\makeatletter

\typeout{``page''}

% cedric: removed for llncs

%page layout
%\oddsidemargin 0cm
%\evensidemargin 0cm
%\topmargin 10pt

%\headheight 0pt	
%\headsep 0pt	
%\footheight 0pt
%\footskip 24pt	
%\textheight 24cm
%\textwidth 15.5cm
%\footnotesep 1cm

%\baselineskip = 24pt plus 4pt minus 3pt
%\voffset=-0.5cm
%\hoffset=0.5cm

\makeatother

\makeatletter

% on  active  et  desactive  le  mode  frtypo  par \frtypotrue et frtypofalse
% quelquesoit le mode les caract\`eres :  ; ?   !   sont actifs. 
% En  particulier  ces  caract\`eres  ne  peuvent  plus \^etre  mis  dans des
% \'etiquettes.

\def\halfspace{\kern .166em}

\def\space@pv{\ifmmode ;\else \halfspace;\fi}
\def\space@dc{\ifmmode :\else \halfspace:\fi}
\def\space@pi{\ifmmode ?\else \halfspace?\fi}
\def\space@pe{\ifmmode !\else \halfspace!\fi}

\let\nospace@pv=;
\let\nospace@dc=:
\let\nospace@pi=?
\let\nospace@pe=!

\catcode`;=\active \catcode`:=\active \catcode`?=\active \catcode`!=\active

\def \frtypo
    {\let;=\space@pv\let:=\space@dc\let!=\space@pe\let?=\space@pi}
\def \entypo 
    {\let;=\nospace@pv\let:=\nospace@dc\let!=\nospace@pe\let?=\nospace@pi}

\frtypo

\def\@sanitize
 {\@makeother\ \@makeother\\\@makeother\$\@makeother\&%
\@makeother\#\@makeother\^\@makeother\^^K\@makeother\_\@makeother\^^A%
\@makeother\%\@makeother\~\@makeother\;\@makeother\?\@makeother%
\:\@makeother\!}

\let \oldspecials \dospecials 
\def \dospecials {\oldspecials \do\:\do\!\do \?\do\;}

%\scrollmode

\makeatletter
%===========================================================================
% Personals macros (They might have strange latex side effects
%-----------------

\def\noparindent{\everypar={\hskip -\parindent\everypar={}}}
\def \para {\medskip\noparindent}
\def \pari {\medskip\noparindent}
\def \parii {\smallskip\noparindent}
\let\paro=\noparindent


%===========================================================================
% Definitions Theorems 
%---------------------

\newif \iffrench 
\if \csname french\endcsname \relax  \frenchfalse \else  \frenchtrue\fi

\if \csname definition\endcsname\relax
\newtheorem{definition}{D\iffrench \'e\else e\fi  finition}\fi
\def\bdf{\begin{definition}\begin{em}}
\def\edf{\ifvmode\vskip-\lastskip\nopagebreak\else
         \penalty 100\fi\end{em}\end{definition}}

\if \csname theorem\endcsname\relax
\newtheorem{theorem}{\iffrench Théorème\else Theorem\fi}\fi
\def\bthm{\begin{theorem}}
\def\ethm{\end{theorem}}

\newtheorem{algorithm}{Algorithm\if\french e\else\fi}
\def\balgo{\begin{algorithm}}
\def\ealgo{\end{algorithm}}

\if \csname proposition\endcsname\relax
\newtheorem{proposition}{Proposition}\fi
\def\bprop{\begin{proposition}}
\def\eprop{\end{proposition}}

\if \csname lemma\endcsname\relax 
\newtheorem{lemma}[proposition]{Lemm\iffrench e\else a\fi}\fi
\def\blem{\begin{lemma}}
\def\elem{\end{lemma}}

\if \csname corollary\endcsname\relax
\newtheorem{corollary}[proposition]{Corollary}\fi
\def\bcor{\begin{corollary}}
\def\ecor{\end{corollary}}

\def\brmk{\trivlist \item[\hskip \labelsep {\bf {Note}}]}
\def\ermk{\endtrivlist}

\newtheorem{Note}{Note}
\def\bnote{\begin{note}\begin{em}}
\def\enote{\end{em}\end{note}}

\if \csname example\endcsname\relax
%\newtheorem{example}[remark]{Ex\iffrench a\else e\fi mple}\fi
\newtheorem{example}{Ex\iffrench a\else e\fi mple}\fi
\def\bxple{\trivlist \item[\hskip \labelsep {\bf {Example}}]}
%{\begin{example}\begin{em}}
\def\exple{\endtrivlist}
%{\end{em}\end{example}}

