fmtlatex.spad

-------------------------------------------------------------------
---
--- FriCAS FormatLaTeX
--- Copyright (C) 2014-2015, 2019-2020  Ralf Hemmecke <ralf@hemmecke.org>
---
-------------------------------------------------------------------
-- Redistribution and use in source and binary forms, with or without
-- modification, are permitted provided that the following conditions
-- are met:
--
-- 1. Redistributions of source code must retain the above copyright
-- notice, this list of conditions and the following disclaimer.
--
-- 2. Redistributions in binary form must reproduce the above
-- copyright notice, this list of conditions and the following
-- disclaimer in the documentation and/or other materials provided
-- with the distribution.
--
-- 3. Neither the name of the copyright holder nor the names of its
-- contributors may be used to endorse or promote products derived
-- from this software without specific prior written permission.
--
-- THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-- "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-- LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
-- FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
-- COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
-- INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
-- (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
-- SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
-- HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
-- STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
-- ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
-- OF THE POSSIBILITY OF SUCH DAMAGE.
-------------------------------------------------------------------
)if LiterateDoc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass{article}
\usepackage{literatedoc}
\usepackage{fricasmath}
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\title{A \LaTeX{} formatter}
\author{Ralf Hemmecke}
\date{14-Jul-2014}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\maketitle

\begin{abstract}
  The formatter \spadtype{FormatLaTeX} is part of the \SYSTEM{}
  formatting framework and transforms elements of
  \spadtype{OutputForm} to \
  spadtype{OutputBox} such that they can be
  included into a \LaTeX{} document when the package
  \url{fricasmath.sty} is used.
\end{abstract}

\tableofcontents

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\section{Overview}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

For an overview of the formatting framework in \SYSTEM{} look into the
\url{fmt.spad} document.

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Unfortunately, there is no document that clearly describes the meaning
of the primitives in \spadtype{OutputForm}. The following code of the
domain \spadtype{FormatLaTeX} is a complete reimplementation, but with
similar intend as the domain \spadtype{TexFormat} (by R. S. Sutor).

The domain \spadtype{OutputForm} as well as the former implementation
of \spadtype{TexFormat} has been analyzed and a new structure of the
code has been designed.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{The Implementation of \spadtype{FormatLaTeX}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
)endif

)abbrev domain FMTLATEX FormatLaTeX
++ \spadtype{FormatLaTeX} provides a coercion from
++ \spadtype{OutputForm} to \LaTeX{} format. The particular dialect of
++ \TeX{} used is \LaTeX{}, but for flexibility reasons
++ \spadtype{FormatLaTeX} outputs everything into a fricasmath
++ environment in which certain additional commands are available.
++ These commands are defined in a .sty file that is distributed with
++ the source code of FriCAS.
FormatLaTeX: Exports == Implementation where
  E   ==> OutputForm
  Z   ==> Integer
  S   ==> String
  LE  ==> List E
  BOX ==> OutputBox
  LBOX ==> S -> BOX -- Label box for prologue and epilogue
  HANDLER ==> (Z, LE) -> OutputBox -- (precedence, arguments) +-> resulting box
  H ==> HANDLER

  Exports ==> FormatterCategory with
    environment: (S, S, S, H) -> H
      ++ \spad{environmnt(env, x, sep)} returns a handler that typesets
      ++ its arguments (without parentheses) in a \LaTeX{} environment
      ++ with name \spad{env}. The string \spad{x} is put right after
      ++ the start of the environment.
      ++ The arguments are separated by the string \spad{sep}.

