TeXで対角成分のみの行列を簡単に書く

diagmatrix.scm

; -*- coding: euc-jp -*-

; こういうコードを TeX で書きたい. (TeX に移植するので Lisp としては少し不自然.)

(use srfi-1)
(use srfi-11)
(use srfi-13)

(define (diagmatrix ufill lfill diagonals)
  (define (dots? str)
    (rxmatch #/^ *(\.\.\.|\\dots)$/ str))
  (define (mask-with e b replacement)
    (if b
        replacement
        e))
  (define (make-row d i b right-cdots left-cdots mask right-line left-line right-dots-line left-dots-line)
    (let-values (((left-mask r) (split-at mask i)))
      (let1 right-mask (cdr r)
        (if b
            `(,@(map (cut mask-with <> <> "") left-dots-line left-mask)
              "\\ddots"
              ,@(map (cut mask-with <> <> "") right-dots-line right-mask))
            `(,@(map (cut mask-with <> <> left-cdots) left-line left-mask)
              ,d
              ,@(map (cut mask-with <> <> right-cdots) right-line right-mask))))))
  (let* ((r (if (string-null? ufill)
                '("" . "")
                '("\\cdots" . "\\vdots")))
         (right-cdots (car r))
         (right-vdots (cdr r))
         (l (if (string-null? lfill)
                '("" . "")
                '("\\cdots" . "\\vdots")))
         (left-cdots (car l))
         (left-vdots (cdr l))
         (mask (map dots? diagonals))
         (size (length diagonals))
         (indice (iota size 0 1))
         (right-line (make-list size ufill))
         (left-line (make-list size lfill))
         (right-dots-line (make-list size right-vdots))
         (left-dots-line (make-list size left-vdots))
         ; row は実際には行列が入る
         (row (map (cut make-row <> <> <>
                        right-cdots left-cdots mask right-line left-line right-dots-line left-dots-line)
                   diagonals indice mask)))
    row))

(diagmatrix "*" "0" '("A" "B" "..." "D"))
; => (("A" #0="*" #1="\\cdots" #0#)
;     (#2="0" "B" #1# #0#)
;     (#3="\\vdots" #3# "\\ddots" "\\vdots")
;     (#2# #2# "\\cdots" "D"))

; 見難いが, (2,4)-成分と(4,2)-成分が空になっている
(format "~s" (diagmatrix "0" "0" '("a_1" "..." "a_i" "..." "a_n")))
; => "((a_1 \\cdots 0 \\cdots 0)\
;     (\\vdots \\ddots \\vdots  \\vdots)\
;     (0 \\cdots a_i \\cdots 0)\
;     (\\vdots  \\vdots \\ddots \\vdots)\
;     (0 \\cdots 0 \\cdots a_n))"
(diagmatrix "0" "0" '("a_1" "..." "a_i" "..." "a_n"))
; => (("a_1" #0="\\cdots" #1="0" #0# #1#)
;     (#2="\\vdots" #3="\\ddots" #4="\\vdots" "" #4#)
;     (#5="0" #6="\\cdots" "a_i" #0# #1#)
;     (#2# "" #2# #3# #4#) (#5# #6# #5# #6# "a_n"))

diagmatrix.tex

% -*- coding: euc-jp -*-

\documentclass[10pt,draft]{amsart}

\usepackage{amsmath,amssymb}
%\usepackage{kmathmacro}
\usepackage{mwmlist}


\makeatletter



\newcount\mwm@@counter
\newif\if@mwm

\def\mwm@is@true#1{#1}
\let\mwm@true\@mwmtrue
\let\mwm@false\@mwmfalse



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\diagmatrix{% [ufill,lfill] CSL ;
% Diagonal matrix whose diagonal elements are CSL, upper triangle filled with ufill,
% lower with lfill. In CSL, the strings "..." and "\dots" following spaces have special meaning.
% Matrix elements of rows and columns <dots> exist are replaced with appropriate dots
% as the element see how many <dots> in the diagonal. For example, if an element sees
% <dots> vertically and no <dots> horizontally, it is replaced with \cdots .
  \begingroup
%  \def\mwm@dm@@upper@filling{}%
%  \def\mwm@dm@@lower@filling{}%
  \@ifnextchar[ \mwm@dm@bite@bracket {\mwm@dm@bite@bracket[,]}%
}
    \def\mwm@dm@bite@bracket[#1]{%
      \mwm@dm@bite@bracket@aux#1,\@nil
      \mwm@dm@main
    }
        \def\mwm@dm@bite@bracket@aux#1,#2\@nil{%
          \def\@tempa{#2}%
          \ifx\@tempa\@empty
            \def\mwm@dm@@upper@filling{#1}%
            \def\mwm@dm@@lower@filling{#1}%
          \else
            \mwm@dm@bite@bracket@aux@two#1,#2\@nil
          \fi
        }
            \def\mwm@dm@bite@bracket@aux@two#1,#2,\@nil{%
              \def\mwm@dm@@upper@filling{#1}%
              \def\mwm@dm@@lower@filling{#2}%
            }
    \def\mwm@dm@main#1;{%
      \let\mwm@dm@@ddots\ddots
      \ifx\mwm@dm@@upper@filling\@empty
        \let\mwm@dm@@right@cdots\relax
        \let\mwm@dm@@right@vdots\relax
      \else
        \let\mwm@dm@@right@cdots\cdots
        \let\mwm@dm@@right@vdots\vdots
      \fi
      \ifx\mwm@dm@@lower@filling\@empty
        \let\mwm@dm@@left@cdots\relax
        \let\mwm@dm@@left@vdots\relax
      \else
        \let\mwm@dm@@left@cdots\cdots
        \let\mwm@dm@@left@vdots\vdots
      \fi
      \mwml@set@list@from@csl\mwm@dm@@diagonals{#1}%
      \mwm@dm@make@mask% make a mask, contained in \mwm@dm@@mask
      \mwml@set@length\mwm@dm@@size\mwm@dm@@diagonals
      % note that the below is incompatible with index of row of matrix
      \mwml@set@iota\mwm@dm@@iota\mwm@dm@@size{0}{1}%
      \mwml@set@make@list\mwm@dm@@right@line\mwm@dm@@size\mwm@dm@@upper@filling
      \mwml@set@make@list\mwm@dm@@left@line\mwm@dm@@size\mwm@dm@@lower@filling
      \mwml@set@make@list\mwm@dm@@left@dots@line\mwm@dm@@size{\mwm@dm@@left@vdots}%
      \mwml@set@make@list\mwm@dm@@right@dots@line\mwm@dm@@size{\mwm@dm@@right@vdots}%
      % A variable \mwm@dm@@row is used to return value by \mwm@dm@make@row .
      \mwml@set@map@three\mwm@dm@@row\mwm@dm@make@row\mwm@dm@@diagonals\mwm@dm@@iota\mwm@dm@@mask
      % But now it contains the matrix we wanted.
      \mwml@output@matrix@with@pmatrix\mwm@dm@@row
      \endgroup
    }
        \def\mwm@dm@make@mask{%
          \mwml@set@map\@tempa\mwm@dm@make@mask@aux\mwm@dm@@diagonals
          \let\mwm@dm@@mask\@tempa
        }
            \def\mwm@dm@make@mask@aux#1{%
              \mwm@dm@is@dots{#1}%
              \if@mwm \def\@tempa{\mwm@true}\else \def\@tempa{\mwm@false}\fi
            }
                \def\mwm@dm@is@dots#1{%
                  \@mwmfalse
                  \mwm@dm@is@dots@a#1...\@nil
                  \mwm@dm@is@dots@b#1\dots\@nil
                }
                    \def\mwm@dm@is@dots@a#1...#2\@nil{%
                      \def\@tempa{#2}%
                      \ifx\@tempa\@empty \else \@mwmtrue \fi
                    }
                    \def\mwm@dm@is@dots@b#1\dots#2\@nil{%
                      \def\@tempa{#2}%
                      \ifx\@tempa\@empty \else \@mwmtrue \fi
                    }
        \def\mwm@dm@make@row#1#2#3{% elem -> index -> boolian -> nothing, row in \mwm@dm@@row
          % \mwm@dm@@row will be `(,@\mwm@dm@@left@row ,\@tempb ,@\mwm@dm@@right@row)
          \mwml@set@take@nth@drop\mwm@dm@@left@mask\@tempa\mwm@dm@@right@mask\mwm@dm@@mask{#2}%
          \mwm@is@true{#3}\if@mwm% if #1 is dots
            \mwml@set@map@two\@tempa\mwm@dm@mask@empty@aux\mwm@dm@@left@dots@line\mwm@dm@@left@mask
            \let\mwm@dm@@left@row\@tempa
            \mwml@set@map@two\@tempa\mwm@dm@mask@empty@aux\mwm@dm@@right@dots@line\mwm@dm@@right@mask
            \let\mwm@dm@@right@row\@tempa
            \def\@tempb{\mwm@dm@@ddots}%
          \else%                   if #1 is not dots
            \mwml@set@map@two\@tempa\mwm@dm@mask@left@aux\mwm@dm@@left@line\mwm@dm@@left@mask
            \let\mwm@dm@@left@row\@tempa
            \mwml@set@map@two\@tempa\mwm@dm@mask@right@aux\mwm@dm@@right@line\mwm@dm@@right@mask
            \let\mwm@dm@@right@row\@tempa
            \def\@tempb{#1}%
          \fi
          \mwm@exnr\mwml@push\@tempb\mwm@dm@@right@row
          \mwml@set@append\mwm@dm@@row\mwm@dm@@left@row\mwm@dm@@right@row
        }
            \def\mwm@dm@mask@left@aux#1#2{%
              \mwm@is@true{#2}\if@mwm
                \def\@tempa{\mwm@dm@@left@cdots}%
              \else
                \def\@tempa{#1}%
              \fi
            }
            \def\mwm@dm@mask@right@aux#1#2{%
              \mwm@is@true{#2}\if@mwm
                \def\@tempa{\mwm@dm@@right@cdots}%
              \else
                \def\@tempa{#1}%
              \fi
            }
            \def\mwm@dm@mask@empty@aux#1#2{%
              \mwm@is@true{#2}\if@mwm
                \def\@tempa{}%
              \else
                \def\@tempa{#1}%
              \fi
            }



