%  Mathpartir --- Math Paragraph for Typesetting Inference Rules
%
%  Copyright (C) 2001, 2002, 2003, 2004, 2005, 2015 Didier Rémy
%
%  Author         : Didier Remy 
%  Version        : 1.3.1
%  Bug Reports    : to author
%  Web Site       : http://pauillac.inria.fr/~remy/latex/
% 
%  Mathpartir 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, or (at your option)
%  any later version.
%  
%  Mathpartir 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 
%  (http://pauillac.inria.fr/~remy/license/GPL).
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  File mathpartir.sty (LaTeX macros)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{mathpartir}
    [2015/11/06 version 1.3.1 Math Paragraph for Typesetting Inference Rules]

%%

%% Identification
%% Preliminary declarations

\RequirePackage {keyval}

%% Options
%% More declarations

%% PART I: Typesetting maths in paragraphe mode

%% \newdimen \mpr@tmpdim
%% Dimens are a precious ressource. Uses seems to be local.
\let \mpr@tmpdim \@tempdima

% To ensure hevea \hva compatibility, \hva should expands to nothing 
% in mathpar or in inferrule
\let \mpr@hva \empty

%% normal paragraph parametters, should rather be taken dynamically
\def \mpr@savepar {%
  \edef \MathparNormalpar
     {\noexpand \lineskiplimit \the\lineskiplimit
      \noexpand \lineskip \the\lineskip}%
  }

\def \mpr@rulelineskip {\lineskiplimit=0.3em\lineskip=0.2em plus 0.1em}
\def \mpr@lesslineskip {\lineskiplimit=0.6em\lineskip=0.5em plus 0.2em}
\def \mpr@lineskip  {\lineskiplimit=1.2em\lineskip=1.2em plus 0.2em}
\let \MathparLineskip \mpr@lineskip
\def \mpr@paroptions {\MathparLineskip}
\let \mpr@prebindings \relax

\newskip \mpr@andskip \mpr@andskip 2em plus 0.5fil minus 0.5em

\def \mpr@goodbreakand
   {\hskip -\mpr@andskip  \penalty -1000\hskip \mpr@andskip}
\def \mpr@and {\hskip \mpr@andskip}
\def \mpr@andcr {\penalty 50\mpr@and}
\def \mpr@cr {\penalty -10000\mpr@and}
%\def \mpr@cr {\penalty -10000\vadjust{\vbox{}}\mpr@and}
\def \mpr@eqno #1{\mpr@andcr #1\hskip 0em plus -1fil \penalty 10}

\def \mpr@bindings {%
  \let \and \mpr@andcr
  \let \par \mpr@andcr
  \let \\\mpr@cr
  \let \eqno \mpr@eqno
  \let \hva \mpr@hva
  } 
\let \MathparBindings \mpr@bindings

% \@ifundefined {ignorespacesafterend}
%    {\def \ignorespacesafterend {\aftergroup \ignorespaces}

\newenvironment{mathpar}[1][]
  {$$\mpr@savepar \parskip 0em \hsize \linewidth \centering
     \vbox \bgroup \mpr@prebindings \mpr@paroptions #1\ifmmode $\else
     \noindent $\displaystyle\fi
     \MathparBindings}
  {\unskip \ifmmode $\fi\egroup $$\ignorespacesafterend}

\newenvironment{mathparpagebreakable}[1][]
  {\begingroup 
   \par
   \mpr@savepar \parskip 0em \hsize \linewidth \centering
      \mpr@prebindings \mpr@paroptions #1%
      \vskip \abovedisplayskip \vskip -\lineskip%
     \ifmmode  \else  $\displaystyle\fi
     \MathparBindings
  }
  {\unskip
   \ifmmode $\fi \par\endgroup
   \vskip \belowdisplayskip
   \noindent
  \ignorespacesafterend}

% \def \math@mathpar #1{\setbox0 \hbox {$\displaystyle #1$}\ifnum
%     \wd0 < \hsize  $$\box0$$\else \bmathpar #1\emathpar \fi}

%%% HOV BOXES

\def \mathvbox@ #1{\hbox \bgroup \mpr@normallineskip 
  \vbox \bgroup \tabskip 0em \let \\ \cr
  \halign \bgroup \hfil $##$\hfil\cr #1\crcr \egroup \egroup
  \egroup}

\def \mathhvbox@ #1{\setbox0 \hbox {\let \\\qquad $#1$}\ifnum \wd0 < \hsize
      \box0\else \mathvbox {#1}\fi}


