% \iffalse meta-comment
%
% expressg.dtx
% Author: Peter Wilson (CUA) now at peter.r.wilson@boeing.com until June 2004
%                            (or: pandgwilson at earthlink dot net) 
% Copyright 1996, 2003, 2004 Peter R. Wilson
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either
% version 1.3 of this license or (at your option) any 
% later version.
% The latest version of the license is in
%    http://www.latex-project.org/lppl.txt
% and version 1.3 or later is part of all distributions of
% LaTeX version 2003/06/01 or later.
%
% This work has the LPPL maintenance status "author-maintained".
%
% This work consists of the files listed in the README file.
%
% If you do not have the docmfp package (available from CTAN in
% tex-archive/macros/latex/contrib/supported), comment out the
% \usepackage{docmfp} line below and uncomment the line following it.
% 
%<*driver>
\documentclass{ltxdoc}
\usepackage{docmfp}
%%%% \newenvironment{variable}[1]{}{} \newenvironment{routine}[1]{}{}
\providecommand{\DescribeVariable}[1]{} \providecommand{\DescribeRoutine}[1]{}
\providecommand{\variablestring}{} \renewcommand{\variablestring}{\space(v)}
\providecommand{\routinestring}{} \renewcommand{\routinestring}{\space(r)}
\EnableCrossrefs
\CodelineIndex
\setcounter{StandardModuleDepth}{1}