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% document
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}



\fbox{test diagmatrix}

\[
  \diagmatrix A,B,C,D ;
\]
\[
  \diagmatrix A,B,...,D ;
\]
\[
  \diagmatrix[0] A,B,...,D ;
\]
\[
  \diagmatrix[0,] A,B,...,D ;
\]
\[
  \diagmatrix[,0] A,B,...,D ;
\]
\[
  \diagmatrix[*,0] A, B, ..., D ;
\]
\[
  \diagmatrix[*,0] a_1, a_2, ..., a_i, ..., a_{n-1}, a_n ;
\]

% test for non-robust elements
% \[
%   \diagmatrix[{\map from X to Y ;},\chi]
%     {\H_{Gal}^1(\aGal_K, A)}, {\H_{et}^1(X_\Kbar, \Ql)}, ..., {\Hom_{cont}(G, A)} ;
% \]



\end{document}

\makeatother

mwmlist.sty

% -*- coding: euc-jp -*-

%%% mwmu -- utilities for mwmath

%\def\mwm@exr#1#2{%
%  \expandafter#1\expandafter{#2}%
%}
%\def\mwm@enr#1#2{%
%  #1{#2}%
%}
%\def\mwm@exxr#1#2#3{%
%  \def\mwm@er@aux##1{\mwm@exr{#1}{#2}{##1}}%
%  \mwm@exr\mwm@er@aux{#3}%
%}
%\def\mwm@exnr#1#2#3{%
%  \mwm@exr{#1}{#2}{#3}%
%}
%\def\mwm@enxr#1#2#3{%
%  \def\mwm@er@aux##1{#1{#2}{##1}}%
%  \mwm@exr\mwm@er@aux{#3}%
%}
%\def\mwm@ennr#1#2#3{%
%  #1{#2}{#3}%
%}
%\def\mwm@exxxr#1#2#3#4{%
%  \def\mwm@er@aux##1{\mwm@exxr{#1}{#2}{#3}{##1}}%
%  \mwm@exr\mwm@er@aux{#4}%
%}
%\def\mwm@exxnr#1#2#3#4{%
%  \mwm@exxr{#1}{#2}{#3}{#4}%
%}
%\def\mwm@exnxr#1#2#3#4{%
%  \def\mwm@er@aux##1{\mwm@exnr{#1}{#2}{#3}{##1}}%
%  \mwm@exr\mwm@er@aux{#4}%
%}
%\def\mwm@exnnr#1#2#3#4{%
%  \mwm@exnr{#1}{#2}{#3}{#4}%
%}
%\def\mwm@enxxr#1#2#3#4{%
%  \def\mwm@er@aux##1{\mwm@enxr{#1}{#2}{#3}{##1}}%
%  \mwm@exr\mwm@er@aux{#4}%
%}
%\def\mwm@enxnr#1#2#3#4{%
%  \mwm@enxr{#1}{#2}{#3}{#4}%
%}
%\def\mwm@ennxr#1#2#3#4{%
%  \def\mwm@er@aux##1{#1{#2}{#3}{##1}}%
%  \mwm@exr\mwm@er@aux{#4}%
%}
%\def\mwm@ennnr#1#2#3#4{%
%  #1{#2}{#3}{#4}%
%}

\def\mwm@exr#1#2{%
  \expandafter#1\expandafter{#2}%
}
\let\mwm@enr\relax

\def\mwm@exxr#1#2#3{%
  \def\mwm@er@aux##1{\mwm@exr#1{#2}{##1}}%
  \mwm@exr\mwm@er@aux{#3}%
}
\let\mwm@exnr\mwm@exr
\def\mwm@enxr#1#2#3{%
  \def\mwm@er@aux##1{#1{#2}{##1}}%
  \mwm@exr\mwm@er@aux{#3}%
}
\let\mwm@ennr\relax

\def\mwm@exxxr#1#2#3#4{%
  \def\mwm@er@aux##1{\mwm@exxr#1{#2}{#3}{##1}}%
  \mwm@exr\mwm@er@aux{#4}%
}
\let\mwm@exxnr\mwm@exxr
\def\mwm@exnxr#1#2#3#4{%
  \def\mwm@er@aux##1{\mwm@exnr#1{#2}{#3}{##1}}%
  \mwm@exr\mwm@er@aux{#4}%
}
\let\mwm@exnnr\mwm@exr
\def\mwm@enxxr#1#2#3#4{%
  \def\mwm@er@aux##1{\mwm@enxr#1{#2}{#3}{##1}}%
  \mwm@exr\mwm@er@aux{#4}%
}
\let\mwm@enxnr\mwm@enxr
\def\mwm@ennxr#1#2#3#4{%
  \def\mwm@er@aux##1{#1{#2}{#3}{##1}}%
  \mwm@exr\mwm@er@aux{#4}%
}
\let\mwm@ennnr\relax

\def\mwm@exxxxr#1#2#3#4#5{%
  \def\mwm@er@aux##1{\mwm@exxxr#1{#2}{#3}{#4}{##1}}%
  \mwm@exr\mwm@er@aux{#5}%
}
\let\mwm@exxxnr\mwm@exxxr
\def\mwm@exxnxr#1#2#3#4#5{%
  \def\mwm@er@aux##1{\mwm@exxnr#1{#2}{#3}{#4}{##1}}%
  \mwm@exr\mwm@er@aux{#5}%
}
\let\mwm@exxnnr\mwm@exxr
\def\mwm@exnxxr#1#2#3#4#5{%
  \def\mwm@er@aux##1{\mwm@exnxr#1{#2}{#3}{#4}{##1}}%
  \mwm@exr\mwm@er@aux{#5}%
}
\let\mwm@exnxnr\mwm@exnxr
\def\mwm@exnnxr#1#2#3#4#5{%
  \def\mwm@er@aux##1{\mwm@exnnr#1{#2}{#3}{#4}{##1}}%
  \mwm@exr\mwm@er@aux{#5}%
}
\let\mwm@exnnnr\mwm@exr
\def\mwm@enxxxr#1#2#3#4#5{%
  \def\mwm@er@aux##1{\mwm@enxxr#1{#2}{#3}{#4}{##1}}%
  \mwm@exr\mwm@er@aux{#5}%
}
\let\mwm@enxxnr\mwm@enxxr
\def\mwm@enxnxr#1#2#3#4#5{%
  \def\mwm@er@aux##1{\mwm@enxnr#1{#2}{#3}{#4}{##1}}%
  \mwm@exr\mwm@er@aux{#5}%
}
\let\mwm@enxnnr\mwm@enxr
\def\mwm@ennxxr#1#2#3#4#5{%
  \def\mwm@er@aux##1{\mwm@ennxr#1{#2}{#3}{#4}{##1}}%
  \mwm@exr\mwm@er@aux{#5}%
}
\let\mwm@ennxnr\mwm@ennxr
\def\mwm@ennnxr#1#2#3#4#5{%
  \def\mwm@er@aux##1{#1{#2}{#3}{#4}{##1}}%
  \mwm@exr\mwm@er@aux{#5}%
}
\let\mwm@ennnnr\relax






\def\mwm@in@group@with@nonlocal#1#2#3{% :: cs -> cs -> block -> nothing
  \begingroup
  #3%
  \global\let\mwm@in@group@with@nonlocal@@a#1%
  \endgroup
  \let#2\mwm@in@group@with@nonlocal@@a
}
\def\mwm@in@group@with@nonlocal@two#1#2#3#4#5{% :: cs -> cs -> cs -> cs -> block -> nothing
  \begingroup
  #5%
  \global\let\mwm@in@group@with@nonlocal@@a#1%
  \global\let\mwm@in@group@with@nonlocal@@b#3%
  \endgroup
  \let#2\mwm@in@group@with@nonlocal@@a
  \let#4\mwm@in@group@with@nonlocal@@b
}
\def\mwm@in@group@with@nonlocal@three#1#2#3#4#5#6#7{% :: cs -> cs -> cs -> cs -> cs -> cs -> block -> nothing
  \begingroup
  #7%
  \global\let\mwm@in@group@with@nonlocal@@a#1%
  \global\let\mwm@in@group@with@nonlocal@@b#3%
  \global\let\mwm@in@group@with@nonlocal@@c#5%
  \endgroup
  \let#2\mwm@in@group@with@nonlocal@@a
  \let#4\mwm@in@group@with@nonlocal@@b
  \let#6\mwm@in@group@with@nonlocal@@c
}
    \def\mwm@in@group@with@nonlocal@@a{}
    \def\mwm@in@group@with@nonlocal@@b{}
    \def\mwm@in@group@with@nonlocal@@c{}

\def\mwm@endgroup@with@nonlocal#1#2{% :: cs -> cs -> nothing
  \global\let\mwm@in@group@with@nonlocal@@a#1%
  \endgroup
  \let#2\mwm@in@group@with@nonlocal@@a
}





%%% mwmlist -- List processing library for mwmath

\newcount\mwml@@counter
\newcount\mwml@@countera
\newif\if@mwml
%\def\mwml@false{\@mwml@false}

%% Local variables
\def\mwml@tempa{}
\def\mwml@tempb{}
\def\mwml@tempc{}
\def\mwml@tempd{}
%% Non-local variables
\def\mwml@tempflasque{}
%% Temporary local variables for arguments
% One may only use these variables to contain arguments, e.g. #1, to avoid overwritting them,
% which causes a problem in the case that one of arguments is a control sequence like \mwml@tempa .
% It is not allowed to pass these variables as control sequence. Expand them.
\def\mwml@arga{}
\def\mwml@argb{}
\def\mwml@argc{}
\def\mwml@argd{}