\def\@begintheorem#1#2{\it \trivlist \item[\hskip \labelsep{\bf #1\ #2}]}
\def\@opargbegintheorem#1#2#3{\it \trivlist
      \item[\hskip \labelsep{\bf #1\ #2\ (#3)}]}
\def\@endtheorem{\endtrivlist}

\newcount \indemo
\def \makeno #1{\global \advance \indemo by 1\global
      \expandafter \edef \csname demo/\the\cdemo/#1\endcsname{\the\indemo}}
\def \refno #1{\if \relax\csname demo/\the\cdemo/#1\endcsname \relax
  \write0 {Demo counter #1 undefined}??\else
   \csname demo/\the\cdemo/#1\endcsname\fi}
\def \labno #1{\makeno {#1}\refno {#1}}

\newif \ifdemo \demotrue
\newcount \cdemo
\newenvironment{demo}{\bdemo}{\edemo}
\def\bdemotrue{\trivlist \item[\hskip \labelsep
  {\underline
        {\iffrench Preuve\else Proof\fi}:}]\advance\cdemo by 1\indemo 0}
\def\edemo{\penalty 100\hfill\rule{2mm}{2mm} \endtrivlist\@doendpe}
\long \def \bdemofalse #1\edemo{\relax}
\outer \def \bdemo 
  {\ifdemo \bdemotrue \else \expandafter \bdemofalse \fi\indent}

\newif \ifhint \hintfalse
\newtheorem{hint}{\rm \underline {Hint}}
\def\bhintiftrue{\trivlist \item[\hskip \labelsep {\underline {Hint}:}]}
\def\ehint{\penalty 100\hfill\noindent\rule{2mm}{2mm}\endtrivlist}
\long \def \bhintiffalse #1\ehint{\relax}
\outer \def \bhint
  {\ifhint \bhintiftrue \else \expandafter \bhintiffalse \fi}

\newif \ifexpert \expertfalse
\newtheorem{expert}{Remark}
\def\bexpertiftrue{\trivlist \item[\hskip \labelsep {\underline {Hint}:}]}
\def\eexpert{\penalty 100\hfill\noindent\rule{2mm}{2mm}\endtrivlist}
\long \def \bexpertiffalse #1\eexpert{\relax}
\outer \def \bexpert 
  {\ifexpert \bexpertiftrue \else  \expandafter \bexpertiffalse \fi}



\def\notitle{\hskip\hsize minus\hsize\nobreak\hbox{}}

\def\notation{\paragraph*{Notation}}
\def\hypothesis{\paragraph*{Assumption}}


\def \caseparagraph{\@startsection
 {case}{6}{\z@}{1.5ex plus .3ex minus .2ex}{-1em}{\normalsize\bf}}
\def \subcaseparagraph{\@startsection
% {subcase}{7}{\parindent}{1.5ex plus .3ex minus .2ex}{-1em}{\normalsize\bf}}
 {subcase}{7}{\z@}{1.5ex plus .3ex minus .2ex}{-1em}{\normalsize\bf}}


\if \csname datefrench\endcsname\relax
\def \langcase {Case}
\def \langsubcase {Subcase}
\else
\def \langcase {Cas}
\def \langsubcase {Sous-cas}
\fi

\def\case#1{\caseparagraph*{\langcase\space #1:}}
\def\othercase#1{\caseparagraph*{#1:}}
\def\mathcase#1{\caseparagraph*{\langcase\space $#1$:}}
\def\subcase#1{\subcaseparagraph*{\langsubcase\space #1:}}

% Send a warning when running latex
\def\warning#1{\immediate\write0{Warning: #1}}

\newenvironment{care}{\bwarning}{\ewarning}
\def\bcare{\trivlist \item[\hskip \labelsep {\bf Warning!}]}
\def\ecare{\endtrivlist}

\def\subst#1#2{^{#1} \!/\! _{#2}}

\def \comment #1{{\em #1}}
%\def \comment #1{}
\makeatother


\makeatletter
%%% To change size in math mode

\let\Ts=\textstyle
\let\Ds=\displaystyle
\let\Ss=\scriptstyle

%%% Abrevs

\let \comp \circ
\let \wild \_


%%% To put text between two formulas on the same line

\def\text#1{\qquad\hbox{#1}\qquad}

%%%  Macros for mathematics

%% Special symbols

\def \nat {{\mathord{I\kern -.33em N}}}
\def \natb {{\mathord{I\kern -.33em\overline{N}}}}

