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--All rights reserved.
--Copyright (C) 2007-2009, 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
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--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
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--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
)abbrev domain PATTERN Pattern
++ Patterns for use by the pattern matcher
++ Author: Manuel Bronstein
++ Date Created: 10 Nov 1988
++ Date Last Updated: 20 June 1991
++ Description: Patterns for use by the pattern matcher.
++ Keywords: pattern, matching.
-- Not exposed.
-- Patterns are optimized for quick answers to structural questions.
Pattern(R:SetCategory): Exports == Implementation where
B ==> Boolean
SI ==> SingleInteger
Z ==> Integer
SY ==> Symbol
O ==> OutputForm
BOP ==> BasicOperator
QOT ==> Record(num:%, den:%)
REC ==> Record(val:%, exponent:NonNegativeInteger)
RSY ==> Record(tag:SI, val: SY, pred:List Any, bad:List Any)
KER ==> Record(tag:SI, op:BOP, arg:List %)
PAT ==> Union(ret:R, ker: KER, exp:REC, qot: QOT, sym:RSY)
-- the following MUST be the name of the formal exponentiation operator
POWER ==> '%power
-- the 4 SYM_ constants must be disting powers of 2 (bitwise arithmetic)
SYM_GENERIC ==> 1::SI
SYM_MULTIPLE ==> 2::SI
SYM_OPTIONAL ==> 4::SI
PAT_PLUS ==> 1::SI
PAT_TIMES ==> 2::SI
PAT_LIST ==> 3::SI
PAT_ZERO ==> 4::SI
PAT_ONE ==> 5::SI
PAT_EXPT ==> 6::SI
Exports ==> Join(SetCategory, RetractableTo R, RetractableTo SY) with
0 : constant -> % ++ 0
1 : constant -> % ++ 1
isPlus : % -> Union(List %, "failed")
++ isPlus(p) returns \spad{[a1,...,an]} if \spad{n > 1}
++ and \spad{p = a1 + ... + an},
++ and "failed" otherwise.
isTimes : % -> Union(List %, "failed")
++ isTimes(p) returns \spad{[a1,...,an]} if \spad{n > 1} and
++ \spad{p = a1 * ... * an}, and
++ "failed" otherwise.
isOp : (%, BOP) -> Union(List %, "failed")
++ isOp(p, op) returns \spad{[a1,...,an]} if \spad{p = op(a1,...,an)}, and
++ "failed" otherwise.
isOp : % -> Union(Record(op:BOP, arg:List %), "failed")
++ isOp(p) returns \spad{[op, [a1,...,an]]} if
++ \spad{p = op(a1,...,an)}, and
++ "failed" otherwise;
isExpt : % -> Union(REC, "failed")
++ isExpt(p) returns \spad{[q, n]} if \spad{n > 0} and \spad{p = q ** n},
++ and "failed" otherwise.
isQuotient : % -> Union(QOT, "failed")
++ isQuotient(p) returns \spad{[a, b]} if \spad{p = a / b}, and
++ "failed" otherwise.
isList : % -> Union(List %, "failed")
++ isList(p) returns \spad{[a1,...,an]} if \spad{p = [a1,...,an]},
++ "failed" otherwise;
isPower : % -> Union(Record(val:%, exponent:%), "failed")
++ isPower(p) returns \spad{[a, b]} if \spad{p = a ** b}, and
++ "failed" otherwise.
elt : (BOP, List %) -> %
++ \spad{elt(op, [a1,...,an])} returns \spad{op(a1,...,an)}.
+ : (%, %) -> %
++ \spad{a + b} returns the pattern \spad{a + b}.
* : (%, %) -> %
++ \spad{a * b} returns the pattern \spad{a * b}.
** : (%, NonNegativeInteger) -> %
++ \spad{a ** n} returns the pattern \spad{a ** n}.
** : (%, %) -> %
++ \spad{a ** b} returns the pattern \spad{a ** b}.
