path: root/src/algebra/symbol.spad.pamphlet

\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{\$SPAD/src/algebra symbol.spad}
\author{Stephen M. Watt}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{domain SYMBOL Symbol}
<<domain SYMBOL Symbol>>=
)abbrev domain SYMBOL Symbol
++ Author: Stephen Watt
++ Date Created: 1986
++ Date Last Updated: 7 Mar 1991, 29 Apr. 1994 (FDLL)
++ Description:
++   Basic and scripted symbols.
++ Keywords: symbol.
Symbol(): Exports == Implementation where
  L ==> List OutputForm
  Scripts ==> Record(sub:L,sup:L,presup:L,presub:L,args:L)

  Exports ==> Join(OrderedSet, ConvertibleTo InputForm,
       ConvertibleTo Symbol,CoercibleFrom String,
        RetractableTo Identifier,
         ConvertibleTo Pattern Integer, ConvertibleTo Pattern Float,
          PatternMatchable Integer, PatternMatchable Float) with
     new: () -> %
       ++ new() returns a new symbol whose name starts with %.
     new: % -> %
       ++ new(s) returns a new symbol whose name starts with %s.
     resetNew: () -> Void
       ++ resetNew() resets the internals counters that new() and
       ++ new(s) use to return distinct symbols every time.
     name: % -> %
       ++ name(s) returns s without its scripts.
     scripted?: % -> Boolean
       ++ scripted?(s) is true if s has been given any scripts.
     scripts: % -> Scripts
       ++ scripts(s) returns all the scripts of s.
     script: (%, List L) -> %
       ++ script(s, [a,b,c,d,e]) returns s with subscripts a,
       ++ superscripts b, pre-superscripts c, pre-subscripts d,
       ++ and argument-scripts e.  Omitted components are taken to be empty.
       ++ For example, \spad{script(s, [a,b,c])} is equivalent to
       ++ \spad{script(s,[a,b,c,[],[]])}.
     script: (%, Scripts) -> %
       ++ script(s, [a,b,c,d,e]) returns s with subscripts a,
       ++ superscripts b, pre-superscripts c, pre-subscripts d,
       ++ and argument-scripts e.
     subscript: (%, L) -> %
       ++ subscript(s, [a1,...,an]) returns s
       ++ subscripted by \spad{[a1,...,an]}.
     superscript: (%, L) -> %
       ++ superscript(s, [a1,...,an]) returns s
       ++ superscripted by \spad{[a1,...,an]}.
     argscript: (%, L) -> %
       ++ argscript(s, [a1,...,an]) returns s
       ++ arg-scripted by \spad{[a1,...,an]}.
     elt: (%, L) -> %
       ++ elt(s,[a1,...,an]) or s([a1,...,an]) returns s subscripted by \spad{[a1,...,an]}.
     string: % -> String
       ++ string(s) converts the symbol s to a string.
       ++ Error: if the symbol is subscripted.
     list: % -> List %
       ++ list(sy) takes a scripted symbol and produces a list
       ++ of the name followed by the scripts.
     sample: constant -> %
       ++ sample() returns a sample of %

  Implementation ==> add
    import %equal: (%,%) -> Boolean   from Foreign Builtin
    import %before?: (%,%) -> Boolean from Foreign Builtin

    count: Reference(Integer) := ref 0
    xcount: AssociationList(%, Integer) := empty()
    istrings:PrimitiveArray(String) :=
                     construct ["0","1","2","3","4","5","6","7","8","9"]
    -- the following 3 strings shall be of empty intersection
    nums:String:="0123456789"
    ALPHAS:String:="ABCDEFGHIJKLMNOPQRSTUVWXYZ"
    alphas:String:="abcdefghijklmnopqrstuvwxyz"

    hd:String    := "*"
    lhd          := #hd
    ord0         := ord char("0")$Character

    istring  : Integer -> String
    syprefix : Scripts -> String
    syscripts: Scripts -> L