  Implementation ==> add
    Rep ==> Record(prolog: BOX, fmt: BOX, epilog: BOX)
    import from Rep
    rep x ==> (x@%) pretend Rep
    per x ==> (x@Rep) pretend %

    FE ==> formatExpression
    MIN ==> minPrecedence()
    MAX ==> maxPrecedence()

    coerce(x: %): OutputForm == rep(x)::OutputForm

)if LiterateDoc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
By default the \LaTeX{} part is introduced by
\verb'\begin{fricasmath}{STEPNUMBER}' and ended by
\verb'\end{fricasmath}'.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
)endif

    defaultPrologue(label: S): BOX ==
        box concat ["\begin{fricasmath}{", label, "}"]
    defaultEpilogue(label: S): BOX == box "\end{fricasmath}"

    -- Functions from FormatterCategory
    parenthesize(left: S, right: S, b: BOX): BOX ==
        if left = "(" and right = ")" then (left := "\PAREN{"; right := "}")
        hconcat [box left, b, box right]

)if LiterateDoc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\spad{texEscapeString(s)} escapes all \TeX{} special characters.
These characters are: \verb|\ { } $ ^ _ % ~ # &|.
We prepend these characters with a backslash in front of them.
Of course, this requires at least for \verb'\\' and \verb'\^' to define
them appropriately in the style file

In order to keep spaces, we also escape spaces by a backslash.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
)endif

    -- local functions: texEscape, tex1, tex1Escape, tex2
    texEscapeString(s: S): S == -- local function
        cc: CharacterClass := charClass " \{}$^_%~#&" --$
        p: Integer := position(cc, s, 1)
        zero? p => s
        str: S := ""
        n: Integer := 1
        while (p := position(cc, s, n)) > 0 repeat
            str := concat(str, s(n..p-1))
            n := p+1
            str := concat(str, concat("\", s.p))
        concat(str, s(n..#s))

    braceBox(b: BOX): BOX == parenthesize("{", "}", b)
    tex1(cmd: S, b: BOX): BOX == hconcat [box cmd, braceBox b]
    tex1Escape(cmd: S, s: S): BOX == tex1(cmd, box texEscapeString s)
    tex2(cmd: S, b1: BOX, b2: BOX): BOX == hconcat [tex1(cmd, b1), braceBox b2]

    -- Take category default for formatInteger
    formatFloat(s: S): BOX == box remove(char "__", s)
    formatString(s: S): BOX == tex1Escape("\STRING", s)
    formatSymbol(s: S): BOX == tex1Escape("\SYMBOL", s)
    formatFunctionSymbol(s: S): BOX == tex1Escape("\FUN", s)

    -- If a is of the form (* x (CONCAT d y)) then replace it
    -- by (INTSEP x (CONCAT d y)).
    integralArgument(a: E): E ==
        import from OutputFormTools
        atom? a => a
        op: E := operator a
        not is_symbol?(op, "*"::Symbol) => a
        args: LE := arguments a
        #args ~= 2 => a
        op2: E := operator(args.2)
        not is_symbol?(op2, "CONCAT"::Symbol) => a
        op3: E := first arguments(args.2)
        not is_symbol?(op3, "d"::Symbol) => a
        elt("INTSEP"::Symbol::E, [args.1, args.2])
        -- create a (INTSEP x (CONCAT d y)) form

    integral(p: Z): H == (prec: Z, args: LE): BOX +->
        -- We can assume #args=3.
        bl: BOX := formatExpression(args.1, MIN) -- lower limit
        bu: BOX := formatExpression(args.2, MIN) -- upper limit
        a: E := integralArgument(args.3)
        ba: BOX := formatExpression(a, MIN)
        if not empty? bl then bl := parenthesize("__{", "}", bl)
        if not empty? bu then bu := parenthesize("^{",  "}", bu)
        parenthesizeIf(p < prec, hconcat [box "\int", bl, bu, braceBox ba])

