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authordos-reis <gdr@axiomatics.org>2007-09-20 04:57:39 +0000
committerdos-reis <gdr@axiomatics.org>2007-09-20 04:57:39 +0000
commitc75b5923cb35d83910e45f13e9d15c981ea25387 (patch)
treea6c3a03b1ac5fef72e01fe1d60873d277222a52b /src/interp/simpbool.boot.pamphlet
parent516d3e4928185c380ffee8249454fe76ab6f2851 (diff)
downloadopen-axiom-c75b5923cb35d83910e45f13e9d15c981ea25387.tar.gz
remove pamphlets - part 7
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diff --git a/src/interp/simpbool.boot.pamphlet b/src/interp/simpbool.boot.pamphlet
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-\documentclass{article}
-\usepackage{axiom}
-\begin{document}
-\title{\$SPAD/src/interp simpbool.boot}
-\author{The Axiom Team}
-\maketitle
-\begin{abstract}
-\end{abstract}
-\eject
-\tableofcontents
-\eject
-\section{License}
-<<license>>=
--- Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--- 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.
-
-@
-<<*>>=
-<<license>>
-
-)package "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
-@
-\eject
-\begin{thebibliography}{99}
-\bibitem{1} nothing
-\end{thebibliography}
-\end{document}