\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/algebra outform.spad}
\author{Stephen M. Watt}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{package NUMFMT NumberFormats}
<<package NUMFMT NumberFormats>>=
)abbrev package NUMFMT NumberFormats
++ SMW March 88
++ Keywords: string manipulation, roman numerals, format
++ Description:
++ NumberFormats provides function to format and read arabic and
++ roman numbers, to convert numbers to strings and to read
++ floating-point numbers.

NumberFormats(): NFexports == NFimplementation where
    PI ==> PositiveInteger
    I  ==> Integer
    C  ==> Character
    F  ==> Float
    S  ==> String
    V  ==> PrimitiveArray

    NFexports ==> with
        FormatArabic: PI -> S
            ++ FormatArabic(n) forms an Arabic numeral
            ++ string from an integer n.
        ScanArabic:   S -> PI
            ++ ScanArabic(s) forms an integer from an Arabic numeral string s.
        FormatRoman:  PI -> S
            ++ FormatRoman(n) forms a Roman numeral string from an integer n.
        ScanRoman:    S -> PI
            ++ ScanRoman(s) forms an integer from a Roman numeral string s.
        ScanFloatIgnoreSpaces: S -> F
            ++ ScanFloatIgnoreSpaces(s) forms a floating point number from
            ++ the string s ignoring any spaces. Error is generated if the
            ++ string is not recognised as a floating point number.
        ScanFloatIgnoreSpacesIfCan: S -> Union(F, "failed")
            ++ ScanFloatIgnoreSpacesIfCan(s) tries to form a floating point number from
            ++ the string s ignoring any spaces.


    NFimplementation ==> add
        import SExpression
        import Symbol
        replaceD: C -> C
        replaced: C -> C
        contract: S -> S
        check: S ->Boolean
        replaceD c ==
          if c = char "D" then char "E" else c
        replaced c ==
          if c = char "d" then char "E" else c
        contract s ==
          s:= map(replaceD,s)
          s:= map(replaced,s)
          ls:List S := split(s,char " ")$String
          s:= concat ls
        check s ==
          NUMBERP(READ_-FROM_-STRING(s)$Lisp)$Lisp and
           -- if there is an "E" then there must be a "."
           -- this is not caught by code above
           -- also if the exponent is v.big the above returns false
           not (any?(#1=char "E",s) and not any?(#1=char ".",s) )

--        Original interpreter function:
--        )lis (defun scanstr(x) (spadcomp::|parseFromString| x))
        sexfloat:SExpression:=convert(coerce("Float")@Symbol)$SExpression
        ScanFloatIgnoreSpaces s ==
          s := contract s
          not check s => error "Non-numeric value"
          sex := interpret(packageTran(ncParseFromString(s)$Lisp)$Lisp)$Lisp
          sCheck := car(car(sex))
          if (sCheck=sexfloat) = true then
             f := (cdr cdr sex) pretend Float
          else
             if integer?(cdr sex) = true then
                f := (cdr sex) pretend Integer
                f::F
             else
                error "Non-numeric value"

        ScanFloatIgnoreSpacesIfCan s ==
          s := contract s
	  not check s => "failed"
          sex := interpret(packageTran(ncParseFromString(s)$Lisp)$Lisp)$Lisp
          sCheck := car(car(sex))
          if (sCheck=sexfloat) = true then
             f := (cdr cdr sex) pretend Float
          else
             if integer?(cdr sex) = true then
                f := (cdr sex) pretend Integer
                f::F
             else
                "failed"

        units:V S :=
           construct ["","I","II","III","IV","V","VI","VII","VIII","IX"]
        tens :V S :=
           construct ["","X","XX","XXX","XL","L","LX","LXX","LXXX","XC"]
        hunds:V S :=
           construct ["","C","CC","CCC","CD","D","DC","DCC","DCCC","CM"]
        umin := minIndex units
        tmin := minIndex tens
        hmin := minIndex hunds
        romval:V I := new(256, -1)
        romval ord char(" ")$C := 0
        romval ord char("I")$C := 1
        romval ord char("V")$C := 5
        romval ord char("X")$C := 10
        romval ord char("L")$C := 50
        romval ord char("C")$C := 100
        romval ord char("D")$C := 500
        romval ord char("M")$C := 1000
        thou:C  := char "M"
        plen:C  := char "("
        pren:C  := char ")"
        ichar:C := char "I"

        FormatArabic n == STRINGIMAGE(n)$Lisp
        ScanArabic   s == PARSE_-INTEGER(s)$Lisp

        FormatRoman pn ==
            n := pn::Integer
            -- Units
            d := (n rem 10) + umin
            n := n quo 10
            s := units.d
            zero? n => s
            -- Tens
            d := (n rem 10) + tmin
            n := n quo 10
            s := concat(tens.d, s)
            zero? n => s
            -- Hundreds
            d := (n rem 10) + hmin
            n := n quo 10
            s := concat(hunds.d, s)
            zero? n => s
            -- Thousands
            d := n rem 10
            n := n quo 10
            s := concat(new(d::NonNegativeInteger, thou), s)
            zero? n => s
            -- Ten thousand and higher
            for i in 2.. while not zero? n repeat
                -- Coefficient of 10**(i+2)
                d := n rem 10
                n := n quo 10
                zero? d => "iterate"
                m0:String := concat(new(i,plen),concat("I",new(i,pren)))
                mm := concat([m0 for j in 1..d]$List(String))
                -- strictly speaking the blank is gratuitous
                if #s > 0 then s := concat(" ", s)
                s  := concat(mm, s)
            s

        -- ScanRoman
        --
        -- The Algorithm:
        --    Read number from right to left.  When the current
        --    numeral is lower in magnitude than the previous maximum
        --    then subtract otherwise add.
        --    Shift left and repeat until done.

        ScanRoman s ==
            s      := upperCase s
            tot: I := 0
            Max: I := 0
            i:   I := maxIndex s
            while i >= minIndex s repeat
                -- Read a single roman digit
                c := s.i; i := i-1
                n := romval ord c
                -- (I)=1000, ((I))=10000, (((I)))=100000, etc
                if n < 0 then
                    c ^= pren =>
                       error ["Improper character in Roman numeral: ",c]
                    nprens: PI := 1
                    while c = pren and i >= minIndex s repeat
                       c := s.i; i := i-1
                       if c = pren then nprens := nprens+1
                    c ^= ichar =>
                       error "Improper Roman numeral: (x)"
                    for k in 1..nprens while i >= minIndex s repeat
                       c := s.i; i := i-1
                       c ^= plen =>
                          error "Improper Roman numeral: unbalanced ')'"
                    n := 10**(nprens + 2)
                if n < Max then
                    tot := tot - n
                else
                    tot := tot + n
                    Max := n
            tot < 0 => error ["Improper Roman numeral: ", tot]
            tot::PI

@
\section{domain OUTFORM OutputForm}
<<domain OUTFORM OutputForm>>=
)abbrev domain OUTFORM OutputForm
++ Keywords: output, I/O, expression
++ SMW March/88
++ Description:
++ This domain is used to create and manipulate mathematical expressions
++ for output.  It is intended to provide an insulating layer between
++ the expression rendering software (e.g.FORTRAN, TeX, or Script) and
++ the output coercions in the various domains.

OutputForm(): SetCategory with
        --% Printing
        print  : $ -> Void
          ++ print(u) prints the form u.
        message: String -> $
          ++ message(s) creates an form with no string quotes
          ++ from string s.
        messagePrint: String -> Void
          ++ messagePrint(s) prints s without string quotes. Note:
          ++ \spad{messagePrint(s)} is equivalent to \spad{print message(s)}.
        --% Creation of atomic forms
        outputForm: Integer -> $
          ++ outputForm(n) creates an form for integer n.
        outputForm: Symbol  -> $
          ++ outputForm(s) creates an form for symbol s.
        outputForm: String  -> $
          ++ outputForm(s) creates an form for string s.
        outputForm: DoubleFloat  -> $
          ++ outputForm(sf) creates an form for small float sf.
        empty   : () -> $
          ++ empty() creates an empty form.