\begin{document}
  \DocInput{expressg.dtx}
\end{document}
%</driver>
%
% \fi
%
% \CheckSum{171}
%
% \DoNotIndex{\',\.,\@M,\@@input,\@addtoreset,\@arabic,\@badmath}
% \DoNotIndex{\@centercr,\@cite}
% \DoNotIndex{\@dotsep,\@empty,\@float,\@gobble,\@gobbletwo,\@ignoretrue}
% \DoNotIndex{\@input,\@ixpt,\@m}
% \DoNotIndex{\@minus,\@mkboth,\@ne,\@nil,\@nomath,\@plus,\@set@topoint}
% \DoNotIndex{\@tempboxa,\@tempcnta,\@tempdima,\@tempdimb}
% \DoNotIndex{\@tempswafalse,\@tempswatrue,\@viipt,\@viiipt,\@vipt}
% \DoNotIndex{\@vpt,\@warning,\@xiipt,\@xipt,\@xivpt,\@xpt,\@xviipt}
% \DoNotIndex{\@xxpt,\@xxvpt,\\,\ ,\addpenalty,\addtolength,\addvspace}
% \DoNotIndex{\advance,\Alph,\alph}
% \DoNotIndex{\arabic,\ast,\begin,\begingroup,\bfseries,\bgroup,\box}
% \DoNotIndex{\bullet}
% \DoNotIndex{\cdot,\cite,\CodelineIndex,\cr,\day,\DeclareOption}
% \DoNotIndex{\def,\DisableCrossrefs,\divide,\DocInput,\documentclass}
% \DoNotIndex{\DoNotIndex,\egroup,\ifdim,\else,\fi,\em,\endtrivlist}
% \DoNotIndex{\EnableCrossrefs,\end,\end@dblfloat,\end@float,\endgroup}
% \DoNotIndex{\endlist,\everycr,\everypar,\ExecuteOptions,\expandafter}
% \DoNotIndex{\fbox}
% \DoNotIndex{\filedate,\filename,\fileversion,\fontsize,\framebox,\gdef}
% \DoNotIndex{\global,\halign,\hangindent,\hbox,\hfil,\hfill,\hrule}
% \DoNotIndex{\hsize,\hskip,\hspace,\hss,\if@tempswa,\ifcase,\or,\fi,\fi}
% \DoNotIndex{\ifhmode,\ifvmode,\ifnum,\iftrue,\ifx,\fi,\fi,\fi,\fi,\fi}
% \DoNotIndex{\input}
% \DoNotIndex{\jobname,\kern,\leavevmode,\let,\leftmark}
% \DoNotIndex{\list,\llap,\long,\m@ne,\m@th,\mark,\markboth,\markright}
% \DoNotIndex{\month,\newcommand,\newcounter,\newenvironment}
% \DoNotIndex{\NeedsTeXFormat,\newdimen}
% \DoNotIndex{\newlength,\newpage,\nobreak,\noindent,\null,\number}
% \DoNotIndex{\numberline,\OldMakeindex,\OnlyDescription,\p@}
% \DoNotIndex{\pagestyle,\par,\paragraph,\paragraphmark,\parfillskip}
% \DoNotIndex{\penalty,\PrintChanges,\PrintIndex,\ProcessOptions}
% \DoNotIndex{\protect,\ProvidesClass,\raggedbottom,\raggedright}
% \DoNotIndex{\refstepcounter,\relax,\renewcommand,\reset@font}
% \DoNotIndex{\rightmargin,\rightmark,\rightskip,\rlap,\rmfamily,\roman}
% \DoNotIndex{\roman,\secdef,\selectfont,\setbox,\setcounter,\setlength}
% \DoNotIndex{\settowidth,\sfcode,\skip,\sloppy,\slshape,\space}
% \DoNotIndex{\symbol,\the,\trivlist,\typeout,\tw@,\undefined,\uppercase}
% \DoNotIndex{\usecounter,\usefont,\usepackage,\vfil,\vfill,\viiipt}
% \DoNotIndex{\viipt,\vipt,\vskip,\vspace}
% \DoNotIndex{\wd,\xiipt,\year,\z@}
%
% \changes{v1.0}{1996/05/09}{First public release}
% \changes{v1.1}{1999/10/30}{Improved documentation using docmfp package}
% \changes{v1.1}{1999/10/30}{Reordered descriptions and code}
% \changes{v1.1}{1999/10/30}{Deleted Express Book examples}
% \changes{v1.1}{1999/10/30}{Updated references}
% \changes{v1.2}{1999/11/15}{Reincluded Express Book examples, plus NIAM and S-M}
% \changes{v1.3}{2000/05/22}{Added smoothing, drawdrum, and others}
% \changes{v1.4}{2000/07/10}{Added sharp and smooth lines}
% \changes{v1.5}{2003/07/31}{Minor bug fixes}
% \changes{v1.6}{2004/02/29}{More boxes}
% \changes{v1.61}{2004/03/17}{Minor namespace feature fix}
%
% \newcommand{\dtxfilename}{\texttt{expressg.dtx}}
% ^^A \def\fileversion{v1.0}
% \def\firstfiledate{1996/05/09}
% ^^A \def\fileversion{v1.1}
% ^^A \def\filedate{1999/10/30}
% ^^A \def\fileversion{v1.2}
% ^^A \def\filedate{1999/11/15}
% ^^A \def\fileversion{v1.3}
% ^^A \def\filedate{2000/05/22}
% \def\fileversion{v1.4} \def\filedate{2000/07/10}
% \def\fileversion{v1.5} \def\filedate{2003/07/31}
% \def\fileversion{v1.6} \def\filedate{2004/02/29}
% \def\fileversion{v1.61} \def\filedate{2004/03/17}
% \newcommand*{\Lpack}[1]{\textsf {#1}}           ^^A typeset a package
% \newcommand*{\Lopt}[1]{\textsf {#1}}            ^^A typeset an option
% \newcommand*{\file}[1]{\texttt {#1}}            ^^A typeset a file
% \newcommand*{\Lcount}[1]{\textsl {\small#1}}    ^^A typeset a counter
% \newcommand*{\pstyle}[1]{\textsl {#1}}          ^^A typeset a pagestyle
% \newcommand*{\Lenv}[1]{\texttt {#1}}            ^^A typeset an environment
% \newcommand*{\Express}{\textsc{express}}
% \newcommand*{\ExpressG}{\textsc{express-g}}
% \newcommand*{\Mpost}{\textsc{MetaPost}}
% \newcommand*{\Mfont}{METAFONT}
% \newcommand*{\fref}[1]{Figure~\ref{#1}}
% \newcommand*{\pref}[1]{page~\pageref{#1}}
% \newcommand*{\PS}{PostScript}
% \newcommand*{\EPS}{Encapsulated \PS}
% \newcommand*{\pdflatex}{pdf\LaTeX}
%
% \title{The \Lpack{Expressg} \Mpost{} package for drawing
%        box-line-annotation diagrams\thanks{This
%        file (\dtxfilename) has version number \fileversion, last revised
%        \filedate.}}
%
% \author{%
% Peter Wilson\\
% Catholic University of America \\
% Now at \texttt{peter.r.wilson@boeing.com}
% }
% \date{(First published \firstfiledate) \\ \filedate}
% \maketitle
% \begin{abstract}
%    The \Lpack{expressg} \Mpost{} package provides facilities to assist in
% drawing diagrams that consist of boxes, lines, and annotations.
% Particular support is provided for creating \ExpressG{} diagrams
% \end{abstract}
% \tableofcontents
% \listoffigures
%
% \StopEventually{}
%
% \section{Introduction}
%
%    \ExpressG{} is an ISO international standard graphical information 
% modeling
% language~\cite{STEP11,EBOOK}, and is a subset of the \Express{} lexical
% object-flavoured information modeling language. Like most graphical
% modeling languages, \ExpressG{} diagrams consist of boxes, lines, and
% annotations associated with the boxes and the lines. As a colleague
% of mine once put it, these kinds of graphical languages are BLA 
% (boxes, lines, annotations) with respect to lexical languages.
%
%    \Mpost~\cite{MPOST} is a powerful lexical language for producing
% \EPS\footnote{\PS{} is a registered trademark of Adobe
% Systems Incorporated.} diagrams, and is based on the \Mfont~\cite{MFONT} 
% language for creating fonts.
%
%    The \Lpack{expressg} package provides extensions to the base
% \Mpost{} language to facilitate the creation of \ExpressG{} diagrams.
% The package may also be used as is, or certainly by
% extension, for the creation of other BLA diagrams. 
%
%    \Mpost{} is typically used to generate pictures for inclusion
% in \LaTeX{} documents~\cite{LATEX}. By default it uses \TeX{} for
% typesetting any text; this behaviour can be modified so that \LaTeX{}
% is used instead. If standard \PS{} fonts (like Times) are
% used, then \LaTeX{} typesetting may be avoided altogether. Running
% \Mpost{} and methods of including \Mpost{} diagrams in (pdf)LaTeX
% documents are described in~\cite{METAFP}.
%
%
%    The \Lpack{expressg} package has been some years 
% in the making. For
% occasional diagrams I got by with using either the simple \LaTeX{}
% picture commands, 
% or general GUI drawing packages. As time went on and the number
% and complexity of the diagrams increased it became, to me at least, more
% important to use a robust and powerful drawing language than fancy
% GUI packages. This was especially important if a diagram had to be
% changed at a later date, as the language denoted exactly how the drawing
% had been produced. With the GUI tools all that you had was the picture
% and whatever graphics file format the tool used --- there was no 
% user-sensible record
% of how any result was achieved. Also, generally speaking I find it quicker
% to use \Mpost{} than a GUI tool as too much time has to be spent using
% a mouse or a cursor to reposition and rescale the drawing elements.
% 
%    Section~\ref{sec:usc} describes the facilities provided by the package.
% Several worked 
% example diagrams are presented in Section~\ref{sec:example}, together
% with information on how to run \Mpost.
% Commented code for the package macros\footnote{If requested, 
% I may be prepared to consider providing additional macros, but no promises.}
% is in Section~\ref{sec:mf}.
%
%    It is assumed that the reader has some understanding of \Mpost, although
% the example in Section~\ref{sec:example} does provide an 
% \textit{aide-memoire} for most of the \Mpost{} constructs that are likely
% to be used in creating BLA diagrams. The definitive \Mpost{}
% manual is~\cite{MPOST} but both~\cite{HOENIG98} and~\cite{GOOSSENS97}
% give some interesting examples of how to use it; in fact the front cover
% of Hoenig's book is a \Mpost{} picture. 
% Similarly, some familiarity with
% BLA diagramming would be of assistance.
%
%    I suggest that on first reading it may be sensible to skim
% Section~\ref{sec:usc} first 
% and then peruse the example in Section~\ref{sec:example} more closely. 
% After this
% go back and re-read Section~\ref{sec:usc} as it then should make 
% more sense.
%
% This manual is typeset according to the conventions of the
% \LaTeX{} \textsc{docstrip} utility which enables the automatic
% extraction of the \LaTeX{} macro source files~\cite{GOOSSENS94}.
%
%
%
% \section{The \Lpack{expressg} package} \label{sec:usc}
%
% \subsection{Internal variables}
%
% The package includes several internal variables that are initialised to
% commonly appropriate values.
%    This section describes the principal internal variables. 
% Short descriptions
% of the others, which
% are likely to be used in diagrams only very occasionally, can be found
% in Section~\ref{sec:mf}.
%
%    The values of internal variables in \Mpost{} can only be changed via
% assignment. For example:
% \begin{verbatim}
% internal_variable := expression;
% \end{verbatim}
%
% \DescribeVariable{u}
% \DescribeVariable{maxx}
% \DescribeVariable{maxy}
% |u| is the value of the unit of length for a diagram; it is initialised
% to 1mm. All lengths, except for line thicknesses,
%  are defined in terms of |u|. 
% |maxx| and |maxy| are the maximum x and y coordinate values
% for a diagram. These are initialised to the maximum size for a diagram
% within an ISO standard document (i.e., |maxx:=159.5u| and |maxy:=210u|).
%
%    The next set of variables control the thickness of lines and the
% dimensions of line end styles.
%
% \DescribeVariable{normalpen}
% Lines with normal linethickness are drawn with |normalpen|.
%
% \DescribeVariable{thickpen}
% Thick lines are drawn with |thickpen|.
%
% \DescribeVariable{thinpenpen}
% Thin lines are drawn with |thinpen|.
%
% \DescribeVariable{dotspen}
% Dotted lines are drawn with |dotspen|.
%
% \DescribeVariable{dotpen}
%  |dotpen| is for drawing the black dot line end style.
%
% \DescribeVariable{dotdiam}
% |dotdiam| is the diameter of an open circle or dot line end style.
%
% \DescribeVariable{smoothrad}
% |smoothrad| is the radius of the circular arc used to round the join between
% two straight lines.
%
% \DescribeVariable{drumlid}
% |drumlid| is the ratio of the minor to major diameter of the ellipse
% forming the top of the drum box; the larger the value the more the 
% apparent viewpoint shifts to above the drum. The default value is 0.2.
%
% \begin{figure}
%   \setlength{\unitlength}{1mm}
%   \centering
%   \begin{picture}(105,40)
%     \put(0,0){\framebox(105,40){}}
%     \put(5,0){\begin{picture}(60,40)
%   ^^A    \put(0,0){\framebox(60,40){}}
%       \thicklines
%       \put(0,20){\line(1,0){10}}
%       \put(10,10){\line(2,1){20}}
%       \put(10,30){\line(2,-1){20}}
%       \put(10,10){\line(0,1){20}}
%       \thinlines
%       \put(10,5){\vector(1,0){20}} \put(10,5){\vector(-1,0){0}}
%       \put(20,3){\makebox(0,0)[t]{length}}
%       \put(35,10){\vector(0,1){20}} \put(35,10){\vector(0,-1){0}}
%       \put(40,20){\makebox(0,0)[l]{base width}}
%     \end{picture}}
%     \put(65,0){\begin{picture}(35,40)
%  ^^A     \put(0,0){\framebox(60,40){}}
%       \thicklines
%       \put(5,20){\line(1,0){30}}
%       \put(5,10){\line(2,1){20}}
%       \put(5,30){\line(2,-1){20}}
%       \thinlines
%       \put(5,5){\vector(1,0){20}} \put(5,5){\vector(-1,0){0}}
%       \put(15,3){\makebox(0,0)[t]{length}}
%       \put(0,10){\vector(0,1){20}} \put(0,10){\vector(0,-1){0}}
%     \end{picture}}
%  \end{picture}
%  \caption{Length parameters for arrowhead and fanin line end styles}\label{fig:trifan}
% \end{figure}
%
%
% \DescribeVariable{gal}
% \DescribeVariable{gab}
% An arrowhead is defined by the height of the triangle and the base of
% the triangle forming the arrowhead, as shown in \fref{fig:trifan}. 
% |gal| and |gab| are the length 
% and base width of arrows for arrowed line end styles. 
% 
% \DescribeVariable{gfl}
% \DescribeVariable{gfb}
% Like an arrowhead, a fanin is defined by the height and the base of
% the triangular fan shape, as shown in \fref{fig:trifan}. 
% |gfl| and |gfb| are the length and base
% width of fans for fanin line end styles. They are initialised to the
% default values.
%
%    The next set of variables control certain geometric aspects of
% the various \ExpressG{} boxes.
%
% \DescribeVariable{onelineh}
% |onelineh| is the minimum height of a box that encloses a single
% line of text. This is initialised to |5u|.
%
% \begin{figure}
%   \setlength{\unitlength}{1mm}
%   \centering
%   \begin{picture}(65,40)
%     \put(0,0){\framebox(65,40){}}
%     \put(5,0){\begin{picture}(60,40)
%  ^^A     \put(0,0){\framebox(60,40){}}
%       \thicklines
%       \put(0,10){\framebox(40,15){}}
%       \put(30,10){\line(0,1){15}}
%       \thinlines
%       \put(0,5){\vector(1,0){40}} \put(0,5){\vector(-1,0){0}}
%       \put(20,3){\makebox(0,0)[t]{length}}
%       \put(45,10){\vector(0,1){15}} \put(45,10){\vector(0,-1){0}}
%       \put(47,17.5){\makebox(0,0)[l]{height}}
%       \put(40,30){\vector(-1,0){10}} \put(40,30){\vector(1,0){0}}
%       \put(35,32){\makebox(0,0)[b]{inset}}
%     \end{picture}}
%  \end{picture}
%  \caption{Parameters for (inset) boxes}\label{fig:bool}
% \end{figure}
%
% \DescribeVariable{sdtbl}
% \DescribeVariable{sdtbh}
% \DescribeVariable{sdtbs}
% The length (|sdtbl|), height (|sdtbh|) and line inset (|sdtbs|) for 
% simple data type boxes (e.g., a BOOLEAN data type box), as illustrated
% in \fref{fig:bool}. These are
% initialised as |22u|, |onelineh| and |2u| respectively.
% 
% \DescribeVariable{sdtebl}
% \DescribeVariable{sdtebh}
% \DescribeVariable{sdtebs}
% The length (|sdtebl|), height (|sdtebh|) and line inset (|sdtebs|) 
% for a simple data type EXPRESSION box. The value of |sdtebl| is |28u|,
% and the other values are the same as for the other simple data type boxes.
%
% \DescribeVariable{sdtbgel}
% \DescribeVariable{sdtbgeh}
% \DescribeVariable{sdtbges}
% The length (|sdtbgel|), height (|sdtbgeh|) and inset for GENERICENT
% data type boxes. The value of |sdtbgel| is |38u|,
% and the other values are the same as for the other simple data type boxes.
%
% \DescribeVariable{pconl}
% \DescribeVariable{pconh}
% The length (|pconl|) of an average numeric (proxy) page connector 
% (e.g., for |(9,9 (9,9))|) 
% and the height (|pconh|)  
% of an average page connector, which is initialised for one line of text.
%
% \DescribeVariable{enth}
% \DescribeVariable{typeh}
% \DescribeVariable{schemah}
% The heights of an average entity (|enth|), 
% type --- including enumeration and select --- (|typeh|),
% and schema (|schemah|) boxes. These are all initialised to cater for
% one line of text.
%
% \DescribeVariable{ish}
% \DescribeVariable{isrh}
% |ish| is the height of an interschema reference box with one line of text.
% |isrh| is the height of an interschema reference box with a rename, where
% there is one line of text each for the original and renamed
% names.
%
% \DescribeVariable{eventh}
% \DescribeVariable{eventslope}
% The height (|eventh|) of a one-lined event box, and the slope (|eventslope|)
% of the sides of an
% event box (e.g., 0.25 or 1/4).
%
%    The next set of variables control the amount of space surrounding text
% on \ExpressG{} diagrams.
%
% \DescribeVariable{nextra}
% |nextra| is the margin around names when put into entity, schema, 
% interschema reference,
% page connector, and event boxes.
% 
% \DescribeVariable{niextra}
% |niextra| is the margin around names when put into type boxes.
% 
% \DescribeVariable{ndextra}
% |ndextra| is the margin around names when used on attribute lines.
%
% \subsection{Routines}
%
% The principal aspects of an \ExpressG{} diagram are lines and line ends of 
% various styles, and boxes of several different kinds. Many routines
% are provided for positioning and drawing these on a diagram.
%
%    The following sections describe most of the routines. Short descriptions
% of the others, which
% are effectively only used as internal support routines, can be found
% in Section~\ref{sec:mf}.
%
%     A note on naming conventions used in describing the routines:
% \begin{itemize}
% \item As usual with \Mpost, a name starting with |z| is a point, and
% names staring with |x| or |y| are x- and y-coordinates respectively.
% \item The letters |i| through |n| denote (point, coordinate) suffixes.
%       Suffixes are usually a number, such as |37|, but may also have 
%       alphanumeric characters after the number (e.g., |37C2D|).
% \end{itemize}
%
%
% \subsubsection{Utility routines}
%
% Several utility routines are provided defining some shortcuts and 
% to ease some of the calculations
% that may be required when producing a diagram.
%
% \DescribeRoutine{VH}
% |VH(j, k)| calculates the intersection point, |zjvh|, between the vertical
% line through the point |zj| and the horizontal line through the point |zk|,
% as shown in \fref{fig:vhvh}.
%
%     
% \DescribeRoutine{VhV}
% |VhV(j, k)| calculates the point |zjvhv| on the vertical line through
% the point |zj| and the point |zkvhv| on the vertical line through the
% point |zk|, such that the line |zjvhv--zkvhv| is horizontal and centered
% vertically between the two given points,
% as shown in \fref{fig:vhvh}.
%
% \begin{figure}
%   \setlength{\unitlength}{1mm}
%   \centering
%   \begin{picture}(130,50)
%     \put(0,0){\framebox(120,50){}}
%     \put(5,5){\begin{picture}(30,40)
%   ^^A    \put(0,0){\framebox(30,40){}}
%       \put(5,35){\circle*{2}}
%       \put(3,37){\makebox(0,0)[br]{\texttt{zj}}}
%       \put(25,5){\circle*{2}}
%       \put(27,3){\makebox(0,0)[tl]{\texttt{zk}}}
%       \put(5,5){\circle{2}}
%       \put(3,3){\makebox(0,0)[tr]{\texttt{zjvh}}}
%       \put(5,0){\line(0,1){40}}
%       \put(0,5){\line(1,0){30}}
%     \end{picture}}
%     \put(45,5){\begin{picture}(30,40)
%   ^^A    \put(0,0){\framebox(30,40){}}
%       \put(5,35){\circle*{2}}
%       \put(3,37){\makebox(0,0)[br]{\texttt{zj}}}
%       \put(25,5){\circle*{2}}
%       \put(27,3){\makebox(0,0)[tl]{\texttt{zk}}}
%       \put(5,20){\circle{2}}
%       \put(3,18){\makebox(0,0)[tr]{\texttt{zjvhv}}}
%       \put(25,20){\circle{2}}
%       \put(27,22){\makebox(0,0)[bl]{\texttt{zkvhv}}}
%       \put(5,40){\line(0,-1){25}}
%       \put(0,20){\line(1,0){30}}
%       \put(25,0){\line(0,1){25}}
%     \end{picture}}
%     \put(85,5){\begin{picture}(30,40)
%   ^^A    \put(0,0){\framebox(30,40){}}
%       \put(5,35){\circle*{2}}
%       \put(3,37){\makebox(0,0)[br]{\texttt{zj}}}
%       \put(25,5){\circle*{2}}
%       \put(27,3){\makebox(0,0)[tl]{\texttt{zk}}}
%       \put(15,35){\circle{2}}
%       \put(17,37){\makebox(0,0)[bl]{\texttt{zjhvh}}}
%       \put(15,5){\circle{2}}
%       \put(13,3){\makebox(0,0)[tr]{\texttt{zkhvh}}}
%       \put(15,0){\line(0,1){40}}
%       \put(0,35){\line(1,0){20}}
%       \put(30,5){\line(-1,0){20}}
%     \end{picture}}
%  \end{picture}
%  \caption[Results of the \texttt{VH}, \texttt{VhV} and \texttt{HvH} 
%          routines]%
%         {Results of the \texttt{VH} (left), \texttt{VhV} (middle)
%          and \texttt{HvH} (right) routines}\label{fig:vhvh}
% \end{figure}
%
% \DescribeRoutine{HvH}
% |HvH(j, k)| calculates the point |zjhvh| on the horizontal line through
% the point |zj| and the point |zkhvh| on the horizontal line through the
% point |zk|, such that the line |zjhvh--zkhvh| is vertical and centered
% horizontally between the two given points,
% as shown in \fref{fig:vhvh}.
%
% \DescribeRoutine{VyV}
% |VyV(j, i, k)| is a generalisation of the |VhV| routine. It calculates
% the point |zjvyv| which is on the vertical line through |zj| and the
% horizontal line through |yi|, and the point |zkvyv| which is on the
% vertical line through |zk| and the horizontal line through |yi|. An example
% result is shown in \fref{fig:vyxh}.
% 
% \begin{figure}
%   \setlength{\unitlength}{1mm}
%   \centering
%   \begin{picture}(90,50)
%     \put(0,0){\framebox(90,50){}}
%     \put(10,5){\begin{picture}(30,40)
%       \put(5,35){\circle*{2}}
%       \put(3,37){\makebox(0,0)[br]{\texttt{zj}}}
%       \put(25,5){\circle{2}}
%       \put(27,3){\makebox(0,0)[tl]{\texttt{zkvyv}}}
%       \put(5,5){\circle{2}}
%       \put(3,3){\makebox(0,0)[tr]{\texttt{zjvyv}}}
%       \put(25,20){\circle*{2}}
%       \put(27,22){\makebox(0,0)[bl]{\texttt{zk}}}
%       \put(5,40){\line(0,-1){40}}  ^^A V through zj
%       \put(0,5){\line(1,0){30}}    ^^A H through yi
%       \put(32,5){\makebox(0,0)[bl]{\texttt{yi}}}
%       \put(25,0){\line(0,1){25}}   ^^A V through zk
%     \end{picture}}
%     \put(50,5){\begin{picture}(30,40)
%       \put(5,35){\circle*{2}}
%       \put(3,37){\makebox(0,0)[br]{\texttt{zj}}}
%       \put(25,5){\circle{2}}
%       \put(27,3){\makebox(0,0)[tl]{\texttt{zkhxh}}}
%       \put(25,35){\circle{2}}
%       \put(27,33){\makebox(0,0)[tl]{\texttt{zjhxh}}}
%       \put(15,5){\circle*{2}}
%       \put(13,3){\makebox(0,0)[tr]{\texttt{zk}}}
%       \put(25,0){\line(0,1){40}}    ^^A V through xi
%       \put(25,42){\makebox(0,0)[b]{\texttt{xi}}}
%       \put(0,35){\line(1,0){30}}    ^^A H through zj
%       \put(30,5){\line(-1,0){20}}   ^^A H through zk
%     \end{picture}}
%  \end{picture}
%  \caption[Results of the \texttt{VyV} and \texttt{HxH} 
%           routines]%
%          {Results of the \texttt{VyV} (left) and \texttt{HxH} (right) 
%           routines}\label{fig:vyxh}
% \end{figure}
%
% \DescribeRoutine{HxH}
% |HxH(j, i, k)| is a generalisation of the |HvH| routine. It calculates
% the point |zjhxh| which is on the horizontal line through |zj| and the
% vertical line through |xi|, and the point |zkhxh| which is on the
% horizontal line through |zk| and the vertical line through |xi|. An example
% result is shown in \fref{fig:vyxh}.
% 
% \DescribeRoutine{namespace}
% |namespace(|\meta{name}|)(|\meta{margin}|)| calculates the length of
% the text string \meta{name} plus the \meta{margin} length. You may
% use it like: \\
% |c = 3/2namespace(btex name etex)(4u)|
%
%     
% \DescribeRoutine{dashes}
% |dashes| is shorthand for a dashed linestyle. Use it like: |draw ... dashes;|.
%     
% \DescribeRoutine{dots}
% |dots| is shorthand for a dotted linestyle. Use it like: |draw ... dots;|.
%     
% \DescribeRoutine{drawgrid}
% |drawgrid| draws a 16 by 21cm, 1cm spaced grid composed of thin dashed lines.
% Labels are typeset giving the distance of the lines from the bottom left
% corner of the grid in millimetres.
%
% \subsubsection{Path routines}
%
%    The package provides some general path making routines.
%
% \DescribeRoutine{sharply}
% |sharply(zi, zj, ... zn)| will generate a piecewise linear
% path consisting of the
% straight lines from point |zi| to point |zj| \ldots to point |zn|.
% It may be used like: \\
% |draw sharply(z1, z2, z3, z4);| \\
% to draw a line through the given points.
%
% \DescribeRoutine{smoothly}
% Like the |sharply| routine, |smoothly(zi, zj, ... zn)| will generate a 
% piecewise linear path consisting of the
% straight lines from point |zi| to point |zj| \ldots to point |zn|, except
% that the corners of the path at the interior points are rounded with an
% arc of radius |smoothrad|.
% It may be used like: \\
% |draw smoothly(z1, z2, z3, z4) dashes;| \\
% to draw a dashed line with rounded corners at the given points. Or if
% a dotted line is needed:
% \begin{verbatim}
% pickup dotspen;
% draw smoothly(z1, z2, z3, z4) dots;
% pickup normalpen;
% \end{verbatim}
%
% \DescribeRoutine{~}
% Like the |&| operator, the binary |~| operator concatenates two paths
% replacing the sharp join with a circular arc of radius |smoothrad|.
%
% \subsubsection{Line drawing routines}
%
%  Routines are provided for drawing a variety of lines with differing line 
% ending styles. Line styles include dotted, dashed, and continuous, and line
% thicknesses may be normal or thick. Line end styles include open circles,
% black dots, open and closed (black) arrowheads, and a fanin style.
%
% The final uppercase characters of a line drawing routine indicate the kind
% of line end style that will be used. 
% The character |O| (uppercase O, not zero) is for an \textbf{O}pen circle, 
% |D| is for a black \textbf{D}ot,
% |OA| is for an \textbf{O}pen \textbf{A}rrowhead,
% |CA| is for a \textbf{C}losed (black) \textbf{A}rrowhead,
% and |F| is for a \textbf{F}anin.
%
%    The line ending drawing routines are described first.
% \DescribeRoutine{drawO}
% |drawO(i, j)| draws an open circle, diameter |dotdiam|, at the |zj| end
% of the vector from |zi| to |zj|.
%
% \DescribeRoutine{drawD}
% |drawD(i, j)| draws a black dot, diameter |dotdiam|, at the |zj| end
% of the vector from |zi| to |zj|.
%
% \DescribeRoutine{drawOA}
% |drawOA(i, j)| draws an open arrowhead, length |gal| and base width
% |gab|, at the |zj| end
% of the vector from |zi| to |zj|.
%
% \DescribeRoutine{drawCA}
% |drawCA(i, j)| draws a closed (black) arrowhead, length |gal| and base width
% |gab|, at the |zj| end
% of the vector from |zi| to |zj|.
%
% \DescribeRoutine{drawF}
% |drawF(i, j)| draws a fanin, length |gfl| and base width |gfb|, 
% at the |zj| end
% of the vector from |zi| to |zj|.
%
%    The line drawing routines are essentially prepackaged versions of
% different combinations of the path and line ending routines.
%     
% \DescribeRoutine{drawdots}
% |drawdots(i, j)| draws the dotted line |zi--zj|.
%
% \DescribeRoutine{drawdotsthree}
% |drawdotsthree(i, j, k)| draws the dotted piecewise linear line |zi--zj--zk|.
%
% \DescribeRoutine{drawdotsfour}
% |drawdotsfour(i, j, k, l)| draws the dotted piecewise linear line |zi--zj--zk--zl|.
%
% \DescribeRoutine{drawdotsO}
% |drawdotsO(i, j)| draws the dotted line |zi--zj|, 
% ending in an open circle, diameter |dotdiam|, at |zj|.
%
% \DescribeRoutine{drawdotsthreeO}
% |drawdotsthreeO(i, j, k)| draws the dotted piecewise linear line |zi--zj--zk|.
% ending in an open circle, diameter |dotdiam|, at |zk|.
%
% \DescribeRoutine{drawdotsfourO}
% |drawdotsfourO(i, j, k, l)| draws the dotted piecewise linear line |zi--zj--zk--zl|,
% ending in an open circle, diameter |dotdiam|, at |zl|.
%
% \DescribeRoutine{drawdotsOO}
% |drawdotsOO(i, j)| draws the dotted line |zi--zj|, 
% ending in open circles, diameter |dotdiam|, at |zi| and |zj|.
%
% \DescribeRoutine{drawdash}
% |drawdash(i, j)| draws the dashed line |zi--zj|.
%
% \DescribeRoutine{drawdashthree}
% |drawdashthree(i, j, k)| draws the dashed piecewise linear line |zi--zj--zk|.
%
% \DescribeRoutine{drawdashfour}
% |drawdashfour(i, j, k, l)| draws the dashed piecewise linear line |zi--zj--zk--zl|.
%
% \DescribeRoutine{drawdashO}
% |drawdashO(i, j)| draws the dashed line |zi--zj|,
% ending in an open circle, diameter |dotdiam|, at |zj|.
%
% \DescribeRoutine{drawdashthreeO}
% |drawdashthreeO(i, j, k)| draws the dashed piecewise linear line |zi--zj--zk|.
% ending in an open circle, diameter |dotdiam|, at |zk|.
%
% \DescribeRoutine{drawdashfourO}
% |drawdashfourO(i, j, k, l)| draws the dashed piecewise linear line |zi--zj--zk--zl|.
% ending in an open circle, diameter |dotdiam|, at |zl|.
%
% \DescribeRoutine{drawdashOO}
% |drawdashOO(i, j)| draws the dashed line |zi--zj--zk--zl|.
% ending in open circles, diameter |dotdiam|, at |zi| and |zj|.
%
% \DescribeRoutine{drawnormal}
% |drawnormal(i, j)| draws the normal thickness line |zi--zj|.
%
% \DescribeRoutine{drawnormalthree}
% |drawnormalthree(i, j, k)| draws the normal thickness piecewise linear 
% line |zi--zj--zk|.
%
% \DescribeRoutine{drawnormalfour}
% |drawnormalfour(i, j, k, l)| draws the normal thickness piecewise linear 
% line |zi--zj--zk--zl|.
%
% \DescribeRoutine{drawnormalO}
% |drawnormalO(i, j)| draws the normal thickness line |zi--zj|,
% ending in an open circle, diameter |dotdiam|, at |zj|.
%
% \DescribeRoutine{drawnormalthreeO}
% |drawnormalthreeO(i, j, k)| draws the normal thickness piecewise linear 
% line |zi--zj--zk|,
% ending in an open circle, diameter |dotdiam|, at |zk|.
%
% \DescribeRoutine{drawnormalfourO}
% |drawnormalfourO(i, j, k, l)| draws the normal thickness piecewise linear 
% line |zi--zj--zk--zl|,
% ending in an open circle, diameter |dotdiam|, at |zl|.
%
% \DescribeRoutine{drawnormalOO}
% |drawnormalOO(i, j)| draws the normal thickness line |zi--zj|,
% ending in open circles, diameter |dotdiam|, at |zi| and |zj|.
%
% \DescribeRoutine{drawnormalD}
% |drawnormalD(i, j)| draws the normal thickness line |zi--zj|,
% ending in a black dot, diameter |dotdiam|, at |zj|.
%
% \DescribeRoutine{drawnormalthreeD}
% |drawnormalthreeD(i, j, k)| draws the normal thickness piecewise linear 
% line |zi--zj--zk|,
% ending in a black dot, diameter |dotdiam|, at |zk|.
%
% \DescribeRoutine{drawnormalfourD}
% |drawnormalfourD(i, j, k, l)| draws the normal thickness piecewise linear 
% line |zi--zj--zk--zl|,
% ending in a black dot, diameter |dotdiam|, at |zl|.
%
% \DescribeRoutine{drawnormalDD}
% |drawnormalDD(i, j)| draws the normal thickness line |zi--zj|,
% ending in black dots, diameter |dotdiam|, at |zi| and |zj|.
