author | blanchet |
Wed, 15 Sep 2010 14:24:29 +0200 | |
changeset 39407 | 9e6faecea412 |
parent 39353 | 7f11d833d65b |
child 39408 | 65a379f4c8f3 |
permissions | -rw-r--r-- |
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(* ========================================================================= *) |
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(* CLAUSE = ID + THEOREM *) |
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(* Copyright (c) 2002-2004 Joe Hurd, distributed under the BSD License *) |
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(* ========================================================================= *) |
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structure Clause :> Clause = |
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struct |
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open Useful; |
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(* ------------------------------------------------------------------------- *) |
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(* Helper functions. *) |
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(* ------------------------------------------------------------------------- *) |
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val newId = |
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let |
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val r = ref 0 |
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in |
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fn () => case r of ref n => let val () = r := n + 1 in n end |
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end; |
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(* ------------------------------------------------------------------------- *) |
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(* A type of clause. *) |
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(* ------------------------------------------------------------------------- *) |
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datatype literalOrder = |
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NoLiteralOrder |
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| UnsignedLiteralOrder |
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| PositiveLiteralOrder; |
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type parameters = |
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{ordering : KnuthBendixOrder.kbo, |
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orderLiterals : literalOrder, |
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orderTerms : bool}; |
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type clauseId = int; |
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type clauseInfo = {parameters : parameters, id : clauseId, thm : Thm.thm}; |
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datatype clause = Clause of clauseInfo; |
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(* ------------------------------------------------------------------------- *) |
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(* Pretty printing. *) |
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(* ------------------------------------------------------------------------- *) |
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val showId = ref false; |
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local |
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val ppIdThm = Print.ppPair Print.ppInt Thm.pp; |
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in |
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fun pp (Clause {id,thm,...}) = |
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if !showId then ppIdThm (id,thm) else Thm.pp thm; |
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end; |
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fun toString cl = Print.toString pp cl; |
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(* ------------------------------------------------------------------------- *) |
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(* Basic operations. *) |
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(* ------------------------------------------------------------------------- *) |
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val default : parameters = |
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{ordering = KnuthBendixOrder.default, |
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39407
9e6faecea412
apply Larry's hacks directly to the "src" files;
blanchet
parents:
39353
diff
changeset
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orderLiterals = UnsignedLiteralOrder (* PositiveLiteralOrder *) (* MODIFIED by Jasmin Blanchette *), |
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orderTerms = true}; |
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fun mk info = Clause info |
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fun dest (Clause info) = info; |
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fun id (Clause {id = i, ...}) = i; |
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fun thm (Clause {thm = th, ...}) = th; |
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fun equalThms cl cl' = Thm.equal (thm cl) (thm cl'); |
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fun new parameters thm = |
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Clause {parameters = parameters, id = newId (), thm = thm}; |
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fun literals cl = Thm.clause (thm cl); |
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fun isTautology (Clause {thm,...}) = Thm.isTautology thm; |
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fun isContradiction (Clause {thm,...}) = Thm.isContradiction thm; |
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(* ------------------------------------------------------------------------- *) |
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(* The term ordering is used to cut down inferences. *) |
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(* ------------------------------------------------------------------------- *) |
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fun strictlyLess ordering x_y = |
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case KnuthBendixOrder.compare ordering x_y of |
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SOME LESS => true |
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| _ => false; |
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fun isLargerTerm ({ordering,orderTerms,...} : parameters) l_r = |
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not orderTerms orelse not (strictlyLess ordering l_r); |
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local |
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fun atomToTerms atm = |
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case total Atom.destEq atm of |
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NONE => [Term.Fn atm] |
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| SOME (l,r) => [l,r]; |
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fun notStrictlyLess ordering (xs,ys) = |
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let |
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fun less x = List.exists (fn y => strictlyLess ordering (x,y)) ys |
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in |
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not (List.all less xs) |
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end; |
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in |
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fun isLargerLiteral ({ordering,orderLiterals,...} : parameters) lits = |
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case orderLiterals of |
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NoLiteralOrder => K true |
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| UnsignedLiteralOrder => |
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let |
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fun addLit ((_,atm),acc) = atomToTerms atm @ acc |
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val tms = LiteralSet.foldl addLit [] lits |
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in |
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fn (_,atm') => notStrictlyLess ordering (atomToTerms atm', tms) |
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end |
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| PositiveLiteralOrder => |
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case LiteralSet.findl (K true) lits of |
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NONE => K true |
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| SOME (pol,_) => |
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let |
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fun addLit ((p,atm),acc) = |