%% Data constructers
% LIST := \mwml@NULL | \mwml@CONS{ELEM}{LIST}
% ELEM := anything
\def\mwml@CONS#1#2{}
\def\mwml@NULL{}



%%% Logic
% implemented: is@true is@false not and or not@and not@or

\def\mwml@is@true#1{% :: boolian -> nothing
  \mwml@not{\mwml@is@false{#1}}%
}
\def\mwml@is@false#1{% :: boolian -> nothing
  \ifx#1\mwml@false
    \@mwmltrue
  \else
    \@mwmlfalse
  \fi
}

\def\mwml@not#1{% (not #1)
  #1%
  \if@mwml
    \@mwmlfalse
  \else
    \@mwmltrue
  \fi
}
\def\mwml@and#1#2{% (and #1 #2)
  #1%
  \if@mwml
    #2%
  \else
    \@mwmlfalse
  \fi
}
\def\mwml@or#1#2{% (or #1 #2)
  #1%
  \if@mwml
  \else
    #2%
  \fi
}
\def\mwml@not@and#1#2{% (not (and #1 #2))
  \mwml@not{\mwml@and{#1}{#2}}%
}
\def\mwml@not@or#1#2{% (not (or #1 #2))
  \mwml@not{\mwml@or{#1}{#2}}%
}



%%% Auxiliary macro
\def\mwml@with@freezed@list#1{%
  \let\mwml@CONS@before\mwml@CONS
  \let\mwml@NULL@before\mwml@NULL
  \let\mwml@CONS\relax
  \let\mwml@NULL\relax
  #1%
  \let\mwml@CONS\mwml@CONS@before
  \let\mwml@NULL\mwml@NULL@before
}


%%% Fundamentals
% \mwml@set@null \mwml@set@copy \mwml@apply

\def\mwml@set@null#1{%
  \def#1{\mwml@NULL}%
}
\def\mwml@set@copy#1#2{%
% Bind copy of #2 to #1
  \mwm@in@group@with@nonlocal#1#1{%
    \mwml@with@freezed@list{%
      \toks2\expandafter{#2}%
      \edef#1{\the\toks2}%
    }%
  }%
}
\def\mwml@apply#1#2{% :: proc -> [a] -> nothing, apply proc to [a]
  \mwml@set@fold\mwml@tempflasque\mwml@apply@kons{}{#2}%
  \expandafter#1\mwml@tempflasque
}
    \def\mwml@apply@kons#1#2{%
      \toks1{#1}%
      \toks2{{#2}}%
      \edef\mwml@tempflasque{\the\toks1 \the\toks2}%
    }



%%% Auxiliary macnros with side effect
\def\mwml@push#1#2{%
  \mwml@set@cons#2{#1}{#2}%
}
\def\mwml@drop@one#1{%
  \mwml@set@cdr#1#1%
}



%%% Constructors
% implemented: cons make-list iota

% \def\mwml@set@cons#1#2#3{%
% % Bind cons of #2 and #3 to #1
%   \mwml@with@freezed@list{%
%     \edef#1{\mwml@CONS{#2}{#3}}%
%   }%
% }
\def\mwml@set@cons#1#2#3{%
% Bind cons of #2 and #3 to #1
  \mwm@in@group@with@nonlocal#1#1{%
    \mwml@with@freezed@list{%
      \toks2{#2}%
      \toks3\expandafter{#3}%
      \edef#1{\mwml@CONS{\the\toks2}{\the\toks3}}%
    }%
  }%
}

\def\mwml@set@make@list#1#2#3{% :: cs -> length -> a -> nothing, [a] in cs
  \mwm@in@group@with@nonlocal\mwml@tempa#1{%
    \mwml@@counter=#2
    \mwml@set@copy\mwml@argc{#3}%
    \mwml@set@null\mwml@tempa
    \ifnum\mwml@@counter>0
      \loop
        \mwm@exnr\mwml@push\mwml@argc\mwml@tempa
        \advance \mwml@@counter by -1
      \ifnum\mwml@@counter>0 \repeat
    \fi
  }%
}

\def\mwml@set@iota#1#2#3#4{% :: cs -> count -> start -> step -> nothing, [a] in cs
  \mwm@in@group@with@nonlocal\mwml@tempa#1{%
    \mwml@@counter=#2\relax% count
    \mwml@@countera=#3\relax% start
    \mwml@set@null\mwml@tempa
    \ifnum\mwml@@counter>0
      \loop
        \mwm@exnr\mwml@push{\the\mwml@@countera}\mwml@tempa
        \advance \mwml@@counter by -1
        \advance \mwml@@countera by #4
      \ifnum\mwml@@counter>0 \repeat
    \fi
    \mwml@reverse\mwml@tempa
  }%
}



%%% Predicates
% implemented: is-null eq-nth test-nth

\def\mwml@is@null#1{%
  \let\mwml@NULL@before\mwml@NULL
  \let\mwml@CONS@before\mwml@CONS
  \let\mwml@NULL\@mwmltrue
  \let\mwml@CONS\mwml@is@null@cons
  #1%
  \let\mwml@NULL\mwml@NULL@before
  \let\mwml@CONS\mwml@CONS@before
}
    \def\mwml@is@null@cons#1#2{%
      \@mwmlfalse
    }

\def\mwml@eq@nth#1#2#3{% :: a -> i -> [a] -> nothing
  \mwml@set@list@ref\mwml@tempflasque{#3}{#2}%
  \def\@tempa{#1}%
  \ifx\@tempa\mwml@tempflasque
    \@mwmltrue
  \else
    \@mwmlfalse
  \fi
}

\def\mwml@test@nth#1#2#3{% :: (a -> nothing, predicate) -> i -> [a] -> nothing
  \mwml@set@list@ref\@tempa{#3}{#2}%
  #1\@tempa
}



%%% Selectors
% implemented: car cdr cadr caddr cadddr list-ref
%              take drop split-at
% take/nth/drop

% \def\mwml@set@car#1#2{%
% % Bind car of #2 to #1
%   \begingroup
%   \def\mwml@CONS##1##2{\def#1{##1}}%
%   \let\mwml@NULL\undefined
%   #2%
% %  \mwm@endgroup@with@nonlocal#1#1
%   \global\let\mwml@result#1
%   \endgroup
%   \let#1\mwml@result
% }
% \def\mwml@set@cdr#1#2{%
% % Bind cdr of #2 to #1
%   \begingroup
%   \def\mwml@CONS##1##2{\def#1{##2}}%
%   \let\mwml@NULL\undefined
%   #2%
%   \global\let\mwml@result#1
%   \endgroup
%   \let#1\mwml@result
% }
\def\mwml@set@car#1#2{%
% Bind car of #2 to #1
  \mwm@in@group@with@nonlocal#1#1{%
    \def\mwml@CONS##1##2{\def#1{##1}}%
    \let\mwml@NULL\undefined
    #2%
  }%
}
\def\mwml@set@cdr#1#2{%
% Bind cdr of #2 to #1
  \mwm@in@group@with@nonlocal#1#1{%
    \def\mwml@CONS##1##2{\def#1{##2}}%
    \let\mwml@NULL\undefined
    #2%
  }%
}
\def\mwml@set@cadr#1#2{\mwml@set@list@ref{#1}{#2}{1}}
\def\mwml@set@caddr#1#2{\mwml@set@list@ref{#1}{#2}{2}}
\def\mwml@set@cadddr#1#2{\mwml@set@list@ref{#1}{#2}{3}}

\def\mwml@set@list@ref#1#2#3{% :: cs -> [a] -> i -> a
% imported from srfi-1
  \mwm@in@group@with@nonlocal\mwml@tempa#1{%
    \mwml@@counter=#3
    \let\mwml@NULL\undefined
    \let\mwml@CONS\mwml@set@list@ref@cons
    #2%
  }%
}
    \def\mwml@set@list@ref@cons#1#2{%
%      \ifnum\mwml@@counter=0
%        \def\mwml@tempa{#1}%
%        \let\mwml@CONS\@gobbletwo
%        \let\mwml@NULL\relax
%      \else
%        \advance \mwml@@counter by -1
%      \fi
%      #2%
      \ifnum\mwml@@counter=0
        \def\mwml@tempa{#1}%
      \else
        \advance \mwml@@counter by -1
        #2%
      \fi
    }

\def\mwml@set@take#1#2#3{% cs -> [a] -> index -> nothing, [a] in cs
  \mwm@in@group@with@nonlocal#1#1{%
    \mwml@set@split@at#1\mwm@devnull{#2}{#3}%
  }%
}
\def\mwml@set@drop#1#2#3{% cs -> [a] -> index -> nothing
  \mwm@in@group@with@nonlocal#1#1{%
    \mwml@set@split@at\mwm@devnull#1{#2}{#3}%
  }%
}
\def\mwml@set@split@at#1#2#3#4{%
% :: cs-take -> cs-drop -> [a] -> index -> nothing, [a] in cs-take, [a] in cs-drop
% return (take x i), (drop x i)
  \mwm@in@group@with@nonlocal@two\mwml@tempa#1\mwml@tempb#2{%
    \mwml@set@copy\mwml@argc{#3}%
    \mwml@set@null\mwml@tempa
    \mwml@@counter=0
    \mwml@@countera=#4
    \ifnum\mwml@@countera=0
      \let\mwml@tempb\mwml@argc
    \else
      \let\mwml@NULL\undefined
      \let\mwml@CONS\mwml@set@split@at@cons
      \mwml@argc
    \fi
    \mwml@reverse\mwml@tempa
  }%
}
    \def\mwml@set@split@at@cons#1#2{%
      \mwml@push{#1}\mwml@tempa
      \advance \mwml@@counter by 1
      \ifnum\mwml@@counter=\mwml@@countera
        \def\mwml@tempb{#2}%
      \else
        #2%
      \fi
    }


