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SandBoxSymbol

Edit detail for SandBoxSymbol revision 3 of 6

	1 2 3 4 5 6
Editor: Bill Page Time: 2015/02/27 21:12:54 GMT+0
Note: merge scripts

added:
      output("symbol oldsc: ",oldsc::OutputForm)$OutputPackage

changed:
-      (concat(concat(syprefix sc, string name sy)::%::OutputForm,
      output("symbol newsc: ",newsc::OutputForm)$OutputPackage
      (concat(concat(syprefix newsc, string name sy)::%::OutputForm,

added:

Examples
\begin{axiom}
A:=superscript('a,['b])
B:=subscript(A,['c])
C:=argscript(B,['x])
D:=subscript(C,['d])
\end{axiom}

Allow adding additional sub/superscripts to symbols.

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.
     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]}.
     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

    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)$Lisp
    x = y                  == EQUAL(x, y)$Lisp
    hashUpdate!(hs, s)     == update!(hs, SXHASH(s)$Lisp)$HashState
    x < y                  == GGREATERP(y, x)$Lisp

    coerce(x : %) : OutputForm ==
        not(scripted? x) => 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)
        x0 := scripts(outputForm(name(x) pretend Symbol), sl)
        a := ss.args
        empty?(a) => x0
        prefix(x0, a)

    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]
      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)$OutputPackage
      newsc:Scripts := [concat(sc.sub,oldsc.sub), _
                        concat(sc.sup,oldsc.sup), _
                        concat(sc.presup,oldsc.presup), _
                        concat(sc.presub,oldsc.presub), _
                        concat(sc.args,oldsc.args)]
      output("symbol newsc: ",newsc::OutputForm)$OutputPackage
      (concat(concat(syprefix newsc, string name sy)::%::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)::%

    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/6497064979997941388-25px001.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: 0.05 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: 0.01 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.

   compiling exported hashUpdate! : (HashState,$) -> HashState

;;;     ***       |SYMBOL;hashUpdate!;Hs$Hs;7| REDEFINED
Time: 0 SEC.

   compiling exported < : ($,$) -> Boolean
      SYMBOL;<;2$B;8 is replaced by GGREATERPyx 

;;;     ***       |SYMBOL;<;2$B;8| REDEFINED
Time: 0.01 SEC.

   compiling exported coerce : $ -> OutputForm

;;;     ***       |SYMBOL;coerce;$Of;9| REDEFINED
Time: 0.01 SEC.

   compiling exported subscript : ($,List OutputForm) -> $

;;;     ***       |SYMBOL;subscript;$L$;10| REDEFINED
Time: 0.02 SEC.

   compiling exported elt : ($,List OutputForm) -> $

;;;     ***       |SYMBOL;elt;$L$;11| REDEFINED
Time: 0 SEC.

   compiling exported superscript : ($,List OutputForm) -> $

;;;     ***       |SYMBOL;superscript;$L$;12| REDEFINED
Time: 0 SEC.

   compiling exported argscript : ($,List OutputForm) -> $

;;;     ***       |SYMBOL;argscript;$L$;13| REDEFINED
Time: 0 SEC.

   compiling exported patternMatch : ($,Pattern Integer,PatternMatchResult(Integer,$)) -> PatternMatchResult(Integer,$)

;;;     ***       |SYMBOL;patternMatch;$P2Pmr;14| REDEFINED
Time: 0 SEC.

   compiling exported patternMatch : ($,Pattern Float,PatternMatchResult(Float,$)) -> PatternMatchResult(Float,$)

;;;     ***       |SYMBOL;patternMatch;$P2Pmr;15| REDEFINED
Time: 0.01 SEC.

   compiling exported convert : $ -> Pattern Float

;;;     ***       |SYMBOL;convert;$P;16| REDEFINED
Time: 0 SEC.

   compiling exported convert : $ -> Pattern Integer

;;;     ***       |SYMBOL;convert;$P;17| REDEFINED
Time: 0 SEC.

   compiling local syprefix : Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm) -> String

;;;     ***       |SYMBOL;syprefix| REDEFINED
Time: 0.01 SEC.

   compiling local syscripts : Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm) -> List OutputForm

;;;     ***       |SYMBOL;syscripts| REDEFINED
Time: 0.01 SEC.

   compiling exported script : ($,List List OutputForm) -> $

;;;     ***       |SYMBOL;script;$L$;20| REDEFINED
Time: 0.01 SEC.

   compiling exported script : ($,Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)) -> $

;;;     ***       |SYMBOL;script;$R$;21| REDEFINED
Time: 0.02 SEC.

   compiling exported string : $ -> String

;;;     ***       |SYMBOL;string;$S;22| REDEFINED
Time: 0 SEC.

   compiling exported latex : $ -> String

;;;     ***       |SYMBOL;latex;$S;23| REDEFINED
Time: 0.03 SEC.

   compiling local anyRadix : (Integer,String) -> String

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

   compiling exported new : () -> $

;;;     ***       |SYMBOL;new;$;25| REDEFINED
Time: 0 SEC.