%% Part II -- operations on lists

\newtoks \mpr@lista
\newtoks \mpr@listb

\long \def\mpr@cons #1\mpr@to#2{\mpr@lista {\\{#1}}\mpr@listb \expandafter
{#2}\edef #2{\the \mpr@lista \the \mpr@listb}}

\long \def\mpr@snoc #1\mpr@to#2{\mpr@lista {\\{#1}}\mpr@listb \expandafter
{#2}\edef #2{\the \mpr@listb\the\mpr@lista}}

\long \def \mpr@concat#1=#2\mpr@to#3{\mpr@lista \expandafter {#2}\mpr@listb
\expandafter {#3}\edef #1{\the \mpr@listb\the\mpr@lista}}

\def \mpr@head #1\mpr@to #2{\expandafter \mpr@head@ #1\mpr@head@ #1#2}
\long \def \mpr@head@ #1#2\mpr@head@ #3#4{\def #4{#1}\def#3{#2}}

\def \mpr@flatten #1\mpr@to #2{\expandafter \mpr@flatten@ #1\mpr@flatten@ #1#2}
\long \def \mpr@flatten@ \\#1\\#2\mpr@flatten@ #3#4{\def #4{#1}\def #3{\\#2}}

\def \mpr@makelist #1\mpr@to #2{\def \mpr@all {#1}%
   \mpr@lista {\\}\mpr@listb \expandafter {\mpr@all}\edef \mpr@all {\the
   \mpr@lista \the \mpr@listb \the \mpr@lista}\let #2\empty 
   \def \mpr@stripof ##1##2\mpr@stripend{\def \mpr@stripped{##2}}\loop
     \mpr@flatten \mpr@all \mpr@to \mpr@one
     \expandafter \mpr@snoc \mpr@one \mpr@to #2\expandafter \mpr@stripof
     \mpr@all \mpr@stripend  
     \ifx \mpr@stripped \empty \let \mpr@isempty 0\else \let \mpr@isempty 1\fi
     \ifx 1\mpr@isempty
   \repeat
}

\def \mpr@rev #1\mpr@to #2{\let \mpr@tmp \empty
   \def \\##1{\mpr@cons ##1\mpr@to \mpr@tmp}#1\let #2\mpr@tmp}

%% Part III -- Type inference rules

\newif \if@premisse
\newbox \mpr@hlist
\newbox \mpr@vlist
\newif \ifmpr@center \mpr@centertrue
\def \mpr@vskip {}
\def \mpr@htovlist {%
   \setbox \mpr@hlist
      \hbox {\strut
             \ifmpr@center \hskip -0.5\wd\mpr@hlist\fi
             \unhbox \mpr@hlist}%
   \setbox \mpr@vlist
      \vbox {\if@premisse
                \box \mpr@hlist
                \ifx \mpr@vskip \empty \else
                  \hrule height 0em depth \mpr@vskip width 0em
                \fi
                \unvbox \mpr@vlist
             \else
                \unvbox \mpr@vlist 
                \ifx \mpr@vskip \empty \else
                  \hrule height 0em depth \mpr@vskip width 0em
                \fi
                \box \mpr@hlist
             \fi}%
}
% OLD version
% \def \mpr@htovlist {%
%    \setbox \mpr@hlist
%       \hbox {\strut \hskip -0.5\wd\mpr@hlist \unhbox \mpr@hlist}%
%    \setbox \mpr@vlist
%       \vbox {\if@premisse \box \mpr@hlist \unvbox \mpr@vlist
%              \else \unvbox \mpr@vlist \box \mpr@hlist
%              \fi}%
% }