\def\mwml@set@take@nth@drop#1#2#3#4#5{% :: cs-take -> cs-nth -> cs-drop -> [a] -> index -> nothing,
% [a] in cs-take, a in cs-nth, [a] in cs-drop
% return (take x i), (nth i x), (drop x (+ i 1))
  \mwm@in@group@with@nonlocal@three\mwml@tempa#1#2#2#3#3{%
    \mwm@ennxnr\mwml@set@split@at\mwml@tempa\mwml@tempb{#4}{#5}%
    \mwml@set@car#2\mwml@tempb
    \mwml@set@cdr#3\mwml@tempb
  }%
}


%%% Selectors with side effect
% Do not use them, they often causes bugs.
\def\mwml@car#1{%
  \mwml@set@car\mwml@tempa{#1}%
  \mwml@tempa
}
\def\mwml@cadr#1{\mwml@list@ref{#1}{1}}
\def\mwml@caddr#1{\mwml@list@ref{#1}{2}}
\def\mwml@cadddr#1{\mwml@list@ref{#1}{3}}
\def\mwml@list@ref#1#2{% :: [a] -> i -> a
  \mwml@set@list@ref\mwml@tempa{#1}{#2}%
  \mwml@tempa
}
\def\mwml@nth#1#2{% :: i -> [a] -> a
  \mwml@set@list@ref\mwml@tempa{#2}{#1}%
  \mwml@tempa
}



%%% Miscellaneous: length, append, concatenate, reverse, zip & count
% implemented: length, append, concatenate reverse, append-reverse, zip (2,3)

% \def\mwml@set@length#1#2{% cs -> [a] -> nothing, length in cs
%   \mwm@in@group@with@nonlocal\mwml@tempa#1{%
%     \mwml@set@fold\mwml@tempa\mwml@set@length@kons{0}{#2}%
%   }%
% }
%     \def\mwml@set@length@kons#1#2{%
%       \mwml@@counter=#1
%       \advance \mwml@@counter by 1
%       \edef\mwml@tempa{\the\mwml@@counter}%
%     }
\def\mwml@set@length#1#2{% cs -> [a] -> nothing, length in cs
  \mwm@in@group@with@nonlocal\mwml@tempa#1{%
    \mwml@set@fold\mwml@tempa\mwml@set@length@kons{0}{#2}%
  }%
}
    \def\mwml@set@length@kons#1#2{%
      \mwml@@counter=#1
      \advance \mwml@@counter by 1
      \edef\mwml@tempa{\the\mwml@@counter}%
    }
\def\mwml@set@length@counter#1#2{% counter -> [a] -> nothing, length in counter
  \mwm@in@group@with@nonlocal\mwml@tempa\mwml@tempflasque{%
    \mwml@set@length\mwml@tempa{#2}%
  }
  #1=\mwml@tempflasque
}


\def\mwml@set@append#1#2#3{% :: cs -> [a] -> [a] -> nothing, [a] in cs
  \mwm@in@group@with@nonlocal#1#1{%
%    \mwml@set@reverse#1{#2}%
%    \mwml@set@append@reverse#1#1{#3}%
    \mwml@set@reverse\mwml@append@@lis{#2}%
    \mwm@enxnr\mwml@set@append@reverse#1\mwml@append@@lis{#3}%
  }%
}
\def\mwml@set@append@reverse#1#2#3{% :: cs -> [a] -> [a] -> nothing, [a] in cs
% (append (reverse #1) #2)
  \mwm@in@group@with@nonlocal\mwml@tempa#1{%
    \mwml@set@copy\mwml@argb{#2}%
    \mwml@set@copy\mwml@tempa{#3}%
    \let\mwml@NULL\relax
    \let\mwml@CONS\mwml@set@append@reverse@cons
    \mwml@argb
  }%
}
    \def\mwml@set@append@reverse@cons#1#2{%
      \mwml@push{#1}\mwml@tempa
      #2%
    }


\def\mwml@set@concatenate#1#2{% :: cs -> [[a]] -> nothing, [a] in cs
  \mwm@in@group@with@nonlocal\mwml@tempa#1{%
    \mwml@set@reverse\mwml@tempb{#2}%
    \mwml@set@fold\mwml@tempa\mwml@set@concatenate@kons\mwml@NULL\mwml@tempb
  }%
}
    \def\mwml@set@concatenate@kons#1#2{%
      \mwml@set@append\mwml@tempa{#2}{#1}%
    }


\def\mwml@reverse#1{%
  \mwm@in@group@with@nonlocal\mwml@tempa#1{%
    \mwml@set@reverse\mwml@tempa{#1}%
  }%
}
\def\mwml@set@reverse#1#2{% :: cs -> [a] -> nothing, [a] in cs
  \mwm@in@group@with@nonlocal\mwml@tempa#1{%
    \mwml@set@copy\mwml@argb{#2}%
    \mwml@set@null\mwml@tempa
    \let\mwml@NULL\relax
    \let\mwml@CONS\mwml@set@reverse@cons
    \mwml@argb
  }%
}
    \def\mwml@set@reverse@cons#1#2{%
      \mwml@push{#1}\mwml@tempa
      #2%
    }


\def\mwml@set@zip@two#1#2#3{% :: cs -> [a] -> [b] -> nothing, [(a,b)] in cs
  \mwm@in@group@with@nonlocal\mwml@tempa#1{%
%    \mwml@set@copy\mwml@tempb{#2}%
%    \mwml@set@copy\mwml@tempc{#3}%
%    \mwml@set@null\mwml@tempa
%    \let\mwml@NULL\relax
%    \let\mwml@CONS\mwml@set@zip@two@cons
%    \mwml@tempb
%    \mwml@reverse\mwml@tempa
    \mwml@set@copy\mwml@argb{#2}%
    \mwml@set@copy\mwml@argc{#3}%
    \mwml@set@null\mwml@tempa
    \mwml@set@copy\mwml@tempb\mwml@argb
    \mwml@set@copy\mwml@tempc\mwml@argc
    \let\mwml@NULL\relax
    \let\mwml@CONS\mwml@set@zip@two@cons
    \mwml@tempb
    \mwml@reverse\mwml@tempa
  }%
}
    \def\mwml@set@zip@two@cons#1#2{%
      \mwml@is@null\mwml@tempb \if@mwml \else
      \mwml@is@null\mwml@tempc \if@mwml \else
        \mwml@set@car\@tempb\mwml@tempb
        \mwml@drop@one\mwml@tempb
        \mwml@set@car\@tempc\mwml@tempc
        \mwml@drop@one\mwml@tempc
        \mwml@set@null\@tempa
        \mwm@exnr\mwml@push\@tempc\@tempa
        \mwm@exnr\mwml@push\@tempb\@tempa
        \mwm@exnr\mwml@push\@tempa\mwml@tempa% (push `(,\@tempb ,\@tempc) \mwml@tempa)
        % I think the below null check is not necessarily needed, but the rack causes an error. Hum...
%        \def\@tempa{#2}%
%        \mwml@is@null\@tempa \if@mwml
%        \else
          #2%
%        \fi
      \fi\fi
    }
\def\mwml@set@zip@three#1#2#3#4{% :: cs -> [a] -> [b] -> [c] -> nothing, [(a,b,c)] in cs
  \mwm@in@group@with@nonlocal\mwml@tempa#1{%
%    \mwml@set@copy\mwml@tempb{#2}%
%    \mwml@set@copy\mwml@tempc{#3}%
%    \mwml@set@copy\mwml@tempd{#4}%
%    \mwml@set@null\mwml@tempa
%    \let\mwml@NULL\relax
%    \let\mwml@CONS\mwml@set@zip@three@cons
%    \mwml@tempb
%    \mwml@reverse\mwml@tempa
    \mwml@set@copy\mwml@argb{#2}%
    \mwml@set@copy\mwml@argc{#3}%
    \mwml@set@copy\mwml@argd{#4}%
    \mwml@set@null\mwml@tempa
    \mwml@set@copy\mwml@tempb\mwml@argb
    \mwml@set@copy\mwml@tempc\mwml@argc
    \mwml@set@copy\mwml@tempd\mwml@argd
    \let\mwml@NULL\relax
    \let\mwml@CONS\mwml@set@zip@three@cons
    \mwml@tempb
    \mwml@reverse\mwml@tempa
  }%
}
    \def\mwml@set@zip@three@cons#1#2{%
      \mwml@is@null\mwml@tempb \if@mwml \else
      \mwml@is@null\mwml@tempc \if@mwml \else
      \mwml@is@null\mwml@tempd \if@mwml \else
        \mwml@set@car\@tempb\mwml@tempb
        \mwml@drop@one\mwml@tempb
        \mwml@set@car\@tempc\mwml@tempc
        \mwml@drop@one\mwml@tempc
        \mwml@set@car\@tempd\mwml@tempd
        \mwml@drop@one\mwml@tempd
        \mwml@set@null\@tempa
        \mwm@exnr\mwml@push\@tempd\@tempa
        \mwm@exnr\mwml@push\@tempc\@tempa
        \mwm@exnr\mwml@push\@tempb\@tempa
        \mwm@exnr\mwml@push\@tempa\mwml@tempa% (push `(,\@tempb ,\@tempc ,\@tempd) \mwml@tempa)
        % see the comment in \mwml@set@zip@two@cons
%        \def\@tempa{#2}%
%        \mwml@is@null\@tempa \if@mwml
%        \else
          #2%
%        \fi
      \fi\fi\fi
    }