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if p = pol then atomToTerms atm @ acc else acc |
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val tms = LiteralSet.foldl addLit [] lits |
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in |
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fn (pol',atm') => |
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if pol <> pol' then pol |
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else notStrictlyLess ordering (atomToTerms atm', tms) |
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end; |
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end; |
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fun largestLiterals (Clause {parameters,thm,...}) = |
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let |
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val litSet = Thm.clause thm |
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val isLarger = isLargerLiteral parameters litSet |
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fun addLit (lit,s) = if isLarger lit then LiteralSet.add s lit else s |
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in |
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LiteralSet.foldr addLit LiteralSet.empty litSet |
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end; |
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(*MetisTrace6 |
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val largestLiterals = fn cl => |
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let |
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val ppResult = LiteralSet.pp |
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val () = Print.trace pp "Clause.largestLiterals: cl" cl |
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val result = largestLiterals cl |
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val () = Print.trace ppResult "Clause.largestLiterals: result" result |
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in |
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result |
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end; |
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*) |
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fun largestEquations (cl as Clause {parameters,...}) = |
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let |
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fun addEq lit ort (l_r as (l,_)) acc = |
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if isLargerTerm parameters l_r then (lit,ort,l) :: acc else acc |
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fun addLit (lit,acc) = |
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case total Literal.destEq lit of |
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NONE => acc |
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| SOME (l,r) => |
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let |
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val acc = addEq lit Rewrite.RightToLeft (r,l) acc |
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val acc = addEq lit Rewrite.LeftToRight (l,r) acc |
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in |
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acc |
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end |
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in |
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LiteralSet.foldr addLit [] (largestLiterals cl) |
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end; |
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local |
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fun addLit (lit,acc) = |
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let |
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fun addTm ((path,tm),acc) = (lit,path,tm) :: acc |
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in |
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foldl addTm acc (Literal.nonVarTypedSubterms lit) |
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end; |
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in |
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fun largestSubterms cl = LiteralSet.foldl addLit [] (largestLiterals cl); |
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fun allSubterms cl = LiteralSet.foldl addLit [] (literals cl); |
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end; |
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(* ------------------------------------------------------------------------- *) |
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(* Subsumption. *) |
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(* ------------------------------------------------------------------------- *) |
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fun subsumes (subs : clause Subsume.subsume) cl = |
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Subsume.isStrictlySubsumed subs (literals cl); |
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(* ------------------------------------------------------------------------- *) |
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(* Simplifying rules: these preserve the clause id. *) |
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(* ------------------------------------------------------------------------- *) |
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fun freshVars (Clause {parameters,id,thm}) = |
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Clause {parameters = parameters, id = id, thm = Rule.freshVars thm}; |
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fun simplify (Clause {parameters,id,thm}) = |
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case Rule.simplify thm of |
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NONE => NONE |
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| SOME thm => SOME (Clause {parameters = parameters, id = id, thm = thm}); |
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fun reduce units (Clause {parameters,id,thm}) = |
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Clause {parameters = parameters, id = id, thm = Units.reduce units thm}; |
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fun rewrite rewr (cl as Clause {parameters,id,thm}) = |
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let |
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fun simp th = |
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let |
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val {ordering,...} = parameters |
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val cmp = KnuthBendixOrder.compare ordering |
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in |
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Rewrite.rewriteIdRule rewr cmp id th |
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end |
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(*MetisTrace4 |
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val () = Print.trace Rewrite.pp "Clause.rewrite: rewr" rewr |
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val () = Print.trace Print.ppInt "Clause.rewrite: id" id |
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val () = Print.trace pp "Clause.rewrite: cl" cl |
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*) |
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val thm = |
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case Rewrite.peek rewr id of |
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NONE => simp thm |
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| SOME ((_,thm),_) => if Rewrite.isReduced rewr then thm else simp thm |
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val result = Clause {parameters = parameters, id = id, thm = thm} |
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(*MetisTrace4 |
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val () = Print.trace pp "Clause.rewrite: result" result |
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*) |
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in |
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result |
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end |
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(*MetisDebug |
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handle Error err => raise Error ("Clause.rewrite:\n" ^ err); |
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*) |
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(* ------------------------------------------------------------------------- *) |
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(* Inference rules: these generate new clause ids. *) |
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(* ------------------------------------------------------------------------- *) |
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fun factor (cl as Clause {parameters,thm,...}) = |