        --% Sizings
        width: $ -> Integer
          ++ width(f) returns the width of form f (an integer).
        height: $ -> Integer
          ++ height(f) returns the height of form f (an integer).
        width: -> Integer
          ++ width() returns the width of the display area (an integer).
        height: -> Integer
          ++ height() returns the height of the display area (an integer).
        subHeight: $ -> Integer
          ++ subHeight(f) returns the height of form f below the base line.
        superHeight: $ -> Integer
          ++ superHeight(f) returns the height of form f above the base line.
         --% Space manipulations
        hspace: Integer -> $  ++ hspace(n) creates white space of width n.
        vspace: Integer -> $  ++ vspace(n) creates white space of height n.
        rspace: (Integer,Integer) -> $
          ++ rspace(n,m) creates rectangular white space, n wide by m high.
        --% Area adjustments
        left: ($,Integer) -> $
          ++ left(f,n) left-justifies form f within space of width n.
        right: ($,Integer) -> $
          ++ right(f,n) right-justifies form f within space of width n.
        center: ($,Integer) -> $
          ++ center(f,n) centers form f within space of width n.
        left: $ -> $
          ++ left(f) left-justifies form f in total space.
        right: $ -> $
          ++ right(f) right-justifies form f in total space.
        center:   $ -> $
          ++ center(f) centers form f in total space.

        --% Area manipulations
        hconcat:  ($,$) -> $
          ++ hconcat(f,g) horizontally concatenate forms f and g.
        vconcat:  ($,$) -> $
          ++ vconcat(f,g) vertically concatenates forms f and g.
        hconcat:  List $ -> $
          ++ hconcat(u) horizontally concatenates all forms in list u.
        vconcat:  List $ -> $
          ++ vconcat(u) vertically concatenates all forms in list u.

        --% Application formers
        prefix:  ($, List $) -> $
          ++ prefix(f,l) creates a form depicting the n-ary prefix
          ++ application of f to a tuple of arguments given by list l.
        infix:   ($, List $) -> $
          ++ infix(f,l) creates a form depicting the n-ary application
          ++ of infix operation f to a tuple of arguments l.
        infix:   ($, $, $) -> $
          ++ infix(op, a, b) creates a form which prints as: a op b.
        postfix: ($, $)    -> $
          ++ postfix(op, a)  creates a form which prints as: a op.
        infix?: $ -> Boolean
          ++ infix?(op) returns true if op is an infix operator,
          ++ and false otherwise.
        elt:     ($, List $) -> $
          ++ elt(op,l) creates a form for application of op
          ++ to list of arguments l.

        --% Special forms
        string:  $ -> $
          ++ string(f) creates f with string quotes.
        label:   ($, $) -> $
          ++ label(n,f) gives form f an equation label n.
        box:     $ -> $
          ++ box(f) encloses f in a box.
        matrix:  List List $ -> $
          ++ matrix(llf) makes llf (a list of lists of forms) into
          ++ a form which displays as a matrix.
        zag:     ($, $) -> $
          ++ zag(f,g) creates a form for the continued fraction form for f over g.
        root:    $ -> $
          ++ root(f) creates a form for the square root of form f.
        root:    ($, $) -> $
          ++ root(f,n) creates a form for the nth root of form f.
        over:    ($, $) -> $
          ++ over(f,g) creates a form for the vertical fraction of f over g.
        slash:   ($, $) -> $
          ++ slash(f,g) creates a form for the horizontal fraction of f over g.
        assign:  ($, $) -> $
          ++ assign(f,g) creates a form for the assignment \spad{f := g}.
        rarrow:  ($, $) -> $
          ++ rarrow(f,g) creates a form for the mapping \spad{f -> g}.
        differentiate: ($, NonNegativeInteger) -> $
          ++ differentiate(f,n) creates a form for the nth derivative of f,
          ++ e.g. \spad{f'}, \spad{f''}, \spad{f'''},
          ++ "f super \spad{iv}".
        binomial: ($, $) -> $
          ++ binomial(n,m) creates a form for the binomial coefficient of n and m.

        --% Scripts
        sub:     ($, $) -> $
          ++ sub(f,n) creates a form for f subscripted by n.
        super:   ($, $) -> $
          ++ super(f,n) creates a form for f superscripted by n.
        presub:  ($, $) -> $
          ++ presub(f,n) creates a form for f presubscripted by n.
        presuper:($, $) -> $
          ++ presuper(f,n) creates a form for f presuperscripted by n.
        scripts: ($, List $) -> $
            ++ \spad{scripts(f, [sub, super, presuper, presub])}
            ++  creates a form for f with scripts on all 4 corners.
        supersub:($, List $) -> $
            ++ supersub(a,[sub1,super1,sub2,super2,...])
            ++ creates a form with each subscript aligned
            ++ under each superscript.

        --% Diacritical marks
        quote:   $ -> $
          ++ quote(f) creates the form f with a prefix quote.
        dot:     $ -> $
          ++ dot(f) creates the form with a one dot overhead.
        dot:     ($, NonNegativeInteger) -> $
          ++ dot(f,n) creates the form f with n dots overhead.
        prime:   $ -> $
          ++ prime(f) creates the form f followed by a suffix prime (single quote).
        prime:   ($, NonNegativeInteger) -> $
          ++ prime(f,n) creates the form f followed by n primes.
        overbar: $ -> $
          ++ overbar(f) creates the form f with an overbar.
        overlabel: ($, $) -> $
          ++ overlabel(x,f) creates the form f with "x overbar" over the top.

        --% Plexes
        sum:     ($)       -> $
          ++ sum(expr) creates the form prefixing expr by a capital sigma.
        sum:     ($, $)    -> $
          ++ sum(expr,lowerlimit) creates the form prefixing expr by
          ++ a capital sigma with a lowerlimit.
        sum:     ($, $, $) -> $
          ++ sum(expr,lowerlimit,upperlimit) creates the form prefixing expr by
          ++ a capital sigma with both a lowerlimit and upperlimit.
        prod:    ($)       -> $
          ++ prod(expr) creates the form prefixing expr by a capital pi.
        prod:    ($, $)    -> $
          ++ prod(expr,lowerlimit) creates the form prefixing expr by
          ++ a capital pi with a lowerlimit.
        prod:    ($, $, $) -> $
          ++ prod(expr,lowerlimit,upperlimit) creates the form prefixing expr by
          ++ a capital pi with both a lowerlimit and upperlimit.
        int:     ($)       -> $
          ++ int(expr) creates the form prefixing expr with an integral sign.
        int:     ($, $)    -> $
          ++ int(expr,lowerlimit) creates the form prefixing expr by an
          ++ integral sign with a lowerlimit.
        int:     ($, $, $) -> $
          ++ int(expr,lowerlimit,upperlimit) creates the form prefixing expr by
          ++ an integral sign with both a lowerlimit and upperlimit.

        --% Matchfix forms
        brace:   $ -> $
          ++ brace(f) creates the form enclosing f in braces (curly brackets).
        brace:   List $ -> $
          ++ brace(lf) creates the form separating the elements of lf
          ++ by commas and encloses the result in curly brackets.
        bracket: $ -> $
          ++ bracket(f) creates the form enclosing f in square brackets.
        bracket: List $ -> $
          ++ bracket(lf) creates the form separating the elements of lf
          ++ by commas and encloses the result in square brackets.
        paren:   $ -> $
          ++ paren(f) creates the form enclosing f in parentheses.
        paren:   List $ -> $
          ++ paren(lf) creates the form separating the elements of lf
          ++ by commas and encloses the result in parentheses.