%%% Fold, unfold & map
% implemented: fold map

% \def\mwml@set@fold{\mwml@set@fold@cont\relax}
% \def\mwml@set@fold@cont#1#2#3#4#5{% :: cont -> cs -> (a -> b -> a) -> a -> [b] -> a
% % #3 have to return value in cs
% % #1: cont (continuation)
% % #2: cs (control sequence used in #3 to return value)
% % #3: a -> b -> a
% % #4: a (accumulator)
% % #5: [b]
%   \mwm@in@group@with@nonlocal#2#2{%
%     \def\mwml@fold@kons##1##2{%
%       \mwm@exnr#3{#2}{##1}%
%       ##2%
%     }%
%     \let\mwml@NULL\relax
%     \let\mwml@CONS\mwml@fold@kons
%     \def#2{#4}%
%     #5%
%   }%
% }
\def\mwml@set@fold#1#2#3#4{% :: cs -> (a -> b -> nothing, a in cs) -> a -> [b] -> nothing, a in cs
% #2 have to return value in #1
% Note that this macro is imported from Haskell (foldl), not from Scheme.
% Take care of the order of arguments of #2.
% #1: cs (control sequence used in #3 to return value)
% #2: a -> b -> a
% #3: a (accumulator)
% #4: [b]
  \mwm@in@group@with@nonlocal#1#1{%
    \def\mwml@fold@kons##1##2{%
      \mwm@exnr#2{#1}{##1}%
      ##2%
    }%
    \let\mwml@NULL\relax
    \let\mwml@CONS\mwml@fold@kons
    \mwml@set@copy\mwml@argd{#4}%
    \def#1{#3}%
    \mwml@argd
  }%
}


\def\mwml@set@map#1#2#3{% :: cs -> (a -> nothing, b in cs) -> [a] -> nothing, [b] in cs
  \mwm@in@group@with@nonlocal\mwml@map@@res#1{%
    \def\mwml@set@map@kons##1##2{%
      #2{##2}%
      \mwm@enxnr\mwml@set@cons\mwml@map@@res#1{##1}%
    }%
    \mwml@set@fold\mwml@map@@res\mwml@set@map@kons\mwml@NULL{#3}%
    \mwml@reverse\mwml@map@@res
  }%
}
\def\mwml@set@map@two#1#2#3#4{%
% :: cs -> (a -> b -> nothing, c in cs) -> [a] -> [b] -> nothing, [c] in cs
  \mwm@in@group@with@nonlocal#1#1{%
    \def\mwml@map@proc##1{%
      \mwml@apply#2{##1}%
    }%
    \mwml@set@zip@two#1{#3}{#4}%
    \mwm@ennxr\mwml@set@map#1\mwml@map@proc{#1}%
  }%
}
\def\mwml@set@map@three#1#2#3#4#5{%
% :: cs -> (a -> b -> c -> nothing, d in cs) -> [a] -> [b] -> [c] -> nothing, [d] in cs
  \mwm@in@group@with@nonlocal#1#1{%
    \def\mwml@map@proc##1{%
      \mwml@apply#2{##1}%
    }%
    \mwml@set@zip@three#1{#3}{#4}{#5}%
    \mwm@ennxr\mwml@set@map#1\mwml@map@proc{#1}%
  }%
}



%%% Filtering & partitioning
% implemented: filter

% TODO: delete
\def\mwml@filter#1#2{%
  \mwml@set@filter\mwml@tempa{#1}{#2}%
  \let#2\mwml@tempa
}
\def\mwml@set@filter#1#2#3{% :: cs -> (a -> nothing, predicate) -> [a] -> nothing, [a] in cs
%  \begingroup
%  \mwml@set@null\mwml@tempa
%  \let\mwml@NULL\relax
%  \let\mwml@CONS\mwml@set@filter@cons
%  \let\mwml@temp@pred#2%
%  #3%
%  \mwml@set@reverse\mwml@@result\mwml@tempa
%  \global\let\mwml@@result\mwml@@result
%  \endgroup
%  \let#1\mwml@@result
  \mwm@in@group@with@nonlocal\mwml@tempa#1{%
    \let\mwml@temp@pred#2%
    \mwml@set@copy\mwml@argc{#3}%
    \let\mwml@NULL\relax
    \let\mwml@CONS\mwml@set@filter@cons
    \mwml@set@null\mwml@tempa
    \mwml@argc
    \mwml@reverse\mwml@tempa
  }%
}
    \def\mwml@set@filter@cons#1#2{%
      \mwml@temp@pred{#1}%
      \if@mwml
        \mwml@push{#1}\mwml@tempa
      \else
      \fi
      #2%
    }



%%% Searching
% implemented: memq

\def\mwml@memq#1#2{% :: a -> [a] -> nothing
  \let\mwml@NULL\@mwmlfalse
  \let\mwml@CONS\mwml@memq@cons
  \mwml@set@copy\mwml@argb{#2}%
  \def\mwml@tempa{#1}%
  \mwml@argb
}
    \def\mwml@memq@cons#1#2{%
      \def\@tempa{#1}%
      \ifx\@tempa\mwml@tempa
        \@mwmltrue
      \else
        #2%
      \fi
    }



%%% Conversion

\def\mwml@csl@from@list#1{%
  \begingroup
  \mwml@set@csl@from@list\mwml@tempa{#1}%
  \mwml@tempa
  \endgroup
}
\def\mwml@set@csl@from@list#1#2{% :: cs -> [a] -> nothing, CSL in cs
% Convert a list #2 to csl #1
  \mwm@in@group@with@nonlocal\mwml@tempa#1{%
    \mwml@set@copy\mwml@argb{#2}%
    \let\mwml@NULL\relax
    \let\mwml@CONS\mwml@set@csl@from@list@loop@first
    \mwml@argb
  }%
}
    \def\mwml@set@csl@from@list@loop@first#1#2{%
      \toks1{{#1}}%
      \edef\mwml@tempa{\the\toks1}%
      \let\mwml@CONS\mwml@set@csl@from@list@loop
      #2%
    }
    \def\mwml@set@csl@from@list@loop#1#2{%
      \toks0\expandafter{\mwml@tempa}%
      \toks1{{#1}}%
      \edef\mwml@tempa{\the\toks0,\the\toks1}%
      #2%
    }

\def\mwml@list@from@csl#1{%
  \begingroup
  \mwml@set@list@from@csl\mwml@tempa{#1}%
  \mwml@tempa
  \endgroup
}
\def\mwml@set@list@from@csl#1#2{% :: cs -> CSL -> nothing, [a] in cs
% Convert a CSL #2 to list #1
% One can't use \mwml@tempa for #2. Expand it.
  \mwm@in@group@with@nonlocal\mwml@tempa#1{%
    \mwml@set@null\mwml@tempa
    \def\mwml@argb{#2}%
    \ifx\mwml@argb\@empty
    \else
      \mwml@set@list@from@csl@loop#2,\@nil
    \fi
    \mwml@reverse\mwml@tempa
  }%
}
    \def\mwml@set@list@from@csl@loop#1,#2\@nil{%
      \mwml@push{#1}\mwml@tempa
      \def\@tempa{#2}%
      \ifx\@tempa\@empty
        \let\@next\@gobble
      \else
        \let\@next\mwml@set@list@from@csl@loop
      \fi
      \@next#2\@nil
    }



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% matrix
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\mwml@set@make@matrix#1#2#3#4{% :: cs -> row -> column -> a -> nothing, [[a]] in cs
  \mwm@in@group@with@nonlocal\mwml@tempb#1{%
  \def\mwml@proc##1{%
    \def\mwml@tempb{#4}%
  }%
  \mwml@set@empty@matrix\mwml@tempa{#2}{#3}%
  \mwml@set@map@matrix\mwml@tempb\mwml@proc\mwml@tempa
  }%
}

\def\mwml@set@empty@matrix#1#2#3{% :: cs -> row -> column -> nothing, [[a]] in cs
  \begingroup
  \def\mwml@proc{%
    \mwml@set@make@list\mwml@tempa{#3}{}%
  }%
  \mwml@set@make@list\mwml@tempa{#2}{}%
  \mwm@ennxr\mwml@set@map\mwml@tempa\mwml@proc\mwml@tempa
  \global\let\mwml@result\mwml@tempa
  \endgroup
  \let#1\mwml@result
}

\def\mwml@set@map@matrix#1#2#3{% :: cs -> (a -> b) -> [[a]] -> nothing, [[b]] in cs
% (a -> b) returns value with cs
  \begingroup
  \def\mwml@map@matrix@proc##1{%
    \mwml@set@map#1#2{##1}%
  }%
  \mwm@ennxr\mwml@set@map#1\mwml@map@matrix@proc{#3}%
  \global\let\mwml@result#1
  \endgroup
  \let#1\mwml@result
}