\def \mpr@item #1{$\displaystyle #1$}
\def \mpr@sep{2em}
\def \mpr@blank { }
\def \mpr@hovbox #1#2{\hbox
  \bgroup
  \ifx #1T\@premissetrue
  \else \ifx #1B\@premissefalse
  \else
     \PackageError{mathpartir}
       {Premisse orientation should either be T or B}
       {Fatal error in Package}%
  \fi \fi
  \def \@test {#2}\ifx \@test \mpr@blank\else
  \setbox \mpr@hlist \hbox {}%
  \setbox \mpr@vlist \vbox {}%
  \if@premisse \let \snoc \mpr@cons \else \let \snoc \mpr@snoc \fi
  \let \@hvlist \empty \let \@rev \empty
  \mpr@tmpdim 0em
  \expandafter \mpr@makelist #2\mpr@to \mpr@flat
  \if@premisse \mpr@rev \mpr@flat \mpr@to \@rev \else \let \@rev \mpr@flat \fi
  \def \\##1{%
     \def \@test {##1}\ifx \@test \empty
        \mpr@htovlist
        \mpr@tmpdim 0em %%% last bug fix not extensively checked
     \else
      \setbox0 \hbox{\mpr@item {##1}}\relax
      \advance \mpr@tmpdim by \wd0
      %\mpr@tmpdim 1.02\mpr@tmpdim
      \ifnum \mpr@tmpdim < \hsize
         \ifnum \wd\mpr@hlist > 0
           \if@premisse
             \setbox \mpr@hlist 
                \hbox {\unhbox0 \hskip \mpr@sep \unhbox \mpr@hlist}%
           \else
             \setbox \mpr@hlist
                \hbox {\unhbox \mpr@hlist  \hskip \mpr@sep \unhbox0}%
           \fi
         \else 
         \setbox \mpr@hlist \hbox {\unhbox0}%
         \fi
      \else
         \ifnum \wd \mpr@hlist > 0
            \mpr@htovlist 
            \mpr@tmpdim \wd0
         \fi
         \setbox \mpr@hlist \hbox {\unhbox0}%
      \fi
      \advance \mpr@tmpdim by \mpr@sep
   \fi
   }%
   \@rev
   \mpr@htovlist
   \ifmpr@center \hskip \wd\mpr@vlist\fi \box \mpr@vlist
   \fi
   \egroup
}

%%% INFERENCE RULES

\@ifundefined{@@over}{%
    \let\@@over\over % fallback if amsmath is not loaded
    \let\@@overwithdelims\overwithdelims
    \let\@@atop\atop \let\@@atopwithdelims\atopwithdelims
    \let\@@above\above \let\@@abovewithdelims\abovewithdelims
  }{}

%% The default

\def \mpr@@fraction #1#2{\hbox {\advance \hsize by -0.5em
    $\displaystyle {#1\mpr@over #2}$}}
\def \mpr@@nofraction #1#2{\hbox {\advance \hsize by -0.5em
    $\displaystyle {#1\@@atop #2}$}}

\let \mpr@fraction \mpr@@fraction

%% A generic solution to arrow

\def \mpr@@fractionaboveskip {0ex}
\def \mpr@@fractionbelowskip {0.22ex}

\def \mpr@make@fraction #1#2#3#4#5{\hbox {%
     \def \mpr@tail{#1}%
     \def \mpr@body{#2}%
     \def \mpr@head{#3}%
     \setbox1=\hbox{$#4$}\setbox2=\hbox{$#5$}%
     \setbox3=\hbox{$\mkern -3mu\mpr@body\mkern -3mu$}%
     \dimen0\ht3\advance\dimen0 by \dp3\relax
     \dimen0 0.5\dimen0\relax
     \advance \dimen0 by \mpr@@fractionaboveskip
     \setbox1=\hbox {\raise \dimen0 \box1}\relax
     \dimen0 -\dimen0\advance \dimen0 \mpr@@fractionaboveskip\dimen0 -\dimen0
     \advance \dimen0 by \mpr@@fractionbelowskip
     \setbox2=\hbox {\lower \dimen0 \box2}\relax
     \setbox0=\hbox {$\displaystyle {\box1 \atop \box2}$}%
     \dimen0=\wd0\box0
     \box0 \hskip -\dimen0\relax
     \hbox to \dimen0 {$%\color{blue}
       \mathrel{\mpr@tail}\joinrel
       \xleaders\hbox{\copy3}\hfil\joinrel\mathrel{\mpr@head}%
     $}}}

%% Old stuff should be removed in next version
\def \mpr@@nothing #1#2
    {$\lower 0.01pt \mpr@@nofraction {#1}{#2}$}
\def \mpr@@reduce #1#2{\hbox
    {$\lower 0.01pt \mpr@@fraction {#1}{#2}\mkern -15mu\rightarrow$}}
\def \mpr@@rewrite #1#2#3{\hbox
    {$\lower 0.01pt \mpr@@fraction {#2}{#3}\mkern -8mu#1$}}
\def \mpr@infercenter #1{\vcenter {\mpr@hovbox{T}{#1}}}

