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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.
)abbrev package IPRNTPK InternalPrintPackage
++ Author: Themos Tsikas
++ Date Created: 09/09/1998
++ Date Last Updated: 09/09/1998
++ Basic Functions:
++ Related Constructors:
++ Also See:
++ AMS Classifications:
++ Keywords:
++ References:
++ Description: A package to print strings without line-feed
++ nor carriage-return.
InternalPrintPackage(): Exports == Implementation where
Exports == with
iprint: String -> Void
++ \axiom{iprint(s)} prints \axiom{s} at the current position
++ of the cursor.
Implementation == add
iprint(s:String) ==
PRINC(coerce(s)@Symbol)$Lisp
FORCE_-OUTPUT()$Lisp
)abbrev package TBCMPPK TabulatedComputationPackage
++ Author: Marc Moreno Maza
++ Date Created: 09/09/1998
++ Date Last Updated: 12/16/1998
++ Basic Functions:
++ Related Constructors:
++ Also See:
++ AMS Classifications:
++ Keywords:
++ References:
++ Description:
++ \axiom{TabulatedComputationPackage(Key ,Entry)} provides some modest support
++ for dealing with operations with type \axiom{Key -> Entry}. The result of
++ such operations can be stored and retrieved with this package by using
++ a hash-table. The user does not need to worry about the management of
++ this hash-table. However, onnly one hash-table is built by calling
++ \axiom{TabulatedComputationPackage(Key ,Entry)}.
++ Version: 2.
TabulatedComputationPackage(Key ,Entry): Exports == Implementation where
Key: SetCategory
Entry: SetCategory
N ==> NonNegativeInteger
H ==> HashTable(Key, Entry, "EQUAL")
iprintpack ==> InternalPrintPackage()
Exports == with
initTable!: () -> Void
++ \axiom{initTable!()} initializes the hash-table.
printInfo!: (String, String) -> Void
++ \axiom{printInfo!(x,y)} initializes the mesages to be printed
++ when manipulating items from the hash-table. If
++ a key is retrieved then \axiom{x} is displayed. If an item is
++ stored then \axiom{y} is displayed.
startStats!: (String) -> Void
++ \axiom{startStats!(x)} initializes the statisitics process and
++ sets the comments to display when statistics are printed
printStats!: () -> Void
++ \axiom{printStats!()} prints the statistics.
clearTable!: () -> Void
++ \axiom{clearTable!()} clears the hash-table and assumes that
++ it will no longer be used.
usingTable?: () -> Boolean
++ \axiom{usingTable?()} returns true iff the hash-table is used
printingInfo?: () -> Boolean
++ \axiom{printingInfo?()} returns true iff messages are printed
++ when manipulating items from the hash-table.
makingStats?: () -> Boolean
++ \axiom{makingStats?()} returns true iff the statisitics process
++ is running.
extractIfCan: Key -> Union(Entry,"failed")
++ \axiom{extractIfCan(x)} searches the item whose key is \axiom{x}.
insert!: (Key, Entry) -> Void
++ \axiom{insert!(x,y)} stores the item whose key is \axiom{x} and whose
++ entry is \axiom{y}.
Implementation == add
table?: Boolean := false
t: H := empty()
info?: Boolean := false
stats?: Boolean := false
used: NonNegativeInteger := 0
ok: String := "o"
ko: String := "+"
domainName: String := empty()$String
initTable!(): Void ==
table? := true
t := empty()
printInfo!(s1: String, s2: String): Void ==
(empty? s1) or (empty? s2) => void()
not usingTable?() =>
error "in printInfo!()$TBCMPPK: not allowed to use hashtable"
info? := true
ok := s1
ko := s2
startStats!(s: String): Void ==
empty? s => void()
not table? =>
error "in startStats!()$TBCMPPK: not allowed to use hashtable"
stats? := true
used := 0
domainName := s
printStats!(): Void ==
not table? =>
error "in printStats!()$TBCMPPK: not allowed to use hashtable"
not stats? =>
error "in printStats!()$TBCMPPK: statistics not started"
output(" ")$OutputPackage
title: String := concat("*** ", concat(domainName," Statistics ***"))
output(title)$OutputPackage
n: N := #t
output(" Table size: ", n::OutputForm)$OutputPackage
output(" Entries reused: ", used::OutputForm)$OutputPackage
clearTable!(): Void ==
not table? =>
error "in clearTable!()$TBCMPPK: not allowed to use hashtable"
t := empty()
table? := false
info? := false
stats? := false
domainName := empty()$String
usingTable?() == table?