%% output
\def\mwml@output@matrix@with@pmatrix#1{% :: [[a]] -> output
  \begingroup
  \mwml@set@make@matrix@contents\mwml@tempa{#1}%
  \begin{pmatrix}
    \mwml@tempa
  \end{pmatrix}
  \endgroup
}
\def\mwml@set@make@matrix@contents#1#2{% :: cs -> [[a]] -> nothing, matrix contents in cs
 \mwm@in@group@with@nonlocal\mwml@tempa#1{%
   % consider the case that #2 = \mwml@tempa
   % \mwml@set@car\mwml@tempa{#2}%
   % \mwm@exr\mwml@matrix@join@with@tab\mwml@tempa
   % \mwml@set@cdr\mwml@tempb{#2}%
   \mwml@set@copy\mwml@tempb{#2}%
   \mwml@set@car\mwml@tempa\mwml@tempb
   \mwm@exr\mwml@matrix@join@with@tab\mwml@tempa
   \mwml@drop@one\mwml@tempb
   \mwm@ennxxr\mwml@set@fold\mwml@tempa\mwml@matrix@join@with@newline\mwml@tempa\mwml@tempb
 }%
}
   \def\mwml@matrix@join@with@newline#1#2{%
     \toks0{\\}%
     \toks1{#1}%
     \mwml@matrix@join@with@tab{#2}%
     \toks2\expandafter{\mwml@tempa}%
     \edef\mwml@tempa{\the\toks1 \the\toks0 \the\toks2}%
   }
   \def\mwml@matrix@join@with@tab#1{% :: [a] -> value in \mwml@tempa
     % (string-join lis " & ")
     \mwm@in@group@with@nonlocal\mwml@tempa\mwml@tempa{%
       \mwml@set@car\mwml@tempa{#1}%
       \mwml@set@cdr\mwml@tempb{#1}%
       \mwm@ennxnr\mwml@set@fold\mwml@tempa\mwml@matrix@join@with@tab@aux\mwml@tempa\mwml@tempb
     }%
   }
       \def\mwml@matrix@join@with@tab@aux#1#2{%
         \toks1{#1}%
         \toks2{#2}%
         \def\mwml@tempa{#1 & #2}%
       }



%\def\datum{1: #1, 2: #2, 11: ##1, 22: ##2}\show\datum

test-mwmlist.tex

% -*- coding: euc-jp -*-

%\documentclass[10pt,draft]{jsarticle}
\documentclass[10pt,draft]{amsart}

%\usepackage{amsmath,amssymb}
\usepackage{kmathmacro}
\usepackage{mwmlist}





\makeatletter










%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% document
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}




















%===========================================
%
%\fbox{test exr}
%
%\def\@tempa{A}
%\def\@tempb{B}
%\def\@tempc{C}
%\def\@tempd{D}
%\def\testA#1{%
% \def\datum{TEST A :: 1: #1}
% \show\datum
%}
%\def\testB#1#2{%
% \def\datum{TEST B :: 1: #1, 2: #2}
% \show\datum
%}
%\def\testC#1#2#3{%
% \def\datum{TEST C :: 1: #1, 2: #2, 3: #3}
% \show\datum
%}
%\def\testD#1#2#3#4{%
% \def\datum{TEST D :: 1: #1, 2: #2, 3: #3, 4: #4}
% \show\datum
%}
%
%\mwm@exr\testA\@tempa
%\mwm@enr\testA\@tempa
%
%\mwm@exxr\testB\@tempa\@tempb
%\mwm@exnr\testB\@tempa\@tempb
%\mwm@enxr\testB\@tempa\@tempb
%\mwm@ennr\testB\@tempa\@tempb
%
%\mwm@exxxr\testC\@tempa\@tempb\@tempc
%\mwm@exxnr\testC\@tempa\@tempb\@tempc
%\mwm@exnxr\testC\@tempa\@tempb\@tempc
%\mwm@exnnr\testC\@tempa\@tempb\@tempc
%\mwm@enxxr\testC\@tempa\@tempb\@tempc
%\mwm@enxnr\testC\@tempa\@tempb\@tempc
%\mwm@ennxr\testC\@tempa\@tempb\@tempc
%\mwm@ennnr\testC\@tempa\@tempb\@tempc
%
%\mwm@exxxxr\testD\@tempa\@tempb\@tempc\@tempd
%\mwm@exxxnr\testD\@tempa\@tempb\@tempc\@tempd
%\mwm@exxnxr\testD\@tempa\@tempb\@tempc\@tempd
%\mwm@exxnnr\testD\@tempa\@tempb\@tempc\@tempd
%\mwm@exnxxr\testD\@tempa\@tempb\@tempc\@tempd
%\mwm@exnxnr\testD\@tempa\@tempb\@tempc\@tempd
%\mwm@exnnxr\testD\@tempa\@tempb\@tempc\@tempd
%\mwm@exnnnr\testD\@tempa\@tempb\@tempc\@tempd
%\mwm@enxxxr\testD\@tempa\@tempb\@tempc\@tempd
%\mwm@enxxnr\testD\@tempa\@tempb\@tempc\@tempd
%\mwm@enxnxr\testD\@tempa\@tempb\@tempc\@tempd
%\mwm@enxnnr\testD\@tempa\@tempb\@tempc\@tempd
%\mwm@ennxxr\testD\@tempa\@tempb\@tempc\@tempd
%\mwm@ennxnr\testD\@tempa\@tempb\@tempc\@tempd
%\mwm@ennnxr\testD\@tempa\@tempb\@tempc\@tempd
%\mwm@ennnnr\testD\@tempa\@tempb\@tempc\@tempd
%
%===========================================




===========================================

\fbox{test car, cadr, list-ref}

\def\listA{%
  \mwml@CONS{A}{\mwml@CONS{B}{\mwml@CONS{C}{\mwml@CONS{D}{\mwml@NULL}}}}}

listA = (A, B, C, D)

car of listA is \mwml@car\listA \par
cadr of listA is \mwml@cadr\listA \par
caddr of listA is \mwml@caddr\listA \par
cadddr of listA is \mwml@cadddr\listA \par

(list-ref listA 0) \mwml@list@ref\listA{0} ,
(list-ref listA 1) \mwml@list@ref\listA{1} ,\par
(list-ref listA 2) \mwml@list@ref\listA{2} ,
(list-ref listA 3) \mwml@list@ref\listA{3} ,

\mwml@drop@one\listA
dropped
(list-ref listA 0) \mwml@list@ref\listA{0} ,
(list-ref listA 1) \mwml@list@ref\listA{1} ,


===========================================

\fbox{test convert list to csl}

\def\listA{\mwml@CONS{A}{\mwml@CONS{B}{\mwml@CONS{C}\mwml@NULL}}}

first \mwml@list@ref\listA{0} ,
second \mwml@list@ref\listA{1} ,
third \mwml@list@ref\listA{2}

(\mwml@csl@from@list\listA)

===========================================

\fbox{test cons and push}

\def\listA{\mwml@CONS{A}{\mwml@CONS{B}{\mwml@CONS{C}\mwml@NULL}}}

(\mwml@csl@from@list\listA)

\mwml@set@cons\listB{consed}\listA
(\mwml@csl@from@list\listB)

\mwml@push{pushed}\listA
\mwml@push{more}\listA
(\mwml@csl@from@list\listA)

===========================================

\fbox{test reverse}

\def\listA{\mwml@CONS{A}{\mwml@CONS{B}{\mwml@CONS{C}\mwml@NULL}}}

listA
(\mwml@csl@from@list\listA)

reversed
\mwml@set@reverse\listB\listA
(\mwml@csl@from@list\listB)

reversed
\mwml@reverse\listA
(\mwml@csl@from@list\listA)

===========================================

\fbox{test convert csl to list}

\mwml@set@list@from@csl\listA{A,B,C,DE}

(A, B, C, DE)  =  (\mwml@csl@from@list\listA)

===========================================

\fbox{test append}

\mwml@set@list@from@csl\listA{A,B,C}
\mwml@set@list@from@csl\listB{1,2,3}
\mwml@set@list@from@csl\listD{}
%\mwml@set@null\listD

listA (\mwml@csl@from@list\listA),
listB (\mwml@csl@from@list\listB),
listD (\mwml@csl@from@list\listD)

(\mwml@csl@from@list\listD)

(append-reverse listA listB) =
\mwml@set@append@reverse\listC\listA\listB
(C, B, A, 1, 2, 3)  =  (\mwml@csl@from@list\listC)

(append listA listB) =
\mwml@set@append\listC\listA\listB
(A, B, C, 1, 2, 3)  =  (\mwml@csl@from@list\listC)

(append listA listD) =
\mwml@set@append\listC\listA\listD
(A, B, C)  =  (\mwml@csl@from@list\listC)

(append listD listB) =
\mwml@set@append\listC\listD\listB
(1, 2, 3)  =  (\mwml@csl@from@list\listC)



===========================================

\fbox{test fold}

\def\mwml@fold@reverse#1{%
  \mwml@set@null\mwml@tempa
  \mwml@set@fold\mwml@tempa\mwml@fold@reverse@kons{}{#1}%
  (\mwm@exr\mwml@csl@from@list\mwml@tempa)%
}
    \def\mwml@fold@reverse@kons#1#2{%
      \mwml@push{#2}\mwml@tempa
    }


\mwml@set@list@from@csl\listA{A,B,C}

\mwml@fold@reverse\listA


===========================================

\fbox{test iota, make-list, map}

\mwml@set@iota\listA{5}{0}{1}

(iota 5 0 1) = (\mwml@csl@from@list\listA)

\mwml@set@iota\listA{5}{10}{2}

(iota 5 10 2) = (\mwml@csl@from@list\listA)

\mwml@set@iota\listA{0}{0}{1}

(iota 0 0 1) = (\mwml@csl@from@list\listA)

\mwml@set@make@list\listA{5}{0}

(make-list 5 0) = (\mwml@csl@from@list\listA)

\mwml@set@make@list\listA{0}{0}

(make-list 0 0) = (\mwml@csl@from@list\listA)



\mwml@set@iota\listA{5}{0}{1}

\def\mwml@map@test#1{%
  \mwml@set@map\mwml@tempa\mwml@map@test@aux{#1}%
  \mwm@exr\mwml@csl@from@list{\mwml@tempa}%
}
    \def\mwml@map@test@aux#1{\edef\mwml@tempa{(#1)}}

(\mwml@map@test\listA)




===========================================

\newpage

\fbox{factorial}

\def\mwml@fact#1{%
  \mwml@set@iota\mwml@tempb{#1}{1}{1}%
  \mwml@set@fold\@tempa\mwml@mul{1}\mwml@tempb
}
\def\mwml@mul#1#2{%
  \mwml@set@make@list\mwml@tempb{#1}{#2}%
  \mwml@set@fold\@tempa\mwml@add{0}\mwml@tempb
}
\def\mwml@add#1#2{%
  \mwml@@counter=#1
  \advance \mwml@@counter by #2
  \edef\@tempa{\the\mwml@@counter}%
}