%
% \DescribeRoutine{drawnormalCA}
% |drawnormalCA(i, j)| draws the normal thickness line |zi--zj|,
% ending in a closed (black) arrowhead, length |gal| and base width |gab|, 
% at |zj|.
%
% \DescribeRoutine{drawnormalthreeCA}
% |drawnormalthreeCA(i, j, k)| draws the normal thickness piecewise linear
% line |zi--zj--zk|
% ending in a closed (black) arrowhead, length |gal| and base width |gab|, 
% at |zk|.
%
% \DescribeRoutine{drawnormalfourCA}
% |drawnormalfourCA(i, j, k, l)| draws the normal thickness piecewise linear
% line |zi--zj--zk--zl|
% ending in a closed (black) arrowhead, length |gal| and base width |gab|, 
% at |zl|.
%
% \DescribeRoutine{drawnormalOA}
% |drawnormalOA(i, j)| draws the normal thickness line |zi--zj|,
% ending in an open arrowhead, length |gal| and base width |gab|, 
% at |zj|.
%
% \DescribeRoutine{drawnormalF}
% |drawnormalF(i, j)| draws the normal thickness line |zi--zj|,
% ending in a fanin, length |gfl| and base width |gfb|, 
% at |zj|.
%
% \DescribeRoutine{drawnormalFO}
% |drawnormalFO(i, j)| draws the normal thickness line |zi--zj|,
% ending in a fanin, length |gfl| and base width |gfb|, 
% at |zi| and an open circle, diameter |dotdiam|, at |zj|.
%
% \DescribeRoutine{drawthick}
% |drawthick(i, j)| draws the thick line |zi--zj|.
%
% \DescribeRoutine{drawthickO}
% |drawthickO(i, j)| draws the thick line |zi--zj|,
% ending in an open circle, diameter |dotdiam|, at |zj|.
%
% \DescribeRoutine{drawthickOO}
% |drawthickOO(i, j)| draws the thick line |zi--zj|,
% ending in open circles, diameter |dotdiam|, at |zi| and |zj|.
%
% \DescribeRoutine{smooth}
% |smooth(i, j, k)| replaces the sharp corner on the line |zi--zj--zk|
% with an arc radius |smoothrad|.
%
% \DescribeRoutine{smoothtwo}
% |smoothtwo(i, j, k, l)| replaces the sharp corners on the line |zi--zj--zk--zl|
% with arcs radius |smoothrad|.
%
% \DescribeRoutine{smoothdash}
% |smoothdash(i, j, k)| replaces the sharp corner on the dashed line |zi--zj--zk|
% with an arc radius |smoothrad|.
%
% \DescribeRoutine{smoothdots}
% |smoothdots(i, j, k)| replaces the sharp corner on the dotted line |zi--zj--zk|
% with an arc radius |smoothrad|.
%
%
%
% \subsubsection{Box drawing routines}
%
%    Routines are provided for drawing the different kinds of \ExpressG{} 
% boxes.
%
%    The first argument to the box drawing routines is the suffix of the
% point that will be the left-hand bottom corner point of the box. The
% last argument, except where noted below, is the text that is to be placed
% at the center of the box. Intermediate arguments, if any, are the length
% and height of the box.
%
%  Every box routine calculates the four corner points of the box and the 
% midpoints of each side of the box. For example, if the suffix is |j|,
% then as illustrated in figure~\ref{fig:boxpoints}, the corner points
% will be called |zjbl|, |zjbr|, |zjtr| and |zjtl| and the midpoints
% will be called |zjbm|, |zjmr|, |zjtm| and |zjml|. The center point for
% postioning the text is |zjc| and the center of the text is placed at
% this point. 
%
%    The text center point is not necessarily the geometric center of the box.
% The geometric center is not calculated but lies at the intersection of
% the lines |zjml--zjmr| and |zjbm--zjtm|.
%
% \begin{figure}
% \centering
% \setlength{\unitlength}{1mm}
% \begin{picture}(50,40)
%   \put(0,0){\framebox(50,40){}}
%   \put(10,10){\begin{picture}(30,20)
%     \put(0,0){\framebox(30,20){}}
%     \multiput(0,0)(15,0){3}{\circle*{2}}
%     \multiput(0,10)(15,0){3}{\circle*{2}}
%     \multiput(0,20)(15,0){3}{\circle*{2}}
%     \put(-2,-2){\makebox(0,0)[tr]{\texttt{zjbl}}}
%     \put(15,-2){\makebox(0,0)[t]{\texttt{zjbm}}}
%     \put(32,-2){\makebox(0,0)[tl]{\texttt{zjbr}}}
%     \put(-2,10){\makebox(0,0)[r]{\texttt{zjml}}}
%     \put(13,10){\makebox(0,0)[r]{\texttt{zjc}}}
%     \put(32,10){\makebox(0,0)[l]{\texttt{zjmr}}}
%     \put(-2,22){\makebox(0,0)[br]{\texttt{zjtl}}}
%     \put(15,22){\makebox(0,0)[b]{\texttt{zjtm}}}
%     \put(32,22){\makebox(0,0)[bl]{\texttt{zjtr}}}
%     \end{picture}}
%  \end{picture}
%  \setlength{\unitlength}{1pt}
%  \caption[Calculated points on rectangular boxes]%
%          {Calculated points on rectangular boxes 
%           (suffix is \texttt{j} and located at \texttt{zjbl=zj})}
%  \label{fig:boxpoints}
% \end{figure}
%     
% \DescribeRoutine{drawSCHEMA}
% A SCHEMA box is rectangular with a normal perimeter and the box is divided
% into top and bottom halves by a horizontal line.
%
% |drawSCHEMA(j, len, ht)(btex schema\_a etex)| draws a SCHEMA double rectangular 
% box of length |len| and height |ht| with its left-hand bottom corner
% at |zj|. The string |schema_a| is placed at the text center of the box,
% which is central within the upper half.
%
% \DescribeRoutine{drawBINARY}
% A simple data type box is rectangular with a solid boundary and a solid
% interior vertical line near the right hand edge.
%
% |drawBINARY(j)| draws a simple data type rectangular 
% box of length |sdtbl| and height |sdtbh| with its left-hand bottom corner
% at |zj|. The string |BINARY| is placed at the text center of the box,
% which is central within the main part of the box.
%
% \DescribeRoutine{drawBOOLEAN}
% |drawBOOLEAN(j)| draws a simple data type rectangular 
% box of length |sdtbl| and height |sdtbh| with its left-hand bottom corner
% at |zj|. The string |BOOLEAN| is placed at the text center of the box,
% which is central within the main part of the box.
%
% \DescribeRoutine{drawCOMPLEX}
% |drawCOMPLEX(j)| draws a simple data type rectangular 
% box of length |sdtbl| and height |sdtbh| with its left-hand bottom corner
% at |zj|. The string |COMPLEX| is placed at the text center of the box,
% which is central within the main part of the box.
%
% \DescribeRoutine{drawEXPRESSION}
% |drawEXPRESSION(j)| draws a simple data type rectangular 
% box of length |sdtbel| and height |sdtbeh| with its left-hand bottom corner
% at |zj|. The string |EXPRESSION| is placed at the text center of the box,
% which is central within the main part of the box.
%
% \DescribeRoutine{drawGENERIC}
% |drawGENERIC(j)| draws a simple data type rectangular 
% box of length |sdtbl| and height |sdtbh| with its left-hand bottom corner
% at |zj|. The string |GENERIC| is placed at the text center of the box,
% which is central within the main part of the box.
%
% \DescribeRoutine{drawINTEGER}
% |drawINTEGER(j)| draws a simple data type rectangular 
% box of length |sdtbl| and height |sdtbh| with its left-hand bottom corner
% at |zj|. The string |INTEGER| is placed at the text center of the box,
% which is central within the main part of the box.
%
% \DescribeRoutine{drawLOGICAL}
% |drawLOGICAL(j)| draws a simple data type rectangular 
% box of length |sdtbl| and height |sdtbh| with its left-hand bottom corner
% at |zj|. The string |LOGICAL| is placed at the text center of the box,
% which is central within the main part of the box.
%
% \DescribeRoutine{drawNUMBER}
% |drawNUMBER(j)| draws a simple data type rectangular 
% box of length |sdtbl| and height |sdtbh| with its left-hand bottom corner
% at |zj|. The string |NUMBER| is placed at the text center of the box,
% which is central within the main part of the box.
%
% \DescribeRoutine{drawREAL}
% |drawREAL(j)| draws a simple data type rectangular 
% box of length |sdtbl| and height |sdtbh| with its left-hand bottom corner
% at |zj|. The string |REAL| is placed at the text center of the box,
% which is central within the main part of the box.
%
% \DescribeRoutine{drawSTRING}
% |drawSTRING(j)| draws a simple data type rectangular 
% box of length |sdtbl| and height |sdtbh| with its left-hand bottom corner
% at |zj|. The string |STRING| is placed at the text center of the box,
% which is central within the main part of the box.
%
% \DescribeRoutine{drawENUM}
% An ENUMERATION box is a rectangular box with a dashed perimeter and an 
% interior dashed vertical line near the right hand edge.
%
% |drawENUM(j, len, ht)(btex an\_enum etex)| draws a rectangular dashed ENUMERATION type
% box of length |len| and height |ht| with its left-hand bottom corner
% at |zj|. The string |an_enum| is placed at the text center of the box,
% which is central within the main part of the box.
%
% \DescribeRoutine{drawSELECT}
% A SELECT box is rectangular with a dashed boundary and an interior
% dashed vertical
% line near the left hand edge.
%
% |drawSELECT(j, len, ht)(btex a\_select etex)| draws a rectangular dashed SELECT type
% box of length |len| and height |ht| with its left-hand bottom corner
% at |zj|. The string |a_select| is placed at the text center of the box,
% which is central within the main part of the box.
%
% \DescribeRoutine{drawTYPE}
% A TYPE box is rectangular with a dashed boundary.
%
% |drawTYPE(j, len, ht)(btex a\_type etex)| draws a rectangular dashed TYPE type
% box of length |len| and height |ht| with its left-hand bottom corner
% at |zj|. The string |a_type| is placed at the text center of the box,
% which is central within the main part of the box.
%
% \DescribeRoutine{drawENT}
% An ENTITY box is a rectangular box with a solid boundary.
%
% |drawENT(j, len, ht)(btex an\_entity etex)| draws a rectangular ENTITY type
% box of length |len| and height |ht| with its left-hand bottom corner
% at |zj|. The string |an_entity| is placed at the text center of the box,
% which is also the geometric center of the box.
%
% \DescribeRoutine{drawPREF}
% A page reference box is a rectangle with rounded ends and a solid boundary.
%
% |drawPREF(j, len, ht)(btex page ref etex)| draws an oval page
% reference 
% box of length |len| and height |ht| with its left-hand bottom corner
% at |zj|. The string |page ref| is placed at the text center of the box,
% which is also the geometric center of the box.
%
% \DescribeRoutine{drawISU}
% An interschema box is a rectangle surrounding a page reference like box.
% The rectangular box may have either a solid or a dashed boundary.
%
% |drawISU(j, len, ht)(btex sch.ent etex)| draws a three-part rectangular
% interschema USE 
% box of length |len| and height |ht| with its left-hand bottom corner
% at |zj|. The string |sch.ent| is placed at the text center of the box,
% which is also the geometric center of the box.
%
% \DescribeRoutine{drawISUR}
% |drawISUR(j, len, ht)(btex sch.ent etex)(btex newname etex)| draws a three-part rectangular
% interschema USE and RENAME
% box of length |len| and height |ht| with its left-hand bottom corner
% at |zj|. The string |sch.ent| is placed at the text center of the box,
% which is also the geometric center of the box. The string |newname| is
% placed at the geometric center of the bottom third of the box (this is
% the point |zjrnm|).
%
% \DescribeRoutine{drawISR}
% |drawISR(j, len, ht)(btex sch.ent etex)| draws a three-part rectangular
% dashed interschema REFERENCE 
% box of length |len| and height |ht| with its left-hand bottom corner
% at |zj|. The string |sch.ent| is placed at the text center of the box,
% which is also the geometric center of the box.
%
% \DescribeRoutine{drawISRR}
% |drawISRR(j, len, ht)(btex sch.ent etex)(btex newname etex)| draws a three-part rectangular
% dashed interschema REFERENCE and RENAME
% box of length |len| and height |ht| with its left-hand bottom corner
% at |zj|. The string |sch.ent| is placed at the text center of the box,
% which is also the geometric center of the box. The string |newname| is
% placed at the geometric center of the bottom third of the box (this is
% the point |zjrnm|).
%
% \DescribeRoutine{drawLEVENT}
% An EVENT box is a rhomboid with a solid boundary.
%
% |drawLEVENT(j, len, ht)(btex local\_event etex)| draws a rhomboidal
% Local EVENT 
% box of length |len|, height |ht| and slope |eventslope|  with its left-hand bottom corner
% at |zj|. The string |local_event| is placed at the text center of the box,
% which is also the geometric center of the box. Like the rectangular boxes,
% the calculated bottom and top middle points are vertically below and above
% the geometric center, but this means that they are \emph{not} midway
% beteen the bottom and top corner points. This is illustrated in
% \fref{fig:eventpoints}.
%
% \begin{figure}
% \centering
% \setlength{\unitlength}{1mm}
% \begin{picture}(55,40)
%   \put(0,0){\framebox(55,40){}}
%   \put(10,10){\begin{picture}(40,20)
% ^^A    \put(0,0){\framebox(30,20){}}
%     \put(0,0){\line(1,0){30}}
%     \put(5,20){\line(1,0){30}}
%     \put(0,0){\line(1,4){5}}
%     \put(30,0){\line(1,4){5}}
%     \multiput(0,0)(30,0){2}{\circle*{2}}
%     \multiput(2.5,10)(30,0){2}{\circle*{2}}
%     \multiput(5,20)(30,0){2}{\circle*{2}}
%     \multiput(17.5,0)(0,10){3}{\circle*{2}}
%     \put(-2,-2){\makebox(0,0)[tr]{\texttt{zjbl}}}
%     \put(17.5,-2){\makebox(0,0)[t]{\texttt{zjbm}}}
%     \put(32,-2){\makebox(0,0)[tl]{\texttt{zjbr}}}
%     \put(0.5,10){\makebox(0,0)[r]{\texttt{zjml}}}
%     \put(15.5,10){\makebox(0,0)[r]{\texttt{zjc}}}
%     \put(34.5,10){\makebox(0,0)[l]{\texttt{zjmr}}}
%     \put(3,22){\makebox(0,0)[br]{\texttt{zjtl}}}
%     \put(17.5,22){\makebox(0,0)[b]{\texttt{zjtm}}}
%     \put(37,22){\makebox(0,0)[bl]{\texttt{zjtr}}}
%     \end{picture}}
%  \end{picture}
%  \setlength{\unitlength}{1pt}
%  \caption[Calculated points on rhomboidal boxes]%
%          {Calculated points on rhomboidal boxes 
%           (suffix is \texttt{j} and located at \texttt{zjbl=zj})}
%  \label{fig:eventpoints}
% \end{figure}
%     
% \DescribeRoutine{drawGEVENT}
% |drawGEVENT(j, len, ht)(btex global\_event etex)| draws a thick rhomboidal 
% Global EVENT 
% box of length |len|, height |ht| and slope |eventslope| with its left-hand bottom corner
% at |zj|. The string |global_event| is placed at the text center of the box,
% which is also the geometric center of the box.
%
%     
% \DescribeRoutine{drawcirclebox}
% A circle box is a circle with a solid boundary.
%
% |drawcirclebox(j, diam)(btex ABC etex)| draws a circle diameter |diam|
% and center at |zj|. The string |ABC| is placed at the center of the circle.
% In this case the four midside points,  |zjbm|, |zjmr|, |zjtm| and |zjml|,
% are at on the circle at the extreme bottom, right, top and left (i.e., at
% the S, E, N and W compass points). The
% corner points, |zjbl|, |zjbr|, |zjtr| and |zjtl|, are also on the 
% circumference midway between the midpoints (i.e., at the SW, SE, NE and NW
% compass points).
%
% \DescribeRoutine{drawdashcircle}
% |drawdashcircle(j, diam)| draws a dashed circle. The location
% and size parameters are the same as for |drawcirclebox|, as are the
% calculated points.
%
% \subsection{Extra BLA variables and routines}
%
%    In addition to the facilities described above for \ExpressG{}
% diagrams, extra line styles and boxes are provided for other
% kinds of diagrams.
%
%    Additional line end styles are coded by: 
% |A| for an \textbf{A}rrowhead,
% |OD| for an \textbf{O}pen \textbf{D}iamond,
% |CD| for a \textbf{C}losed \textbf{D}iamond.
%
% \DescribeVariable{gdl}
% \DescribeVariable{gdb}
% The variables |gdl| and |gdb| hold the the length and base width of
% diamond line end styles (see \fref{fig:diales}), 
% analagous to the corresponding variables
% for arrow heads and fanin. By default, |gdl| is twice the default
% arrowhead length and |gdb| is three quarters of the default
% arrowhead base width.
%
% \begin{figure}
%   \setlength{\unitlength}{1mm}
%   \centering
%   \begin{picture}(90,40)
%     \put(0,0){\framebox(90,40){}}
%     \put(5,0){\begin{picture}(85,40)
%   ^^A    \put(0,0){\framebox(85,40){}}
%       \thicklines
%       \put(0,20){\line(1,0){10}}
%  ^^A     \put(10,10){\line(2,1){20}}
%  ^^A     \put(10,30){\line(2,-1){20}}
%  ^^A     \put(10,10){\line(0,1){20}}
%       \put(10,20){\line(2,1){20}}
%       \put(10,20){\line(2,-1){20}}
%       \put(50,20){\line(-2,1){20}}
%       \put(50,20){\line(-2,-1){20}}
%       \thinlines
%  ^^A     \put(10,5){\vector(1,0){20}} \put(10,5){\vector(-1,0){0}}
%  ^^A     \put(20,3){\makebox(0,0)[t]{length}}
%  ^^A     \put(35,10){\vector(0,1){20}} \put(35,10){\vector(0,-1){0}}
%  ^^A     \put(40,20){\makebox(0,0)[l]{base width}}
%       \put(10,5){\vector(1,0){40}} \put(10,5){\vector(-1,0){0}}
%       \put(30,3){\makebox(0,0)[t]{length}}
%       \put(55,10){\vector(0,1){20}} \put(55,10){\vector(0,-1){0}}
%       \put(60,20){\makebox(0,0)[l]{base width}}
%     \end{picture}}
%  \end{picture}
%  \caption{Length parameters for diamond line end styles}\label{fig:diales}
% \end{figure}
%
% \DescribeRoutine{drawA}
% |drawA(i, j)| draws a simple arrowhead, length |gal| and base width
% |gab|, at the |zj| end
% of the vector from |zi| to |zj|.
%
%
% \DescribeRoutine{drawDCA}
% |drawDCA(i, j)| draws a double closed arrowhead, each of length |gal| 
% and base width
% |gab|, at the |zj| end
% of the vector from |zi| to |zj|.
%
%
% \DescribeRoutine{drawOD}
% |drawOD(i, j)| draws an open diamond, length |gdl| and base width
% |gdb|, at the |zj| end
% of the vector from |zi| to |zj|.
%
% \DescribeRoutine{drawCD}
% |drawCD(i, j)| draws a closed (black) diamond, length |gdl| and base width
% |gdb|, at the |zj| end
% of the vector from |zi| to |zj|.
%
%
% \DescribeRoutine{drawdashA}
% |drawdashA(i, j)| draws the dashed line |zi--zj|,
% ending in an arrowhead, length |gal| and base width |gab|, 
% at |zj|.
%
% \DescribeRoutine{drawdashOA}
% |drawdashOA(i, j)| draws the dashed line |zi--zj|,
% ending in an open arrowhead, length |gal| and base width |gab|, 
% at |zj|.
%
% \DescribeRoutine{drawnormalOD}
% |drawnormalOD(i, j)| draws the normal thickness line |zi--zj|,
% ending in an open diamond, length |gdl| and base width |gdb|, 
% at |zj|.
%
% \DescribeRoutine{drawnormalCD}
% |drawnormalCD(i, j)| draws the normal thickness line |zi--zj|,
% ending in a closed (black) diamond, length |gdl| and base width |gdb|, 
% at |zj|.
%
% \DescribeRoutine{drawcircleA}
% |drawcircleA(j, diam)| draws a circle diameter |diam| centered at |zj|.
% A counterclockwise pointing arrow is placed at the top of the circle.
% The midside and `corner' points are the same as calculated by
% the |drawcirclebox| routine.
%
% \DescribeRoutine{drawDot}
% |drawDot(j, diam)| draws a black dot, diameter |diam| centered at |zj|.
% There are no calculated points.
%
% \DescribeRoutine{drawCircledDot}
% |drawCircledDot(j, diam)| draws a black dot with a circle outside
% it, overall diameter |diam|, centered at |zj|.
% There are no calculated points. This could be used for a UML
% `bullseye'. The white ring should obscure anything 
% drawn earlier that lies underneath it (by definition the black dot covers 
% up anything underneath itself). For example: 
% \begin{verbatim}
% draw z1--z2;            % line from z1 to z2
% drawCircledDot(2, len); % obscures last len of above line
% draw z3--z2;            % not obscured
% \end{verbatim}
%
%    Commands of the form |draw...box| have a text argument
% which is printed at the center of the box. If an empty box is
% required the text argument should be an empty string (|""|). For
% example |draw...box(...)("")|.
%
% \DescribeRoutine{drawcardbox}
% |drawcardbox(j, len, ht, fold)(btex note etex)| draws a rectangular
% box, length |len| and height |ht|, with its bottom left corner at |zj|.
% The top right corner of the box is folded down, with the side length
% of the fold given by |fold|. The string |note| is placed at the
% center of the box. If no text is required, then use an empty string (i.e.,
% |""|), as in \\
% |\drawcardbox(23, el, eh, 1/8eh)("")|
%
% \DescribeRoutine{drawdiamondbox}
% |drawdiamondbox(j, len, ht)(btex str etex)| draws a diamond shaped 
% box, length |len| and height |ht|, with its center at |zj|. The usual
% corner, center and midpoints are also calculated except that the points
% |z$tm| etc., are at the corners of the diamond and the points |z$tl| etc.,
% are at the middle of each line, as shown in \fref{fig:diamondpoints}.
% The text |str| is placed at the center of the box.
%
% \begin{figure}
% \centering
% \setlength{\unitlength}{1mm}
% \begin{picture}(50,40)
%   \put(0,0){\framebox(50,40){}}
%   \put(10,10){\begin{picture}(30,20)
%  ^^A   \put(0,0){\framebox(30,20){}}
%     \put(0,10){\line(3,2){15}}
%     \put(0,10){\line(3,-2){15}}
%     \put(30,10){\line(-3,2){15}}
%     \put(30,10){\line(-3,-2){15}}
%     \multiput(0,10)(15,0){3}{\circle*{2}}
%     \multiput(15,0)(0,20){2}{\circle*{2}}
%     \multiput(7.5,5)(0,10){2}{\circle*{2}}
%     \multiput(22.5,5)(0,10){2}{\circle*{2}}
%     \put(13,10){\makebox(0,0)[r]{\texttt{zjc}}}
%     \put(15,-2){\makebox(0,0)[t]{\texttt{zjbm}}}
%     \put(-2,10){\makebox(0,0)[r]{\texttt{zjml}}}
%     \put(32,10){\makebox(0,0)[l]{\texttt{zjmr}}}
%     \put(15,22){\makebox(0,0)[b]{\texttt{zjtm}}}
%
%     \put(5.5,3){\makebox(0,0)[tr]{\texttt{zjbl}}}
%     \put(24.5,3){\makebox(0,0)[tl]{\texttt{zjbr}}}
%     \put(5.5,17){\makebox(0,0)[br]{\texttt{zjtl}}}
%     \put(24.5,17){\makebox(0,0)[bl]{\texttt{zjtr}}}
%     \end{picture}}
%  \end{picture}
%  \setlength{\unitlength}{1pt}
%  \caption[Calculated points on diamond boxes]%
%          {Calculated points on diamond boxes 
%           (suffix is \texttt{j} and located at \texttt{zjc=zj})}
%  \label{fig:diamondpoints}
% \end{figure}
%     
%
% \DescribeRoutine{drawtwodiamondbox}
% |drawtwodiamondbox(j, len, ht, inset)(btex str etex)| draws a diamond shaped 
% box, length |len| and height |ht|, with its center at |zj|. 
% The text |str| is placed at the center of the box.
% A second diamond is drawn inside the first. The parameter |inset| is
% the space between adjacent outer and inner lines.
% No calculated points are available for the inner diamond.
%
% \DescribeRoutine{drawdoublerectangle}
% |drawdoublerectangle(j, len, ht, tf)| draws a rectangular box, length |len|
% and height |ht|, located with its bottom left corner at |zj|. The box
% is divided horizontally
% into a top and bottom portion, with the height of the top portion being
% the fraction |tf| of the total height of the box. The center points of
% the two portions are calculated as |zjct| and |zjcb| for the top and
% bottom respectively. 
% The ends of the dividing line are at |zjtfl| and |zjtfr|.
%
% \DescribeRoutine{drawtriplerectangle}
% |drawtriplerectangle(j, len, ht, tf, bf)| draws a rectangular box, length |len|
% and height |ht|, located with its bottom left corner at |zj|. The box
% is divided horizontally
% into a top, middle and bottom portion.
% The height of the top portion is the fraction |tf| of the total height 
% of the box. 
% The height of the bottom portion is the fraction |bf| of the total height 
% of the box. 
% The center points of
% the three portions are calculated as |zjct|, |zjcm| and |zjcb| for the 
% top, middle and bottom respectively.
% The ends of the dividing lines are at |zjtfl| and |zjtfr| for the upper
% line, and at |zjbfl| and |zjbfr| for the lower line.
%
% \DescribeRoutine{hiderectangle}
% |hiderectangle(j, len, ht)| draws an invisible rectangular box, length |len|
% and height |ht|, located with its bottom left corner at |zj|. The box
% covers up anything underneath it. Note that unlike all the other boxes
% the only point handle to the box is the bottom left corner --- the
% |zjbl|, |zjtr|, etc.,  points are not available and hence cannot
% be used for positioning or alignment purposes.
%
% \DescribeRoutine{drawdashboxover}
% |drawdashboxover(j, len, ht)| draws a dashed rectangular box, length |len|
% and height |ht|, located with its bottom left corner at |zj|. The box
% covers up anything underneath it.
%
% \DescribeRoutine{drawindexbox}
% |drawindexbox(j, len, ht, lenp, htp)(btex str etex)| 
% draws a rectangular box, length |len|
% and height |ht|, located with its bottom left corner at |zj|. Another
% rectangular box, length |lenp| and height |htp|, is drawn with its
% bottom left corner at the top left corner of the first box (like an index
% card). The main box points are |zjbl| etc., but the secondary box
% points are |zjP.bl|, |zjP.bm| etc. The text |str| is placed at the center
% (|zjP.c|) of the secondary box.
%
% \DescribeRoutine{drawroundedbox}
% |drawroundedbox(j, len, ht, rad)(btex str etex)| 
% draws a rectangular box, length |len|
% and height |ht|, located with its bottom left corner at |zj|. The corners
% of the box are rounded using radius |rad|. If |2rad| is greater
% than |len| or |ht|, then |2rad| is reduced to the lesser of |len| and
% |ht|, thereby producing at least one pair of semicircular sides.
% The text |str| is placed at the center of the box.
%
% \DescribeRoutine{drawovalbox}
% |drawovalbox(j, len, ht)(btex str etex)|
% draws an elliptical box, 
% horizontal diameter |len|
% and vertical diameter |ht|, located with its center at |zj|. Like the 
% diamond box, |zjtm|, |zjmr|, etc., are at the extremes of the ellipse
% and the points |zjtr|, |zjbr|, etc., are on the ellipse approximately
% halfway between the extremum points, similar to the positions shown
% in \fref{fig:diamondpoints}. The text |str| is placed at the center 
% of the box.
%
% \DescribeRoutine{drawoutputbox}
% |drawoutputbox(j, len, ht)(btex str etex)|
% draws a box, 
% length |len| and height |ht|, located with its bottom left corner at |zj|. 
% The bottom of the box is a wavy line and the other three sides
% are straight. The text |str| is placed at the center of the box.
% This kind of box is often used as a flowchart symbol for output; 
% it is meant to be a represention of printed paper which has been
% torn from a long continuous roll.
%
%
% \DescribeRoutine{drawdashellipse}
% |drawdashellipse(j, len, ht)| 
% draws a dashed ellipse. The location and dimensional parameters 
% correspond to those for |drawovalbox|, as do the calculated points.
% 
% \DescribeRoutine{drawdrum}
% |drawdrum(j, len, ht)(btex str etex)|
% draws a `drum' box. This is constructed as a rectangular box of width
% width |len| and height |ht|, with its bottom left hand corner at |zj|.
% The horizontal line at the bottom of the
% rectangle is replaced by a half-ellipse with a major diameter of |len|
% and the minor diameter given by |drumlid*len|. The horizontal line
% at the top is replaced by a full ellipse with the same dimensions.
%
%\begin{figure}
%\centering
%\setlength{\unitlength}{0.6mm}
%
%\begin{picture}(100,100)
%  \put(0,0){\framebox(120,120){}}
%  \put(20,20){\begin{picture}(80,80)
%    \put(0,10){\line(0,1){60}}
%    \put(80,10){\line(0,1){60}}
%    \qbezier(0,10)(0,0)(40,0)
%    \qbezier(40,0)(80,0)(80,10)
%
%    \qbezier(0,70)(0,80)(40,80)
%    \qbezier(40,80)(80,80)(80,70)
%    \qbezier(0,70)(0,60)(40,60)
%    \qbezier(40,60)(80,60)(80,70)
%
%    \multiput(0,10)(0,30){3}{\circle*{2}}
%    \put(-2,10){\makebox(0,0)[r]{\texttt{zjbl}}}
%    \put(-2,40){\makebox(0,0)[r]{\texttt{zjml}}}
%    \put(-2,70){\makebox(0,0)[r]{\texttt{zjtl}}}
%    \multiput(80,10)(0,30){3}{\circle*{2}}
%    \put(82,10){\makebox(0,0)[l]{\texttt{zjbr}}}
%    \put(82,40){\makebox(0,0)[l]{\texttt{zjmr}}}
%    \put(82,70){\makebox(0,0)[l]{\texttt{zjtr}}}
%    \put(40,0){\circle*{2}}
%    \put(40,-2){\makebox(0,0)[t]{\texttt{zjbm}}}
%    \put(40,80){\circle*{2}}
%    \put(40,82){\makebox(0,0)[b]{\texttt{zjtm}}}
%    \put(40,35){\circle*{2}}
%    \put(40,37){\makebox(0,0)[b]{\texttt{zjc}}}
%
%    \put(20,1){\circle*{2}}
%    \put(20,-1){\makebox(0,0)[t]{\texttt{zjbml}}}
%    \put(60,1){\circle*{2}}
%    \put(60,-1){\makebox(0,0)[t]{\texttt{zjbmr}}}
%    \put(20,79){\circle*{2}}
%    \put(20,81){\makebox(0,0)[b]{\texttt{zjtml}}}
%    \put(60,79){\circle*{2}}
%    \put(60,81){\makebox(0,0)[b]{\texttt{zjtmr}}}
%    
%  \end{picture}}
%\end{picture}
%\setlength{\unitlength}{1pt}
%\caption[Calculated points on a drum]{Calculated points on a drum 
%         (suffix is \texttt{j} and located at \texttt{zjbl=zj})} 
%  \label{fig:drum}
%\end{figure}
%
% As shown in Figure~\ref{fig:drum}, 
% the calculated points on the vertical sides of the drum are the same
% as for a rectangular box. There are three calculated points on the base
% of the drum, called |zjbml|, |zjbm| and |zjbmr|. Similarly there are
% three points on the top of the drum called |zjtml|, |zjtm| and |zjtmr|.
% The center point, |zjc| is halfway between the sides and halfway between
% the two lower ellipse halves. The text |str| is placed at this center point.
%
% \DescribeRoutine{drawstickman}
% |drawstickman(j, len, ht)|
% draws a genderless full frontal (or rear) stick figure enclosed in 
% an invisible box, 
% length |len| and height |ht|, located with its bottom left corner at |zj|. 
% This can be used, for example to represent an actor in a UML Use Case
% diagram. Setting the height to be twice the length produces a reasonable
% result, for instance:
% \verb?drawstickman(3, wd, 2wd);?
%
%     
% \section{An example} \label{sec:example}
%
%    The example attempts to bring out the main methods that can be used
% in defining \ExpressG{} diagrams. The code for eleven diagrams is provided, none
% of which necessarily has anything to do with a real example of \ExpressG{}
% modeling, but rather is meant to be illustrative of diagramming techniques.
%
%    This section is best studied with a copy of the printed diagrams to
% hand. Section~\ref{sec:run} on \pref{sec:run} explains briefly how
% to run the example and obtain the diagrams.
% 
%    The default extension for a \Mpost{} file is \file{.mp}.
%    \begin{macrocode}
%<*eg>
%%% EXPEG.MP  Example MetaPost EXPRESS-G diagrams

