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/****************************************************************************** |
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* Top contributors (to current version): |
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* Mudathir Mohamed, Gereon Kremer, Aina Niemetz |
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* |
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* This file is part of the cvc5 project. |
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* |
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* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS |
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* in the top-level source directory and their institutional affiliations. |
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* All rights reserved. See the file COPYING in the top-level source |
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* directory for licensing information. |
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* **************************************************************************** |
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* |
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* Bags theory rewriter. |
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*/ |
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#include "theory/bags/bags_rewriter.h" |
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#include "theory/bags/normal_form.h" |
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#include "util/statistics_registry.h" |
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using namespace cvc5::kind; |
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namespace cvc5 { |
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namespace theory { |
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namespace bags { |
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3137 |
BagsRewriteResponse::BagsRewriteResponse() |
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: d_node(Node::null()), d_rewrite(Rewrite::NONE) |
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{ |
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} |
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BagsRewriteResponse::BagsRewriteResponse(Node n, Rewrite rewrite) |
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: d_node(n), d_rewrite(rewrite) |
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{ |
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} |
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BagsRewriteResponse::BagsRewriteResponse(const BagsRewriteResponse& r) |
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: d_node(r.d_node), d_rewrite(r.d_rewrite) |
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{ |
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} |
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BagsRewriter::BagsRewriter(HistogramStat<Rewrite>* statistics) |
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: d_statistics(statistics) |
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{ |
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d_nm = NodeManager::currentNM(); |
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d_zero = d_nm->mkConst(Rational(0)); |
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d_one = d_nm->mkConst(Rational(1)); |
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} |
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|
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RewriteResponse BagsRewriter::postRewrite(TNode n) |
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{ |
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BagsRewriteResponse response; |
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if (n.isConst()) |
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{ |
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// no need to rewrite n if it is already in a normal form |
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response = BagsRewriteResponse(n, Rewrite::NONE); |
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} |
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else if (n.getKind() == EQUAL) |
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{ |
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response = postRewriteEqual(n); |
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} |
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else if (NormalForm::areChildrenConstants(n)) |
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{ |
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Node value = NormalForm::evaluate(n); |
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response = BagsRewriteResponse(value, Rewrite::CONSTANT_EVALUATION); |
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} |
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else |
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{ |
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Kind k = n.getKind(); |
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switch (k) |
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{ |
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case MK_BAG: response = rewriteMakeBag(n); break; |
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case BAG_COUNT: response = rewriteBagCount(n); break; |
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case DUPLICATE_REMOVAL: response = rewriteDuplicateRemoval(n); break; |
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case UNION_MAX: response = rewriteUnionMax(n); break; |
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case UNION_DISJOINT: response = rewriteUnionDisjoint(n); break; |
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case INTERSECTION_MIN: response = rewriteIntersectionMin(n); break; |
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case DIFFERENCE_SUBTRACT: response = rewriteDifferenceSubtract(n); break; |
