%% File abbrev.sty

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                      DOCUMENTATION                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% This file defines the abbreviate environment, which allows you to do
% things like typing $=>$ instead of $\Rightarrow$.  It also defines
% a few useful commands, including one to make math-mode use ordinary
% italic characters.
%
%
% THE abbreviate ENVIRONMENT
% ~~~~~~~~~~~~~~~~~~~~~~~~~~
% This environment is explained in terms of the following example:
% 
%    \begin{abbreviate}{FOO}{=#(}{=#(}
%      \x ==>  {\Longrightarrow}
%      \x ==   {==}
%      \x =>  {\Rightarrow}
%      \x =   {=}
%      \x #   {\neq}
%      \x (+) {\oplus}
%      \x (+  {(+}
%      \x (   {(}
%    \end{abbreviate}
% 
% This defines the declaration \FOO that does the following:
%   * Makes the three characters  
%           =  #  ( 
%     active--so they are commands like the character ~ (tilde).
% 
%   * Defines these characters in such a way that 
%       ==> is an abbreviation for  \Logrightarrow, 
%       ==  does what it normally does 
%       =   does what it normally does
%       #   is an abbreviation for \neq
%       etc.
% 
% It also defines the declaration \noFOO to undo the effects of the
% declaration \FOO.  Here are the rules
% 
%    * The following characters can appear as the first character
%      of an abbreviation:
% 
%         ! @ # $ % ^ & * ( ) _ - + = ~ ` | [ ] : ; " ' < > , . ? /
% 
%    * The other characters in an abbreviation can be anything except
%      the three characters  \  {  } .  They can contain % only if
%      %  appears in the last two arguments of the abbreviate environment.
%
%    * The second and third arguments of the abbreviate environment consist 
%      of the first characters that appear in abbreviations.  However,
%      ~ (tilde) does not appear in these arguments, even if it's
%      used as the first character of an abbreviation. [As a NOTE below
%      explains, the second and third arguments need not always have
%      the same characters.]
% 
%    * An abbreviation definition consists of \x followed by
%      the abbreviation, followed by one or more spaces, followed
%      by its definition, enclosed in braces.
%
%    * The sequence of abbreviations being defined must obey the following 
%      rules:
%
%         - The first abbreviation is arbitrary.
%
%         - Every subsequent abbreviation must be obtained by deleting
%           the last character from the previous abbreviation and adding
%           any (possibly empty) string of characters.
%
%         - The last abbreviation defined must be a single character.
%
%      It is a consequence of these rules that, to define an abbreviation,
%      It is necessary to define every prefix of that abbreviation.
%
%
%   NOTE: You can have multiple abbreviate environments to define
%   different sets of abbreviations.  
%
%   WARNING: When a character is active, it doesn't behave like it normally
%   does.  In particular, if  [  or  ]  is active, then [ ] cannot be
%   used to enclose optional arguments.   Use something like
%
%           \noFOO \command[arg] \FOO   or  {\noFOO \command[arg]}
%
%   if you need a command with optional arguments.
%
%   NOTE: In the example above, the command \FOO both activates the
%   characters  = # ( and defines their active versions appropriately.
%   The abbreviate environment also defines the command \FOOact, 
%   which just activates the characters.  Since the definitions 
%   aren't changed by \noFOO, the sequence of commands
%
%      \FOO \noFOO \FOOact 
%
%   is equivalent to \FOO.  If you're writing macros that do a lot
%   of messing around, you may want to take advantage of this.
%
%   NOTE: You can use commands of the form \<single-letter>, such
%   as \: in an abbreviation, as long as it's not the first letter.
%   If you use such a command, it must go in the third argument (but
%   NOT the second) of the abbreviate environment.
%
%
%   USEFUL COMMANDS
%   ~~~~~~~~~~~~~~~
%
% \ensuremath{FORMULA}
%    Typesets FORMULA in math mode, regardless of current mode.
%    (This is a standard LaTeX-2e command.)
%
% \noTeXmath
% \TeXmath   
%    In math mode, TeX normally typesets characters in math italic,
%    which makes $different$ look like $d$ time $i$ times $f$ times ...
%    and not like {\it different}.  The \noTeXmath causes TeX to use
%    ordinary italic, so $different$ is the same as {\it different}.
%    This makes it easier to use multi-letter identifiers in formulas.
%    The \TeXmath command reverts to TeX's normal behavior
%
% \makeactive{CHARS} : 
%    CHARS should be a string of characters, not containing any of the
%    three characters "\", "{", or "}".  This activates all the characters
%    (sets their catcode to active [catcode = 13]).
%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                THE abbreviate ENVIRONMENT                      %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% DEFINE COUNTERS
%
\newcounter{abr@ctr}
\newcounter{abr@level} \setcounter{abr@level}{0}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% THE abbreviate ENVIRONMENT
%
% \abbreviate{PREFIX}{ACTIVECHARS}{ACTIVECHARS}
%
\def\abbreviate#1{%
  \def\abr@prefix{#1}%      \abr@prefix := PREFIX
  \global\let\abr@tilde~%   \abr@tilde  := real tilde
  \gdef\abr@activechars{}%
  \let~\relax
  \abr@sanitize
  \abr@abbreva}