printingInfo?() == info?
makingStats?() == stats?
extractIfCan(k: Key): Union(Entry,"failed") ==
not table? => "failed" :: Union(Entry,"failed")
s: Union(Entry,"failed") := search(k,t)
s case Entry =>
if info? then iprint(ok)$iprintpack
if stats? then used := used + 1
return s
"failed" :: Union(Entry,"failed")
insert!(k: Key, e:Entry): Void ==
not table? => void()
t.k := e
if info? then iprint(ko)$iprintpack
)abbrev domain SPLNODE SplittingNode
++ Author: Marc Moereno Maza
++ Date Created: 07/05/1996
++ Date Last Updated: 07/19/1996
++ Basic Functions:
++ Related Constructors:
++ Also See:
++ AMS Classifications:
++ Keywords:
++ References:
++ References:
++ Description:
++ This domain exports a modest implementation for the
++ vertices of splitting trees. These vertices are called
++ here splitting nodes. Every of these nodes store 3 informations.
++ The first one is its value, that is the current expression
++ to evaluate. The second one is its condition, that is the
++ hypothesis under which the value has to be evaluated.
++ The last one is its status, that is a boolean flag
++ which is true iff the value is the result of its
++ evaluation under its condition. Two splitting vertices
++ are equal iff they have the sane values and the same
++ conditions (so their status do not matter).
SplittingNode(V,C) : Exports == Implementation where
V:Join(SetCategory,Aggregate)
C:Join(SetCategory,Aggregate)
Z ==> Integer
B ==> Boolean
O ==> OutputForm
VT ==> Record(val:V, tower:C)
VTB ==> Record(val:V, tower:C, flag:B)
Exports == SetCategory with
empty : () -> %
++ \axiom{empty()} returns the same as
++ \axiom{[empty()$V,empty()$C,false]$%}
empty? : % -> B
++ \axiom{empty?(n)} returns true iff the node n is \axiom{empty()$%}.
value : % -> V
++ \axiom{value(n)} returns the value of the node n.
condition : % -> C
++ \axiom{condition(n)} returns the condition of the node n.
status : % -> B
++ \axiom{status(n)} returns the status of the node n.
construct : (V,C,B) -> %
++ \axiom{construct(v,t,b)} returns the non-empty node with
++ value v, condition t and flag b
construct : (V,C) -> %
++ \axiom{construct(v,t)} returns the same as
++ \axiom{construct(v,t,false)}
construct : VT -> %
++ \axiom{construct(vt)} returns the same as
++ \axiom{construct(vt.val,vt.tower)}
construct : List VT -> List %
++ \axiom{construct(lvt)} returns the same as
++ \axiom{[construct(vt.val,vt.tower) for vt in lvt]}
construct : (V, List C) -> List %
++ \axiom{construct(v,lt)} returns the same as
++ \axiom{[construct(v,t) for t in lt]}
copy : % -> %
++ \axiom{copy(n)} returns a copy of n.
setValue! : (%,V) -> %
++ \axiom{setValue!(n,v)} returns n whose value
++ has been replaced by v if it is not
++ empty, else an error is produced.
setCondition! : (%,C) -> %
++ \axiom{setCondition!(n,t)} returns n whose condition
++ has been replaced by t if it is not
++ empty, else an error is produced.
setStatus!: (%,B) -> %
++ \axiom{setStatus!(n,b)} returns n whose status
++ has been replaced by b if it is not
++ empty, else an error is produced.
setEmpty! : % -> %
++ \axiom{setEmpty!(n)} replaces n by \axiom{empty()$%}.
infLex? : (%,%,(V,V) -> B,(C,C) -> B) -> B
++ \axiom{infLex?(n1,n2,o1,o2)} returns true iff
++ \axiom{o1(value(n1),value(n2))} or
++ \axiom{value(n1) = value(n2)} and
++ \axiom{o2(condition(n1),condition(n2))}.
