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Diffstat (limited to 'src/proof/arith_proof.cpp')
| -rw-r--r-- | src/proof/arith_proof.cpp | 833 |
1 files changed, 833 insertions, 0 deletions
diff --git a/src/proof/arith_proof.cpp b/src/proof/arith_proof.cpp new file mode 100644 index 000000000..a1287b667 --- /dev/null +++ b/src/proof/arith_proof.cpp @@ -0,0 +1,833 @@ +/********************* */ +/*! \file arith_proof.cpp + ** \verbatim + ** Top contributors (to current version): + ** Guy Katz + ** This file is part of the CVC4 project. + ** Copyright (c) 2009-2016 by the authors listed in the file AUTHORS + ** in the top-level source directory) and their institutional affiliations. + ** All rights reserved. See the file COPYING in the top-level source + ** directory for licensing information.\endverbatim + ** + ** [[ Add lengthier description here ]] + + ** \todo document this file + +**/ + +#include "proof/theory_proof.h" +#include "proof/proof_manager.h" +#include "proof/arith_proof.h" +#include "theory/arith/theory_arith.h" +#include <stack> + +namespace CVC4 { + +inline static Node eqNode(TNode n1, TNode n2) { + return NodeManager::currentNM()->mkNode(n1.getType().isBoolean() ? kind::IFF : kind::EQUAL, n1, n2); +} + +// congrence matching term helper +inline static bool match(TNode n1, TNode n2) { + Debug("pf::arith") << "match " << n1 << " " << n2 << std::endl; + if(ProofManager::currentPM()->hasOp(n1)) { + n1 = ProofManager::currentPM()->lookupOp(n1); + } + if(ProofManager::currentPM()->hasOp(n2)) { + n2 = ProofManager::currentPM()->lookupOp(n2); + } + Debug("pf::arith") << "+ match " << n1 << " " << n2 << std::endl; + if(n1 == n2) { + return true; + } + if(n1.getType().isFunction() && n2.hasOperator()) { + if(ProofManager::currentPM()->hasOp(n2.getOperator())) { + return n1 == ProofManager::currentPM()->lookupOp(n2.getOperator()); + } else { + return n1 == n2.getOperator(); + } + } + if(n2.getType().isFunction() && n1.hasOperator()) { + if(ProofManager::currentPM()->hasOp(n1.getOperator())) { + return n2 == ProofManager::currentPM()->lookupOp(n1.getOperator()); + } else { + return n2 == n1.getOperator(); + } + } + if(n1.hasOperator() && n2.hasOperator() && n1.getOperator() != n2.getOperator()) { + return false; + } + for(size_t i = 0; i < n1.getNumChildren() && i < n2.getNumChildren(); ++i) { + if(n1[i] != n2[i]) { + return false; + } + } + return true; +} + + +void ProofArith::toStream(std::ostream& out) { + Trace("theory-proof-debug") << "; Print Arith proof..." << std::endl; + //AJR : carry this further? + LetMap map; + toStreamLFSC(out, ProofManager::getArithProof(), d_proof, map); +} + +void ProofArith::toStreamLFSC(std::ostream& out, TheoryProof * tp, theory::eq::EqProof * pf, const LetMap& map) { + Debug("lfsc-arith") << "Printing arith proof in LFSC : " << std::endl; + pf->debug_print("lfsc-arith"); + Debug("lfsc-arith") << std::endl; + toStreamRecLFSC( out, tp, pf, 0, map ); +} + +Node ProofArith::toStreamRecLFSC(std::ostream& out, TheoryProof * tp, theory::eq::EqProof * pf, unsigned tb, const LetMap& map) { + Debug("pf::arith") << std::endl << std::endl << "toStreamRecLFSC called. tb = " << tb << " . proof:" << std::endl; + pf->debug_print("pf::arith"); + Debug("pf::arith") << std::endl; + + if(tb == 0) { + Assert(pf->d_id == theory::eq::MERGED_THROUGH_TRANS); + Assert(!pf->d_node.isNull()); + Assert(pf->d_children.size() >= 2); + + int neg = -1; + theory::eq::EqProof subTrans; + subTrans.d_id = theory::eq::MERGED_THROUGH_TRANS; + subTrans.d_node = pf->d_node; + + size_t i = 0; + while (i < pf->d_children.size()) { + // Look for the negative clause, with which we will form a contradiction. + if(!pf->d_children[i]->d_node.isNull() && pf->d_children[i]->d_node.getKind() == kind::NOT) { + Assert(neg < 0); + neg = i; + ++i; + } + + // Handle congruence closures over equalities. + else if (pf->d_children[i]->d_id==theory::eq::MERGED_THROUGH_CONGRUENCE && pf->d_children[i]->d_node.isNull()) { + Debug("pf::arith") << "Handling congruence over equalities" << std::endl; + + // Gather the sequence of consecutive congruence closures. + std::vector<const theory::eq::EqProof *> congruenceClosures; + unsigned count; + Debug("pf::arith") << "Collecting congruence sequence" << std::endl; + for (count = 0; + i + count < pf->d_children.size() && + pf->d_children[i + count]->d_id==theory::eq::MERGED_THROUGH_CONGRUENCE && + pf->d_children[i + count]->d_node.isNull(); + ++count) { + Debug("pf::arith") << "Found a congruence: " << std::endl; + pf->d_children[i+count]->debug_print("pf::arith"); + congruenceClosures.push_back(pf->d_children[i+count]); + } + + Debug("pf::arith") << "Total number of congruences found: " << congruenceClosures.size() << std::endl; + + // Determine if the "target" of the congruence sequence appears right before or right after the sequence. + bool targetAppearsBefore = true; + bool targetAppearsAfter = true; + + if ((i == 0) || (i == 1 && neg == 0)) { + Debug("pf::arith") << "Target does not appear before" << std::endl; + targetAppearsBefore = false; + } + + if ((i + count >= pf->d_children.size()) || + (!pf->d_children[i + count]->d_node.isNull() && + pf->d_children[i + count]->d_node.getKind() == kind::NOT)) { + Debug("pf::arith") << "Target does not appear after" << std::endl; + targetAppearsAfter = false; + } + + // Assert that we have precisely one target clause. + Assert(targetAppearsBefore != targetAppearsAfter); + + // Begin breaking up the congruences and ordering the equalities correctly. + std::vector<theory::eq::EqProof *> orderedEqualities; + + + // Insert target clause first. + if (targetAppearsBefore) { + orderedEqualities.push_back(pf->d_children[i - 1]); + // The target has already been added to subTrans; remove it. + subTrans.d_children.pop_back(); + } else { + orderedEqualities.push_back(pf->d_children[i + count]); + } + + // Start with the congruence closure closest to the target clause, and work our way back/forward. + if (targetAppearsBefore) { + for (unsigned j = 0; j < count; ++j) { + if (pf->d_children[i + j]->d_children[0]->d_id != theory::eq::MERGED_THROUGH_REFLEXIVITY) + orderedEqualities.insert(orderedEqualities.begin(), pf->d_children[i + j]->d_children[0]); + if (pf->d_children[i + j]->d_children[1]->d_id != theory::eq::MERGED_THROUGH_REFLEXIVITY) + orderedEqualities.insert(orderedEqualities.end(), pf->d_children[i + j]->d_children[1]); + } + } else { + for (unsigned j = 0; j < count; ++j) { + if (pf->d_children[i + count - 1 - j]->d_children[0]->d_id != theory::eq::MERGED_THROUGH_REFLEXIVITY) + orderedEqualities.insert(orderedEqualities.begin(), pf->d_children[i + count - 1 - j]->d_children[0]); + if (pf->d_children[i + count - 1 - j]->d_children[1]->d_id != theory::eq::MERGED_THROUGH_REFLEXIVITY) + orderedEqualities.insert(orderedEqualities.end(), pf->d_children[i + count - 1 - j]->d_children[1]); + } + } + + // Copy the result into the main transitivity proof. + subTrans.d_children.insert(subTrans.d_children.end(), orderedEqualities.begin(), orderedEqualities.end()); + + // Increase i to skip over the children that have been processed. + i += count; + if (targetAppearsAfter) { + ++i; + } + } + + // Else, just copy the child proof as is + else { + subTrans.d_children.push_back(pf->d_children[i]); + ++i; + } + } + Assert(neg >= 0); + + Node n1; + std::stringstream ss; + //Assert(subTrans.d_children.size() == pf->d_children.size() - 1); + Debug("pf::arith") << "\nsubtrans has " << subTrans.d_children.size() << " children\n"; + if(pf->d_children.size() > 2) { + n1 = toStreamRecLFSC(ss, tp, &subTrans, 1, map); + } else { + n1 = toStreamRecLFSC(ss, tp, subTrans.d_children[0], 1, map); + Debug("pf::arith") << "\nsubTrans unique child " << subTrans.d_children[0]->d_id << " was proven\ngot: " << n1 << std::endl; + } + + Node n2 = pf->d_children[neg]->d_node; + Assert(n2.getKind() == kind::NOT); + out << "(clausify_false (contra _ "; + Debug("pf::arith") << "\nhave proven: " << n1 << std::endl; + Debug("pf::arith") << "n2 is " << n2[0] << std::endl; + + if (n2[0].getNumChildren() > 0) { Debug("pf::arith") << "\nn2[0]: " << n2[0][0] << std::endl; } + if (n1.getNumChildren() > 1) { Debug("pf::arith") << "n1[1]: " << n1[1] << std::endl; } + + if(n2[0].getKind() == kind::APPLY_UF) { + out << "(trans _ _ _ _ "; + out << "(symm _ _ _ "; + out << ss.str(); + out << ") (pred_eq_f _ " << ProofManager::getLitName(n2[0]) << ")) t_t_neq_f))" << std::endl; + } else { + Assert((n1[0] == n2[0][0] && n1[1] == n2[0][1]) || (n1[1] == n2[0][0] && n1[0] == n2[0][1])); + if(n1[1] == n2[0][0]) { + out << "(symm _ _ _ " << ss.str() << ")"; + } else { + out << ss.str(); + } + out << " " << ProofManager::getLitName(n2[0]) << "))" << std::endl; + } + return Node(); + } + + switch(pf->d_id) { + case theory::eq::MERGED_THROUGH_CONGRUENCE: { + Debug("pf::arith") << "\nok, looking at congruence:\n"; + pf->debug_print("pf::arith"); + std::stack<const theory::eq::EqProof*> stk; + for(const theory::eq::EqProof* pf2 = pf; pf2->d_id == theory::eq::MERGED_THROUGH_CONGRUENCE; pf2 = pf2->d_children[0]) { + Assert(!pf2->d_node.isNull()); + Assert(pf2->d_node.getKind() == kind::PARTIAL_APPLY_UF || pf2->d_node.getKind() == kind::BUILTIN || pf2->d_node.getKind() == kind::APPLY_UF || pf2->d_node.getKind() == kind::SELECT || pf2->d_node.getKind() == kind::STORE); + Assert(pf2->d_children.size() == 2); + out << "(cong _ _ _ _ _ _ "; + stk.push(pf2); + } + Assert(stk.top()->d_children[0]->d_id != theory::eq::MERGED_THROUGH_CONGRUENCE); + NodeBuilder<> b1(kind::PARTIAL_APPLY_UF), b2(kind::PARTIAL_APPLY_UF); + const theory::eq::EqProof* pf2 = stk.top(); + stk.pop(); + Assert(pf2->d_id == theory::eq::MERGED_THROUGH_CONGRUENCE); + Node n1 = toStreamRecLFSC(out, tp, pf2->d_children[0], tb + 1, map); + out << " "; + std::stringstream ss; + Node n2 = toStreamRecLFSC(ss, tp, pf2->d_children[1], tb + 1, map); + Debug("pf::arith") << "\nok, in FIRST cong[" << stk.size() << "]" << "\n"; + pf2->debug_print("pf::arith"); + Debug("pf::arith") << "looking at " << pf2->d_node << "\n"; + Debug("pf::arith") << " " << n1 << "\n"; + Debug("pf::arith") << " " << n2 << "\n"; + int side = 0; + if(match(pf2->d_node, n1[0])) { + //if(tb == 1) { + Debug("pf::arith") << "SIDE IS 0\n"; + //} + side = 0; + } else { + //if(tb == 1) { + Debug("pf::arith") << "SIDE IS 1\n"; + //} + if(!match(pf2->d_node, n1[1])) { + Debug("pf::arith") << "IN BAD CASE, our first subproof is\n"; + pf2->d_children[0]->debug_print("pf::arith"); + } + Assert(match(pf2->d_node, n1[1])); + side = 1; + } + if(n1[side].getKind() == kind::APPLY_UF || n1[side].getKind() == kind::PARTIAL_APPLY_UF || n1[side].getKind() == kind::SELECT || n1[side].getKind() == kind::STORE) { + if(n1[side].getKind() == kind::APPLY_UF || n1[side].getKind() == kind::PARTIAL_APPLY_UF) { + b1 << n1[side].getOperator(); + } else { + b1 << ProofManager::currentPM()->mkOp(n1[side].getOperator()); + } + b1.append(n1[side].begin(), n1[side].end()); + } else { + b1 << n1[side]; + } + if(n1[1-side].getKind() == kind::PARTIAL_APPLY_UF || n1[1-side].getKind() == kind::APPLY_UF || n1[side].getKind() == kind::SELECT || n1[side].getKind() == kind::STORE) { + if(n1[1-side].getKind() == kind::PARTIAL_APPLY_UF || n1[1-side].getKind() == kind::APPLY_UF) { + b2 << n1[1-side].getOperator(); + } else { + b2 << ProofManager::currentPM()->mkOp(n1[1-side].getOperator()); + } + b2.append(n1[1-side].begin(), n1[1-side].end()); + } else { + b2 << n1[1-side]; + } + Debug("pf::arith") << "pf2->d_node " << pf2->d_node << std::endl; + Debug("pf::arith") << "b1.getNumChildren() " << b1.getNumChildren() << std::endl; + Debug("pf::arith") << "n1 " << n1 << std::endl; + Debug("pf::arith") << "n2 " << n2 << std::endl; + Debug("pf::arith") << "side " << side << std::endl; + if(pf2->d_node[b1.getNumChildren() - (pf2->d_node.getMetaKind() == kind::metakind::PARAMETERIZED ? 0 : 1)] == n2[side]) { + b1 << n2[side]; + b2 << n2[1-side]; + out << ss.str(); + } else { + Assert(pf2->d_node[b1.getNumChildren() - (pf2->d_node.getMetaKind() == kind::metakind::PARAMETERIZED ? 0 : 1)] == n2[1-side]); + b1 << n2[1-side]; + b2 << n2[side]; + out << "(symm _ _ _ " << ss.str() << ")"; + } + out << ")"; + while(!stk.empty()) { + if(tb == 1) { + Debug("pf::arith") << "\nMORE TO DO\n"; + } + pf2 = stk.top(); + stk.pop(); + Assert(pf2->d_id == theory::eq::MERGED_THROUGH_CONGRUENCE); + out << " "; + ss.str(""); + n2 = toStreamRecLFSC(ss, tp, pf2->d_children[1], tb + 1, map); + Debug("pf::arith") << "\nok, in cong[" << stk.size() << "]" << "\n"; + Debug("pf::arith") << "looking at " << pf2->d_node << "\n"; + Debug("pf::arith") << " " << n1 << "\n"; + Debug("pf::arith") << " " << n2 << "\n"; + Debug("pf::arith") << " " << b1 << "\n"; + Debug("pf::arith") << " " << b2 << "\n"; + if(pf2->d_node[b1.getNumChildren()] == n2[side]) { + b1 << n2[side]; + b2 << n2[1-side]; + out << ss.str(); + } else { + Assert(pf2->d_node[b1.getNumChildren()] == n2[1-side]); + b1 << n2[1-side]; + b2 << n2[side]; + out << "(symm _ _ _ " << ss.str() << ")"; + } + out << ")"; + } + n1 = b1; + n2 = b2; + Debug("pf::arith") << "at end assert, got " << pf2->d_node << " and " << n1 << std::endl; + if(pf2->d_node.getKind() == kind::PARTIAL_APPLY_UF) { + Assert(n1 == pf2->d_node); + } + if(n1.getOperator().getType().getNumChildren() == n1.getNumChildren() + 1) { + if(ProofManager::currentPM()->hasOp(n1.getOperator())) { + b1.clear(ProofManager::currentPM()->lookupOp(n2.getOperator()).getConst<Kind>()); + } else { + b1.clear(kind::APPLY_UF); + b1 << n1.getOperator(); + } + b1.append(n1.begin(), n1.end()); + n1 = b1; + Debug("pf::arith") << "at[2] end assert, got " << pf2->d_node << " and " << n1 << std::endl; + if(pf2->d_node.getKind() == kind::APPLY_UF) { + Assert(n1 == pf2->d_node); + } + } + if(n2.getOperator().getType().getNumChildren() == n2.getNumChildren() + 1) { + if(ProofManager::currentPM()->hasOp(n2.getOperator())) { + b2.clear(ProofManager::currentPM()->lookupOp(n2.getOperator()).getConst<Kind>()); + } else { + b2.clear(kind::APPLY_UF); + b2 << n2.getOperator(); + } + b2.append(n2.begin(), n2.end()); + n2 = b2; + } + Node n = (side == 0 ? eqNode(n1, n2) : eqNode(n2, n1)); + if(tb == 1) { + Debug("pf::arith") << "\ncong proved: " << n << "\n"; + } + return n; + } + + case theory::eq::MERGED_THROUGH_REFLEXIVITY: + Assert(!pf->d_node.isNull()); + Assert(pf->d_children.empty()); + out << "(refl _ "; + tp->printTerm(NodeManager::currentNM()->toExpr(pf->d_node), out, map); + out << ")"; + return eqNode(pf->d_node, pf->d_node); + + case theory::eq::MERGED_THROUGH_EQUALITY: + Assert(!pf->d_node.isNull()); + Assert(pf->d_children.empty()); + out << ProofManager::getLitName(pf->d_node.negate()); + return pf->d_node; + + case theory::eq::MERGED_THROUGH_TRANS: { + Assert(!pf->d_node.isNull()); + Assert(pf->d_children.size() >= 2); + std::stringstream ss; + Debug("pf::arith") << "\ndoing trans proof[[\n"; + pf->debug_print("pf::arith"); + Debug("pf::arith") << "\n"; + Node n1 = toStreamRecLFSC(ss, tp, pf->d_children[0], tb + 1, map); + Debug("pf::arith") << "\ndoing trans proof, got n1 " << n1 << "\n"; + if(tb == 1) { + Debug("pf::arith") << "\ntrans proof[0], got n1 " << n1 << "\n"; + } + + bool identicalEqualities = false; + bool evenLengthSequence; + Node nodeAfterEqualitySequence; + + std::map<size_t, Node> childToStream; + + for(size_t i = 1; i < pf->d_children.size(); ++i) { + std::stringstream ss1(ss.str()), ss2; + ss.str(""); + + // It is possible that we've already converted the i'th child to stream. If so, + // use previously stored result. Otherwise, convert and store. + Node n2; + if (childToStream.find(i) != childToStream.end()) + n2 = childToStream[i]; + else { + n2 = toStreamRecLFSC(ss2, tp, pf->d_children[i], tb + 1, map); + childToStream[i] = n2; + } + + // The following branch is dedicated to handling sequences of identical equalities, + // i.e. trans[ a=b, a=b, a=b ]. + // + // There are two cases: + // 1. The number of equalities is odd. Then, the sequence can be collapsed to just one equality, + // i.e. a=b. + // 2. The number of equalities is even. Now, we have two options: a=a or b=b. To determine this, + // we look at the node after the equality sequence. If it needs a, we go for a=a; and if it needs + // b, we go for b=b. If there is no following node, we look at the goal of the transitivity proof, + // and use it to determine which option we need. + if(n2.getKind() == kind::EQUAL || n2.getKind() == kind::IFF) { + if (((n1[0] == n2[0]) && (n1[1] == n2[1])) || ((n1[0] == n2[1]) && (n1[1] == n2[0]))) { + // We are in a sequence of identical equalities + + Debug("pf::arith") << "Detected identical equalities: " << std::endl << "\t" << n1 << std::endl; + + if (!identicalEqualities) { + // The sequence of identical equalities has started just now + identicalEqualities = true; + + Debug("pf::arith") << "The sequence is just beginning. Determining length..." << std::endl; + + // Determine whether the length of this sequence is odd or even. + evenLengthSequence = true; + bool sequenceOver = false; + size_t j = i + 1; + + while (j < pf->d_children.size() && !sequenceOver) { + std::stringstream dontCare; + nodeAfterEqualitySequence = toStreamRecLFSC(dontCare, tp, pf->d_children[j], tb + 1, map ); + + if (((nodeAfterEqualitySequence[0] == n1[0]) && (nodeAfterEqualitySequence[1] == n1[1])) || + ((nodeAfterEqualitySequence[0] == n1[1]) && (nodeAfterEqualitySequence[1] == n1[0]))) { + evenLengthSequence = !evenLengthSequence; + } else { + sequenceOver = true; + } + + ++j; + } + + if (evenLengthSequence) { + // If the length is even, we need to apply transitivity for the "correct" hand of the equality. + + Debug("pf::arith") << "Equality sequence of even length" << std::endl; + Debug("pf::arith") << "n1 is: " << n1 << std::endl; + Debug("pf::arith") << "n2 is: " << n2 << std::endl; + Debug("pf::arith") << "pf-d_node is: " << pf->d_node << std::endl; + Debug("pf::arith") << "Next node is: " << nodeAfterEqualitySequence << std::endl; + + ss << "(trans _ _ _ _ "; + + // If the sequence is at the very end of the transitivity proof, use pf->d_node to guide us. + if (!sequenceOver) { + if (match(n1[0], pf->d_node[0])) { + n1 = eqNode(n1[0], n1[0]); + ss << ss1.str() << " (symm _ _ _ " << ss1.str() << ")"; + } else if (match(n1[1], pf->d_node[1])) { + n1 = eqNode(n1[1], n1[1]); + ss << " (symm _ _ _ " << ss1.str() << ")" << ss1.str(); + } else { + Debug("pf::arith") << "Error: identical equalities over, but hands don't match what we're proving." + << std::endl; + Assert(false); + } + } else { + // We have a "next node". Use it to guide us. + + Assert(nodeAfterEqualitySequence.getKind() == kind::EQUAL || + nodeAfterEqualitySequence.getKind() == kind::IFF); + + if ((n1[0] == nodeAfterEqualitySequence[0]) || (n1[0] == nodeAfterEqualitySequence[1])) { + + // Eliminate n1[1] + ss << ss1.str() << " (symm _ _ _ " << ss1.str() << ")"; + n1 = eqNode(n1[0], n1[0]); + + } else if ((n1[1] == nodeAfterEqualitySequence[0]) || (n1[1] == nodeAfterEqualitySequence[1])) { + + // Eliminate n1[0] + ss << " (symm _ _ _ " << ss1.str() << ")" << ss1.str(); + n1 = eqNode(n1[1], n1[1]); + + } else { + Debug("pf::arith") << "Error: even length sequence, but I don't know which hand to keep!" << std::endl; + Assert(false); + } + } + + ss << ")"; + + } else { + Debug("pf::arith") << "Equality sequence length is odd!" << std::endl; + ss.str(ss1.str()); + } + + Debug("pf::arith") << "Have proven: " << n1 << std::endl; + } else { + ss.str(ss1.str()); + } + + // Ignore the redundancy. + continue; + } + } + + if (identicalEqualities) { + // We were in a sequence of identical equalities, but it has now ended. Resume normal operation. + identicalEqualities = false; + } + + Debug("pf::arith") << "\ndoing trans proof, got n2 " << n2 << "\n"; + if(tb == 1) { + Debug("pf::arith") << "\ntrans proof[" << i << "], got n2 " << n2 << "\n"; + Debug("pf::arith") << (n2.getKind() == kind::EQUAL || n2.getKind() == kind::IFF) << "\n"; + + if ((n1.getNumChildren() >= 2) && (n2.getNumChildren() >= 2)) { + Debug("pf::arith") << n1[0].getId() << " " << n1[1].getId() << " / " << n2[0].getId() << " " << n2[1].getId() << "\n"; + Debug("pf::arith") << n1[0].getId() << " " << n1[0] << "\n"; + Debug("pf::arith") << n1[1].getId() << " " << n1[1] << "\n"; + Debug("pf::arith") << n2[0].getId() << " " << n2[0] << "\n"; + Debug("pf::arith") << n2[1].getId() << " " << n2[1] << "\n"; + Debug("pf::arith") << (n1[0] == n2[0]) << "\n"; + Debug("pf::arith") << (n1[1] == n2[1]) << "\n"; + Debug("pf::arith") << (n1[0] == n2[1]) << "\n"; + Debug("pf::arith") << (n1[1] == n2[0]) << "\n"; + } + } + ss << "(trans _ _ _ _ "; + + if((n2.getKind() == kind::EQUAL || n2.getKind() == kind::IFF) && + (n1.getKind() == kind::EQUAL || n1.getKind() == kind::IFF)) + // Both elements of the transitivity rule are equalities/iffs + { + if(n1[0] == n2[0]) { + if(tb == 1) { Debug("pf::arith") << "case 1\n"; } + n1 = eqNode(n1[1], n2[1]); + ss << "(symm _ _ _ " << ss1.str() << ") " << ss2.str(); + } else if(n1[1] == n2[1]) { + if(tb == 1) { Debug("pf::arith") << "case 2\n"; } + n1 = eqNode(n1[0], n2[0]); + ss << ss1.str() << " (symm _ _ _ " << ss2.str() << ")"; + } else if(n1[0] == n2[1]) { + if(tb == 1) { Debug("pf::arith") << "case 3\n"; } + n1 = eqNode(n2[0], n1[1]); + ss << ss2.str() << " " << ss1.str(); + if(tb == 1) { Debug("pf::arith") << "++ proved " << n1 << "\n"; } + } else if(n1[1] == n2[0]) { + if(tb == 1) { Debug("pf::arith") << "case 