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/****************************************************************************** |
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* Top contributors (to current version): |
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* Andrew Reynolds, 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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* Implementation of quantifiers proof checker. |
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*/ |
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#include "theory/quantifiers/proof_checker.h" |
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#include "expr/node_algorithm.h" |
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#include "expr/skolem_manager.h" |
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#include "theory/builtin/proof_checker.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 quantifiers { |
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|
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void QuantifiersProofRuleChecker::registerTo(ProofChecker* pc) |
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{ |
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// add checkers |
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pc->registerChecker(PfRule::SKOLEM_INTRO, this); |
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pc->registerChecker(PfRule::EXISTS_INTRO, this); |
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pc->registerChecker(PfRule::SKOLEMIZE, this); |
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pc->registerChecker(PfRule::INSTANTIATE, this); |
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pc->registerChecker(PfRule::ALPHA_EQUIV, this); |
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// trusted rules |
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pc->registerTrustedChecker(PfRule::QUANTIFIERS_PREPROCESS, this, 3); |
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} |
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Node QuantifiersProofRuleChecker::checkInternal( |
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PfRule id, const std::vector<Node>& children, const std::vector<Node>& args) |
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{ |
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NodeManager* nm = NodeManager::currentNM(); |
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SkolemManager* sm = nm->getSkolemManager(); |
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// compute what was proven |
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if (id == PfRule::EXISTS_INTRO) |
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{ |
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Assert(children.size() == 1); |
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Assert(args.size() == 1); |
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Node p = children[0]; |
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Node exists = args[0]; |
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if (exists.getKind() != kind::EXISTS || exists[0].getNumChildren() != 1) |
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{ |
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return Node::null(); |
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} |
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std::unordered_map<Node, Node> subs; |
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if (!expr::match(exists[1], p, subs)) |
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{ |
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return Node::null(); |
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} |
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// substitution must contain only the variable of the existential |
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for (const std::pair<const Node, Node>& s : subs) |
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{ |
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if (s.first != exists[0][0]) |
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{ |
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return Node::null(); |
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} |
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} |
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return exists; |
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} |
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else if (id == PfRule::SKOLEM_INTRO) |
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{ |
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Assert(children.empty()); |
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Assert(args.size() == 1); |
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Node t = SkolemManager::getOriginalForm(args[0]); |
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return args[0].eqNode(t); |
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} |
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else if (id == PfRule::SKOLEMIZE) |
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{ |
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Assert(children.size() == 1); |
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Assert(args.empty()); |
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// can use either negated FORALL or EXISTS |
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if (children[0].getKind() != EXISTS |
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&& (children[0].getKind() != NOT || children[0][0].getKind() != FORALL)) |
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{ |
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return Node::null(); |
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} |
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Node exists; |
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if (children[0].getKind() == EXISTS) |
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{ |
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exists = children[0]; |
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} |
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else |
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{ |
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std::vector<Node> echildren(children[0][0].begin(), children[0][0].end()); |
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echildren[1] = echildren[1].notNode(); |
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exists = nm->mkNode(EXISTS, echildren); |
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} |
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std::vector<Node> skolems; |
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Node res = sm->mkSkolemize(exists, skolems, "k"); |
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return res; |
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} |
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else if (id == PfRule::INSTANTIATE) |
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{ |
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Assert(children.size() == 1); |
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// note we may have more arguments than just the term vector |
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if (children[0].getKind() != FORALL |
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|| args.size() < children[0][0].getNumChildren()) |
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{ |
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return Node::null(); |
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} |
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Node body = children[0][1]; |
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std::vector<Node> vars; |
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std::vector<Node> subs; |
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for (size_t i = 0, nc = children[0][0].getNumChildren(); i < nc; i++) |
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{ |
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vars.push_back(children[0][0][i]); |
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subs.push_back(args[i]); |
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} |
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Node inst = |
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body.substitute(vars.begin(), vars.end(), subs.begin(), subs.end()); |
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return inst; |
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} |
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else if (id == PfRule::ALPHA_EQUIV) |
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{ |
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Assert(children.empty()); |
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if (args[0].getKind() != kind::FORALL) |
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{ |
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return Node::null(); |
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} |
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// arguments must be equalities that are bound variables that are |
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// pairwise unique |
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std::unordered_set<Node> allVars[2]; |
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std::vector<Node> vars; |
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std::vector<Node> newVars; |
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for (size_t i = 1, nargs = args.size(); i < nargs; i++) |
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{ |
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if (args[i].getKind() != kind::EQUAL) |
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{ |
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return Node::null(); |
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} |
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for (size_t j = 0; j < 2; j++) |
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{ |
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Node v = args[i][j]; |
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if (v.getKind() != kind::BOUND_VARIABLE |
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|| allVars[j].find(v) != allVars[j].end()) |
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{ |
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return Node::null(); |
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} |
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allVars[j].insert(v); |
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} |
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vars.push_back(args[i][0]); |
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newVars.push_back(args[i][1]); |
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} |
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Node renamedBody = args[0].substitute( |
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vars.begin(), vars.end(), newVars.begin(), newVars.end()); |
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return args[0].eqNode(renamedBody); |
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} |
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else if (id == PfRule::QUANTIFIERS_PREPROCESS) |
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{ |
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Assert(!args.empty()); |
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Assert(args[0].getType().isBoolean()); |
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return args[0]; |
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} |
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// no rule |
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return Node::null(); |
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} |
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} // namespace quantifiers |
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} // namespace theory |
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} // namespace cvc5 |