/ : (%, %) -> %
++ \spad{a / b} returns the pattern \spad{a / b}.
depth : % -> NonNegativeInteger
++ depth(p) returns the nesting level of p.
convert : List % -> %
++ \spad{convert([a1,...,an])} returns the pattern \spad{[a1,...,an]}.
copy : % -> %
++ copy(p) returns a recursive copy of p.
inR? : % -> B
++ inR?(p) tests if p is an atom (i.e. an element of R).
quoted? : % -> B
++ quoted?(p) tests if p is of the form 's for a symbol s.
symbol? : % -> B
++ symbol?(p) tests if p is a symbol.
constant? : % -> B
++ constant?(p) tests if p contains no matching variables.
generic? : % -> B
++ generic?(p) tests if p is a single matching variable.
multiple? : % -> B
++ multiple?(p) tests if p is a single matching variable
++ allowing list matching or multiple term matching in a
++ sum or product.
optional? : % -> B
++ optional?(p) tests if p is a single matching variable
++ which can match an identity.
hasPredicate?: % -> B
++ hasPredicate?(p) tests if p has predicates attached to it.
predicates : % -> List Any
++ predicates(p) returns \spad{[p1,...,pn]} such that the predicate
++ attached to p is p1 and ... and pn.
setPredicates: (%, List Any) -> %
++ \spad{setPredicates(p, [p1,...,pn])} attaches the predicate
++ p1 and ... and pn to p.
withPredicates:(%, List Any) -> %
++ \spad{withPredicates(p, [p1,...,pn])} makes a copy of p and attaches
++ the predicate p1 and ... and pn to the copy, which is
++ returned.
patternVariable: (SY, B, B, B) -> %
++ patternVariable(x, c?, o?, m?) creates a pattern variable x,
++ which is constant if \spad{c? = true}, optional if \spad{o? = true},
++ and multiple if \spad{m? = true}.
setTopPredicate: (%, List SY, Any) -> %
++ \spad{setTopPredicate(x, [a1,...,an], f)} returns x with
++ the top-level predicate set to \spad{f(a1,...,an)}.
topPredicate: % -> Record(var:List SY, pred:Any)
++ topPredicate(x) returns \spad{[[a1,...,an], f]} where the top-level
++ predicate of x is \spad{f(a1,...,an)}.
++ Note: n is 0 if x has no top-level
++ predicate.
hasTopPredicate?: % -> B
++ hasTopPredicate?(p) tests if p has a top-level predicate.
resetBadValues: % -> %
++ resetBadValues(p) initializes the list of "bad values" for p
++ to \spad{[]}.
++ Note: p is not allowed to match any of its "bad values".
addBadValue: (%, Any) -> %
++ addBadValue(p, v) adds v to the list of "bad values" for p.
++ Note: p is not allowed to match any of its "bad values".
getBadValues: % -> List Any
++ getBadValues(p) returns the list of "bad values" for p.
++ Note: p is not allowed to match any of its "bad values".
variables: % -> List %
++ variables(p) returns the list of matching variables
++ appearing in p.
optpair: List % -> Union(List %, "failed")
++ optpair(l) returns l has the form \spad{[a, b]} and
++ a is optional, and
++ "failed" otherwise;
Implementation ==> add
Rep := Record(cons?: B, pat:PAT, lev: NonNegativeInteger,
topvar: List SY, toppred: Any)
dummy:BOP := operator(new()$Symbol)
nopred := coerce(0$Integer)$AnyFunctions1(Integer)
mkPat : (B, PAT, NonNegativeInteger) -> %
mkrsy : (SY, B, B, B) -> RSY
SYM2O : RSY -> O
PAT2O : PAT -> O
patcopy : PAT -> PAT
bitSet? : (SI , SI) -> B
pateq? : (PAT, PAT) -> B
LPAT2O : ((O, O) -> O, List %) -> O
taggedElt : (SI, List %) -> %
isTaggedOp: (%, SI) -> Union(List %, "failed")
incmax : List % -> NonNegativeInteger
coerce(r:R):% == mkPat(true, [r], 0)
mkPat(c, p, l) == [c, p, l, empty(), nopred]
hasTopPredicate? x == not empty?(x.topvar)
topPredicate x == [x.topvar, x.toppred]
setTopPredicate(x, l, f) == (x.topvar := l; x.toppred := f; x)
constant? p == p.cons?