        --% Separators for aggregates
        pile:     List $ -> $
          ++ pile(l) creates the form consisting of the elements of l which
          ++ displays as a pile, i.e. the elements begin on a new line and
          ++ are indented right to the same margin.

        commaSeparate: List $ -> $
          ++ commaSeparate(l) creates the form separating the elements of l
          ++ by commas.
        semicolonSeparate:  List $ -> $
          ++ semicolonSeparate(l) creates the form separating the elements of l
          ++ by semicolons.
        blankSeparate: List $ -> $
          ++ blankSeparate(l) creates the form separating the elements of l
          ++ by blanks.
        --% Specific applications
        "=":     ($, $) -> $
          ++ f = g creates the equivalent infix form.
        "^=":    ($, $) -> $
          ++ f ^= g creates the equivalent infix form.
        "<":     ($, $) -> $
          ++ f < g creates the equivalent infix form.
        ">":     ($, $) -> $
          ++ f > g creates the equivalent infix form.
        "<=":    ($, $) -> $
          ++ f <= g creates the equivalent infix form.
        ">=":    ($, $) -> $
          ++ f >= g creates the equivalent infix form.
        "+":     ($, $) -> $
          ++ f + g creates the equivalent infix form.
        "-":     ($, $) -> $
          ++ f - g creates the equivalent infix form.
        "-":     ($)    -> $
          ++ - f creates the equivalent prefix form.
        "*":     ($, $) -> $
          ++ f * g creates the equivalent infix form.
        "/":     ($, $) -> $
          ++ f / g creates the equivalent infix form.
        "**":    ($, $) -> $
          ++ f ** g creates the equivalent infix form.
        "div":   ($, $) -> $
          ++ f div g creates the equivalent infix form.
        "rem":   ($, $) -> $
          ++ f rem g creates the equivalent infix form.
        "quo":   ($, $) -> $
          ++ f quo g creates the equivalent infix form.
        "exquo": ($, $) -> $
          ++ exquo(f,g) creates the equivalent infix form.
        "and":   ($, $) -> $
          ++ f and g creates the equivalent infix form.
        "or":    ($, $) -> $
          ++ f or g creates the equivalent infix form.
        "not":   ($)    -> $
          ++ not f creates the equivalent prefix form.
        SEGMENT: ($,$)  -> $
          ++ SEGMENT(x,y) creates the infix form: \spad{x..y}.
        SEGMENT: ($)    -> $
          ++ SEGMENT(x) creates the prefix form: \spad{x..}.

    == add
        import NumberFormats

        -- Todo:
        --   program forms, greek letters
        --   infix, prefix, postfix, matchfix support in OUT BOOT
        --   labove rabove, corresponding overs.
        --   better super script, overmark, undermark
        --   bug in product, paren blankSeparate []
        --   uniformize integrals, products, etc as plexes.

        cons ==> CONS$Lisp
        car  ==> CAR$Lisp
        cdr  ==> CDR$Lisp

        Rep := List $

        a, b: $
        l: List $
        s: String
        e: Symbol
        n: Integer
        nn:NonNegativeInteger

        sform:    String  -> $
        eform:    Symbol  -> $
        iform:    Integer -> $

        print x              == mathprint(x)$Lisp
        message s            == (empty? s => empty(); s pretend $)
        messagePrint s       == print message s
        (a:$ = b:$):Boolean  == EQUAL(a, b)$Lisp
        (a:$ = b:$):$        == [sform "=",     a, b]
        coerce(a):OutputForm  == a pretend OutputForm
        outputForm n          == n pretend $
        outputForm e          == e pretend $
        outputForm(f:DoubleFloat) == f pretend $
        sform s               == s pretend $
        eform e               == e pretend $
        iform n               == n pretend $

        outputForm s ==
          sform concat(quote()$Character, concat(s, quote()$Character))

        width(a) == outformWidth(a)$Lisp
        height(a) == height(a)$Lisp
        subHeight(a) == subspan(a)$Lisp
        superHeight(a) == superspan(a)$Lisp
        height() == 20
        width() == 66

        center(a,w)   == hconcat(hspace((w - width(a)) quo 2),a)
        left(a,w)     == hconcat(a,hspace((w - width(a))))
        right(a,w)    == hconcat(hspace(w - width(a)),a)
        center(a)     == center(a,width())
        left(a)       == left(a,width())
        right(a)      == right(a,width())

        vspace(n) ==
          n = 0 => empty()
          vconcat(sform " ",vspace(n - 1))

        hspace(n) ==
          n = 0 => empty()
          sform(fillerSpaces(n)$Lisp)

        rspace(n, m) ==
          n = 0 or m = 0 => empty()
          vconcat(hspace n, rspace(n, m - 1))

        matrix ll ==
            lv:$ := [LIST2VEC$Lisp l for l in ll]
            CONS(eform MATRIX, LIST2VEC$Lisp lv)$Lisp

        pile l              == cons(eform SC, l)
        commaSeparate l     == cons(eform AGGLST,  l)
        semicolonSeparate l == cons(eform AGGSET,  l)
        blankSeparate l     ==
           c:=eform CONCATB
           l1:$:=[]
           for u in reverse l repeat
               if EQCAR(u,c)$Lisp
                  then l1:=[:cdr u,:l1]
                  else l1:=[u,:l1]
           cons(c, l1)

        brace a        == [eform BRACE,   a]
        brace l        == brace commaSeparate l
        bracket a      == [eform BRACKET, a]
        bracket l      == bracket commaSeparate l
        paren a        == [eform PAREN,   a]
        paren l        == paren commaSeparate l

        sub     (a,b)  == [eform SUB, a, b]
        super   (a, b) == [eform SUPERSUB,a,sform " ",b]
        presub(a,b) == [eform SUPERSUB,a,sform " ",sform " ",sform " ",b]
        presuper(a, b) == [eform SUPERSUB,a,sform " ",sform " ",b]
        scripts (a, l) ==
            null l => a
            null rest l => sub(a, first l)
            cons(eform SUPERSUB, cons(a, l))
        supersub(a, l) ==
            if odd?(#l) then l := append(l, [empty()])
            cons(eform ALTSUPERSUB, cons(a, l))

        hconcat(a,b)  == [eform CONCAT, a, b]
        hconcat l     == cons(eform CONCAT, l)
        vconcat(a,b)  == [eform VCONCAT, a, b]
        vconcat l     == cons(eform VCONCAT, l)

        a ^= b      == [sform "^=",    a, b]
        a < b       == [sform "<",     a, b]
        a > b       == [sform ">",     a, b]
        a <= b      == [sform "<=",    a, b]
        a >= b      == [sform ">=",    a, b]

        a + b       == [sform "+",     a, b]
        a - b       == [sform "-",     a, b]
        - a         == [sform "-",     a]
        a * b       == [sform "*",     a, b]
        a / b       == [sform "/",     a, b]
        a ** b      == [sform "**",    a, b]
        a div b     == [sform "div",   a, b]
        a rem b     == [sform "rem",   a, b]
        a quo b     == [sform "quo",   a, b]
        a exquo b   == [sform "exquo", a, b]
        a and b     == [sform "and",   a, b]
        a or b      == [sform "or",    a, b]
        not a       == [sform "not",   a]
        SEGMENT(a,b)== [eform SEGMENT, a, b]
        SEGMENT(a)  == [eform SEGMENT, a]
        binomial(a,b)==[eform BINOMIAL, a, b]

        empty() == [eform NOTHING]

        infix? a ==
            e:$ :=
                IDENTP$Lisp a => a
                STRINGP$Lisp a => INTERN$Lisp a
                return false
            if GET(e,QUOTE(INFIXOP$Lisp)$Lisp)$Lisp then true else false

        elt(a, l) ==
            cons(a, l)
        prefix(a,l)   ==
            not infix? a => cons(a, l)
            hconcat(a, paren commaSeparate l)
        infix(a, l) ==
            null l => empty()
            null rest l => first l
            infix? a => cons(a, l)
            hconcat [first l, a, infix(a, rest l)]
        infix(a,b,c)  ==
            infix? a => [a, b, c]
            hconcat [b, a, c]
        postfix(a, b) ==
            hconcat(b, a)