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let |
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val lits = largestLiterals cl |
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fun apply sub = new parameters (Thm.subst sub thm) |
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in |
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map apply (Rule.factor' lits) |
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end; |
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(*MetisTrace5 |
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val factor = fn cl => |
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let |
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val () = Print.trace pp "Clause.factor: cl" cl |
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val result = factor cl |
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val () = Print.trace (Print.ppList pp) "Clause.factor: result" result |
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in |
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result |
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end; |
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*) |
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fun resolve (cl1,lit1) (cl2,lit2) = |
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let |
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(*MetisTrace5 |
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val () = Print.trace pp "Clause.resolve: cl1" cl1 |
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val () = Print.trace Literal.pp "Clause.resolve: lit1" lit1 |
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val () = Print.trace pp "Clause.resolve: cl2" cl2 |
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val () = Print.trace Literal.pp "Clause.resolve: lit2" lit2 |
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*) |
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val Clause {parameters, thm = th1, ...} = cl1 |
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and Clause {thm = th2, ...} = cl2 |
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val sub = Literal.unify Subst.empty lit1 (Literal.negate lit2) |
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(*MetisTrace5 |
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val () = Print.trace Subst.pp "Clause.resolve: sub" sub |
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*) |
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val lit1 = Literal.subst sub lit1 |
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val lit2 = Literal.negate lit1 |
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val th1 = Thm.subst sub th1 |
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and th2 = Thm.subst sub th2 |
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val _ = isLargerLiteral parameters (Thm.clause th1) lit1 orelse |
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(*MetisTrace5 |
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(trace "Clause.resolve: th1 violates ordering\n"; false) orelse |
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*) |
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raise Error "resolve: clause1: ordering constraints" |
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val _ = isLargerLiteral parameters (Thm.clause th2) lit2 orelse |
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(*MetisTrace5 |
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(trace "Clause.resolve: th2 violates ordering\n"; false) orelse |
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*) |
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raise Error "resolve: clause2: ordering constraints" |
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val th = Thm.resolve lit1 th1 th2 |
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(*MetisTrace5 |
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val () = Print.trace Thm.pp "Clause.resolve: th" th |
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*) |
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val cl = Clause {parameters = parameters, id = newId (), thm = th} |
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(*MetisTrace5 |
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val () = Print.trace pp "Clause.resolve: cl" cl |
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*) |
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in |
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cl |
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end; |
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fun paramodulate (cl1,lit1,ort1,tm1) (cl2,lit2,path2,tm2) = |
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let |
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(*MetisTrace5 |
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val () = Print.trace pp "Clause.paramodulate: cl1" cl1 |
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val () = Print.trace Literal.pp "Clause.paramodulate: lit1" lit1 |
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val () = Print.trace Rewrite.ppOrient "Clause.paramodulate: ort1" ort1 |
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val () = Print.trace Term.pp "Clause.paramodulate: tm1" tm1 |
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val () = Print.trace pp "Clause.paramodulate: cl2" cl2 |
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val () = Print.trace Literal.pp "Clause.paramodulate: lit2" lit2 |
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val () = Print.trace Term.ppPath "Clause.paramodulate: path2" path2 |
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val () = Print.trace Term.pp "Clause.paramodulate: tm2" tm2 |
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*) |
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val Clause {parameters, thm = th1, ...} = cl1 |
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and Clause {thm = th2, ...} = cl2 |
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val sub = Subst.unify Subst.empty tm1 tm2 |
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val lit1 = Literal.subst sub lit1 |
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and lit2 = Literal.subst sub lit2 |
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and th1 = Thm.subst sub th1 |
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and th2 = Thm.subst sub th2 |
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val _ = isLargerLiteral parameters (Thm.clause th1) lit1 orelse |
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raise Error "Clause.paramodulate: with clause: ordering" |
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val _ = isLargerLiteral parameters (Thm.clause th2) lit2 orelse |
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raise Error "Clause.paramodulate: into clause: ordering" |
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val eqn = (Literal.destEq lit1, th1) |
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val eqn as (l_r,_) = |
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case ort1 of |
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Rewrite.LeftToRight => eqn |
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| Rewrite.RightToLeft => Rule.symEqn eqn |
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(*MetisTrace6 |
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val () = Print.trace Rule.ppEquation "Clause.paramodulate: eqn" eqn |
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*) |
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val _ = isLargerTerm parameters l_r orelse |
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raise Error "Clause.paramodulate: equation: ordering constraints" |
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val th = Rule.rewrRule eqn lit2 path2 th2 |
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(*MetisTrace5 |
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val () = Print.trace Thm.pp "Clause.paramodulate: th" th |
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*) |
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in |
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Clause {parameters = parameters, id = newId (), thm = th} |
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end |
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(*MetisTrace5 |
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handle Error err => |
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let |
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val () = trace ("Clause.paramodulate: failed: " ^ err ^ "\n") |
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in |
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raise Error err |
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end; |
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*) |
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end |