASCII",
+%%%     keywords        = "LaTeX, VDM specification language",
+%%%     supported       = "yes",
+%%%     docstring       = "LaTeX macros for typesetting VDM
+%%%                        specifications.
+%%%                        NOTE
+%%%                        Mario no longer works at Manchester
+%%%                        This is a minimal update to LaTeX2e
+%%%                        By David Carlisle",
+%%%  }
+%%% ====================================================================
+%
+%       BSI VDM documentstyle option for LaTeX
+%
+%       M. Wolczko
+%
+%
+% Dept. of Computer Science   Internet:      mario@cs.man.ac.uk
+% The University              uucp:    mcsun!uknet!man.cs!mario
+% Manchester M13 9PL          JANET:         mario@uk.ac.man.cs
+% U.K.                        Tel: +44-61-275 6146  (FAX: 6236)
+%
+% Version for LaTeX2e by David Carlisle.
+% Just constructed by removing all the old font wierdness.
+% Not tested at all!
+%
+%
+%----------------------------------------------------------------
+%
+%       Installation-dependent features
+%
+
+
+\newif\ifams@ 
+
+\ams@true
+
+\ifams@
+ \RequirePackage{amsfonts}
+\fi
+
+%----------------------------------------------------------------
+%
+%       The vdm environment
+%
+% record whether we were in horizontal mode when entering...
+\newif\ifhm@
+
+\def\vdm{\ifhmode\hm@true\else\hm@false\fi
+  \@changeMathmodeCatcodes\@postUnderPenalty10000\relax}
+
+% after an \end{vdm} the next paragraph is not indented unless a \par
+% comes first (if we entered in horizontal mode).  This is a bit of a
+% kludge!
+\def\endvdm{\ifhm@\else
+  \global\let\par=\@undonoindent
+  \global\everypar={{\setbox0=\lastbox}\global\everypar={}%
+                        \global\let\par=\@@par}%
+  \fi}
+
+\def\@undonoindent{\global\everypar={}\global\let\par=\@@par\@@par}
+
+%-----------------------------------------------------------------
+%
+%       Controlling line and page breaks
+%
+% Text within the vdm environment is essentially mathematical in
+% nature, so requires special care.  Whenever outer vertical mode is
+% entered, the \@beginVerticalVDM command should be used.  This sets
+% up \leftskip, \rightskip, \baselineskip, \lineskip and
+% \lineskiplimit to conform with the overall style.
+%
+% When entering unrestricted horizontal mode, the \@beginHorizontalVDM
+% command should be used.  This sets up:
+%       \leftskip and \rightskip to 0,
+%       \\ to do line breaking
+%       ragged right line breaking, with special penalties, and
+%       enters math mode.
+% \@endHorizontalVDM should be called when leaving unrestricted
+% horizontal mode.
+
+\def\@beginVerticalVDM{\@changeMargins\@changeBaselineskip}
+
+\def\@beginHorizontalVDM{\@restoreLineSeparator
+  \@restoreMargins\@raggedRight\noindent$\strut\relax}
+\def\@endHorizontalVDM{\relax\strut$}
+
+% \VDMindent is used for \leftskip within VDM, \VDMrindent for
+% \rightskip, \VDMbaselineskip for \baselineskip
+\newdimen\VDMindent \VDMindent=\parindent
+\newdimen\VDMrindent \VDMrindent=\parindent
+\def\VDMbaselineskip{\baselineskip}
+
+\def\@changeMargins{\leftskip=\VDMindent \rightskip=\VDMrindent}
+\def\@restoreMargins{\advance\hsize by-\leftskip
+  \advance\hsize by-\rightskip
+  \leftskip=0pt \rightskip=0pt}
+\def\@changeBaselineskip{\baselineskip=\VDMbaselineskip
+  \lineskip=0pt \lineskiplimit=0pt
+  % need to alter the size of struts, too
+  \setbox\strutbox\hbox{\vrule height.7\baselineskip
+      depth.3\baselineskip width\z@}}
+
+% these are used in externals, records and cases
+\def\@changeLineSeparator{\let\\=\cr} % for usr within \halign
+\def\@restoreLineSeparator{\let\\=\newline}
+
+\def\@raggedRight{\rightskip=0pt plus 1fil
+  \hyphenpenalty=-100 \linepenalty=200
+  \binoppenalty=10000 \relpenalty=10000 \pretolerance=-1}
+
+% ------------------------------------------------------------------------
+
+%       Font and Character Changes
+
+% make a-zA-Z use the \it family within math mode, and ~ mean \hook.
+% Digits 0-9 remain as normal.
+\everymath=\expandafter{\the\everymath\vdm@it
+        \@changeMathmodeCatcodes}%
+\everydisplay=\expandafter{\the\everydisplay\vdm@it
+        \@changeMathmodeCatcodes}%
+
+\def\vdm@it{\@fontswitch\it\mathit}
+
+\mathcode`\0="0030
+\mathcode`\1="0031
+\mathcode`\2="0032
+\mathcode`\3="0033
+\mathcode`\4="0034
+\mathcode`\5="0035
+\mathcode`\6="0036
+\mathcode`\7="0037
+\mathcode`\8="0038
+\mathcode`\9="0039
+
+\mathchardef\Gamma="0000
+\mathchardef\Delta="0001
+\mathchardef\Theta="0002
+\mathchardef\Lambda="0003
+\mathchardef\Xi="0004
+\mathchardef\Pi="0005
+\mathchardef\Sigma="0006
+\mathchardef\Upsilon="0007
+\mathchardef\Phi="0008
+\mathchardef\Psi="0009
+\mathchardef\Omega="000A
+
+% If the user really wants the normal codes, she can call \defaultMathcodes
+%\def\defaultMathcodes{\let\vdm@it\relax}
+\def\defaultMathcodes{\let\vdm@it\relax}
+
+
+% remember the original mathcode of minus sign
+\edef\@minuscode{\the\mathcode`\-}
+
+\def\mathminus{\mathcode`\-=\@minuscode }
+\def\textminus{\mathcode`\-="002D }
+% by default, use text minus
+%\textminus
+
+% make a : into punctuation, a - into a letter, and | mean \mid
+ % NFSS-change
+ % \mathcode`\-="042D changed to \mathcode`\-="002D as we can not rely on
+ % \itfam being fam 4.