\def\Vdash {\mathrel{\hbox{\vrule\kern .1ex$\vdash$}}}
\def\VVdash {\mathrel{\hbox{\vrule\kern .2ex\vrule\kern .1ex $\vdash$}}}

% An open box to end demonstrations with

\def\Box{\hbox
  {\vbox
    {\hrule height .033em
     \hbox to .5em
       {\vrule width .033em
        \hbox{\vbox to .5em{\vss}\hss}
        \vrule width .033em}
     \hrule height .033em
    }}}


%% Balanced symbols

\def\absolute#1{\mathopen\mid#1\mathclose\mid}

%% Operators

\def \domain {\dv}
%\def \domain {\dvmathop{\sl dom\,}}
\def \image {\mathop{\sl im\,}}
\def \modulo {\mathbin{\rm modulo}}
\def \inverse{{}^{-1}}
\def \cardinal {{\sl Card\,}}
%\def \restrict #1{\mathbin{\mid}_{#1}}
\def \restrict
   {\mathbin{\hbox{$\mid$\kern-.24em\lower.09em\hbox{\rm\char'22}$\!$}}}
\let \arity = \varrho


%% Quantifiers

\def \fall #1,{\forall #1,\;}
\def \exist #1,{\exists #1,\;}
\def \qt #1.{\forall\,#1.\,}
\def \ex #1.{\exists\,#1.\,}

%% Arrows

\let\ar=\rightarrow
\let\dar=\Rightarrow
\def\imply{\Longrightarrow}


\def \rewrite {\mathrel{-}\joinrel\leadsto}


%% Equalities

%\def \axiom {\mathrel {\mathop =^!}}
\def \axiom {=}
\def \eqdef {\mathrel {\mathop {=\joinrel=}\limits^{def}}}

%% Sizes

\def\({\left(}
\def\){\right)}

\def\Mid{\mathrel{\Big|}}

%% Indices  see also indices.def

\def \ind #1#2{_{#1\in[1,#2]}}

%%

%% names 

\let \th \vdash
\let \tth \Vdash
\let \ttth \VVdash
\let \thh \models

\def\Cal#1{{\cal #1}}

\let \eset = \emptyset



%% Aligned constructions in math mode

% For internal use only

\def\noskip{\lineskiplimit=\the\lineskiplimit
                \lineskip=\the\lineskip}
\def\moreskip{\lineskiplimit=0.4em\lineskip=0.4em plus 0.2em}
\def\moremoreskip{\lineskiplimit=1.2em\lineskip=1.2em plus 0.2em}

\def\vatrix#1{\null\,\vcenter{\normalbaselines\moreskip\m@th
    \let \and \cr
    \ialign{$\displaystyle##$\hfil
      &\quad$\displaystyle##$\hfil&\quad##\hfil\crcr
      \mathstrut\crcr\noalign{\kern-\baselineskip}
      #1\crcr\mathstrut\crcr\noalign{\kern-\baselineskip}}}\,}

% A sequence of expressions is writen on separate lines to form one expression

\def \band #1{\left\{\vatrix{#1}\right.}          % brace and
\def \wand #1{\wedge\band{#1}}                    % wedge  and
\def \vand #1{\vee\band{#1}}                      % vee  and
\def \vor  #1{\vee\left[\vatrix{#1}\right.}       % vee and or
\def \Wand #1{\bigwedge\band{#1}}                 % big wedge and
\def \Vand #1{\bigvee\band{#1}}                   % big vee and
\def \Wor  #1{\bigvee\left[\vatrix{#1}\right.}    % big vee and



% A general usage tabulation in math mode.
%     Indentation is alternatively left and right, so that good place for
%     tabs will produce many different

% \dalign { & blabla :& blabla    \cr 
%           &    bla :& blablabla \cr
%         }
 
% \dalign {  blabla :&& blabla    \cr 
%            bla :   && blablabla \cr
%         }
 
% \dalign { & blabla :&    blabla \cr 
%           &    bla :& blablabla \cr
%         }