    -- local
    operatorWithLimits(s: String, p: Z): H == (prec: Z, args: LE): BOX +->
        -- We can assume #args>=2.
        bl: BOX := formatExpression(args.1, MIN) -- lower limit
        bu: BOX := empty() -- upper limit
        ba: BOX := formatExpression(args.2, MIN) -- upper limit or arg
        if #args = 3 then
            bu := ba                             -- upper limit
            ba := formatExpression(args.3, p)    -- arg
        if not empty? bl then bl := parenthesize("__{", "}", bl)
        if not empty? bu then bu := parenthesize("^{",  "}", bu)
        parenthesizeIf(p < prec, hconcat [box s, bl, bu, braceBox ba])

    sum(p: Z): H == operatorWithLimits("\sum", p)
    product(p: Z): H == operatorWithLimits("\prod", p)

    theMap(prec: Z, args: LE): BOX ==
        import from OutputFormTools
        a: E := first args
        s: S :=
            atom? a and not string? a and not symbol? a => ";?;"
            b: BOX := formatExpression(a, MIN) -- assume only one line!!!
            first lines b -- strings are already run through texEscape
        p1 := position(char ";", s)
        p2 := position(char ";", s, p1+1)
        tex1("\theMap", box s(p1+1..p2-1)) -- \theMap{FUNNAME}

    overbar(p: Z, hh: H): H == (prec: Z, args: LE): BOX +->
        parenthesizeIf(p < prec, tex1("\overline", hh(p, args)))

    box(hh: H): H == (prec: Z, args: LE): BOX +->
        tex1("\BOX", hh(prec, [args.1]))

    -- \sqrt[n]{x}
    nthRoot(p: Z, h1: H, h2: H): H == (prec: Z, args: LE): BOX +->
        bx: BOX := bracket("{", "}", h1)(p, [args.1])
        bn: BOX := empty()
        if #args > 1 then bn := bracket("[", "]", h2)(p, [args.2])
        parenthesizeIf(p < prec, hconcat [box "\sqrt", bn, bx])

    -- This handles multi-dots super(x,"....").
    -- scripts(f, [sub, super, presuper, presub]) -->
    -- \SCRIPTS{f}{d}{u}{pu}{pd}
    -- can assume #args>2
    scripts(p: Z): H == (prec: Z, args: LE): BOX +->
        import from OutputFormTools
        b: BOX := tex1("\SCRIPTS", formatExpression(first args, p))
        args := rest args
        for i in 1..4 repeat
            empty? args => b := hconcat [b, box "{}"]
            a := first args
            args := rest args
            string? a and string a = " " => b := hconcat [b, box "{}"]
            b := hconcat [b, box "{", formatExpression(a, MIN), box "}"]
        parenthesizeIf(p < prec, b)

    subscript(p: Z): H == (prec: Z, args: LE): BOX +->
        b1: BOX := formatExpression(args.1, p+1)
        b2: BOX := formatExpression(args.2, MIN)
        parenthesizeIf(p < prec, tex2("\SUB", b1, b2))


)if LiterateDoc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The handler \spad{altsupersub} treats an expression that is generated by
\begin{verbcode}
supersub(a, [sub1, super1, sub2, super2, ...])
\end{verbcode}
from \spadtype{OutputForm}.
We basically turn it into something like
\begin{verbcode}
\ALTSUPERSUB{a}{_{sub1}^{super1}_{sub2}^{super2}...}
\end{verbcode}
and let an appropriate \LaTeX{} package deal with the actual formatting,
for example, the \href{http://www.ctan.org/pkg/tensor}{tensor package}.

For example, for
\begin{verbcode}
supersub(x, [a, b, 1, 2+b, 1/3, 4])
\end{verbcode}
the above code then looks like this
\begin{verbcode}
\ALTSUPERSUB{\SYMBOL{x}}{_{\SYMBOL{a}}^{\SYMBOL{b}}_{1}^{2+\SYMBOL{b}}_{\frac{1}{3}}^{4}}
\end{verbcode}
and is printed like this.
\begin{fricasmath}{}
\ALTSUPERSUB{\SYMBOL{x}}{_{\SYMBOL{a}}^{\SYMBOL{b}}_{1}^{2+\SYMBOL{b}}_{\frac{1}{3}}^{4}}
\end{fricasmath}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
)endif

    altsupersub(p: Z): H == (prec: Z, args: LE): BOX +->
        b1: BOX := formatExpression(first args, p)
        lb: List BOX := empty()
        for a in rest args for i in 1.. repeat
            -- add "_{a}" or "^{a}"
            o: S := if odd? i then "__" else "^"
            lb := cons(tex1(o, formatExpression(a, MIN)), lb)
        b2: BOX := hconcat reverse! lb
        parenthesizeIf(p < prec, tex2("\ALTSUPERSUB", b1, b2))