\def \mpr@empty {}
\def \mpr@inferrule
  {\bgroup
     \ifnum \linewidth<\hsize \hsize \linewidth\fi
     \mpr@rulelineskip
     \let \and \qquad
     \let \hva \mpr@hva
     \let \@rulename \mpr@empty
     \let \@rule@options \mpr@empty
     \let \mpr@over \@@over
     \mpr@inferrule@}
\newcommand {\mpr@inferrule@}[3][]
  {\everymath={\displaystyle}%       
   \def \@test {#2}\ifx \empty \@test
      \setbox0 \hbox {$\vcenter {\mpr@hovbox{B}{#3}}$}%
   \else 
   \def \@test {#3}\ifx \empty \@test
      \setbox0 \hbox {$\vcenter {\mpr@hovbox{T}{#2}}$}%
   \else
   \setbox0 \mpr@fraction {\mpr@hovbox{T}{#2}}{\mpr@hovbox{B}{#3}}%
   \fi \fi
   \def \@test {#1}\ifx \@test\empty \box0
   \else \vbox 
%%% Suggestion de Francois pour les etiquettes longues
%%%   {\hbox to \wd0 {\RefTirName {#1}\hfil}\box0}\fi
      {\hbox {\DefTirName {#1}}\box0}\fi
   \egroup}

\def \mpr@vdotfil #1{\vbox to #1{\leaders \hbox{$\cdot$} \vfil}}

% They are two forms
% \inferrule [label]{[premisses}{conclusions}
% or
% \inferrule* [options]{[premisses}{conclusions}
%
% Premisses and conclusions are lists of elements separated by \\
% Each \\ produces a break, attempting horizontal breaks if possible, 
% and  vertical breaks if needed. 
% 
% An empty element obtained by \\\\ produces a vertical break in all cases. 
%
% The former rule is aligned on the fraction bar. 
% The optional label appears on top of the rule
% The second form to be used in a derivation tree is aligned on the last
% line of its conclusion
% 
% The second form can be parameterized, using the key=val interface. The
% folloiwng keys are recognized:
%       
%  width                set the width of the rule to val
%  narrower             set the width of the rule to val\hsize
%  before               execute val at the beginning/left
%  lab                  put a label [Val] on top of the rule
%  lskip                add negative skip on the right
%  left                 put a left label [Val]
%  Left                 put a left label [Val],  ignoring its width 
%  right                put a right label [Val]
%  Right                put a right label [Val], ignoring its width
%  leftskip             skip negative space on the left-hand side
%  rightskip            skip negative space on the right-hand side
%  vdots                lift the rule by val and fill vertical space with dots
%  after                execute val at the end/right
%  
%  Note that most options must come in this order to avoid strange
%  typesetting (in particular  leftskip must preceed left and Left and
%  rightskip must follow Right or right; vdots must come last 
%  or be only followed by rightskip. 
%  

%% Keys that make sence in all kinds of rules
\def \mprset #1{\setkeys{mprset}{#1}}
\define@key {mprset}{andskip}[]{\mpr@andskip=#1}
\define@key {mprset}{lineskip}[]{\lineskip=#1}
\define@key {mprset}{lessskip}[]{\lineskip=0.5\lineskip}
\define@key {mprset}{flushleft}[]{\mpr@centerfalse}
\define@key {mprset}{center}[]{\mpr@centertrue}
\define@key {mprset}{rewrite}[]{\let \mpr@fraction \mpr@@rewrite}
\define@key {mprset}{atop}[]{\let \mpr@fraction \mpr@@nofraction}
\define@key {mprset}{myfraction}[]{\let \mpr@fraction #1}
\define@key {mprset}{fraction}[]{\def \mpr@fraction {\mpr@make@fraction #1}}
% To be documented.
\define@key {mprset}{defaultfraction}[]{\let \mpr@fraction \mpr@@fraction}
\define@key {mprset}{sep}{\def\mpr@sep{#1}}
\define@key {mprset}{fractionaboveskip}{\def\mpr@@fractionaboveskip{#1}}
\define@key {mprset}{fractionbelowskip}{\def\mpr@@fractionbelowskip{#1}}
\define@key {mprset}{style}[1]{\def\TirNameStyle{#1}def}
\define@key {mprset}{rightstyle}[1]{\def\RightTirNameStyle{#1}}
\define@key {mprset}{leftstyle}[1]{\def\LeftTirNameStyle{#1}}
\define@key {mprset}{vskip}[1]{\def \mpr@vskip{#1}}