+ \def\@changeOtherMathcodes{\mathcode`\:="603A \textminus
+  \mathcode`\|="326A \mathchardef\Or="325F }% this is a rel to get 5mu spacing
+ \def\relbar{\mathrel{\smash\minus}}% redefine because mathcode of -
+                                    % has changed
+
+
+% alternative underscore
+\def\@VDMunderscore{\leavevmode
+  \kern.06em\vbox{\hrule\@height .2ex\@width .3em}\penalty\@postUnderPenalty
+  \hskip 0.1em}
+
+% Allow line breaks after an underscore, but not in vdm mode (see
+% \vdm).  This is so long identifiers can be broken when run
+% into paragraphs.
+\newcount\@postUnderPenalty \@postUnderPenalty=200
+
+% now require some catcode trickery to enable us to change _ when we want to
+{\catcode`\_=\active 
+ \gdef\@changeGlobalCatcodes{% make _ a normal char
+        \catcode`\_=\active \let_=\@VDMunderscore}
+ \gdef\@changeMathmodeCatcodes{%
+        % make ~ mean \hook, " do text, @ mean subscript
+        \let~=\hook
+        \catcode`\@=8
+        \mathcode`\"="8000 }
+        \uccode`\~=`\"%
+ \gdef\underscoreoff{% make _ a normal char
+        \catcode`\_=\active \let_=\@VDMunderscore}
+ \gdef\underscoreon{% restore underscore to usual meaning
+        \catcode`\_=8}
+\uppercase{\gdef~}#1"{\nfss@text{\rm #1}}}
+
+%----------------------------------------------------------------
+%
+%       Keywords
+%
+\ifx\fmtname\@fmtname
+        \def\keywordFontBeginSequence{\sf}%     user-definable
+\else\ifx\fmtname\@psfmtname
+        \def\keywordFontBeginSequence{\sf}% Helvetica is OK
+\else
+        \def\keywordFontBeginSequence{\bf}% good for SliTeX
+\fi\fi
+
+\def\kw#1{\hbox{\keywordFontBeginSequence #1\/}}
+
+\def\makeNewKeyword#1#2{% use \newcommand for extra checks
+        \newcommand{#1}{\hbox{\keywordFontBeginSequence #2\/}}}
+
+\makeNewKeyword{\nil}{nil}
+\makeNewKeyword{\True}{true}
+\makeNewKeyword{\true}{true}
+\makeNewKeyword{\False}{false}
+\makeNewKeyword{\false}{false}
+\makeNewKeyword{\rem}{ rem }
+
+\def\where{\par\moveright\VDMindent\hbox{\keywordFontBeginSequence where\/}}
+
+%----------------------------------------------------------------
+%
+%       monadic operator creation
+%
+\def\newMonadicOperator#1#2{\newcommand{#1}{\kw{#2\kern.16667em}\nobreak}}
+
+%----------------------------------------------------------------
+%
+%       primitive numeric types
+%
+% use the AMS fonts for these if possible
+
+\ifams@
+  \DeclareMathSymbol{\Bool} {\mathord}{AMSb}{"42}   % Booleans
+  \DeclareMathSymbol{\Nat}  {\mathord}{AMSb}{"4E}   % Natural numbers
+  \def\Nati{\Nat_1}             % Positive natural numbers
+  \DeclareMathSymbol{\Int}  {\mathord}{AMSb}{"5A}   % Integers
+  \DeclareMathSymbol{\Real} {\mathord}{AMSb}{"52}   % Reals
+  \DeclareMathSymbol{\Rat}  {\mathord}{AMSb}{"51}   % Rationals
+\else
+  \def\Bool{\nfss@text{\bfseries B\/}}
+  \def\Nat{\nfss@text{\bfseries N\/}}
+  \def\Nati{\hbox{$\nfss@text{\bfseries N}_1$}}
+  \def\Int{\nfss@text{\bfseries Z\/}}
+  \def\Real{\nfss@text{\bfseries R\/}}
+  \def\Rat{\nfss@text{\bfseries Q\/}}
+\fi
+\let\Natone=\Nati % just for an alternative
+
+%----------------------------------------------------------------
+%
+%       Operations
+%
+% The op environment.  Within op you can specify args,
+% result, etc. which are gathered into registers, and output when the
+% op env. ends.
+%
+% The optional argument is the operation name
+
+% shorthand for an operation on its own: the vdmop env.
+\def\vdmop{\vdm\op} \def\endvdmop{\endop\endvdm}
+
+% registers constructed within an op environment
+\newtoks\@operationName
+\newbox\@operationNameBox
+\newif\ifArgumentListEncountered@
+\newtoks\@argumentListTokens
+\newtoks\@resultNameAndTypeTokens
+\newbox\@externalsBox
+\newbox\@preConditionBox
+\newbox\@postConditionBox
+\newbox\@errConditionBox
+
+\def\op{% clear temporaries, deal with optional arg
+        \setbox\@operationNameBox=\hbox{}%
+        \@argumentListTokens={}\ArgumentListEncountered@false
+        \@resultNameAndTypeTokens={}%
+        \setbox\@externalsBox=\box\voidb@x
+        \setbox\@preConditionBox=\box\voidb@x
+        \setbox\@postConditionBox=\box\voidb@x
+        \par\preOperationHook
+        \vskip\preOperationSkip
+        \@beginVerticalVDM
+        \@ifnextchar [{\@opname}{}}
+
+% breaking parameters
+\newcount\preOperationPenalty \preOperationPenalty=0
+\newcount\preExternalPenalty \preExternalPenalty=2000
+\newcount\prePreConditionPenalty \prePreConditionPenalty=800
+\newcount\prePostConditionPenalty \prePostConditionPenalty=500
+\newcount\preErrConditionPenalty \preErrConditionPenalty=500
+\newcount\postOperationPenalty \postOperationPenalty=-500
+
+% gaps between bits of operations
+\newskip\preOperationSkip \preOperationSkip=2ex plus 0.5ex minus 0.2ex
+\newskip\postOperationSkip \postOperationSkip=2ex plus 0.5ex minus 0.2ex
+\newskip\postHeaderSkip \postHeaderSkip=.5ex plus .2ex minus .2ex
+\newskip\postExternalsSkip \postExternalsSkip=.5ex plus .2ex minus .2ex
+\newskip\postPreConditionSkip \postPreConditionSkip=.5ex plus .2ex minus .2ex
+\newskip\preErrConditionSkip \preErrConditionSkip=.5ex plus .2ex minus .2ex
+
+\def\endop{% make up operation
+        % IMPORTANT---don't remove the vskips in this macro
+        % if you don't want one, set it to 0pt
+        \vskip 0pt
+        \@setOperationHeader
+        \betweenHeaderAndExternalsHook
+        \vskip\postHeaderSkip
+        \ifvoid\@externalsBox
+              \betweenExternalsAndPreConditionHook
+        \else \moveright\VDMindent\box\@externalsBox
+              \betweenExternalsAndPreConditionHook
+              \vskip\postExternalsSkip
+        \fi
+        \ifvoid\@preConditionBox
+              \betweenPreAndPostConditionHook
+        \else \moveright\VDMindent\box\@preConditionBox
+              \betweenPreAndPostConditionHook
+              \vskip\postPreConditionSkip
+        \fi
+        \ifvoid\@postConditionBox
+              \betweenPostAndErrHook
+        \else \moveright\VDMindent\box\@postConditionBox
+              \betweenPostAndErrConditionHook
+        \fi
+        \ifvoid\@errConditionBox
+        \else \vskip\preErrConditionSkip
+              \moveright\VDMindent\box\@errConditionBox
+        \fi
+        \postOperationHook
+        \vskip\postOperationSkip}
+
+% hooks for user-defined expansion
+% TeX is in outer vertical mode when these are called.