subNode? : (%,%,(C,C) -> B) -> B
++ \axiom{subNode?(n1,n2,o2)} returns true iff
++ \axiom{value(n1) = value(n2)} and
++ \axiom{o2(condition(n1),condition(n2))}
Implementation == add
Rep == VTB
empty() == per [empty()$V,empty()$C,false]$Rep
empty?(n:%) == empty?((rep n).val)$V and empty?((rep n).tower)$C
value(n:%) == (rep n).val
condition(n:%) == (rep n).tower
status(n:%) == (rep n).flag
construct(v:V,t:C,b:B) == per [v,t,b]$Rep
construct(v:V,t:C) == [v,t,false]$%
construct(vt:VT) == [vt.val,vt.tower]$%
construct(lvt:List VT) == [[vt]$% for vt in lvt]
construct(v:V,lt: List C) == [[v,t]$% for t in lt]
copy(n:%) == per copy rep n
setValue!(n:%,v:V) ==
(rep n).val := v
n
setCondition!(n:%,t:C) ==
(rep n).tower := t
n
setStatus!(n:%,b:B) ==
(rep n).flag := b
n
setEmpty!(n:%) ==
(rep n).val := empty()$V
(rep n).tower := empty()$C
n
infLex?(n1,n2,o1,o2) ==
o1((rep n1).val,(rep n2).val) => true
(rep n1).val = (rep n2).val =>
o2((rep n1).tower,(rep n2).tower)
false
subNode?(n1,n2,o2) ==
(rep n1).val = (rep n2).val =>
o2((rep n1).tower,(rep n2).tower)
false
-- sample() == empty()
n1:% = n2:% ==
(rep n1).val ~= (rep n2).val => false
(rep n1).tower = (rep n2).tower
n1:% ~= n2:% ==
(rep n1).val = (rep n2).val => false
(rep n1).tower ~= (rep n2).tower
coerce(n:%):O ==
l1,l2,l3,l : List O
l1 := [message("value == "), ((rep n).val)::O]
o1 : O := blankSeparate l1
l2 := [message(" tower == "), ((rep n).tower)::O]
o2 : O := blankSeparate l2
if ((rep n).flag)
then
o3 := message(" closed == true")
else
o3 := message(" closed == false")
l := [o1,o2,o3]
bracket commaSeparate l
)abbrev domain SPLTREE SplittingTree
++ Author: Marc Moereno Maza
++ Date Created: 07/05/1996
++ Date Last Updated: 07/19/1996
++ Basic Functions:
++ Related Constructors:
++ Also See:
++ AMS Classifications:
++ Keywords:
++ References:
++ M. MORENO MAZA "Calculs de pgcd au-dessus des tours
++ d'extensions simples et resolution des systemes d'equations
++ algebriques" These, Universite P.etM. Curie, Paris, 1997.
++ Description:
++ This domain exports a modest implementation of splitting
++ trees. Spliiting trees are needed when the
++ evaluation of some quantity under some hypothesis
++ requires to split the hypothesis into sub-cases.
++ For instance by adding some new hypothesis on one
++ hand and its negation on another hand. The computations
++ are terminated is a splitting tree \axiom{a} when
++ \axiom{status(value(a))} is \axiom{true}. Thus,
++ if for the splitting tree \axiom{a} the flag
++ \axiom{status(value(a))} is \axiom{true}, then
++ \axiom{status(value(d))} is \axiom{true} for any
++ subtree \axiom{d} of \axiom{a}. This property
++ of splitting trees is called the termination
++ condition. If no vertex in a splitting tree \axiom{a}
++ is equal to another, \axiom{a} is said to satisfy
++ the no-duplicates condition. The splitting
++ tree \axiom{a} will satisfy this condition
++ if nodes are added to \axiom{a} by mean of
++ \axiom{splitNodeOf!} and if \axiom{construct}
++ is only used to create the root of \axiom{a}
++ with no children.
SplittingTree(V,C) : Exports == Implementation where
V:Join(SetCategory,Aggregate)
C:Join(SetCategory,Aggregate)
B ==> Boolean
O ==> OutputForm
NNI ==> NonNegativeInteger
VT ==> Record(val:V, tower:C)
VTB ==> Record(val:V, tower:C, flag:B)
S ==> SplittingNode(V,C)
A ==> Record(root:S,subTrees:List(%))
Exports == RecursiveAggregate(S) with
shallowlyMutable
finiteAggregate
extractSplittingLeaf : % -> Union(%,"failed")
++ \axiom{extractSplittingLeaf(a)} returns the left
++ most leaf (as a tree) whose status is false
++ if any, else "failed" is returned.
updateStatus! : % -> %
++ \axiom{updateStatus!(a)} returns a where the status
++ of the vertices are updated to satisfy
++ the "termination condition".