depth p == p.lev
inR? p == p.pat case ret
symbol? p == p.pat case sym
isPlus p == isTaggedOp(p, PAT_PLUS)
isTimes p == isTaggedOp(p, PAT_TIMES)
isList p == isTaggedOp(p, PAT_LIST)
isExpt p == (p.pat case exp => p.pat.exp; "failed")
isQuotient p == (p.pat case qot => p.pat.qot; "failed")
hasPredicate? p == not empty? predicates p
quoted? p == symbol? p and zero?(p.pat.sym.tag)
generic? p == symbol? p and bitSet?(p.pat.sym.tag, SYM_GENERIC)
multiple? p == symbol? p and bitSet?(p.pat.sym.tag,SYM_MULTIPLE)
optional? p == symbol? p and bitSet?(p.pat.sym.tag,SYM_OPTIONAL)
bitSet?(a, b) == (a /\ b) ~= 0
coerce(p:%):O == PAT2O(p.pat)
p1:% ** p2:% == taggedElt(PAT_EXPT, [p1, p2])
LPAT2O(f, l) == reduce(f, [x::O for x in l])$List(O)
retract(p:%):R == (inR? p => p.pat.ret; error "Not retractable")
convert(l:List %):% == taggedElt(PAT_LIST, l)
retractIfCan(p:%):Union(R,"failed") ==(inR? p => p.pat.ret;"failed")
withPredicates(p, l) == setPredicates(copy p, l)
coerce(sy:SY):% == patternVariable(sy, false, false, false)
copy p == [constant? p, patcopy(p.pat), p.lev, p.topvar, p.toppred]
-- returns [a, b] if #l = 2 and optional? a, "failed" otherwise
optpair l ==
empty? rest rest l =>
b := first rest l
optional?(a := first l) => l
optional? b => reverse l
"failed"
"failed"
incmax l ==
1 + reduce("max", [p.lev for p in l], 0)$List(NonNegativeInteger)
p1 = p2 ==
(p1.cons? = p2.cons?) and (p1.lev = p2.lev) and
(p1.topvar = p2.topvar) and
((%peq(p1.toppred,p2.toppred)$Foreign(Builtin)) pretend B) and
pateq?(p1.pat, p2.pat)
isPower p ==
(u := isTaggedOp(p, PAT_EXPT)) case "failed" => "failed"
[first(u::List(%)), second(u::List(%))]
taggedElt(n, l) ==
mkPat(every?(constant?, l), [[n, dummy, l]$KER], incmax l)
elt(o, l) ==
is?(o, POWER) and #l = 2 => first(l) ** last(l)
mkPat(every?(constant?, l), [[0, o, l]$KER], incmax l)
isOp p ==
(p.pat case ker) and zero?(p.pat.ker.tag) =>
[p.pat.ker.op, p.pat.ker.arg]
"failed"
isTaggedOp(p,t) ==
(p.pat case ker) and (p.pat.ker.tag = t) => p.pat.ker.arg
"failed"
if R has Monoid then
1 == 1::R::%
else
1 == taggedElt(PAT_ONE, empty())
if R has AbelianMonoid then
0 == 0::R::%
else
0 == taggedElt(PAT_ZERO, empty())
p:% ** n:NonNegativeInteger ==
p = 0 and positive? n => 0
p = 1 or zero? n => 1
one? n => p
mkPat(constant? p, [[p, n]$REC], 1 + (p.lev))
p1 / p2 ==
p2 = 1 => p1
mkPat(constant? p1 and constant? p2, [[p1, p2]$QOT],
1 + max(p1.lev, p2.lev))
p1 + p2 ==
p1 = 0 => p2
p2 = 0 => p1
(u1 := isPlus p1) case List(%) =>
(u2 := isPlus p2) case List(%) =>
taggedElt(PAT_PLUS, concat(u1::List %, u2::List %))
taggedElt(PAT_PLUS, concat(u1::List %, p2))
(u2 := isPlus p2) case List(%) =>
taggedElt(PAT_PLUS, concat(p1, u2::List %))
taggedElt(PAT_PLUS, [p1, p2])
p1 * p2 ==
p1 = 0 or p2 = 0 => 0
p1 = 1 => p2
p2 = 1 => p1
(u1 := isTimes p1) case List(%) =>
(u2 := isTimes p2) case List(%) =>
taggedElt(PAT_TIMES, concat(u1::List %, u2::List %))
taggedElt(PAT_TIMES, concat(u1::List %, p2))
(u2 := isTimes p2) case List(%) =>
taggedElt(PAT_TIMES, concat(p1, u2::List %))
taggedElt(PAT_TIMES, [p1, p2])
isOp(p, o) ==
(p.pat case ker) and zero?(p.pat.ker.tag) and (p.pat.ker.op =o) =>
p.pat.ker.arg
"failed"
predicates p ==
symbol? p => p.pat.sym.pred
empty()
setPredicates(p, l) ==