\def\abr@abbreva#1{%          %% \abr@activate  := catcode characters to active
  \gdef\abr@activate{}%       %% \abr@deactivate := make everything normal
  \gdef\abr@deactivate{}%
  \@tfor\i:=#1\do{%
    %%\typeout{Loop: i = \i}
    \xdef\abr@activate{\abr@activate\catcode`\i\active}%
    \xdef\abr@deactivate{\abr@deactivate\catcode`\i12\relax}}%
    \xdef\abr@deactivate{\abr@deactivate\noexpand\abr@unsanitize
                         \noexpand\let\noexpand~\noexpand\abr@tilde}%
   \abr@activate
   \abr@abbrevb}

\def\abr@abbrevb#1{%   % Let all active characters to \relax and 
   \@tfor\i:=#1\do{%   % let \x to \abr@getsub
     \expandafter\let\i\relax}%
   \let\x\abr@getsub}

\def\endabbreviate{%
  \expandafter\abr@defineactives\abr@activechars\do\abr@tempx
  \expandafter\global\expandafter\let\csname\abr@prefix\endcsname\abr@tempx
  \expandafter\global\expandafter\let
         \csname\abr@prefix act\endcsname\abr@activate
  \expandafter\global\expandafter\let
      \csname no\abr@prefix\endcsname\abr@deactivate}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% THE INVARIANT
%
% The following invariant is maintained in the body of the abbreviate
% environment, where def_i[foo] is the definition of (the macro
% expansion of) foo at \begingroup nesting level i.  (Nesting level 0 is
% the top.)
% 
% IF the last command processed was
%     c_0 ... c_n {val} 
% THEN Exists \cmd_1 ... \cmd_n :
%   LET X(i) == \abr@ifnextchar c_i{\cmd_i}{\csname def_i[abr@else]\endcsname}
%   IN  * \value{abr@level} = n
%       * current \begingroup nesting level = n
%       *   \csname \abr@prefix\string c_0] \endcsname  =g  IF n = 0 THEN val
%                                                                    ELSE X(1)
%       * For all i in {1, ... ,n-1} : 
%          \cmd_i =g c_i -> X(i+1)
%       * For all i in {1, ... , n} :
%          \csname def_i[abr@else]\endcsname is undefined at level 0.
% 
%       * \cmd_n =g c_n -> the right sequence to process c_0...c_n
%       * \prefix@activechars = ... c_0
% 

% \abr@addcmd{STRING}{VAL} 
%    The guts of the abbreviate environment. \x STRING {VAL} expands
%    to \abr@addcmd{STRING}{VAL}.  
%
%  BEGIN
%    abr@ctr := 0
%    Remaining := STRING
%    WHILE Remaining # empty
%    DO  \char     := Head(Remaining)
%        Remaining := Tail(Remaining)
%        IF abr@ctr < abr@level
%          THEN %%%  Do nothing
%          ELSE %%% Current string length >= previous one
%               IF abr@ctr = abr@level 
%                 THEN %% this is beginning of new string suffix
%                      IF abr@level = 0
%                        THEN %% new beginning char
%                              \abr@then :=g \abr@prefix \string\char
%                              \abr@activechars := 
%                                 \abr@activechars :o: \char
%                        ELSE %% have to clean up preceding char
%                             \abr@temp :=g \abr@else
%                             \abr@then :=g new_cs
%                             \abr@else := new_cs
%                             \gdef \csname \abr@temp\endcsname 
%                                  {\abr@ifnextch {\char}%
%                                       {\csname\abr@then\endcsname}%
%                                       {\csname\abr@else\endcsname}}
%                      FI
%                 ELSE %% We've gotten started on new suffix
%                      \abr@temp :=g \abr@then
%                      \abr@then :=g new_cs
%                      \begingroup
%                      \abr@else := new_cs
%                      IF abr@ctr = 1
%                        THEN %% previous char was first one
%                             \gdef \csname \abr@temp\endcsname
%                               {\abr@ifnextch {\char}%
%                                       {\csname\abr@then\endcsname}%
%                                       {\csname\abr@else\endcsname}}
%                        ELSE \gdef \csname \abr@temp\endcsname \lastchar
%                               {\abr@ifnextch {\char}%
%                                       {\csname\abr@then\endcsname}%
%                                       {\csname\abr@else\endcsname}}
%                      FI
%               FI
%               \prevchar := \char
%        FI
%        abr@ctr := abr@ctr + 1
%    OD
%    %% 
%    IF abr@ctr = abr@level
%      THEN %% Current string one char shorter than previous one.
%           \gdef \csname \abr@else \endcsname {VAL}
%           \endgroup
%      ELSE %% Current string of length >= previous one.
%           IF abr@ctr = 1
%             THEN %% just a one-char string
%                  \gdef\csname \abr@then \endcsname{VAL}
%             ELSE %% multi-char string
%                  \gdef\csname \abr@then \endcsname \prevchar{VAL}
%           FI
%    FI
%    abr@level = abr@ctr - 1
% END definition of \abr@addcmd