+% ALWAYS leave TeX in vertical mode after these macros have been called
+\def\preOperationHook{\penalty\preOperationPenalty }
+\def\betweenHeaderAndExternalsHook{\penalty\preExternalPenalty }
+\def\betweenExternalsAndPreConditionHook{\penalty\prePreConditionPenalty }
+\def\betweenPreAndPostConditionHook{\penalty\prePostConditionPenalty }
+\def\betweenPostAndErrConditionHook{\penalty\preErrConditionPenalty }
+\def\postOperationHook{\penalty\postOperationPenalty }
+
+% combine the operation name, argument list and result
+\def\@setOperationHeader{%
+        \moveright\VDMindent\vtop{%
+                \ifArgumentListEncountered@
+                        \setbox\@operationNameBox=%
+                                \hbox{\unhbox\@operationNameBox$($}\fi
+                \hangindent=\wd\@operationNameBox \hangafter=1
+                \noindent\kern-.05em\box\@operationNameBox
+                \@beginHorizontalVDM
+                \ifArgumentListEncountered@\the\@argumentListTokens)\fi
+                \ \the\@resultNameAndTypeTokens
+                \@endHorizontalVDM}}
+
+% set the operation name
+% \opname{name-of-operation}
+\def\opname#1{\@opname[#1]}
+\def\@opname[#1]{\@operationName={#1}%
+  \global\setbox\@operationNameBox=\hbox{$\relax#1$\ }}
+
+% set up the argument list
+% \args{ argument \\ argument \\ argument... } where \\ forces a line break
+% This is also used in the fn environment
+\def\args{\global\ArgumentListEncountered@true \global\@argumentListTokens=}
+
+% result name and type
+\def\res{\global\@resultNameAndTypeTokens=}
+
+% externals list
+%
+% An external list could be either very long or very short, so we provide
+% two forms.  One is the short \ext{..} command, the other is the externals
+% environment.
+% Externals are always separated by \\
+%
+
+% we have to mess a little to get the catcode of : right
+\def\ext{\bgroup\@makeColonActive\@ext}
+\def\@ext#1{\externals#1\endexternals\egroup}
+
+\def\externals{\global\setbox\@externalsBox=%
+        \@beginIndentedPara{\hsize}{ext }{\@setUpExternals}}
+\def\endexternals{\@endIndentedPara{\@endAlignment}}
+
+\def\@setUpExternals{\@makeColonActive\@changeLineSeparator\@beginAlignment}
+
+% more catcode trickery for :
+{\catcode`\:=\active
+ \gdef\@makeColonActive{\catcode`\:=\active \let:=&}}
+
+% the \expandafters are necessary because TeX doesn't expand
+% \halign specs when scanning for # and &
+\def\@beginAlignment{\expandafter\halign\expandafter\bgroup
+        \the\@extAlign\strut\enspace&:\enspace$##$\hfil\cr}
+\def\@endAlignment{\crcr\egroup}
+
+% the user can decide on the exact alignment of the field names
+\newtoks\@extAlign
+\def\leftExternals{\@extAlign={$##$\hfil}}
+\def\rightExternals{\@extAlign={\hfil$##$}}
+\leftExternals
+
+\makeNewKeyword{\Rd}{rd } \makeNewKeyword{\Wr}{wr }
+
+% pre-condition, post-condition and err-condition
+%
+% once again we provide short forms \pre, \post, \err and environments
+% precond, postcond and errcond
+\def\pre#1{\precond#1\endprecond}
+\def\precond{\global\setbox\@preConditionBox=%
+        \@beginMathIndentedPara{\hsize}{pre }}
+\def\endprecond{\@endMathIndentedPara}
+
+\def\post#1{\postcond#1\endpostcond}
+\def\postcond{\global\setbox\@postConditionBox=%
+        \@beginMathIndentedPara{\hsize}{post }}
+\def\endpostcond{\@endMathIndentedPara}
+
+\def\err#1{\errcond#1\enderrcond}
+\def\errcond{\global\setbox\@errConditionBox=%
+        \@beginMathIndentedPara{\hsize}{errs }}
+\def\enderrcond{\@endMathIndentedPara}
+
+
+%----------------------------------------------------------------
+%
+%       Box man\oe uvres
+%
+% Here's where all the tricky box manipulation commands go
+%
+% \@beginIndentedPara begins construction of a \hbox of width #1
+% which contains keyword #2 to the left of a para in a vtop.
+% #3 is evaluated within the inner vtop.
+% endIndentedPara closes the box off; its arg. is evaluated just
+% before closing the box.
