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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 strings proof checker. |
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*/ |
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#include "theory/strings/proof_checker.h" |
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#include "expr/sequence.h" |
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#include "options/strings_options.h" |
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#include "theory/rewriter.h" |
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#include "theory/strings/core_solver.h" |
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#include "theory/strings/regexp_elim.h" |
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#include "theory/strings/regexp_operation.h" |
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#include "theory/strings/term_registry.h" |
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#include "theory/strings/theory_strings_preprocess.h" |
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#include "theory/strings/theory_strings_utils.h" |
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#include "theory/strings/word.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 strings { |
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|
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void StringProofRuleChecker::registerTo(ProofChecker* pc) |
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{ |
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pc->registerChecker(PfRule::CONCAT_EQ, this); |
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pc->registerChecker(PfRule::CONCAT_UNIFY, this); |
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pc->registerChecker(PfRule::CONCAT_CONFLICT, this); |
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pc->registerChecker(PfRule::CONCAT_SPLIT, this); |
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pc->registerChecker(PfRule::CONCAT_CSPLIT, this); |
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pc->registerChecker(PfRule::CONCAT_LPROP, this); |
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pc->registerChecker(PfRule::CONCAT_CPROP, this); |
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pc->registerChecker(PfRule::STRING_DECOMPOSE, this); |
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pc->registerChecker(PfRule::STRING_LENGTH_POS, this); |
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pc->registerChecker(PfRule::STRING_LENGTH_NON_EMPTY, this); |
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pc->registerChecker(PfRule::STRING_REDUCTION, this); |
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pc->registerChecker(PfRule::STRING_EAGER_REDUCTION, this); |
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pc->registerChecker(PfRule::RE_INTER, this); |
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pc->registerChecker(PfRule::RE_UNFOLD_POS, this); |
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pc->registerChecker(PfRule::RE_UNFOLD_NEG, this); |
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pc->registerChecker(PfRule::RE_UNFOLD_NEG_CONCAT_FIXED, this); |
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pc->registerChecker(PfRule::RE_ELIM, this); |
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pc->registerChecker(PfRule::STRING_CODE_INJ, this); |
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pc->registerChecker(PfRule::STRING_SEQ_UNIT_INJ, this); |
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// trusted rule |
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pc->registerTrustedChecker(PfRule::STRING_INFERENCE, this, 2); |
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} |
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Node StringProofRuleChecker::checkInternal(PfRule id, |
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const std::vector<Node>& children, |
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const std::vector<Node>& args) |
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{ |
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NodeManager* nm = NodeManager::currentNM(); |
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// core rules for word equations |
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if (id == PfRule::CONCAT_EQ || id == PfRule::CONCAT_UNIFY |
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|| id == PfRule::CONCAT_CONFLICT || id == PfRule::CONCAT_SPLIT |
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|| id == PfRule::CONCAT_CSPLIT || id == PfRule::CONCAT_LPROP |
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|| id == PfRule::CONCAT_CPROP) |
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{ |
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Trace("strings-pfcheck") << "Checking id " << id << std::endl; |
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Assert(children.size() >= 1); |
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Assert(args.size() == 1); |
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// all rules have an equality |
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if (children[0].getKind() != EQUAL) |
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{ |
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return Node::null(); |
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} |
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// convert to concatenation form |
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std::vector<Node> tvec; |
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std::vector<Node> svec; |
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utils::getConcat(children[0][0], tvec); |
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utils::getConcat(children[0][1], svec); |
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size_t nchildt = tvec.size(); |
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size_t nchilds = svec.size(); |
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TypeNode stringType = children[0][0].getType(); |
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// extract the Boolean corresponding to whether the rule is reversed |
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bool isRev; |
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if (!getBool(args[0], isRev)) |
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{ |
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return Node::null(); |
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} |
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if (id == PfRule::CONCAT_EQ) |
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{ |
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Assert(children.size() == 1); |
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size_t index = 0; |
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std::vector<Node> tremVec; |
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std::vector<Node> sremVec; |