construct : S -> %
++ \axiom{construct(s)} creates a splitting tree
++ with value (i.e. root vertex) given by
++ \axiom{s} and no children. Thus, if the
++ status of \axiom{s} is false, \axiom{[s]}
++ represents the starting point of the
++ evaluation \axiom{value(s)} under the
++ hypothesis \axiom{condition(s)}.
construct : (V,C, List %) -> %
++ \axiom{construct(v,t,la)} creates a splitting tree
++ with value (i.e. root vertex) given by
++ \axiom{[v,t]$S} and with \axiom{la} as
++ children list.
construct : (V,C,List S) -> %
++ \axiom{construct(v,t,ls)} creates a splitting tree
++ with value (i.e. root vertex) given by
++ \axiom{[v,t]$S} and with children list given by
++ \axiom{[[s]$% for s in ls]}.
construct : (V,C,V,List C) -> %
++ \axiom{construct(v1,t,v2,lt)} creates a splitting tree
++ with value (i.e. root vertex) given by
++ \axiom{[v,t]$S} and with children list given by
++ \axiom{[[[v,t]$S]$% for s in ls]}.
conditions : % -> List C
++ \axiom{conditions(a)} returns the list of the conditions
++ of the leaves of a
result : % -> List VT
++ \axiom{result(a)} where \axiom{ls} is the leaves list of \axiom{a}
++ returns \axiom{[[value(s),condition(s)]$VT for s in ls]}
++ if the computations are terminated in \axiom{a} else
++ an error is produced.
nodeOf? : (S,%) -> B
++ \axiom{nodeOf?(s,a)} returns true iff some node of \axiom{a}
++ is equal to \axiom{s}
subNodeOf? : (S,%,(C,C) -> B) -> B
++ \axiom{subNodeOf?(s,a,sub?)} returns true iff for some node
++ \axiom{n} in \axiom{a} we have \axiom{s = n} or
++ \axiom{status(n)} and \axiom{subNode?(s,n,sub?)}.
remove : (S,%) -> %
++ \axiom{remove(s,a)} returns the splitting tree obtained
++ from a by removing every sub-tree \axiom{b} such
++ that \axiom{value(b)} and \axiom{s} have the same
++ value, condition and status.
remove! : (S,%) -> %
++ \axiom{remove!(s,a)} replaces a by remove(s,a)
splitNodeOf! : (%,%,List(S)) -> %
++ \axiom{splitNodeOf!(l,a,ls)} returns \axiom{a} where the children
++ list of \axiom{l} has been set to
++ \axiom{[[s]$% for s in ls | not nodeOf?(s,a)]}.
++ Thus, if \axiom{l} is not a node of \axiom{a}, this
++ latter splitting tree is unchanged.
splitNodeOf! : (%,%,List(S),(C,C) -> B) -> %
++ \axiom{splitNodeOf!(l,a,ls,sub?)} returns \axiom{a} where the children
++ list of \axiom{l} has been set to
++ \axiom{[[s]$% for s in ls | not subNodeOf?(s,a,sub?)]}.
++ Thus, if \axiom{l} is not a node of \axiom{a}, this
++ latter splitting tree is unchanged.
Implementation == add
Rep == A
construct(s:S) ==
per [s,[]]$A
construct(v:V,t:C,la:List(%)) ==
per [[v,t]$S,la]$A
construct(v:V,t:C,ls:List(S)) ==
per [[v,t]$S,[[s]$% for s in ls]]$A
construct(v1:V,t:C,v2:V,lt:List(C)) ==
[v1,t,([v2,lt]$S)@(List S)]$%
empty?(a:%) == empty?((rep a).root) and empty?((rep a).subTrees)
empty() == [empty()$S]$%
remove(s:S,a:%) ==
empty? a => a
(s = value(a)) and (status(s) = status(value(a))) => empty()$%
la := children(a)
lb : List % := []
while (not empty? la) repeat
lb := cons(remove(s,first la), lb)
la := rest la
lb := reverse remove(empty?,lb)
[value(value(a)),condition(value(a)),lb]$%
remove!(s:S,a:%) ==
empty? a => a
(s = value(a)) and (status(s) = status(value(a))) =>
(rep a).root := empty()$S
(rep a).subTrees := []
a
la := children(a)
lb : List % := []
while (not empty? la) repeat
lb := cons(remove!(s,first la), lb)
la := rest la
lb := reverse remove(empty()$%,lb)
setchildren!(a,lb)
value(a:%) ==
(rep a).root
children(a:%) ==
(rep a).subTrees
leaf?(a:%) ==
empty? a => false
empty? (rep a).subTrees
setchildren!(a:%,la:List(%)) ==
(rep a).subTrees := la
a
setvalue!(a:%,s:S) ==
(rep a).root := s
s
cyclic?(a:%) == false
map(foo:(S -> S),a:%) ==
empty? a => a
b : % := [foo(value(a))]$%
leaf? a => b
setchildren!(b,[map(foo,c) for c in children(a)])
map!(foo:(S -> S),a:%) ==
empty? a => a
setvalue!(a,foo(value(a)))
leaf? a => a
setchildren!(a,[map!(foo,c) for c in children(a)])
copy(a:%) ==
map(copy,a)
eq?(a1:%,a2:%) ==
error"in eq? from SPLTREE : la vache qui rit est-elle folle?"