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case DIFFERENCE_REMOVE: response = rewriteDifferenceRemove(n); break; |
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case BAG_CHOOSE: response = rewriteChoose(n); break; |
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case BAG_CARD: response = rewriteCard(n); break; |
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case BAG_IS_SINGLETON: response = rewriteIsSingleton(n); break; |
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case BAG_FROM_SET: response = rewriteFromSet(n); break; |
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case BAG_TO_SET: response = rewriteToSet(n); break; |
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default: response = BagsRewriteResponse(n, Rewrite::NONE); break; |
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} |
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} |
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Trace("bags-rewrite") << "postRewrite " << n << " to " << response.d_node |
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<< " by " << response.d_rewrite << "." << std::endl; |
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if (d_statistics != nullptr) |
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{ |
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(*d_statistics) << response.d_rewrite; |
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} |
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if (response.d_node != n) |
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{ |
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return RewriteResponse(RewriteStatus::REWRITE_AGAIN_FULL, response.d_node); |
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} |
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return RewriteResponse(RewriteStatus::REWRITE_DONE, n); |
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} |
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RewriteResponse BagsRewriter::preRewrite(TNode n) |
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{ |
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BagsRewriteResponse response; |
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Kind k = n.getKind(); |
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switch (k) |
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{ |
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case EQUAL: response = preRewriteEqual(n); break; |
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case SUBBAG: response = rewriteSubBag(n); break; |
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default: response = BagsRewriteResponse(n, Rewrite::NONE); |
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} |
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Trace("bags-rewrite") << "preRewrite " << n << " to " << response.d_node |
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<< " by " << response.d_rewrite << "." << std::endl; |
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if (d_statistics != nullptr) |
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{ |
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(*d_statistics) << response.d_rewrite; |
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} |
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if (response.d_node != n) |
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{ |
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return RewriteResponse(RewriteStatus::REWRITE_AGAIN_FULL, response.d_node); |
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} |
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return RewriteResponse(RewriteStatus::REWRITE_DONE, n); |
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} |
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BagsRewriteResponse BagsRewriter::preRewriteEqual(const TNode& n) const |
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{ |
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Assert(n.getKind() == EQUAL); |
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if (n[0] == n[1]) |
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{ |
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// (= A A) = true where A is a bag |
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return BagsRewriteResponse(d_nm->mkConst(true), Rewrite::IDENTICAL_NODES); |
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} |
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return BagsRewriteResponse(n, Rewrite::NONE); |
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} |
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BagsRewriteResponse BagsRewriter::rewriteSubBag(const TNode& n) const |
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{ |
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Assert(n.getKind() == SUBBAG); |
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// (bag.is_included A B) = ((difference_subtract A B) == emptybag) |
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Node emptybag = d_nm->mkConst(EmptyBag(n[0].getType())); |
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Node subtract = d_nm->mkNode(DIFFERENCE_SUBTRACT, n[0], n[1]); |
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Node equal = subtract.eqNode(emptybag); |
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return BagsRewriteResponse(equal, Rewrite::SUB_BAG); |
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} |
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BagsRewriteResponse BagsRewriter::rewriteMakeBag(const TNode& n) const |
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{ |
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Assert(n.getKind() == MK_BAG); |
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// return emptybag for negative or zero multiplicity |
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if (n[1].isConst() && n[1].getConst<Rational>().sgn() != 1) |
