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-- Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
-- All rights reserved.
-- Copyright (C) 2007, 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.
import macros
namespace BOOT
simpBool x == dnf2pf reduceDnf be x
reduceDnf u ==
-- (OR (AND ..b..) b) ==> (OR b )
atom u => u
for x in u repeat
ok := true
for y in u repeat
x = y => 'skip
dnfContains(x,y) => return (ok := false)
ok = true => acc := [x,:acc]
nreverse acc
dnfContains([a,b],[c,d]) == fn(a,c) and fn(b,d) where
fn(x,y) == and/[member(u,x) for u in y]
prove x ==
world := [p for y in listOfUserIds x | (p := getPredicate y)] =>
'false = be mkpf([['NOT,x],:world],'AND) => true
'false = be mkpf([x,:world],'AND) => false
x
'false = (y := be x) => 'false
y = 'true => true
dnf2pf y
simpBoolGiven(x,world) ==
world =>
'false = be mkpf([['NOT,x],:world],'AND) => true
'false = (y := be mkpf([x,:world],'AND)) => false
(u := andReduce(dnf2pf y,world)) is ['AND,:v] and
(w := SETDIFFERENCE(v,world)) ~= v => simpBool ['AND,:w]
u
'false = (y := be x) => false
'true = y => true
dnf2pf y
andReduce(x,y) ==
x is ['AND,:r] =>
y is ['AND,:s] => mkpf(S_-(r,s),'AND)
mkpf(S_-(r,[s]),'AND)
x
dnf2pf(x) ==
x = 'true => 'T
x = 'false => nil
atom x => x
mkpf(
[mkpf([:[k for k in b],:[['not,k] for k in a]],'AND) for [a,b] in x],'OR)
be x == b2dnf x
b2dnf x ==
x = 'T => 'true
x = NIL => 'false
atom x => bassert x
[op,:argl] := x
MEMQ(op,'(AND and)) => band argl
MEMQ(op,'(OR or)) => bor argl
MEMQ(op,'(NOT not)) => bnot first argl
bassert x
band x ==
x is [h,:t] => andDnf(b2dnf h,band t)
'true
bor x ==
x is [a,:b] => orDnf(b2dnf a,bor b)
'false
bnot x == notDnf b2dnf x
bassert x == [[nil,[x]]]
bassertNot x == [[[x],nil]]
------------------------Disjunctive Normal Form Code-----------------------
-- dnf is true | false | [coaf ... ]
-- coaf is true | false | [item ... ]
-- item is anything
orDnf(a,b) == -- or: (dnf, dnf) -> dnf
a = 'false => b
b = 'false => a
a = 'true or b = 'true => 'true
null a => b --null list means false
a is [c] = coafOrDnf(c,b)
coafOrDnf(first a,orDnf(rest a,b))
andDnf(a,b) == -- and: (dnf, dnf) -> dnf
a = 'true => b
b = 'true => a
a = 'false or b = 'false => 'false
null a => 'false --null list means false
a is [c] => coafAndDnf(c,b)
x := coafAndDnf(first a,b)
y := andDnf(rest a,b)
x = 'false => y
y = 'false => x
ordUnion(x,y)
notDnf l == -- not: dnf -> dnf
l = 'true => 'false
l = 'false => 'true
null l => 'true --null list means false
l is [x] => notCoaf x
andDnf(notCoaf first l,notDnf rest l)
coafOrDnf(a,l) == -- or: (coaf, dnf) -> dnf
a = 'true or l = 'true => 'true
a = 'false => l
member(a,l) => l
y := notCoaf a
x := ordIntersection(y,l)
null x => orDel(a,l)
x = l => 'true
x = y => ordSetDiff(l,x)
ordUnion(notDnf ordSetDiff(y,x),l)
coafAndDnf(a,b) == --and: (coaf, dnf) -> dnf
a = 'true => b
a = 'false => 'false
[c,:r] := b
null r => coafAndCoaf(a,c)
x := coafAndCoaf(a,c) --dnf
y := coafAndDnf(a,r) --dnf
x = 'false => y
y = 'false => x
ordUnion(x,y)
coafAndCoaf([a,b],[p,q]) == --and: (coaf,coaf) -> dnf
ordIntersection(a,q) or ordIntersection(b,p) => 'false
[[ordUnion(a,p),ordUnion(b,q)]]
notCoaf [a,b] == [:[[nil,[x]] for x in a],:[[[x],nil] for x in b]]
list1 l ==
l isnt [h,:t] => nil
null h => list1 t
[[h,nil,nil],:list1 t]
list2 l ==
l isnt [h,:t] => nil
null h => list2 t
[[nil,h,nil],:list2 t]
list3 l ==
l isnt [h,:t] => nil
null h => list3 t
[[nil,nil,h],:list3 t]
orDel(a,l) ==
l is [h,:t] =>
a = h => t
?ORDER(a,h) => [a,:l]
[h,:orDel(a,t)]
[a]
ordList l ==
l is [h,:t] and t => orDel(h,ordList t)
l
ordUnion(a,b) ==
a isnt [c,:r] => b
b isnt [d,:s] => a
c=d => [c,:ordUnion(r,s)]
?ORDER(a,b) => [c,:ordUnion(r,b)]
[d,:ordUnion(s,a)]
ordIntersection(a,b) ==
a isnt [h,:t] => nil
member(h,b) => [h,:ordIntersection(t,b)]
ordIntersection(t,b)
ordSetDiff(a,b) ==
b isnt [h,:t] => a
member(h,a) => ordSetDiff(delete(h,a),t)
ordSetDiff(a,t)
-------------
testPredList u ==
for x in u repeat
y := simpBool x
x = y => nil
pp x
pp '"==========>"
pp y
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