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author | Karl Berry <karl@freefriends.org> | 2006-07-10 21:24:34 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2006-07-10 21:24:34 +0000 |
commit | ac151dac1f876a711cd50b4127c3c5aa8e837556 (patch) | |
tree | 622db4347270a735b6aefdf88f1b6954526665a1 /Master/texmf-dist/doc/latex | |
parent | a9018e6c8e9ffc9fdf4f881ab4726e90c01508d9 (diff) |
remove vdm package, since license is unstated, author apparently uncontactable, ancient stuff anyway
git-svn-id: svn://tug.org/texlive/trunk@1808 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex')
-rw-r--r-- | Master/texmf-dist/doc/latex/vdm/vdm.dvi | bin | 68980 -> 0 bytes | |||
-rw-r--r-- | Master/texmf-dist/doc/latex/vdm/vdm.tex | 1562 |
2 files changed, 0 insertions, 1562 deletions
diff --git a/Master/texmf-dist/doc/latex/vdm/vdm.dvi b/Master/texmf-dist/doc/latex/vdm/vdm.dvi Binary files differdeleted file mode 100644 index 268896fa44e..00000000000 --- a/Master/texmf-dist/doc/latex/vdm/vdm.dvi +++ /dev/null diff --git a/Master/texmf-dist/doc/latex/vdm/vdm.tex b/Master/texmf-dist/doc/latex/vdm/vdm.tex deleted file mode 100644 index ddce8336f38..00000000000 --- a/Master/texmf-dist/doc/latex/vdm/vdm.tex +++ /dev/null @@ -1,1562 +0,0 @@ -%%% ==================================================================== -%%% @LaTeX-file{ -%%% author = "Mario Wolczko", -%%% version = "3.02", -%%% date = "14 October 1994", -%%% filename = "vdm.tex", -%%% 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 = "Documentation for vdm.sty -%%% NOTE -%%% Mario no longer works at Manchester -%%% This is a minimal update to LaTeX2e -%%% By David Carlisle", -%%% } -%%% ==================================================================== -\documentclass{article} - -\usepackage{latexsym,vdm,verbatim} - - - -\title{Typesetting BSI VDM with \LaTeX} -\author{Mario Wolczko\\ -Dept. of Computer Science\\ -The University\\ -Manchester M13 9PL\\ -U.K.\\ -\texttt{mario@cs.man.ac.uk}, {\tt ...!uknet!man.cs!mario}} -\date{09 June 1992 \\ -Version 3.01} - -\newcommand{\Vdm}{{\tt vdm\/}} - -\newenvironment{dangerous}{\par\vspace{5pt}\bgroup\small\noindent}% - {\par\egroup\vspace{5pt}} - -\newlength{\righthalf} \setlength{\righthalf}{0.5\textwidth} -\newlength{\lefthalf} \setlength{\lefthalf}{0.4\textwidth} - -\newenvironment{leftside}{\noindent\hspace{0.1\textwidth}% - \minipage[t]{\lefthalf}\vspace{10pt}% - \noindent\begin{vdm}\leftskip=0pt\VDMindent=0pt}% - {\end{vdm}\endminipage} -\newenvironment{rightside}{\minipage[t]{\righthalf}\verbatim}% - {\endverbatim\endminipage} - - -\renewcommand{\^}[1]{$\langle${\rm #1\/}$\rangle$} - -\newcommand{\mmexp}{\^{math-mode-expression}} -\newcommand{\cs}[1]{\leavevmode\hbox{\tt \string#1}} - -\setlength{\VDMindent}{3\parindent} - -\setlength{\preOperationSkip}{0pt} -\setlength{\preFunctionSkip}{0pt} -\setlength{\preTypeSkip}{0pt} -\setlength{\preCompositeSkip}{0pt} -\setlength{\preRecordSkip}{0pt} -\setlength{\preFormulaSkip}{0pt} - -\begin{document} - -\maketitle - -\tableofcontents - -\section{Overview} - -This document describes a style option, \Vdm, for use with -\LaTeX. The purpose of \Vdm\ is to make the typesetting of VDM -specifications easy. Other goals are: -\begin{itemize} -\item To enable users of \Vdm\ to communicate their specifications - to others, possibly in a variety of concrete syntaxes, without - having to change their source files -\item To enable a user of \Vdm\ to concentrate on his% - \footnote{Read `his/her' for every occurence of `his'.} - specifications, and ignore the detailed layout as much as - possible. A side effect of this is that the effort required - to improve layout is concentrated in one place, within the - \Vdm\ macros. -\end{itemize} -(This version of the \Vdm\ style option uses the {\sc bsi} concrete -syntax. Any document prepared using earlier versions is still -accepted, but the way it is typeset will match more closely the {\sc -bsi} standard concrete syntax. There are also a few additional -commands (summarised at the end). Note that this is {\em not\/} a -complete style file for all of {\sc bsi vdm}.) - -But enough evangelising. Let's get to the the real meat. This -document is broken up into the following sections: -\begin{itemize} -\item General points about using \Vdm -\item Typesetting formulas -\item How to typeset data types -\item How to typeset functions -\item How to typeset operations -\item How to typeset proofs -\item How to tailor/extend the system for your own - application. -\end{itemize} -You should definitely read the first two sections---then you'll know -roughly what you're in for, and whether you want to continue. The -remaining sections can be read as and when you need them. - -\begin{dangerous} -In keeping with the best traditions of \TeX\ documentation, paragraphs -that contain material that is not essential for novices, but vital if -you want to parameterise or extend the system, are in smaller type, -like this one. -\end{dangerous} - -Just to give a preliminary example, here is some output from \Vdm, and -the corresponding input: - -\begin{vdm} -\begin{fn}{dec}{ptrs,om} \\ -\signature{ - \setof{Oop} \x \mapof{Oop}{Object} \to \mapof{Oop}{Object} -} -\If ptrs = \emptyset -\Then om -\Else \Let gone = \set{p \in ptrs | RC(om(p)) = 1} \In - \Let om' = gone \dsub om \In - \Let om'' = om' \owr - \map{p \mapsto \chg{om'(p)}{RC}{RC\minus 1}\R - | p \in ptrs \diff gone} \In - dec(\Union\set{\elems{BODY(om(p))} | p \in gone}, om'') -\Fi -\end{fn} - -\begin{op}[DESTROYPTR]\label{op-ex} -\args{ Obj, Ptr : Oop } -\ext{ \Wr OM : \mapof{Oop}{Basic_Object} } -\pre{ ptr \in \elems{BODY(om(obj))} } -\post{ om = ~{om} \owr \map{ obj \mapsto - \chg{om(obj)}{BODY}{BODY \diff \set{ptr}}}} -\end{op} -\end{vdm} - -% this is verbatim input -\begin{verbatim} -\begin{vdm} -\begin{fn}{dec}{ptrs,om} \\ -\signature{ - \setof{Oop} \x \mapof{Oop}{Object} \to \mapof{Oop}{Object} -} -\If ptrs = \emptyset -\Then om -\Else \Let gone = \set{p \in ptrs | RC(om(p)) = 1} \In - \Let om' = gone \dsub om \In - \Let om'' = om' \owr - \map{p \mapsto \chg{om'(p)}{RC}{RC\minus 1} - | p \in ptrs \diff gone} \In - dec(\Union\set{\elems{BODY(om(p))} | p \in gone}, om'') -\Fi -\end{fn} - -\begin{op}[DESTROYPTR] -\args{ Obj, Ptr : Oop } -\ext{ \Wr OM : \mapof{Oop}{Basic_Object} } -\pre{ ptr \in \elems{BODY(om(obj))} } -\post{ om = ~{om} \owr \map{ obj \mapsto - \chg{om(obj)}{BODY}{BODY \diff \set{ptr}}}} -\end{op} -\end{vdm} - -\end{verbatim} - - - -\section{Using \Vdm---General Points} - -To get at \Vdm, include {\tt vdm\/} as a document style option, e.g.: -\begin{verbatim} - \documentstyle[12pt,vdm]{report} -\end{verbatim} -\begin{dangerous} -To the best of my knowledge, the use of \Vdm\ does not conflict with -any of the other document styles, except when something has been -redefined. An attempt will be made to document all such redefinitions. -\end{dangerous} -Once \Vdm\ has been included, you can then use the {\tt vdm\/} -environment. For example, -\begin{verbatim} - \begin{vdm} - .... - \end{vdm} -\end{verbatim} -All specification material should be placed within the {\tt vdm\/} -environment. The use of \Vdm\ only affects text within the {\tt vdm\/} -environment, except for the following global changes (which are only -relevant when in math or display math mode): - - -\begin{enumerate} -\item The mathcodes of a\dots z and A\dots Z have been changed. In - plain English, this means that when you type letters in math - mode the inter-letter spacing may be different than it would be - had you not included \Vdm\ as an option.\footnote{This is not - the case if you are using PS\LaTeX, as that does not - distinguish text italic from math italic.} This is because - \LaTeX\ math mode is usually tuned for single letter - identifiers, as used by mathematicians for millenia. However, - you and I both know that most meaningful identifiers have more - than one letter in them, so \Vdm\ provides better spacing for - them. As an example, if you type \verb;$identifier$;, \LaTeX\ - would normally print {\defaultMathcodes$identifier$}, whereas - the use of \Vdm\ will yield $identifier$. - \begin{dangerous}If you really want to use the - `normal' inter-letter spacing, say \cs\defaultMathcodes. - \end{dangerous} -\item Underscore gives you an underscore, and not a subscript. If - you want a subscript use \verb;@;, e.g.,~$x@0$ is typed - \verb;x@0;, or use \TeX's \cs\sb\ macro. An \verb;@; is still an - @ when not in math mode. Occasionally you may find that an @ - in math mode {\em doesn't\/} give you a subscript - (particularly when used with moving arguments). Should - this happen, you are advised to use \TeX's \cs\sb\ macro, - e.g.,~\verb;$x\sb{0}$;. - \begin{dangerous} - If you don't use - underscores much, and you want to use \verb;_; for subscripts, - you can say \cs\underscoreon\ (and \cs\underscoreoff\ to - make it revert to its usual meaning in \Vdm). - \end{dangerous} -\item \verb;-; typesets a hyphen, and not a minus sign. VDM specifications - usually contain a lot more - \begin{vdm}$long-identifiers$\end{vdm}\ - than subtractions, so - on the whole this alteration should save effort. - If you really want - to do a single subtraction sign, use \cs\minus. - If you find the default is inappropriate, you can revert to - the original behaviour using \cs\mathminus; \cs\textminus\ is - the inverse. Example: \verb;a-b \ne\mathminus a-b; gives - \begin{vdm}$a-b \ne\mathminus a-b$\end{vdm}. -\item \verb;|; gives you a \begin{vdm}$|$\end{vdm}, and not a $\vert$. - Do you see the difference? No? The former goes between things, - e.g., \begin{vdm}$\set{x|p(x)}$\end{vdm}, while the latter is - a delimiter, e.g.,~$\vert x\vert$. - In VDM, most people use the former more than the latter, so again this - seems reasonable. - If you really want a $\vert$ (the second kind), - say \cs\vert. -\item In \TeX\ and \LaTeX\ \verb;~; has always been a tie (a space - between words at which the line is never broken). Well - in \Vdm\ it isn't. \verb;~x; will give you a - \begin{vdm}$~x$\end{vdm}. For long identifiers, such as - \begin{vdm}$~{long}$\end{vdm}, say - \verb;~{long};. - {\em Note that this only applies in math - mode; elsewhere a \verb;~; is still a tie.} -\item In math mode, the double quote character \verb;''; is actually - a macro. Placing text between pairs of double quotes causes - that text to be set in the normal text font. For example, - \verb;$x="a variable"$; gives you $x="a variable"$. - \begin{dangerous} - \indent If you want to change the font used for text placed between - quotes, redefine the command \cs\mathTextFont. By default - it is defined to be \cs\rm\ (\cs\mathrm\ for the New Font - Selection Scheme). - \end{dangerous} -\item The following macros have been altered in a non-trivial way: - \cs\forall, \cs\exists\ (see later). -\end{enumerate} - -\begin{dangerous} -When you typeset some VDM within the {\tt vdm\/} environment, by -default it is set in from the left margin by an amount equal to -\cs\parindent, the indentation at the beginning of each paragraph. -If you want to change this, change the value of \cs\VDMindent, e.g.: -\begin{verbatim} - \setlength{\VDMindent}{0cm} -\end{verbatim} -will make your specs come out flush left. This document has been -typeset with \cs\VDMindent\ equal to $3\times \cs\parindent$. - -Similarly, the right hand margin is controlled by a parameter called -\cs\VDMrindent. By default it is also set to \cs\parindent. -\end{dangerous} - -\begin{dangerous} -You can have a particular line spacing in force within the -{\tt vdm} environment. -The spacing within a {\tt vdm} environment is dictated by the -\cs\VDMbaselineskip\ command. Note that this is {\em not\/} a -length, but a command. By default it expands to \cs\baselineskip\ -so that the line spacing is that of the surrounding text, whatever -size that may be. To make it smaller, you may want to say -\begin{verbatim} - \renewcommand{\VDMbaselineskip}{0.8\baselineskip} -\end{verbatim} -for example. -\end{dangerous} - - -\section{Typesetting formulas} - -Most of the text you enter within {\tt vdm\/} environments will be in -\TeX's math mode, but VDM does its best to conceal this fact from you, -so that you should rarely, if ever, have to type a dollar sign. -However, several new features have been provided for the typesetting -of logical formulas. Firstly, operators with sensible names have been -provided: use \cs\Iff, \cs\Implies, \cs\Or, \cs\And\ -and \cs\Not\ for the operators~\begin{vdm}% -$\Leftrightarrow,\Rightarrow,\Or,\And$ and $\Not$\end{vdm}. -(To retain compatibility with a previous version, \cs\iff, -\cs\implies, \cs\and\ and \cs\neg\ are still provided, but -\cs\or\ is not.) - -A major change has come in the area of quantified expressions. In -VDM, they -have very well-defined forms, so the \LaTeX\ sequences \cs\forall\ -and \cs\exists\ have been re-defined to take arguments. For -example, to get -\begin{vdm} -\begin{formula} -\exists{x \in S}{p(x)} -\end{formula} -\end{vdm} -\noindent type -\begin{verbatim} - \exists{x \in S}{p(x)} -\end{verbatim} -Note the separating dot that was put in auto\-matically. If you want -one of these dots by itself, you can have one by saying -\cs\suchthat. - -In addition, two new quantifiers, \cs\unique\ and \cs\nexists, have -been added: - - -\noindent\begin{minipage}{\textwidth}\begin{leftside} -\begin{formula} -\unique{x \in S}{p(x)} -\end{formula} -\begin{formula} -\nexists{x \in S}{p(x)} -\end{formula} -\end{leftside}\begin{rightside} -\unique{x \in S}{p(x)} -\nexists{x \in S}{p(x)} -\end{rightside} -\end{minipage} - -Additionally, to complement \cs\unique, there is \cs\uniqueval. This -is the so-called ``iota-function'' that returns the unique value, if -there is one: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} -\begin{formula} -\uniqueval{x \in S}{p(x)} -\end{formula} -\end{leftside}\begin{rightside} -\uniqueval{x \in S}{p(x)} -\end{rightside} -\end{minipage} - - -\begin{dangerous} -If you want to use the old versions of \cs\forall\ and -\cs\exists\ they are available under the pseudonyms of -\cs\Forall\ and \cs\Exists. -\end{dangerous} - -If you find that the body of the quantified expression is too long to -fit comfortably on a line, there are *-forms of the above commands -that place the body of the quantified expression on a new line, -slightly indented. For example, - -\begin{vdm} -\begin{formula} -\exists*{x \in S}{ - p(x) \And q(x) \Or \Not p(x) \Implies r(x) \And S(x)} -\end{formula} -\end{vdm} - -\noindent can be obtained with -\begin{verbatim} - \exists*{x \in S}{p(x) \And q(x) \Or \Not p(x) - \Implies r(x) \And S(x)} -\end{verbatim} - -If you need ``Strachey'' brackets, e.g., $M\term{e}$, place the -material to appear within the brackets within \verb;\term{ ... };, -thus: \verb;$M\term{e}$;. - -A special control sequence, \cs\const, is available for constants. -To get, for example, $\const{Yes}|\const{No}$, type -\verb;\const{Yes}|\const{No};. -\begin{dangerous} -If you don't like the font that constants are set in, you can change -them by redefining the command \cs\constantFont. By -default it expands to \cs\sc. -\end{dangerous} - -\subsection{The {\tt formula} Environment} - -Occasionally you may want a formula on its own, between paragraphs of -text, say. Normally, the provided environments and commands suffice, -but sometimes they don't. If you need an odd equation to stand on its -own, use the {\tt formula} environment: -\begin{verbatim} - \begin{formula} - x = 10 - \Or \forall{i \in \Nat}{i \ne 10 \Implies i \ne x} - \end{formula} -\end{verbatim} -\sloppy -The {\tt formula} environment is similar to displayed math mode, -except: formulas are indented by \cs\VDMindent, not -\cs\mathindent, and line breaks can be made using \cs\\. -Also, within the {\tt formula} environment everything appears flush -left, as opposed to being centred. - -\subsection{Constructions} - -A particularly nice feature of \Vdm\ is that you can typeset multi-line -constructions such as those in the earlier example without having to -worry about, say, lining up ``thens'' and ``elses'' with ``ifs''. -In the following definitions, whenever you see the term \mmexp, you -should type an expression as if in math mode, but you needn't put -dollar signs in. All of the constructions described below can be used -where a \mmexp\ is required. Each construction is shown by example; -the output on the left results from the input on the right. -Also note that each macro name begins with an upper-case letter. -\TeX\ and \LaTeX\ frequently use the lower-case variants for -completely unrelated things. Naturally, chaos will ensue if you mix -the names up. - -Typesetting an \kw{if} is done using \cs\If\ \mmexp \cs\Then\ \mmexp -\cs\Else\ \mmexp \cs\Fi. - -\noindent\begin{minipage}{\textwidth}\begin{leftside} - \begin{formula} - \If x\in S - \Then S \diff x - \Else \emptyset - \Fi - \end{formula} -\end{leftside}% -\begin{rightside} -\If x\in S -\Then S \diff x -\Else \emptyset -\Fi -\end{verbatim} -\end{rightside} -\end{minipage} - -If you nest \cs\If{}s then you must enclose inner \cs\If{}s within -braces: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} - \begin{formula} - \If \ldots - \Then{ - \If \ldots - \Then \ldots - \Else \ldots - \Fi - }\Else - \Fi - \end{formula} -\end{leftside}\begin{rightside} -\If ... -\Then{ - \If ... - \Then ... - \Else ... - \Fi -}\Else -\Fi -\end{rightside} -\end{minipage} - -You are advised to place the extra braces exactly as above; don't let -extraneous spaces intervene between the keywords and the braces. - -The \cs\If\ macro always starts a new line for the \kw{then} and -\kw{else} parts. If you want \TeX\ to try to choose line breaks, use -\cs\SIf\ instead: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} - \begin{formula} - \SIf a=b - \Then c=d+e - \Else p=q+r+s+t+u - \Fi - \end{formula} -\end{leftside}% -\begin{rightside} -\SIf a=b -\Then c=d+e -\Else p=q+r+s+t+u -\Fi -\end{rightside} -\end{minipage} - -\mbox{\kw{let}\dots\kw{in}} constructions are done in a similar way: -\cs\Let{} \mmexp{} \cs\In{} \mmexp, and \cs\SLet{} \mmexp{} -\cs\In{} \mmexp. - -\noindent\begin{minipage}{\textwidth}\begin{leftside} - \begin{formula} - \Let x=f(y,z) \In - g(x)+h(x) - \end{formula} -\end{leftside}% -\begin{rightside} -\Let x=f(y,z) \In -g(x)+h(x) -\end{rightside} -\end{minipage} - -\noindent\begin{minipage}{\textwidth}\begin{leftside} - \begin{formula} - \SLet x=f(y,z) \In{x^2} - \end{formula} -\end{leftside}% -\begin{rightside} -\SLet x=f(y,z) \In{x^2} -\end{rightside} -\end{minipage} - -Notice that \cs\SLet\ takes a second argument, which is part of the -same `paragraph', where \cs\Let\ does not. - -The typesetting of a \kw{cases} clause is more complicated. It takes -the form: -\begin{verse} -\verb;\Cases{; \mmexp \verb;}; \\ -from-\mmexp \verb;&; to-\mmexp \cs\\ \\ -from-\mmexp \verb;&; to-\mmexp \cs\\ \\ -\dots \\ -\verb;\Otherwise{; \mmexp \verb;}; \\ -\verb;\Endcases; -\end{verse} - -The \cs\Otherwise\ field is optional. This construction follows a -general pattern that is common in \Vdm\ input: lists of things are -separated by \cs\\s, and subfields are separated by \verb;&;s or -\verb;:;s. -\begin{dangerous} -In reality, there is another, optional argument, after the -\cs\Endcases. If you were to try typesetting something like -\begin{verbatim} - (... var = \Cases ... - \Endcases) -\end{verbatim} -you'd