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{ |
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// (mkBag x c) = emptybag where c <= 0 |
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Node emptybag = d_nm->mkConst(EmptyBag(n.getType())); |
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return BagsRewriteResponse(emptybag, Rewrite::MK_BAG_COUNT_NEGATIVE); |
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} |
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return BagsRewriteResponse(n, Rewrite::NONE); |
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} |
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BagsRewriteResponse BagsRewriter::rewriteBagCount(const TNode& n) const |
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{ |
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Assert(n.getKind() == BAG_COUNT); |
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if (n[1].isConst() && n[1].getKind() == EMPTYBAG) |
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{ |
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// (bag.count x emptybag) = 0 |
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return BagsRewriteResponse(d_zero, Rewrite::COUNT_EMPTY); |
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} |
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if (n[1].getKind() == MK_BAG && n[0] == n[1][0]) |
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{ |
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// (bag.count x (mkBag x c) = c |
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return BagsRewriteResponse(n[1][1], Rewrite::COUNT_MK_BAG); |
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} |
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return BagsRewriteResponse(n, Rewrite::NONE); |
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} |
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BagsRewriteResponse BagsRewriter::rewriteDuplicateRemoval(const TNode& n) const |
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{ |
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Assert(n.getKind() == DUPLICATE_REMOVAL); |
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if (n[0].getKind() == MK_BAG && n[0][1].isConst() |
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&& n[0][1].getConst<Rational>().sgn() == 1) |
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{ |
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// (duplicate_removal (mkBag x n)) = (mkBag x 1) |
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// where n is a positive constant |
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Node bag = d_nm->mkBag(n[0][0].getType(), n[0][0], d_one); |
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return BagsRewriteResponse(bag, Rewrite::DUPLICATE_REMOVAL_MK_BAG); |
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} |
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return BagsRewriteResponse(n, Rewrite::NONE); |
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} |
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BagsRewriteResponse BagsRewriter::rewriteUnionMax(const TNode& n) const |
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{ |
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Assert(n.getKind() == UNION_MAX); |
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if (n[1].getKind() == EMPTYBAG || n[0] == n[1]) |
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{ |
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// (union_max A A) = A |
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// (union_max A emptybag) = A |
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return BagsRewriteResponse(n[0], Rewrite::UNION_MAX_SAME_OR_EMPTY); |
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} |
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if (n[0].getKind() == EMPTYBAG) |
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{ |
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// (union_max emptybag A) = A |
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return BagsRewriteResponse(n[1], Rewrite::UNION_MAX_EMPTY); |
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} |
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if ((n[1].getKind() == UNION_MAX || n[1].getKind() == UNION_DISJOINT) |
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&& (n[0] == n[1][0] || n[0] == n[1][1])) |
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{ |
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// (union_max A (union_max A B)) = (union_max A B) |
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// (union_max A (union_max B A)) = (union_max B A) |
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// (union_max A (union_disjoint A B)) = (union_disjoint A B) |
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// (union_max A (union_disjoint B A)) = (union_disjoint B A) |
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return BagsRewriteResponse(n[1], Rewrite::UNION_MAX_UNION_LEFT); |
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} |
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if ((n[0].getKind() == UNION_MAX || n[0].getKind() == UNION_DISJOINT) |
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&& (n[0][0] == n[1] || n[0][1] == n[1])) |
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{ |
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// (union_max (union_max A B) A)) = (union_max A B) |
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// (union_max (union_max B A) A)) = (union_max B A) |
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// (union_max (union_disjoint A B) A)) = (union_disjoint A B) |
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// (union_max (union_disjoint B A) A)) = (union_disjoint B A) |
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return BagsRewriteResponse(n[0], Rewrite::UNION_MAX_UNION_RIGHT); |