4\n"; } + n1 = eqNode(n1[0], n2[1]); + ss << ss1.str() << " " << ss2.str(); + } else { + Warning() << "\n\ntrans proof failure at step " << i << "\n\n"; + Warning() << "0 proves " << n1 << "\n"; + Warning() << "1 proves " << n2 << "\n\n"; + pf->debug_print("pf::arith",0); + //toStreamRec(Warning.getStream(), pf, 0); + Warning() << "\n\n"; + Unreachable(); + } + Debug("pf::arith") << "++ trans proof[" << i << "], now have " << n1 << std::endl; + } else if(n1.getKind() == kind::EQUAL || n1.getKind() == kind::IFF) { + // n1 is an equality/iff, but n2 is a predicate + if(n1[0] == n2) { + n1 = n1[1]; + ss << "(symm _ _ _ " << ss1.str() << ") (pred_eq_t _ " << ss2.str() << ")"; + } else if(n1[1] == n2) { + n1 = n1[0]; + ss << ss1.str() << " (pred_eq_t _ " << ss2.str() << ")"; + } else { + Unreachable(); + } + } else if(n2.getKind() == kind::EQUAL || n2.getKind() == kind::IFF) { + // n2 is an equality/iff, but n1 is a predicate + if(n2[0] == n1) { + n1 = n2[1]; + ss << "(symm _ _ _ " << ss2.str() << ") (pred_eq_t _ " << ss1.str() << ")"; + } else if(n2[1] == n1) { + n1 = n2[0]; + ss << ss2.str() << " (pred_eq_t _ " << ss1.str() << ")"; + } else { + Unreachable(); + } + } else { + // Both n1 and n2 are prediacates. Don't know what to do... + Unreachable(); + } + + ss << ")"; + } + out << ss.str(); + Debug("pf::arith") << "\n++ trans proof done, have proven " << n1 << std::endl; + return n1; + } + + default: + Assert(!pf->d_node.isNull()); + Assert(pf->d_children.empty()); + Debug("pf::arith") << "theory proof: " << pf->d_node << " by rule " << int(pf->d_id) << std::endl; + AlwaysAssert(false); + return pf->d_node; + } +} + +ArithProof::ArithProof(theory::arith::TheoryArith* arith, TheoryProofEngine* pe) + : TheoryProof(arith, pe), d_realMode(false) +{} + +void ArithProof::registerTerm(Expr term) { + Debug("pf::arith") << "Arith register term: " << term << ". Kind: " << term.getKind() + << ". Type: " << term.getType() << std::endl; + + if (term.getType().isReal() && !term.getType().isInteger()) { + Debug("pf::arith") << "Entering real mode" << std::endl; + d_realMode = true; + } + + // recursively declare all other terms + for (unsigned i = 0; i < term.getNumChildren(); ++i) { + // could belong to other theories + d_proofEngine->registerTerm(term[i]); + } +} + +void LFSCArithProof::printOwnedTerm(Expr term, std::ostream& os, const LetMap& map) { + Debug("pf::arith") << "Arith print term: " << term << ". Kind: " << term.getKind() + << ". Type: " << term.getType() + << ". Number of children: " << term.getNumChildren() << std::endl; + + // !d_realMode <--> term.getType().isInteger() + + Assert (theory::Theory::theoryOf(term) == theory::THEORY_ARITH); + switch (term.getKind()) { + + case kind::CONST_RATIONAL: { + Assert (term.getNumChildren() == 0); + Assert (term.getType().isInteger() || term.getType().isReal()); + + const Rational& r = term.getConst<Rational>(); + bool neg = (r < 0); + + os << (!d_realMode ? "(a_int " : "(a_real "); + + if (neg) { + os << "(~ "; + } + + if (!d_realMode) { + os << r.abs(); + } else { + os << r.abs().getNumerator(); + os << "/"; + os << r.getDenominator(); + } + + if (neg) { + os << ") "; + } + + os << ") "; + return; + } + + case kind::UMINUS: { + Assert (term.getNumChildren() == 1); + Assert (term.getType().isInteger() || term.getType().isReal()); + os << (!d_realMode ? "(u-_Int " : "(u-_Real "); + d_proofEngine->printBoundTerm(term[0], os, map); + os << ") "; + return; + } + + case kind::PLUS: { + Assert (term.getNumChildren() >= 2); + + std::stringstream paren; + for (unsigned i = 0; i < term.getNumChildren() - 1; ++i) { + os << (!d_realMode ? "(+_Int " : "(+_Real "); + d_proofEngine->printBoundTerm(term[i], os, map); + os << " "; + paren << ") "; + } + + d_proofEngine->printBoundTerm(term[term.getNumChildren() - 1], os, map); + os << paren.str(); + return; + } + + case kind::MINUS: { + Assert (term.getNumChildren() >= 2); + + std::stringstream paren; + for (unsigned i = 0; i < term.getNumChildren() - 1; ++i) { + os << (!d_realMode ? "(-_Int " : "(-_Real "); + d_proofEngine->printBoundTerm(term[i], os, map); + os << " "; + paren << ") "; + } + + d_proofEngine->printBoundTerm(term[term.getNumChildren() - 1], os, map); + os << paren.str(); + return; + } + + case kind::MULT: { + Assert (term.getNumChildren() >= 2); + + std::stringstream paren; + for (unsigned i = 0; i < term.getNumChildren() - 1; ++i) { + os << (!d_realMode ? "(*_Int " : "(*_Real "); + d_proofEngine->printBoundTerm(term[i], os, map); + os << " "; + paren << ") "; + } + + d_proofEngine->printBoundTerm(term[term.getNumChildren() - 1], os, map); + os << paren.str(); + return; + } + + case kind::DIVISION: + case kind::DIVISION_TOTAL: { + Assert (term.getNumChildren() >= 2); + + std::stringstream paren; + for (unsigned i = 0; i < term.getNumChildren() - 1; ++i) { + os << (!d_realMode ? "(/_Int " : "(/_Real "); + d_proofEngine->printBoundTerm(term[i], os, map); + os << " "; + paren << ") "; + } + + d_proofEngine->printBoundTerm(term[term.getNumChildren() - 1], os, map); + os << paren.str(); + return; + } + + case kind::GT: + Assert (term.getNumChildren() == 2); + os << (!d_realMode ? "(>_Int " : "(>_Real "); + d_proofEngine->printBoundTerm(term[0], os, map); + os << " "; + d_proofEngine->printBoundTerm(term[1], os, map); + os << ") "; + return; + + case kind::GEQ: + Assert (term.getNumChildren() == 2); + os << (!d_realMode ? "(>=_Int " : "(>=_Real "); + d_proofEngine->printBoundTerm(term[0], os, map); + os << " "; + d_proofEngine->printBoundTerm(term[1], os, map); + os << ") "; + return; + + case kind::LT: + Assert (term.getNumChildren() == 2); + os << (!d_realMode ? "(<_Int " : "(<_Real "); + d_proofEngine->printBoundTerm(term[0], os, map); + os << " "; + d_proofEngine->printBoundTerm(term[1], os, map); + os << ") "; + return; + + case kind::LEQ: + Assert (term.getNumChildren() == 2); + os << (!d_realMode ? "(<=_Int " : "(<=_Real "); + d_proofEngine->printBoundTerm(term[0], os, map); + os << " "; + d_proofEngine->printBoundTerm(term[1], os, map); + os << ") "; + return; + + default: + Debug("pf::arith") << "Default printing of term: " << term << std::endl; + os << term; + return; + } +} + +void LFSCArithProof::printOwnedSort(Type type, std::ostream& os) { + Debug("pf::arith") << "Arith print sort: " << type << std::endl; + + if (type.isInteger() && d_realMode) { + // If in "real mode", don't use type Int for, e.g., equality. + os << "Real "; + } else { + os << type << " "; + } +} + +void LFSCArithProof::printTheoryLemmaProof(std::vector<Expr>& lemma, std::ostream& os, std::ostream& paren) { + os << " ;; Arith Theory Lemma \n;;"; + for (unsigned i = 0; i < lemma.size(); ++i) { + os << lemma[i] <<" "; + } + os <<"\n"; + //os << " (clausify_false trust)"; + ArithProof::printTheoryLemmaProof( lemma, os, paren ); +} + +void LFSCArithProof::printSortDeclarations(std::ostream& os, std::ostream& paren) { +} + +void LFSCArithProof::printTermDeclarations(std::ostream& os, std::ostream& paren) { +} + +void LFSCArithProof::printDeferredDeclarations(std::ostream& os, std::ostream& paren) { + // Nothing to do here at this point. +} + +} /* CVC4 namespace */ |