path: root/macros/latex/contrib/fmp/fmp.dtx

% \iffalse meta-comment
%
% Copyright 2001 Marco Kuhlmann
%
% This program is distributed under the conditions of the
% LaTeX Project Public License, which can be found in
% http://www.latex-project.org/lppl.txt
%
% This program consists of the files fmp.ins and fmp.dtx
%
% \fi
%
%
% \CheckSum{260}
%
% \changes{v1.0a}{2001/04/03}{%
%   Initial release.}
%
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%
% \title{Functional {\MP} for {\LaTeX}\thanks{%
%     This file has version number \fileversion.}}
% \author{Marco Kuhlmann\thanks{%
%     E-Mail: \texttt{marco.kuhlmann@gmx.net}}}
% \date{\filedate}
% \maketitle
%
%
% \begin{abstract}
%   Functional {\MP} (\FMP) is a powerful frontend to the {\MP}
%   language. This package adds basic {\FMP} support to {\LaTeX},
%   enabling users to keep {\FMP} source code within their
%   documents and, by a two-run mechanism, including
%   automatically generated {\FMP} figures.
% \end{abstract}
%
%
% \section{Introduction}
%
% Functional {\MP} by Joachim Korittky (\cite{Diplomarbeit}) adds
% a high-level interface to the {\MP} language (\cite{MetaPost1},
% \cite{MetaPost2}), enabling the user to program their graphics
% using the Haskell language. Impressive examples of Functional
% {\MP} can be found in Korittky's diploma thesis; some of them
% will be given below. The system and the documentation can be
% downloaded from
% \begin{quote}
%   \texttt{http://www.informatik.uni-bonn.de/\~{}ralf/software.html}
% \end{quote}
%
% Using Functional {\MP} as my standard graphics developing tool,
% I felt a need to write a {\LaTeX} package which smoothly
% integrates {\FMP} into daily work, similar to the |emp| package
% by Thorsten Ohl (\cite{EMP}); this is how |fmp| came to being.
% The earliest version supported only the possibility to
% automatically produce shell-scripts for graphics generation.
% Since then, I have added the possibility to encapsulate {\FMP}
% code -- though I still ask myself if this way of maintaining
% code is as natural for {\FMP} as it is for pure {\MP} in |emp|.
%
% In case you have any questions or comments on this package,
% feel free to send me an email. May |fmp| help {\FMP} to spread
% around the world. \texttt{:-)}
%
%
% \subsection{Examples of Functional {\MP}}
%
% Before I start to present the |fmp| package, let me first give
% you two mouth-watering examples of {\FMP} (the Haskell code for
% them can be found at the end of this document):
% figure~\ref{figure:example1} gives a binominal tree of
% rank~$5$, figure~\ref{figure:example2} shows a simple Venn
% diagram. Among other things, these examples exhibit two
% features in which {\FMP} is superior to many other graphics
% drawing packages around:
% \begin{itemize}
% \item By embedding {\MP} into the Haskell programming language,
%   {\FMP} gives the user (and especially users who have previous
%   experience in functional programming) a great tool to program
%   graphics on a very high-level level of abstraction. This not
%   only helps you to focus on the logical structure rather than
%   on layout questions, but also is especially important if you
%   want to scale and re-use old material.
% \item {\FMP} can be easily extended. For example, for
%   figure~\ref{figure:example1}, the core language has been
%   augmented by tree drawing features, using much better
%   algorithms than those of any other tree drawing package
%   around. This is especially good news for computer scientists,
%   who need trees very often, but did not yet have a package to
%   draw them on such a level of abstraction.
% \end{itemize}
%
% \begin{figure}
%   \begin{center}
%     \fmpfigure{example1}
%   \end{center}
%   \caption{A binominal tree of rank~$5$}
%   \label{figure:example1}
% \end{figure}
%
% \begin{figure}
%   \begin{center}
%     \fmpfigure{example2}
%   \end{center}
%   \caption{A Venn diagram (cf.\ figure~22 in \cite{MetaPost2})}
%   \label{figure:example2}
% \end{figure}
%
% To be able to use {\FMP}, you need a Haskell interpreter, such
% as |hugs|, and the {\MP} program, which should be part of any
% somewhat complete distribution of {\LaTeX}. Having produced a
% Haskell source, you feed it into |hugs| and issue the
% |generate| command provided by {\FMP}. This will translate your
% code into low-level {\MP} commands, and finally produce a
% ready-to use PostScript file.