%    \end{macrocode}
%
%    Assuming that the diagrams are to be eventually embedded in, or processed
% through, a \LaTeX{} document then any \TeX{} macros must come at the
% start of the file between a |verbatimtex| \ldots |etex| pair. When dealing
% with text, \Mpost{} does not handle more than a single line. The macro
% below is to enable two lines of text to be handled by \Mpost.
%     
%    \begin{macrocode}

% use btex \twolines{first}{second} etex for two-line labels
verbatimtex \def\twolines#1#2{\vbox{\hbox{#1} \hbox{#2}}} etex

%    \end{macrocode}
%
%    The \Lpack{expressg} package file has to be input to make the routines
% available.
%    \begin{macrocode}
input expressg

%    \end{macrocode}
%
% \subsection{Diagram 1: Some boxes and lines}
%
%   Many diagrams can be defined in one file. Each diagram starts with
% |beginfig(N)|, where N is a unique integer, and ends with |endfig;|.
% \EPS{} for each diagram is written to a file called
% \file{mproot.N}, where \file{mproot} is the root name of the input file. 
% In our
% case the output files will be \file{expeg.1} through \file{expeg.11}.
%    \begin{macrocode}
beginfig(1)

%    \end{macrocode}
%
%    The first diagram consists of some of the \Lpack{expressg} box and line styles.
% The main point is to illustrate how \Mpost{} allows the boxes to be aligned.
% Start off by defining a point |z1| at the origin. By default, a variable name
% starting with the letter |z| is assumed to be a point. Similarly, variables
% starting with |x| and |y| are assumed to be x- and y-coordinates. If |zk|
% is defined with a value then automatically |xk| is the value of the x 
% coordinate of 
% the point |zk| and |yk| is the value of the
% y coordinate. Conversely, if |xj| and |yj| are defined, |zj| is automatically
% defined.
%
%    Note that the |=| sign denotes an equation, not an assignment. The power
% of \Mpost{} comes from its ability to solve linear equations.
%
%    Having defined the point |z1|, draw an EXPRESSION box with its bottom
% left hand corner at |z1|.
%    \begin{macrocode}
z1=(0,0);
drawEXPRESSION(1);

%    \end{macrocode}
%
%    Remember that when a box is drawn, its corner and mid points are 
% calculated. These can be used in defining other points. In particular
% there is the point |z1tr| which is the top right hand corner
% of the EXPRESSION box. Also, if another box is drawn at point |z2| then
% it will have its bottom left hand corner at |z2bl|.
%
%    The point |z2bl| is defined by a linear equation with respect to
% the point |z2|. As \Mpost{} can solve linear equations, given the
% point |z2bl| it can solve for the point |z2|. 
%
%    The next box has its bottom left hand corner at the top right hand
% corner of the EXPRESSION box, by specifying that the
% point |z2bl| and |z1tr| are the same location and then drawing a box located
% at |z2|. The third (BOOLEAN) box is also stacked in the same way with 
% respect to the second (INTEGER) box.
% 
%    \begin{macrocode}
z2bl=z1tr;
drawINTEGER(2);

z3bl=z2tr;
drawBOOLEAN(3);

%    \end{macrocode}
%
%    Next a piece of circled text is drawn. Using the same method as before,
% the bottom of the circle is made to be coincident with the middle of the top
% of the BOOLEAN box. The |namespace| routine is used to specify the circle
% diameter. Note that an argument to a routine can itself be a routine.
%    \begin{macrocode}
z4bm=z3tm;
drawcirclebox(4, namespace(btex ABS etex)(nextra))(btex ABS etex);

%    \end{macrocode}
%
% \Mpost{} is a typed language, and new variables can be declared of a
% particular type. A |numeric| variable holds a number (or a length).
% The diameter of the circle just drawn is going to be used as a length
% in later parts of this diagram, so it is sensible to store its value
% in a new variable called |diam|. We then use it in drawing another
% circle directly on top of the first one.
%    \begin{macrocode}
numeric diam;
diam = namespace(btex ABS etex)(nextra);

z5bm=z4tm;
drawcirclebox(5, diam)(btex SAB etex);

%    \end{macrocode}
%
% The next element in the diagram is an ENTITY box. 
% We use the default height for the entity box and the default page connector
% length as its length (no reason, but it saves inventing another variable 
% or value).
%
%    The ENTITY box is positioned with respect to the SAB circle, but in a
% slightly more complicated way than earlier positions. We want the left hand
% side of the box to align with the right hand side of the circle. Also,
% the middle of the box should align with the top of the circle. 
%
%    The ENTITY box will be located at point |z6|. The easiest way is to
% specify |z6| is |z6ml=(x5mr, y5tm)|, but to demonstrate more of \Mpost's
% equation solving abilities a more complicated approach is taken to the 
% specification of the x coordinate. The horizontal distance between the
% points |z5ml| and |z5tl| on the circle is the same as the distance
% between the points |z5tr| and |z5mr|. We can express this as
% |x5ml-x5tl = x5tr-x5mr|. As we want |x6ml|, which is the same as |x6bl|,
%  to be the same as |x5mr| we
% can substitute into this equation, as done in the code below. Note that
% \Mpost{} can solve for the unknown |x6bl| even though it is on  
% the right hand side
% of the equation because the other three values are known.
%
%     The y coordinate of the point |z6mr| is specified as
% equal to the y coordinate of the top of the circle. Because of the linear
% relations involving all the points on a box, it is sufficient to provide
% one x coordinate and one y coordinate to fix all the points on the box.
%    \begin{macrocode}
x5ml-x5tl = x5tr-x6bl;
y6mr=y5tm;
drawENT(6, pconl, enth)(btex an\_ent etex);

%    \end{macrocode}
%
%    The geometric center of the next box, an LEVENT, is vertically above
% the geometric center of the ENTITY box, and the bottom of LEVENT is slightly
% (one lenth unit) above the top of the ENTITY box. This is accomplished here
% by specifying |z7bm| in terms of expressions involving the coordinates
% of the point |z6tm|.
%    \begin{macrocode}
z7bm=(x6tm,y6tm+u);
drawLEVENT(7, pconl, eventh)(btex levent etex);

%    \end{macrocode}
%
%    At point |z8| a GEVENT box is drawn. It's bottom left hand corner is
% vertically above the top left hand corner of the LEVENT box. If you look
% at the resulting diagram, you will see that GEVENT is shifted right with
% respect to LEVENT. For vertical alignment of EVENT boxes it is best to
% use the middle rather than corner points.
%    \begin{macrocode}
z8=(x7tl, y7tr+u);
drawGEVENT(8, pconl, eventh)(btex gevent etex);

