Allow adding additional sub/superscripts to symbols.

(1) -> <spad>

)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, OpenMath,
        ConvertibleTo Symbol,
         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.
     conjugate : % -> %
       ++ conjugate(s) returns the symbolic conjugate of s.
     resetNew : () -> Void
       ++ resetNew() resets the internals counters that new() and
       ++ new(s) use to return distinct symbols every time.
     coerce : String -> %
       ++ coerce(s) converts the string s to a symbol.
     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]}.
     _^ : (%,L) -> %
     string : % -> String
       ++ string(s) converts the symbol s to a string.
       ++ Error: if the symbol is subscripted.
     sample : constant -> %
       ++ sample() returns a sample of %

  Implementation ==> add

    import from Character
    import from List(OutputForm)
    import from List(%)

    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"

    writeOMSym(dev : OpenMathDevice, x : %) : Void ==
      scripted? x =>
        error "Cannot convert a scripted symbol to OpenMath"
      OMputVariable(dev, x pretend Symbol)

    OMwrite(dev : OpenMathDevice, x : %, wholeObj : Boolean) : Void ==
      if wholeObj then
        OMputObject(dev)
      writeOMSym(dev, x)
      if wholeObj then
        OMputEndObject(dev)

    hd:String    := "*"
    lhd          := #hd
    ord0         := ord char("0")$Character
    pcnt         ==> 4
    conj:String  := "*"

    istring  : Integer -> String
    syprefix : Scripts -> String
    syscripts : Scripts -> L
    conjugate? : % -> Boolean

    convert(s : %) : InputForm ==
      --conjugate? s => prefix(outputForm 'conjugate,[conjugate(s) pretend OutputForm]) pretend InputForm
      conjugate? s => convert([convert('conjugate)@InputForm,conjugate(s) pretend InputForm]$List(InputForm))@InputForm
      scripted? s =>
         sc:Scripts := scripts s
         convert([convert('script)@InputForm,name(s) pretend InputForm, _
                   convert([convert('construct)@InputForm, _
                     prefix(outputForm 'construct, sc.sub pretend List OutputForm) _
                       pretend InputForm, _
                     prefix(outputForm 'construct, sc.sup pretend List OutputForm) _
                       pretend InputForm, _
                     prefix(outputForm 'construct, sc.presub pretend List OutputForm) _
                       pretend InputForm, _
                     prefix(outputForm 'construct, sc.presub pretend List OutputForm) _
                       pretend InputForm, _
                     prefix(outputForm 'construct, sc.args pretend List OutputForm) _
                       pretend InputForm _
                   ]$List(InputForm))@InputForm _
                 ]$List(InputForm))@InputForm
      convert(s pretend Symbol)$InputForm
    convert(s : %) : Symbol    == s pretend Symbol
    coerce(s : String) : %     == VALUES(INTERN(s)$Lisp)$Lisp
    x = y                  == EQUAL(x, y)$Lisp
    hashUpdate!(hs, s)     == update!(hs, SXHASH(s)$Lisp)$HashState
    x < y                  == GGREATERP(y, x)$Lisp

    coerce(x : %) : OutputForm ==
        not(scripted? x) =>
          conjugate? x => overbar(outputForm(conjugate x pretend Symbol))
          outputForm(x pretend Symbol)
        ss : Scripts := scripts x
        rsl : List(L) := [ss.presub, ss.presup, ss.sup, ss.sub]
        sl : L := []
        for si in rsl repeat
            empty?(sl) and empty?(si) => "iterate"
            se :=
                #si = 1 => first(si)
                commaSeparate(si)
            sl := cons(se, sl)
        if conjugate? x then
          x0 := scripts(outputForm(conjugate name(x) pretend Symbol), sl)
        else
          x0 := scripts(outputForm(name(x) pretend Symbol), sl)
        a := ss.args
        if not empty?(a) then x0 := prefix(x0, a)
        conjugate? x => overbar x0
        x0

    subscript(sy, lx)      == script(sy, [lx, nil, nil(), nil(), nil()])
    elt(sy, lx)            == subscript(sy, lx)
    sy ^ lx                == superscript(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]
      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"
      oldsc:=scripts(sy)
      --output("symbol oldsc: ",oldsc::OutputForm)$OutputPackage
      newsc:Scripts := [concat(oldsc.sub,sc.sub), _
                        concat(oldsc.sup,sc.sup), _
                        concat(oldsc.presup,sc.presup), _
                        concat(oldsc.presub,sc.presub), _
                        concat(oldsc.args,sc.args)]
      --output("symbol newsc: ",newsc::OutputForm)$OutputPackage
      (concat(concat(syprefix newsc, string name sy)::% pretend OutputForm,
                                                syscripts newsc)) 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)
      void

    scripted? sy ==
      not ATOM(sy)$Lisp

    of_list(x : %) : L == x pretend L

    name sy ==
        not scripted? sy => sy
        str := string(first(of_list(sy)) pretend %)
        si := lhd + pcnt + 2
        str(si..#str)::%

    conjugate? sy ==
        str:=string(name sy)
        str(#str..#str)=conj

    conjugate sy ==
        str:=string(name sy)
        if conjugate? sy then
          str:=str(1..#str-1)
        else
          str:=concat(str,conj)
        str
        not scripted? sy => str::%
        script(str::%, scripts sy)