% Internal and personal use
\def\Dalign#1#2{\vcenter
 \bgroup
   \let\>=\qquad
   \def\title##1{\crcr\noalign{\medskip}\multispan#1{\hfil\bf##1\hfil}}
%   \halign{$##$\hfil\qquad&&\hfil$##{}$&${}##$\hfil\qquad\cr#2\crcr}
%   \halign{$##$\hfil&&\qquad\hfil$##{}$&${}##$\hfil\cr#2\crcr}
   \halign{&${}##$\hfil&\hfil$##{}$\cr#2\crcr}
 \egroup}
% End internal use

\def\align#1{\vcenter
 \bgroup
   \let\>=\qquad
   \halign{#1\crcr}
 \egroup}

%\def\aligndef#1#2{\expandafter\def\csname aligndef#1\endcsname{#2}}
%\aligndef ]{\argalign}
%\aligndef l{&\hfil$##{}$}
%\aligndef r{&${}##$\hfil}
%\aligndef c{&\hfil$##$\hfil}
%\aligndef -{\qquad}
%\aligndef L{&\hfil##$}
%\aligndef R{&##\hfil}
%\aligndef C{&\hfil##\hfil}
%\def\argalign#1{\relax}
%\def\prealign#1{\csname aligndef#1\endcsname\prealign}
%\def\doalign#1]{\dohalign{\prealign#1]}}
%\def\dohalign#1#2{\expandafter\halign{#1\cr#2\crcr}}



%\def\dalign#1{\ifx#1[\doalign\else\Dalign3{#1}\fi}
\def\dalign{\Dalign3}


\def\Strut{\raise .4em\hbox{\strut}\raise -.4em\hbox{\strut}}

\def \deftitle #1
   {\def \title ##1
      {\crcr\noalign{\medskip}\multispan#1{\hfil\bf##1\hfil}}}



\bgroup
 \catcode `\^^M \active
 \gdef \obeycr {\catcode `\^^M\active \let ^^M\crcr}
\egroup


\ifx \csname linewidth\endcsname \hsize 
 \let  \realwidth \hsize 
\else
 \let \realwidth \linewidth
\fi

\def \oris {\crcr \mid&}
\def \syntaxtable #1
  {\def\is {::=&}
   \def \\{\cr\noalign{\medskip}}\def\cont{\cr&}\vbox 
   \bgroup
   \tabskip=100pt plus 1000pt minus 1000pt
   \halign to \realwidth
       {\hfil$##{}$\tabskip=0pt&
        ${}##$\hfil \tabskip=100pt plus 1000pt minus 1000pt&
        &##\hfil \cr#1\crcr}
   \egroup}


\def \assertions #1
  {\deftitle2 \vbox
   \bgroup
     \halign {\hfil$##{}$&$##$\hfil&&\quad##\hfil\cr#1\crcr}
   \egroup}


%%% old version

\def\malign#1{\vcenter\bgroup
   \deftitle #1
   \def \lign ##1\cr {\noalign {##1}}
   \def \textlign##1{\noalign {\medskip \vbox {\noindent ##1}\medskip}}
   \tabskip=100pt plus 1000pt minus 1000pt
   \halign to \realwidth
       {\hfil$##{}$\tabskip=0pt&
        ${}##$\hfil \tabskip=100pt plus 1000pt minus 1000pt&
        &##\hfil&$##$\hfil&  \cr#1\crcr\egroup}}

\newif \ifhsize \hsizefalse

\newskip \nullskip \nullskip 0pt
\newskip \fullskip \fullskip 100pt plus 1000pt minus 1000pt
\def \maligntrue {\tabskip \fullskip
                   \halign to \realwidth \bgroup}
\def \malignfalse {\halign \bgroup}
\def \malign {\vcenter \bgroup \ifhsize \expandafter \maligntrue \else \expandafter \malignfalse \fi}
\def \endmalign {\crcr \egroup \egroup}

\def \makeword #1#2#3{\expandafter
   \def \noexpand#3{#2 {#1\expandafter \let \expandafter \dummy\string #3}}}

\let \vect \overrightarrow

\def \uad {\hskip 0.5em}


\newskip \mathandskip 
\newskip\mathmargin \mathmargin  0em

\mathandskip 2em plus 0.5fil minus 0.5em
\def \mathand {\hskip \mathandskip}
\def \mathleftright {\hfill{}\hskip 0em plus -2fill\penalty 50{}\hfill}
\def \mathandcr {\penalty 50\mathand}
\def \mathcr {\penalty -10000\mathand}
\def \mathcrleft {\hfill{}\hskip 0em plus -2fill\penalty -10000{}\hskip
     \mathmargin}
\def \mathbreak {\penalty 50}