find the closing right parenthesis in an unexpected place (on -the same line as the $=$, in fact). To get text to the right of the -\cs\Endcases\ you can place an optional argument within brackets -after it: -\begin{verbatim} - (... var = \Cases ... - \Endcases[)] -\end{verbatim} -Admittedly, this looks a little strange, but it does work. -\end{dangerous} - -Here is an example of \cs\Cases\ in action: - -\begin{formula} - \Cases{ select(x) } - \nil & \emptyset \\ - mk-Lst(hd,tl) & \set{hd} \union \elems{tl} - \Otherwise{ x } - \Endcases -\end{formula} - -\begin{verbatim} - \Cases{ select(x) } - \nil & \emptyset \\ - mk-Lst(hd,tl) & \set{hd} \union \elems{tl} - \Otherwise{ x } - \Endcases -\end{verbatim} - -Note the \cs\\ is a {\em separator\/} and not a {\em -terminator\/}---you don't need one after the last item. Also, the -\cs\Otherwise\ can appear anywhere between the \verb;\Cases{}; and the -\cs\Endcases, but it will always be typeset last. -\begin{dangerous} -Some people prefer the selectors to appear lined up on the left, some -on the right. If you want them to appear on the left, say -\cs\leftCases; if you want them on the right, say -\cs\rightCases. The scope of the \cs\leftCases\ and -\cs\rightCases\ commands is the current group. By default, you -get \cs\rightCases. -\end{dangerous} - -\subsubsection{The {\tt formbox} Environment} - -Occasionally you might find that you want to put a line break in a -place that can't handle \cs\\. For example, if you have a \cs\Cases\ -command and the rhs of a particular case is too big, you can't use -\cs\\ to break the line directly, as it will be interpreted as the -separator between cases. Then you must the {\tt formbox} environment. -It is similar to the {\tt formula} environment in that you can put all -sorts of things in it, but it can be used within other constructions, -unlike the {\tt formula} environment, which can only be used at the -outermost level. - -This example should convey the general idea: -\begin{verbatim} - \Cases{ f(x) } - mk-Very_long_constructor(foo,bar) & - {\begin{formbox} - long_predicate_with(foo) \\ - \And long_predicate_with(bar) - \end{formbox}} - ... -\end{verbatim} -\begin{vdm} -\begin{formula} - \Cases{ f(x) } - mk-Very_long_constructor(foo,bar) & - {\begin{formbox} - long_predicate_with(foo) \\ - \And long_predicate_with(bar) - \end{formbox}}\\ - \ldots - \Endcases -\end{formula} -\end{vdm} -Note the extras braces around the {\tt formbox}; these are required to -``hide'' the \cs\\ from the \cs\Cases. - -\subsection{Other General Points about Formulas} - -\cs\\ will% -\footnote{For `will' read `should'.} -{\em always\/} -start a new line. Sometimes this is done in addition to some other -function (as in the \cs\Cases\ macro, where it delimits a -particular case), but you should be able to use \cs\\ almost -anywhere to force a line break. Indeed, sooner or later you'll want -to typeset a long formula and \TeX\ will not be able to break the line -sensibly, or will choose an unpleasant break. In this case you'll -have to use \cs\\. - -Frequently you need to indent things within multi-line formulas. To -help you do this, a command is provided which breaks a line, and -indents the next line by an amount which you can supply (in units of -{\tt ems}). The \cs\T\ command takes a single argument that controls -how much the next line will be indented: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} -\begin{formula} -a \And b \T2 -\Implies b \And a \T1 -\Or d \And e -\end{formula} -\end{leftside}\begin{rightside} -a \And b \T2 -\Implies b \And a \T1 -\Or d \And e -\end{rightside} -\end{minipage} - -Along similar lines is the \cs\R\ command. This does a line break, -like \cs\\, but then pushes the formula on the next line as far to the -right as it can: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} -\begin{formula} -(a \And b \Implies b \And a) \R -\Or d \And e -\end{formula} -\end{leftside}\begin{rightside} -(a \And b \Implies b \And a) \R -\Or d \And e -\end{rightside} -\end{minipage} - -Beware: it may end up pushing it further to the right than you -expected! This is {\sc A Bug}, and {\sc Will Not Be Fixed}, so you'll -have to work around it. - -The \cs\If, \cs\Let, etc., constructions are all unusual in -that it's impossible to typeset something sensibly to the right of -them. For example, if you try -\begin{verbatim} - \exists{x \in S}{ - \If x=0 \Then S=Q \Else S=P \Fi} - \Or S=\emptyset -\end{verbatim} -then you'll get - -\begin{vdm} - \begin{formula} - \exists{x \in S}{\If x=0 \Then S=Q \Else S=P \Fi} \Or S=\emptyset - \end{formula} -\end{vdm} - -\noindent which is unlikely to be what you wanted. - -You should also remember that where \Vdm\ wants a \mmexp, \TeX\ will -be placed in math mode. This is usually the right thing to do, but -occasionally you might want a natural language comment to appear -there. -In this case you'll have to insert an \cs\mbox\ or a \cs\parbox\ -depending on whether your comment might span one or more lines: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} - \begin{formula} - \If \mbox{the condition is true} - \Then \mbox{do the true part} - \Else "do the false part" - \Fi - \end{formula} -\end{leftside}\begin{rightside} -\If \mbox{the condition is true} -\Then \mbox{do the true part} -\Else "do the false part" -\Fi -\end{rightside} -\end{minipage} -The else-part illustrates how quotes can be used an an abbreviation -for \verb;\mbox{...}; within math mode. - -Finally, all the constructions above will not break at a page -boundary. This means that you're in big trouble if you want to -typeset a three-page \cs\Cases. The only statement I can make to -mitigate this is: you shouldn't have expressions that complicated in -the first place---who do you expect to read them? Remember: ``truth -is beauty'', so if your formulas are not beautiful, then chances are -they're not true either. - - - - - -\section{Typesetting data types} - -The following table lists the primitive types and values available: - -\begin{center} -\begin{tabular}{|l|l|l|} -\hline -$\set{0,1,\dots}$ & $\Nat$ & \cs\Nat \\ -$\set{1,2,\dots}$ & $\Natone$ & \cs\Natone,\cs\Nati \\ -$\set{\dots,\minus1,0,1,\dots}$& $\Int$ & \cs\Int \\ -Rationals & $\Rat$ & \cs\Rat \\ -Real numbers & $\Real$ & \cs\Real \\ -$\set{\true,\false}$ & $\Bool$ & \cs\Bool \\ -Truth & $\true$ & \cs\true,\cs\True \\ -Falsehood & $\false$ & \cs\false,\cs\False\\ -Nil & $\nil$ & \cs\nil \\ -\hline -\end{tabular} -\end{center} - -If you need a new keyword, you can create one easily. For example, if -your favourite brand of logic has ``maybe'' as a value, you can say -\begin{verbatim} - \makeNewKeyword{\maybe}{maybe} -\end{verbatim} -and henceforth \cs\maybe\ is a valid control sequence that produces -the text \kw{maybe}. The text of the second argument to -\cs\makeNewKeyword\ can be anything; it doesn't have to match your -control sequence name. -\begin{dangerous} -If you don't like the font that keywords are set in, you can change -it by redefining the command \cs\keywordFontBeginSequence. By -default it expands to \cs\sf. -\end{dangerous} - -The following type-related commands are provided: - -\begin{center} -\begin{tabular}{|l|l|l|} -\hline -Output & Input & \\ -\hline -$\setof{x}$ & \verb;\setof{x}; & set type constructor \\ -$\set{a,b,c}$ & \verb;\set{a,b,c}; & set enumeration \\ -$\emptyset$ & \cs\emptyset & the empty set \\ -$\seqof{x}$ & \verb;\seqof{x}; & seq. type constructor\\ -$\seq{a,b,a,c}$ & \verb;\seq{a,b,a,c}; & seq. enumeration\\ -$\emptyseq$ & \cs\emptyseq & the empty sequence \\ -$\mapof{x}{y}$ & \verb;\mapof{x}{y}; & map type constructor \\ -$\mapinto{x}{y}$& \verb;\mapinto{x}{y}; & one-one map type \\ -$\map{p\mapsto x}$ - & \verb;\map{p\mapsto x}; & map enumeration\\ -$\emptymap$ & \cs\emptymap & the empty map \\ -\hline -\end{tabular} -\end{center} - -\noindent Here are the relevant operators: - -\begin{center}\small -\begin{tabular}{llllll} -$\in$ & \cs\in & - $\owr$ & \cs\owr & - $\sconc$ & \cs\sconc \\ -$\notin$ & \cs\notin & - $\dres$ & \cs\dres & - $\len{l}$ & \verb;\len{l};\\ -$\subset$ & \cs\subset& - $\rres$ & \cs\rres & - $\hd{l}$ & \verb;\hd{l}; \\ -$\subseteq$ & \cs\subseteq& - $\dsub$ & \cs\dsub & - $\tl{l}$ & \verb;\tl{l}; \\ -$\inter$ & \cs\inter,\cs\intersection;& - $\rsub$ & \cs\rsub & - $\elems{l}$ & \verb;\elems{l};\\ -$\Inter$ & \cs\Inter,\cs\Intersection;& - $\dom{m}$&\verb;\dom{m};& - $\inds{l}$ & \verb;\inds{l};\\ -$\union$ & \cs\union & - $\rng{m}$&\verb;\rng{m};& - $\Conc{l}$ & \verb;\Conc{l};\\ -$\Union$ & \cs\Union & - $\Min{s}$& \verb;\Min{s};& - $\cons{h,t}$ & \verb;\cons{h,t};\\ -$\diff$ & \cs\diff,\cs\difference;& - $\Max{s}$& \verb;\Max{s};& - & \\ -$\card{s}$ & \verb;\card{s};& - & & - & -\end{tabular} -\end{center} - -\begin{dangerous} -If you invent a new monadic keyword operator (like \dom{}, etc.), -then you can have \Vdm\ define for you a control sequence which -switches font, and puts the right spacing in. For example, -\begin{verbatim} - \newMonadicOperator{\inv}{inv} -\end{verbatim} -will define the \cs\inv\ control sequence to print -{\keywordFontBeginSequence inv\/}. Henceforth you can say, e.g., -\verb;\inv{Foo};. All such sequences take one argument (they are -monadic, after all). -\end{dangerous} - -You can define a new type using -\verb;\type{;type-name\verb;}{;type\verb;};: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} - \type{Complex}{\Real\x \Real} -\end{leftside}% -\begin{rightside} -\type{Complex}{\Real\x \Real} -\end{rightside} -\end{minipage} - -Composites types can be typeset using the {\tt composite} environment: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} - \begin{composite}{Datec} - day:\set{1,\ldots,366}, \\ - year:\set{1583,\ldots,2599} - \end{composite} -\end{leftside}% -\begin{rightside} -\begin{composite}{Datec} - day :\set{1,\ldots,366}, \\ - year:\set{1583,\ldots,2599} -\end{composite} -\end{rightside} -\end{minipage} - -There is also a {\tt composite*} environment (and an equivalent -\cs\scompose\ control sequence) that places the entire composite -type on a single line: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} - \begin{composite*}{Celsius} - \Real - \end{composite*} -\end{leftside}% -\begin{rightside} -\begin{composite*}{Celsius} - \Real -\end{composite*} -\end{rightside} -\end{minipage} - -\noindent\begin{minipage}{\textwidth}\begin{leftside} - \scompose{Celsius}{\Real} -\end{leftside}% -\begin{rightside} -\scompose{Celsius}{\Real} -\end{rightside} -\end{minipage} - -`Records' can be defined using the {\tt record\/} environment: - -\begin{verse} -\verb;\begin{record}{;record-type-name\verb;}; \\ -field-name \verb;:; field-type \cs\\ \\ -\dots \\ -\verb;\end{record}; -\end{verse} -The colons are used as sub-field separators. - -\noindent\begin{minipage}{\textwidth}\begin{leftside} - \begin{record}{PERSON} - NM : \seqof{Char} \\ - FEM : \Bool - \end{record} -\end{leftside}% -\begin{rightside} - \begin{record}{PERSON} - NM : \seqof{Char} \\ - FEM : \Bool - \end{record} -\end{rightside} -\end{minipage} - -If the definition is short, you may prefer to use a short form: -\begin{verbatim} - \defrecord{PERSON}{ - NM : \seqof{Char} \\ - FEM : \Bool - } -\end{verbatim} - -\begin{dangerous} -Some people prefer the field names to appear lined up on the left, some -on the right. If you want them to appear on the left, say -\cs\leftRecord; if you want them on the right, say -\cs\rightRecord. The scope of the \cs\leftRecord\ and -\cs\rightRecord\ commands are the current group. By default, you -get \cs\rightRecord. -\end{dangerous} - -Updating fields of composites using the $\mu$-function can be -specified using \cs\chg: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} - \begin{formula} - \chg{p}{FEM}{\Not man(q)} - \end{formula} -\end{leftside}% -\begin{rightside} -\chg{p}{FEM}{\Not man(q)} -\end{rightside} -\end{minipage} - -Notice that the $\mu$, parentheses, comma and $\mapsto$ were inserted -automatically. - - - -\section{How to Typeset Functions} - -Typesetting $\lambda$-expressions is easy: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} - \begin{formula} - \LambdaFn{x,y}{x^2+y^2} - \end{formula} -\end{leftside}% -\begin{rightside} -\LambdaFn{x,y}{x^2+y^2} -\end{rightside} -\end{minipage} - -As with \cs\forall, \cs\exists\ and \cs\unique, -\cs\LamdbaFn\ has a *-form that places the body of the function -below and to the right: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} - \begin{formula} - \LambdaFn*{x,y,z}{ - (x^2+y^2+z^2)^{\frac12}} - \end{formula} -\end{leftside}% -\begin{rightside} -\LambdaFn*{x,y,z}{ - (x^2+y^2+z^2)^{\frac12}} -\end{rightside} -\end{minipage} - -There is also a {\tt fn\/} (function) environment for defining named -functions. It has the following structure: -\begin{verse} -\verb;\begin{fn}{;name-of-function\verb;}{; argument-list \verb;}; \\ -\verb;\signature{;signature-of-function\verb;}; \\ -\^{optional precondition}\\ -\^{optional postcondition}\\ - body of function (a \mmexp) \\ -\verb;\end{fn}; -\end{verse} - -See the third page for an example. The \cs\signature\ is optional -and can be placed anywhere within the body---it will always be typeset -before the body. Useful macros within the \cs\signature\ are: -\cs\x\ and \cs\to, which yield $\x$ and~$\to$. Note that you can also -enter functions defined implicitly with pre- and post-conditions; see the -next section on how to enter them. - -All of the material in the section on formulas is relevant within the -body of the function. - -\sloppy\sloppy -If you frequently intersperse your function definitions with text (and you -should), you can save some typing by using the {\tt vdmfn\/} environment. -\cs\begin\verb;{vdmfn}; \dots \cs\end\verb;{vdmfn}; is equivalent to -\cs\begin\verb;{vdm};\cs\begin\verb;{fn}; \dots -\cs\end\verb;{fn};\cs\end\verb;{vdm};. - -The {\tt fn} environment also has a *-form that does not insert -parentheses around the argument list. For example: - - -\noindent\begin{minipage}{\textwidth}\begin{leftside} -\begin{fn*}{MP}{\term{p}\rho\sigma} -\ldots -\end{fn*} -\end{leftside}\begin{rightside} -\begin{fn*}{MP}{ - \term{p}\rho\sigma} -... -\end{fn*} -\end{rightside} -\end{minipage} - -If you require the $\DEF$ symbol by itself, then you can get it by -saying \cs\DEF. - -\subsection{Invariants} - -To typeset an invariant on a composite object, use the following -structure: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} -\begin{record}{D} - day : Day \\ - year : Year -\end{record} -\where -\begin{fn}{inv-D}{mk-D(d,y)} - is-leapyr(y) \Or d \le 365 -\end{fn} -\end{leftside}\begin{rightside} -\begin{record}{D} - day : Day \\ - year : Year -\end{record} -\where -\begin{fn}{inv-D}{mk-D(d,y)} - is-leapyr(y) \Or d \le 365 -\end{fn} -\end{rightside} -\end{minipage} - - -\section{How to Typeset Operations} - -Operations are typeset within the {\tt op\/} environment. -The general structure is: - -\begin{verse} -\verb;\begin{op}[;\^{name-of-operation}\verb;]; \\ -\verb;\args{;\^{list-of-arguments}\verb;}; \\ -\verb;\res{;\^{result(s)}\verb;}; \\ -\verb;\ext{;\^{list-of-externals}\verb;}; \\ -\^{pre-condition} \\ -\^{post-condition} \\ -\verb;\end{op}; -\end{verse} - -The order of the various parts within the {\tt op} environment is not -important; they will always be printed in a canonical style (see -page~\pageref{op-ex} for an example). - -Any of \cs\args, \cs\res, \cs\ext, \^{pre-condition} or -\^{post-condition} may be omitted. \verb;\begin{vdmop}; is an -abbreviation for \verb;\begin{vdm}\begin{op};; \verb;\end{vdmop}; is an -abbreviation for \verb;\end{op}\end{vdm};. - -The \^{name-of-operation} can be any one-line expression; it is -typeset in math mode. An alternative way of specifying the name of -the operation is to omit the optional argument (within \verb;[];), and -use \verb;\opname{;\^{name-of-operation}\verb;};, anywhere within the -body of the {\tt op} environment. - -The \^{list-of-arguments} is a \mmexp\ that can span multiple lines; -force a newline with \cs\\. If present it is placed within -parentheses. - -The \^{result(s)} is also any \mmexp. It is typeset to the right of -any arguments. - -The \^{list-of-externals} takes the following form: -\begin{verse} -\verb;\ext{; \\ -\quad $\langle$optional \cs\Rd\ or \cs\Wr$\rangle$ - \^{external-name(s)} {\tt :\/} \^{external-types} \cs\\ \\ -\quad $\langle$optional \cs\Rd\ or \cs\Wr$\rangle$ - \^{external-name(s)} {\tt :\/} \^{external-types} \cs\\ \\ -\dots \\ -\verb;}; -\end{verse} -Alternatively, if the list of externals is long (say, more than five -lines) the {\tt externals\/} environmment can be used: -\begin{verse} -\verb;\begin{externals}; \\ -\quad $\langle$optional \cs\Rd\ or \cs\Wr$\rangle$ - \^{external-name(s)} {\tt :\/} \^{external-types} \cs\\ \\ -\quad $\langle$optional \cs\Rd\ or \cs\Wr$\rangle$ - \^{external-name(s)} {\tt :\/} \^{external-types} \cs\\ \\ -\dots \\ -\verb;\end{externals}; -\end{verse} -\begin{dangerous} -Some people prefer the externals identifiers to appear lined up on the -left, some on the right. If you want them to appear on the left, say -\cs\leftExternals; if you want them on the right, say -\cs\rightExternals. The scope of the \cs\leftExternals\ and -\cs\rightExternals\ commands are the current group. By default, -you get \cs\leftExternals. -\end{dangerous} - - -The \^{pre-condition} and \^{post-condition} take similar forms: -\begin{verse} -\verb;\pre{;\mmexp\verb;}; \\ -\end{verse} -or -\begin{verse} -\verb;\begin{precond}; \\ -\mmexp \\ -\verb;\end{precond}; -\end{verse} -and -\begin{verse} -\verb;\post{;\mmexp\verb;}; \\ -\end{verse} -or -\begin{verse} -\verb;\begin{postcond}; \\ -\mmexp \\ -\verb;\end{postcond}; -\end{verse} -Use the \cs\begin\dots\cs\end\ style if the \mmexp\ is longer -than a few lines. -All of the constructs mentioned in the section on formulas can be used -within pre- and post-conditions. - -\section{Proofs} - -Here's an example of typesetting proofs in the ``natural deduction'' -style. - -\begin{proof} - \From E@1 \Or E@2 \\ -1 \From E@1 \\ - \Infer E@2 \Or E@1 \` $\vee$-I(h1) \\ -2 \From E@2 \\ - \Infer E@2 \Or E@1 \` $\vee$-I(h2) \\ - \Infer E@2 \Or E@1 \` $\vee$-E(h,1,2)\\ -\end{proof} -\begin{verbatim} - \begin{proof} - \From E@1 \Or E@2 \\ - 1 \From E@1 \\ - \Infer E@2 \Or E@1 \by $\vee$-I(h1) \\ - 2 \From E@2 \\ - \Infer E@2 \Or E@1 \by $\vee$-I(h2) \\ - \Infer E@2 \Or E@1 \by $\vee$-E(h,1,2) \\ - \end{proof} -\end{verbatim} - -Proofs are embedded within the {\tt proof} environment. (A proof does -not have to be within a {\tt vdm} environment.) Each line of the -proof ends with \cs\\. Lines that begin a subproof -have \cs\From\ after the equation number. Lines that end a -subproof have \cs\Infer\ after the equation number. Other lines -have \cs\& after the equation number (see next example). If you -don't need an equation number, just omit it, but you must have one of -either \cs\From, \cs\Infer\ or \cs\& on each proof line. -If you want to include a justification of a particular proof line at -the right hand end of the line, type it after a \cs\by. \cs\by\ -is optional; you needn't include it if you don't need a justification. - -Points worth bearing in mind: -\begin{itemize} -\item You are automatically placed in math mode after the - \cs\From, \cs\Infer\ or \cs\&; the math mode ends - at the next \cs\by\ or \cs\\. -\item You {\em cannot} break a line in the middle