\def\abr@addcmd#1#2{%
\setcounter{abr@ctr}{0}%
\@tfor\char:=#1\do{%
  \ifnum \value{abr@ctr} < \value{abr@level}%
    \else \ifnum \value{abr@ctr} = \value{abr@level}%
              \ifnum \value{abr@level} = \z@
                 \xdef\abr@then{\abr@prefix \expandafter\string\char}
                  \xdef\abr@activechars{\abr@activechars\char}
                 %\typeout{ELSE THEN THEN, abr@then := \abr@then}
                \else  \xdef\abr@temp{\abr@else}%
                       \abr@gnewcs\abr@then
                       \abr@newcs\abr@else
                        %\typeout{ELSE THEN ELSE, abr@temp = \abr@temp}
                       \expandafter\xdef\csname\abr@temp\endcsname{%
                           \noexpand\abr@ifnextch\char%
                           {\expandafter\noexpand\csname\abr@then\endcsname}%
                           {\expandafter\noexpand\csname\abr@else\endcsname}}
              \fi
            \else  \xdef\abr@temp{\abr@then}
                   \abr@gnewcs\abr@then
                   \begingroup
                   \abr@newcs\abr@else
                   \ifnum \value{abr@ctr}=\@ne
                       %\typeout{ELSE ELSE THEN, abr@temp = \abr@temp}
                      \expandafter\xdef\csname\abr@temp\endcsname{%
                           \noexpand\abr@ifnextch\char%
                           {\expandafter\noexpand\csname\abr@then\endcsname}%
                           {\expandafter\noexpand\csname\abr@else\endcsname}}
                     \else                    
                       %\typeout{ELSE ELSE ELSE, abr@temp = \abr@temp}
                        \expandafter\expandafter\expandafter\xdef
                           \expandafter\csname\expandafter\abr@temp
                           \expandafter\endcsname\prevchar{%
                           \noexpand\abr@ifnextch\char%
                           {\expandafter\noexpand\csname\abr@then\endcsname}%
                           {\expandafter\noexpand\csname\abr@else\endcsname}}
                   \fi
          \fi
          \let\prevchar\char
  \fi
  \addtocounter{abr@ctr}{1}%
 }%
  \ifnum \value{abr@ctr} = \value{abr@level}%
    %\typeout{DONE THEN abr@else = \abr@else}
    \expandafter\gdef\csname \abr@else \endcsname{#2}%
     \endgroup
   \else \ifnum \value{abr@ctr}=\@ne
           %\typeout{DONE ELSE THEN abr@then = \abr@then}
            \expandafter\gdef\csname\abr@then\endcsname{#2}
          \else 
            %\typeout{DONE ELSE ELSE abr@then = \abr@then}
            \expandafter\abr@gdef\prevchar{\abr@then}{#2}%
          \fi
  \fi
  \setcounter{abr@level}{\value{abr@ctr}}
  \addtocounter{abr@level}{-1}} %% END definition of \abr@addcmd