    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(of_list(sy)) pretend %)
      nstr := #str
      m := minIndex nscripts
      for i in m.. for j in (lhd + 1)..(lhd + pcnt + 1) 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(of_list(sy))
      m := minIndex lscripts
      for i in m.. for n in nscripts repeat
        #allscripts < n => error "Improper script count in symbol"
        lscripts.i := 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)

    sample() == "aSymbol"::%

--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.</spad>

Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/2136517885840098381-25px001.spad
      using old system compiler.
   SYMBOL abbreviates domain Symbol 
------------------------------------------------------------------------
   initializing NRLIB SYMBOL for Symbol 
   compiling into NRLIB SYMBOL 
   importing Character
   importing List OutputForm
   importing List %
   compiling local writeOMSym : (OpenMathDevice,%) -> Void

;;;     ***       |SYMBOL;writeOMSym| REDEFINED
Time: 0.04 SEC.

   compiling exported OMwrite : (OpenMathDevice,%,Boolean) -> Void

;;;     ***       |SYMBOL;OMwrite;Omd%BV;2| REDEFINED
Time: 0 SEC.

   processing macro definition pcnt ==> 4 
   compiling exported convert : % -> InputForm

;;;     ***       |SYMBOL;convert;%If;3| REDEFINED
Time: 0.45 SEC.

   compiling exported convert : % -> Symbol
      SYMBOL;convert;2%;4 is replaced by s 

;;;     ***       |SYMBOL;convert;2%;4| REDEFINED
Time: 0 SEC.

   compiling exported coerce : String -> %

;;;     ***       |SYMBOL;coerce;S%;5| REDEFINED
Time: 0 SEC.

   compiling exported = : (%,%) -> Boolean
      SYMBOL;=;2%B;6 is replaced by EQUAL 

;;;     ***       |SYMBOL;=;2%B;6| REDEFINED
Time: 0 SEC.

************* USER ERROR **********
available signatures for hashUpdate!: 
     hashUpdate!: ((|HashState|),(|Character|)) -> (|HashState|)
     hashUpdate!: ((|HashState|),(|List| (|OutputForm|))) -> (|HashState|)
     hashUpdate!: ((|HashState|),(|List| %)) -> (|HashState|)
     hashUpdate!: ((|HashState|),(|NonNegativeInteger|)) -> (|HashState|)
     hashUpdate!: ((|HashState|),(|Integer|)) -> (|HashState|)
     hashUpdate!: ((|HashState|),(|AssociationList| % (|Integer|))) -> (|HashState|)
     hashUpdate!: ((|HashState|),(|String|)) -> (|HashState|)
     hashUpdate!: ((|HashState|),(|PrimitiveArray| (|String|))) -> (|HashState|)
     hashUpdate!: ((|HashState|),(|List| (|String|))) -> (|HashState|)
NEED hashUpdate!: (NIL,NIL) -> ?
   Semantic Errors: 
      [1] hashUpdate!: argument hs of (hashUpdate! hs s) is not declared
      [2] hashUpdate!: argument s of (hashUpdate! hs s) is not declared

   Warnings: 
      [1] convert: pretend(List (OutputForm)) -- should replace by @
      [2] convert:  args has no value

****** comp fails at level 1 with expression: ******
((DEF (|hashUpdate!| |hs| |s|) (NIL NIL NIL)
  ((|Sel| (|HashState|) |update!|) |hs| ((|Sel| |Lisp| SXHASH) |s|))))
****** level 1  ******
$x:= (DEF (hashUpdate! hs s) (NIL NIL NIL) ((Sel (HashState) update!) hs ((Sel Lisp SXHASH) s)))
$m:= $EmptyMode
$f:=
((((|conjugate?| #) (|syscripts| #) (|syprefix| #) (|istring| #) ...)
  ((|writeOMSym| #) (|coerce| #) (|void| #) (|$DomainsInScope| # # #) ...)))

   >> Apparent user error:
   unspecified error

Examples

conjugate x

(1)

conjugate %

(2)

test(conjugate conjugate x = x)

(3)

x[1][2]

   >> Error detected within library code:
   Cannot add scripts to a scripted symbol

InputForm

conjugate(x)::InputForm

(4)

convert(conjugate(x))$Symbol@InputForm

   There are 23 exposed and 12 unexposed library operations named 
      convert having 1 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                             )display op convert
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named 
      convert with argument type(s) 
                             Expression(Integer)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.