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} |
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return BagsRewriteResponse(n, Rewrite::NONE); |
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} |
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BagsRewriteResponse BagsRewriter::rewriteUnionDisjoint(const TNode& n) const |
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{ |
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Assert(n.getKind() == UNION_DISJOINT); |
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if (n[1].getKind() == EMPTYBAG) |
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{ |
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// (union_disjoint A emptybag) = A |
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return BagsRewriteResponse(n[0], Rewrite::UNION_DISJOINT_EMPTY_RIGHT); |
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} |
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if (n[0].getKind() == EMPTYBAG) |
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{ |
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// (union_disjoint emptybag A) = A |
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return BagsRewriteResponse(n[1], Rewrite::UNION_DISJOINT_EMPTY_LEFT); |
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} |
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if ((n[0].getKind() == UNION_MAX && n[1].getKind() == INTERSECTION_MIN) |
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|| (n[1].getKind() == UNION_MAX && n[0].getKind() == INTERSECTION_MIN)) |
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{ |
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// (union_disjoint (union_max A B) (intersection_min A B)) = |
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// (union_disjoint A B) // sum(a,b) = max(a,b) + min(a,b) |
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// check if the operands of union_max and intersection_min are the same |
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std::set<Node> left(n[0].begin(), n[0].end()); |
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std::set<Node> right(n[1].begin(), n[1].end()); |
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if (left == right) |
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{ |
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Node rewritten = d_nm->mkNode(UNION_DISJOINT, n[0][0], n[0][1]); |
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return BagsRewriteResponse(rewritten, Rewrite::UNION_DISJOINT_MAX_MIN); |
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} |
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} |
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return BagsRewriteResponse(n, Rewrite::NONE); |
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} |
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BagsRewriteResponse BagsRewriter::rewriteIntersectionMin(const TNode& n) const |
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{ |
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Assert(n.getKind() == INTERSECTION_MIN); |
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if (n[0].getKind() == EMPTYBAG) |
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{ |
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// (intersection_min emptybag A) = emptybag |
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return BagsRewriteResponse(n[0], Rewrite::INTERSECTION_EMPTY_LEFT); |
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} |
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if (n[1].getKind() == EMPTYBAG) |
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{ |
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// (intersection_min A emptybag) = emptybag |
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return BagsRewriteResponse(n[1], Rewrite::INTERSECTION_EMPTY_RIGHT); |
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} |
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if (n[0] == n[1]) |
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{ |
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// (intersection_min A A) = A |
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return BagsRewriteResponse(n[0], Rewrite::INTERSECTION_SAME); |
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} |
279 |
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if (n[1].getKind() == UNION_DISJOINT || n[1].getKind() == UNION_MAX) |
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{ |
281 |
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if (n[0] == n[1][0] || n[0] == n[1][1]) |
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{ |
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// (intersection_min A (union_disjoint A B)) = A |
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// (intersection_min A (union_disjoint B A)) = A |
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// (intersection_min A (union_max A B)) = A |
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// (intersection_min A (union_max B A)) = A |
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return BagsRewriteResponse(n[0], Rewrite::INTERSECTION_SHARED_LEFT); |
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} |
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} |
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291 |
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if (n[0].getKind() == UNION_DISJOINT || n[0].getKind() == UNION_MAX) |
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{ |
293 |
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if (n[1] == n[0][0] || n[1] == n[0][1]) |
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{ |
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// (intersection_min (union_disjoint A B) A) = A |
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// (intersection_min (union_disjoint B A) A) = A |
