% program.sty, Version 3.3.4
% Version History:
% 3.3.1: Fix name clash with new AmsTeX (\@prime)
% 3.3.2: Minor spacing tweaks. Added \sfvariables for a different style.
% 3.3.3: Added \| to the definition of \dospecials, so that | will
%        still work in a verbatim environment.
% 3.3.4: Added \ifVBarOutsideProgram switch -- The command \normalbaroutside
%        makes | to act normally outside the program environment
%
% A LaTeX2e style file for typesetting algorithms.
% Copyright 1991 Martin Ward
% Email: Martin.Ward@durham.ac.uk
%    or: Martin.Ward%DURHAM.AC.UK@CUNYVM.CUNY.EDU
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software
% Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
%
%
% This is the "program" style option which sets up the
% program and programbox environments,
% keywords for programs and a few goodies.
% NOTE: Within the program environment:
% (1) Newlines are significant.
% (2) Each line is in math mode, so for example spaces in the input
%     file are not significant.
% (3) \\ within a line causes a linebreak in the output.
%
% We also define a "programbox" environment which typesets a program in a box.
% Useful for keeping a pice of code on one page or for typesetting small 
% programs in running text.
% We also redefine \( and \) as \begin{programbox} and \end{programbox}.
% The \tab and \untab commands are defined to have no effect while outside 
% a program environment, hence a single-line program can be typeset in 
% maths mode without the overhead associated with programbox.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Section (1). The Keywords.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% Set up ";" to add a thick maths space after it when active in math mode:
\let\@semicolon=;
\catcode`\;=12\relax
\mathcode`\;="8000 % Makes ; active in math mode
{\catcode`\;=\active \gdef;{\ifmmode\semicolon\;\else\@semicolon\fi}}
\mathchardef\semicolon="603B

% Set up ` so that ``...'' typesets the string in tt (in math mode):
\mathcode`\`="8000 % Makes ` active in math mode only.
{%\catcode`\'=\active 
 \catcode`\`=\active
 \gdef`{\startstring@}
}
\newif\ifMathsModeStrings \MathsModeStringsfalse
\def\startstring@`#1''{\ifMathsModeStrings
			 \mbox{``}#1\mbox{''}\else
			 \mbox{``{\tt #1}''}\fi}

% Set up a larger array of tabs since programs set lots of tabs.
% This section can be extended if more tabs are needed:
\newdimen\@gtempa 
\chardef\@firsttab=\the\allocationnumber
\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa
\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa
\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa
\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa
\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa
\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa
\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa
\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa
\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa
\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa
\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa
\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa\newdimen\@gtempa
\newdimen\@gtempa 
\chardef\@maxtab=\the\allocationnumber

% NB: can't use \pushtabns and \poptabs to reduce the need for tabs
% since \@curtab, \@curtabmar and \@nxttabmar are global variables
% which would also need to be saved and restored.

% The program environment.
% This is based on the tabbing environment with each line put in math mode,
% \obeylines in force and ";" as an active character.
\def\@programcr{$\@stopline\@startline\ignorespaces$}
\def\programnewpage{$\@stopline\newpage\@startline\ignorespaces$}

% Line numbers on programs:
\newcounter{programline}
\newif\ifNumberPrograms
% Default is no line numbers:
\NumberProgramsfalse

% Program text size hook:
\let\programsize=\relax

% Set switch to false if you want | to act normally 
% outside the program environment:
\newif\ifVBarOutsideProgram \VBarOutsideProgramtrue
\def\normalbaroutside{\catcode`\|=12 \VBarOutsideProgramfalse}

\def\program{%
  \ifVBarOutsideProgram\else\catcode`\|=\active\fi %% added line
  \if@minipage\else\leavevmode\fi
  \ifNumberPrograms\setcounter{programline}{0}\fi
  \normalshape
  \obeycr %% added line
  % activate tabbing commands:
  \@tabcommandson %% added line
  \global\let\DO=\@oldDO %% added line
  \lineskip \z@\let\>\@rtab\let\<\@ltab\let\=\@settab
  \let\+\@tabplus\let\-\@tabminus\let\`\@tabrj\let\'\@tablab
  \let\\=\@programcr %% changed from \let\\=\tabcr
  \global\@hightab\@firsttab
  \global\@nxttabmar\@firsttab
  \dimen\@firsttab\@totalleftmargin
  \global\@tabpush0 \global\@rjfieldfalse
  \trivlist \item[]%\if@minipage\else\vskip\parskip\fi
  \programsize
  \setbox\@tabfbox\hbox{\rlap{\indent\hskip\@totalleftmargin
    \the\everypar}}\def\@itemfudge{\box\@tabfbox}\@startline\ignorespaces
  $\@gobblecr %% added line
}

\def\endprogram{$\@stopline\ifnum\@tabpush > 0 \@badpoptabs \fi\endtrivlist%
  \restorecr \@tabcommandsoff %% added line
  \ifVBarOutsideProgram\else\catcode`\|=12\fi %% added line
\@gobblecr
}

\def\smallprogram{%
  \let\programsize=\small\program
}

\def\endsmallprogram{%
  \let\programsize=\relax\endprogram
}

% - version which puts the whole program in a box.
\newif\if@programbox \@programboxfalse
\newenvironment{programbox}%
    {\begin{minipage}[t]{\textwidth}%
     \@programboxtrue
     \begin{program}}%
    {\end{program}%
     \@programboxfalse
     \end{minipage}%
}