%    \end{macrocode}
%
% \DescribeRoutine{mediation}
%    For the last of the aligned boxes another aspect of \Mpost{} is used.
% \Mpost{} provides a \emph{mediation} facility whose syntax is |frac[a,b]|.
% The result of a mediation is a value that is |frac| between the value |a|
% and the value |b|. For example, the result of |0.25[10,30]| is 15. Similarly,
% the result of |1/3[zj,zk]| is the point one third of the way between point
% |zj| and point |zk|.
%
%    The SCHEMA box is positioned with its bottom right hand corner at one
% eighth of the way along, and at the top of, the BOOLEAN box.
%    \begin{macrocode}
z9br=1/8[z3tl,z3tr];
drawSCHEMA(9, pconl, schemah)(btex a\_schema etex);

%    \end{macrocode}
%
%    The second half of the diagram illustrates various line and end 
% styles. These are all horizontal, the same length and are aligned 
% vertically, so
% define the x coordinate |xmid| of the left hand end of the lines, and
% the length |len| of the lines.
%    \begin{macrocode}
numeric xmid, len;
xmid = x8tr + diam;
len = 2diam;

%    \end{macrocode}
%
% \DescribeRoutine{shifted}
%    The next line of code exhibits another \Mpost{} function. A point can
% be specified as being some other point that is \emph{shifted} by given
% amounts in the x and y directions. More precisely, the shift is specified
% by a pair of values, written as |(a,b)|. The first line is aligned
% vertically with the center of the first box and its start point is |z11|.
% The end point, |z111|, is specified as being the start point shifted 
% horizontally by the length of the line.
%    \begin{macrocode}
z11=(xmid, y1ml); z111=z11 shifted (len, 0);
drawdashO(11, 111);

%    \end{macrocode}
%
%    Because we will be using the same horizontal shift for all the lines,
% define a \emph{pair}, called |moveright|, that is the required shift.
% The next two lines are also aligned vertically with the centers of the
% second and third boxes.
%    \begin{macrocode}
pair moveright;
moveright = (len, 0);

z12=(xmid, y2ml); z121=z12 shifted moveright;
drawnormalO(12, 121);

z13=(xmid, y3ml); z131=z13 shifted moveright;
drawthickO(13, 131);

%    \end{macrocode}
%
%   The remaining lines will have the same vertical spacing as the first three,
% so define another pair, |moveup|, that we can use for vertical shift.
%    \begin{macrocode}
pair moveup;
moveup = (0, y13-y12);

z14=z13 shifted moveup; z141=z14 shifted moveright;
drawnormalD(14, 141);

z15=z14 shifted moveup; z151=z15 shifted moveright;
drawnormalCA(15, 151);

z16=z15 shifted moveup; z161=z16 shifted moveright;
drawnormalOA(16, 161);

z17=z16 shifted moveup; z171=z17 shifted moveright;
drawnormalF(17, 171);

%    \end{macrocode}
%
%    The upper part of the diagram illustrates some of the additional
% line styles and boxes provided that are not part of the
% \ExpressG{} language. 
% \changes{v1.1}{1999/10/30}{Extended upper half of diagram 1 for new box
%  types}
%
%    The upper half is seperated from the bottom half by a dashed line, just
% to make the distinction. The line is set above the highest box so far,
% which is located at |z8|, and extends across the width of the diagram.
%    \begin{macrocode}
z300=(0,y8tm+diam); z301=(x111,y300);
draw z300--z301 dashes;

%    \end{macrocode}
% Define |mup| to be a distance, which we will use for vertical seperation.
%    \begin{macrocode}
numeric mup; mup := onelineh;

%    \end{macrocode}
%
%    As previously, we'll start with the boxes which will be placed in
% a column at the left side of the diagram. The first box, high enough
% for one line of enclosed text, has its top right hand corner folded 
% down by one quarter the box height. Text is placed at the center
% of the box, but if this is not required then it can be given as an
% empty string (i.e., |""|).
%    \begin{macrocode}
z302=(0,y300+mup);
drawcardbox(302, pconl, onelineh, 1/4onelineh)("");

%    \end{macrocode}
%
% The next box is a diamond shape. Unlike the rectangular and rhomboidal
% boxes, these are positioned
% via the center of the box instead of the bottom left hand corner.
%    \begin{macrocode}
z303bm=(x302tm, y302tm+mup);
drawdiamondbox(303, pconl, 2onelineh)(btex jewel etex);

%    \end{macrocode}
%
%   Now there is a double box with the top portion being 3/4 of the box 
% height. Text is put into the top half of the box using \Mpost's
% labeling routine (see \pref{page:label}).
%    \begin{macrocode}
z304=(0, y303tm+mup);
drawdoublerectangle(304, pconl, 2onelineh, 3/4);
label(btex top etex, z304ct);

%    \end{macrocode}
%
%   Next comes a triple box with the bottom portion being one fifth of
% the height, and the top portion being two fifths of the height.
% Text is placed in the top and middle portions, but not into the bottom.
%    \begin{macrocode}
z305=(0, y304tm+mup);
drawtriplerectangle(305, pconl, 3onelineh, 2/5, 0.2);
label(btex top etex, z305ct);
label("middle", z305cm);

%    \end{macrocode}
%
%   Some languages include a box that looks a little like an index card, and
% this is shown next.
% A small box is also drawn inside the main part of the index box, 
% just to illustrate
% that drawings may be placed inside boxes.
%    \begin{macrocode}
z306=(0,y305tm+mup);
drawindexbox(306, 2pconl, 3onelineh, 3/4pconl, onelineh)(btex pack etex);
z307=1/8[z306bl,z306tr];
drawENT(307, 1/4pconl, onelineh)(btex E etex);

%    \end{macrocode}
%
% Another box shown here is a dotted box that covers up anything that
% is underneath it. To demonstrate, a folded corner box is drawn first, 
% and then the
% dashed box is drawn second. They have to be done in this order.
% (The reason for the notation |y306P.tl| is explained under diagram 2
% on \pref{page:dotsuffix}).
%    \begin{macrocode}
z308=(0, y306P.tl+mup);
z309ml=z308c;
drawcardbox(308, pconl, 2onelineh, 1/4onelineh)(btex covered etex);
drawdashboxover(309, pconl, onelineh);

%    \end{macrocode}
%
%    An oval box comes next. The perimeter is an ellipse.
%    \begin{macrocode}
z310bm=(x306bm,y309tm+mup);
drawovalbox(310, 2pconl, 2onelineh)("");

%    \end{macrocode}
%
%    Now we have two rounded boxes. In the first one the corner radius is
% small and the corners are neatly rounded. The radius is large in the
% second case, and it is automatically reduced to give semicircular ends.
% Further, the center portion of the second of these boxes is `deleted'
% by putting a |hiderectangle| over it.
%    \begin{macrocode}
z311ml=(x310mr+mup, y310ml);
drawroundedbox(311, 2pconl, 2onelineh, 1/2onelineh)("rounded");

z312ml=(x311mr+mup, y311mr);
drawroundedbox(312, 2pconl, 2onelineh, 3/2onelineh)(btex large radius etex);

z314=(x312bm-1/4pconl, y312bm-1/2mup);
hiderectangle(314, 1/2pconl, (3/2onelineh + mup));

%    \end{macrocode}
%
%    The last of the simple enclosed shapes are a dashed ellipse and a dashed circle,
% which are aligned below the partially obscured rounded box.
%    \begin{macrocode}
z315tm=(x312bm, y312bm-mup);
drawdashellipse(315, 2pconl, 2onelineh);

z316tm=(x315bm, y315bm-mup);
drawdashcircle(316, diam);

%    \end{macrocode}
%
%    A drum box is now presented. This is centered with respect to the 
% rounded box and aligned with the bottom of the triple box. It is the
% same nominal size as the triple box.
%    \begin{macrocode}
z317bc=(x311bm,y304br);
drawdrum(317, pconl, 3onelineh)(btex drum etex);
%    \end{macrocode}
% To be a little different, I'll add a `handle' to the top of the drum. The
% top of the handle will be above the drum at the point |z317A|, and the
% attachement points are at the |tml| and |tmr| points on the drum. The
% normally sharp join in the middle of the handle is smoothed off.
%    \begin{macrocode}
z317A=(x317tc, y317tc+2onelineh);
drawnormalthree(317tml, 317A, 317tmr);
smooth(317tml, 317A, 317tmr);

%    \end{macrocode}
%
% Below the drum box is a stick figure. It is centered with respect to the
% drum box and based on the bottom row.
% \changes{v1.6}{2004/02/29}{Added stickman to example drawing}
%    \begin{macrocode}
z320bm = (x317bm, y302);
drawstickman(320, onelineh, 2onelineh);

%    \end{macrocode}
%
%   Above the drum box there is an output box, vertically aligned with the
% stick figure, labelled `output'.
% \changes{v1.6}{2004/02/29}{Added output box to example drawing}
%    \begin{macrocode}
z325bm = (x320bm, y306);
drawoutputbox(325, pconl, 2onelineh)(btex output etex);

%    \end{macrocode}
%
%   Above the output box there is a simple circled dot.
% \changes{v1.6}{2004/02/29}{Added circled dot to example drawing}
%    \begin{macrocode}
z330 = (x320bm, y309ml);
drawCircledDot(330, 3/2onelineh);

%    \end{macrocode}
%
%    As in the bottom half, line styles are drawn on the right side of
% of the diagram. First, though, there is an arrowed circle symbol.
% This is vertically aligned with the centers of the lines.
%    \begin{macrocode}
z401bm=(1/2[x11,x111], y301+mup);
drawcircleA(401, diam);

%    \end{macrocode}
%
%    Finish off with assorted linestyles.
%    \begin{macrocode}
z402=(xmid, y401tm+mup); z502=(x111, y402);
drawdashA(402, 502);

z403=(xmid, y402+mup); z503=(x111, y403);
drawdashOA(403, 503);

z404=(xmid, y403+mup); z504=(x111, y404);
drawnormalOD(404, 504);

z405=(xmid, y404+mup); z505=(x111, y405);
drawnormalCD(405, 505);

z406=(xmid, y405+mup); z506=(x111, y406);
drawnormalDCA(406, 506);

%    \end{macrocode}
%
%    Lines can be drawn at any angle, and the non-circular line end styles
% remain aligned.
%    
%    A set of lines and endstyles are drawn rotating about the common
% start point of the lines.
% \DescribeRoutine{rotatedaround}
% |pt1 rotatatedaround(pt2, ang)| is \Mpost{} code that rotates
% the point |pt1| around the point |pt2| counterclockwise through the angle 
% |ang| in degrees.
%
%    \begin{macrocode}
numeric ang; ang = 180/7;
z600=(xmid, y406+2mup);
z699=(x600+len, y600);
z601=z699 rotatedaround(z600, ang);
z602=z699 rotatedaround(z600, 2ang);
z603=z699 rotatedaround(z600, 3ang);
z604=z699 rotatedaround(z600, 4ang);
z605=z699 rotatedaround(z600, 5ang);
z606=z699 rotatedaround(z600, 6ang);
z607=z699 rotatedaround(z600, 7ang);
drawnormalCA(600,601);
drawnormalOA(600,602);
drawnormalF(600,603);
drawdashA(600,604);
drawnormalOD(600,605);
drawnormalCD(600,606);

%    \end{macrocode}
%
%    This is the end of the first diagram.
%    \begin{macrocode}
endfig;   % end figure 1

%    \end{macrocode}
%
% \subsection{Diagrams 2--5: EXPRESS-G like models}
%
%    The diagrams in this section are all drawn using the \ExpressG{}
% specific routines. Nevertheless, they do illustrate general BLA techniques.
%
% \subsubsection{Diagram 2: Schema level diagram}
%
%    In contrast to the first diagram, this one is much more like an 
% \ExpressG{} diagram. It illustrates a diagram consisting of SCHEMA
% boxes and interconnections.
%
%    \begin{macrocode}
beginfig(2)                       % schema level model

%    \end{macrocode}
%
%    First define some lengths to assist in laying out the diagram, which is
% going to consists of three rows of boxes with varying numbers of boxes
% in each row; the bottom row has two, the middle has four, and the top row
% has one. We also want to align the boxes vertically in a `nice' manner.
%
%    \begin{macrocode}
numeric lb, hb;                 % length & height of boxes
lb=20u; hb=schemah;
numeric upshift;                % vertical distance between rows
upshift = 20u;
numeric sideshift;              % horizontal distance between boxes
sideshift = 10u;

%    \end{macrocode}
%
%    The bottom row has two boxes and the second four. The two bottom boxes
% will be aligned vertically under the two middle boxes in the middle row.
% Allowance must be made for a `missing' box at the start of the bottom
% row. The second box on the bottom row is spaced from the first one. 
%    \begin{macrocode}
%%% bottom row

z9=(lb+sideshift,0); 
drawSCHEMA(9, lb, hb)("nine"); 

z11=(x9br+sideshift,y9); 
drawSCHEMA(11, lb, hb)("eleven"); 

%    \end{macrocode}
%
%    The bottom of the boxes on the second row are all at a fixed distance
% above the top of the boxes on the first row. We only need to specify the
% y coordinate of the bottom of one box in the row, and use that for the 
% remainder,
%    \begin{macrocode}
%%% middle row

z1=(0,y9tl+upshift); 
drawSCHEMA(1, lb, hb)("one"); 

z3=(x1br+sideshift, y1); 
drawSCHEMA(3, lb, hb)("three"); 

z5=(x3br+sideshift, y1); 
drawSCHEMA(5, lb, hb)("five");  

z7=(x5br+sideshift, y1); 
drawSCHEMA(7, lb, hb)("seven"); 

%    \end{macrocode}
%
%    The single box on the top row will be position centrally above the
% two middle boxes of the middle row. Mediation is used to calculate
% the x coordinate that is halfway between the right side of the left
% box and the left side of the right box.
%    \begin{macrocode}
%%% top row

x50 = 1/2[x3br,x5bl];
z31bm=(x50,y1tl+upshift); 
drawSCHEMA(31, lb, hb)("thirtyone"); 

%    \end{macrocode}
%
%    This completes the boxes. The diagram is finished off by drawing 
% connections between the boxes. The first set of connections are just
% straight lines between known points on boxes.
%    \begin{macrocode}
%%% connectors

drawdashOO(9tm, 3bm);   % three/nine 
drawdashO(5bm, 11tm);   % five/eleven 
drawdashO(3ml, 1mr);    % three/one 
drawdashO(3mr, 5ml);    % three/five 
drawdashOO(9mr, 11ml);  % nine/eleven

%    \end{macrocode}
%
%    The next connection is more complex. It goes from schema thirtyone 
% to schema nine on a three-legged route. It goes horizontally left from
% thirtynine, then vertically down, and finally horizontally right to nine. It
% also passes to the left of schema one. 
%
%    The route is constructed by specifying a point |z90| to the left of
% schema nine, and the point |z31A| on the left hand of schema thirtynine.
% The |VH| routine is then called to generate the corner point on the 
% (rotated) L shaped path between |z90| and |z31A|. The connection is then
% drawn using these four points.
%    \begin{macrocode}
%%% thirtyone/nine 
z90=((x1bl-sideshift), y9ml);
z31A=3/4[z31bl,z31tl];
VH(90, 31A);
drawdashO(90vh, 31A);
drawdashthreeO(90vh, 90, 9ml);
%    \end{macrocode}
%
% \DescribeRoutine{pickup}
%    To demonstrate another aspect of \Mpost, a dot is drawn at the location
% of |z90|. If the drawing pen is thick enough, just drawing one point is
% sufficient to make a noticeable dot. The code |pickup thickpen;| drops
% the current pen and picks up 
% the thickpen for drawing. The code |pickup normalpen;| picks up the
% normal pen, which is the one that is normally used.
%
% \DescribeRoutine{label}
% \DescribeRoutine{dotlabel}
%    The last line of code here is |label.lft("z90", z90);| which puts the
% text `z90' at the left of point |z90|.\label{page:label} 
% The label routine has two arguments,
% the first the text and the second the point at or near which the text is
% to be placed. The simplest form of the routine is |label("text", zk)| which
% centers the text over the point |zk|. A
% suffix can be used after the |label| (e.g., |.lft| in the code below) to
% modify the placement. |.lft| positions the text at the left of the point.
% The other modifiers are: |.rt|, |.top|, |.bot|, |.ulft|, |.urt|, |.llft| and
% |.lrt|. There is also a |dotlabel.suffix("text", zk)| routine which draws
% the point as well. For complicated diagrams it can be useful to label 
% some points during development, and then comment them out for the final 
% picture.
%    \begin{macrocode}
pickup thickpen;
draw z90;
pickup normalpen;
label.lft("z90", z90);

%    \end{macrocode}
%
%    The next two connectors, between schemas one and eleven and between
% thirtyone and eleven are of a similar U shape. There is, though, one tricky
% point to remember. Up till now, all point arguments to the \Lpack{expressg} 
% routines have been of the form |3| or |4bm|; 
% that is, either a number or a number
% followed by letter(s). For example, |VH(3,4bm)| will calculate
% the point |z3vh|. However, if a routine adds more letters to an argument
% that already has letters, such as |VH(4bm,3)|, the calculated point is 
% \emph{not} |z4bmvh| as might be expected, but instead 
% is |z4bm.vh|.\label{page:dotsuffix}
% This has tripped me up on several occasions.
%    \begin{macrocode}
%%% one/eleven 
z1A=1/3[z1bl,z1br];
z11A=(x11bm, (y11bm-sideshift));
VH(1A, 11A);
drawdashthree(1A, 1A.vh, 11A);   % note it is 1A.vh and not 1Avh
drawdashO(11A, 11bm);
dotlabel.rt("z11A", z11A);
dotlabel.lft("z1A.vh", z1A.vh);   % note it is z1A.vh and not z1Avh

%    \end{macrocode}
%
%    The connector between thirtyone and eleven is the same general shape
% as the thirtyone to nine connector. This time, I'll use the |HxH| routine
% to calculate the turning points
%    \begin{macrocode}
%%% thirtyone/eleven 
z31B=3/4[z31br,z31tr];
x31BC=x7br+sideshift;
HxH(31B, 31BC, 11mr);
drawdashfourO(31B, 31B.hxh, 11mr.hxh, 11mr);

%    \end{macrocode}
%
%    The next two connectors, between thirtyone and seven, and between 
% thirtyone and one, are simple L shapes, which are easier to produce than the
% U shaped ones.
%    \begin{macrocode}
%%% thirtyone/seven 
z31D=1/4[z31br,z31tr];
VH(7tm, 31D);
drawnormalthreeO(31D, 7tm.vh, 7tm);

%%% thirtyone/one 
z31C=1/4[z31bl,z31tl];
VH(1tm, 31C);
drawdashO(1tm.vh, 31C);
drawdashO(1tm.vh, 1tm);