generic? p => (p.pat.sym.pred := l; p)
error "Can only attach predicates to generic symbol"
resetBadValues p ==
generic? p => (p.pat.sym.bad := empty()$List(Any); p)
error "Can only attach bad values to generic symbol"
addBadValue(p, a) ==
generic? p =>
if not member?(a, p.pat.sym.bad) then
p.pat.sym.bad := concat(a, p.pat.sym.bad)
p
error "Can only attach bad values to generic symbol"
getBadValues p ==
generic? p => p.pat.sym.bad
error "Not a generic symbol"
SYM2O p ==
sy := (p.val)::O
empty?(p.pred) => sy
paren infix(" | "::O, sy,
reduce("and",[sub("f"::O, i::O) for i in 1..#(p.pred)])$List(O))
variables p ==
constant? p => empty()
generic? p => [p]
q := p.pat
q case ret => empty()
q case exp => variables(q.exp.val)
q case qot => concat!(variables(q.qot.num), variables(q.qot.den))
q case ker => concat [variables r for r in q.ker.arg]
empty()
PAT2O p ==
p case ret => (p.ret)::O
p case sym => SYM2O(p.sym)
p case exp => (p.exp.val)::O ** (p.exp.exponent)::O
p case qot => (p.qot.num)::O / (p.qot.den)::O
p.ker.tag = PAT_PLUS => LPAT2O("+", p.ker.arg)
p.ker.tag = PAT_TIMES => LPAT2O("*", p.ker.arg)
p.ker.tag = PAT_LIST => (p.ker.arg)::O
p.ker.tag = PAT_ZERO => 0::Integer::O
p.ker.tag = PAT_ONE => 1::Integer::O
l := [x::O for x in p.ker.arg]$List(O)
(u:=display(p.ker.op)) case nothing =>prefix(name(p.ker.op)::O,l)
(u::(List O -> O)) l
patcopy p ==
p case ret => [p.ret]
p case sym =>
[[p.sym.tag, p.sym.val, copy(p.sym.pred), copy(p.sym.bad)]$RSY]
p case ker=>[[p.ker.tag,p.ker.op,[copy x for x in p.ker.arg]]$KER]
p case qot => [[copy(p.qot.num), copy(p.qot.den)]$QOT]
[[copy(p.exp.val), p.exp.exponent]$REC]
pateq?(p1, p2) ==
p1 case ret => (p2 case ret) and (p1.ret = p2.ret)
p1 case qot =>
(p2 case qot) and (p1.qot.num = p2.qot.num)
and (p1.qot.den = p2.qot.den)
p1 case sym =>
(p2 case sym) and (p1.sym.val = p2.sym.val)
and {p1.sym.pred} =$Set(Any) {p2.sym.pred}
and {p1.sym.bad} =$Set(Any) {p2.sym.bad}
p1 case ker =>
(p2 case ker) and (p1.ker.tag = p2.ker.tag)
and (p1.ker.op = p2.ker.op) and (p1.ker.arg = p2.ker.arg)
(p2 case exp) and (p1.exp.exponent = p2.exp.exponent)
and (p1.exp.val = p2.exp.val)
retractIfCan(p:%):Union(SY, "failed") ==
symbol? p => p.pat.sym.val
"failed"
mkrsy(t, c?, o?, m?) ==
c? => [0, t, empty(), empty()]
mlt := (m? => SYM_MULTIPLE; 0)
opt := (o? => SYM_OPTIONAL; 0)
[(SYM_GENERIC \/ mlt) \/ opt, t, empty(), empty()]
patternVariable(sy, c?, o?, m?) ==
rsy := mkrsy(sy, c?, o?, m?)
mkPat(zero?(rsy.tag), [rsy], 0)
)abbrev package PATTERN1 PatternFunctions1
++ Utilities for handling patterns
++ Author: Manuel Bronstein
++ Date Created: 28 Nov 1989
++ Date Last Updated: 5 Jul 1990
++ Description: Tools for patterns;
++ Keywords: pattern, matching.
PatternFunctions1(R:SetCategory, D:Type): with
suchThat : (Pattern R, D -> Boolean) -> Pattern R
++ suchThat(p, f) makes a copy of p and adds the predicate
++ f to the copy, which is returned.
suchThat : (Pattern R, List(D -> Boolean)) -> Pattern R
++ \spad{suchThat(p, [f1,...,fn])} makes a copy of p and adds the
++ predicate f1 and ... and fn to the copy, which is returned.
suchThat : (Pattern R, List Symbol, List D -> Boolean) -> Pattern R
++ \spad{suchThat(p, [a1,...,an], f)} returns a copy of p with
++ the top-level predicate set to \spad{f(a1,...,an)}.