\def\({\begin{programbox}}
\def\){\end{programbox}}

% A new version of @stopline which ignores blank lines (lines with 
% width 0pt). To print a blank line, put "\ " on it!
%
\def\@stopline{%
  \unskip\@stopfield
  \if@rjfield
    \global\@rjfieldfalse
    \@tempdima\@totalleftmargin \advance\@tempdima\linewidth
    \hbox to\@tempdima{\@itemfudge\@printlineno\hskip\dimen\@curtabmar
		       \box\@curline\hfil\box\@curfield}%
  \else
    \@addfield
    \ifdim\wd\@curline=0pt\else
      \hbox{\@itemfudge\@printlineno\hskip\dimen\@curtabmar\box\@curline}%
  \fi
\fi
}

\def\@printlineno{\ifNumberPrograms
		     \global\def\@currentlabel{\theprogramline}%
		     \hskip\leftmargini
		     \llap{{\prognumstyle\theprogramline}\hskip\labelsep}\fi}

\def\prognumstyle{\scriptsize\em}

\def\@startline{\global\@curtabmar\@nxttabmar
   \grefstepcounter{programline}% Added by M.Ward
   \global\@curtab\@curtabmar\global\setbox\@curline\hbox % missing \global
    {}\@startfield\strut}                                 % added 17 Jun 86

\def\grefstepcounter#1{\stepcounter{#1}\let\@tempa\protect
  \def\protect{\noexpand\protect\noexpand}%
  \global\edef\@currentlabel{\csname p@#1\endcsname\csname the#1\endcsname}%
  \let\protect\@tempa}
 


% A switch to allow \BAR...\BAR without untabbing twice:
\newif\ifBarDone \BarDonefalse

% a switch to allow \IF or \ELSIF with no \THEN (Grrr...):
\newif\ifTHEN

% For saving and restoring tab numbers (if a structure may contain
% "unbalanced" \tab ... \untab pairs:
\newcount\old@nxttabmar

% These are the commands used to set the tabs.
% They have different definitione inside and outside tebbing environments:

\def\@tabcommandson{% activate tabbing commands:
  % \tab sets a tab stop and adds one to the margin tab:
  \def\tab{$\=\+$}%
  % \qtab sets a tab stop at one quad of indentation:
  \def\qtab{\quad$\=\+$\kern-1em}%
  % \untab removes one tab stop and moves left if at the beginning of a line:
  \def\untab{$\@finishfield\@ifatmargin\@ltab\else\relax\fi\-$}%
  % Must finish current field before testing if at margin:
  \def\@finishfield{\@stopfield\@addfield\@startfield}%
  % \@marginspace adds an extra space unless there is no text on the line:
  \def\@marginspace{$\@finishfield$\@ifatmargin\relax\else\ \fi}%
  % \rcomment{...} provides a comment flush to the right margin:
  \def\rcomment##1{$\`##1$}%
  % \llapm{...} is like \llap{...} but also leaves and re-enters math
  % mode so that "\llapm{stuff}(" does not put any space between the stuff
  % and the "(". This means it will line up with "\llapm{stuff}X"
  % Note this is only used when \@tabcommandson is in force so we are in
  % normal math mode, not display math mode.
  % The 1sp space is so that a line with just an \llapm item on it is not 
  % considered to be empty!
  \def\llapm##1{\@ifatmargin
		  \llap{$##1$}$\hskip 1sp$%
		\else ##1 \fi}%
  \def\savetab{\global\old@nxttabmar\@nxttabmar}
  \def\restoretab{\global\@nxttabmar\old@nxttabmar}
  % Use this to typeset "..." at a higher tab position:
  \def\utdots{$\@finishfield\@ifatmargin\@ltab\@ltab\else\relax\fi$\dots}
  % For typesetting a relation:
  \def\llapr##1{\@ifatmargin
		  \llap{$\ ##1\ $}${}$%
		\else\ ##1\ \fi}%
}

\def\@tabcommandsoff{% deactivate tabbing commands:
  \let\tab=\relax%
  \let\qtab=\relax%
  \let\@finishfield=\relax%
  \let\untab=\relax%
  \let\@marginspace=\ % never at margin thus always a space
  \def\rcomment##1{\qquad\mbox{##1}}%
  \let\savetab=\relax%
  \let\restoretab=\relax%
  \let\utdots=\dots%
  \def\llapm##1{##1}%
  \def\llapr##1{##1}%
}


%% Now for the keywords:

\def\IF{\keyword{if}\global\THENfalse\ \tab}
\def\THEN{\@marginspace\keyword{then}\global\THENtrue\ \tab}
% else has the same width as then and lines up with it on right:
\def\ELSE{\@marginspace\llapm{\keyword{else}\ }}%
% elsf lines up with the if:
\def\ELSF{\@marginspace\untab\ifTHEN\untab\fi%
	  \global\THENfalse\keyword{elsf}\ \tab}
\def\ELSIF{\@marginspace\untab\ifTHEN\untab\fi%
	   \global\THENfalse\keyword{elsif}\ \tab}
% \AR is the arrow for Dijkstra if and do:
% \AR* starts a newline with one quad indentation:
\def\AR{\@marginspace\rightarrow\global\THENtrue\@ifstar%
	{\\\quad\tab\global\BarDonefalse\@gobblecr}%
	{\ \tab\global\BarDonefalse}}%
% bar lines up on right with if or do keyword:
\def\BAR{\@marginspace\ifBarDone\else\untab\fi\global\BarDonetrue
	 \llapm{\barsymbol\ }}%
\def\FI{\@marginspace\untab\ifTHEN\untab\fi\keyword{fi}}
\def\AWAIT{\keyword{await}\ }% \THEN provides the \tab
\def\DO{\keyword{do}\ \tab}
\let\@oldDO=\DO
\def\OD{\@marginspace\untab\keyword{od}}
% \WHILE, \FOR, \FOREACH and \ATEACH temporarily change \DO to not set a tab:
\def\WHILE{\keyword{while}\ \tab
	   \gdef\DO{\@marginspace\keyword{do}\ \global\let\DO=\@oldDO}}
\def\FOR{\keyword{for}\ \tab
	 \gdef\DO{\@marginspace\keyword{do}\ \global\let\DO=\@oldDO}}
\def\FOREACH{\qtab\keyword{foreach}\ %
	     \gdef\DO{\@marginspace\keyword{do}\ \global\let\DO=\@oldDO}}
\def\ATEACH{\qtab\keyword{ateach}\ %
	    \gdef\DO{\@marginspace\keyword{do}\ \global\let\DO=\@oldDO}}
\def\STEP{\@marginspace\keyword{step}\ }
\def\TO{\@marginspace\keyword{to}\ }
% \BEGIN, \REP, \ACTIONEQ and \WHERE
% make sure next statement starts on a new line
% with one quad of indentation:
\def\BEGIN{\qtab\hbox{\keyword{begin}}\ }%
\def\REP{\qtab\hbox{\keyword{rep}}\ }%
\def\ACTIONEQ{\ \equiv\\\quad\tab}%
\def\WHERE{\@marginspace\untab\qtab\hbox{\keyword{where}}\ }%
\def\IFMATCH#1#2{\qtab\keyword{ifmatch}\ #1{#2}\ }
\def\FILL#1#2{\keyword{fill}\ \tab#1{#2}\ \savetab}
\def\ENDFILL{\@marginspace\restoretab\untab\keyword{endfill}}
\def\EDIT{\keyword{edit}\ \tab}
\def\EDITPARENT{\qtab\keyword{editparent}\ }
\def\ENDEDIT{\@marginspace\untab\keyword{endedit}}
\def\ENDMATCH{\@marginspace\untab\untab\keyword{endmatch}}
\def\EXIT{\keyword{exit}}
% Generalised expression brackets:
\def\EXP{\openexp\tab}
\def\ENDEXP{\untab\closexp}
\def\VAR{\qtab\keyword{var}\ }
\def\var{\ \keyword{var}\ }
\def\END{\@marginspace\untab\keyword{end}}
\def\ENDVAR{\@marginspace\untab\keyword{end}}
\def\ENDREP{\@marginspace\untab\keyword{endrep}}
\def\WHERE{\@marginspace\untab\tab\keyword{where}\ }
\def\WITHIN{\@marginspace\untab\keyword{within}\ }
\def\PROC{\qtab\keyword{proc}\ 
	  \gdef\EQ{\EQsymbol\global\let\EQ=\@oldEQ}}
\def\ENDPROC{\fullstop}
\def\FUNCT{\qtab\keyword{funct}\ 
	   \gdef\EQ{\EQsymbol\global\let\EQ=\@oldEQ}}
\def\ENDFUNCT{\fullstop\global\let\EQ=\@oldEQ}
\def\JOIN{\keyword{join}\ \tab}
\def\NIOJ{\@marginspace\untab\keyword{nioj}}
\let\ENDJOIN=\NIOJ
\def\ONEOF{\keyword{oneof}\ \tab}
\def\FOENO{\@marginspace\untab\keyword{foeno}}

\def\ACTIONS{\tab\keyword{actions}\ \global\let\EQ=\@oldEQ}
\def\ENDACTIONS{\@marginspace\untab\keyword{endactions}}
\def\ENDACTION{\fullstop}
\def\CALL{\keyword{call}\ }
\def\LLAC{}
\let\ENDCALL=\LLAC
\def\COMMENT#1{\keyword{comment}\mbox{: #1}}
\def\C#1{\keyword{C}:\ \mbox{#1}}
\def\ARRAY{\keyword{array}\ }

% The symbols used in programs:
\def\BODY{\EQsymbol}
\def\QE{\fullstop} % end of == definition.

% Expression brackets:
\def\openexp{\mathopen {\mbox{\rule[-0.5ex]{0.04em}{2.3ex}%
			      \rule[1.7ex]{0.4em}{0.1ex}}}}
\def\closexp{\mathclose{\mbox{\rule[-0.5ex]{0.4em}{0.1ex}%
			      \rule[-0.5ex]{0.04em}{2.3ex}}}}

% \fullstop ends an action, proc or funct definition:
\def\fullstop{\untab{\mbox{\bf .}}}
\def\barsymbol{{\rlap{$\sqcap$}\sqcup}}

% \join and \choice symbols:
\def\join{\@marginspace\llapm{\sqcup\ }}%
\def\choice{\@marginspace\llapm{\sqcap\ }}%
% \EQ puts more space around symbol in program environment:
% (this gets redefined by \PROC and \FUNCT):
\def\EQ{\EQsymbol\tab}%
\def\@oldEQ{\EQsymbol\tab}%
\def\EQsymbol{\mathrel{\EQspace\equiv\EQspace}}