    -- we must treat the special format of a prime expression
    prime(p: Z): H == (prec: Z, args: LE): BOX +->
        b1: BOX := formatExpression(args.1, p+1)
        b2: BOX := formatExpression(args.2, MIN)
        parenthesizeIf(p < prec, tex2("\PRIME", b1, b2))

    -- local
    aux2(s: S, p: Z, h1: H, h2: H): H == (prec: Z, args: LE): BOX +->
        parenthesizeIf(p < prec, tex2(s, h1(p, [args.1]), h2(p, [args.2])))

    power(p: Z, h1: H, h2: H): H == aux2("\SUPER", p, h1, h2)
    fraction(p: Z, h1: H, h2: H): H == aux2("\frac", p, h1, h2)
    slash(p: Z, h1: H, h2: H): H == aux2("\SLASH", p, h1, h2)

    binomial(prec: Z, args: LE): BOX ==
        b1: BOX := formatExpression(args.1, MIN)
        b2: BOX := formatExpression(args.2, MIN)
        tex2("\binom", b1, b2)

    -- \def\ZAG##1##2{\frac{\left.{##1}\right|}{\left|{##2}\right.}}%
    zag(prec: Z, args: LE): BOX ==
        b1: BOX := formatExpression(args.1, MIN)
        b2: BOX := formatExpression(args.2, MIN)
        tex2("\ZAG", b1, b2)

)if LiterateDoc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The function \spad{environment} is a general handler to create a
\LaTeX{} environment.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
)endif

    environment(env: S, x: S, sep: S, h: H): H == (prec: Z, args: LE): BOX +->
        -- We must return a box with just one line, but we want to see
        -- newlines in the actual tex-output. Therefore, we introduce
        -- explicit newlines.
        empty? args => empty()
        b: BOX := box concat ["\begin{", env, "}", x]
        e: BOX := box concat ["\end{", env, "}"]
        entries: BOX := nary(sep, MIN, h)(MIN, args)
        hconcat [b, entries, e]

    vconcat(h: H): H == environment("VCONCAT", "", "\\", h)
    pile(h: H): H == environment("PILE", "", "\\", h)

    matrix(left: S, right: S): H == (prec: Z, args: LE): BOX +->
        -- We ignore the left and right parameters and rather use
        -- LaTeX definitions to do the formatting. We also rely on an
        -- entry for the ROW operator to be present in the
        -- operatorHandlers table.

        -- format for args is [[], [ROW ...], [ROW ...], [ROW ...]]
        import from OutputFormTools
        n: S := concat ["{", convert(# arguments first rest args), "}"]
        environment("MATRIX", n, "\\", FE MIN)(MIN, rest args)


)if LiterateDoc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Now all function are defined and we can fill the \spad{oh}
data structure.
The operators have been mainly extracted from the definitions of
\spadtype{OutputForm} and the original implementation of
\spadtype{TexFormat} by R. S. Sutor
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
)endif

    setOperatorHandlers!(oh: OperatorHandlers H): OperatorHandlers H ==
        NARY ==> -1 -- means n-ary.
        PAREN p ==> bracket("\PAREN{", "}", FE p)
        BRACE p ==> bracket("{", "}", FE p)
        BRACE2(p1, p2) ==> binary(BRACE p1, BRACE p2)

        o(n, op, hdl) ==> setHandler!(oh, n, op, hdl)

        o(0, "NOTHING",     nothing())
        o(0, "%pi",         formatConstant "\pi ")
        o(0, "%e",          formatConstant "\EulerE ")
        o(0, "%i",          formatConstant "\ImaginaryI ")
        o(0, "%Infinity",   formatConstant "\infty ")
        o(0, "infinity",    formatConstant "\infty ") -- for %minusInfinity
        o(0, "...",         formatConstant "\ldots ")