%
% \subsection{How this package works}
%
% Calling |hugs| and typing in the generation commands is a
% tedious job if you keep more than but a few illustrations
% around. This package offers the |\fmpfigure| command, which
% generates a shell script (at present, this only works for
% $*$n$*$x), which you then can execute to have all the graphics
% files generated at once. At the next run of {\LaTeX}, these
% graphic files will appear at their proper positions.  Besides,
% |fmp| enables you to store Haskell code within a {\LaTeX} file,
% in case you want to have all the code for one document at one
% place.
%
%
% \section{Usage}
%
% \subsection{Including graphics}
%
% \changes{v1.0b}{2001/10/22}{%
%   Documentation: Improvements as suggested by Peter Bartke.}
% Using \verb|fmp| to include graphics from some {\FMP} source is
% straightforward. Let us assume that you keep two {\FMP} figures
% (Haskell values) \verb|example1| and \verb|example2| in a file
% called \verb|fmp-doc.hs|. A minimal document using the package to
% include these two figures would then look like this:
%
% \medskip\noindent\bgroup\small
% \verb|\documentclass{article}|\\
% \verb|\usepackage{fmp}|\\
% \verb|\fmpsourcefilename{fmp-doc}|\\
% \verb|\begin{document}|\\
% \verb|\fmpfigure{example1}|\\
% \verb|\fmpfigure{example2}|\\
% \verb|\end{document}|\\
% \verb|\end{verbatim}|
% \medskip\par\egroup
%
% \DescribeMacro{\fmpfigure} You include a figure into your
% {\LaTeX} document by using the |\fmpfigure| macro. It takes, as
% its mandatory argument, the string identifying the figure in
% the Haskell source, and creates a shell script containing all
% the |hugs| calls needed for the actual generation. After the
% shell script has been written, you can execute it and run
% {\LaTeX} again; if everything went right, the graphics file
% will appear at the place where you issued the |\fmpfigure|
% command.
%
% \changes{v1.1a}{2001/11/19}{%
%   Documentation: Optional arguments to \cs{fmpfigure} are now
%   passed to the \texttt{graphicx} package.}
% Any optional arguments to |\fmpfigure| will be passed to the
% |graphicx| package and interpreted as if they appeared together
% with a |\includegraphics| command. This allows you to change
% the visual appearance of the included figure (e.\,g., the size
% to which the figure shall be scaled). Refer to \cite{graphicx}
% for more information about possible paramters.
%
% \subsection{Including code}
%
% \DescribeEnv{fmp} You can also store your {\FMP} code in the same
% file than your {\LaTeX} source, included within the |fmp|
% environment. During compilation, the contents of this environment
% are written to an external file (see below).
%
% \subsection{Changing file names}
%
% \DescribeMacro{\fmpsourcefilename}
% \DescribeMacro{\fmpscriptfilename}
% \DescribeMacro{\fmpfigurebasename}
% You can control the names of three different files:
% \begin{itemize}
% \item the Haskell source (|\fmpsourcefilename|, defaults to
%   \meta{jobname}|.hs|),
% \item the shell script (|\fmpscriptfilename|, defaults to
%   |fmpgenerate.sh|) and
% \item the graphics file base name (|\fmpfigurebasename|,
%   defaults to |fmpfigure|), which is the base file name of the
%   graphics files that will be generated by |hugs|. (An index
%   number specifying their order in the document will be
%   appended to this name.)
% \end{itemize}
% You can modify all three file names by calling the respective
% macros, each of which takes the new name as its argument.