\def \incrmargin #1{\advance\mathmargin by #1em\advance\mathmargin by #1em}
\def \mathslash#1{\let \do \mathcrleft
   \ifx #1[\let\do\mathdoskip\fi\do#1}
\def \mathdoskip#1#2]{\incrmargin {#2}\mathcrleft}

% Type inference rules

\let \mathmoreskip=\moremoreskip
\def \nomoreskip {\let \mathmoreskip \relax}

\def \bmaths {\let \and \mathandcr  \hsize \realwidth
    \centering \vbox \bgroup \mathmoreskip  \noindent 
    $\displaystyle \let \\ \mathslash}
\def \emaths {\unskip$\egroup}
\def \mathflushleft {\def \emaths {\hfill$\egroup}\nomoreskip}
\newenvironment {maths}{\bmaths}{\emaths}

\def \maths #1{\bmaths #1\emaths}

\def \whereis {\leftarrow}
\def \where #1{[{\let \is \whereis #1}]}
\def \dowhere #1\is#2\is{[\ifx#2\empty #1\else #2/#1\fi]}
\def \where #1{\let \is \relax\dowhere #1\is\empty\is}

\let \closeplus\relax
\let \Empty \relax
\let \is \relax
\def \plus #1{\PLUS #1\is\is\END}
\def \PLUS #1\is#2\is#3\END{\oplus\ifx #3\is (#1\plustoken#2)\else #1\fi}
\let \plustoken \mapsto

\let \diverge \uparrow

\def \set #1{\{#1\}}
\def \sem #1{\lbrack\!\lbrack#1\rbrack\!\rbrack}


\def\mathrm #1{\mathrel {\rm #1}}
\let \coerce \leq
\makeatother

\makeatletter


%% see infer.doc for a documentation

% Judgements

\let\th=\vdash

% naming

\expandafter \ifx \csname name\endcsname\relax
   \def\name#1{\hbox{\sc #1}}\else \relax \fi

\def \labname #1{{\rm(\name{#1})}}
\let \lab = \labname
\def \clab #1{\hbox {$\smash {\lab{#1}}$}}
\newskip \beforelabskip \beforelabskip = 0.5em
\def \eqlab {\eqno \lab}

%% inside rules

\def \nmir #1[#2]{\crcr \hrulefill \cr}
\def \rmir #1[#2]{\crcr \hrulefill & \clab {#2} \cr}
\def \lmir #1[#2]{\relax}                         
\def \Lmir #1[#2]{\crcr \Llabo {#2}\hrulefill \cr}     
\def \Rmir #1[#2]{\crcr \hrulefill \Rlabo {#2}\cr}    
\def \imir {\crcr \hrulefill\cr}

% outside rules

\def \rlabo #1{\hskip \beforelabskip \clab {#1}} 
\def \llabo #1{\clab {#1}\hskip \beforelabskip}
\def \Rlabo #1{\rlap {\rlabo {#1}}}   
\def \Llabo #1{\llap {\llabo {#1}}}   
\let \labr \rlabo \let \labl \llabo \let \labR \Rlabo \let \labL \Llabo


\def \rlab #1 {\rlap {\lab {#1}}}
\def \llab #1 {\llap {\lab {#1}}}


% A good separator for multiple hypothesis

\let \and \qquad
\let \andcr \cr


% Single rules

\def \lessskip  {\lineskiplimit=.3em\lineskip= .2em plus .1em}

\makeatletter
\def \mathrulename {\scriptsize \labname}
\def \ignoredash #1{\let\next\ignoredash
         \ifx #1-\relax\else\let\next#1\fi\next}
\def \mathrule {\@ifnextchar [{\mathrulelab}{\@mathrule}}
\def \mathrulelab[#1]#2{\hbox
   {\vbox {\hbox {\mathrulename {#1}}\nointerlineskip\smallskip
           \hbox {$\@mathrule{#2}$}}}}
\def \@mathrule #1{{\let \and \qquad \let \rlab \rl \let \llab \ll
     \def \mir {MiR}\def\endrule {EnDrUlE}
     \displaystyle \offinterlineskip \lessskip  \bgroup \openrule 
     \beginrule #1\mir \mir \endrule}}
\def \beginrule #1\mir#2{#1\ifx #2\mir \let \next \finishrule 
     \else \def \next {\middlerule\openrule \beginrule\ignoredash#2}\fi\next} 
\def\finishrule#1\endrule{\closerule\egroup}