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                      USEFUL COMMANDS                           %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% 
% \makeactive{CHARS} : 
%    CHARS should be a string of characters, not containing any of the
%    three characters "\", "{", or "}".  This \catcodes all the characters
%    to active (catcode 13).
%
\def\abr@makeactive#1{\catcode`#1\active}
\def\makeactive#1{\@tfor\i:=#1\do{\expandafter\abr@makeactive\i}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \ensuremath{FORMULA}
%    Typesets FORMULA in math mode, regardless of current mode.
%
\def\ensuremath#1{\relax\ifmmode #1\else $#1$\fi}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \noTeXmath
% \TeXmath   
%    The \noTeXmath causes TeX to use ordinary italic instead of math
%    italic in math mode.  The \TeXmath command reverts to TeX's normal
%    behavior.  (Modified 10 Aug to work with arbitrary \itfam.)
%    

\newcommand{\abr@c}{\c@abr@ctr\advance\c@abr@ctr\@ne}

% Let it work with LaTeX2e's native mode:
% D. Roegel, 29/8/1994
\ifx\documentclass\undefined
\else
  \DeclareSymbolFont{tlaitalics}{\encodingdefault}{cmr}{m}{it}
  \let\itfam\symtlaitalics
\fi

\newcommand{\noTeXmath}{%
\c@abr@ctr=\itfam
\multiply\c@abr@ctr"100\relax
\advance\c@abr@ctr "7061\relax
\mathcode`a=\abr@c
\mathcode`b=\abr@c
\mathcode`c=\abr@c
\mathcode`d=\abr@c
\mathcode`e=\abr@c
\mathcode`f=\abr@c
\mathcode`g=\abr@c
\mathcode`h=\abr@c
\mathcode`i=\abr@c
\mathcode`j=\abr@c
\mathcode`k=\abr@c
\mathcode`l=\abr@c
\mathcode`m=\abr@c
\mathcode`n=\abr@c
\mathcode`o=\abr@c
\mathcode`p=\abr@c
\mathcode`q=\abr@c
\mathcode`r=\abr@c
\mathcode`s=\abr@c
\mathcode`t=\abr@c
\mathcode`u=\abr@c
\mathcode`v=\abr@c
\mathcode`w=\abr@c
\mathcode`x=\abr@c
\mathcode`y=\abr@c
\mathcode`z=\abr@c
\c@abr@ctr=\itfam
\multiply\c@abr@ctr"100\relax
\advance\c@abr@ctr "7041\relax
\mathcode`A=\abr@c
\mathcode`B=\abr@c
\mathcode`C=\abr@c
\mathcode`D=\abr@c
\mathcode`E=\abr@c
\mathcode`F=\abr@c
\mathcode`G=\abr@c
\mathcode`H=\abr@c
\mathcode`I=\abr@c
\mathcode`J=\abr@c
\mathcode`K=\abr@c
\mathcode`L=\abr@c
\mathcode`M=\abr@c
\mathcode`N=\abr@c
\mathcode`O=\abr@c
\mathcode`P=\abr@c
\mathcode`Q=\abr@c
\mathcode`R=\abr@c
\mathcode`S=\abr@c
\mathcode`T=\abr@c
\mathcode`U=\abr@c
\mathcode`V=\abr@c
\mathcode`W=\abr@c
\mathcode`X=\abr@c
\mathcode`Y=\abr@c
\mathcode`Z=\abr@c}