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// (intersection_min (union_max A B) A) = A |
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// (intersection_min (union_max B A) A) = A |
299 |
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return BagsRewriteResponse(n[1], Rewrite::INTERSECTION_SHARED_RIGHT); |
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} |
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} |
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303 |
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return BagsRewriteResponse(n, Rewrite::NONE); |
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} |
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306 |
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BagsRewriteResponse BagsRewriter::rewriteDifferenceSubtract( |
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const TNode& n) const |
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{ |
309 |
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Assert(n.getKind() == DIFFERENCE_SUBTRACT); |
310 |
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if (n[0].getKind() == EMPTYBAG || n[1].getKind() == EMPTYBAG) |
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{ |
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// (difference_subtract A emptybag) = A |
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// (difference_subtract emptybag A) = emptybag |
314 |
4 |
return BagsRewriteResponse(n[0], Rewrite::SUBTRACT_RETURN_LEFT); |
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} |
316 |
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if (n[0] == n[1]) |
317 |
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{ |
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// (difference_subtract A A) = emptybag |
319 |
4 |
Node emptyBag = d_nm->mkConst(EmptyBag(n.getType())); |
320 |
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return BagsRewriteResponse(emptyBag, Rewrite::SUBTRACT_SAME); |
321 |
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} |
322 |
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323 |
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if (n[0].getKind() == UNION_DISJOINT) |
324 |
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{ |
325 |
4 |
if (n[1] == n[0][0]) |
326 |
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{ |
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// (difference_subtract (union_disjoint A B) A) = B |
328 |
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return BagsRewriteResponse(n[0][1], |
329 |
2 |
Rewrite::SUBTRACT_DISJOINT_SHARED_LEFT); |
330 |
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} |
331 |
2 |
if (n[1] == n[0][1]) |
332 |
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{ |
333 |
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// (difference_subtract (union_disjoint B A) A) = B |
334 |
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return BagsRewriteResponse(n[0][0], |
335 |
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Rewrite::SUBTRACT_DISJOINT_SHARED_RIGHT); |
336 |
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} |
337 |
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} |
338 |
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|
339 |
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if (n[1].getKind() == UNION_DISJOINT || n[1].getKind() == UNION_MAX) |
340 |
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{ |
341 |
8 |
if (n[0] == n[1][0] || n[0] == n[1][1]) |
342 |
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{ |
343 |
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// (difference_subtract A (union_disjoint A B)) = emptybag |
344 |
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// (difference_subtract A (union_disjoint B A)) = emptybag |
345 |
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// (difference_subtract A (union_max A B)) = emptybag |
346 |
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// (difference_subtract A (union_max B A)) = emptybag |
347 |
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Node emptyBag = d_nm->mkConst(EmptyBag(n.getType())); |
348 |
8 |
return BagsRewriteResponse(emptyBag, Rewrite::SUBTRACT_FROM_UNION); |
349 |
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} |
350 |
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} |
351 |
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|
352 |
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if (n[0].getKind() == INTERSECTION_MIN) |
353 |
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{ |
354 |
4 |
if (n[1] == n[0][0] || n[1] == n[0][1]) |
355 |
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{ |
356 |
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// (difference_subtract (intersection_min A B) A) = emptybag |
357 |
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// (difference_subtract (intersection_min B A) A) = emptybag |
358 |
8 |
Node emptyBag = d_nm->mkConst(EmptyBag(n.getType())); |
359 |
4 |
return BagsRewriteResponse(emptyBag, Rewrite::SUBTRACT_MIN); |
360 |
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} |
361 |
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} |
362 |
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363 |
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return BagsRewriteResponse(n, Rewrite::NONE); |
364 |
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} |
365 |
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|
366 |
18 |
BagsRewriteResponse BagsRewriter::rewriteDifferenceRemove(const TNode& n) const |
367 |
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{ |
368 |
18 |
Assert(n.getKind() == DIFFERENCE_REMOVE); |
369 |
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|
370 |
18 |
if (n[0].getKind() == EMPTYBAG || n[1].getKind() == EMPTYBAG) |
371 |
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{ |
372 |
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// (difference_remove A emptybag) = A |