% default is tab commands deactivated:
\@tabcommandsoff

% define \normalshape if not present:
\@ifundefined{normalshape}
  {\def\normalshape{\rm}}
  {\relax}

% Underline through descenders:
\let\undertext=\underbar
\def\lowundertext#1{\ifmmode\underline{\vphantom{y}\mbox{#1}}\else
			    $\underline{\vphantom{y}\mbox{#1}}$\fi}

\def\boldvar#1{{\mbox{\normalshape\bf #1}}}

% The Boolean values:
\def\true{\boldvar{true}}
\def\false{\boldvar{false}}

% The simple programs:
\def\ABORT{\boldvar{abort}}
\def\SKIP{\boldvar{skip}}
\def\NULL{\boldvar{null}}

% An abbreviation:
\def\aeq{\ACTIONEQ}

%% Draw a box round something in a program:
\def\progbox#1{%
  % Set #1 in a box, with no tab settings, and restore horizontal position:
  \rlap{\kern-\fboxsep\kern-0.4pt%
	\fbox{$\@tabcommandsoff\phantom{#1}$}}%
  % Then set it again as normal:
  #1\ }

%% For a larger box, covering several lines, put \tl at the top left
%% corner, and \br at the bottom right. THIS REQUIRES pstricks AND pst-node
\def\tl{\llap{\rnode{tl}{\strut}\hspace{2pt}}}
\def\br{\rlap{\hspace{2pt}\rnode{br}{\strut}}%
	      \ncangles[linewidth=0.4pt, linearc=0pt, nodesep=0pt, angle=90,%
			armA=1.5ex, armB=1.5ex]{-}{tl}{br}%
	      \ncangles[linewidth=0.4pt, linearc=0pt, nodesep=0pt, angle=-90,%
			armA=1.4ex, armB=1.4ex]{-}{br}{tl}}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Section (2). |Variable_Names|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%% We use an idea from Rainer Schopf's verbatim style
%%% This allows !@#$%^&*() in variable names as well as _
%%% This version should cope better with missing | delimiters:

% First we define the default \variablefont, \variablefontend and \keyword:

% Default variable font is slanted, so \variablefontend adds italic correction:
\newif\if@corr
\let\variablefont=\sl%
\def\variablefontend#1{\begingroup\futurelet\temp\@corr}% gobble the \egroup
\def\no@corr{\do{.}\do{,}}
\def\@corr{\def\do##1{\ifx\temp##1\@corrfalse\fi}\@corrtrue\no@corr
	    \if@corr\/\else\fi\endgroup\egroup} % put back the \egroup

% Default keyword style is bold underlined:
\def\keyword#1{\mbox{\underbar{\normalshape\bf #1}}}

% For sans-serif variables and keywords (no underbar):
\def\sfvariables{%
  \def\variablefont{\normalshape\sf}%
  \def\variablefontend{}%
  \def\keyword##1{\mbox{\normalshape\bf\sf ##1}}%
  \def\boldvar##1{\mbox{\normalshape\bf\sf ##1}}%
}

% Use \scriptvar|foo| for sub/super-script variables:
\def\scriptvariablefont{\scriptsize\@variablefont}%
\def\scriptvar{\let\@variablefont=\variablefont%
	       \let\variablefont=\scriptvariablefont%
	       \let\@variablefontend=\variablefontend%
	       \def\variablefontend{\let\variablefont=\@variablefont%
				    \let\variablefontend=\@variablefontend%
				    \@variablefontend}}

% This section is modified from verbatim.sty:
\newif\ifwasinmmode \wasinmmodefalse
\begingroup
  \lccode`\~=`\^^M
  \lccode`\V=`\V
  \lowercase{%
    \gdef\variable{% first save mmode status:
      \ifmmode\wasinmmodetrue\else\wasinmmodefalse\fi
      \mbox\bgroup\begingroup
      \variablefont
      \catcode`\^^M\active
      \safeat
      \def~{\endgroup\egroup\\
	    \@latexerr{Variable name ended by end of line.}\@ehc}%
      \catcode`\_\active
      \let\do\@makeother
      \do\{\do\}\do\$\do\&%
      \do\#\do\^\do\^^K\do\^^A\do\%\do\~\do\@\@svariable}}
\endgroup
\def\@svariable{%
  \catcode`\|\active
  \lccode`\~`\|%
  \lowercase{\def~{\endgroup% if we were not in mmode, do italic corr:
		   \ifwasinmmode\let\next=\/% was \relax
		     \else\let\next=\variablefontend\fi
		   \next
		   \egroup}%
	     \let\@dovar~}%
  \leavevmode\null}

\catcode`\|=12\relax
\let\origbar=|
\catcode`\|\active

% Make @ active and equal to \char 64:
\begingroup
  \catcode`\@=\active
  \gdef\safeat{\catcode`\@=\active\def@{\char64\relax}}%
\endgroup

\def|{\ifx\@sharp\relax\origbar\else\relax\p@dovar\fi}
\def\p@dovar#1{#1\protect\@dovar\null}
\def\@dovar{\variable} % #1 = \fi from defn of |

%% Set up _ as \_ outside math mode and \sb in math mode:
%% (in case you use _ outside math mode)
\catcode`\_=\active \def_{\ifmmode\sb\else\p@sb\fi}
\def\p@sb{\protect\@sb}
\def\@sb{\_}