        string a   == [eform STRING,  a]
        quote  a   == [eform QUOTE,   a]
        overbar a  == [eform OVERBAR, a]
        dot a      == super(a, sform ".")
        prime a    == super(a, sform ",")
        dot(a,nn)   == (s := new(nn, char "."); super(a, sform s))
        prime(a,nn) == (s := new(nn, char ","); super(a, sform s))

        overlabel(a,b) == [eform OVERLABEL, a, b]
        box a      == [eform BOX,     a]
        zag(a,b)   == [eform ZAG,     a, b]
        root a     == [eform ROOT,    a]
        root(a,b)  == [eform ROOT,    a, b]
        over(a,b)  == [eform OVER,    a, b]
        slash(a,b) == [eform SLASH,   a, b]
        assign(a,b)== [eform LET,     a, b]

        label(a,b) == [eform EQUATNUM, a, b]
        rarrow(a,b)== [eform TAG, a, b]
        differentiate(a, nn)==
            zero? nn => a
            nn < 4 => prime(a, nn)
            r := FormatRoman(nn::PositiveInteger)
            s := lowerCase(r::String)
            super(a, paren sform s)

        sum(a)     == [eform SIGMA,  empty(), a]
        sum(a,b)   == [eform SIGMA,  b, a]
        sum(a,b,c) == [eform SIGMA2, b, c, a]
        prod(a)    == [eform PI,     empty(), a]
        prod(a,b)  == [eform PI,     b, a]
        prod(a,b,c)== [eform PI2,    b, c, a]
        int(a)     == [eform INTSIGN,empty(), empty(), a]
        int(a,b)   == [eform INTSIGN,b, empty(), a]
        int(a,b,c) == [eform INTSIGN,b, c, a]

@
\section{OUTFORM.lsp BOOTSTRAP} 
{\bf OUTFORM} depends on itself.
We need to break this cycle to build the algebra. So we keep a
cached copy of the translated {\bf OUTFORM} category which we can write
into the {\bf MID} directory. We compile the lisp code and copy the
{\bf OUTFORM.o} file to the {\bf OUT} directory.  This is eventually
forcibly replaced by a recompiled version.

Note that this code is not included in the generated catdef.spad file.

<<OUTFORM.lsp BOOTSTRAP>>=

(|/VERSIONCHECK| 2) 

(PUT (QUOTE |OUTFORM;print;$V;1|) (QUOTE |SPADreplace|) (QUOTE |mathprint|)) 

(DEFUN |OUTFORM;print;$V;1| (|x| |$|) (|mathprint| |x|)) 

(DEFUN |OUTFORM;message;S$;2| (|s| |$|) (COND ((SPADCALL |s| (QREFELT |$| 11)) (SPADCALL (QREFELT |$| 12))) ((QUOTE T) |s|))) 

(DEFUN |OUTFORM;messagePrint;SV;3| (|s| |$|) (SPADCALL (SPADCALL |s| (QREFELT |$| 13)) (QREFELT |$| 8))) 

(PUT (QUOTE |OUTFORM;=;2$B;4|) (QUOTE |SPADreplace|) (QUOTE EQUAL)) 

(DEFUN |OUTFORM;=;2$B;4| (|a| |b| |$|) (EQUAL |a| |b|)) 

(DEFUN |OUTFORM;=;3$;5| (|a| |b| |$|) (LIST (|OUTFORM;sform| "=" |$|) |a| |b|)) 

(PUT (QUOTE |OUTFORM;coerce;2$;6|) (QUOTE |SPADreplace|) (QUOTE (XLAM (|a|) |a|))) 

(DEFUN |OUTFORM;coerce;2$;6| (|a| |$|) |a|) 

(PUT (QUOTE |OUTFORM;outputForm;I$;7|) (QUOTE |SPADreplace|) (QUOTE (XLAM (|n|) |n|))) 

(DEFUN |OUTFORM;outputForm;I$;7| (|n| |$|) |n|) 

(PUT (QUOTE |OUTFORM;outputForm;S$;8|) (QUOTE |SPADreplace|) (QUOTE (XLAM (|e|) |e|))) 

(DEFUN |OUTFORM;outputForm;S$;8| (|e| |$|) |e|) 

(PUT (QUOTE |OUTFORM;outputForm;Df$;9|) (QUOTE |SPADreplace|) (QUOTE (XLAM (|f|) |f|))) 

(DEFUN |OUTFORM;outputForm;Df$;9| (|f| |$|) |f|) 

(PUT (QUOTE |OUTFORM;sform|) (QUOTE |SPADreplace|) (QUOTE (XLAM (|s|) |s|))) 

(DEFUN |OUTFORM;sform| (|s| |$|) |s|) 

(PUT (QUOTE |OUTFORM;eform|) (QUOTE |SPADreplace|) (QUOTE (XLAM (|e|) |e|))) 

(DEFUN |OUTFORM;eform| (|e| |$|) |e|) 

(PUT (QUOTE |OUTFORM;iform|) (QUOTE |SPADreplace|) (QUOTE (XLAM (|n|) |n|))) 

(DEFUN |OUTFORM;iform| (|n| |$|) |n|) 

(DEFUN |OUTFORM;outputForm;S$;13| (|s| |$|) (|OUTFORM;sform| (SPADCALL (SPADCALL (QREFELT |$| 26)) (SPADCALL |s| (SPADCALL (QREFELT |$| 26)) (QREFELT |$| 27)) (QREFELT |$| 28)) |$|)) 

(PUT (QUOTE |OUTFORM;width;$I;14|) (QUOTE |SPADreplace|) (QUOTE |outformWidth|)) 

(DEFUN |OUTFORM;width;$I;14| (|a| |$|) (|outformWidth| |a|)) 

(PUT (QUOTE |OUTFORM;height;$I;15|) (QUOTE |SPADreplace|) (QUOTE |height|)) 

(DEFUN |OUTFORM;height;$I;15| (|a| |$|) (|height| |a|)) 

(PUT (QUOTE |OUTFORM;subHeight;$I;16|) (QUOTE |SPADreplace|) (QUOTE |subspan|)) 

(DEFUN |OUTFORM;subHeight;$I;16| (|a| |$|) (|subspan| |a|)) 

(PUT (QUOTE |OUTFORM;superHeight;$I;17|) (QUOTE |SPADreplace|) (QUOTE |superspan|)) 

(DEFUN |OUTFORM;superHeight;$I;17| (|a| |$|) (|superspan| |a|)) 

(PUT (QUOTE |OUTFORM;height;I;18|) (QUOTE |SPADreplace|) (QUOTE (XLAM NIL 20))) 

(DEFUN |OUTFORM;height;I;18| (|$|) 20) 

(PUT (QUOTE |OUTFORM;width;I;19|) (QUOTE |SPADreplace|) (QUOTE (XLAM NIL 66))) 

(DEFUN |OUTFORM;width;I;19| (|$|) 66) 

(DEFUN |OUTFORM;center;$I$;20| (|a| |w| |$|) (SPADCALL (SPADCALL (QUOTIENT2 (|-| |w| (SPADCALL |a| (QREFELT |$| 30))) 2) (QREFELT |$| 36)) |a| (QREFELT |$| 37))) 

(DEFUN |OUTFORM;left;$I$;21| (|a| |w| |$|) (SPADCALL |a| (SPADCALL (|-| |w| (SPADCALL |a| (QREFELT |$| 30))) (QREFELT |$| 36)) (QREFELT |$| 37))) 

(DEFUN |OUTFORM;right;$I$;22| (|a| |w| |$|) (SPADCALL (SPADCALL (|-| |w| (SPADCALL |a| (QREFELT |$| 30))) (QREFELT |$| 36)) |a| (QREFELT |$| 37))) 