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// scan the concatenation until we exhaust child proofs |
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while (index < nchilds && index < nchildt) |
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{ |
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Node currT = tvec[isRev ? (nchildt - 1 - index) : index]; |
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Node currS = svec[isRev ? (nchilds - 1 - index) : index]; |
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if (currT != currS) |
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{ |
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if (currT.isConst() && currS.isConst()) |
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{ |
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size_t sindex; |
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// get the equal prefix/suffix, strip and add the remainders |
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Node currR = Word::splitConstant(currT, currS, sindex, isRev); |
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if (!currR.isNull()) |
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{ |
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// add the constant to remainder vec |
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std::vector<Node>& rem = sindex == 0 ? tremVec : sremVec; |
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rem.push_back(currR); |
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// ignore the current component |
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index++; |
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// In other words, if we have (currS,currT) = ("ab","abc"), then |
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// we proceed to the next component and add currR = "c" to |
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// tremVec. |
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} |
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// otherwise if we are not the same prefix, then both will be added |
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// Notice that we do not add maximal prefixes, in other words, |
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// ("abc", "abd") may be added to the remainder vectors, and not |
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// ("c", "d"). |
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} |
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break; |
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} |
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index++; |
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} |
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Assert(index <= nchildt); |
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Assert(index <= nchilds); |
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// the remainders are equal |
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tremVec.insert(isRev ? tremVec.begin() : tremVec.end(), |
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tvec.begin() + (isRev ? 0 : index), |
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tvec.begin() + nchildt - (isRev ? index : 0)); |
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sremVec.insert(isRev ? sremVec.begin() : sremVec.end(), |
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svec.begin() + (isRev ? 0 : index), |
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svec.begin() + nchilds - (isRev ? index : 0)); |
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// convert back to node |
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Node trem = utils::mkConcat(tremVec, stringType); |
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Node srem = utils::mkConcat(sremVec, stringType); |
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return trem.eqNode(srem); |
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} |
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// all remaining rules do something with the first child of each side |
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Node t0 = tvec[isRev ? nchildt - 1 : 0]; |
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Node s0 = svec[isRev ? nchilds - 1 : 0]; |
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if (id == PfRule::CONCAT_UNIFY) |
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{ |
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Assert(children.size() == 2); |
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if (children[1].getKind() != EQUAL) |
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{ |
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return Node::null(); |
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} |
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for (size_t i = 0; i < 2; i++) |
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{ |
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Node l = children[1][i]; |
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if (l.getKind() != STRING_LENGTH) |
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{ |
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return Node::null(); |
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} |
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Node term = i == 0 ? t0 : s0; |
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if (l[0] == term) |
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{ |
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continue; |
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} |
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// could be a spliced constant |
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bool success = false; |
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if (term.isConst() && l[0].isConst()) |
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{ |
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size_t lenL = Word::getLength(l[0]); |
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success = (isRev && l[0] == Word::suffix(term, lenL)) |
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|| (!isRev && l[0] == Word::prefix(term, lenL)); |
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} |
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if (!success) |
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{ |
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return Node::null(); |
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} |
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} |
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return children[1][0][0].eqNode(children[1][1][0]); |
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} |
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else if (id == PfRule::CONCAT_CONFLICT) |
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{ |
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Assert(children.size() == 1); |
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if (!t0.isConst() || !s0.isConst()) |