\mwml@add{2}{3}
$2 + 3 = \@tempa$

\mwml@mul{2}{3}
$2 \times 3 = \@tempa$

\mwml@fact{5}
$5! = \@tempa$

\mwml@set@iota\listA{7}{1}{1}%
\mwml@set@map\@tempa\mwml@fact\listA
(map fact (iota 7 1 1)) = (\mwml@csl@from@list\@tempa)

===========================================

\fbox{test logic}

(not t) =
\mwml@not{\@mwmltrue}
\if@mwml TRUE \else FALSE \fi

(not f) =
\mwml@not{\@mwmlfalse}
\if@mwml TRUE \else FALSE \fi


\def\logictest#1#2{%
#1{t}{t} =
#2{\@mwmltrue}{\@mwmltrue}
\if@mwml TRUE \else FALSE \fi

#1{t}{f} =
#2{\@mwmltrue}{\@mwmlfalse}
\if@mwml TRUE \else FALSE \fi

#1{f}{t} =
#2{\@mwmlfalse}{\@mwmltrue}
\if@mwml TRUE \else FALSE \fi

#1{f}{f} =
#2{\@mwmlfalse}{\@mwmlfalse}
\if@mwml TRUE \else FALSE \fi
}


\def\logictestand#1#2{(and #1 #2)}%
\logictest\logictestand\mwml@and

\def\logictestor#1#2{(or #1 #2)}%
\logictest\logictestor\mwml@or

\def\logictestnotand#1#2{(not (and #1 #2))}%
\logictest\logictestnotand\mwml@not@and

\def\logictestnotor#1#2{(not (or #1 #2))}%
\logictest\logictestnotor\mwml@not@or


false is false?
\mwml@is@false\mwml@false
\if@mwml TRUE \else FALSE \fi

A is false?
\mwml@is@false{A}
\if@mwml TRUE \else FALSE \fi

false is true?
\mwml@is@true\mwml@false
\if@mwml TRUE \else FALSE \fi

A is true?
\mwml@is@true{A}
\if@mwml TRUE \else FALSE \fi


===========================================

\fbox{test if}

\mwml@set@list@from@csl\listA{A,B,C}
listA = (\mwml@csl@from@list\listA)
\mwml@set@null\listB
listB = (\mwml@csl@from@list\listB)

\mwml@is@null\listA
(null? listA) = \if@mwml TRUE \else FALSE \fi

\mwml@is@null\listB
(null? listB) = \if@mwml TRUE \else FALSE \fi



===========================================

\fbox{test if}

\def\mwml@even@p#1{%
  \ifodd#1
    \@mwmlfalse
  \else
    \@mwmltrue
  \fi
}


\mwml@set@list@from@csl\listA{A,B,C}
listA = (\mwml@csl@from@list\listA)


(eq A (nth 0 listA)) =
\mwml@eq@nth{A}{0}\listA
\if@mwml TRUE \else FALSE \fi

(eq A (nth 1 listA)) =
\mwml@eq@nth{A}{1}\listA
\if@mwml TRUE \else FALSE \fi


(memq A listA) =
\mwml@memq{A}\listA
\if@mwml TRUE \else FALSE \fi

(memq C listA) =
\mwml@memq{C}\listA
\if@mwml TRUE \else FALSE \fi

(memq 1 listA) =
\mwml@memq{1}\listA
\if@mwml TRUE \else FALSE \fi


\mwml@set@list@from@csl\listA{0,1,2}
listA = (\mwml@csl@from@list\listA)

(even? (nth 0 listA)) =
\mwml@test@nth\mwml@even@p{0}\listA
\if@mwml TRUE \else FALSE \fi

(even? (nth 1 listA)) =
\mwml@test@nth\mwml@even@p{1}\listA
\if@mwml TRUE \else FALSE \fi

===========================================

\fbox{test filter}

\mwml@set@iota\listA{5}{0}{1}

listA = (\mwml@csl@from@list\listA)

(filter even? listA) =
\mwml@filter\mwml@even@p\listA
(\mwml@csl@from@list\listA)



===========================================

\fbox{}



===========================================

\fbox{}



===========================================

\fbox{}



===========================================

\fbox{}



==========================================

\fbox{test matrix}

\mwml@set@empty@matrix\listA 2 2
%\show\listA

\def\insA#1{\def\@tempa{A}}

\mwml@set@map@matrix\@tempa\insA\listA
%\show\@tempa

\mwml@set@list@from@csl\listA{A,B,C}
listA = (\mwml@csl@from@list\listA)

\mwml@set@map\@tempa\insA\listA
%\show\@tempa

\mwml@set@make@matrix\matrixA{2}{2}{B}
%\show\matrixA


===========================================

\fbox{}

%\mwml@set@list@from@csl\listA{A,B,C}
%listA = (\mwml@csl@from@list\listA)
%
%\mwml@matrix@convert@line\listA
%\show\mwml@tempa
%
\mwml@set@make@matrix\matrixA{2}{2}{B}
%\show\matrixA

\def\matrixA{%
  \mwml@CONS {\mwml@CONS {A}{\mwml@CONS {B}{\mwml@NULL }}}%
 {\mwml@CONS {\mwml@CONS {C}{\mwml@CONS {D}{\mwml@NULL }}}%
 {\mwml@NULL }}}%
%\show\matrixA


%\mwml@set@make@matrix@contents\mwml@tempa\matrixA
%\show\mwml@tempa

\[
  \mwml@output@matrix@with@pmatrix\matrixA
\]
% \let\mwml@tempa\matrixA
% \[
%   \mwml@output@matrix@with@pmatrix\mwml@tempa
% \]
% \[
%   \mwm@exr\mwml@output@matrix@with@pmatrix\mwml@tempa
% \]

Does it look like the following?
\[
  \begin{pmatrix}
    A & B \\
    C & D
  \end{pmatrix}
\]


===========================================

\fbox{test apply}

\def\testapply#1#2{1 #1 2 #2 done}

\mwml@set@list@from@csl\listA{A,B,C}
listA = (\mwml@csl@from@list\listA)

\mwml@apply\relax\listA
%\show\mwml@tempflasque

\mwml@apply\testapply\listA

===========================================

\fbox{test zip}

\def\testzip#1{%
  \mwml@set@csl@from@list\@tempa{#1}%
  \edef\@tempa{(\@tempa)}%
}

\mwml@set@list@from@csl\listA{A,B,C}
listA = (\mwml@csl@from@list\listA)
\mwml@set@list@from@csl\listB{1,2,3,4,5}
listB = (\mwml@csl@from@list\listB)
\mwml@set@list@from@csl\listC{a,b,c}
listC = (\mwml@csl@from@list\listC)
% \mwml@set@list@from@csl\listA{A,C}
% listA = (\mwml@csl@from@list\listA)
% \mwml@set@list@from@csl\listB{B,D}
% listB = (\mwml@csl@from@list\listB)

\mwml@set@zip@two\mwml@tempa\listA\listB
%\show\mwml@tempa

% \[
%   \mwml@output@matrix@with@pmatrix\mwml@tempa
% \]


\mwml@set@map\@tempa\testzip\mwml@tempa
%\show\@tempa
\testzip\@tempa
%\show\@tempa
\@tempa

\[
  \mwml@output@matrix@with@pmatrix\mwml@tempa
\]


\mwml@set@zip@two\mwml@tempa\listB\listA
%\show\@tempa
\mwml@set@map\@tempa\testzip\mwml@tempa
\testzip\@tempa
\@tempa



\mwml@set@csl@from@list\@tempa\listA
%\show\@tempa
(\@tempa)

\mwml@set@zip@three\mwml@tempa\listA\listB\listC
\mwml@set@map\@tempa\testzip\mwml@tempa
%\show\@tempa
\testzip\@tempa
%\show\@tempa
\@tempa

\mwml@set@zip@three\mwml@tempa\listB\listC\listA
\mwml@set@map\@tempa\testzip\mwml@tempa
\testzip\@tempa
\@tempa

\mwml@set@zip@three\mwml@tempa\listC\listA\listB
\mwml@set@map\@tempa\testzip\mwml@tempa
\testzip\@tempa
\@tempa


\def\testmaptwo#1#2{%
  \def\@tempa{(#1 + #2)}%
}
\def\testmapthree#1#2#3{%
  \def\@tempa{(#1 + #2 - #3)}%
}

\mwml@set@map@two\@tempa\testmaptwo\listA\listB
(\mwml@csl@from@list\@tempa)

\mwml@set@map@three\@tempa\testmapthree\listA\listB\listC
(\mwml@csl@from@list\@tempa)


===========================================

\fbox{test length}

\mwml@set@list@from@csl\listA{A,B,C}
listA = (\mwml@csl@from@list\listA)
\mwml@set@list@from@csl\listB{1,2,3,4,5}
listB = (\mwml@csl@from@list\listB)

(length listA) =
\mwml@set@length\@tempa\listA
\@tempa

(length listB) =
\mwml@set@length\@tempa\listB
\@tempa

\mwml@set@length@counter\mwml@@counter\listA
(length listA) = \the\mwml@@counter

===========================================

\fbox{test take drop}

\mwml@set@list@from@csl\listA{A,B,C,D,E}
listA = (\mwml@csl@from@list\listA)

\mwml@set@split@at\@tempa\@tempb\listA{2}
(split-at 2 listA) = ((\mwml@csl@from@list\@tempa), (\mwml@csl@from@list\@tempb))

\mwml@set@split@at\@tempa\@tempb\listA{0}
(split-at 0 listA) = ((\mwml@csl@from@list\@tempa), (\mwml@csl@from@list\@tempb))