simply by using - \cs\\ before \cs\by; you must use separate proof lines - to split a formula. -\item You are within a {\tt tabbing} environment within a proof, so - you can use all the usual {\tt tabbing} commands (\cs\=, - \cs\>, etc.) to line things up across proof lines. Note - that you will explicitly have to enter math mode again after - any of these commands though. -\end{itemize} - -Here's another example: - -\begin{proof} - \From \forall{x\in X}{E(x); s\in X} \\ -1 \& \Not\exists{x\in X}{\Not E(x)} \` $\Forall$-defn(h)\\ -2 \& \Not\Not E(s/x) \` $\Not\Exists$-E(1,h)\\ - \Infer E(s/x) \\ -\end{proof} -\begin{verbatim} -\begin{proof} - \From \forall{x\in X}{E(x); s\in X} \\ -1 \& \Not\exists{x\in X}{\Not E(x)} \by $\Forall$-defn(h)\\ -2 \& \Not\Not E(s/x) \by $\Not\Exists$-E(1,h)\\ - \Infer E(s/x) \\ -\end{proof} -\end{verbatim} - -\begin{dangerous} -The amount of space used by the proof number can be changed by -changing the length \cs\ProofNumberWidth. The distance from the -left margin to the proof number is dictated by \cs\ProofIndent. -\end{dangerous} - - -\section{Customising the Style} - -{\em Some people are never satisfied.} We all know that it's true. -In order to cater for those who aren't satisfied with the output from -\Vdm, some attempt has been made to allow a limited degree of -customisation by the user. In particular, you can alter some of the -internal spacing chosen by \Vdm, and even have your own macros called -at chosen places within \Vdm's macros. Naturally, you are not advised -to try this unless you feel you have some idea of what you want, and -what you are doing. In this section we list the things that you can -change, in order of increasing difficulty. - -\subsection{Changing the Spacing} - -In several places, essentially arbitrary spacings have been chosen by -the author. The dimensions of these spaces are given by {\em rubber -lengths.}\footnote{See the \LaTeX\ book for an explanation of rubber -lengths} If you want to change any of them, use \LaTeX's -\cs\setlength\ or \cs\addtolength\ commands. -For example, -\begin{verbatim} - \setlength{\postHeaderSkip}{13.33pt plus 2pt minus 1pt} -\end{verbatim} - -\begin{dangerous} -The {\tt plus} and {\tt minus} parts of a length let you say how much -that length can grow or shrink by. For example, {\tt 12pt plus 2pt -minus 1pt} means that the length will be in the range 11--14pt, with -12pt as its ``natural'' length. -\end{dangerous} - -The spaces in question all appear around \Vdm\ items such as -operations, and in between major parts of such items. The names of -the lengths should convey where they apply. The following table lists -all the lengths, and their default settings. Note that an {\tt ex} is -about the height of an ``x'' in the current font, and an {\tt em} is -about the width of an ``M'' in the current font. - -\begin{center} -\begin{tabular}{|l|l|l|} -\hline -\em Length &\em Default size &\em Used within \\ -\hline -\cs\preOperationSkip &2ex $+$ 0.5ex $\minus$ 0.2ex & {\tt op} env \\ -\cs\postOperationSkip &2ex $+$ 0.5ex $\minus$ 0.2ex &\\ -\cs\postHeaderSkip &.5ex $+$ .2ex $\minus$ .2ex &\\ -\cs\postExternalsSkip &.5ex $+$ .2ex $\minus$ .2ex &\\ -\cs\postPreConditionSkip &.5ex $+$ .2ex $\minus$ .2ex &\\ -\hline -\cs\preFunctionSkip &2ex $+$ .5ex $\minus$ .2ex & {\tt fn} env \\ -\cs\postFunctionSkip &2ex $+$ .5ex $\minus$ .2ex &\\ -\cs\betweenSignatureAndBodySkip&1.2ex $+$ .3ex $\minus$ .2ex &\\ -\cs\betweenFunctionAndPreSkip&1.2ex $+$ .3ex $\minus$ .2ex &\\ -\hline -\cs\preTypeSkip &1.2ex $+$ .5ex $\minus$ .3ex & {\tt type} command \\ -\cs\postTypeSkip &1.2ex $+$ .5ex $\minus$ .3ex &\\ -\hline -\cs\preCompositeSkip &1.2ex $+$ .5ex $\minus$ .3ex & {\tt -composite} env \\ -\cs\postCompositeSkip &1.2ex $+$ .5ex $\minus$ .3ex &\\ -\hline -\cs\preRecordSkip &.75ex $+$ .3ex $\minus$ .2ex & {\tt -record} env \\ -\cs\postRecordSkip &.75ex $+$ .3ex $\minus$ .2ex &\\ -\hline -\cs\preFormulaSkip &1.2ex $+$ .5ex $\minus$ .3ex & {\tt -formula} env \\ -\cs\postFormulaSkip &1.2ex $+$ .5ex $\minus$ .3ex &\\ -\hline -\cs\preProofSkip &.75ex $+$ .3ex $\minus$ .2ex & {\tt -proof} env \\ -\cs\postProofSkip &.75ex $+$ .3ex $\minus$ .2ex &\\ -\hline -\end{tabular} -\end{center} - -\subsection{Controlling Line and Paragraph Breaks} - -\TeX\ uses the notion of {\em penalties\/} to decide where line and -page breaks go. Various values of penalty are used at places within -\Vdm\ to control breaks. To fully understand how to choose breaks, -read {\em The \TeX{}book}. However, put simply, penalties are whole -numbers in the range $\minus10000$~to $10000$. A value of $10000$ -means ``never break here,'' and a value of $\minus10000$ means -``always break here.'' Values in between penalise or encourage -breaking proportionally, so that, e.g.,~a value of $\minus500$ -encourages a break, but by no means forces it. A value of zero is -neutral. - -To assign to a penalty~\cs\p, write {\tt \cs\p=1000}, for example. -The table below list the penalties used by \Vdm, and their default -values. - -\begin{center} -\begin{tabular}{|l|l|l|} -\hline -\em Penalty Name & Default Value & Where Used \\ -\hline -\cs\preOperationPenalty & 0 & {\tt op} env \\ -\cs\preExternalPenalty & 2000 & \\ -\cs\prePreConditionPenalty & 800 & \\ -\cs\prePostConditionPenalty & 500 & \\ -\cs\postOperationPenalty & -500 & \\ -\hline -\cs\preFunctionPenalty & 0 & {\tt fn} env \\ -\cs\betweenSignatureAndBodyPenalty&500&\\ -\cs\betweenFunctionAndPrePenalty&1000&\\ -\cs\postFunctionPenalty & -500 & \\ -\hline -\cs\preRecordPenalty & 0 & {\tt record} env\\ -\cs\postRecordPenalty & -100 & \\ -\hline -\cs\preProofPenalty & -100 & {\tt proof} env\\ -\cs\postProofPenalty & 0 & \\ -\hline -\cs\preFormulaPenalty & -100 & {\tt formula} env\\ -\cs\postFormulaPenalty & 0 & \\ -\hline -\end{tabular} -\end{center} - - -\subsection{Unforeseen Changes} - -It is a truism that no matter how good the designer of a piece of -software is, he can never foresee all of its uses. In this case, the -author is quite certain that people will use \Vdm\ for all sorts of -things apart from typesetting VDM specifications. To cater for those -who find that \Vdm\ does almost, but not quite, what they want, a -number of {\em hooks\/} have been left in place. These hooks are -macros, which at the moment do little or nothing, but which can be -redefined by users to change the basic operation of \Vdm (see the {\tt -vdmindex} style for one such use). Needless to -say, anyone wishing