+%
+\def\@beginIndentedPara#1#2#3{\hbox to #1\bgroup \setbox0=\kw{#2}%
+        \copy0 \strut \vtop\bgroup \advance\hsize by -\wd0 #3}
+\def\@endIndentedPara#1{\strut#1\egroup\hss\egroup}
+
+% \@beginMathIndentedPara places the para in vdm mode
+\def\@beginMathIndentedPara#1#2{\@beginIndentedPara{#1}{#2}%
+        {\@beginHorizontalVDM}}
+\def\@endMathIndentedPara{\@endIndentedPara{\@endHorizontalVDM}}
+
+% \@belowAndIndent#1#2 places #2 in a vbox below and to the right of #1
+\def\@belowAndIndent#1#2{#1\hfil\break
+        \@beginMathIndentedPara{\hsize}{\qquad}#2\@endMathIndentedPara}
+
+% \@mathIndentedPara does the whole thing
+\def\@mathIndentedPara#1#2#3{\@beginMathIndentedPara{#1}{#2}#3%
+        \@endMathIndentedPara}
+%----------------------------------------------------------------
+%
+%       Constructions
+%
+% Here are all the standard constructions.
+% The only tricky one is \cases.
+% Those that construct a box must be made to make that box of 0 width,
+% and force a line break immediately afterwards.
+
+% \If mm-exp \Then mm-exp \Else mm-exp \Fi
+% multi-line indented if-then-else
+%
+\def\If#1\Then#2\Else#3\Fi{\vtop{%
+        \@mathIndentedPara{0pt}{if }{#1}%
+        \@mathIndentedPara{0pt}{then }{#2}%
+        \@mathIndentedPara{0pt}{else }{#3}}}
+
+% \SIf mm-exp \Then mm-exp \Else mm-exp \Fi
+% single line if-then-else
+\def\SIf#1\Then#2\Else#3\Fi{\hbox to 0pt{\vtop{\@beginHorizontalVDM
+        \kw{if }\nobreak#1\penalty0\hskip 0.5em
+        \kw{then }\nobreak#2\penalty-100\hskip 0.5em % break here OK
+        \kw{else }\nobreak#3\@endHorizontalVDM}\hss}}
+
+% \Let mm-exp \In mm-exp2
+% multi-line let..in ; mm-exp2 is `curried'
+\def\Let#1\In{\vtop{%
+        \@mathIndentedPara{0pt}{let }{#1\hskip 0.5em\kw{in}}}\hfil\break}
+
+% \SLet mm-exp \In mm-exp
+% single-line let..in
+\def\SLet#1\In#2{\hbox to 0pt{\vtop{\@beginHorizontalVDM
+        \kw{let }\nobreak#1\hskip 0.5em
+        \kw{in }\penalty-100 #2\@endHorizontalVDM}\hss}}
+
+% multi-line cases
+%
+% \Cases{ selecting-mm-exp }
+% from-case1 & to-case1 \\
+% from-case2 & to-case2 \\
+%           ...
+% from-casen & to-casen
+% \Otherwise{ mm-exp }
+% \Endcases[optional text for the rest of the line]
+
+\newif\ifOtherwiseEncountered@
+\newtoks\@OtherwiseTokens
+
+\def\Cases#1{\hbox to 0pt\bgroup \vtop\bgroup
+                \@mathIndentedPara{\hsize}{cases }{\strut
+                        #1\hskip 0.5em\strut\kw{of}}%
+                \bgroup % we might be in a nested case, so we have to
+                        % save the \Otherwise bits we might lose
+                \OtherwiseEncountered@false \@changeLineSeparator
+                \@beginCasesAlignment}
+
+% the user can decide on the exact alignment
+\newtoks\@casesDef
+\def\leftCases{\@casesDef={$##$\hfil}}
+\def\rightCases{\@casesDef={\hfil$##$}}
+\rightCases
+
+% the \expandafters are necessary because TeX doesn't expand
+% \halign specs when scanning for # and &
+\def\@beginCasesAlignment{\expandafter\halign\expandafter\bgroup
+        \the\@casesDef&$\,\rightarrow##$\hfil\cr}
+
+\def\Otherwise{\global\OtherwiseEncountered@true \global\@OtherwiseTokens=}
+\let\Others=\Otherwise
+
+\def\Endcases{\@endCasesAlignment \@setOtherwise \egroup \@setEndcases}
+\def\@endCasesAlignment{\crcr\egroup}
+\def\@setOtherwise{\ifOtherwiseEncountered@ % have an otherwise clause
+        \@mathIndentedPara{\hsize}{others }{%
+                \strut\the\@OtherwiseTokens\strut}
+        \fi}
+
+% must test for the optional arg to follow the end
+\def\@setEndcases{\noindent
+        \strut\kw{end}\@ifnextchar [{\@unbracket}{\@finalCaseEnd}}
+\def\@unbracket[#1]{$#1$\@finalCaseEnd}
+\def\@finalCaseEnd{\egroup\hss\egroup}%\hfil\break
+
+%----------------------------------------------------------------
+%
+%       special symbols
+
+% defined as
+\def\DEF{\raise.5ex
+        \hbox{\footnotesize\underline{$\mathchar"3234$}}}% a \triangle
+
+
+% cross product
+\let\x=\times
+
+%       logical connectives
+%
+\def\Iff{\penalty-50\mskip 7mu plus 2mu minus 2mu
+        \Leftrightarrow\mskip 7mu plus 2mu minus 2mu}
+\let\iff=\Iff
+\def\Implies{\penalty-35\mskip 6mu plus 2mu minus 1mu \Rightarrow
+        \mskip 6mu plus 2mu minus 1mu}
+\let\implies=\Implies
+% see changeOtherMathcodes for \Or
+\let\And=\land
+\let\@and=\and
+\def\and{\ifmmode\And\else\@and\fi}
+%  use \neg for logical not, or
+\def\Not{\neg\,}
+
+%       quantification
+%
+
+\DeclareMathSymbol{\Exists}   {\mathord}{symbols}{"39}
+\DeclareMathSymbol{\Forall}   {\mathord}{symbols}{"38}
+\DeclareMathSymbol{\suchthat} {\mathbin}{symbols}{"01}
+
+\def\exists{\@ifstar{\@splitExists}{\@normalExists}}
+\ifams@
+  \DeclareMathSymbol{\@nexists} {\mathop}{AMSb}{"40}
+               % crossed out existential quantifier
+\else
+  \def\@nexists{\hbox to 0pt{\raise0.15ex\hbox{/}\hss}\Exists}
+\fi