    convert(s:%):InputForm == convert(s pretend Symbol)$InputForm
    convert(s:%):Symbol    == s pretend Symbol
    coerce(s:String):%     == VALUES(INTERN(s)$Lisp)$Lisp
    x = y                  == %equal(x,y)
    x < y                  == %before?(x,y)
    coerce(x:%):OutputForm == outputForm(x pretend Symbol)
    subscript(sy, lx)      == script(sy, [lx, nil, nil(), nil(), nil()])
    elt(sy,lx)             == subscript(sy,lx)
    superscript(sy, lx)    == script(sy,[nil(),lx, nil(), nil(), nil()])
    argscript(sy, lx)      == script(sy,[nil(),nil(), nil(), nil(), lx])

    patternMatch(x:%,p:Pattern Integer,l:PatternMatchResult(Integer,%))==
      (patternMatch(x pretend Symbol, p, l pretend
       PatternMatchResult(Integer, Symbol))$PatternMatchSymbol(Integer))
         pretend PatternMatchResult(Integer, %)

    patternMatch(x:%, p:Pattern Float, l:PatternMatchResult(Float, %)) ==
      (patternMatch(x pretend Symbol, p, l pretend
       PatternMatchResult(Float, Symbol))$PatternMatchSymbol(Float))
         pretend PatternMatchResult(Float, %)

    convert(x:%):Pattern(Float) ==
      coerce(x pretend Symbol)$Pattern(Float)

    convert(x:%):Pattern(Integer) ==
      coerce(x pretend Symbol)$Pattern(Integer)

    syprefix sc ==
      ns: List Integer := [#sc.presub, #sc.presup, #sc.sup, #sc.sub]
      while #ns >= 2 and zero? first ns repeat ns := rest ns
      concat concat(concat(hd, istring(#sc.args)),
                                 [istring n for n in reverse! ns])

    syscripts sc ==
      all := sc.presub
      all := concat(sc.presup, all)
      all := concat(sc.sup, all)
      all := concat(sc.sub, all)
      concat(all, sc.args)

    script(sy: %, ls: List L) ==
      sc: Scripts := [nil(), nil(), nil(), nil(), nil()]
      if not null ls then (sc.sub    := first ls; ls := rest ls)
      if not null ls then (sc.sup    := first ls; ls := rest ls)
      if not null ls then (sc.presup := first ls; ls := rest ls)
      if not null ls then (sc.presub := first ls; ls := rest ls)
      if not null ls then (sc.args   := first ls; ls := rest ls)
      script(sy, sc)

    script(sy: %, sc: Scripts) ==
      scripted? sy => error "Cannot add scripts to a scripted symbol"
      (concat(concat(syprefix sc, string name sy)::%::OutputForm,
                                                syscripts sc)) pretend %

    string e ==
      not scripted? e => PNAME(e)$Lisp
      error "Cannot form string from non-atomic symbols."