to redefine a hook should already be competent in -the ways of \LaTeX\ at least, and probably \TeX\ as well. Rather than -trying to explain what the hooks do, and where they do it, the user -should look through the commented version of \Vdm\ (usually stored as -{\tt vdm.doc}) and figure it out for himself. Below are listed all -the provided hooks, their default definitions, and where they are used. - -\begin{center}\footnotesize -\begin{tabular}{|l|l|} -\hline -\em Name of hook & \em Default definition \\ -\hline -\multicolumn{2}{|c|}{{\tt op} environment} \\ -\hline -\cs\preOperationHook - &\verb*;\penalty\preOperationPenalty ;\\ -\cs\betweenHeaderAndExternalsHook - &\verb*;\penalty\preExternalPenalty ;\\ -\cs\betweenExternalsAndPreConditionHook - &\verb*;\penalty\prePreConditionPenalty ;\\ -\cs\betweenPreAndPostConditionHook - &\verb*;\penalty\prePostConditionPenalty ;\\ -\cs\postOperationHook - &\verb*;\penalty\postOperationPenalty ;\\ -\hline -\multicolumn{2}{|c|}{{\tt fn} environment} \\ -\hline -\cs\preFunctionHook - &\verb*;\penalty\preFunctionPenalty ;\\ -\cs\betweenSignatureAndBodyHook - &\verb*;\penalty\betweenSignatureAndBodyPenalty ; \\ -\cs\betweenFunctionAndPreHook&\verb*;\vskip-\lastskip ;\\ - &\verb;\vskip\betweenFunctionAndPreSkip ;\\ - &\verb*;\penalty\betweenSignatureAndBodyPenalty ; \\ -\cs\postFunctionHook - &\verb*;\penalty\postFunctionPenalty ; \\ -\hline -\multicolumn{2}{|c|}{{\tt record} environment} \\ -\hline -\cs\preRecordHook - &\verb*;\penalty\preRecordPenalty ;\\ -\cs\postRecordHook - &\verb*;\penalty\postRecordPenalty ; \\ -\hline -\multicolumn{2}{|c|}{{\tt proof} environment} \\ -\hline -\cs\preProofHook - &\verb*;\penalty\preProofPenalty ;\\ -\cs\postProofHook - &\verb*;\penalty\postProofPenalty ; \\ -\hline -\multicolumn{2}{|c|}{{\tt formula} environment} \\ -\hline -\cs\preFormulaHook - &\verb*;\penalty\preFormulaPenalty ;\\ -\cs\postFormulaHook - &\verb*;\penalty\postFormulaPenalty ; \\ -\hline -\end{tabular} -\end{center} - - -\section{Installing the \Vdm\ files} - -Place the file {\tt vdm.sty} in your standard directory for \LaTeX\ -style files (your system administrator will know where this is). If -you have the AMS fonts, change the appropriate line in {\tt vdm.sty} -(see instructions at the head of the file). -%If you're on a -%UNIX\footnote{UNIX is a trademark of AT\&T} system, you can make the -%{\tt .sty} file from the {\tt .doc} file with the command: -%\begin{verbatim} -% sed -e '/^[ ]*%/d' -e 's/%.*/%/' -e '/^$/d' vdm.doc > vdm.sty -%\end{verbatim} -%There are two characters between the square brackets: a tab and a -%space. If you're on some other system, figure out an equivalent -%command, or make the two files the same. - - -\section{New \Vdm\ commands (introduced for the {\sc bsi} version)} - -\begin{itemize} - \item There is a new keyword, \cs\rem. - \item Operations can also have an {\em error condition\/} part, typeset - after the postcondition. The error condition is placed in an {\tt - errcond} environment. An alternative short form, \cs\err, is also - available, which works in the same way as \cs\pre\ and \cs\post. - - {\emergencystretch=4pt In support of this new part, there is a hook, - \cs\betweenPostAndErrConditionHook, defined to be - \cs\penalty\ \cs\preErrConditionPenalty\ (the default penalty is - 500). The preceding white space is defined by - \cs\preErrConditionSkip\ (default .5ex $+$ .2ex $\minus$ .2ex).} - - \item \cs\Others\ is an alias for \cs\Otherwise. - \item Sequents are supported using the {\tt sequent} command, - thus: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} -\begin{formula} -\sequent{A}{B}\\ -\sequent*{Truth,Beauty,eq-intr}{Truth=Beauty} -\end{formula} -\end{leftside}\begin{rightside} -\sequent{A}{B} -\sequent*{Truth,Beauty,eq-intr} - {Truth=Beauty} -\end{rightside} -\end{minipage} - - \item Optional items can be typeset using \cs\Opt, thus: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} -$\Opt{fred}$ -\end{leftside}\begin{rightside} -\Opt{fred} -\end{rightside} -\end{minipage} - - \item There are two new monadic operators, \cs\abs\ and \cs\merge. - - \item A non-empty sequence type can be defined using \cs\neseqof, - thus: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} -\begin{formula} -\neseqof{\Nat} -\end{formula} -\end{leftside}\begin{rightside} -\neseqof{\Nat} -\end{rightside} -\end{minipage} - - \item Restricted types (those with invariants) can be typeset, with - or without initialisation, using \cs\ritype\ and \cs\rtype, thus: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} -\rtype{Partition}{\setof{(\setof{\Nat})}}{inv-Partition(p)} -\ritype{Dict}{\Bool \x (\mapof{Letter}{Dict})}{\true}{(\true,\emptymap)} -\end{leftside}\begin{rightside} -\rtype{Partition} - {\setof{(\setof{\Nat})}} - {inv-Partition(p)} -\ritype{Dict} - {\Bool \x (\mapof{Letter}{Dict})} - {\true} - {(\true,\emptymap)} -\end{rightside} -\end{minipage} - - Accompanying these commands are \cs\betweenTypeAndInvSkip\ (default - .5ex $+$ .3ex $\minus$ .2ex) and \cs\betweenInvAndInitSkip\ - (same default). - - \item Record types may also have invariants and initial states - attached, using the \cs\inv\ and \cs\init\ commands within the {\tt - record} environment, thus: - -\noindent\begin{minipage}{\textwidth}\begin{leftside} -\begin{record}{D} - day : Day \\ - year : Year -\inv{(mk-D(d,y)) \DEF\\ -\quad is-leapyr(y) \Or d \le 365} -\init{day=40 \And year=1962} -\end{record} -\end{leftside}\begin{rightside} -\begin{record}{D} - day : Day \\ - year : Year -\inv{(mk-D(d,y)) \DEF - is-leapyr(y) \Or d \le 365} -\init{day=40 \And year=1962} -\end{record} -\end{rightside} -\end{minipage} - - {\emergencystretch=4pt To go with these are \cs\betweenRecordAndInvHook, - \cs\betweenInvAndInitHook, \cs\betweenRecordAndInvSkip\ (default - .5ex $+$ .2ex $\minus$ .1ex), and \cs\betweenInvAndInitSkip\ - (same default).} - -\end{itemize} - -\section{Acknowledgements} - -Many people have passed on useful suggestions and comments about \Vdm\ -and this documentation; many thanks to all of them. In particular I -would like to acknowledge the extensive testing done by Lynn Marshall -while preparing her thesis, and her helpful comments and ideas, and -the numerous worthwhile discussions with Cliff Jones. Cliff, in -particular, deserves the highest commendation for bravery, in actually -using these macros in his book. Thanks to David Carlisle for helping -with the conversion to \TeX~3. - -\end{document} - |