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{ |
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// not constants |
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return Node::null(); |
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} |
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size_t sindex; |
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Node r0 = Word::splitConstant(t0, s0, sindex, isRev); |
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if (!r0.isNull()) |
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{ |
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// Not a conflict due to constants, i.e. s0 is a prefix of t0 or vice |
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// versa. |
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return Node::null(); |
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} |
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return nm->mkConst(false); |
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} |
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else if (id == PfRule::CONCAT_SPLIT) |
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{ |
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Assert(children.size() == 2); |
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if (children[1].getKind() != NOT || children[1][0].getKind() != EQUAL |
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|| children[1][0][0].getKind() != STRING_LENGTH |
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|| children[1][0][0][0] != t0 |
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|| children[1][0][1].getKind() != STRING_LENGTH |
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|| children[1][0][1][0] != s0) |
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{ |
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return Node::null(); |
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} |
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} |
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else if (id == PfRule::CONCAT_CSPLIT) |
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{ |
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Assert(children.size() == 2); |
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Node zero = nm->mkConst(Rational(0)); |
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Node one = nm->mkConst(Rational(1)); |
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if (children[1].getKind() != NOT || children[1][0].getKind() != EQUAL |
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|| children[1][0][0].getKind() != STRING_LENGTH |
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|| children[1][0][0][0] != t0 || children[1][0][1] != zero) |
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{ |
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return Node::null(); |
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} |
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if (!s0.isConst() || !s0.getType().isStringLike() || Word::isEmpty(s0)) |
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{ |
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return Node::null(); |
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} |
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} |
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else if (id == PfRule::CONCAT_LPROP) |
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{ |
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Assert(children.size() == 2); |
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if (children[1].getKind() != GT |
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|| children[1][0].getKind() != STRING_LENGTH |
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|| children[1][0][0] != t0 |
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|| children[1][1].getKind() != STRING_LENGTH |
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|| children[1][1][0] != s0) |
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{ |
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return Node::null(); |
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} |
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} |
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else if (id == PfRule::CONCAT_CPROP) |
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{ |
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Assert(children.size() == 2); |
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Node zero = nm->mkConst(Rational(0)); |
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Trace("pfcheck-strings-cprop") |
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<< "CONCAT_PROP, isRev=" << isRev << std::endl; |
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if (children[1].getKind() != NOT || children[1][0].getKind() != EQUAL |
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|| children[1][0][0].getKind() != STRING_LENGTH |
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|| children[1][0][0][0] != t0 || children[1][0][1] != zero) |
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{ |
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Trace("pfcheck-strings-cprop") |
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<< "...failed pattern match" << std::endl; |
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return Node::null(); |
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} |
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if (tvec.size() <= 1) |
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{ |
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Trace("pfcheck-strings-cprop") |
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<< "...failed adjacent constant" << std::endl; |
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return Node::null(); |
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} |
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Node w1 = tvec[isRev ? nchildt - 2 : 1]; |
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if (!w1.isConst() || !w1.getType().isStringLike() || Word::isEmpty(w1)) |
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{ |
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Trace("pfcheck-strings-cprop") |
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<< "...failed adjacent constant content" << std::endl; |
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return Node::null(); |
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} |
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Node w2 = s0; |
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if (!w2.isConst() || !w2.getType().isStringLike() || Word::isEmpty(w2)) |
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{ |
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Trace("pfcheck-strings-cprop") << "...failed constant" << std::endl; |
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return Node::null(); |
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} |