%    \end{macrocode}
%
% The last two connectors are also simple, each consisting of vertical then 
% horizontal then vertical lines and the turning points can be calculated 
% by the |VhV| routine..
%    \begin{macrocode}
%%% thirtyone/three 
z31E=1/4[z31bl,z31br];
VhV(31E, 3tm);
drawnormalfourO(31E, 31E.vhv, 3tm.vhv, 3tm);

%%% thirtyone/five 
z31F=3/4[z31bl,z31br];
VhV(31F, 5tm);
drawnormalfourO(31F, 31F.vhv, 5tm.vhv, 5tm);

%    \end{macrocode}
%
%    The last element in the diagram is a vertical closed arrowheaded line
% with a label alongside. The arrowhead is on the top line of the connector
% between thirtyone and eleven. Note the point mediation expression expression
% in the |label| routine call.
%    \begin{macrocode}
%%% labeled arrow
z3111=1/4[z31B,z31B.hxh];
numeric arrowsize;
arrowsize := schemah;
z3112=(x3111, y3111+arrowsize);
drawnormalCA(3112, 3111);
label.rt(btex an\_import etex, 1/2[z3111, z3112]);

%    \end{macrocode}
%
%    The end of this diagram.
%    \begin{macrocode}
endfig;  % end fig 2

%    \end{macrocode}
%
%
% \subsubsection{Diagram 3: Tree structure}
%
%    This diagram is the first of three that are related in style. It is
% useful at this point to define some variables, and values for some of
% these as they will probably be used in all three diagrams.
%
%    Values are assigned (e.g., |var := val;|) so that they can be changed
% later if necessary (e.g., |var := newval;|). If values were equated like
% |var = val;| then they cannot be changed afterwards\footnote{Except
% by assignment.} as |var = newval;|
% will then have specified two incompatible equations for |var| and \Mpost will
% report a problem.
%    \begin{macrocode}

%%%% some commonly used variables & values

numeric pl, ph;           % length & height of numeric page connectors
pl:=pconl; ph:=pconh;     % for eg., 9,9 (9,9)
numeric plnamed;          % length of named page connector
numeric irh;              % height of interschema boxes
irh:=ish;                 % normally one line of text
numeric sdtl, sdth;       % length & height of SDT (e.g. INTEGER) boxes
sdtl:=sdtbl; sdth:=sdtbh;
numeric edtl, edth;       % length & height of enum boxes (inset is sdtbs)
edth:=sdtbh;              % normally one text line
numeric el, eh;           % length & height of entity boxes
eh:=enth;                 % normally one text line
numeric upshift;          % vertical space between rows of boxes
numeric nextup;           % vertical space between bases of rows of boxes
%    \end{macrocode}
%
%    Now another bit of \Mpost. There is another type of variable called
% a |picture| variable. This can hold something as trivial as a dot or
% a text string, up to a complete diagram. References to an Index
% type is a common element in some of the diagrams. It is useful to
% create a shorthand for these by using picture variables.
%    \begin{macrocode}
picture sindex, pindex;
sindex := btex eleven.Index etex;      % interschema reference text
pindex := btex 9,9 Index etex;         % page reference text
numeric slindex, plindex;
slindex := namespace(sindex)(nextra);  % length of Index interschema 
plindex := namespace(pindex)(nextra);  % length of Index page reference
%    \end{macrocode}
%
%    Yet more new \Mpost. Array variables are supported. These are declared
% by giving the variable name immediately followed by a pair of square 
% brackets. An element of an array can be simply accessed by suffixing the
% variable name with the integer number denoting the desired position.
% Actually we have been using array variables all along, as |z3| or |x7|
% are elements of the arrays |z[]| and |x[]| respectively. We define
% two arrays, one to be used for specifying horizontal spaces (lengths)
% and the other for vertical (y) coordinates. 
%    \begin{macrocode}
numeric hspace[];         % horizontal spaces
numeric lyc[];            % Y coords of box bases

%%%%%%%%%%% end commonly used variables & values

%    \end{macrocode}
%
% Diagram 3 consists of type boxes. We will make these all the same length
% and height.
%    \begin{macrocode}
beginfig(3)                      % example fig 3 
%%%drawgrid;

%    \end{macrocode}
%
%    The space required for the longest name is |edtl|.
%    \begin{macrocode}
edtl := namespace(btex standard\_data\_name etex)(niextra);
%    \end{macrocode}
%
%    There are several rows in the diagram. Specify the vertical space
% between the rows, and the space between the bottoms of the boxes (the
% height of a box is the normal height, |sdth|,  for a type box). Also
% specify the y coordinates for each row, counting from the bottom.
%    \begin{macrocode}
upshift=2sdth;
nextup=sdth+upshift;
%%%        the y coords of box bases
lyc1:=0;
lyc2:=lyc1+nextup;
lyc3:=lyc2+nextup;
lyc4:=lyc3+nextup;
lyc5:=lyc4+nextup;
lyc6:=lyc5+nextup;
lyc7:=lyc6+nextup;
lyc8:=lyc7+nextup;
%    \end{macrocode}
% Specify two horizontal spaces.
%    \begin{macrocode}
hspace1 := 1/3edtl;  % space between data enums
hspace2 := 2/3edtl;  % initial space at start of second row

%    \end{macrocode}
%    Draw the 3 boxes in the first row and the 3 in the second; these are
% staggered with respect to each other and overlap as otherwise there
% there is not enough space to get them all onto one page. 
% I'll use a numbering scheme for
% points so that |zCR| is a point in the Cth column and the Rth row.
%    \begin{macrocode}
%%% bottom two rows (1 & 2)

z11=(0,lyc1);
drawENUM(11, edtl, edth)(btex coordinates etex);

z22=(hspace2, lyc2);
drawENUM(22, edtl, edth)(btex solution\_data etex);

z31=(x11br+hspace1, lyc1);
drawENUM(31, edtl, edth)(btex pressure\_loads etex);

z42=(x22br+hspace1, lyc2);
drawENUM(42, edtl, edth)(btex nondimensional etex);

z51=(x31br+hspace1, lyc1);
drawENUM(51, edtl, edth)(btex temperature etex);

z62=(x42br+hspace1, lyc2);
drawENUM(62, edtl, edth)(btex force\_loads etex);

%    \end{macrocode}
%
% The third `row' consists of a horizontal line stretching from the middle
% of the leftmost box to the middle of the rightmost box. There are 
% connections from this line to the top middle of each of the boxes. We can
% use the |VyV| routine for the end points of the line.
%    \begin{macrocode}
%%% third row (horizontal line between 2 & 4 row)

z13=(x11tm,lyc3); 
VyV(11tm, 13, 62tm);
drawnormal(11tm.vyv, 62tm.vyv);
%    \end{macrocode}
%
%    Calculate the points on this line vertically above the midpoints of
% the boxes and draw the connections.
%    \begin{macrocode}
z23=(x22tm,lyc3); z33=(x31tm,lyc3); z43=(x42tm,lyc3); z53=(x51tm,lyc3);
drawnormalO(11tm.vyv,11tm);
drawnormalO(23,22tm);
drawnormalO(33,31tm);
drawnormalO(43,42tm);
drawnormalO(53,51tm);
drawnormalO(62tm.vyv,62tm);

%    \end{macrocode}
%
%    The fourth row consists of three boxes. There is a vertical line 
% from the bottom
% of the leftmost box to the horizontal line drawn in row 4. The three
% boxes are aligned horizontally with respect to this line.
%    \begin{macrocode}
%%% fourth row 

z3224=1/3[z13,z62tm.vyv];
z3554=2/3[z13,z62tm.vyv];

%%% standard_data_name
z24bm=(x3224,lyc4);
drawSELECT(24, edtl, edth)(btex standard\_data\_name etex);
drawnormal(24bm,3224);

%%% adhoc_data_name
z54bm=(x3554,lyc4);
drawTYPE(54, edtl, edth)(btex adhoc\_data\_name etex);

%%% STRING
z64br=(x62br,lyc4);
drawSTRING(64);

%    \end{macrocode}
%
%    The fifth `row' consists of two vertical connectors to the tops of
% the SELECT and TYPE boxes, with a horizontal line connecting the tops
% of the connectors.
%    \begin{macrocode}
%%% fifth row

z35=(1/2[x24tm,x54tm], lyc5);
VyV(24tm, 35, 54tm);
drawnormalthreeO(35, 24tm.vyv, 24tm);
drawnormalthreeO(35, 54tm.vyv, 54tm);

%    \end{macrocode}
%
%    The top row consists of a SELECT box vertically aligned above the center
% of the horizontal line from the 5th row, together with a line joining
% these two, and also a page reference box
% off towards the right hand side
%    \begin{macrocode}
%%% sixth row

z36bm=(x35,lyc6);
drawSELECT(36,edtl, edth)(btex data\_name etex);
drawnormal(36bm,35);

%%% data_name
z66=(x62,lyc6);
drawPREF(66, sdtl, ph)(btex 3,1 (4) etex);

%    \end{macrocode}
%
%    The remaining elements on the diagram are: 
% a connector on the 4th row from adhoc\_data\_name to STRING;
% and a connector on the 6th row from the page reference to data\_name.
%    \begin{macrocode}
%%%% rest of the connectors 

%%% adhoc/STRING (54, 64)
drawnormalO(54mr,64ml);

%%% PREF/data_name (36, 66)
drawdashO(66ml,36mr);

%    \end{macrocode}
%
%    The end of this diagram
%    \begin{macrocode}
endfig;                         % end fig 3

%    \end{macrocode}
%
% \subsubsection{Diagram 4: Supertypes and subtypes}
%
%    This diagram consists of a supertype entity and its four subtypes. The
% entities have various attributes.
%
%    \begin{macrocode}

beginfig(4)                     % example 4 
%%%drawgrid;

%    \end{macrocode}
%
%    Define some useful lengths.
%    \begin{macrocode}
%%% length of named page reference boxes
plnamed := namespace(btex 9,9 data\_name etex)(nextra);

%%% length of entity boxes
el := namespace(btex (ABS) Data\_t etex)(nextra);

upshift := 2sdth;         % vertical space between boxes
nextup := sdth+upshift;   % vertical space between bases of boxes
hspace1 := 1/2el;         % space between entity boxes

%%% the y coords of box bases
lyc1:=0;
lyc2:=lyc1+nextup;
lyc3:=lyc2+nextup;
lyc4:=lyc3+nextup;
lyc5:=lyc4+nextup;
lyc6:=lyc5+nextup;
lyc7:=lyc6+nextup;
lyc8:=lyc7+nextup;

%    \end{macrocode}
%
%    We'll start with the second row which consists of 4 entity (subtype)
% boxes. The numbering scheme for point suffixes is |zCR|, where |C|
% is the column number and |R| is the row number.
%    \begin{macrocode}
%%%% 2nd row

%%% IntArray
z12=(0,lyc2);
drawENT(12, el, eh)(btex IntArray etex);

%%% RealArray
z22=(x12br+hspace1, lyc2);
drawENT(22, el, eh)(btex RealArray etex);

%%% CharArray
z42=(x22br+hspace1, lyc2);
drawENT(42, el, eh)(btex CharArray etex);

%%% BitArray
z52=(x42br+hspace1, lyc2);
drawENT(52, el, eh)(btex BitArray etex);

%    \end{macrocode}
%
%    The first row is four simple data type boxes, aligned underneath the
% entity boxes.
%    \begin{macrocode}
%%%% 1st row

z11bm=(x12bm,lyc1);
drawINTEGER(11);

z21bm=(x22bm,lyc1);
drawREAL(21);

z41bm=(x42bm,lyc1);
drawSTRING(41);

z51bm=(x52bm,lyc1);
drawBINARY(51);

%    \end{macrocode}
%
%    The third `row' is the thick lines connecting the subtype boxes.
%    \begin{macrocode}
%%% 3rd row

y13=       y23=       y43=       y53=lyc3;
x13=x12tm; x23=x22tm; x43=x42tm; x53=x52tm;
drawthick(13,53);      % horizontal line
%%% vertical connectors
drawthickO(13,12tm); drawthickO(23,22tm); 
drawthickO(43, 42tm); drawthickO(53, 52tm);

z33=1/2[z13,z53];   % midpoint of horizontal line

%    \end{macrocode}
%
%    The 4th row is an abstract supertype entity box, which is made 3 times
% taller than the default entity box height. The entity box is centered 
% with respect to the row of subtype boxes and is connected to the
% subtype boxes connector. The digit 1 is placed near the connection point.
%  There is also a page reference
% and an INTEGER box at the left and right (as attributes of the supertype).
%    \begin{macrocode}
%%% 4th row

%%% Data_t
z34bm=(x33,lyc4);
drawENT(34, el, 3eh)(btex \twolines{(ABS)}{Data\_t} etex);
drawthick(34bm,33);
label.urt("1", z33);   % label the connection point

%%% Index
z14=(0,lyc4);
drawPREF(14, plindex, ph)(pindex);

%%% INTEGER
z54br=(x51br,lyc4);
drawINTEGER(54);

%    \end{macrocode}
%
%    The 5th row has page reference boxes at the left and right 
% (as attributes of the supertype).
%    \begin{macrocode}
%%% 5th row

lyc5:=y34tm-ph;   % change the initial y coord value

%%% Index
z15=(0,lyc5);
drawPREF(15, plindex, ph)(pindex);

%%% DataType
z55=(x54,lyc5);
drawPREF(55, plnamed, ph)(btex 3,1 data\_name etex);

%    \end{macrocode}
%
%    The 6th, and last, row, just consists of a page reference centered
% above the supertype box.
%    \begin{macrocode}
%%% 6th row

%%% PREF to Data_t
lyc6:=lyc5+nextup;
z36bm=(x34tm,lyc6);
drawPREF(36, pl, ph)(btex 7,5 (6) etex);

%    \end{macrocode}
%
%    The rest of the diagram consists of the labelled attribute lines.
%    \begin{macrocode}
%%%% attributes

%%% Sizes  Data_t/Index (34, 14)
z3414=(x34,y14mr);
drawnormal(3414,14mr);
label.ulft(btex Sizes A[1:Limit] etex, z3414);

%%% num  Data_t/INTEGER (34, 54)
z3454=(x34mr,y54ml);
drawnormalO(3454,54ml);
label.urt(btex (DER) num etex, z3454);

%%% Limit Data_t/Index (34, 15)
z3415=(x34,y15mr);
drawnormal(3415,15mr);
label.ulft(btex Limit etex, z3415);

%%% Kind Data_t/data_name (34, 55)
z3455=(x34mr, y55ml);
drawnormal(3455, 55ml);
label.urt(btex Kind etex, z3455);

%%% PREF into Data_t (36, 34)
drawdashO(36bm, 34tm);

%%% Data IntArray/INTEGER (12, 11)
drawnormalO(12bm, 11tm);
label.lrt(btex Data A[1:num] etex, z12bm);

%%% Data RealArray/REAL (22, 21)
drawnormalO(22bm, 21tm);
label.lrt(btex Data A[1:num] etex, z22bm);

%%% Data CharArray/STRING (42, 41)
drawnormalO(42bm, 41tm);
label.lrt(btex Data A[1:num] etex, z42bm);

%%% Data BitArray/BINARY (52, 51)
drawnormalO(52bm, 51tm);
label.lrt(btex Data A[1:num] etex, z52bm);

%    \end{macrocode}
%
%     The end of this diagram.
%    \begin{macrocode}
endfig;                              % end fig 4

%    \end{macrocode}
%
%    \subsubsection{Diagram 5: Portion of larger model}
%
%    This diagram is more complex than the previous ones. It is, nevertheless,
% presented with virtually no commentary. It consists of three entity boxes
% and various page reference and interschema boxes to support the
% entities' attributes.
%
%    \begin{macrocode}
beginfig(5)                 % example 5 
%%drawgrid;

%    \end{macrocode}
%
%    As usual, specify commonly used variables and values.
%    \begin{macrocode}
plnamed := namespace(btex 7,4 Unstructured\_Donor etex)(nextra);

numeric irls, irll;             % length of short and long ISR boxes
irls = namespace(btex eleven.MeshLocation etex)(nextra);
irll = namespace(btex eleven.MeshConnectivityType etex)(nextra);

upshift := irh;
nextup := irh+upshift;

numeric maxrx;         % max x coordinate value of LH of right column boxes
maxrx := maxx-irrl; 
numeric xmid;          % x coord of figure center
xmid := 1/2[irls, maxx-irll];

el := namespace(btex MeshConnectivity1\_1 etex)(nextra);
eh := irh;

%%% y coords
lyc1 := 0;
lyc2 := lyc1+nextup;
lyc3 := lyc2+nextup;
lyc4 := lyc3+nextup+irh;
lyc5 := lyc4+nextup;
lyc6 := lyc5+nextup;
lyc7 := lyc6+nextup;
lyc8 := lyc7+nextup;
lyc9 := lyc8+nextup;

%    \end{macrocode}
%
%    Rows one and two have one centered box each.
%    \begin{macrocode}
%%% Zcol/row
%%% row 1

%%% PREF for Overlapping
z21bm=(xmid,lyc1);
drawPREF(21, pl, ph)(btex 5,3 (8) etex)

%%% row 2

%%% OverlappingArea
z22bm=(x21bm,lyc2);
drawENT(22, el, eh)(btex OverlappingArea etex);

%    \end{macrocode}
%
%    Row three has three boxes, and the middle one is centered.
%    \begin{macrocode}
%%% row 3

%%% IndexArray
z13=(pl,lyc3);
drawISR(13, irls, irh)(btex eleven.IndexArray etex);

%%% Index
z23bm=(x22bm,lyc3);
drawISR(23, slindex, irh)(sindex);

%%% MeshLocation
z33br=(maxx,lyc3);
drawISR(33, irls, irh)(btex eleven.MeshLocation etex);

%    \end{macrocode}
%
%    Row four has three boxes, and the middle one is centered.
%    \begin{macrocode}
%%% row 4

%%% MeshConnectivity
z24bm=(x23bm,lyc4);
drawENT(24, el, eh)(btex MeshConnectivity etex);

%%% PREF for MeshConnectivity
z14ml=(pl,y24ml);
drawPREF(14, pl, ph)(btex 5,2 (8) etex);

%%% Structured_Donor
z34br=(maxx,lyc4);
drawPREF(34, plnamed, ph)(btex 7,5 Structured\_Donor etex);

%    \end{macrocode}
%
%    Rows five and six have one box each, at the right hand side.
%    \begin{macrocode}
%%% row 5

%%% Unstructured_donor
z35br=(maxx,lyc5);
drawPREF(35, plnamed, ph)(btex 7,4 Unstructured\_Donor etex);

%%% row 6

%%% MeshConnType
z36br=(maxx,lyc6);
drawISR(36, irll, irh)(btex eleven.MeshConnectivityType etex);

%    \end{macrocode}
%
%    Row seven has three boxes, and the middle one is centered.
%    \begin{macrocode}
%%% row 7

%%% IndexRange
z17=(0,lyc7);
drawISR(17, irls, irh)(btex eleven.IndexRange etex);

%%% INTEGER
x27bm=x24bm; y27ml=y17mr;
drawINTEGER(27);