%% Make sure | still works in \verb and verbatim (it is now a "special"):
\def\dospecials{\do\ \do\\\do\{\do\}\do\$\do\&%
  \do\#\do\^\do\_\do\%\do\~\do\|}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Section (3). Program Schemas.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% Definitions for bold subscripted symbols, eg:
%  \B1  or \B{}  or  \B{12} ... etc.
% We check for ' so \B', \S''' etc will work as expected.
\def\A{\boldsub{A}}
\def\B{\boldsub{B}}
\def\P{\boldsub{P}}
\def\Q{\boldsub{Q}}
\def\R{\boldsub{R}}
\def\S{\boldsub{S}}
\def\T{\boldsub{T}}
\def\Z{\boldsub{Z}}

% some bold letters:
\def\d{\boldsub{d}}
\def\e{\boldsub{e}}
\def\t{\boldsub{t}}
\def\w{\boldsub{w}}
\def\x{\boldsub{x}}
\def\y{\boldsub{y}}
\def\z{\boldsub{z}}

\newif\ifMmode \Mmodefalse

\def\boldsub#1{%
  \relax% to fool array and other alignments
  \ifmmode
    \Mmodetrue
  \else
    $\Mmodefalse
  \fi
 \mbox{\normalshape\bf #1}%
 \@boldsub
}

   % Use \mathchoice (typesets all 4) if this is needed for
   % subscripts or superscripts (costs ~0.5 seconds per symbol!):
   % NB use of \text should fix this with AMSLaTeX.
   %\mathchoice{\mbox{\series{bx}\shape{n}\selectfont #1}}%
   %           {\mbox{\series{bx}\shape{n}\selectfont #1}}%
   %           {\mbox{\normalshape\bf\scriptsize #1}}%
   %           {\mbox{\normalshape\bf\tiny #1}}%

\def\@nothing{} \def\prog@prime{'}
\def\@boldsub#1{%
   \def\@boldsubthing{#1}% subscript
   \ifx\@boldsubthing\@nothing% empty
      \let\@boldsubnext\@boldsubfinish
   \else
      \ifx\@boldsubthing\prog@prime%
	 \def\@boldsubnext{^\bgroup\prime\@absorbprimes}%
      \else
	 \def\@boldsubnext{_{#1}\@boldsubfinish}\fi
   \fi
   \@boldsubnext
}

\def\@absorbprimes{\futurelet\@boldsubnext\@seeifprime}
\def\@seeifprime{%
   \ifx\@boldsubnext'%
      \def\@boldsubnext{\@getprime}%
   \else
      \def\@boldsubnext{\egroup\@boldsubfinish}%
   \fi
   \@boldsubnext
}
\def\@getprime'{\prime\@absorbprimes}
\def\@boldsubfinish{\ifMmode\else$\fi}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Section (4). Maths notation used in programs
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% Notation for sets of the form {...|...} :
% Eg: \set{x \in N | x>0}  becomes:
% \left\{\left.\,  x \in N \:\right\origbar\: x>0 \,\right\}
% set brackets and | grow to fit the size if their contents.
% Also: \bigset{...|...} becomes: 
%                        \bigl\{\, ... \mathrel{\bigm\origbar} ... \, \bigr\}
% \bigset is in an aligned environment, so it can include \\
% (AMSLaTeX only)
%
\def\set#1{\@@set#1\@end} % strip of the {} and pass to \@@set
\def\@@set#1|#2\@end{\left\{\left.\, #1 \:\right\origbar\:
		     #2 \,\right\} }
\def\bigset#1{\@bigset#1\@end} % strip of the {} and pass to \@bigset
\@ifundefined{aligned}
{% Not AMSLaTeX:
  \def\@bigset#1|#2\@end{\bigl\{\, #1 {\:\bigm\origbar\:}
			 #2 \,\bigr\} }
}{% With AMSLaTeX:
  \def\@bigset#1|#2\@end{\begin{aligned}[t]\bigl\{\, #1 {\:\bigm\origbar\:}&
			 \let\@oldcr=\\\def\\{\@oldcr&{}}
			 #2 \,\bigr\} \end{aligned} }
}

% Notation for substitution in programs:
\def\sub[#1/#2|#3]{\left[\left.#1\,/\,#2\,\right\origbar\,#3\,\right]}
\def\bigsub[#1/#2|#3]{\bigl[#1\,\bigm/\,#2\,\bigm\origbar\,#3\,\bigr]}
% Use \modbar{x} for |x|:
\def\modbar#1{\origbar #1\origbar}

% Notation for a sequence in angle brackets:
% \bigseq uses big size of brackets:
% \def\seq#1{\left< #1 \right>}
\def\seq#1{\langle #1 \rangle}
\def\bigseq#1{\bigl< #1 \bigr>}

% Notation for subsequences analogous to set notation:
\def\subseq#1{\@@subseq#1\@end} % strip of the {} and pass to \@@subseq
\def\@@subseq#1|#2\@end{\left<\left.\, #1 \:\right\origbar\:
			#2 \,\right>}
\def\bigsubseq#1{\@bigsubseq#1\@end} % strip of the {} and pass to \@bigsubseq
\@ifundefined{aligned}
{% Not AMSLaTeX:
  \def\@bigsubseq#1|#2\@end{\bigl<\, #1 {\:\bigm\origbar\:}
			    #2 \,\bigr> }
}{% With AMSLaTeX:
  \def\@bigsubseq#1|#2\@end{\begin{aligned}[t]\bigl<\, #1 {\:\bigm\origbar\:}&
			    \let\@oldcr=\\\def\\{\@oldcr&{}}
			    #2 \,\bigr> \end{aligned} }
}