        o(1, "cos",         prefix("\cos",    900, PAREN MIN))
        o(1, "cot",         prefix("\cot",    900, PAREN MIN))
        o(1, "csc",         prefix("\csc",    900, PAREN MIN))
        o(1, "log",         prefix("\log",    900, PAREN MIN))
        o(1, "sec",         prefix("\sin",    900, PAREN MIN))
        o(1, "sin",         prefix("\sin",    900, PAREN MIN))
        o(1, "tan",         prefix("\tan",    900, PAREN MIN))
        o(1, "cosh",        prefix("\cosh",   900, PAREN MIN))
        o(1, "coth",        prefix("\coth",   900, PAREN MIN))
        o(1, "csch",        prefix("\csch",   900, PAREN MIN))
        o(1, "sech",        prefix("\sech",   900, PAREN MIN))
        o(1, "sinh",        prefix("\sinh",   900, PAREN MIN))
        o(1, "tanh",        prefix("\tanh",   900, PAREN MIN))
        o(1, "acos",        prefix("\arccos", 900, PAREN MIN))
        o(1, "asin",        prefix("\arcsin", 900, PAREN MIN))
        o(1, "atan",        prefix("\arctan", 900, PAREN MIN))
        o(1, "erf",         prefix("\erf",    900, PAREN MIN))

        o(1, "-",           prefix("-",       710, FE 715))
        o(1, "not",         prefix("\lnot ",  710, FE 715))

        o(1, "QUOTE",       bracket("\QUOTE{", "}",  FE 990))
        o(1, "OVERBAR",     overbar(MAX, FE MIN))
        o(1, "BOX",         box FE MIN)
        o(1, "Aleph",       bracket("\SUB{\aleph}{", "}", FE MIN))
        o(1, "BRACE",       bracket("\BRACE{", "}", FE MIN))
        o(1, "BRACKET",     bracket("\BRACKET{", "}", FE MIN))
        o(1, "PAREN",       bracket("\PAREN{", "}", FE MIN))
        o(1, "Gamma",       bracket("\Gamma\PAREN{", "}", FE MIN))
        o(1, "ROOT",        bracket("\sqrt{", "}", FE MIN))
        o(1, "SEGMENT",     bracket("\SEGMENTi{", "}", FE MIN))
        o(1, "STRING",      bracket("\STRING{", "}", FE MIN))

        o(2, "rem",  infix("", 810, bracket("\REM{",   "}", FE 811), BRACE 811))
        o(2, "quo",  infix("", 810, bracket("\QUO{",   "}", FE 811), BRACE 811))
        o(2, "exquo",infix("", 810, bracket("\EXQUO{", "}", FE 811), BRACE 811))

        o(2, "^",           power(950, FE 960, FE MIN))
        o(2, "/",           fraction(910, FE MIN, FE MIN))
        o(2, "OVER",        fraction(910, FE MIN, FE MIN))
        o(2, "SLASH",       slash(880, FE 881, FE 882))
        o(2, "ZAG",         zag)
        o(2, "BINOMIAL",    binomial)
        o(2, "PRIME",       prime 950)

        o(2, "ROOT",        nthRoot(970, FE MIN, FE MIN))
        o(2, "SUB",         subscript 950)

        o(2, "SEGMENT",     prefix("\SEGMENTii", 100, BRACE2(100, 100)))

        o(2, "TENSOR",      infix("\otimes ",    850, FE 850, FE 850))

        o(2, "EQUATNUM",    prefix("\EQUATNUM",  MAX, BRACE2(MIN, MIN)))
        o(2, "OVERLABEL",   prefix("\OVERLABEL", MAX, BRACE2(MIN, MIN)))

        o(2, "==",          nary("==",         400, FE 401))