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// getConclusion expects the adjacent constant to be included |
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t0 = nm->mkNode(STRING_CONCAT, isRev ? w1 : t0, isRev ? t0 : w1); |
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} |
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// use skolem cache |
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SkolemCache skc(false); |
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std::vector<Node> newSkolems; |
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Node conc = CoreSolver::getConclusion(t0, s0, id, isRev, &skc, newSkolems); |
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return conc; |
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} |
283 |
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else if (id == PfRule::STRING_DECOMPOSE) |
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{ |
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Assert(children.size() == 1); |
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Assert(args.size() == 1); |
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bool isRev; |
288 |
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if (!getBool(args[0], isRev)) |
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{ |
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return Node::null(); |
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} |
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Node atom = children[0]; |
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if (atom.getKind() != GEQ || atom[0].getKind() != STRING_LENGTH) |
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{ |
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return Node::null(); |
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} |
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SkolemCache sc(false); |
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std::vector<Node> newSkolems; |
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Node conc = CoreSolver::getConclusion( |
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atom[0][0], atom[1], id, isRev, &sc, newSkolems); |
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return conc; |
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} |
303 |
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else if (id == PfRule::STRING_REDUCTION |
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|| id == PfRule::STRING_EAGER_REDUCTION |
305 |
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|| id == PfRule::STRING_LENGTH_POS) |
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{ |
307 |
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Assert(children.empty()); |
308 |
4 |
Assert(args.size() >= 1); |
309 |
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// These rules are based on calling a C++ method for returning a valid |
310 |
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// lemma involving a single argument term. |
311 |
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// Must convert to skolem form. |
312 |
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Node t = args[0]; |
313 |
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Node ret; |
314 |
4 |
if (id == PfRule::STRING_REDUCTION) |
315 |
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{ |
316 |
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Assert(args.size() == 1); |
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// we do not use optimizations |
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SkolemCache skc(false); |
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std::vector<Node> conj; |
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ret = StringsPreprocess::reduce(t, conj, &skc); |
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conj.push_back(t.eqNode(ret)); |
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ret = nm->mkAnd(conj); |
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} |
324 |
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else if (id == PfRule::STRING_EAGER_REDUCTION) |
325 |
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{ |
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Assert(args.size() == 1); |
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SkolemCache skc(false); |
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ret = TermRegistry::eagerReduce(t, &skc); |
329 |
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} |
330 |
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else if (id == PfRule::STRING_LENGTH_POS) |
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{ |
332 |
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Assert(args.size() == 1); |
333 |
4 |
ret = TermRegistry::lengthPositive(t); |
334 |
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} |
335 |
4 |
if (ret.isNull()) |
336 |
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{ |
337 |
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return Node::null(); |
338 |
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} |
339 |
4 |
return ret; |
340 |
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} |
341 |
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else if (id == PfRule::STRING_LENGTH_NON_EMPTY) |
342 |
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{ |
343 |
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Assert(children.size() == 1); |
344 |
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Assert(args.empty()); |
345 |
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Node nemp = children[0]; |
346 |
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if (nemp.getKind() != NOT || nemp[0].getKind() != EQUAL |
347 |
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|| !nemp[0][1].isConst() || !nemp[0][1].getType().isStringLike()) |
348 |
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{ |
349 |
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return Node::null(); |
350 |
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} |
351 |
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if (!Word::isEmpty(nemp[0][1])) |
352 |
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{ |
353 |
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return Node::null(); |
354 |
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} |
355 |
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Node zero = nm->mkConst(Rational(0)); |
356 |
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Node clen = nm->mkNode(STRING_LENGTH, nemp[0][0]); |
357 |
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return clen.eqNode(zero).notNode(); |
358 |
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} |
359 |
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else if (id == PfRule::RE_INTER) |
360 |
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{ |
361 |
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Assert(children.size() >= 1); |
362 |
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Assert(args.empty()); |
363 |
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std::vector<Node> reis; |