%
% \subsection{Preamble and postamble}
%
% \DescribeMacro{\fmpsourcepreamble}
% \DescribeMacro{\fmpaddtosourcepreamble}
% \DescribeMacro{\fmpscriptpreamble}
% \DescribeMacro{\fmpaddtoscriptpreamble}
% \DescribeMacro{\fmpsourcepostamble}
% \DescribeMacro{\fmpaddtosourcepostamble}
% \DescribeMacro{\fmpscriptpostamble}
% \DescribeMacro{\fmpaddtoscriptpostamble}
% Before something is written to the source file or the shell
% script file, the package will output a \emph{preamble} to that
% file. The source code preamble could contain everything from
% comments to Haskell module identifications and basic imports,
% while the shell script preamble should probably contain the
% line that calls |hugs| and tells it to input the rest of the
% file as comment. Have a sample run to see the default contents
% of the preamble. If you wish to change the text: you can set a
% new preamble by the |\fmpsourcepreamble| command, and you can
% append a new line to the current preamble calling
% |\fmpaddtosourcepreamble|. (Similar commands are available for
% the shell script preamble.) There is also a postamble, which is
% written as the very last thing to the source code or shell
% script.
%
% \MP\ uses the environment variable \verb|$TEX| to determine which
% \TeX\ it has to call when generating labels etc. On many systems,
% this variable defaults to \verb|tex|, which is certainly not what
% you want in conjunction with \verb|fmp|. One common usage for the
% preamble therefore is to include a line like
% \verb|export TEX=latex| (or something similar, depending on your
% shell) into the generation script.
%
% \subsection{Graphics file formats}
%
% The |graphicx| package is used to handle the inclusion of
% generated {\FMP} figures. If |fmp| is called from within
% |pdflatex|, |graphicx| is loaded with the |pdftex| driver
% option.  In this case, the fall-back behaviour when
% encountering an |\fmpfigure| command is to read the
% corresponding graphics file as |mps| ({\MP} output); it will
% then internally be converted to \textsc{pdf} by |graphicx|.
% When called from within normal |latex|, graphics files are
% handled as |eps| (encapsulated PostScript).  You probably need
% to load a specific PostScript driver for |graphicx| in this
% case -- do so by supplying |fmp| with the same package option
% that you would use for |graphicx| (see the |graphicx| user
% manual for further information on that).
%
%
% \subsection*{Acknowledgements}
%
% The help of Ralf Hinze and the suggestions of Peter Bartke and
% Ferenc Wagner are gratefully acknowledged.
%
%
% \section*{Source code for the examples}
%
% \verbatiminput{fmp-doc.hs}
%
%
% \StopEventually{%
%   \begin{thebibliography}{XXX99}
%   \bibitem[Hob89]{MetaPost1}
%     \textsc{John D.\ Hobby:}
%     \emph{A {\MF}-like System with PostScript Output.}
%     TUGboat vol.~10, no.~2, pp.\ 505--512, 1989
%   \bibitem[Hob92]{MetaPost2}
%     \textsc{John D.\ Hobby:}
%     \emph{A User's manual for {\MP}.}
%     Computing Science Technical Report no.~162, AT\&T Bell
%     Laboratories, Murray Hill, New Jersey, 1992
%   \bibitem[Kor98]{Diplomarbeit}
%     \textsc{Joachim Korittky:}
%     \emph{functional {\MP}. Eine Beschreibungsspra\-che
%       f\"ur Grafiken.}
%     Diplomarbeit an der Rheinischen
%     Friedrich-Wilhelms-Universit\"at Bonn, 1998
%   \bibitem[Ohl97]{EMP}
%     \textsc{Thorsten Ohl:}
%     \emph{EMP: Encapsulated {\MP} for {\LaTeX}.}
%     Technische Hochschule Darmstadt, 1998
%   \bibitem[Car99]{graphicx}
%     \changes{v1.1a}{2001/11/19}{%
%       Added to bibliography: Reference to \texttt{graphicx}
%       package user documentation.}
%     \textsc{David Carlisle:}
%     \emph{Packages in the `graphics' bundle.}
%     User documentation, 1999
%   \end{thebibliography}}
%
%
% \section{The Documentation Driver File}
%
%    \begin{macrocode}
%<*driver>
\documentclass{ltxdoc}
\usepackage{fmp}
\usepackage{mflogo}
\OnlyDescription
\GetFileInfo{fmp.sty}
\newcommand*{\FMP}{\textsc{fmp}}
\fmpsourcefilename{fmp-doc}
\setcounter{topnumber}{1}
\makeatletter
\let\verbatim@oldfont=\verbatim@font
\def\verbatim@font{\small\verbatim@oldfont}
\makeatother
\tolerance=2000
\emergencystretch=20pt
\RecordChanges
\begin{document}
\DocInput{fmp.dtx}
\PrintChanges
\end{document}
%</driver>
%    \end{macrocode}
%
%
% \section{The Implementation}
%
% \subsection{Setup}
%
%    \begin{macrocode}
%<*package>
%    \end{macrocode}
%
% We start with the usual identification procedure. All the
% options that |fmp| cannot cater for itself are passed to the
% |graphicx| package, as they probably are requests for special
% PostScript drivers (see above).