-- Scripts ==> Record(sub:L,sup:L,presup:L,presub:L,args:L)
    latex e ==
      s : String := (PNAME(name e)$Lisp) pretend String
      if #s > 1 and s.1 ~= char "\" then
        s := concat("\mbox{\it ", concat(s, "}")$String)$String
      not scripted? e => s
      ss : Scripts := scripts e
      lo : List OutputForm := ss.sub
      sc : String
      if not empty? lo then
        sc := "__{"
        while not empty? lo repeat
            sc := concat(sc, latex first lo)$String
            lo := rest lo
            if not empty? lo then sc := concat(sc, ", ")$String
        sc := concat(sc, "}")$String
        s := concat(s, sc)$String
      lo := ss.sup
      if not empty? lo then
        sc := "^{"
        while not empty? lo repeat
            sc := concat(sc, latex first lo)$String
            lo := rest lo
            if not empty? lo then sc := concat(sc, ", ")$String
        sc := concat(sc, "}")$String
        s := concat(s, sc)$String
      lo := ss.presup
      if not empty? lo then
        sc := "{}^{"
        while not empty? lo repeat
            sc := concat(sc, latex first lo)$String
            lo := rest lo
            if not empty? lo then sc := concat(sc, ", ")$String
        sc := concat(sc, "}")$String
        s := concat(sc, s)$String
      lo := ss.presub
      if not empty? lo then
        sc := "{}__{"
        while not empty? lo repeat
            sc := concat(sc, latex first lo)$String
            lo := rest lo
            if not empty? lo then sc := concat(sc, ", ")$String
        sc := concat(sc, "}")$String
        s := concat(sc, s)$String
      lo := ss.args
      if not empty? lo then
        sc := "\left( {"
        while not empty? lo repeat
            sc := concat(sc, latex first lo)$String
            lo := rest lo
            if not empty? lo then sc := concat(sc, ", ")$String
        sc := concat(sc, "} \right)")$String
        s := concat(s, sc)$String
      s

    anyRadix(n:Integer,s:String):String ==
      ns:String:=""
      repeat
        qr := divide(n,#s)
        n  := qr.quotient
        ns := concat(s.(qr.remainder+minIndex s),ns)
        if zero?(n) then return ns
      
    new() ==
      sym := anyRadix(count()::Integer,ALPHAS)
      count() := count() + 1
      concat("%",sym)::%

    new x ==
      n:Integer :=
        (u := search(x, xcount)) case "failed" => 0
        inc(u::Integer)
      xcount(x) := n
      xx := 
        not scripted? x => string x
        string name x
      xx := concat("%",xx)
      xx :=
        (position(xx.maxIndex(xx),nums)>=minIndex(nums)) => 
          concat(xx, anyRadix(n,alphas))
        concat(xx, anyRadix(n,nums))
      not scripted? x => xx::%
      script(xx::%,scripts x)

    resetNew() ==
      count() := 0
      for k in keys xcount repeat remove!(k, xcount)

    scripted? sy ==
      %pair?(sy)$Foreign(Builtin)

    name sy ==
      not scripted? sy => sy
      str := string first list sy
      for i in lhd+1..#str repeat
        not digit?(str.i) => return((str.(i..#str))::%)
      error "Improper scripted symbol"

    scripts sy ==
      not scripted? sy => [nil(), nil(), nil(), nil(), nil()]
      nscripts: List NonNegativeInteger := [0, 0, 0, 0, 0]
      lscripts: List L := [nil(), nil(), nil(), nil(), nil()]
      str  := string first list sy
      nstr := #str
      m := minIndex nscripts
      for i in m.. for j in lhd+1..nstr while digit?(str.j) repeat
          nscripts.i := (ord(str.j) - ord0)::NonNegativeInteger
      -- Put the number of function scripts at the end.
      nscripts := concat(rest nscripts, first nscripts)
      allscripts := rest list sy
      m := minIndex lscripts
      for i in m.. for n in nscripts repeat
        #allscripts < n => error "Improper script count in symbol"
        lscripts.i := [a::OutputForm for a in first(allscripts, n)]
        allscripts := rest(allscripts, n)
      [lscripts.m, lscripts.(m+1), lscripts.(m+2),
                                         lscripts.(m+3), lscripts.(m+4)]

    istring n ==
      n > 9 => error "Can have at most 9 scripts of each kind"
      istrings.(n + minIndex istrings)

    list sy ==
      not scripted? sy =>
         error "Cannot convert a symbol to a list if it is not subscripted"
      sy pretend List(%)

    sample() == 'aSymbol
    coerce(x: Identifier): % == x : %
    retractIfCan(x): Union(Identifier,"failed") ==
      scripted? x => x : Identifier
      "failed"

@

\section{License}

<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
-- Copyright (C) 2007-2010, Gabriel Dos Reis.
-- 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>>

<<domain SYMBOL Symbol>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}