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--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.
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-- - Redistributions in binary form must reproduce the above copyright
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-- - Neither the name of The Numerical ALgorithms Group Ltd. nor the
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-- derived from this software without specific prior written permission.
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--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
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--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
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--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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--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.
)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(deref count,ALPHAS)
setref(count, deref 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() ==
setref(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"
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