(DEFUN |OUTFORM;center;2$;23| (|a| |$|) (SPADCALL |a| (SPADCALL (QREFELT |$| 35)) (QREFELT |$| 38))) 

(DEFUN |OUTFORM;left;2$;24| (|a| |$|) (SPADCALL |a| (SPADCALL (QREFELT |$| 35)) (QREFELT |$| 39))) 

(DEFUN |OUTFORM;right;2$;25| (|a| |$|) (SPADCALL |a| (SPADCALL (QREFELT |$| 35)) (QREFELT |$| 40))) 

(DEFUN |OUTFORM;vspace;I$;26| (|n| |$|) (COND ((EQL |n| 0) (SPADCALL (QREFELT |$| 12))) ((QUOTE T) (SPADCALL (|OUTFORM;sform| " " |$|) (SPADCALL (|-| |n| 1) (QREFELT |$| 44)) (QREFELT |$| 45))))) 

(DEFUN |OUTFORM;hspace;I$;27| (|n| |$|) (COND ((EQL |n| 0) (SPADCALL (QREFELT |$| 12))) ((QUOTE T) (|OUTFORM;sform| (|fillerSpaces| |n|) |$|)))) 

(DEFUN |OUTFORM;rspace;2I$;28| (|n| |m| |$|) (COND ((OR (EQL |n| 0) (EQL |m| 0)) (SPADCALL (QREFELT |$| 12))) ((QUOTE T) (SPADCALL (SPADCALL |n| (QREFELT |$| 36)) (SPADCALL |n| (|-| |m| 1) (QREFELT |$| 46)) (QREFELT |$| 45))))) 

(DEFUN |OUTFORM;matrix;L$;29| (|ll| |$|) (PROG (#1=#:G82748 |l| #2=#:G82749 |lv|) (RETURN (SEQ (LETT |lv| (PROGN (LETT #1# NIL |OUTFORM;matrix;L$;29|) (SEQ (LETT |l| NIL |OUTFORM;matrix;L$;29|) (LETT #2# |ll| |OUTFORM;matrix;L$;29|) G190 (COND ((OR (ATOM #2#) (PROGN (LETT |l| (CAR #2#) |OUTFORM;matrix;L$;29|) NIL)) (GO G191))) (SEQ (EXIT (LETT #1# (CONS (LIST2VEC |l|) #1#) |OUTFORM;matrix;L$;29|))) (LETT #2# (CDR #2#) |OUTFORM;matrix;L$;29|) (GO G190) G191 (EXIT (NREVERSE0 #1#)))) |OUTFORM;matrix;L$;29|) (EXIT (CONS (|OUTFORM;eform| (QUOTE MATRIX) |$|) (LIST2VEC |lv|))))))) 

(DEFUN |OUTFORM;pile;L$;30| (|l| |$|) (CONS (|OUTFORM;eform| (QUOTE SC) |$|) |l|)) 

(DEFUN |OUTFORM;commaSeparate;L$;31| (|l| |$|) (CONS (|OUTFORM;eform| (QUOTE AGGLST) |$|) |l|)) 

(DEFUN |OUTFORM;semicolonSeparate;L$;32| (|l| |$|) (CONS (|OUTFORM;eform| (QUOTE AGGSET) |$|) |l|)) 

(DEFUN |OUTFORM;blankSeparate;L$;33| (|l| |$|) (PROG (|c| |u| #1=#:G82757 |l1|) (RETURN (SEQ (LETT |c| (|OUTFORM;eform| (QUOTE CONCATB) |$|) |OUTFORM;blankSeparate;L$;33|) (LETT |l1| NIL |OUTFORM;blankSeparate;L$;33|) (SEQ (LETT |u| NIL |OUTFORM;blankSeparate;L$;33|) (LETT #1# (SPADCALL |l| (QREFELT |$| 53)) |OUTFORM;blankSeparate;L$;33|) G190 (COND ((OR (ATOM #1#) (PROGN (LETT |u| (CAR #1#) |OUTFORM;blankSeparate;L$;33|) NIL)) (GO G191))) (SEQ (EXIT (COND ((EQCAR |u| |c|) (LETT |l1| (SPADCALL (CDR |u|) |l1| (QREFELT |$| 54)) |OUTFORM;blankSeparate;L$;33|)) ((QUOTE T) (LETT |l1| (CONS |u| |l1|) |OUTFORM;blankSeparate;L$;33|))))) (LETT #1# (CDR #1#) |OUTFORM;blankSeparate;L$;33|) (GO G190) G191 (EXIT NIL)) (EXIT (CONS |c| |l1|)))))) 

(DEFUN |OUTFORM;brace;2$;34| (|a| |$|) (LIST (|OUTFORM;eform| (QUOTE BRACE) |$|) |a|)) 

(DEFUN |OUTFORM;brace;L$;35| (|l| |$|) (SPADCALL (SPADCALL |l| (QREFELT |$| 51)) (QREFELT |$| 56))) 

(DEFUN |OUTFORM;bracket;2$;36| (|a| |$|) (LIST (|OUTFORM;eform| (QUOTE BRACKET) |$|) |a|)) 

(DEFUN |OUTFORM;bracket;L$;37| (|l| |$|) (SPADCALL (SPADCALL |l| (QREFELT |$| 51)) (QREFELT |$| 58))) 

(DEFUN |OUTFORM;paren;2$;38| (|a| |$|) (LIST (|OUTFORM;eform| (QUOTE PAREN) |$|) |a|)) 

(DEFUN |OUTFORM;paren;L$;39| (|l| |$|) (SPADCALL (SPADCALL |l| (QREFELT |$| 51)) (QREFELT |$| 60))) 

(DEFUN |OUTFORM;sub;3$;40| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE SUB) |$|) |a| |b|)) 

(DEFUN |OUTFORM;super;3$;41| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE SUPERSUB) |$|) |a| (|OUTFORM;sform| " " |$|) |b|)) 

(DEFUN |OUTFORM;presub;3$;42| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE SUPERSUB) |$|) |a| (|OUTFORM;sform| " " |$|) (|OUTFORM;sform| " " |$|) (|OUTFORM;sform| " " |$|) |b|)) 

(DEFUN |OUTFORM;presuper;3$;43| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE SUPERSUB) |$|) |a| (|OUTFORM;sform| " " |$|) (|OUTFORM;sform| " " |$|) |b|)) 

(DEFUN |OUTFORM;scripts;$L$;44| (|a| |l| |$|) (COND ((SPADCALL |l| (QREFELT |$| 66)) |a|) ((SPADCALL (SPADCALL |l| (QREFELT |$| 67)) (QREFELT |$| 66)) (SPADCALL |a| (SPADCALL |l| (QREFELT |$| 68)) (QREFELT |$| 62))) ((QUOTE T) (CONS (|OUTFORM;eform| (QUOTE SUPERSUB) |$|) (CONS |a| |l|))))) 

(DEFUN |OUTFORM;supersub;$L$;45| (|a| |l| |$|) (SEQ (COND ((ODDP (SPADCALL |l| (QREFELT |$| 71))) (LETT |l| (SPADCALL |l| (LIST (SPADCALL (QREFELT |$| 12))) (QREFELT |$| 73)) |OUTFORM;supersub;$L$;45|))) (EXIT (CONS (|OUTFORM;eform| (QUOTE ALTSUPERSUB) |$|) (CONS |a| |l|))))) 

(DEFUN |OUTFORM;hconcat;3$;46| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE CONCAT) |$|) |a| |b|)) 

(DEFUN |OUTFORM;hconcat;L$;47| (|l| |$|) (CONS (|OUTFORM;eform| (QUOTE CONCAT) |$|) |l|)) 

(DEFUN |OUTFORM;vconcat;3$;48| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE VCONCAT) |$|) |a| |b|)) 

(DEFUN |OUTFORM;vconcat;L$;49| (|l| |$|) (CONS (|OUTFORM;eform| (QUOTE VCONCAT) |$|) |l|)) 