+\def\nexists{\@ifstar{\@splitNExists}{\@normalNExists}}
+\def\forall{\@ifstar{\@splitForall}{\@normalForall}}
+\def\unique{\@ifstar{\@splitUnique}{\@normalUnique}}
+\def\uniqueval{\@ifstar{\@splitUniqueval}{\@normalUniqueval}}
+
+\def\@normalExists#1#2{{\Exists#1}\suchthat #2}
+\def\@normalNExists#1#2{{\@nexists#1}\suchthat #2}
+\def\@normalForall#1#2{{\Forall#1}\suchthat #2}
+\def\@normalUnique#1#2{{\Exists!\,#1}\suchthat #2}
+\def\@normalUniqueval#1#2{{\iota\,#1}\suchthat #2}
+
+\def\@splitExists#1{\@belowAndIndent{\Exists#1\suchthat}}
+\def\@splitNExists#1{\@belowAndIndent{\@nexists#1\suchthat}}
+\def\@splitForall#1{\@belowAndIndent{\Forall#1\suchthat}}
+\def\@splitUnique#1{\@belowAndIndent{\Exists!\,#1\suchthat}}
+\def\@splitUniqueval#1{\@belowAndIndent{\iota\,#1\suchthat}}
+%
+%       sequents
+%
+\let\Tstlp=\vdash
+%
+\def\sequent{\@ifstar{\@splitSequent}{\@normalSequent}}
+\def\@normalSequent#1#2{{#1}\:\Tstlp\: #2}
+\def\@splitSequent#1{\@belowAndIndent{#1\;\Tstlp}}
+
+%
+%       strachey brackets
+%
+% (see TeXbook, p.437)
+\def\term#1{[\mkern-\thinmuskip[#1\relax]\mkern-\thinmuskip]}
+
+%       function composition
+%
+\let\compf=\circ
+
+%----------------------------------------------------------------
+%
+%       function environment
+%
+% This environment is similar to the op environment, but is used for
+% function definition.
+%
+% The mandatory first parameter is the name of the function, the
+% second is the argument list.
+%
+% The *-form simply doesn't force the parentheses round the argument list
+
+\def\fn{\parens@true\@beginVDMfunction}
+\@namedef{fn*}{\parens@false\@beginVDMfunction}
+\@namedef{endfn*}{\endfn}
+
+% short form
+\def\vdmfn{\vdm\parens@true \@beginVDMfunction}
+\def\endvdmfn{\endfn\endvdm}
+\@namedef{vdmfn*}{\vdm\parens@false \@beginVDMfunction}
+\@namedef{endvdmfn*}{\endfn\endvdm}
+
+% registers used within the fn environment
+\newtoks\@fnName
+\newbox\@fnNameBox
+\newif\ifsignatureEncountered@
+\newtoks\@signatureTokens
+\newbox\@fnDefnBox
+\newif\ifparens@
+
+\def\@beginVDMfunction#1#2{%
+        \@fnName={#1}%
+        \setbox\@fnNameBox=\hbox{$#1$}%
+        \setbox\@preConditionBox=\box\voidb@x % for people who want to do
+        \setbox\@postConditionBox=\box\voidb@x% implicit defns
+        \@signatureTokens={}\signatureEncountered@false
+        \ifparens@
+                \@argumentListTokens={(#2)}%
+        \else
+                \@argumentListTokens={#2}%
+        \fi
+        \par\preFunctionHook
+        \vskip\preFunctionSkip
+        \@beginVerticalVDM
+        \@beginFnDefn}
+
+% read in a signature
+\def\signature{\global\signatureEncountered@true \global\@signatureTokens=}
+
+\def\@beginFnDefn{\global\setbox\@fnDefnBox=\vtop\bgroup
+        \hangindent=2em \hangafter=1 \@beginHorizontalVDM
+        \advance\hsize by-2em % this fools vboxes within the
+        % function body about the hanging indent...yuk.
+        % If you change the size of the indent, change the
+        % corresponding line in \endfn.
+        \copy\@fnNameBox \the\@argumentListTokens
+        \quad\DEF\penalty-100\quad }
+
+\newskip\preFunctionSkip \preFunctionSkip=2ex plus .5ex minus .2ex
+\newskip\postFunctionSkip \postFunctionSkip=2ex plus .5ex minus .2ex
+\newskip\betweenSignatureAndBodySkip
+\betweenSignatureAndBodySkip=1.2ex plus .3ex minus .2ex
+\newskip\betweenFunctionAndPreSkip
+\betweenFunctionAndPreSkip=1.2ex plus .3ex minus .2ex
+
+\def\endfn{%
+        \advance\hsize by 2em% matches the dirty \advance in \@beginFnDefn
+        \@endHorizontalVDM
+        \egroup  % this ends the vtop we started in \@beginFnDefn
+        \ifsignatureEncountered@
+                \setbox0=\hbox{\unhbox\@fnNameBox$\;\mathpunct:\,$}%
+                \dimen255=\wd0 \noindent \box0
+                \vtop{\advance\hsize by-\dimen255 \@beginHorizontalVDM
+                        \the\@signatureTokens \@endHorizontalVDM}\par
+                \betweenSignatureAndBodyHook
+                \vskip\betweenSignatureAndBodySkip
+        \fi
+        \moveright\VDMindent\box\@fnDefnBox\,
+        \ifvoid\@preConditionBox
+              \betweenPreAndPostConditionHook
+              \vskip\postFunctionSkip
+        \else \betweenFunctionAndPreHook
+              \vskip\betweenFunctionAndPreSkip
+              \moveright\VDMindent\box\@preConditionBox
+              \betweenPreAndPostConditionHook
+              \vskip\postPreConditionSkip
+        \fi
+        \ifvoid\@postConditionBox
+              \postFunctionHook
+        \else \moveright\VDMindent\box\@postConditionBox
+              \postFunctionHook
+              \vskip\postOperationSkip
+        \fi}
+
+\newcount\preFunctionPenalty \preFunctionPenalty=0
+\newcount\betweenSignatureAndBodyPenalty
+ \betweenSignatureAndBodyPenalty=10000
+\newcount\betweenFunctionAndPrePenalty \betweenFunctionAndPrePenalty=1000