        o(2, "=",           nary("=",          400, FE 400))
        o(2, "~=",          nary("\ne ",       400, FE 400))
        o(2, "<",           nary("<",          400, FE 400))
        o(2, ">",           nary(">",          400, FE 400))
        o(2, "<=",          nary("\leq ",      400, FE 400))
        o(2, ">=",          nary("\geq ",      400, FE 400))
        o(2, "and",         nary("\land ",     300, FE 300))
        o(2, "or",          nary("\lor ",      200, FE 200))
        o(2, "LET",         nary("\coloneqq ", 125, FE 125))
        o(2, "->",          nary("\to ",       1001, FE 1001))
        o(2, "~>",          nary("\leadsto ",  100, FE 100))
        o(2, "+->",         nary("\mapsto ",   100, FE 100))
        o(2, "|",           nary("\mid ",      100, FE 100))

        o(2, "SIGMA",       sum 750)
        o(2, "PI",          product 750)

        o(3, "SIGMA2",      sum 750)
        o(3, "PI2",         product 750)
        o(3, "INTSIGN",     integral 700)
        o(2, "INTSEP",      infix("\, ", MAX, FE MIN, FE MIN)) -- non-OutputForm

        o(NARY, "+",           naryPlus("+", "-",  700, FE 700))
        -- Does n-ary minus ever appear in OutputForm???
        o(NARY, "-",           naryPlus("+", "-",  700, FE 700))

        o(NARY, "*",           nary("\TIMES ",     800, FE 800))

        o(NARY, "AGGLST",      nary("\COMMA ",     MAX, FE MIN))
        o(NARY, "AGGSET",      nary("\SEMICOLON ", MAX, FE MIN))
        o(NARY, "CONCAT",      nary("",            MAX, FE MIN))
        o(NARY, "CONCATB",     nary("\ ",          MAX, FE MIN))

        o(NARY, "ALTSUPERSUB", altsupersub 900)
        o(NARY, "SUPERSUB",    scripts 900)
        o(NARY, "SC",          pile FE MIN) -- pile notation
        o(NARY, "VCONCAT",     vconcat FE MIN)

        o(NARY, "ROW",         nary("&", MAX, FE MIN))
        o(NARY, "MATRIX",      matrix("[", "]"))
        o(NARY, "theMap",      theMap) -- one or two arguments

        return oh

    -- local variable declarations and definitions
    operatorData: OperatorHandlers(H) := setOperatorHandlers! new()
    operatorHandlers(): OperatorHandlers(HANDLER) == operatorData

)if LiterateDoc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{A style file for use with output of \spadtype{FormatLaTeX}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{verbcode}
%% fricasmath.sty
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Copyright (c) 2014, 2020  Ralf Hemmecke <ralf@hemmecke.org>
%% All rights reserved.
%%
%% Redistribution and use in source and binary forms, with or without
%% modification, are permitted provided that the following conditions are
%% met:
%%
%% 1. Redistributions of source code must retain the above copyright
%% notice, this list of conditions and the following disclaimer.
%%
%% 2. Redistributions in binary form must reproduce the above
%% copyright notice, this list of conditions and the following
%% disclaimer in the documentation and/or other materials provided
%% with the distribution.
%%
%% 3. Neither the name of the copyright holder nor the names of its
%% contributors may be used to endorse or promote products derived
%% from this software without specific prior written permission.
%%
%% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
%% "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
%% LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
%% FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
%% COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
%% INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
%% (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
%% SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
%% HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
%% STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
%% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
%% OF THE POSSIBILITY OF SUCH DAMAGE.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\usepackage{amsmath}
\usepackage[mathstyleoff]{breqn}
\usepackage{tensor}
\usepackage{mleftright}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newenvironment{fricasmath}[1]%
  {\def\arg{#1}%
   \ifx\arg\empty \def\BEGIN{\begin{dmath*}[compact]}%
                  \def\END{\end{dmath*}}%
            \else \def\BEGIN{\begin{dmath}[compact,number={#1}]}%
                  \def\END{\end{dmath}}%