(DEFUN |OUTFORM;^=;3$;50| (|a| |b| |$|) (LIST (|OUTFORM;sform| "^=" |$|) |a| |b|)) 

(DEFUN |OUTFORM;<;3$;51| (|a| |b| |$|) (LIST (|OUTFORM;sform| "<" |$|) |a| |b|)) 

(DEFUN |OUTFORM;>;3$;52| (|a| |b| |$|) (LIST (|OUTFORM;sform| ">" |$|) |a| |b|)) 

(DEFUN |OUTFORM;<=;3$;53| (|a| |b| |$|) (LIST (|OUTFORM;sform| "<=" |$|) |a| |b|)) 

(DEFUN |OUTFORM;>=;3$;54| (|a| |b| |$|) (LIST (|OUTFORM;sform| ">=" |$|) |a| |b|)) 

(DEFUN |OUTFORM;+;3$;55| (|a| |b| |$|) (LIST (|OUTFORM;sform| "+" |$|) |a| |b|)) 

(DEFUN |OUTFORM;-;3$;56| (|a| |b| |$|) (LIST (|OUTFORM;sform| "-" |$|) |a| |b|)) 

(DEFUN |OUTFORM;-;2$;57| (|a| |$|) (LIST (|OUTFORM;sform| "-" |$|) |a|)) 

(DEFUN |OUTFORM;*;3$;58| (|a| |b| |$|) (LIST (|OUTFORM;sform| "*" |$|) |a| |b|)) 

(DEFUN |OUTFORM;/;3$;59| (|a| |b| |$|) (LIST (|OUTFORM;sform| "/" |$|) |a| |b|)) 

(DEFUN |OUTFORM;**;3$;60| (|a| |b| |$|) (LIST (|OUTFORM;sform| "**" |$|) |a| |b|)) 

(DEFUN |OUTFORM;div;3$;61| (|a| |b| |$|) (LIST (|OUTFORM;sform| "div" |$|) |a| |b|)) 

(DEFUN |OUTFORM;rem;3$;62| (|a| |b| |$|) (LIST (|OUTFORM;sform| "rem" |$|) |a| |b|)) 

(DEFUN |OUTFORM;quo;3$;63| (|a| |b| |$|) (LIST (|OUTFORM;sform| "quo" |$|) |a| |b|)) 

(DEFUN |OUTFORM;exquo;3$;64| (|a| |b| |$|) (LIST (|OUTFORM;sform| "exquo" |$|) |a| |b|)) 

(DEFUN |OUTFORM;and;3$;65| (|a| |b| |$|) (LIST (|OUTFORM;sform| "and" |$|) |a| |b|)) 

(DEFUN |OUTFORM;or;3$;66| (|a| |b| |$|) (LIST (|OUTFORM;sform| "or" |$|) |a| |b|)) 

(DEFUN |OUTFORM;not;2$;67| (|a| |$|) (LIST (|OUTFORM;sform| "not" |$|) |a|)) 

(DEFUN |OUTFORM;SEGMENT;3$;68| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE SEGMENT) |$|) |a| |b|)) 

(DEFUN |OUTFORM;SEGMENT;2$;69| (|a| |$|) (LIST (|OUTFORM;eform| (QUOTE SEGMENT) |$|) |a|)) 

(DEFUN |OUTFORM;binomial;3$;70| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE BINOMIAL) |$|) |a| |b|)) 

(DEFUN |OUTFORM;empty;$;71| (|$|) (LIST (|OUTFORM;eform| (QUOTE NOTHING) |$|))) 

(DEFUN |OUTFORM;infix?;$B;72| (|a| |$|) (PROG (#1=#:G82802 |e|) (RETURN (SEQ (EXIT (SEQ (LETT |e| (COND ((IDENTP |a|) |a|) ((STRINGP |a|) (INTERN |a|)) ((QUOTE T) (PROGN (LETT #1# (QUOTE NIL) |OUTFORM;infix?;$B;72|) (GO #1#)))) |OUTFORM;infix?;$B;72|) (EXIT (COND ((GET |e| (QUOTE INFIXOP)) (QUOTE T)) ((QUOTE T) (QUOTE NIL)))))) #1# (EXIT #1#))))) 

(PUT (QUOTE |OUTFORM;elt;$L$;73|) (QUOTE |SPADreplace|) (QUOTE CONS)) 

(DEFUN |OUTFORM;elt;$L$;73| (|a| |l| |$|) (CONS |a| |l|)) 

(DEFUN |OUTFORM;prefix;$L$;74| (|a| |l| |$|) (COND ((NULL (SPADCALL |a| (QREFELT |$| 98))) (CONS |a| |l|)) ((QUOTE T) (SPADCALL |a| (SPADCALL (SPADCALL |l| (QREFELT |$| 51)) (QREFELT |$| 60)) (QREFELT |$| 37))))) 

(DEFUN |OUTFORM;infix;$L$;75| (|a| |l| |$|) (COND ((SPADCALL |l| (QREFELT |$| 66)) (SPADCALL (QREFELT |$| 12))) ((SPADCALL (SPADCALL |l| (QREFELT |$| 67)) (QREFELT |$| 66)) (SPADCALL |l| (QREFELT |$| 68))) ((SPADCALL |a| (QREFELT |$| 98)) (CONS |a| |l|)) ((QUOTE T) (SPADCALL (LIST (SPADCALL |l| (QREFELT |$| 68)) |a| (SPADCALL |a| (SPADCALL |l| (QREFELT |$| 101)) (QREFELT |$| 102))) (QREFELT |$| 75))))) 

(DEFUN |OUTFORM;infix;4$;76| (|a| |b| |c| |$|) (COND ((SPADCALL |a| (QREFELT |$| 98)) (LIST |a| |b| |c|)) ((QUOTE T) (SPADCALL (LIST |b| |a| |c|) (QREFELT |$| 75))))) 

(DEFUN |OUTFORM;postfix;3$;77| (|a| |b| |$|) (SPADCALL |b| |a| (QREFELT |$| 37))) 

(DEFUN |OUTFORM;string;2$;78| (|a| |$|) (LIST (|OUTFORM;eform| (QUOTE STRING) |$|) |a|)) 

(DEFUN |OUTFORM;quote;2$;79| (|a| |$|) (LIST (|OUTFORM;eform| (QUOTE QUOTE) |$|) |a|)) 

(DEFUN |OUTFORM;overbar;2$;80| (|a| |$|) (LIST (|OUTFORM;eform| (QUOTE OVERBAR) |$|) |a|)) 

(DEFUN |OUTFORM;dot;2$;81| (|a| |$|) (SPADCALL |a| (|OUTFORM;sform| "." |$|) (QREFELT |$| 63))) 

(DEFUN |OUTFORM;prime;2$;82| (|a| |$|) (SPADCALL |a| (|OUTFORM;sform| "," |$|) (QREFELT |$| 63))) 

(DEFUN |OUTFORM;dot;$Nni$;83| (|a| |nn| |$|) (PROG (|s|) (RETURN (SEQ (LETT |s| (|MAKE-FULL-CVEC| |nn| (SPADCALL "." (QREFELT |$| 110))) |OUTFORM;dot;$Nni$;83|) (EXIT (SPADCALL |a| (|OUTFORM;sform| |s| |$|) (QREFELT |$| 63))))))) 

(DEFUN |OUTFORM;prime;$Nni$;84| (|a| |nn| |$|) (PROG (|s|) (RETURN (SEQ (LETT |s| (|MAKE-FULL-CVEC| |nn| (SPADCALL "," (QREFELT |$| 110))) |OUTFORM;prime;$Nni$;84|) (EXIT (SPADCALL |a| (|OUTFORM;sform| |s| |$|) (QREFELT |$| 63))))))) 

(DEFUN |OUTFORM;overlabel;3$;85| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE OVERLABEL) |$|) |a| |b|)) 

