/* This file is part of solidity. solidity is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. solidity is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with solidity. If not, see . */ // SPDX-License-Identifier: GPL-3.0 #include #include #include #include using namespace solidity; using namespace solidity::smtutil; Z3CHCInterface::Z3CHCInterface(std::optional _queryTimeout): CHCSolverInterface(_queryTimeout), m_z3Interface(std::make_unique(m_queryTimeout)), m_context(m_z3Interface->context()), m_solver(*m_context) { Z3_get_version( &std::get<0>(m_version), &std::get<1>(m_version), &std::get<2>(m_version), &std::get<3>(m_version) ); // These need to be set globally. z3::set_param("rewriter.pull_cheap_ite", true); if (m_queryTimeout) m_context->set("timeout", int(*m_queryTimeout)); else z3::set_param("rlimit", Z3Interface::resourceLimit); setSpacerOptions(); } void Z3CHCInterface::declareVariable(std::string const& _name, SortPointer const& _sort) { smtAssert(_sort, ""); m_z3Interface->declareVariable(_name, _sort); } void Z3CHCInterface::registerRelation(Expression const& _expr) { m_solver.register_relation(m_z3Interface->functions().at(_expr.name)); } void Z3CHCInterface::addRule(Expression const& _expr, std::string const& _name) { z3::expr rule = m_z3Interface->toZ3Expr(_expr); if (m_z3Interface->constants().empty()) m_solver.add_rule(rule, m_context->str_symbol(_name.c_str())); else { z3::expr_vector variables(*m_context); for (auto const& var: m_z3Interface->constants()) variables.push_back(var.second); z3::expr boundRule = z3::forall(variables, rule); m_solver.add_rule(boundRule, m_context->str_symbol(_name.c_str())); } } std::tuple Z3CHCInterface::query(Expression const& _expr) { CheckResult result; try { z3::expr z3Expr = m_z3Interface->toZ3Expr(_expr); switch (m_solver.query(z3Expr)) { case z3::check_result::sat: { result = CheckResult::SATISFIABLE; // z3 version 4.8.8 modified Spacer to also return // proofs containing nonlinear clauses. if (m_version >= std::tuple(4, 8, 8, 0)) { auto proof = m_solver.get_answer(); return {result, Expression(true), cexGraph(proof)}; } break; } case z3::check_result::unsat: { result = CheckResult::UNSATISFIABLE; auto invariants = m_z3Interface->fromZ3Expr(m_solver.get_answer()); return {result, std::move(invariants), {}}; } case z3::check_result::unknown: { result = CheckResult::UNKNOWN; break; } } // TODO retrieve model / invariants } catch (z3::exception const& _err) { std::set msgs{ /// Resource limit (rlimit) exhausted. "max. resource limit exceeded", /// User given timeout exhausted. "canceled" }; if (msgs.count(_err.msg())) result = CheckResult::UNKNOWN; else result = CheckResult::ERROR; } return {result, Expression(true), {}}; } void Z3CHCInterface::setSpacerOptions(bool _preProcessing) { // Spacer options. // These needs to be set in the solver. // https://github.com/Z3Prover/z3/blob/master/src/muz/base/fp_params.pyg z3::params p(*m_context); // These are useful for solving problems with arrays and loops. // Use quantified lemma generalizer. p.set("fp.spacer.q3.use_qgen", true); p.set("fp.spacer.mbqi", false); // Ground pobs by using values from a model. p.set("fp.spacer.ground_pobs", false); // Spacer optimization should be // - enabled for better solving (default) // - disable for counterexample generation p.set("fp.xform.slice", _preProcessing); p.set("fp.xform.inline_linear", _preProcessing); p.set("fp.xform.inline_eager", _preProcessing); m_solver.set(p); } /** Convert a ground refutation into a linear or nonlinear counterexample. The counterexample is given as an implication graph of the form `premises => conclusion` where `premises` are the predicates from the body of nonlinear clauses, representing the proof graph. This function is based on and similar to https://github.com/Z3Prover/z3/blob/z3-4.8.8/src/muz/spacer/spacer_context.cpp#L2919 (spacer::context::get_ground_sat_answer) which generates linear counterexamples. It is modified here to accept nonlinear CHCs as well, generating a DAG instead of a path. */ CHCSolverInterface::CexGraph Z3CHCInterface::cexGraph(z3::expr const& _proof) { /// The root fact of the refutation proof is `false`. /// The node itself is not a hyper resolution, so we need to /// extract the `query` hyper resolution node from the /// `false` node (the first child). /// The proof has the shape above for z3 >=4.8.8. /// If an older version is used, this check will fail and no /// counterexample will be generated. if (!_proof.is_app() || fact(_proof).decl().decl_kind() != Z3_OP_FALSE) return {}; CexGraph graph; std::stack proofStack; proofStack.push(_proof.arg(0)); auto const& root = proofStack.top(); graph.nodes.emplace(root.id(), m_z3Interface->fromZ3Expr(fact(root))); std::set visited; visited.insert(root.id()); while (!proofStack.empty()) { z3::expr proofNode = proofStack.top(); smtAssert(graph.nodes.count(proofNode.id()), ""); proofStack.pop(); if (proofNode.is_app() && proofNode.decl().decl_kind() == Z3_OP_PR_HYPER_RESOLVE) { smtAssert(proofNode.num_args() > 0, ""); for (unsigned i = 1; i < proofNode.num_args() - 1; ++i) { z3::expr child = proofNode.arg(i); if (!visited.count(child.id())) { visited.insert(child.id()); proofStack.push(child); } if (!graph.nodes.count(child.id())) { graph.nodes.emplace(child.id(), m_z3Interface->fromZ3Expr(fact(child))); graph.edges[child.id()] = {}; } graph.edges[proofNode.id()].push_back(child.id()); } } } return graph; } z3::expr Z3CHCInterface::fact(z3::expr const& _node) { smtAssert(_node.is_app(), ""); if (_node.num_args() == 0) return _node; return _node.arg(_node.num_args() - 1); } std::string Z3CHCInterface::name(z3::expr const& _predicate) { smtAssert(_predicate.is_app(), ""); return _predicate.decl().name().str(); } std::vector Z3CHCInterface::arguments(z3::expr const& _predicate) { smtAssert(_predicate.is_app(), ""); std::vector args; for (unsigned i = 0; i < _predicate.num_args(); ++i) args.emplace_back(_predicate.arg(i).to_string()); return args; }