\def \openrule {\hbox \bgroup \vbox \bgroup
     \halign \bgroup \hfil $##$\hfil &\hskip \beforelabskip$##$\hfil \cr}
\def \closerule {\crcr\egroup\egroup\egroup}
%\def \endrule {\closerule \egroup}

\def \singleRule {\crcr\noalign {\vskip -0.1em}\closerule \over}
\let \middlerule \singleRule


% Double and Tripple rules see infer-more.def

% Logic and rewriterules

\def \logicrule #1{\let \mir \Longrightarrow #1}


\def \longleadsto {\mathrel{-}\joinrel\leadsto}

\def \rewriterule #1{\displaystyle \offinterlineskip \lessskip
     \bgroup\let \mir \longleadsto \openrule#1\endrule}

\def \suspend #1{\vbox to #1 {\leaders \hbox {$\cdot$}\vfill}}


\if \relax \csname keywordstyle\endcsname  \let \keywordstyle \tt \fi

%\def \keyword #1{{\hbox {\keywordstyle #1}}}
\def \keyword #1{{\keywordstyle #1}}
\def \mathtoken #1{\ifmmode
   \mathopen{}\keyword {#1}\mathclose{}\else \keyword{#1}\fi}
\def \mathpostfix #1{\mathrel{\keyword {#1}}\mathclose{}}
\def \mathprefix #1{\mathopen{}\mathrel{\keyword {#1}}}
\def \mathinfix #1{\mathrel{\keyword {#1}}}

\def\ignorefirst #1{}
\def \lwt #1{\expandafter \lowercase \expandafter \bgroup 
  \expandafter \ignorefirst \string #1\egroup}


\def \makeprefix #1#2{\expandafter\def \noexpand #1{\mathprefix  {#2}}}
\def \makepostfix #1#2{\expandafter\def \noexpand #1{\mathpostfix  {#2}}}
\def \maketoken #1#2{\expandafter\def \noexpand #1{\mathtoken {#2}}}
\def \makeinfix #1#2{\expandafter\def \noexpand #1{\mathinfix {#2}}}

\def \makein #1{\expandafter\def
  \noexpand #1##1in{\keyword {\lwt #1}\,\,##1\,\,\keyword {in}\,\,}}

\let \@ \;
\def \Let #1=#2in{\keyword {let}\@ {#1 = #2} \@\keyword {in}\@}
\def \fun (#1){\keyword {fun}\@ #1 \rightarrow}
\def \type #1=#2in{\keyword {type}\@ #1 = #2 \@\keyword {in}\@}

\makeatother

\let \cont \kappa
\let \t \tau
\let \l \ell
\let \s \sigma
\let \tv \alpha
\let \vect \bar

\def \Gen {{\rm Gen}}

\def \tplus #1{\TPLUS #1\is\is\END}
\def \TPLUS #1\is#2\is#3\END{\oplus\ifx #3\is (#1:#2)\else #1\fi}

%%%%%%%%%%%%%%% light programs

\makeatletter
\def \progstyle {\tt}
\newskip \programindent \programindent 4em
\def \program {\par \begingroup 
    \medskip \parindent \programindent \@tempswafalse
    \frenchspacing \@vobeyspaces \let \par \programpar
    \obeylines \progstyle
    \catcode``=13 \@noligs \let \do \@makeother \dospecials 
    \catcode `\\ 0 \catcode `\{ 1 \catcode `\} 2
    \prog@specials \prog@initspecials \obeyspaces}

\def \programpar {\if@tempswa\hbox{}\fi\@tempswatrue\@@par}

\bgroup
\gdef \less@specials {\relax
 \catcode `| \active 
 \catcode `< \active
 \catcode `> \active
 \catcode `- \active
 \catcode `\' \active 
}
\gdef \more@specials {\relax
 \catcode `( \active
 \catcode `) \active
}
\gdef \prog@specials {\less@specials\more@specials}
\prog@specials
\gdef \prog@initspecials {\def
    -{\minus@program}\def
    '{\acurate@program}\def
    |{\bar@program}\def
    <{\less@program}\def
    >{\greater@program}\def
    ({\less@program}\def
    ){\greater@program}}
 \gdef \bar@@program {\let\do \eattoken
  \ifx \token >$\droite$\else ${}\mid{}$\let \do \relax\fi \do}
 \gdef \minus@@program {\let\do \eattoken
  \ifx \token >$\ar$\else -\let \do \relax\fi \do}
\egroup