% range dots, like \ldots but with two dots only (for 1..n etc.):
\def\rdots{\mathinner{\ldotp\ldotp}}

% Atomic Specification statement: for eg <x>/<y>.Q use: \atspec x/y. Q
% This uses "/" and "." as argument delimiters:
% \def\atspec #1/#2.{\seq{#1}\!/\!\seq{#2}\!.}
\def\atspec #1/#2.{\seq{#1}/\seq{#2}.}

% \Forall vars.formula and \Exists vars.formula:
\def\Forall#1.{\forall #1.\,}
\def\Exists#1.{\exists #1.\,}

\let\EQspace=\  % default space around \EQ \EQT and \LE
\def\EQT{\mathrel{\EQspace\approx\EQspace}} % program equivalence.
\def\LE{\mathrel{\EQspace\le\EQspace}}      % program refinement.
\def\NOT{\neg}
% \AND and \OR relations have an extra thin space around them:
\def\AND{\mathrel{\,\wedge\,}}
\def\OR{\mathrel{\,\vee\,}}
\def\EOR{\mathrel{\,\oplus\,}}
\def\sbs{\subseteq}
\def\im{\Rightarrow}
% (use \iff and \implies for the "long" arrows)
\def\union{\cup}
\def\intersect{\cap}
\def\lar{\leftarrow}
\def\rar{\rightarrow}
\def\wflt{\prec}
\def\wfle{\preccurlyeq}
\def\succstar{\mathrel{\succ\!\!^*}}
\def\succeqstar{\mathrel{\succeq\!^*}}
\def\gt{\ifmmode>\else{$>$}\fi}
\def\lt{\ifmmode>\else{$<$}\fi}
\def\tw{\ifmmode{}^\sim\else{${}^\sim$}\fi}


% map and reduce operators:
\def\bstar{\mathrel{\boldsymbol{*}}} % for *
\def\bdiv{\boldsymbol{/}} % for /


% Various arrows (taken from oz.sty):
\let \rel       \leftrightarrow
\let \tfun      \rightarrow
\let \tinj      \rightarrowtail
\def \tsur      {\mathrel{\ooalign{$\tfun$\hfil\cr$\mkern4mu\tfun$}}}
\def \pfun      {\p\tfun}
\def \pinj      {\p\tinj}
\def \psur      {\p\tsur}
\def \ffun      {\f\tfun}
\def \finj      {\f\tinj}
\def \bij       {\mathrel{\ooalign{$\tinj$\hfil\cr$\mkern5mu\tfun$}}}
\def\p#1{\mathrel{\ooalign{\hfil$\mapstochar\mkern 5mu$\hfil\cr$#1$}}}
\def\f#1{\mathrel{\ooalign{\hfil
	$\mapstochar\mkern 3mu\mapstochar\mkern 5mu$\hfil\cr$#1$}}}

%% Logical exclusive or:
\def\exor{\oplus}

%% Sequence concatenation:
\def\concat{\mathrel{+\!\!\!+}}

\def\rmtiny{\normalshape\rm\tiny}

%% Stack operations:
\def\push{\mathrel{\overset{\mbox{\rmtiny push}}{\longleftarrow}}}
\def\pop {\mathrel{\overset{\mbox{\rmtiny  pop}}{\longleftarrow}}}
\def\pick{\mathrel{\overset{\mbox{\rmtiny pick}}{\longleftarrow}}}
\def\last{\mathrel{\overset{\mbox{\rmtiny last}}{\longleftarrow}}}

%% bitwise operators
\def\bitand {\mathrel{\overset{\mbox{\tiny bit}}{\wedge}}}
\def\bitor  {\mathrel{\overset{\mbox{\tiny bit}}{\vee}}} 
\def\bitexor{\mathrel{\overset{\mbox{\tiny bit}}{\vphantom\vee\smash\oplus}}}
\def\bitnot{{\overset{\mbox{\tiny bit}}{\vphantom\vee\neg}}}