\mwml@set@split@at\@tempa\@tempb\listA{5}
(split-at 5 listA) = ((\mwml@csl@from@list\@tempa), (\mwml@csl@from@list\@tempb))

% expect error
% \mwml@set@split@at\@tempa\@tempb\listA{6}
% (split-at 6 listA) = ((\mwml@csl@from@list\@tempa), (\mwml@csl@from@list\@tempb))


\mwml@set@take@nth@drop\@tempa\@tempb\@tempc\listA{2}
(take/nth/drop 2 listA) = ((\mwml@csl@from@list\@tempa), \@tempb, (\mwml@csl@from@list\@tempc))

\mwml@set@take@nth@drop\@tempa\@tempb\@tempc\listA{0}
(take/nth/drop 0 listA) = ((\mwml@csl@from@list\@tempa), \@tempb, (\mwml@csl@from@list\@tempc))

\mwml@set@take@nth@drop\@tempa\@tempb\@tempc\listA{4}
(take/nth/drop 4 listA) = ((\mwml@csl@from@list\@tempa), \@tempb, (\mwml@csl@from@list\@tempc))

% expect error
% (take/nth/drop 5 listA) =
% \mwml@set@take@nth@drop\@tempa\@tempb\@tempc\listA{5}
% ((\mwml@csl@from@list\@tempa), \@tempb, (\mwml@csl@from@list\@tempc))


\mwml@set@take\@tempa\listA{2}
(take 2 listA) = (\mwml@csl@from@list\@tempa)

\mwml@set@take\@tempa\listA{0}
(take 0 listA) = (\mwml@csl@from@list\@tempa)

\mwml@set@take\@tempa\listA{5}
(take 5 listA) = (\mwml@csl@from@list\@tempa)


\mwml@set@drop\@tempa\listA{2}
(drop 2 listA) = (\mwml@csl@from@list\@tempa)

\mwml@set@drop\@tempa\listA{0}
(drop 0 listA) = (\mwml@csl@from@list\@tempa)

\mwml@set@drop\@tempa\listA{5}
(drop 5 listA) = (\mwml@csl@from@list\@tempa)













===========================================

\fbox{test treating non-robust command}

\def\A{\greedysubscript{A}}

\def\listA{\mwml@CONS{A}{\mwml@CONS{B}{\mwml@CONS{C}\mwml@NULL}}}
\def\listAh{\mwml@CONS{\H_{Gal}^1(\aGal_K, A)}{\mwml@CONS{\H_{et}^1(X_\kbar, \Ql)}{\mwml@CONS{\A_0_L}\mwml@NULL}}}
\def\listAm{\mwml@CONS{\map f from X to Y ;}{\mwml@CONS{B}{\mwml@CONS{C}\mwml@NULL}}}

\mwml@set@cons\listB{Z}\listA
%\show\listB

\mwml@set@cons\listB{\H_{Gal}^1(\aGal_K, A)}\listAh
%\show\listB

\mwml@set@cons\listB{Z}\listAm
%\show\listB


\mwml@set@car\@tempa\listA
%\show\@tempa
\mwml@set@car\@tempa\listAh
%\show\@tempa
$\@tempa$
\mwml@set@car\@tempa\listAm
%\show\@tempa
$\@tempa$

\mwml@set@cdr\listB\listA
(cdr listA) = (\mwml@csl@from@list\listB)
\mwml@set@cdr\listB\listAh
(cdr listAh) = $(\mwml@csl@from@list\listB)$
\mwml@set@cdr\listB\listAm
(cdr listAm) = (\mwml@csl@from@list\listB)


(list-ref listAh 0) $\mwml@list@ref\listAh{0}$,
(list-ref listAh 1) $\mwml@list@ref\listAh{1}$ ,\par
(list-ref listAh 2) $\mwml@list@ref\listAh{2}$ ,

\mwml@set@cons\listB{\Hom_{cont}(G, A)}\listAh
\mwml@set@cons\listB{consed}\listB
$(\mwml@csl@from@list\listB)$

\mwml@push{pushed}\listB
\mwml@push{more}\listB
\mwml@push{\map g from Y to Z ;}\listB
$(\mwml@csl@from@list\listB)$



\mwml@set@copy\listB\listAh
$(\mwml@csl@from@list\listB)$



listAh
$(\mwml@csl@from@list\listAh)$

reversed
\mwml@set@reverse\listB\listA
$(\mwml@csl@from@list\listB)$

reversed
\mwml@set@reverse\listB\listAh
$(\mwml@csl@from@list\listB)$

% reversed
% \mwml@reverse\listAh
% $(\mwml@csl@from@list\listAh)$




\mwml@set@list@from@csl\listB{A,B,{\map f from X to Y ;},{\H_{Gal}^1(\aGal_K, A)}}

(A, B, C, DE)  =  $(\mwml@csl@from@list\listB)$







\def\outinmath#1{$(\mwml@csl@from@list#1)$}

\mwml@set@null\listD
listD = (\mwml@csl@from@list\listD)

\mwml@set@append@reverse\listB\listAh\listAm
(append-reverse listAh listAm) = \outinmath\listB

\mwml@set@append\listB\listAh\listAm
(append listAh listAm) = \outinmath\listB

\mwml@set@append\listB\listAh\listD
(append listAh listD) = \outinmath\listB
$(\mwml@csl@from@list\listB)$

(append listD listAh) =
\mwml@set@append\listB\listD\listAh
(append listD listAh) = \outinmath\listB




\mwml@set@make@list\listB{5}{\H_{Gal}^1(\aGal_K, A)}
(make-list 5 H1) = \outinmath\listB



\def\mwml@map@test#1{%
  \mwml@set@map\mwml@tempa\mwml@map@test@aux{#1}%
}
   \def\mwml@map@test@aux#1{\edef\mwml@tempa{(#1)}}

\outinmath\listA
\mwml@map@test\listA
(\mwm@exr\mwml@csl@from@list{\mwml@tempa})


% \mwm@enxr\mwml@set@csl@from@list\listB{\mwml@tempa}%
% \show\listB
% \mwml@set@list@from@csl\listB{A,B,C}%
% \mwml@set@csl@from@list\listB\listB
% \show\listB


\mwml@is@null\listAh
(null? listAh) = \if@mwml TRUE \else FALSE \fi

\mwml@set@null\listB
\mwml@is@null\listB
(null? listB) = \if@mwml TRUE \else FALSE \fi

















===========================================

\fbox{test apply}

\def\testapply#1#2{1 #1 2 #2 done}

$\mwml@apply\testapply\listAh$

===========================================

\fbox{test zip}

\def\testzip#1{%
  \mwml@set@csl@from@list\@tempa{#1}%
% \edef\@tempa{(\@tempa)}%
  \toks0\expandafter{\@tempa}%
  \edef\@tempa{(\the\toks0)}%
}

\mwml@set@list@from@csl\listA{A,B,C}
listA = (\mwml@csl@from@list\listA)
\mwml@set@list@from@csl\listB{1,2,3,4,5}
listB = (\mwml@csl@from@list\listB)
\mwml@set@list@from@csl\listC{a,b,c}
listC = (\mwml@csl@from@list\listC)

\mwml@set@zip@two\mwml@tempa\listAh\listB
%\mwml@set@zip@two\mwml@tempa\listB\listA
%\show\mwml@tempa

\[
  \mwml@output@matrix@with@pmatrix\mwml@tempa
\]


\mwml@set@map\@tempa\testzip\mwml@tempa
\outinmath\@tempa


\mwml@set@zip@three\mwml@tempa\listAh\listB\listC
\mwml@set@map\@tempa\testzip\mwml@tempa
\outinmath\@tempa


\def\testmaptwo#1#2{%
  \def\@tempa{(#1 + #2)}%
}
\def\testmapthree#1#2#3{%
  \def\@tempa{(#1 + #2 - #3)}%
}

\mwml@set@map@two\@tempa\testmaptwo\listAh\listB
\outinmath\@tempa

\mwml@set@map@three\@tempa\testmapthree\listAh\listB\listC
\outinmath\@tempa











%===========================================
%
%\fbox{}
%
%%\mwml@set@list@from@csl\listA{A,B,C}
%%listA = (\mwml@csl@from@list\listA)
%%
%%\mwml@matrix@convert@line\listA
%%\show\mwml@tempa
%%
%%\mwml@set@make@matrix\matrixA{2}{2}{B}
%%\show\matrixA
%
%\def\matrixA{%
%  \mwml@CONS {\mwml@CONS {A}{\mwml@CONS {B}{\mwml@NULL }}}%
% {\mwml@CONS {\mwml@CONS {C}{\mwml@CONS {D}{\mwml@NULL }}}%
% {\mwml@NULL }}}%
%%\show\matrixA
%
%
%%\mwml@set@make@matrix@contents\mwml@tempa\matrixA
%%\show\mwml@tempa
%
%\[
%  \mwml@output@matrix@with@pmatrix\matrixA
%\]
%% \let\mwml@tempa\matrixA
%% \[
%%   \mwml@output@matrix@with@pmatrix\mwml@tempa
%% \]
%% \[
%%   \mwm@exr\mwml@output@matrix@with@pmatrix\mwml@tempa
%% \]
%
%Does it look like the following?
%\[
%  \begin{pmatrix}
%    A & B \\
%    C & D
%  \end{pmatrix}
%\]




\let\@tempa\relax
\def\matrixA{%
   \mwml@CONS {\mwml@CONS {A}{\mwml@CONS {B}{\mwml@NULL }}}%
  {\mwml@CONS {\mwml@CONS {C}{\mwml@CONS {D}{\mwml@NULL }}}%
  {\mwml@NULL }}}%

\mwml@set@concatenate\@tempa\matrixA
(A, B, C, D)  =  (\mwml@csl@from@list\@tempa)



\end{document}

\makeatother