373 |
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// (difference_remove emptybag B) = emptybag |
374 |
4 |
return BagsRewriteResponse(n[0], Rewrite::REMOVE_RETURN_LEFT); |
375 |
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} |
376 |
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|
377 |
14 |
if (n[0] == n[1]) |
378 |
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{ |
379 |
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// (difference_remove A A) = emptybag |
380 |
4 |
Node emptyBag = d_nm->mkConst(EmptyBag(n.getType())); |
381 |
2 |
return BagsRewriteResponse(emptyBag, Rewrite::REMOVE_SAME); |
382 |
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} |
383 |
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|
384 |
12 |
if (n[1].getKind() == UNION_DISJOINT || n[1].getKind() == UNION_MAX) |
385 |
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{ |
386 |
8 |
if (n[0] == n[1][0] || n[0] == n[1][1]) |
387 |
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{ |
388 |
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// (difference_remove A (union_disjoint A B)) = emptybag |
389 |
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// (difference_remove A (union_disjoint B A)) = emptybag |
390 |
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// (difference_remove A (union_max A B)) = emptybag |
391 |
|
// (difference_remove A (union_max B A)) = emptybag |
392 |
16 |
Node emptyBag = d_nm->mkConst(EmptyBag(n.getType())); |
393 |
8 |
return BagsRewriteResponse(emptyBag, Rewrite::REMOVE_FROM_UNION); |
394 |
|
} |
395 |
|
} |
396 |
|
|
397 |
4 |
if (n[0].getKind() == INTERSECTION_MIN) |
398 |
|
{ |
399 |
4 |
if (n[1] == n[0][0] || n[1] == n[0][1]) |
400 |
|
{ |
401 |
|
// (difference_remove (intersection_min A B) A) = emptybag |
402 |
|
// (difference_remove (intersection_min B A) A) = emptybag |
403 |
8 |
Node emptyBag = d_nm->mkConst(EmptyBag(n.getType())); |
404 |
4 |
return BagsRewriteResponse(emptyBag, Rewrite::REMOVE_MIN); |
405 |
|
} |
406 |
|
} |
407 |
|
|
408 |
|
return BagsRewriteResponse(n, Rewrite::NONE); |
409 |
|
} |
410 |
|
|
411 |
2 |
BagsRewriteResponse BagsRewriter::rewriteChoose(const TNode& n) const |
412 |
|
{ |
413 |
2 |
Assert(n.getKind() == BAG_CHOOSE); |
414 |
2 |
if (n[0].getKind() == MK_BAG && n[0][1].isConst()) |
415 |
|
{ |
416 |
|
// (bag.choose (mkBag x c)) = x where c is a constant > 0 |
417 |
2 |
return BagsRewriteResponse(n[0][0], Rewrite::CHOOSE_MK_BAG); |
418 |
|
} |
419 |
|
return BagsRewriteResponse(n, Rewrite::NONE); |
420 |
|
} |
421 |
|
|
422 |
4 |
BagsRewriteResponse BagsRewriter::rewriteCard(const TNode& n) const |
423 |
|
{ |
424 |
4 |
Assert(n.getKind() == BAG_CARD); |
425 |
4 |
if (n[0].getKind() == MK_BAG && n[0][1].isConst()) |
426 |
|
{ |
427 |
|
// (bag.card (mkBag x c)) = c where c is a constant > 0 |
428 |
2 |
return BagsRewriteResponse(n[0][1], Rewrite::CARD_MK_BAG); |
429 |
|
} |
430 |
|
|
431 |
2 |
if (n[0].getKind() == UNION_DISJOINT) |
432 |
|
{ |
433 |
|
// (bag.card (union-disjoint A B)) = (+ (bag.card A) (bag.card B)) |
434 |
4 |
Node A = d_nm->mkNode(BAG_CARD, n[0][0]); |
435 |
4 |
Node B = d_nm->mkNode(BAG_CARD, n[0][1]); |
436 |
4 |
Node plus = d_nm->mkNode(PLUS, A, B); |
437 |
2 |
return BagsRewriteResponse(plus, Rewrite::CARD_DISJOINT); |
438 |
|
} |
439 |
|
|
440 |
|
return BagsRewriteResponse(n, Rewrite::NONE); |
441 |
|
} |
442 |
|
|
443 |
2 |
BagsRewriteResponse BagsRewriter::rewriteIsSingleton(const TNode& n) const |
444 |
|
{ |
445 |
2 |
Assert(n.getKind() == BAG_IS_SINGLETON); |
446 |
2 |
if (n[0].getKind() == MK_BAG) |
447 |
|
{ |
448 |
|
// (bag.is_singleton (mkBag x c)) = (c == 1) |
449 |
4 |
Node equal = n[0][1].eqNode(d_one); |
450 |
2 |
return BagsRewriteResponse(equal, Rewrite::IS_SINGLETON_MK_BAG); |
451 |
|
} |
452 |
|
return BagsRewriteResponse(n, Rewrite::NONE); |
453 |
|
} |
454 |
|
|
455 |
2 |
BagsRewriteResponse BagsRewriter::rewriteFromSet(const TNode& n) const |
456 |
|
{ |
457 |
2 |
Assert(n.getKind() == BAG_FROM_SET); |
458 |
2 |
if (n[0].getKind() == SINGLETON) |
459 |
|
{ |
460 |
|
// (bag.from_set (singleton (singleton_op Int) x)) = (mkBag x 1) |
461 |
4 |
TypeNode type = n[0].getType().getSetElementType(); |
462 |
4 |
Node bag = d_nm->mkBag(type, n[0][0], d_one); |
463 |
2 |
return BagsRewriteResponse(bag, Rewrite::FROM_SINGLETON); |
464 |
|
} |
465 |
|
return BagsRewriteResponse(n, Rewrite::NONE); |
466 |
|
} |
467 |
|
|
468 |
2 |
BagsRewriteResponse BagsRewriter::rewriteToSet(const TNode& n) const |
469 |
|
{ |
470 |
2 |
Assert(n.getKind() == BAG_TO_SET); |
471 |
8 |
if (n[0].getKind() == MK_BAG && n[0][1].isConst() |
472 |
8 |
&& n[0][1].getConst<Rational>().sgn() == 1) |
473 |
|
{ |
474 |
|
// (bag.to_set (mkBag x n)) = (singleton (singleton_op T) x) |
475 |
|
// where n is a positive constant and T is the type of the bag's elements |
476 |
4 |
Node set = d_nm->mkSingleton(n[0][0].getType(), n[0][0]); |
477 |
2 |
return BagsRewriteResponse(set, Rewrite::TO_SINGLETON); |
478 |
|
} |
479 |
|
return BagsRewriteResponse(n, Rewrite::NONE); |
480 |
|
} |
481 |
|
|
482 |
504 |
BagsRewriteResponse BagsRewriter::postRewriteEqual(const TNode& n) const |
483 |
|
{ |
484 |
504 |
Assert(n.getKind() == kind::EQUAL); |
485 |
504 |
if (n[0] == n[1]) |
486 |
|
{ |
487 |
|
Node ret = d_nm->mkConst(true); |
488 |
|
return BagsRewriteResponse(ret, Rewrite::EQ_REFL); |
489 |
|
} |
490 |
|
|
491 |
504 |
if (n[0].isConst() && n[1].isConst()) |
492 |
|
{ |
493 |
26 |
Node ret = d_nm->mkConst(false); |
494 |
13 |
return BagsRewriteResponse(ret, Rewrite::EQ_CONST_FALSE); |
495 |
|
} |
496 |
|
|
497 |
|
// standard ordering |
498 |
491 |
if (n[0] > n[1]) |
499 |
|
{ |
500 |
94 |
Node ret = d_nm->mkNode(kind::EQUAL, n[1], n[0]); |
501 |
47 |
return BagsRewriteResponse(ret, Rewrite::EQ_SYM); |
502 |
|
} |
503 |
444 |
return BagsRewriteResponse(n, Rewrite::NONE); |
504 |
|
} |
505 |
|
|
506 |
|
} // namespace bags |
507 |
|
} // namespace theory |
508 |
27735 |
} // namespace cvc5 |