%% Logical, decimal and floating point operators:
\def\lplus {\mathrel{\overset{\mbox{\tiny log}}{+}}}
\def\lminus{\mathrel{\overset{\mbox{\tiny log}}{-}}}
\def\lmult {\mathrel{\overset{\mbox{\tiny log}}{\times}}}
\def\ldiv  {\mathrel{\overset{\mbox{\tiny log}}{\div}}}
\def\lequ  {\mathrel{\overset{\mbox{\tiny log}}{=}}}
\def\lneq  {\mathrel{\overset{\mbox{\tiny log}}{\neq}}}
\def\lless {\mathrel{\overset{\mbox{\tiny log}}{<}}}
\def\lgreat{\mathrel{\overset{\mbox{\tiny log}}{>}}}
\def\lleq  {\mathrel{\overset{\mbox{\tiny log}}{\leq}}}
\def\lgreq {\mathrel{\overset{\mbox{\tiny log}}{\geq}}}
\def\dplus {\mathrel{\overset{\mbox{\tiny dec}}{+}}}
\def\dminus{\mathrel{\overset{\mbox{\tiny dec}}{-}}}
\def\dmult {\mathrel{\overset{\mbox{\tiny dec}}{\times}}}
\def\ddiv  {\mathrel{\overset{\mbox{\tiny dec}}{\div}}}
\def\deq   {\mathrel{\overset{\mbox{\tiny dec}}{=}}}
\def\dneq  {\mathrel{\overset{\mbox{\tiny dec}}{\neq}}}
\def\dless {\mathrel{\overset{\mbox{\tiny dec}}{<}}}
\def\dgreat{\mathrel{\overset{\mbox{\tiny dec}}{>}}}
\def\dleq  {\mathrel{\overset{\mbox{\tiny dec}}{\leq}}}
\def\dgreq {\mathrel{\overset{\mbox{\tiny dec}}{\geq}}}
\def\fplus {\mathrel{\overset{\mbox{\tiny fpt}}{+}}}
\def\fminus{\mathrel{\overset{\mbox{\tiny fpt}}{-}}}
\def\fmult {\mathrel{\overset{\mbox{\tiny fpt}}{\times}}}
\def\fdiv  {\mathrel{\overset{\mbox{\tiny fpt}}{\div}}}
\def\feq   {\mathrel{\overset{\mbox{\tiny fpt}}{=}}}
\def\fneq  {\mathrel{\overset{\mbox{\tiny fpt}}{\neq}}}
\def\fless {\mathrel{\overset{\mbox{\tiny fpt}}{<}}}
\def\fgreat{\mathrel{\overset{\mbox{\tiny fpt}}{>}}}
\def\fleq  {\mathrel{\overset{\mbox{\tiny fpt}}{\leq}}}
\def\fgreq {\mathrel{\overset{\mbox{\tiny fpt}}{\geq}}}

%% mod and div:
\def\MOD{\mathrel{\text{mod}}}
\def\DIV{\mathrel{\text{div}}}

%% add the definition of overset if not present:
\@ifundefined{overset}%
  {\def\overset#1#2{\binrel@{#2}%
     \binrel@@{\mathop{\kern\z@#2}\limits^{#1}}}
   \def\binrel@#1{\setboxz@h{\thinmuskip0mu
      \medmuskip\m@ne mu\thickmuskip\@ne mu$#1\m@th$}%
     \setbox@ne\hbox{\thinmuskip0mu\medmuskip\m@ne mu\thickmuskip
      \@ne mu${}#1{}\m@th$}%
     \setbox\tw@\hbox{\hskip\wd@ne\hskip-\wdz@}}
   \def\binrel@@#1{\ifdim\wd2<\z@\mathbin{#1}\else\ifdim\wd\tw@>\z@
     \mathrel{#1}\else{#1}\fi\fi}%
   \def\setboxz@h{\setbox\z@\hbox}%
   \def\setbox@ne{\setbox\@ne}%
   \def\wd@ne{\wd\@ne}%
   \def\wdz@{\wd\z@}%
  }{}

%% =df symbol (with thick space around it):
\def\edf{\mathrel{\;=_{{}_{\mbox{\rmtiny DF}}}\;}}

%% empty set symbol: (use \varnothing if available)
\@ifundefined{varnothing}%
	     {\let\nullset=\emptyset}%
	     {\let\nullset=\varnothing}%

%% Powerset symbol:
\@ifundefined{DeclareMathSymbol}{%
%% check if \teurm defined - if not then use \oldwp (Large and raised):
\@ifundefined{teurm}%
  {\def\powerset{\raisebox{0.5ex}{\Large$\oldwp$}}}% no \eurm
  {\def\powerset{\raisebox{0.5ex}{\Large\teurm\char"7D}}}% Use Euler roman p
}{%
\DeclareSymbolFont{eulerletters}{U}{eur}{m}{n}%
\DeclareMathSymbol{\powersetsymbol}{\mathord}{eulerletters}{"7D}%
\newsavebox{\powersetbox}
\sbox{\powersetbox}{\raisebox{0.5ex}{\mbox{\Large$\powersetsymbol$}}}
\def\powerset{\usebox{\powersetbox}}
% old defn -- with amslatex this makes the whole maths item \Large!
%\def\powerset{\raisebox{0.5ex}{\Large$\powersetsymbol$}}
}%


%% The stmaryrd style and fonts include \bigsqcap, but if you don't have
%% it, here is an alternative using rules (only works at standard size):
\@ifundefined{bigsqcap}
  {\def\bigsqcap{\mathop{%
		\rule[-0.2ex]{.07em}{2.17ex}%
		\rule[1.8ex]{0.5em}{.17ex}%
		\rule[-0.2ex]{.07em}{2.17ex}}}}
  {\relax}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Section (5). Miscellaneous bits and pieces
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%% Substitute for some AMSLaTeX things if they are missing:
\@ifundefined{text}{\let\text=\mbox}{}
\@ifundefined{boldsymbol}{\def\boldsymbol#1{\mbox{\bf #1}}}{}
\@ifundefined{implies}{\def\implies{\;\Longrightarrow\;}}{}
\@ifundefined{operatorname}{\def\operatorname#1{\mathop{#1}}}{}