\newcommand{\TeXmath}{%
\mathcode`a="7161%
\mathcode`b="7162%
\mathcode`c="7163%
\mathcode`d="7164%
\mathcode`e="7165%
\mathcode`f="7166%
\mathcode`g="7167%
\mathcode`h="7168%
\mathcode`i="7169%
\mathcode`j="716A%
\mathcode`k="716B%
\mathcode`l="716C%
\mathcode`m="716D%
\mathcode`n="716E%
\mathcode`o="716F%
\mathcode`p="7170%
\mathcode`q="7171%
\mathcode`r="7172%
\mathcode`s="7173%
\mathcode`t="7174%
\mathcode`u="7175%
\mathcode`v="7176%
\mathcode`w="7177%
\mathcode`x="7178%
\mathcode`y="7179%
\mathcode`z="717A%
\mathcode`A="7141%
\mathcode`B="7142%
\mathcode`C="7143%
\mathcode`D="7144%
\mathcode`E="7145%
\mathcode`F="7146%
\mathcode`G="7147%
\mathcode`H="7148%
\mathcode`I="7149%
\mathcode`J="714A%
\mathcode`K="714B%
\mathcode`L="714C%
\mathcode`M="714D%
\mathcode`N="714E%
\mathcode`O="714F%
\mathcode`P="7150%
\mathcode`Q="7151%
\mathcode`R="7152%
\mathcode`S="7153%
\mathcode`T="7154%
\mathcode`U="7155%
\mathcode`V="7156%
\mathcode`W="7157%
\mathcode`X="7158%
\mathcode`Y="7159%
\mathcode`Z="715A}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                      AUXILIARY COMMANDS                        %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \abr@newcs\CMD   
% \abr@gnewcs\CMD :
%    Defines \CMD to be a new string prefixed with \abr@prefix.  
%    The definition is local with \abr@newcs, and global with
%    \abr@gnewcs
%
\newcount\abr@csctr
\def\abr@newcs#1{\global\advance\abr@csctr\@ne
                 \edef#1{\abr@prefix\the\abr@csctr}}
\def\abr@gnewcs#1{\global\advance\abr@csctr\@ne
                 \xdef#1{\abr@prefix\the\abr@csctr}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \abr@sanitize   
% \abr@unsanitize 
%    "sanitizing" catcodes $ & # ^ _ %  to "other".
%    "unsanitizing" catcodes these characters back to normal.
%
\def\abr@mkother#1{\catcode`#112\relax}
\begingroup
\abr@mkother$\abr@mkother&\abr@mkother#\abr@mkother^\abr@mkother_
\catcode`\%12\relax
\gdef\abr@sanitize{\abr@mkother$\abr@mkother&\abr@mkother#\abr@mkother
                 ^\abr@mkother_\abr@mkother%}
\gdef\abr@unsanitize{\catcode`$3\catcode`&4\catcode`#6\catcode`^7\catcode
                     `_8\catcode`%14\relax}
\endgroup

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \abr@gdef CHAR{STRING}{DEF} 
%    CHAR must be a character.  
%    This command does \gdef\STRING CHAR{DEF}
%
\def\abr@gdef#1#2#3{\expandafter\gdef\csname#2\endcsname#1{#3}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \abr@defineactive{CHARS}\CS
%    CHARS must be a string of active characters.
%    Defines \CS to do a \let c=\csname \abr@prefix\string c,
%    For all characters c in the string CHARS.

\def\abr@defineactive#1#2{\gdef#2{}%
  \let\abr@temp\relax
  \@tfor\char:=#1\do{%
    \xdef#2{#2\expandafter\abr@temp\char}}%
    \def\abr@temp##1{%
        \noexpand\let\noexpand##1\expandafter\noexpand
        \csname\abr@prefix\string##1\endcsname}%
  %\show#2
   \xdef#2{#2}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \abr@getsub STRING \do {VAL}
%   Expands to \abr@addcmd{STRING}{VAL}, where
%   STRING is evaluated with the special characters activated,
%   and VAL is evalued with them deactivated.  
%   It assumes that the characters are activated, and it
%   leaves them activated.
%
\def\abr@getsub#1 {\def\abr@temp{#1}\abr@deactivate\abr@getsuba}
\def\abr@getsuba#1{%
  \abr@activate 
  \let~\relax
  \expandafter\abr@addcmdx\abr@temp\do{#1}}
%\def\abr@addcmdx#1\do#2{\abr@addcmd{#1}{#2\relax}}  
\def\abr@addcmdx#1\do#2{\abr@addcmd{#1}{#2}}  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \abr@ifnextch{c}{TRUE}{FALSE}
%   If the immediately following character is c, then TRUE, else FALSE.
%   This should be at the end of whatever macro is looking ahead.

\def\abr@ifnextch#1#2#3{\let\@tempe =#1\def\@tempa{#2}\def\@tempb{#3}\futurelet
    \@tempc\abr@ifnsnch}
\def\abr@ifnsnch{\ifx 
   \@tempc \@tempe\let\@tempd\@tempa\else\let\@tempd\@tempb\fi \@tempd}

% \abr@defineactives\do\CS
%    CHARS must be a string of active characters.
%    Defines \CS to do \abr@activate followed by a 
%       \let c=\csname \abr@prefix\string c, 
%    for all characters c in the string.
%
\def\abr@defineactives#1\do#2{\gdef#2{}%
  \let\abr@temp\relax
  \@tfor\char:=#1\do{%
    \xdef#2{#2\expandafter\abr@temp\char}}%
    \def\abr@temp##1{%
        \noexpand\let\noexpand##1\expandafter\noexpand
        \csname\abr@prefix\string##1\endcsname}%
   \xdef#2{\abr@activate#2}}

%%%%%%%%%%%%%%%%%%%%%%%
%  DEBUGGING
%
%  \@show{FOO} : \show\FOO
\newcommand{\@show}[1]{\expandafter\show\csname#1\endcsname}