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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.
--
-- - 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 files for the functional world should be compiled in the
-- following order:
--
-- op KL expr function
)abbrev category CACHSET CachableSet
++ Sets whose elements can cache an integer
++ Author: Manuel Bronstein
++ Date Created: 31 Oct 1988
++ Date Last Updated: 14 May 1991
++ Description:
++ A cachable set is a set whose elements keep an integer as part
++ of their structure.
CachableSet: Category == SetCategory with
position : % -> NonNegativeInteger
++ position(x) returns the integer n associated to x.
setPosition: (%, NonNegativeInteger) -> Void
++ setPosition(x, n) associates the integer n to x.
)abbrev package SCACHE SortedCache
++ Cache of elements in a set
++ Author: Manuel Bronstein
++ Date Created: 31 Oct 1988
++ Date Last Updated: 14 May 1991
++ A sorted cache of a cachable set S is a dynamic structure that
++ keeps the elements of S sorted and assigns an integer to each
++ element of S once it is in the cache. This way, equality and ordering
++ on S are tested directly on the integers associated with the elements
++ of S, once they have been entered in the cache.
SortedCache(S:CachableSet): Exports == Implementation where
N ==> NonNegativeInteger
DIFF ==> 1024
Exports ==> with
clearCache : () -> Void
++ clearCache() empties the cache.
cache : () -> List S
++ cache() returns the current cache as a list.
enterInCache: (S, S -> Boolean) -> S
++ enterInCache(x, f) enters x in the cache, calling \spad{f(y)} to
++ determine whether x is equal to y. It returns x with an integer
++ associated with it.
enterInCache: (S, (S, S) -> Integer) -> S
++ enterInCache(x, f) enters x in the cache, calling \spad{f(x, y)} to
++ determine whether \spad{x < y (f(x,y) < 0), x = y (f(x,y) = 0)}, or
++ \spad{x > y (f(x,y) > 0)}.
++ It returns x with an integer associated with it.
Implementation ==> add
import Reference List S
shiftCache : (List S, N) -> Void
insertInCache: (List S, List S, S, N) -> S
cach := ref(nil$List(S))
cache() == deref cach
shiftCache(l, n) ==
for x in l repeat
setPosition(x, n + position x)
clearCache() ==
for x in cache() repeat
setPosition(x, 0)
setref(cach,nil$List(S))
enterInCache(x:S, equal?:S -> Boolean) ==
scan := cache()
while not null scan repeat
equal?(y := first scan) =>
setPosition(x, position y)
return y
scan := rest scan
setPosition(x, 1 + #cache())
setref(cach,concat(cache(), x))
x
enterInCache(x:S, triage:(S, S) -> Integer) ==
scan := cache()
pos:N:= 0
for i in 1..#scan repeat
zero?(n := triage(x, y := first scan)) =>
setPosition(x, position y)
return y
negative? n => return insertInCache(first(cache(),(i-1)::N),scan,x,pos)
scan := rest scan
pos := position y
setPosition(x, pos + DIFF)
setref(cach, concat(cache(), x))
x
insertInCache(before, after, x, pos) ==
if ((pos+1) = position first after) then shiftCache(after, DIFF)
setPosition(x, pos + (((position first after) - pos)::N quo 2))
setref(cach, concat(before, concat(x, after)))
x
)abbrev domain KERNEL Kernel
++ Operators applied to elements of a set
++ Author: Manuel Bronstein
++ Date Created: 22 March 1988
++ Date Last Updated: May 09, 2009
++ Description:
++ A kernel over a set S is an operator applied to a given list
++ of arguments from S.
Kernel(S: SetCategory): Exports == Implementation where
macro O == OutputForm
macro N == NonNegativeInteger
macro OP == BasicOperator
Exports == Join(CachableSet, OrderedSet, Patternable S) with
operator: % -> OP
++ operator(op(a1,...,an)) returns the operator op.
argument: % -> List S
++ argument(op(a1,...,an)) returns \spad{[a1,...,an]}.
height : % -> N
++ height(k) returns the nesting level of k.
kernel : (OP, List S, N) -> %
++ kernel(op, [a1,...,an], m) returns the kernel \spad{op(a1,...,an)}
++ of nesting level m.