   compiling exported new : $ -> $

;;;     ***       |SYMBOL;new;2$;26| REDEFINED
Time: 0.07 SEC.

   compiling exported resetNew : () -> Void

;;;     ***       |SYMBOL;resetNew;V;27| REDEFINED
Time: 0 SEC.

   compiling exported scripted? : $ -> Boolean

;;;     ***       |SYMBOL;scripted?;$B;28| REDEFINED
Time: 0 SEC.

   compiling local of_list : $ -> List OutputForm
      SYMBOL;of_list is replaced by x 

;;;     ***       |SYMBOL;of_list| REDEFINED
Time: 0 SEC.

   compiling exported name : $ -> $

;;;     ***       |SYMBOL;name;2$;30| REDEFINED
Time: 0 SEC.

   compiling exported scripts : $ -> Record(sub: List OutputForm,sup: List OutputForm,presup: List OutputForm,presub: List OutputForm,args: List OutputForm)

;;;     ***       |SYMBOL;scripts;$R;31| REDEFINED
Time: 0.04 SEC.

   compiling local istring : Integer -> String

;;;     ***       |SYMBOL;istring| REDEFINED
Time: 0 SEC.

   compiling exported sample : () -> $

;;;     ***       |SYMBOL;sample;$;33| REDEFINED
Time: 0.01 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |Symbol| REDEFINED

;;;     ***       |Symbol| REDEFINED
Time: 0 SEC.

   Warnings: 
      [1] coerce:  presup has no value
      [2] coerce:  sl has no value
      [3] coerce:  args has no value
      [4] syprefix:  presup has no value
      [5] syprefix:  args has no value
      [6] syscripts:  presup has no value
      [7] syscripts:  args has no value
      [8] script:  presup has no value
      [9] script:  args has no value
      [10] latex: pretend(String) -- should replace by @
      [11] latex:  s has no value
      [12] latex:  sc has no value
      [13] latex:  presup has no value
      [14] latex:  args has no value
      [15] anyRadix:  quotient has no value
      [16] anyRadix:  remainder has no value

   Cumulative Statistics for Constructor Symbol
      Time: 0.35 seconds

   finalizing NRLIB SYMBOL 
   Processing Symbol for Browser database:
--------constructor---------
--------(new (%))---------
--------(new (% %))---------
--------(resetNew ((Void)))---------
--------(coerce (% (String)))---------
--------(name (% %))---------
--------(scripted? ((Boolean) %))---------
--------(scripts ((Record (: sub (List (OutputForm))) (: sup (List (OutputForm))) (: presup (List (OutputForm))) (: presub (List (OutputForm))) (: args (List (OutputForm)))) %))---------
--------(script (% % (List (List (OutputForm)))))---------
--------(script (% % (Record (: sub (List (OutputForm))) (: sup (List (OutputForm))) (: presup (List (OutputForm))) (: presub (List (OutputForm))) (: args (List (OutputForm))))))---------
--------(subscript (% % (List (OutputForm))))---------
--------(superscript (% % (List (OutputForm))))---------
--------(argscript (% % (List (OutputForm))))---------
--------(elt (% % (List (OutputForm))))---------
--------(string ((String) %))---------
--------(sample (%) constant)---------
; compiling file "/var/aw/var/LatexWiki/SYMBOL.NRLIB/SYMBOL.lsp" (written 27 FEB 2015 09:12:52 PM):

; /var/aw/var/LatexWiki/SYMBOL.NRLIB/SYMBOL.fasl written
; compilation finished in 0:00:00.167
------------------------------------------------------------------------
   Symbol is now explicitly exposed in frame initial 
   Symbol will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/SYMBOL.NRLIB/SYMBOL

Examples

fricas

A:=superscript('a,['b])

   symbol oldsc:  [sub= [],sup= [],presup= [],presub= [],args= []]
   symbol newsc:  [sub= [],sup= [b],presup= [],presub= [],args= []]

$\label{eq1}a^{b}$

(1)

Type: Symbol

fricas

B:=subscript(A,['c])

   symbol oldsc:  [sub= [],sup= [b],presup= [],presub= [],args= []]
   symbol newsc:  [sub= [c],sup= [b],presup= [],presub= [],args= []]

$\label{eq2}a_{c}^{b}$

(2)

Type: Symbol

fricas

C:=argscript(B,['x])

   symbol oldsc:  [sub= [c],sup= [b],presup= [],presub= [],args= []]
   symbol newsc:  [sub= [c],sup= [b],presup= [],presub= [],args= [x]]

$\label{eq3}{a_{c}^{b}}\left({x}\right)$

(3)

Type: Symbol

fricas

D:=subscript(C,['d])

   symbol oldsc:  [sub= [c],sup= [b],presup= [],presub= [],args= [x]]
   symbol newsc:  [sub= [d,c],sup= [b],presup= [],presub= [],args= [x]]

$\label{eq4}{a_{d , \: c}^{b}}\left({x}\right)$

(4)

Type: Symbol