%    \begin{macrocode}
\NeedsTeXFormat{LaTeX2e}[1995/05/16]
\ProvidesPackage{fmp}
[2001/11/19 v1.1a Support for Functional MetaPost]
\DeclareOption*{\PassOptionsToPackage{\CurrentOption}{graphicx}}
\ProcessOptions
%    \end{macrocode}
%
% Depending on whether or not |fmp| is called from within
% |pdflatex|, the |graphicx| package has to be loaded with or
% without the |pdftex| option. A fall-back rule is declared for
% |\includegraphics| commands.
%    \begin{macrocode}
\@ifundefined{pdfoutput}{%
  \RequirePackage{graphicx}[1999/02/16]%
  \DeclareGraphicsRule{*}{eps}{*}{}}{%
  \RequirePackage[pdftex]{graphicx}[1994/12/15]%
  \DeclareGraphicsRule{*}{mps}{*}{}}
%    \end{macrocode}
%
% The |verbatim| package is used for writing the contents of the
% |fmp| environment (see below) into a file.
%    \begin{macrocode}
\RequirePackage{verbatim}
%    \end{macrocode}
%
% We set up new streams |\fmp@sourceout| and |\fmp@scriptout| for
% the Haskell source and the shell script to be written, as well
% as conditionals to remember whether or not we have already
% opened these streams.
%    \begin{macrocode}
\newwrite\fmp@sourceout
\newwrite\fmp@scriptout
\newif\iffmp@sourceio
\fmp@sourceiofalse
\newif\iffmp@scriptio
\fmp@scriptiofalse
%    \end{macrocode}
%
% Finally, we need a counter for the figures that we want to
% generate.
%    \begin{macrocode}
\newcounter{fmpfigure}
%    \end{macrocode}
%
% \subsection{Writing the source code}
%
% \begin{environment}{fmp}
% The |fmp| environment writes its contents into the
% |\fmp@sourceout| stream. This is done in an almost
% ``classical'' way, employing the |verbatim| package.
%    \begin{macrocode}
\newenvironment*{fmp}{}{}
\def\fmp{%
  \begingroup
    \@bsphack
    \let\do\@makeother\dospecials
    \catcode`\^^M\active
    \def\verbatim@processline{\fmp@sourcewrite{\the\verbatim@line}}%
    \verbatim@start}
\def\endfmp{%
    \@esphack
  \endgroup}
%    \end{macrocode}
% \end{environment}
%
% \begin{macro}{\fmp@sourcewrite}
% This is the wrapper used for writing to the source file.  Every
% time it is called, it checks whether or not the
% |\fmp@sourceout| stream has already been opened. If not, it
% calls |\fmp@sourceopen| to do so. (I do so because I want to
% avoid situations like in the |emp| package, where the outstream
% is opened and a file is created, even when at the end nothing
% is written to it. Is this too expensive?)
%    \begin{macrocode}
\def\fmp@sourcewrite#1{%
  \iffmp@sourceio \else \global\fmp@sourceiotrue\fmp@sourceopen \fi%
  \immediate\write\fmp@sourceout{#1}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\fmp@sourceopen}
% Opens the output stream for the source file and writes the
% preamble.
%    \begin{macrocode}
\def\fmp@sourceopen{%
  \immediate\openout\fmp@sourceout\fmp@sourcefilename%
  \edef\@tempa{\the\fmp@sourcepreamble}%
  \immediate\write\fmp@sourceout{\@tempa}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\fmpsourcefilename}
% \begin{macro}{\fmp@sourcefilename}
% Set the filename of the source file.