% \snugbox is by Victor Eijhout, eijkhout@cs.utk.edu, TUGboat 13, 1, 1992.
% It sets a box containing paragraphs as wide ``as it really is''
\def\snugbox{\mbox\bgroup
%            ^^^^^ changed from \hbox by M.Ward
  \setbox\z@\vbox\bgroup
    \leftskip\z@
    \bgroup\aftergroup\make@snug
    \let\next=}
\def\make@snug{\par\sn@gify\egroup
  \box\z@\egroup}
\def\sn@gify
  {\skip\z@=\lastskip \unskip
   \advance\skip\z@\lastskip \unskip
   \unpenalty
   \setbox\z@\lastbox
   \ifvoid\z@ \nointerlineskip
     \else {\sn@gify} \fi
   \hbox{\unhbox\z@}\nointerlineskip
   \vskip\skip\z@
   }
% To vertically centre the box:
\def\textvcenter{\hbox\bgroup$
  \everyvbox{\everyvbox{}%
    \aftergroup$%
    \aftergroup\egroup}
  \vcenter}


%% Cases environment:
%% based on description environment with numbering:
\def\Cases{
  \ifnum \@enumdepth >3 \@toodeep\else
    \advance\@enumdepth \@ne
    \edef\@enumctr{enum\romannumeral\the\@enumdepth}%
     \@ifundefined{mathindent}
     {\list{\kern-1em\hbox{\normalshape\bf Case \arabic{\@enumctr}:}}%
	   {\usecounter{\@enumctr}%
	     \def\makelabel##1{##1}}}%
     {\list{\kern-1em\hbox{\normalshape\bf Case \arabic{\@enumctr}:}}% 
	   {\mathindent 0pt \usecounter{\@enumctr}%
	     \def\makelabel##1{##1}}}%
  \fi}

\let\endCases=\endlist

%% \CASES is redundant with amstex.sty
\def\CASES#1{\left\{\,\vcenter{{\let\\=\cr\normalbaselines\m@th
    \ialign{$##\hfil$&\quad##\hfil\crcr#1\crcr}}}\right.}

%% Environment romanenumerate for lists numbered by roman numerals:
\def\romanenumerate{\begingroup
  \def\theenumi{\normalshape(\myroman{enumi})}%
  \def\p@enumi{}%
  \def\labelenumi{\theenumi}%
  \enumerate}
\def\endromanenumerate{\endenumerate\endgroup}

%% A fix to get lower case Roman numerals for use as labels:
\def\myroman#1{\@myroman{\@nameuse{c@#1}}}
\def\@myroman#1{\expandafter{\romannumeral #1}}

%% \proof macro for theorems and lemmas:
\def\proof{\normalshape{\setlength{\parskip}{0pt}\par\addvspace\medskipamount
			\noindent{\bf Proof: }}\ignorespaces}

%% require the {...} for \wp and \WP
\let\oldwp=\wp % save old \wp (curly p character)
%\def\wp#{\@wp}
%\def\@wp#1{\mbox{\normalshape wp}(#1)}
%\def\WP#{\@WP}
%\def\@WP#1{\mbox{\normalshape WP}(#1)}
%% Don't require {...}, ie use normal parentheses where required:
\def\wp{\mbox{\normalshape wp}}
\def\WP{\mbox{\normalshape WP}}


%% Two line displayed equation, eg:
%% \[  \twoline{ a_very_long_left_hand_side \\
%%                   {} = a_fairly_long_right_hand_side } \]
%% Use in displayed maths mode.
%% NB this is superseded by AMSLaTeX's multline environment.
\def\twoline#1{\def\\{\hfill\cr\hfill}% \def only lasts to end of display
	       \displaylines{\quad #1 \quad\cr}}

%% Add a definition of \Bbb if not present:
% We use poor man's bold to give an ``extra bold'' letter:
\@ifundefined{Bbb}
  {\def\Bbb{\protect\pBbb}
   \def\pBbb#1{\setbox0=\hbox{\bf #1}
	       \kern-.025em\copy0\kern-\wd0
	       \kern.05em\copy0\kern-\wd0
	       \kern-.025em\raise.0433em\box0 }}
  {\relax}

%% Add a definition of cases environment if not present:
\@ifundefined{endcases}
  {\def\cases{\left\{\def\arraystretch{1.2}\hskip-\arraycolsep
     \array{l@{\quad}l}}
   \def\endcases{\endarray\hskip-\arraycolsep\right.}}
  {\relax}

%% draw a line accross the page:
\def\dashes{$\makebox[6in]{\hrulefill}$}

%% A \qed command for the end of a proof:
\@ifundefined{blacksquare}
  {\def\qedsymbol{\vrule width.6em height.5em depth.1em\relax}}
  {\let\qedsymbol=\blacksquare}
\def\qed{\ifx\\\@eqncr\let\next\eqnarrayqed\else
  \ifmmode\let\next\eqnqed\else
    \let\next\textqed\fi\fi\next}
%\def\eqnqed#1\]{\belowdisplayskip\z@\belowdisplayshortskip\z@
%  \postdisplaypenalty\@M\relax#1
%  \]\par{\lineskip\z@\baselineskip\z@\vbox to\z@{\vss\noindent\textqed}}} 
%% simpler version from ROGERS@se.physto.vana using the primitive \eqno:
\def\eqnqed#1\]{\relax#1\eqno\qedsymbol$$\ignorespaces}
\def\textqed{{\unskip\nobreak\hfil\penalty50\hskip2em\null\nobreak\hfil
	      $\qedsymbol$\parfillskip\z@\finalhyphendemerits0\par}}
\def\eqnarrayqed{\\\noalign{\vspace{-\jot}%
  {\lineskip\z@\baselineskip\z@%
    \vbox to\z@{\vss\noindent\textqed}}%
  \vspace{-\baselineskip}}}