+\newcount\postFunctionPenalty \postFunctionPenalty=-500
+
+% These are called in outer vertical mode---they must also exit in this mode
+\def\preFunctionHook{\penalty\preFunctionPenalty }
+\def\betweenSignatureAndBodyHook{\penalty\betweenSignatureAndBodyPenalty }
+\def\betweenFunctionAndPreHook{\penalty\betweenFunctionAndPrePenalty }
+\def\postFunctionHook{\penalty\postFunctionPenalty }
+
+%       other function-related things
+%
+
+% function arrow
+\def\to{\penalty-100\rightarrow}
+
+% explicit lamdba function
+\def\LambdaFn{\@ifstar{\@splitLambdaFn}{\@normalLambdaFn}}
+\def\@normalLambdaFn#1#2{{\lambda#1}\suchthat#2}
+\def\@splitLambdaFn#1#2{% place body in a separate box below and to the right
+        {\lambda#1}\suchthat\hfil\break
+        \@mathIndentedPara{\hsize}{\qquad}{#2}}
+
+%----------------------------------------------------------------
+%
+%       Optional fields
+%
+\def\Opt#1{\big[#1\big]}
+
+
+%----------------------------------------------------------------
+%
+%       Sets
+
+% new set type
+\def\setof#1{#1-\kw{set}}
+
+% set enumeration
+\def\set#1{\{#1\}}
+
+% empty set
+\def\emptyset{\{\,\}}
+
+% usual LaTeX operators apply: \in \notin \subset \subseteq
+\let\inter=\cap \let\intersection=\inter
+\let\Inter=\bigcap \let\Intersection=\Inter
+\let\union=\cup
+\let\Union=\bigcup
+
+\mathchardef\minus="2200
+
+\def\diff{\minus} \let\difference=\diff
+
+\newMonadicOperator{\card}{card}
+\newMonadicOperator{\Min}{min}
+\newMonadicOperator{\Max}{max}
+\newMonadicOperator{\abs}{abs}
+
+%----------------------------------------------------------------
+%
+%       Map type
+
+% new map type
+\def\mapof#1#2{#1\buildrel m\over\longrightarrow#2}
+
+% one-one map
+\def\mapinto#1#2{#1\buildrel m\over\longleftrightarrow#2}
+
+% map enumeration
+\def\map#1{\{#1\}}
+
+% empty map
+\def\emptymap{\{\,\}}
+
+%       map operators
+%
+% use \mapsto for |->
+% overwrite
+\def\owr{\dagger}
+
+\let\dres=\lhd
+\let\rres=\rhd
+
+
+% domain subtraction
+\def\dsub{\mathbin{\hbox{$\rlap{$\mathord\minus$}\mkern-1.5mu
+        \lower.1ex\hbox{$\dres$}$}}}
+
+% range subtraction
+\def\rsub{\mathbin{\hbox{$\rlap{$\mathord\minus$}\mkern-1.5mu
+        \lower.1ex\hbox{$\rres$}$}}}
+
+\newMonadicOperator{\dom}{dom}
+\newMonadicOperator{\rng}{rng}
+\newMonadicOperator{\merge}{merge}
+
+%----------------------------------------------------------------
+%
+%       Sequences
+%
+
+% new type
+\def\seqof#1{#1^*}
+
+% non-empty sequence
+\def\neseqof#1{#1^+}
+
+% enumeration
+\def\seq#1{[#1]}
+
+% empty sequence
+\def\emptyseq{[\,]}
+
+\newMonadicOperator{\len}{len}
+\newMonadicOperator{\hd}{hd}
+\newMonadicOperator{\tl}{tl}
+\newMonadicOperator{\elems}{elems}
+\newMonadicOperator{\inds}{inds}
+\def\cons#1{\kw{cons}\nobreak(#1)}
+
+% sequence concatenation
+
+\DeclareMathSymbol{\@sc@nc} {\mathbin}{AMSb}{"79}
+
+\ifams@
+  \def\sconc{\mathbin{\hbox{\raise1ex\hbox{$\@sc@nc$}}}}
+\else
+  % this is truly yukky
+  \def\sconc{\mathbin{\hbox{\raise1ex\hbox{$\frown$}\kern-0.47em
+        \raise0.2ex\hbox{\it\char"12}}}}
+\fi
+
+% distributed concatenation
+\newMonadicOperator{\Conc}{dconc}
+
+%----------------------------------------------------------------
+%
+%       type equation
+%
+\newtoks\@typeName
+\def\type#1#2{{\@typeName{#1} \preTypeHook \vskip\preTypeSkip
+        \@beginVerticalVDM
+        \moveright\VDMindent\vtop{\@beginHorizontalVDM #1=#2%
+                \@endHorizontalVDM}
+        \postTypeHook \vskip\postTypeSkip}}
+
+% restricted type (has invariant)
+\def\rtype#1#2#3{{\@typeName{#1} \preTypeHook \vskip\preTypeSkip
+        \@beginVerticalVDM
+        \moveright\VDMindent\vtop{\@beginHorizontalVDM #1=#2%
+                \@endHorizontalVDM}
+        \vskip\betweenTypeAndInvSkip
+        \moveright\VDMindent\@mathIndentedPara{\hsize}{inv }{#3}%
+        \postTypeHook \vskip\postTypeSkip}}
+
+% initialised type
+\def\ritype#1#2#3#4{{\@typeName{#1} \preTypeHook \vskip\preTypeSkip
+        \@beginVerticalVDM
+        \moveright\VDMindent\vtop{\@beginHorizontalVDM #1=#2%
+                \@endHorizontalVDM}
+        \vskip\betweenTypeAndInvSkip
+        \moveright\VDMindent\@mathIndentedPara{\hsize}{inv }{#3}%
+        \vskip\betweenInvAndInitSkip
+        \moveright\VDMindent\@mathIndentedPara{\hsize}{init }{#4}%
+        \postTypeHook \vskip\postTypeSkip}}
+
+\def\preTypeHook{} \def\postTypeHook{}
+\newskip\preTypeSkip \preTypeSkip=1.2ex plus .5ex minus .3ex
+\newskip\postTypeSkip \postTypeSkip=1.2ex plus .5ex minus .3ex
+\newskip\betweenTypeAndInvSkip
+  \betweenTypeAndInvSkip=.5ex plus .3ex minus .2ex
+\newskip\betweenInvAndInitSkip
+  \betweenInvAndInitSkip=.5ex plus .3ex minus .2ex
+
+%----------------------------------------------------------------
+%
+%       Composite Objects
+%
+
+% literal composition; we have a compose and a composite env.