%%% Zone
z37br=(maxx,lyc7);
drawISR(37, irls, irh)(btex seven.Zone etex);

%    \end{macrocode}
%
%    Rows eight and nine have one centered box each.
%    \begin{macrocode}
%%% row 8

%%% 1to1
z28bm=(x24bm,lyc8);
drawENT(28, el, eh)(btex MeshConnectivity1\_1 etex);

%%% row 9

%%% PREF to 1to1
z29bm=(x28bm,lyc9);
drawPREF(29, pl, ph)(btex 5,1 (8) etex);

%    \end{macrocode}
%
%    All the boxes have been drawn. The remainder is adding and labelling
% attribute lines. First page references to subtype entities.
%    \begin{macrocode}
%%%% attributes, etc

drawthickO(21tm,22bm);   % PREF to Overlap (21, 22)
drawthickO(14mr,24ml);   % PREF to MeshConn (14, 24)
drawthickO(29bm,28tm);   % PREF to 1to1 (29, 28)

%    \end{macrocode}
%
%    The attributes of entity OverlappingArea (|z22|)
%    \begin{macrocode}
%%% PointListSize (22, 23)
drawdashO(22tm,23bm);
label.llft(btex PointListSize etex, z23bm);

%%% PointRange (22, 17)
z22A=1/4[z22bl,z22tl]; z17A=(1/2[0,x13], y17);
VH(17A,22A);
drawdashthreeO(22A, 17A.vh, 17A);
label.ulft(btex PointRange etex, z22A);

%%% PointList (22, 13)
z22B=3/4[z22bl,z22tl];
VH(13bm,22B);
drawdashthreeO(22B, 13bm.vh, 13bm);
label.ulft(btex PointList etex, z22B);

%%% MeshLocation (22, 33)
z22C=1/4[z22br,z22tr];
z33B=2/3[z33bl,z33br];
VH(33B,22C);
drawnormalthreeO(22C, 33B.vh, 33B);
label.urt(btex (DER) Location etex, z22C);

%%% Meshloc (22, 33)
z22D=3/4[z22br,z22tr];
z33A=1/3[z33bl,z33br];
VH(33A,22D);
drawdashthreeO(22D, 33A.vh, 33A);
label.urt(btex Meshloc etex, z22D);

%    \end{macrocode}
%
%    The attributes of entity MeshConnectivity (|z24|).
%    \begin{macrocode}
%%% PointListSize (24, 23)
drawnormalO(24bm, 23tm);
label.ulft(btex PointListSize etex, z23tm);

%%% StructuredDonor (24, 34)
z24A=(x24br,y34ml);
draw z24A--z34ml dashes;
label.lrt(btex StructuredDonor etex, z24A);

%%% UnstructuredDonor (24, 35)
z24B=3/4[z24br,z24tr];
HvH(24B,35ml);
drawdashfourO(24B, 24B.hvh, 35ml.hvh, 35ml);
label.urt(btex UnstructuredDonor etex, z24B.hvh);

%%% Meshloc (24, 33)
z24C=4/6[z24bl,z24br];
z33C=(x33A,y33tm);
y2433C=1/3[y33C,y24C];
VyV(24C, 2433C, 33C);
drawdashfourO(24C, 24C.vyv, 33C.vyv, 33C);
label.lrt(btex Meshloc etex, z24C.vyv);

%%% Location (24, 33)
z24D=5/6[z24bl,z24br];
z33D=(x33B,y33tm);
y2433D=2/3[y33D,y24D];
VyV(24D, 2433D, 33D);
drawnormalfourO(24D, 24D.vyv, 33D.vyv, 33D);
label.lrt(btex (DER) Location etex, z24D.vyv);

%%% ConnectivityType (24, 36)
z24H=(x24D,y24tr); 
z36H=z36bm;
y2436H=1/2[y35tr,y36br];
VyV(24H, 2436H, 36H);
drawnormalfourO(24H, 24H.vyv, 36H.vyv, 36H);
label.urt(btex (DER) ConnectivityType etex, z24H.vyv);

%%% Meshcon (24, 36)
z24G=(x24C,y24tr);
z36G=z36ml;
VH(24G,36G);
drawdashthreeO(24G, 24G.vh, 36G);
label.urt(btex Meshcon etex, z24G.vh);

%%% K (24, 27)
drawnormalO(24tm, 27bm);
label.ulft(btex K etex, z24tm);

%%% PointRange (24, 17)
z24E=1/4[z24tl,z24tr];
x17br-x17E = x17A-x17bl;
y17E = y17A;
VhV(24E,17E);
drawdashfourO(24E, 24E.vhv, 17E.vhv, 17E);
label.ulft(btex PointRange etex, z24E);

%%% PointList (24, 13)
z24F=1/4[z24bl,z24br];
z13F=1/2[z13tl,z13tr];
VhV(24F,13F);
drawnormalfourO(24F, 24F.vhv, 13F.vhv, 13F);
label.llft(btex PointList etex, z24F);
 
%    \end{macrocode}
%
%    The attributes of entity MeshConnectivity1\_1 (|z28|)
%    \begin{macrocode}
%%% N (28, 27)
z27A=1/5[z27tl,z27tr];
z28A=(x27A,y28bl);
drawnormalO(28A,27A);
label.llft(btex N etex, z28A);

%%% trans (28, 27)
z27B=1/2[z27tl,z27tr];
z28B=(x27B,y28bl);
drawdashO(28B,27B);
label.lrt(btex \twolines{trans}{A[1:N]} etex, z28B);

%%% Transform (28, 27)
z27C=1/2[z27br,z27tr];
z28C=(1/2[x27C,x28br], y28br);
VH(28C,27C);
drawnormalthreeO(28C,28C.vh,27C);
label.lrt(btex (DER) Transform A[1:N] etex , z28C);

%%% DonorZone (28, 37)
z28D=1/2[z28br,z28tr];
z37D=z37tm;
VH(37D,28D);
drawdashthreeO(28D,37D.vh,37D);
label.urt(btex DonorZone etex, z28D);

%%% DonorPointRange (28, 17)
z28G=3/4[z28bl,z28tl];
z17G=(x17A,y17tl);
VH(17G,28G);
drawnormalthreeO(28G,17G.vh,17G);
label.ulft(btex DonorPointRange etex, z28G);

%%% PointRange (28, 17)
z28H=1/4[z28bl,z28tl];
z17H=(x17E,y17G);
VH(17H,28H);
drawnormalthreeO(28H,17H.vh,17H);
label.ulft(btex PointRange etex, z28H);

%    \end{macrocode}
%
%    The end of this diagram.
%    \begin{macrocode}
endfig;                             % end fig 5

%    \end{macrocode}
%
% \subsection{Diagrams 6--11: Car model}
%
%    The diagrams in this section are all taken from~\cite[Chapter~2]{EBOOK}.
% A simple information/data model of a car, car model, and car manufacturer
% is presented in a variety of BLA languages, among which is, 
% of course, \ExpressG. In words, the model is:
% \begin{quote} \itshape
%     A car is made by a manufacturer. Each manufacturer has a unique name.
% A manufacturer constructs cars in several models and a car is of a
% particular model. A manufacturer gives a serial number to each car 
% he produces and this is unique across all cars produced by that
% manufacturer. Each model also has a name, and this is unique across
% all models. A car has a year of production.
% \end{quote}
% This model is a small portion of a conceptual model developed as a common
% specification for comparing modeling languages~\cite{TR9007}.
%
% The purpose of these diagrams is to 
% illustrate how the \Lpack{expressg} package supports a range of graphical
% languages.
%
%
% \subsubsection{Diagram 6: \ExpressG}
%
%    Having already seen several examples of \ExpressG{} diagrams, this one
% is presented with no further comments.
%    \begin{macrocode}

beginfig(6)            % example 6  EXPRESS-G
%%%drawgrid;

upshift := 3/2onelineh;
nextup := onelineh+upshift;

el := namespace(btex manufacturer etex)(nextra);
eh := onelineh;

hspace1 := 1/2el;

%%% y coords
lyc1 := 0;
lyc2 := lyc1+nextup;
lyc3 := lyc2+nextup;
lyc4 := lyc3+nextup;
lyc5 := lyc4+nextup;

%%% Zcol/row

%%% rows 4 and 5
z14=(0,lyc4);
drawENT(14, el, eh)(btex manufacturer etex);

z25=(x14br+hspace1, lyc5);
drawSTRING(25);

z34=(x25br+hspace1, lyc4);
drawENT(34, el, eh)(btex car\_model etex);

%%% row 3

z33bm=(x34bm, lyc3);
drawENT(33, el, eh)(btex car etex);

%%% row 2

z22=(x25, lyc2);
drawINTEGER(22);

%%% row 1

z21=(x22, lyc1);
drawSTRING(21);

%%% attributes

%%% manufacturer name (14, 25)
VH(14tm, 25ml);
drawnormalthreeO(14tm, 14tm.vh, 25ml);
label.urt(btex *name etex, z14tm.vh);

%%% model name (34, 25)
VH(34tm, 25mr);
drawnormalthreeO(34tm, 34tm.vh, 25mr);
label.ulft(btex *name etex, z34tm.vh);

%%% made_by (34, 14)
drawnormalO(34ml, 14mr);
label.ulft(btex made\_by etex, z34ml);

%%% model_type (33, 34)
drawnormalO(33tm, 34bm);
label.urt(btex model\_type etex, z33tm);

%%% DER made_by (33, 14)
VH(14bm, 33ml);
drawnormalthreeO(33ml, 14bm.vh, 14bm);
label.ulft(btex (DER) *made\_by etex, z33ml);

%%% year (33, 22)
z33A=1/3[z33bl, z33br];
VH(33A, 22mr);
drawnormalthreeO(33A, 33A.vh, 22mr);
label.ulft(btex year etex, z33A.vh);

%%% serial_no
z33B=2/3[z33bl, z33br];
VH(33B, 21mr);
drawnormalthreeO(33B, 33B.vh, 21mr);
label.ulft(btex *serial\_no etex, z33B.vh);

%    \end{macrocode}
%
% The end of this diagram
%    \begin{macrocode}
endfig;               % end fig 6

%    \end{macrocode}
%
%
% \subsubsection{Diagram 7: Shlaer-Mellor}
%
%    The Shlaer-Mellor graphical language~\cite{SHLAER88} is fairly simple,
% consisting basically of rectangles and arrowheaded lines. However, unlike
% \ExpressG{} each box usually has several lines of text. These are placed
% individually at the desired positions within each box.
%
%    Notice below that
% I have used |drawENT| with an empty string to draw the rectangular boxes;
% the routines for \ExpressG{} diagrams can, if suitable, be used in any
% sort of diagram.
%
%    \begin{macrocode}

beginfig(7)            % example 7
%%%drawgrid;

el := namespace(btex MANUFACTURER etex)(niextra);
eh := onelineh;

hspace1 := namespace(btex made by maker of etex)(4ndextra);

hspace2 := 6onelineh;   % height of CAR
hspace3 := 5onelineh;   % space between rows
hspace4 := 3onelineh;   % height of MANUFACTURER

%%% y coords
lyc1 := 0;
lyc2 := lyc1+hspace2+hspace3;

%%% Zcol/row

%%% row 2

z12=(0, lyc2);
drawENT(12, el, hspace4)("");
x121=x12+sdtbs;
label.rt(btex MANUFACTURER etex, (x121, 2/3[y12bl, y12tl]));
label.rt(btex * manuf-name etex, (x121, 1/3[y12bl, y12tl]));

z22=(x12br+hspace1, lyc2);
drawENT(22, el, hspace4)("");
x221=x22+sdtbs;
label.rt(btex CAR-MODEL etex, (x221, 2/3[y12bl, y12tl]));
label.rt(btex * model-name etex, (x221, 1/3[y12bl, y12tl]));

%%% row 1

z21=(x22, lyc1);
drawENT(21, el, hspace2)("");
x211=x21+sdtbs;
label.rt(btex CAR etex,         (x211, 5/6[y21bl, y21tl]));
label.rt(btex o year etex,      (x211, 4/6[y21bl, y21tl]));
label.rt(btex o model (R) etex, (x211, 3/6[y21bl, y21tl]));
label.rt(btex * serial-no etex, (x211, 2/6[y21bl, y21tl]));
label.rt(btex * maker (R) etex, (x211, 1/6[y21bl, y21tl]));

%%%%% relationship lines

%    \end{macrocode}
% In this diagram the labels on the relationship lines tend to bump
% into the line ending symbol. \Mpost{} ignores initial and final spaces
% within |btex...etex|. The paired braces below, each enclosing one space,
%  supply non-discarded spaces. (These could also have been written as 
% |\space|).
%    \begin{macrocode}
%%% MANUFACTURER / CAR-MODEL (12, 22)
drawnormalDCA(12mr, 22ml);
drawnormalCA(22ml, 12mr);
label.urt(btex { }{ }made by etex, z12mr);
label.llft(btex maker of{ }{ } etex, z22ml);

%%% MANUFACTURER / CAR (12, 21)
VH(12bm, 21ml);
drawnormalCA(12bm.vh, 12bm);
drawnormalDCA(12bm.vh, 21ml);
label.llft(btex { }{ }made by etex, z12bm);
label.ulft(btex maker of{ }{ }  etex, z21ml);

%%% CAR-MODEL / CAR (22, 21)
drawnormalDCA(22bm, 21tm);
drawnormalCA(21tm, 22bm);
label.lrt(btex { }one of etex, z22bm);
label.ulft(btex type of{ }  etex, z21tm);

%    \end{macrocode}
%
% The end of this diagram
%    \begin{macrocode}
endfig;               % end fig 7

%    \end{macrocode}
%
%
% \subsubsection{Diagram 8: IDEF1X}
%
%    IDEF1X is a popular language in America for representing the structure
% of relational databases, and was developed under the auspices of the 
% US Air Force~\cite{IDEF1X}.
%
%    The general layout of the diagram mimics the previous one. All the boxes
% are divided horizontally into an upper and lower part. 
% The |drawdoublerectangle| is used for the rectangular boxes, but the dividing
% line in the rounded box has to be added by hand, as it were.
%
%    \begin{macrocode}

beginfig(8)            % example 8  IDEF1X
%%%drawgrid;

el := namespace(btex MANUFACTURER etex)(niextra);
eh := onelineh;

hspace1 := namespace(btex made by maker of etex)(4ndextra);

hspace2 := 5onelineh;   % height of CAR
hspace3 := 5onelineh;   % space between rows
hspace4 := 3onelineh;   % height of MANUFACTURER

%%% y coords
lyc1 := 0;
lyc2 := lyc1+hspace2+hspace3;

%%% Zcol/row

%%% row 2

z12=(0, lyc2);
drawdoublerectangle(12, el, hspace4, 1/2);
label.urt(btex Manufacturer etex, z12tl);
x121=x12+sdtbs;
label.rt(btex manuf-name etex, (x121, 3/4[y12bl, y12tl]));

z22=(x12br+hspace1, lyc2);
drawdoublerectangle(22, el, hspace4, 1/2);
label.urt(btex Car-model etex, z22tl);
x221=x22+sdtbs;
label.rt(btex Model-name etex, (x221, 3/4[y12bl, y12tl]));
label.rt(btex Manuf-name (FK) etex, (x221, 1/4[y12bl, y12tl]));

%%% row 1

z21=(x22, lyc1);
drawroundedbox(21, el, hspace2, 2sdtbs)("");
label.urt(btex Car etex, z21tl);
draw z21ml--z21mr;
x211=x21+sdtbs;
label.rt(btex Serial-no etex,       (x211, 5/6[y21bl, y21tl]));
label.rt(btex Manuf-name (FK) etex, (x211, 4/6[y21bl, y21tl]));
label.rt(btex Model-name (FK) etex, (x211, 2/6[y21bl, y21tl]));
label.rt(btex Year etex,            (x211, 1/6[y21bl, y21tl]));

%%%%% relationship lines

%%% MANUFACTURER / CAR-MODEL (12, 22)
drawnormalD(12mr, 22ml);
label.top(btex of etex, 1/2[z12mr, z22ml]);

%%% MANUFACTURER / CAR (12, 21)
VH(12bm, 21ml);
drawnormalthreeD(12bm, 12bm.vh, 21ml);
label.top(btex makes etex, 1/2[z12bm.vh, z21ml]);
label.ulft(btex P{ }  etex, z21ml);

%%% CAR-MODEL / CAR (22, 21)
drawnormalD(22bm, 21tm);
label.lft(btex of etex, 1/2[z21tm,z22bm]);
label.urt(btex { }P etex, z21tm);

%    \end{macrocode}
%
% The end of this diagram
%    \begin{macrocode}
endfig;               % end fig 8

%    \end{macrocode}
%
%
% \subsubsection{Diagram 9: OMT}
%
%    OMT~\cite{RUMBAUGH91} was the precursor to the currently popular UML
% structure modeling language. 
%    If you are curious as to why I believe that lexical languages are in 
% general better than BLA languages, the chapter on developing a compiler
% for OMT highlights, probably unintentionally, some of the disadvantages 
% of BLAs.
%
% The general look of the OMT diagram is almost identical
% to the IDEF1X diagram.
%
%    \begin{macrocode}

beginfig(9)            % example 9  OMT
%%%drawgrid;

el := namespace(btex {\bf MANUFACTURER} etex)(niextra);
eh := onelineh;

hspace1 := namespace(btex made by maker of etex)(4ndextra);

hspace2 := 4onelineh;   % height of CAR
hspace3 := 4onelineh;   % space between rows
hspace4 := 3onelineh;   % height of MANUFACTURER

%%% y coords
lyc1 := 0;
lyc2 := lyc1+hspace2+hspace3;

%%% Zcol/row

%%% row 2

z12=(0, lyc2);
drawdoublerectangle(12, el, hspace4, 1/2);
x121=x12+sdtbs;
label.rt(btex {\bf Manufacturer} etex, (x121, 3/4[y12bl, y12tl]));
label.rt(btex name : String etex,      (x121, 1/4[y12bl, y12tl]));

z22=(x12br+hspace1, lyc2);
drawdoublerectangle(22, el, hspace4, 1/2);
x221=x22+sdtbs;
label.rt(btex {\bf Car Model} etex, (x221, 3/4[y22bl, y22tl]));
label.rt(btex name: String etex,    (x221, 1/4[y22bl, y22tl]));

%%% row 1

z21=(x22, lyc1);
drawdoublerectangle(21, el, hspace2, 1/3);
x211=x21+sdtbs;
label.rt(btex {\bf Car} etex,          (x211, 5/6[y21bl, y21tl]));
label.rt(btex serial-no : String etex, (x211, 4/9[y21bl, y21tl]));
label.rt(btex year : Integer etex,     (x211, 2/9[y21bl, y21tl]));

%%%%% relationship lines

%%% MANUFACTURER / CAR-MODEL (12, 22)
drawnormalD(12mr, 22ml);
label.top(btex {\it makes} etex, 1/2[z12mr, z22ml]);
label.ulft(btex 1+{ } etex, z22ml);

%%% MANUFACTURER / CAR (12, 21)
VH(12bm, 21ml);
drawnormalthreeD(12bm, 12bm.vh, 21ml);
label.top(btex {\it makes} etex, 1/2[z12bm.vh, z21ml]);
label.ulft(btex 1+{ }  etex, z21ml);