(DEFUN |OUTFORM;box;2$;86| (|a| |$|) (LIST (|OUTFORM;eform| (QUOTE BOX) |$|) |a|)) 

(DEFUN |OUTFORM;zag;3$;87| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE ZAG) |$|) |a| |b|)) 

(DEFUN |OUTFORM;root;2$;88| (|a| |$|) (LIST (|OUTFORM;eform| (QUOTE ROOT) |$|) |a|)) 

(DEFUN |OUTFORM;root;3$;89| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE ROOT) |$|) |a| |b|)) 

(DEFUN |OUTFORM;over;3$;90| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE OVER) |$|) |a| |b|)) 

(DEFUN |OUTFORM;slash;3$;91| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE SLASH) |$|) |a| |b|)) 

(DEFUN |OUTFORM;assign;3$;92| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE LET) |$|) |a| |b|)) 

(DEFUN |OUTFORM;label;3$;93| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE EQUATNUM) |$|) |a| |b|)) 

(DEFUN |OUTFORM;rarrow;3$;94| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE TAG) |$|) |a| |b|)) 

(DEFUN |OUTFORM;differentiate;$Nni$;95| (|a| |nn| |$|) (PROG (#1=#:G82832 |r| |s|) (RETURN (SEQ (COND ((ZEROP |nn|) |a|) ((|<| |nn| 4) (SPADCALL |a| |nn| (QREFELT |$| 112))) ((QUOTE T) (SEQ (LETT |r| (SPADCALL (PROG1 (LETT #1# |nn| |OUTFORM;differentiate;$Nni$;95|) (|check-subtype| (|>| #1# 0) (QUOTE (|PositiveInteger|)) #1#)) (QREFELT |$| 125)) |OUTFORM;differentiate;$Nni$;95|) (LETT |s| (SPADCALL |r| (QREFELT |$| 126)) |OUTFORM;differentiate;$Nni$;95|) (EXIT (SPADCALL |a| (SPADCALL (|OUTFORM;sform| |s| |$|) (QREFELT |$| 60)) (QREFELT |$| 63)))))))))) 

(DEFUN |OUTFORM;sum;2$;96| (|a| |$|) (LIST (|OUTFORM;eform| (QUOTE SIGMA) |$|) (SPADCALL (QREFELT |$| 12)) |a|)) 

(DEFUN |OUTFORM;sum;3$;97| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE SIGMA) |$|) |b| |a|)) 

(DEFUN |OUTFORM;sum;4$;98| (|a| |b| |c| |$|) (LIST (|OUTFORM;eform| (QUOTE SIGMA2) |$|) |b| |c| |a|)) 

(DEFUN |OUTFORM;prod;2$;99| (|a| |$|) (LIST (|OUTFORM;eform| (QUOTE PI) |$|) (SPADCALL (QREFELT |$| 12)) |a|)) 

(DEFUN |OUTFORM;prod;3$;100| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE PI) |$|) |b| |a|)) 

(DEFUN |OUTFORM;prod;4$;101| (|a| |b| |c| |$|) (LIST (|OUTFORM;eform| (QUOTE PI2) |$|) |b| |c| |a|)) 

(DEFUN |OUTFORM;int;2$;102| (|a| |$|) (LIST (|OUTFORM;eform| (QUOTE INTSIGN) |$|) (SPADCALL (QREFELT |$| 12)) (SPADCALL (QREFELT |$| 12)) |a|)) 

(DEFUN |OUTFORM;int;3$;103| (|a| |b| |$|) (LIST (|OUTFORM;eform| (QUOTE INTSIGN) |$|) |b| (SPADCALL (QREFELT |$| 12)) |a|)) 

(DEFUN |OUTFORM;int;4$;104| (|a| |b| |c| |$|) (LIST (|OUTFORM;eform| (QUOTE INTSIGN) |$|) |b| |c| |a|)) 

(DEFUN |OutputForm| NIL (PROG NIL (RETURN (PROG (#1=#:G82846) (RETURN (COND ((LETT #1# (HGET |$ConstructorCache| (QUOTE |OutputForm|)) |OutputForm|) (|CDRwithIncrement| (CDAR #1#))) ((QUOTE T) (|UNWIND-PROTECT| (PROG1 (CDDAR (HPUT |$ConstructorCache| (QUOTE |OutputForm|) (LIST (CONS NIL (CONS 1 (|OutputForm;|)))))) (LETT #1# T |OutputForm|)) (COND ((NOT #1#) (HREM |$ConstructorCache| (QUOTE |OutputForm|)))))))))))) 

(DEFUN |OutputForm;| NIL (PROG (|dv$| |$| |pv$|) (RETURN (PROGN (LETT |dv$| (QUOTE (|OutputForm|)) . #1=(|OutputForm|)) (LETT |$| (GETREFV 138) . #1#) (QSETREFV |$| 0 |dv$|) (QSETREFV |$| 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #1#)) (|haddProp| |$ConstructorCache| (QUOTE |OutputForm|) NIL (CONS 1 |$|)) (|stuffDomainSlots| |$|) (QSETREFV |$| 6 (|List| |$|)) |$|)))) 