\def \acurate@program {\futurelet \token \acurate@@program}
\def \acurate@@program {\let \do \eattoken
  \ifx \token a$\alpha$\else 
   \ifx \token b$\beta$\else 
    \char `\' \let \do \relax\fi\fi \do}
\def \less@program {\hbox{$<$}}
\def \greater@program {\hbox{$>$}}
\def \bar@program {\futurelet \token \bar@@program}
\def \minus@program {\futurelet \token \minus@@program}


\def \endprogram {\ifdim\lastskip >\z@ \@tempskipa\lastskip 
       \vskip -\lastskip\fi\medskip \endgroup
     \@endpetrue}

\def\prog {\begingroup \hbox \bgroup
  \catcode ``=13 \@noligs
  \let \do \@makeother \dospecials \progstyle
   \prog@specials \prog@initspecials
    \catcode `\\ 0 \catcode `\{ 1 \catcode `\} 2
  \@prog}
\def\@prog#1{\obeyspaces \frenchspacing \catcode `\  10
            \def\@tempa ##1#1{##1\egroup\endgroup}\@tempa}
\makeatother

%%%%%%%%%%%%%%%%%%%  "quotations"

\makeatletter
% on  active  le cararectere " et on s'en sert pour le mode \prog
% s'il est défini ou \verb autrement

\bgroup
\@makeother \"
\gdef \progquote {\prog"}
\catcode `\" \active
\gdef "{\progquote}
\egroup

\def \quoteon {
\let \quote@sanitize \@sanitize
\def \@sanitize {\quote@sanitize \@makeother\"}
\let \quote@specials \dospecials 
\def \dospecials {\quote@specials \do\"}
\def \quoteon {\catcode `\" \active}\quoteon}

\def \quoteoff {\@makeother \"}
\makeatother



%%%%%%%%%%%%%%%%
\def \lift #1{\;{}^{#1}}
\def \inu #1{\lift {i \in 1..#1}}
\def \jnu #1{\lift {j \in 1..#1}}

%% typo

\mathchardef \le "313C
\mathchardef \ge "313E

\mathcode `< "4268
\mathcode `> "5269


\catcode `\| \active 
\let \olspecials \dospecials \def \dospecials {\olspecials \do \|}

%\def \droite {\mathrel {\,\hbox {\large$\triangleright$}\,}}
\def \droite {\mathrel{\tt =}}

\makeatletter
\def |{\baractive}
\def \baractive {\futurelet\token \next@baractive}
\def \eattoken #1{}
\def \next@baractive{\let\do\eattoken
    \ifx \token>\droite\else \mid \let \do \relax \fi \do}


\def \Def #1in{\mathprefix {let}#1\mathinfix{in}}
\def \Let#1in{\mathprefix {let}#1\mathinfix{in}}
\def \Reply#1to{\mathprefix {reply}#1\mathinfix{to}}
\def \>{\droite}
\def \And {\mathrel{\tt and}}
\def \tuple #1{{\tt (}#1{\tt )}}
\def \<#1> {\tuple {#1}}

\let \bcup \cup
\let \thd \th
\def \fv {fv}
\def \defines {::}
\def \produces #1{\Ds\mathop{\Longrightarrow}^{#1}}
\def \reduces {\longrightarrow}
\let \red \reduces
\let \redcham \mapsto

\let \plus \tplus

\makeatother
 

\def \dd {{\cal D}}
\def \pp {{\cal P}}

\def \dv {dv}

\def \redsoupe {\mathrel {\mathop {\red} \limits^s}}
\let \redstruct \rightleftharpoons
\let \redchaud \rightharpoonup
\let \redfroid \leftharpoondown
\let \cool \leftharpoondown
\let \heat \rightharpoonup

\def\redstep{\mathrel{\mathpalette\redstepaux{}}}
\def\redstepaux#1{\vcenter{\hbox{\ooalign{\hfil
      \raise2pt \hbox{$\rightharpoonup$}\hfil\cr\hfil
      \lower2pt\hbox {$\leftharpoondown$}\hfil\crcr
      $\longrightarrow$}}}}


\let \redsoupe \red
\let \redx \red


\def \Comment #1{}
\let \agree \approx
\quoteon

\maketoken \int {int}