%%% CAR-MODEL / CAR (22, 21)
drawnormalD(22bm, 21tm);
label.lft(btex {\it produced as} etex, 1/2[z21tm,z22bm]);

%    \end{macrocode}
%
% The end of this diagram
%    \begin{macrocode}
endfig;               % end fig 9

%    \end{macrocode}
%
%
% \subsubsection{Diagram 10: E-R}
%
%    There are several flavours of Entity-Relationship modeling icons.
% I have used a style from~\cite{ELMASRI89}.
%
%    This example introduces some new icons and \Mpost{} modeling.
%
%    \begin{macrocode}

beginfig(10)            % example 10 E-R
%%%drawgrid;

numeric diam; diam := 2onelineh;

upshift := diam;            % circle diameter
nextup := diam+upshift;

el := namespace(btex MANUFACTURER etex)(niextra);
eh := onelineh;

numeric dl, dh;             % length and height of diamond boxes
dl := 1/2el; dh := 2eh;

numeric marg; marg := 4u;   % double the seperation between parallel lines

hspace1 := 1/2el;

%%% y coords
lyc1 := 0;
lyc2 := lyc1+nextup;
lyc3 := lyc2+nextup;
lyc4 := lyc3+nextup;
lyc5 := lyc4+nextup;

%    \end{macrocode}
%
%    The diagram has 5 rows. Start with the 4th as it is the widest row.
%    \begin{macrocode}
%%% Zcol/row
%%% row 4

z14=(0,lyc4);
drawENT(14, el, eh)(btex manufacturer etex);

z34ml=(x14br+hspace1, y14mr);
drawdiamondbox(34, dl, dh)(btex has etex);

z54ml=(x34mr+hspace1, y34mr);
drawENT(54, el, eh)(btex car\_model etex);

%%% row 5

z15bm=(x14bm, lyc5);
drawcirclebox(15, diam)(btex Name etex);

z55bm=(x54bm, lyc5);
drawcirclebox(55, diam)(btex Name etex);

%    \end{macrocode}
%
%    The third row consists of an ordinary diamond box at the right and
% a doubly enclosed diamond on the left. The |drawtwodiamondbox| routine
% is used for the latter. Note that values of |marg| are
% used to make the oustside of the double diamond larger than the single
% diamonds. 
%    \begin{macrocode}
%%% row 3

z53bm=(x54bm, lyc3);
drawdiamondbox(53, dl, dh)(btex of etex);

z13c=(x14bm, y53c);
drawtwodiamondbox(13, dl+marg, dh+marg, 2/5marg)(btex Makes etex);

%    \end{macrocode}
%
%    The second row just consists of a doubly enclosed rectangular box.
% There is no explicit routine for drawing this, so two |drawENT| routines
% are used for drawing smaller and larger superimposed boxes (one with
% an empty text argument).
%    \begin{macrocode}
%%% row 2

z32bm=(x34bm, lyc2);
drawENT(32, el, eh)(btex car etex);
z31c=z32c;
drawENT(31, el+marg, eh+marg)("");

%%% row 1

z21bm=(x32bl, lyc1);
drawcirclebox(21, 5/4diam)(btex \twolines{Serial}{No} etex);

z41bm=(x32br, lyc1);
drawcirclebox(41, diam)(btex Year etex);

%%%%%% lines

%%% Name / manufacturer (15, 14)
drawnormal(15bm, 14tm);

%%% Name / model (55, 54)
drawnormal(55bm, 54tm);

%%% Mnf / has (14, 34)
drawnormal(14mr, 34ml);
label.top(btex 1 etex, 1/2[z14mr,z34ml]);

%%% has/ model (34, 54)
drawnormal(34mr, 54ml);
label.top(btex N etex, 1/2[z34mr,z54ml]);

%%% Mnf / makes (14, 13)
drawnormal(14bm, 13tm);
label.rt(btex 1 etex, 1/2[z14bm,z13tm]);

%%% model / of (54, 53)
drawnormal(54bm, 53tm);
label.rt(btex 1 etex, 1/2[z54bm,z53tm]);

%    \end{macrocode}
%    In the diagrams so far, except trivially in the first, 
% the lines have all been vertical and/or
% horizontal. Now we meet lines in arbitrary directions, and parallel 
% to boot. 
%
%    A pair of parallel lines joins the bottom of the doubly enclosed diamond
% to the left side of the doubly enclosed rectangle. Drawing one of these is
% simple --- just draw a straight line between the bottom middle of the
% diamond to the middle left of the rectangle.
%    \begin{macrocode}
%%% makes / car (13, 31)
drawnormal(13bm, 31ml);
%    \end{macrocode}
%
%    The point |z31A| is |1/2marg| above the point |z31ml|. This is one end
% of the parallel line.
%    \begin{macrocode}
z31A=(x31ml, y31ml+1/2marg);
%    \end{macrocode}
%
%    The \Mpost{} equation |z1-z2 = frac*(z3-z4)| means that 
% (a) the line |z1--z2| is parallel to the line |z3--z4|, and (b)
% the length of the line |z1--z2| is |frac| of the length of |z3--z4|.
% We next specify that the line |z13U--z31A| is parallel to, and the same
% length as, the line |z13bm--z31ml|;
%    \begin{macrocode}
z13U-z31A = z13bm-z31ml;
%    \end{macrocode}
%
%    The final part of the calculation is to determine the point |z13A| so
% that the line |z31A--z13A| is parallel to our first line and starts
% and ends at the outer perimeters of the boxes (and we already
% know what |z31A| is).
%
% \DescribeVariable{whatever}
%    Remember mediation? A point, |z1234| is on the line |z1--z2| if \\
% |z1234=frac1[z1,z2| holds. \\
% Similarly a point |z1234| is on the line |z3--z4| if \\
% |z1234=frac2[z3,z4]| holds.
%
%    These two equations are linear and provided enough variables are known 
% it is easy, even if tedious and error
% prone, to solve
% for all the unknowns using simple mathematics. Fortunately \Mpost{} has an
% idiom for this kind of calculation using the built-in variable 
% called |whatever|. Each time |whatever| is used it is internally given
% a new name which saves a lot of name inventions on the part of the user.
% The following line of code results in \Mpost{} calculating the intersection
% point, which I call |z13A|, between the two lines |z13U,z31A|, which is
% our parallel lines whose points are known, and the line |z13bm--z13mr|
% which is the lower right line of the outer diamond whose points are known.
%    \begin{macrocode}
z13A = whatever[z13U,z31A] = whatever[z13bm,z13mr];
%    \end{macrocode}
%
%    Finally, draw the second parallel line in the desired position and length.
%    \begin{macrocode}
draw z13A--z31A;
label.urt(btex N etex, 1/2[z13A,z31A]);

%    \end{macrocode}
%
%    Another pair of parallel lines connects the doubly bounded rectangle
% and the singly bounded diamond, and we use a similar calculation as above.
%    \begin{macrocode}
%%% of / car (53, 31)
drawnormal(53bm, 31mr);
z31B=(x31mr, y31mr+1/2marg);
z53U - z31B = z53bm - z31mr;
z53B = whatever[z53U,z31B] = whatever[z53bm,z53ml];
draw z53B--z31B;
label.ulft(btex N etex, 1/2[z53B,z31B]);

%    \end{macrocode}
%
% That's the end of the tricky bits for this diagram.
%    \begin{macrocode}
%%% car / serial no (31, 21)
z31C=(x21tm, y31bl);
drawnormal(31C, 21tm);

%%% car / year (31, 41)
z31D=(x41tm, y31br);
drawnormal(31D, 41tm);

%    \end{macrocode}
%
% The end of this diagram
%    \begin{macrocode}
endfig;               % end fig 10

%    \end{macrocode}
%
%
% \subsubsection{Diagram 11: NIAM}
%
%    Like IDEF1X, NIAM~\cite{NIJSSEN89} is a language for relational database
% structures. In Europe it tends to be preferred to IDEF1X.
%
%    Although the layout and icons of the NIAM illustration differ from 
% the prior
% diagrams, no new techniques are used. The most obvious of the differences
% are the use of oval and circular boxes in place of the rectangular boxes,
% and the use of pairs of rectangular boxes in the middle of the relationship
% lines.
%    \begin{macrocode}

beginfig(11)            % example 11  NIAM
%%%drawgrid;

numeric diam; diam := 2onelineh;    % circle diameter

upshift := diam;
nextup := diam+upshift;

numeric hel, vel;        % length of horizontal and vertical box pairs
eh := onelineh;
hel = namespace(btex made by etex)(nextra);
vel = namespace(btex of prod etex)(nextra);

numeric del, deh;        % horizontal & vertical diameters of oval boxes
del := namespace(btex MANUFACTURER etex)(niextra);
deh := 2eh;

numeric marg; marg := 2u;       % margin for doubly enclosed oval boxes
numeric lmarg; lmarg := marg;   % gap for short lines

numeric dashel, dasheh;         % diameters of dashed ellipses
dashel := del+2marg;
dasheh := deh+2marg;

hspace1 := diam;

%%% y coords
lyc1 := 0;
lyc2 := lyc1+nextup;
lyc3 := lyc2+nextup;

%%% Zcol/row

%%% row 3

x13ml=0; y13bm=lyc3;
drawovalbox(13, del, deh)(btex manufacturer etex);
z14=z13c;
drawdashellipse(14, dashel, dasheh);

z23ml=(x14mr+hspace1, y14mr);
drawENT(23, hel, eh)(btex of etex);

z33bl=z23br;
drawENT(33, hel, eh)(btex made by etex);

z44ml=(x33mr+hspace1, y33mr);
drawdashellipse(44, dashel, dasheh);
z43=z44c;
drawovalbox(43, del, deh)(btex car model etex);

z53ml=(x44mr+hspace1, y44mr);
drawdashcircle(53, diam);
label(btex year etex, z53c);

%%% row 2

z22c=(x23bm,lyc2);
drawcirclebox(22, namespace(btex U etex)(2nextra))(btex U etex);

x42tm=x43bm; y42ml=lyc2;
drawdoublerectangle(42, vel, 2eh, 1/2);
label(btex of etex, z42ct);
label(btex is of etex, z42cb);

%%z52c=(x53x,lyc2);
x52tm=x53bm; y52ml=lyc2;
drawdoublerectangle(52, vel, 2eh, 1/2);
label(btex of prod etex, z52ct);
label(btex prod in etex, z52cb);

%%% row 1

z11ml=(x13ml,lyc1);
drawdashellipse(11, del, deh);
label(btex serial no etex, z11c);

z21ml=(x23ml,lyc1);
drawENT(21, hel, eh)(btex of etex);

z31bl=z21br;
drawENT(31, hel, eh)(btex has etex);

z41c=(x43c,lyc1);
drawcirclebox(41, diam)(btex car etex);

%%%%%% lines

%%% manufacturer / of (14, 23)
drawnormal(14mr, 23ml);

%%% made by / car model (33, 44)
drawnormal(33mr, 44ml);
draw (x33tl, y33tl+lmarg)--(x33tr, y33tl+lmarg);
draw (x33mr, y33mr+lmarg)--(x33mr+eh, y33mr+lmarg);

%%% serial no / of (11, 21)
drawnormal(11mr, 21ml);

%%% of / of (23, 22, 21)
drawnormal(23bm, 22tm); drawnormal(22bm, 21tm);
label.rt(btex id etex, z22mr);

%%% has / car (31, 41)
drawnormal(31mr, 41ml);
draw (x31tl, y31tl+lmarg)--(x31tr, y31tl+lmarg);
draw (x31mr, y31mr+lmarg)--(x33mr+eh, y31mr+lmarg);

%%% model / of (44, 42)
drawnormal(43bm, 42tm);

%%% is of / car (42, 41)
drawnormal(42bm, 41tm);
draw (x42tfr+lmarg, y42tfr)--(x42tfr+lmarg, y42br);
draw (x42bm+lmarg, y42bm)--(x42bm+lmarg, y42bm-eh);

%%% year / of prod (53, 52)
drawnormal(53bm, 52tm);

%%% prod in / car (52, 41)
VH(52bm,41mr);
drawnormalthree(52bm, 52bm.vh, 41mr);
draw (x52tfr+lmarg, y52tfr)--(x52tfr+lmarg, y52br);
draw (x52bm+lmarg, y52bm)--(x52bm+lmarg, y52bm-eh);

%    \end{macrocode}
%
% The end of this diagram
%    \begin{macrocode}
endfig;               % end fig 11

%    \end{macrocode}
%
%    Note that the centers of the boxes on the bottom row are all at |y=0|,
% and hence the bottom halves have negative y values. This does not matter
% as \Mpost{} determines the actual space required for a diagram and does
% not base it on the origin of the coordinate system.
%
%
%    The end of the \Mpost{} examples file.
%    \begin{macrocode}
end

%    \end{macrocode}
%     The end of the example.
%    \begin{macrocode}
%</eg>
%    \end{macrocode}
%
% \subsection{Comments}
%
%    Everyone is likely to have a different style of diagramming. You have
% seen how I do it but that might not be what suits you. Nevertheless,
% the following comments may be of assistance.
%   
%    In my own work I tend to draw a lot of diagrams, using different 
% \file{.mp} files, that have similar sets of `commonly used variables 
% \& values'. Rather than repeating the list in each file, I create a
% \Mpost{} file, called say \file{mycommons.mp}, that includes these 
% and then |input mycommons| after the |input expressg| near the start
% of each diagram file.
%
%    I find it a help to sketch out the diagrams using pencil and paper
% before coding them up. I have to admit, though, that the final results
% often look very different from my initial ideas of the layout.
%
%    You might have noticed that I start the coding at different places
% in the diagrams. Basically I try and plan on getting the boxes aligned
% roughly in rows and/or columns. I then typically start with the longest
% column, or more often with the widest row, and then fill in the rest 
% from there.
%
% \subsection{Running the \Mpost{} example file} \label{sec:run}
%
%    The \file{expeg.mp} file has to be processed by \Mpost{} to obtain
% \EPS{} (\file{eps}) files for viewing or printing. 
% Depending on your installation the command to run \Mpost{} may be
% either: \\
% |mpost expeg| or \\
% |mp expeg| \\
% or perhaps something similar. This will produce eleven files, \file{expeg.1}
% to \file{expeg.11}, each of which is an \file{eps} file for the corresponding
% |beginfig(N)| in \file{expeg.mp}. \Mpost{} defaults to using \TeX{} for
% processing labels which outputs them using Computer Modern
% fonts. Unfortunately \PS{} applications do not understand these so it
% is necessary to get the fonts inserted. This is most simply done by 
% \LaTeX ing a document that includes the \Mpost{} output. A suitable
% file is provided below and is configured to be processed by either
% \LaTeX{} or \pdflatex. Run \LaTeX{} and then dvips (or what you normally
% use to generate printable output) and you will get all eleven diagrams.
%
%
%    \begin{macrocode}
%<*egt>
%    \end{macrocode}
%
%    \begin{macrocode}
%%% expeg.tex    display expressg.dtx MetaPost examples

\documentclass[11pt]{article}
\newif\ifpdf
\ifx\pdfoutput\undefined
  \pdffalse
\else
  \pdftrue
\fi

\ifpdf
  \pdfoutput=1
  \usepackage[pdftex,final]{graphicx}
  \DeclareGraphicsRule{*}{mps}{*}{}
\else
  \usepackage[final]{graphicx}
\fi

%%%% page sizes for ISO document on A4 paper
\setlength{\headheight}{11pt}
\setlength{\headsep}{10mm}
\setlength{\topskip}{11pt}
\setlength{\footskip}{11mm}
\setlength{\textwidth}{160mm}
\setlength{\textheight}{221.5mm}
\setlength{\columnsep}{10mm}
\setlength{\topmargin}{0mm}
\setlength{\oddsidemargin}{0mm}
\setlength{\evensidemargin}{0mm}
\setlength{\marginparwidth}{0pt}
\setlength{\marginparsep}{0pt}
\setlength{\marginparpush}{0pt}
\setlength{\footnotesep}{12pt}
  %%%% for US letterpaper need to change some margins
\setlength{\topmargin}{-9.4mm}
\setlength{\oddsidemargin}{1.55mm}
\setlength{\evensidemargin}{1.55mm}

\begin{document}

\begin{figure}
\centering
  \includegraphics{expeg.1}
\caption{Some boxes and line styles}
\end{figure}

\begin{figure}
\centering
  \includegraphics{expeg.2}
\caption{Example schema level diagram}
\end{figure}

\begin{figure}
\centering
  \includegraphics{expeg.3}
\caption{Example diagram of a tree structure}
\end{figure}

\begin{figure}
\centering
  \includegraphics{expeg.4}
\caption{Supertypes and subtypes}
\end{figure}

\begin{figure}
\centering
  \includegraphics{expeg.5}
\caption{A portion of a large model}
\end{figure}

\begin{figure}
\centering
  \includegraphics{expeg.6}
\caption{Car model using EXPRESS-G}
\end{figure}

\begin{figure}
\centering
  \includegraphics{expeg.7}
\caption{Car model using Shlaer-Mellor}
\end{figure}

\begin{figure}
\centering
  \includegraphics{expeg.8}
\caption{Car model using IDEF1X}
\end{figure}

\begin{figure}
\centering
  \includegraphics{expeg.9}
\caption{Car model using OMT}
\end{figure}

\begin{figure}
\centering
  \includegraphics{expeg.10}
\caption{Car model using E-R}
\end{figure}

\begin{figure}
\centering
  \includegraphics{expeg.11}
\caption{Car model using NIAM}
\end{figure}

\end{document}

%    \end{macrocode}
%
% The end of the \LaTeX{} file.
%    \begin{macrocode}
%</egt>
%    \end{macrocode}
%
% \subsubsection{Using \pdflatex}
%
%    \pdflatex{} generates a \file{.pdf} file directly from \LaTeX{} source
% instead of a \file{.dvi} file. Unfortunately \pdflatex{} does not understand
% \EPS{} in general, but it \emph{does} understand the restricted form
% of \EPS{} generated by \Mpost. By default \pdflatex{} will recognise
% files with an \file{.mps} extension as coming from \Mpost, but \Mpost{}
% generates files with a numeric extension. 
% If you like to use both \Mpost{} and \pdflatex, then it can
% get tedious changing all the numeric extensions to \file{.mps}. The
% following two scripts can help with this. The first is a shell 
% script\footnote{You may well have to modify this to run on your
% operating system.} which calls a Perl script. 
%
% The shell script is called \file{n2mps.sh}. To get suitable versions
% of the example \Mpost{} output files for use with \pdflatex, just do: \\
% |n2mps.sh expeg| \\
% after having run \Mpost{} on \file{expeg.mp}.
%
%    \begin{macrocode}
%<*shell>
#! /bin/sh

#####################################################################
# Shell script n2mps.sh
# Call as: n2mps.sh basename
# List each file basename.* in the directory and run the Perl script
# to copy each basename.N to basenameN.mps, where N is an integer
#
# Copyright 2000, Mauro S. Costa and Peter R. Wilson
###