++ Error: if op is k-ary for some k not equal to m.
kernel : Symbol -> %
++ kernel(x) returns x viewed as a kernel.
symbolIfCan: % -> Union(Symbol, "failed")
++ symbolIfCan(k) returns k viewed as a symbol if k is a symbol, and
++ "failed" otherwise.
is? : (%, OP) -> Boolean
++ is?(op(a1,...,an), f) tests if op = f.
is? : (%, Symbol) -> Boolean
++ is?(op(a1,...,an), s) tests if the name of op is s.
if S has ConvertibleTo InputForm then ConvertibleTo InputForm
Implementation ==> add
macro SYMBOL == '%symbol
macro PMPRED == '%pmpredicate
macro PMOPT == '%pmoptional
macro PMMULT == '%pmmultiple
macro PMCONST == '%pmconstant
macro SPECIALDISP == '%specialDisp
macro SPECIALEQUAL == '%specialEqual
macro SPECIALINPUT == '%specialInput
import SortedCache(%)
Rep == Record(op: OP, arg: List S, nest: N, posit: N)
B2Z : Boolean -> Integer
triage: (%, %) -> Integer
preds : OP -> List Any
is?(k:%, s:Symbol) == is?(operator k, s)
is?(k:%, o:OP) == (operator k) = o
height k == rep(k).nest
operator k == rep(k).op
argument k == rep(k).arg
position k == rep(k).posit
setPosition(k, n) == rep(k).posit := n
B2Z flag == (flag => -1; 1)
kernel s == kernel(assert(operator(s,0),SYMBOL), nil(), 1)
preds o ==
(u := property(o, PMPRED)) case nothing => nil()
(u@None) pretend List(Any)
symbolIfCan k ==
has?(operator k, SYMBOL) => name operator k
"failed"
k1 = k2 ==
if rep(k1).posit = 0 then enterInCache(k1, triage)
if rep(k2).posit = 0 then enterInCache(k2, triage)
rep(k1).posit = rep(k2).posit
k1 < k2 ==
if rep(k1).posit = 0 then enterInCache(k1, triage)
if rep(k2).posit = 0 then enterInCache(k2, triage)
rep(k1).posit < rep(k2).posit
kernel(fn, x, n) ==
(#x)::Arity ~= arity fn and (arity fn ~= arbitrary()) =>
error "Wrong number of arguments"
enterInCache(per [fn, x, n, 0], triage)
-- SPECIALDISP contains a map List S -> OutputForm
-- it is used when the converting the arguments first is not good,
-- for instance with formal derivatives.
coerce(k:%):OutputForm ==
(v := symbolIfCan k) case Symbol => v@Symbol::OutputForm
(f := property(o := operator k, SPECIALDISP)) case None =>
((f@None) pretend (List S -> OutputForm)) (argument k)
l := [x::OutputForm for x in argument k]$List(OutputForm)
(u := display o) case nothing => prefix(name(o)::OutputForm, l)
(u::(List OutputForm -> OutputForm)) l
triage(k1, k2) ==
rep(k1).nest ~= rep(k2).nest => B2Z(rep(k1).nest < rep(k2).nest)
rep(k1).op ~= rep(k2).op => B2Z(rep(k1).op < rep(k2).op)
(n1 := #(argument k1)) ~= (n2 := #(argument k2)) => B2Z(n1 < n2)
((func := property(operator k1, SPECIALEQUAL)) case None) and
(((func@None) pretend ((%, %) -> Boolean)) (k1, k2)) => 0
for x1 in argument(k1) for x2 in argument(k2) repeat
x1 ~= x2 => return B2Z before?(x1,x2)
0
if S has ConvertibleTo InputForm then
convert(k:%):InputForm ==
(v := symbolIfCan k) case Symbol => convert(v@Symbol)@InputForm
(f := property(o := operator k, SPECIALINPUT)) case None =>
((f@None) pretend (List S -> InputForm)) (argument k)
l := [convert x for x in argument k]$List(InputForm)
(u := input operator k) case nothing =>
convert concat(convert name operator k, l)
(u::(List InputForm -> InputForm)) l
if S has ConvertibleTo Pattern Integer then
convert(k:%):Pattern(Integer) ==
o := operator k
(v := symbolIfCan k) case Symbol =>
s := patternVariable(v@Symbol,
has?(o, PMCONST), has?(o, PMOPT), has?(o, PMMULT))
empty?(l := preds o) => s
setPredicates(s, l)
o [convert x for x in rep(k).arg]$List(Pattern Integer)
if S has ConvertibleTo Pattern Float then
convert(k:%):Pattern(Float) ==
o := operator k
(v := symbolIfCan k) case Symbol =>
s := patternVariable(v@Symbol,
has?(o, PMCONST), has?(o, PMOPT), has?(o, PMMULT))
empty?(l := preds o) => s
setPredicates(s, l)
o [convert x for x in rep(k).arg]$List(Pattern Float)
)abbrev package KERNEL2 KernelFunctions2
++ Description:
++ This package exports some auxiliary functions on kernels
KernelFunctions2(R: SetCategory, S: SetCategory): with
constantKernel: R -> Kernel S
++ constantKernel(r) \undocumented
constantIfCan : Kernel S -> Union(R, "failed")
++ constantIfCan(k) \undocumented
== add
import BasicOperatorFunctions1(R)
constantKernel r == kernel(constantOperator r, nil(), 1)
constantIfCan k == constantOpIfCan operator k
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