predicate : Pattern R -> (D -> Boolean)
++ predicate(p) returns the predicate attached to p, the
++ constant function true if p has no predicates attached to it.
satisfy? : (D, Pattern R) -> Boolean
++ satisfy?(v, p) returns f(v) where f is the predicate
++ attached to p.
satisfy? : (List D, Pattern R) -> Boolean
++ \spad{satisfy?([v1,...,vn], p)} returns \spad{f(v1,...,vn)}
++ where f is the
++ top-level predicate attached to p.
addBadValue: (Pattern R, D) -> Pattern R
++ addBadValue(p, v) adds v to the list of "bad values" for p;
++ p is not allowed to match any of its "bad values".
badValues : Pattern R -> List D
++ badValues(p) returns the list of "bad values" for p;
++ p is not allowed to match any of its "bad values".
== add
A1D ==> AnyFunctions1(D)
A1 ==> AnyFunctions1(D -> Boolean)
A1L ==> AnyFunctions1(List D -> Boolean)
applyAll: (List Any, D) -> Boolean
st : (Pattern R, List Any) -> Pattern R
st(p, l) == withPredicates(p, concat(predicates p, l))
predicate p == applyAll(predicates p, #1)
addBadValue(p, v) == addBadValue(p, coerce(v)$A1D)
badValues p == [retract(v)$A1D for v in getBadValues p]
suchThat(p, l, f) == setTopPredicate(copy p, l, coerce(f)$A1L)
suchThat(p:Pattern R, f:D -> Boolean) == st(p, [coerce(f)$A1])
satisfy?(d:D, p:Pattern R) == applyAll(predicates p, d)
satisfy?(l:List D, p:Pattern R) ==
empty?((rec := topPredicate p).var) => true
retract(rec.pred)$A1L l
applyAll(l, d) ==
for f in l repeat
not(retract(f)$A1 d) => return false
true
suchThat(p:Pattern R, l:List(D -> Boolean)) ==
st(p, [coerce(f)$A1 for f in l])
)abbrev package PATTERN2 PatternFunctions2
++ Lifting of maps to patterns
++ Author: Manuel Bronstein
++ Date Created: 28 Nov 1989
++ Date Last Updated: 12 Jan 1990
++ Description: Lifts maps to patterns;
++ Keywords: pattern, matching.
PatternFunctions2(R:SetCategory, S:SetCategory): with
map: (R -> S, Pattern R) -> Pattern S
++ map(f, p) applies f to all the leaves of p and
++ returns the result as a pattern over S.
== add
map(f, p) ==
(r := (retractIfCan p)@Union(R, "failed")) case R =>
f(r::R)::Pattern(S)
(u := isOp p) case Record(op:BasicOperator, arg:List Pattern R) =>
ur := u::Record(op:BasicOperator, arg:List Pattern R)
(ur.op) [map(f, x) for x in ur.arg]
(v := isQuotient p) case Record(num:Pattern R, den:Pattern R) =>
vr := v::Record(num:Pattern R, den:Pattern R)
map(f, vr.num) / map(f, vr.den)
(l := isPlus p) case List(Pattern R) =>
reduce("+", [map(f, x) for x in l::List(Pattern R)])
(l := isTimes p) case List(Pattern R) =>
reduce("*", [map(f, x) for x in l::List(Pattern R)])
(x := isPower p) case
Record(val:Pattern R, exponent: Pattern R) =>
xr := x::Record(val:Pattern R, exponent: Pattern R)
map(f, xr.val) ** map(f, xr.exponent)
(w := isExpt p) case
Record(val:Pattern R, exponent: NonNegativeInteger) =>
wr := w::Record(val:Pattern R, exponent: NonNegativeInteger)
map(f, wr.val) ** wr.exponent
sy := retract(p)@Symbol
setPredicates(sy::Pattern(S), copy predicates p)
)abbrev category PATAB Patternable
++ Category of sets that can be converted to useful patterns
++ Author: Manuel Bronstein
++ Date Created: 29 Nov 1989
++ Date Last Updated: 29 Nov 1989
++ Description:
++ An object S is Patternable over an object R if S can
++ lift the conversions from R into \spadtype{Pattern(Integer)} and
++ \spadtype{Pattern(Float)} to itself;
++ Keywords: pattern, matching.
Patternable(R:Type): Category == with
if R has ConvertibleTo Pattern Integer then
ConvertibleTo Pattern Integer
if R has ConvertibleTo Pattern Float then
ConvertibleTo Pattern Float
|