nodes(a:%) ==
empty? a => []
leaf? a => [a]
cons(a,concat([nodes(c) for c in children(a)]))
leaves(a:%) ==
empty? a => []
leaf? a => [value(a)]
concat([leaves(c) for c in children(a)])
members(a:%) ==
empty? a => []
leaf? a => [value(a)]
cons(value(a),concat([members(c) for c in children(a)]))
#(a:%) ==
empty? a => 0$NNI
leaf? a => 1$NNI
reduce("+",[#c for c in children(a)],1$NNI)$(List NNI)
a1:% = a2:% ==
empty? a1 => empty? a2
empty? a2 => false
leaf? a1 =>
not leaf? a2 => false
value(a1) =$S value(a2)
leaf? a2 => false
value(a1) ~=$S value(a2) => false
children(a1) = children(a2)
-- sample() == [sample()$S]$%
localCoerce(a:%,k:NNI):O ==
s : String
if k = 1 then s := "* " else s := "-> "
for i in 2..k repeat s := concat("-+",s)$String
ro : O := left(hconcat(message(s)$O,value(a)::O)$O)$O
leaf? a => ro
lo : List O := [localCoerce(c,k+1) for c in children(a)]
lo := cons(ro,lo)
vconcat(lo)$O
coerce(a:%):O ==
empty? a => vconcat(message(" ")$O,message("* []")$O)
vconcat(message(" ")$O,localCoerce(a,1))
extractSplittingLeaf(a:%) ==
empty? a => "failed"::Union(%,"failed")
status(value(a))$S => "failed"::Union(%,"failed")
la := children(a)
empty? la => a
while (not empty? la) repeat
esl := extractSplittingLeaf(first la)
(esl case %) => return(esl)
la := rest la
"failed"::Union(%,"failed")
updateStatus!(a:%) ==
la := children(a)
(empty? la) or (status(value(a))$S) => a
done := true
while (not empty? la) and done repeat
done := done and status(value(updateStatus! first la))
la := rest la
setStatus!(value(a),done)$S
a
result(a:%) ==
empty? a => []
not status(value(a))$S =>
error"in result from SLPTREE : mad cow!"
ls : List S := leaves(a)
[[value(s),condition(s)]$VT for s in ls]
conditions(a:%) ==
empty? a => []
ls : List S := leaves(a)
[condition(s) for s in ls]
nodeOf?(s:S,a:%) ==
empty? a => false
s =$S value(a) => true
la := children(a)
while (not empty? la) and (not nodeOf?(s,first la)) repeat
la := rest la
not empty? la
subNodeOf?(s:S,a:%,sub?:((C,C) -> B)) ==
empty? a => false
-- s =$S value(a) => true
status(value(a)$%)$S and subNode?(s,value(a),sub?)$S => true
la := children(a)
while (not empty? la) and (not subNodeOf?(s,first la,sub?)) repeat
la := rest la
not empty? la
splitNodeOf!(l:%,a:%,ls:List(S)) ==
ln := removeDuplicates ls
la : List % := []
while not empty? ln repeat
if not nodeOf?(first ln,a)
then
la := cons([first ln]$%, la)
ln := rest ln
la := reverse la
setchildren!(l,la)$%
if empty? la then (rep l).root := [empty()$V,empty()$C,true]$S
updateStatus!(a)
splitNodeOf!(l:%,a:%,ls:List(S),sub?:((C,C) -> B)) ==
ln := removeDuplicates ls
la : List % := []
while not empty? ln repeat
if not subNodeOf?(first ln,a,sub?)
then
la := cons([first ln]$%, la)
ln := rest ln
la := reverse la
setchildren!(l,la)$%
if empty? la then (rep l).root := [empty()$V,empty()$C,true]$S
updateStatus!(a)
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