%    \begin{macrocode}
\newcommand*{\fmpsourcefilename}[1]{%
  \gdef\fmp@sourcefilename{#1}}
\@onlypreamble{\fmpsourcefilename}
\def\fmp@sourcefilename{\jobname.hs}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\fmp@sourcepreamble}
% \begin{macro}{\fmpsourcepreamble}
% \begin{macro}{\fmpaddtosourcepreamble}
% Sets up the preamble for the source file, as well as macros to
% reset them or append new lines to it.
%    \begin{macrocode}
\newtoks\fmp@sourcepreamble
\newcommand*{\fmpsourcepreamble}[1]{%
  \global\fmp@sourcepreamble={#1}}
\@onlypreamble{\fmpsourcepreamble}
\newcommand*{\fmpaddtosourcepreamble}[1]{%
  \fmp@sourcepreamble=\expandafter{\the\fmp@sourcepreamble#1}}
\@onlypreamble{\fmpaddtosourcepreamble}
\fmp@sourcepreamble={-- This is file `\fmp@sourcefilename',
  created automatically. Do not edit!^^J}
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\fmp@sourceclose}
% This is added to \LaTeX's |\@enddocumenthook|. It writes the
% postamble to the source file and closes the output stream.
%    \begin{macrocode}
\def\fmp@sourceclose{%
  \iffmp@sourceio
    \edef\@tempa{\the\fmp@sourcepostamble}%
    \fmp@sourcewrite{\@tempa}%
    \immediate\closeout\fmp@sourceout
  \fi}
\AtEndDocument{\fmp@sourceclose}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\fmp@sourcepostamble}
% \begin{macro}{\fmpsourcepostamble}
% \begin{macro}{\fmpaddtosourcepostamble}
% Sets up the postamble for the source file, as well as macros to
% reset and update it.
%    \begin{macrocode}
\newtoks\fmp@sourcepostamble
\newcommand*{\fmpsourcepostamble}[1]{%
  \global\fmp@sourcepostamble={#1}}
\@onlypreamble{\fmpsourcepostamble}
\newcommand*{\fmpaddtosourcepostamble}[1]{%
  \fmp@sourcepostamble=\expandafter{\the\fmp@sourcepostamble#1}}
\@onlypreamble{\fmpaddtosourcepostamble}
\fmp@sourcepostamble={^^J-- End of file `\fmp@sourcefilename'}
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \subsection{Writing the shell script}
%
% \begin{macro}{\fmpfigure}
% \changes{v1.1a}{2001/11/19}{%
%   Pass through optional arguments to the \texttt{graphicx}
%   package, as suggested by Ferenc Wagner.}
% Writes a new line to the |\fmp@scriptout| stream, which is
% connected to the generation shell script file, telling |hugs|
% to generate a graphics file with the name specified. Any
% optional argument is passed to the |graphicx| package.
%    \begin{macrocode}
\newcommand*{\fmpfigure}[2][]{%
  \fmp@scriptwrite{%
    generate "\fmp@figurebasename" \thefmpfigure\space #2}%
  \fmp@includegraphics{#1}{\fmp@figurebasename}{\thefmpfigure}%
  \refstepcounter{fmpfigure}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\fmp@scriptwrite}
% Wrapper for writing to the shell script file.
%    \begin{macrocode}
\def\fmp@scriptwrite#1{%
  \iffmp@scriptio \else \global\fmp@scriptiotrue\fmp@scriptopen \fi%
  \immediate\write\fmp@scriptout{#1}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\fmp@scriptopen}
% Opens the output stream for the shell script file and writes
% the preamble.
%    \begin{macrocode}
\def\fmp@scriptopen{%
  \immediate\openout\fmp@scriptout\fmp@scriptfilename%
  \edef\@tempa{\the\fmp@scriptpreamble}%
  \immediate\write\fmp@scriptout{\@tempa}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\fmp@scriptpreamble}
% \begin{macro}{\fmpscriptpreamble}
% \begin{macro}{\fmpaddtoscriptpreamble}
% Set up the preamble for the shell script file as well as macros
% to reset and append information to it.