(MAKEPROP (QUOTE |OutputForm|) (QUOTE |infovec|) (LIST (QUOTE #(NIL NIL NIL NIL NIL NIL (QUOTE |Rep|) (|Void|) |OUTFORM;print;$V;1| (|Boolean|) (|String|) (0 . |empty?|) |OUTFORM;empty;$;71| |OUTFORM;message;S$;2| |OUTFORM;messagePrint;SV;3| |OUTFORM;=;2$B;4| |OUTFORM;=;3$;5| (|OutputForm|) |OUTFORM;coerce;2$;6| (|Integer|) |OUTFORM;outputForm;I$;7| (|Symbol|) |OUTFORM;outputForm;S$;8| (|DoubleFloat|) |OUTFORM;outputForm;Df$;9| (|Character|) (5 . |quote|) (9 . |concat|) (15 . |concat|) |OUTFORM;outputForm;S$;13| |OUTFORM;width;$I;14| |OUTFORM;height;$I;15| |OUTFORM;subHeight;$I;16| |OUTFORM;superHeight;$I;17| |OUTFORM;height;I;18| |OUTFORM;width;I;19| |OUTFORM;hspace;I$;27| |OUTFORM;hconcat;3$;46| |OUTFORM;center;$I$;20| |OUTFORM;left;$I$;21| |OUTFORM;right;$I$;22| |OUTFORM;center;2$;23| |OUTFORM;left;2$;24| |OUTFORM;right;2$;25| |OUTFORM;vspace;I$;26| |OUTFORM;vconcat;3$;48| |OUTFORM;rspace;2I$;28| (|List| 49) |OUTFORM;matrix;L$;29| (|List| |$|) |OUTFORM;pile;L$;30| |OUTFORM;commaSeparate;L$;31| |OUTFORM;semicolonSeparate;L$;32| (21 . |reverse|) (26 . |append|) |OUTFORM;blankSeparate;L$;33| |OUTFORM;brace;2$;34| |OUTFORM;brace;L$;35| |OUTFORM;bracket;2$;36| |OUTFORM;bracket;L$;37| |OUTFORM;paren;2$;38| |OUTFORM;paren;L$;39| |OUTFORM;sub;3$;40| |OUTFORM;super;3$;41| |OUTFORM;presub;3$;42| |OUTFORM;presuper;3$;43| (32 . |null|) (37 . |rest|) (42 . |first|) |OUTFORM;scripts;$L$;44| (|NonNegativeInteger|) (47 . |#|) (|List| |$$|) (52 . |append|) |OUTFORM;supersub;$L$;45| |OUTFORM;hconcat;L$;47| |OUTFORM;vconcat;L$;49| |OUTFORM;^=;3$;50| |OUTFORM;<;3$;51| |OUTFORM;>;3$;52| |OUTFORM;<=;3$;53| |OUTFORM;>=;3$;54| |OUTFORM;+;3$;55| |OUTFORM;-;3$;56| |OUTFORM;-;2$;57| |OUTFORM;*;3$;58| |OUTFORM;/;3$;59| |OUTFORM;**;3$;60| |OUTFORM;div;3$;61| |OUTFORM;rem;3$;62| |OUTFORM;quo;3$;63| |OUTFORM;exquo;3$;64| |OUTFORM;and;3$;65| |OUTFORM;or;3$;66| |OUTFORM;not;2$;67| |OUTFORM;SEGMENT;3$;68| |OUTFORM;SEGMENT;2$;69| |OUTFORM;binomial;3$;70| |OUTFORM;infix?;$B;72| |OUTFORM;elt;$L$;73| |OUTFORM;prefix;$L$;74| (58 . |rest|) |OUTFORM;infix;$L$;75| |OUTFORM;infix;4$;76| |OUTFORM;postfix;3$;77| |OUTFORM;string;2$;78| |OUTFORM;quote;2$;79| |OUTFORM;overbar;2$;80| |OUTFORM;dot;2$;81| |OUTFORM;prime;2$;82| (63 . |char|) |OUTFORM;dot;$Nni$;83| |OUTFORM;prime;$Nni$;84| |OUTFORM;overlabel;3$;85| |OUTFORM;box;2$;86| |OUTFORM;zag;3$;87| |OUTFORM;root;2$;88| |OUTFORM;root;3$;89| |OUTFORM;over;3$;90| |OUTFORM;slash;3$;91| |OUTFORM;assign;3$;92| |OUTFORM;label;3$;93| |OUTFORM;rarrow;3$;94| (|PositiveInteger|) (|NumberFormats|) (68 . |FormatRoman|) (73 . |lowerCase|) |OUTFORM;differentiate;$Nni$;95| |OUTFORM;sum;2$;96| |OUTFORM;sum;3$;97| |OUTFORM;sum;4$;98| |OUTFORM;prod;2$;99| |OUTFORM;prod;3$;100| |OUTFORM;prod;4$;101| |OUTFORM;int;2$;102| |OUTFORM;int;3$;103| |OUTFORM;int;4$;104| (|SingleInteger|))) (QUOTE #(|~=| 78 |zag| 84 |width| 90 |vspace| 99 |vconcat| 104 |supersub| 115 |superHeight| 121 |super| 126 |sum| 132 |subHeight| 150 |sub| 155 |string| 161 |slash| 166 |semicolonSeparate| 172 |scripts| 177 |rspace| 183 |root| 189 |right| 200 |rem| 211 |rarrow| 217 |quote| 223 |quo| 228 |prod| 234 |print| 252 |prime| 257 |presuper| 268 |presub| 274 |prefix| 280 |postfix| 286 |pile| 292 |paren| 297 |overlabel| 307 |overbar| 313 |over| 318 |outputForm| 324 |or| 344 |not| 350 |messagePrint| 355 |message| 360 |matrix| 365 |left| 370 |latex| 381 |label| 386 |int| 392 |infix?| 410 |infix| 415 |hspace| 428 |height| 433 |hconcat| 442 |hash| 453 |exquo| 458 |empty| 464 |elt| 468 |dot| 474 |div| 485 |differentiate| 491 |commaSeparate| 497 |coerce| 502 |center| 507 |bracket| 518 |brace| 528 |box| 538 |blankSeparate| 543 |binomial| 548 |assign| 554 |and| 560 |^=| 566 SEGMENT 572 |>=| 583 |>| 589 |=| 595 |<=| 607 |<| 613 |/| 619 |-| 625 |+| 636 |**| 642 |*| 648)) (QUOTE NIL) (CONS (|makeByteWordVec2| 1 (QUOTE (0 0 0))) (CONS (QUOTE #(|SetCategory&| |BasicType&| NIL)) (CONS (QUOTE #((|SetCategory|) (|BasicType|) (|CoercibleTo| 17))) (|makeByteWordVec2| 137 (QUOTE (1 10 9 0 11 0 25 0 26 2 10 0 0 25 27 2 10 0 25 0 28 1 6 0 0 53 2 6 0 0 0 54 1 6 9 0 66 1 6 0 0 67 1 6 2 0 68 1 6 70 0 71 2 72 0 0 0 73 1 72 0 0 101 1 25 0 10 110 1 124 10 123 125 1 10 0 0 126 2 0 9 0 0 1 2 0 0 0 0 115 0 0 19 35 1 0 19 0 30 1 0 0 19 44 1 0 0 49 76 2 0 0 0 0 45 2 0 0 0 49 74 1 0 19 0 33 2 0 0 0 0 63 2 0 0 0 0 129 3 0 0 0 0 0 130 1 0 0 0 128 1 0 19 0 32 2 0 0 0 0 62 1 0 0 0 105 2 0 0 0 0 119 1 0 0 49 52 2 0 0 0 49 69 2 0 0 19 19 46 1 0 0 0 116 2 0 0 0 0 117 1 0 0 0 43 2 0 0 0 19 40 2 0 0 0 0 89 2 0 0 0 0 122 1 0 0 0 106 2 0 0 0 0 90 3 0 0 0 0 0 133 1 0 0 0 131 2 0 0 0 0 132 1 0 7 0 8 2 0 0 0 70 112 1 0 0 0 109 2 0 0 0 0 65 2 0 0 0 0 64 2 0 0 0 49 100 2 0 0 0 0 104 1 0 0 49 50 1 0 0 49 61 1 0 0 0 60 2 0 0 0 0 113 1 0 0 0 107 2 0 0 0 0 118 1 0 0 10 29 1 0 0 23 24 1 0 0 21 22 1 0 0 19 20 2 0 0 0 0 93 1 0 0 0 94 1 0 7 10 14 1 0 0 10 13 1 0 0 47 48 1 0 0 0 42 2 0 0 0 19 39 1 0 10 0 1 2 0 0 0 0 121 3 0 0 0 0 0 136 2 0 0 0 0 135 1 0 0 0 134 1 0 9 0 98 2 0 0 0 49 102 3 0 0 0 0 0 103 1 0 0 19 36 0 0 19 34 1 0 19 0 31 1 0 0 49 75 2 0 0 0 0 37 1 0 137 0 1 2 0 0 0 0 91 0 0 0 12 2 0 0 0 49 99 2 0 0 0 70 111 1 0 0 0 108 2 0 0 0 0 88 2 0 0 0 70 127 1 0 0 49 51 1 0 17 0 18 1 0 0 0 41 2 0 0 0 19 38 1 0 0 0 58 1 0 0 49 59 1 0 0 49 57 1 0 0 0 56 1 0 0 0 114 1 0 0 49 55 2 0 0 0 0 97 2 0 0 0 0 120 2 0 0 0 0 92 2 0 0 0 0 77 1 0 0 0 96 2 0 0 0 0 95 2 0 0 0 0 81 2 0 0 0 0 79 2 0 0 0 0 16 2 0 9 0 0 15 2 0 0 0 0 80 2 0 0 0 0 78 2 0 0 0 0 86 1 0 0 0 84 2 0 0 0 0 83 2 0 0 0 0 82 2 0 0 0 0 87 2 0 0 0 0 85)))))) (QUOTE |lookupComplete|))) 

(MAKEPROP (QUOTE |OutputForm|) (QUOTE NILADIC) T) 
@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
--
--Redistribution and use in source and binary forms, with or without
--modification, are permitted provided that the following conditions are
--met:
--
--    - Redistributions of source code must retain the above copyright
--      notice, this list of conditions and the following disclaimer.
--
--    - 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.
--
--    - Neither the name of The Numerical ALgorithms Group Ltd. 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 OWNER
--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.
@
<<*>>=
<<license>>

<<package NUMFMT NumberFormats>>
<<domain OUTFORM OutputForm>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}