+
+% single line compose
+\@namedef{composite*}#1{\kw{compose }$\relax#1\relax$\kw{ of }$\relax}
+\@namedef{endcomposite*}{\relax$\kw{ end}}
+
+% multiple line version
+\def\composite#1{\bgroup\vskip\preCompositeSkip
+    \@beginVerticalVDM
+    \moveright\VDMindent\vtop\bgroup
+        \@beginHorizontalVDM
+        \kw{compose }#1\kw{ of}%
+        \@endHorizontalVDM
+        \@makeColonActive\@changeLineSeparator
+        \expandafter\halign\expandafter\bgroup\expandafter\qquad
+                \the\@recordAlign\strut\enspace&:\enspace$##$\hfil\cr}
+\def\endcomposite{\crcr\egroup % closes \halign
+        \kw{end}\egroup % ends the \vtop
+        \vskip\postCompositeSkip\egroup}
+
+\def\scompose#1#2{\@nameuse{composite*}{#1}{#2}\@nameuse{endcomposite*}}
+
+\newskip\preCompositeSkip \preCompositeSkip=1.2ex plus .5ex minus .3ex
+\newskip\postCompositeSkip \postCompositeSkip=1.2ex plus .5ex minus .3ex
+
+% record composites; likewise we have a short and a long form
+\newtoks\@recordName
+
+\def\record#1{%
+  \InvEncountered@false \InitEncountered@false
+  \@invTokens={}\@initTokens={}
+  \@recordName{#1}
+  \par\preRecordHook
+  \vskip\preRecordSkip
+  \@beginVerticalVDM
+  \moveright\VDMindent\hbox\bgroup
+          \setbox0=\hbox{$#1$\enspace::\enspace}%
+          \@makeColonActive\@changeLineSeparator
+          \advance\hsize by-\wd0 \box0
+          \@restoreMargins
+          %
+          % the \expandafters are necessary because TeX doesn't expand
+          % \halign specs when scanning for # and &
+          \vtop\bgroup\expandafter\halign\expandafter\bgroup
+                  \the\@recordAlign\strut\enspace&:\enspace$##$\hfil\cr}
+
+\def\endrecord{\crcr\egroup% closes halign
+        \egroup% closes vtop
+        \egroup% closes hbox
+  \ifInvEncountered@
+        \betweenRecordAndInvHook
+        \vskip\betweenRecordAndInvSkip
+        \moveright\VDMindent\@mathIndentedPara{\hsize}{inv }{%
+                \the\@invTokens}
+  \fi
+  \ifInitEncountered@
+        \betweenInvAndInitHook
+        \vskip\betweenInvAndInitSkip
+        \moveright\VDMindent\@mathIndentedPara{\hsize}{init }{%
+                \the\@initTokens}
+  \fi
+  \par\postRecordHook
+  \vskip\postRecordSkip}
+
+\def\inv{\global\InvEncountered@true \global\@invTokens=}
+\def\init{\global\InitEncountered@true \global\@initTokens=}
+
+\newif\ifInvEncountered@
+\newif\ifInitEncountered@
+\newtoks\@invTokens
+\newtoks\@initTokens
+\def\betweenRecordAndInvHook{}
+\def\betweenInvAndInitHook{}
+\newskip\betweenRecordAndInvSkip
+  \betweenRecordAndInvSkip=0.5ex plus 0.2ex minus 0.1ex
+\newskip\betweenInvAndInitSkip
+  \betweenInvAndInitSkip=0.5ex plus 0.2ex minus 0.1ex
+
+% the user can decide on the exact alignment of the field names
+\newtoks\@recordAlign
+\def\leftRecord{\@recordAlign={$##$\hfil}}
+\def\rightRecord{\@recordAlign={\hfil$##$}}
+\rightRecord
+
+% more catcode trickery
+\def\defrecord{\bgroup\@makeColonActive\@defrecord}
+\def\@defrecord#1#2{\record{#1}#2\endrecord\egroup}
+
+\newskip\preRecordSkip \preRecordSkip=.75ex plus .3ex minus .2ex
+\newskip\postRecordSkip \postRecordSkip=.75ex plus .3ex minus .2ex
+\newcount\preRecordPenalty \preRecordPenalty=0
+\newcount\postRecordPenalty \postRecordPenalty=-100
+\def\preRecordHook{\penalty\preRecordPenalty }
+\def\postRecordHook{\penalty\postRecordPenalty }
+
+% \chg: mu function on composites
+\def\chg#1#2#3{\mu(#1,#2\mapsto#3)}
+
+%----------------------------------------------------------------
+%
+%       Hooks
+%
+% hooked identifiers --- these are taken from the TeXbook, p.357, 359
+\def\leftharpoonupfill{$\m@th \mathord\leftharpoonup \mkern-6mu
+  \cleaders\hbox{$\mkern-2mu \mathord\minus \mkern-2mu$}\hfill
+  \mkern-6mu \mathord\minus$}  % p.357, \leftarrowfill
+
+\def\overleftharpoonup#1{{%
+  \boxmaxdepth=\maxdimen % this fixes Lamport's figures, but isn't necessary
+                         % for versions after 15 Dec 87
+  \vbox{\ialign{##\crcr % p.359, \overleftarrow
+    \leftharpoonupfill\crcr\noalign{\kern-\p@\nointerlineskip}
+    $\hfil\displaystyle{#1}\hfil$\crcr}}}}
+
+\let\hook=\overleftharpoonup  % c'est simple comme bonjour
+
+%-----------------------------------------------------------------
+%
+%       General formula environment, a bit like \[ \] but is
+%       indented to \VDMindent and will take \\
+%
+%
+\def\form#1{\formula #1\endformula}
+
+\def\formula{\par\preFormulaHook
+        \vskip\preFormulaSkip
+        \@beginVerticalVDM
+        \bgroup
+        \moveright\VDMindent\vtop\bgroup\@beginHorizontalVDM}
+\def\endformula{\@endHorizontalVDM\egroup % ends the vtop
+        \egroup % ends the overall group
+        \par\postFormulaHook
+        \vskip\postFormulaSkip}
+
+\newskip\preFormulaSkip \preFormulaSkip=1.2ex plus .5ex minus .3ex
+\newskip\postFormulaSkip \postFormulaSkip=1.2ex plus .5ex minus .3ex
+\newcount\preFormulaPenalty \preFormulaPenalty=0