\newbox \mpr@right
\define@key {mpr}{flushleft}[]{\mpr@centerfalse}
\define@key {mpr}{center}[]{\mpr@centertrue}
\define@key {mpr}{rewrite}[]{\let \mpr@fraction \mpr@@rewrite}
\define@key {mpr}{myfraction}[]{\let \mpr@fraction #1}
\define@key {mpr}{fraction}[]{\def \mpr@fraction {\mpr@make@fraction #1}}
\define@key {mpr}{width}{\hsize #1}
\define@key {mpr}{sep}{\def\mpr@sep{#1}}
\define@key {mpr}{before}{#1}
\define@key {mpr}{lab}{\let \DefTirName \LabTirName \def \mpr@rulename {#1}}
\define@key {mpr}{Lab}{\let \DefTirName \LabTirName \def \mpr@rulename {#1}}
\define@key {mpr}{style}[1]{\def\TirNameStyle{#1}def}
\define@key {mpr}{rightstyle}[1]{\def\RightTirNameStyle{#1}}
\define@key {mpr}{leftstyle}[1]{\def\LeftTirNameStyle{#1}}
\define@key {mpr}{vskip}[1]{\def \mpr@vskip{#1}}
\define@key {mpr}{narrower}{\hsize #1\hsize}
\define@key {mpr}{leftskip}{\hskip -#1}
\define@key {mpr}{reduce}[]{\let \mpr@fraction \mpr@@reduce}
\define@key {mpr}{rightskip}
  {\setbox \mpr@right \hbox {\unhbox \mpr@right \hskip -#1}}
\define@key {mpr}{LEFT}{\setbox0 \hbox {$#1$}\relax
     \advance \hsize by -\wd0\box0}

\define@key {mpr}{left}{\setbox0 \hbox {$\LeftTirName {#1}\;$}\relax
     \advance \hsize by -\wd0\box0}
\define@key {mpr}{Left}{\llap{$\LeftTirName {#1}\;$}}
\define@key {mpr}{right}
  {\setbox0 \hbox {$\;\RightTirName {#1}$}\relax \advance \hsize by -\wd0
   \setbox \mpr@right \hbox {\unhbox \mpr@right \unhbox0}}
\define@key {mpr}{RIGHT}
  {\setbox0 \hbox {$#1$}\relax \advance \hsize by -\wd0
   \setbox \mpr@right \hbox {\unhbox \mpr@right \unhbox0}}
\define@key {mpr}{Right}
  {\setbox \mpr@right \hbox {\unhbox \mpr@right \rlap {$\;\RightTirName {#1}$}}}
\define@key {mpr}{vdots}{\def \mpr@vdots {\@@atop \mpr@vdotfil{#1}}}
\define@key {mpr}{after}{\edef \mpr@after {\mpr@after #1}}
\define@key {mpr}{vcenter}[]{\mpr@vcentertrue}

\newif \ifmpr@vcenter \mpr@vcenterfalse
\newcommand \mpr@inferstar@ [3][]{\begingroup
  \setbox0 \hbox
        {\let \mpr@rulename \mpr@empty \let \mpr@vdots \relax
         \setbox \mpr@right \hbox{}%
         \setkeys{mpr}{#1}%
         $\ifx \mpr@rulename \mpr@empty \mpr@inferrule {#2}{#3}\else
          \mpr@inferrule [{\mpr@rulename}]{#2}{#3}\fi
          \box \mpr@right \mpr@vdots$
          \ifmpr@vcenter \aftergroup \mpr@vcentertrue \fi}
  \ifmpr@vcenter
     \box0
  \else 
     \setbox1 \hbox {\strut}  
     \@tempdima \dp0 \advance \@tempdima by -\dp1
     \raise \@tempdima \box0
  \fi
  \endgroup}

\def \mpr@infer {\@ifnextchar *{\mpr@inferstar}{\mpr@inferrule}}
\newcommand \mpr@err@skipargs[3][]{}
\def \mpr@inferstar*{\ifmmode 
    \let \@do \mpr@inferstar@
  \else 
    \let \@do \mpr@err@skipargs
    \PackageError {mathpartir}
      {\string\inferrule* can only be used in math mode}{}%
  \fi \@do}


%%% Exports

% Envirnonment mathpar

\let \inferrule \mpr@infer

% make a short name \infer is not already defined
\@ifundefined {infer}{\let \infer \mpr@infer}{}

\def \TirNameStyle #1{\small \textsc{#1}}
\def \LeftTirNameStyle #1{\TirNameStyle {#1}}
\def \RightTirNameStyle #1{\TirNameStyle {#1}}

\def \lefttir@name #1{\hbox {\small \LeftTirNameStyle{#1}}}
\def \righttir@name #1{\hbox {\small \RightTirNameStyle{#1}}}
\let \TirName \lefttir@name
\let \LeftTirName \lefttir@name
\let \DefTirName \lefttir@name
\let \LabTirName \lefttir@name
\let \RightTirName \righttir@name

%%% Other Exports

% \let \listcons \mpr@cons
% \let \listsnoc \mpr@snoc
% \let \listhead \mpr@head
% \let \listmake \mpr@makelist




\endinput