%    \begin{macrocode}
\newtoks\fmp@scriptpreamble
\newcommand*{\fmpscriptpreamble}[1]{%
  \global\fmp@scriptpreamble={#1}}
\@onlypreamble{\fmpscriptpreamble}
\newcommand*{\fmpaddtoscriptpreamble}[1]{%
  \fmp@scriptpreamble=\expandafter{\the\fmp@scriptpreamble#1}}
\@onlypreamble{\fmpaddtoscriptpreamble}
\fmp@scriptpreamble={hugs \fmp@sourcefilename\space <<!}
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\fmpscriptfilename}
% \begin{macro}{\fmp@scriptfilename}
% This sets the filename of the shell script which can be used
% for generation.
%    \begin{macrocode}
\newcommand*{\fmpscriptfilename}[1]{%
  \gdef\fmp@scriptfilename{#1}}
\@onlypreamble{\fmpscriptfilename}
\def\fmp@scriptfilename{fmpgenerate.sh}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\fmpfigurebasename}
% \begin{macro}{\fmp@figurebasename}
% This sets the base name for the graphics files that will be
% created by |hugs|. 
%    \begin{macrocode}
\newcommand*{\fmpfigurebasename}[1]{%
  \gdef\fmp@figurebasename{#1}}
\@onlypreamble{\fmpfigurebasename}
\def\fmp@figurebasename{fmpfigure}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\fmp@includegraphics}
% \changes{v1.1a}{2001/11/19}{%
%   Pass through optional arguments to the \texttt{graphicx}
%   package, as suggested by Ferenc Wagner.}
% This is a wrapper for the |\includegraphics| command. If the
% |graphicx| package has been loaded correctly, it should be able
% to import the graphics file, either directly in |eps| format,
% or after a transformation to |pdf| by the Con{\TeX}t macros
% included in the |pdftex| driver.
%    \begin{macrocode}
\def\fmp@includegraphics#1#2#3{%
  \leavevmode
  \IfFileExists{#2.#3}%
  {\includegraphics[#1]{#2.#3}}%
  {\typeout{fmp: Could not find file #2.#3}}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\fmp@scriptclose}
% Write the shell script postamble and close the output stream.
%    \begin{macrocode}
\def\fmp@scriptclose{%
  \iffmp@scriptio
    \edef\@tempa{\the\fmp@scriptpostamble}%
    \fmp@scriptwrite{\@tempa}%
    \immediate\closeout\fmp@scriptout
  \fi}
\AtEndDocument{\fmp@scriptclose}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\fmp@scriptpostamble}
% \begin{macro}{\fmpscriptpostamble}
% \begin{macro}{\fmpaddtoscriptpostamble}
% Set up the postamble for the shell script file as well as macros
% to reset and append information to it.
%    \begin{macrocode}
\newtoks\fmp@scriptpostamble
\newcommand*{\fmpscriptpostamble}[1]{%
  \global\fmp@scriptpostamble={#1}}
\@onlypreamble{\fmpscriptpostamble}
\newcommand*{\fmpaddtoscriptpostamble}[1]{%
  \fmp@scriptpostamble=\expandafter{\the\fmp@scriptpostamble#1}}
\@onlypreamble{\fmpaddtoscriptpostamble}
\fmp@scriptpostamble={:quit}
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
%    \begin{macrocode}
%</package>
%    \end{macrocode}
%
%
% \Finale
%
%
%<*examples>
module FMPDoc where
import FMP
import FMPTree

example1           = binom 5
    where
    ce             = circle empty
    binom 0        = node ce []
    binom n        = node ce [edge (binom i)
                              | i <- [(n-1),(n-2)..0]]
                     #setAlign AlignRight

example2           = box (math "U" |||
                          ooalign [toPicture [cArea a 0.7,
                                              cArea b 0.7,
                                              cArea ab 0.4],
                                   bOverA])
    where
    cArea a c      = toArea a #setColor c
    bOverA         = column [math "B" #setBGColor white,
                             vspace 50,
                             math "A" #setBGColor white]
    a              = transformPath (scaled 30) fullcircle
    b              = transformPath (scaled 30 & shifted (0,-30))
                     fullcircle
    ab             = buildCycle a b
%</examples>