+\newcount\postFormulaPenalty \postFormulaPenalty=-100
+\def\preFormulaHook{\penalty\preFormulaPenalty }
+\def\postFormulaHook{\penalty\postFormulaPenalty }
+
+%----------------------------------------------------------------
+%
+%       Formula within a box, when width is unknown
+%
+%       equivalent to \parbox[t]{\hsize}{\@beginHorizontalVDM
+%               ...\@endHorizontalVDM}
+%
+\def\formbox{\vtop\bgroup\@beginHorizontalVDM}
+\def\endformbox{\strut\@endHorizontalVDM\egroup}
+
+%----------------------------------------------------------------
+%
+%       special font for constants
+%
+\def\constantFont{\sc}
+\def\const#1{\hbox{\constantFont{#1}\/}}
+
+%----------------------------------------------------------------
+%
+%       line break and indent
+%
+\def\T#1{\\\hbox to #1em{}}
+
+%----------------------------------------------------------------
+%
+%       line break and push line after to RHS
+%
+\def\R{\\\hspace*{\fill}}
+
+%----------------------------------------------------------------
+%
+%       Proofs
+%
+% a proof environment for typesetting proofs in the "natural
+% deduction" style.
+
+\newdimen\ProofIndent \ProofIndent=\VDMindent
+\newdimen\ProofNumberWidth \ProofNumberWidth=\parindent
+
+\def\proof{\par\preProofHook
+        \vskip\preProofSkip
+        \let\&=\@proofLine
+        \moveright\ProofIndent\vtop\bgroup
+                \@indentLevel=1
+                \advance\linewidth by-\ProofIndent
+                \begin{tabbing}%
+                \hbox to\ProofNumberWidth{}\=\kill}     % template line
+\def\endproof{\end{tabbing}\advance\linewidth by\ProofIndent
+        \egroup % ends the \vtop
+        \par\postProofHook
+        \vskip\postProofSkip}
+
+\newskip\preProofSkip \preProofSkip=1.2ex plus .5ex minus .3ex
+\newskip\postProofSkip \postProofSkip=1.2ex plus .5ex minus .3ex
+
+\newcount\preProofPenalty \preProofPenalty=-100
+\newcount\postProofPenalty \postProofPenalty=0
+\def\preProofHook{\penalty\preProofPenalty }
+\def\postProofHook{\penalty\postProofPenalty }
+
+\def\From{\@indentProof\kw{from }\=%
+        \global\advance\@indentLevel by 1
+        \@enterMathMode}
+\def\Infer{\global\advance\@indentLevel by-1
+        \@indentProof\kw{infer }\@enterMathMode}
+\def\@proofLine{\@indentProof\@enterMathMode}
+\def\by{\`}
+
+\newcount\@indentLevel
+\newcount\@indentCount
+\def\@indentProof{% do \>, \@indentLevel times
+        \global\@indentCount=\@indentLevel
+        \@gloop \>\global\advance\@indentCount by-1
+        \ifnum\@indentCount>0
+        \repeat}
+
+% need special loop macros that works in across boxes
+\def\@gloop#1\repeat{\gdef\@body{#1}\@giterate}
+\def\@giterate{\@body \global\let\@gloopNext=\@giterate
+        \else \global\let\@gloopNext=\relax \fi \@gloopNext}
+
+% this enters math mode and sets the LaTeX macros \@stopfield up
+% to exit math mode
+\def\@enterMathMode{\def\@stopfield{$\egroup}$}
+
+%----------------------------------------------------------------
+\def\VDMauthor{M.Wolczko,
+CS Dept.,
+Univ. of Manchester, UK.
+mario@cs.man.ac.uk
+uknet!man.cs!mario}
+
+\def\VDMversion{vdm3.0}
+
+\typeout{BSI VDM style option <9 Jun 1992>}
+%----------------------------------------------------------------
+%
+%       Global changes
+%
+% All things that have to be invoked before the user's stuff appears
+% should go here.
+%
+% by default the math spacing and changes to @ and _ apply everywhere
+\@changeOtherMathcodes \@changeGlobalCatcodes
+%
+%-------------------the end--------------------------------------
+\endinput
+%
+%       Summary of penalties
+%
+%       Penalties in vertical mode
+%
+% \preOperationPenalty          before an op begins
+% \preExternalPenalty           between the header and externals of an op
+% \prePreConditionPenalty       before the precondition
+% \prePostConditionPenalty      before the postcondition
+% \postOperationPenalty         at the end of an op
+%
+% \preFunctionPenalty           before a fn begins
+% \betweenSignatureAndBodyPenalty -guess
+% \postFunctionPenalty          after a fn ends
+%
+% \preRecordPenalty             before a record
+% \postRecordPenalty            after a record
+%
+%       etc for formula, proof
+%
+%       Penalties in horizontal mode in boxes
+%
+% \linepenalty                  101             \@raggedRight
+% `if mm-exp ^ then..'          0               \SIf
+% `if ... then mm-exp ^ else'   -100            \SIf
+% `let mm-exp in ^ ...'         -100            \SLet
+% `map mm-exp ^ to ...'         -50             \map
+% ^\iff                         -50             \iff
+% ^\implies                     -35             \implies
+% func(args) \DEF^              -100            \begin{fn}
+% \binoppenalty                 10000
+% \relpenalty                   10000
+% \hyphenpenalty                -100            \suchthat
+% ^\to                          -100            \to
+% _^                            100             \@VDMunderscore
+%