   \fi
   \def\EulerE{e}% %e
   \def\ImaginaryI{i}% %i
   \def\csch{\operatorname{csch}}%
   \def\erf{\operatorname{erf}}%
   \def\coloneqq{\mathrel{:\mkern-1.2mu=}}%
   \def\embrace##1##2##3{\left##1\relax##3\right##2\relax}%
   \def\BRACE{\embrace{\{}{\}}}%
   \def\BRACKET{\embrace{[}{]}}%
   \def\PAREN##1{\mleft(##1\mright)}%
   \def\ZAG##1##2{\frac{\left.{##1}\right|}{\left|{##2}\right.}}%
   \def\QUOTE##1{\texttt{'}##1}%
   \def\BOX##1{\boxed{##1}}%
   \def\SEGMENTi##1{{##1}\operatorname{..}}%
   \def\SEGMENTii##1##2{{##1}\operatorname{..}{##2}}%
   \def\SUB##1##2{{{##1}_{##2}}}%
   \def\SUPER##1##2{{{##1}^{##2}}}%
   \def\SLASH##1##2{\left.##1\vphantom{{##1}{##2}}\right/ ##2}%
   \def\PRIMEx##1{{##1}\endgroup}%
   % Translate comma into \prime.
   \def\PRIME##1{\begingroup% redefinitions are only local
     {##1}%
     % for the second parameter redefine \STRING and \PAREN
     \def\PAREN{\def\STRING{\embrace{(}{)}}}%
     \def\STRING{\begingroup\lccode`\~=`\,\lowercase{\endgroup\def~{\prime}}}%
     ^\PRIMEx}%
   \def\OVERLABEL##1{\FUN{OVERLABEL}(##1)}%
   \def\REM##1##2{{##1}\mathbin{\mathrm{rem}}{##2}}%
   \def\QUO##1##2{{##1}\mathbin{\mathrm{quo}}{##2}}%
   \def\EXQUO##1##2{{##1}\mathbin{\mathrm{exquo}}{##2}}%
   \def\EQUATNUM##1##2{(##1)\qquad ##2}%
   \def\COMMA{,\linebreak[2]\:}% allow breaks in lists and sets
   \def\SEMICOLON{;\:}%
   \def\TIMES{\,}%
   \def\theMap##1{\FUN{theMap}(\FUN{##1})}%
   \def\ALTSUPERSUB##1##2{\tensor*{##1}{*##2}}%
   \def\SCRIPTS##1##2##3##4##5{\tensor*[^{##4}_{##5}]{##1}{_{##2}^{##3}}}%
   \newenvironment{MATRIX}[1]%
     {\setcounter{MaxMatrixCols}{##1}\begin{bmatrix}}{\end{bmatrix}}%
   \newenvironment{PILE}{\begin{array}[t]{l}}{\end{array}}%
   \newenvironment{VCONCAT}{\begin{array}{c}}{\end{array}}%
   \def\DefSpecialChars{%
     \def\^{{\tiny\ensuremath{^{\wedge}}}}%
     \def\\{\ensuremath{\backslash}}%
     \def\~{\char`~}%
   }%
   % If there is only one letter in the argument of \FUN, then
   % do not typeset it with \operatorname.
   \def\FUN##1{{\DefSpecialChars\DEFOPNAME##1\ENDDEFOPNAME\OPNAME{##1}}}%
   \def\DEFOPNAME##1##2\ENDDEFOPNAME{\def\arg{##2}%
     \ifx\arg\empty\def\OPNAME{}\else\def\OPNAME{\operatorname}\fi}%
   \def\STRING##1{\texttt{\DefSpecialChars ##1}}%
   \def\SYMBOL##1{{\DefSpecialChars ##1}}%
   \BEGIN{}}%
  {\END{}}
\end{verbcode}
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\section{Customization}
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The visual appearance of expressions in a \LaTeX{} document can be
customized in two places. The definitions of the \TeX{} commands in
the style file \url{fricasmath.sty} can be changed. Furthermore also
the internal data structure of the handlers can be modified, see
documentation of the formatting framework in \SYSTEM{}.

\end{document}
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)endif