364 |
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Node x; |
365 |
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// make the regular expression intersection that summarizes all |
366 |
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// memberships in the explanation |
367 |
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for (const Node& c : children) |
368 |
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{ |
369 |
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bool polarity = c.getKind() != NOT; |
370 |
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Node catom = polarity ? c : c[0]; |
371 |
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if (catom.getKind() != STRING_IN_REGEXP) |
372 |
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{ |
373 |
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return Node::null(); |
374 |
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} |
375 |
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if (x.isNull()) |
376 |
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{ |
377 |
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x = catom[0]; |
378 |
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} |
379 |
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else if (x != catom[0]) |
380 |
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{ |
381 |
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// different LHS |
382 |
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return Node::null(); |
383 |
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} |
384 |
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Node xcurr = catom[0]; |
385 |
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Node rcurr = |
386 |
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polarity ? catom[1] : nm->mkNode(REGEXP_COMPLEMENT, catom[1]); |
387 |
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reis.push_back(rcurr); |
388 |
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} |
389 |
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Node rei = reis.size() == 1 ? reis[0] : nm->mkNode(REGEXP_INTER, reis); |
390 |
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return nm->mkNode(STRING_IN_REGEXP, x, rei); |
391 |
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} |
392 |
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else if (id == PfRule::RE_UNFOLD_POS || id == PfRule::RE_UNFOLD_NEG |
393 |
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|| id == PfRule::RE_UNFOLD_NEG_CONCAT_FIXED) |
394 |
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{ |
395 |
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Assert(children.size() == 1); |
396 |
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Assert(args.empty()); |
397 |
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Node skChild = children[0]; |
398 |
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if (id == PfRule::RE_UNFOLD_NEG || id == PfRule::RE_UNFOLD_NEG_CONCAT_FIXED) |
399 |
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{ |
400 |
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if (skChild.getKind() != NOT || skChild[0].getKind() != STRING_IN_REGEXP) |
401 |
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{ |
402 |
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Trace("strings-pfcheck") << "...fail, non-neg member" << std::endl; |
403 |
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return Node::null(); |
404 |
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} |
405 |
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} |
406 |
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else if (skChild.getKind() != STRING_IN_REGEXP) |
407 |
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{ |
408 |
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Trace("strings-pfcheck") << "...fail, non-pos member" << std::endl; |
409 |
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return Node::null(); |
410 |
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} |
411 |
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Node conc; |
412 |
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if (id == PfRule::RE_UNFOLD_POS) |
413 |
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{ |
414 |
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std::vector<Node> newSkolems; |
415 |
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SkolemCache sc; |
416 |
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conc = RegExpOpr::reduceRegExpPos(skChild, &sc, newSkolems); |
417 |
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} |
418 |
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else if (id == PfRule::RE_UNFOLD_NEG) |
419 |
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{ |
420 |
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conc = RegExpOpr::reduceRegExpNeg(skChild); |
421 |
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} |
422 |
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else if (id == PfRule::RE_UNFOLD_NEG_CONCAT_FIXED) |
423 |
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{ |
424 |
|
if (skChild[0][1].getKind() != REGEXP_CONCAT) |
425 |
|
{ |
426 |
|
Trace("strings-pfcheck") << "...fail, no concat regexp" << std::endl; |
427 |
|
return Node::null(); |
428 |
|
} |
429 |
|
size_t index; |
430 |
|
Node reLen = RegExpOpr::getRegExpConcatFixed(skChild[0][1], index); |
431 |
|
if (reLen.isNull()) |
432 |
|
{ |
433 |
|
Trace("strings-pfcheck") << "...fail, non-fixed lengths" << std::endl; |
434 |
|
return Node::null(); |
435 |
|
} |
436 |
|
conc = RegExpOpr::reduceRegExpNegConcatFixed(skChild, reLen, index); |
437 |
|
} |
438 |
|
return conc; |
439 |
|
} |
440 |
|
else if (id == PfRule::RE_ELIM) |
441 |
|
{ |
442 |
|
Assert(children.empty()); |
443 |
|
Assert(args.size() == 2); |
444 |
|
bool isAgg; |
445 |
|
if (!getBool(args[1], isAgg)) |
446 |
|
{ |
447 |
|
return Node::null(); |
448 |
|
} |
449 |
|
Node ea = RegExpElimination::eliminate(args[0], isAgg); |
450 |
|
// if we didn't eliminate, then this trivially proves the reflexive equality |
451 |
|
if (ea.isNull()) |
452 |
|
{ |
453 |
|
ea = args[0]; |
454 |
|
} |
455 |
|
return args[0].eqNode(ea); |
456 |
|
} |
457 |
|
else if (id == PfRule::STRING_CODE_INJ) |
458 |
|
{ |
459 |
|
Assert(children.empty()); |
460 |
|
Assert(args.size() == 2); |
461 |
|
Assert(args[0].getType().isStringLike() |
462 |
|
&& args[1].getType().isStringLike()); |
463 |
|
Node c1 = nm->mkNode(STRING_TO_CODE, args[0]); |
464 |
|
Node c2 = nm->mkNode(STRING_TO_CODE, args[1]); |
465 |
|
Node eqNegOne = c1.eqNode(nm->mkConst(Rational(-1))); |
466 |
|
Node deq = c1.eqNode(c2).negate(); |
467 |
|
Node eqn = args[0].eqNode(args[1]); |
468 |
|
return nm->mkNode(kind::OR, eqNegOne, deq, eqn); |
469 |
|
} |
470 |
|
else if (id == PfRule::STRING_SEQ_UNIT_INJ) |
471 |
|
{ |
472 |
|
Assert(children.size() == 1); |
473 |
|
Assert(args.empty()); |
474 |
|
if (children[0].getKind() != EQUAL) |
475 |
|
{ |
476 |
|
return Node::null(); |
477 |
|
} |
478 |
|
Node t[2]; |
479 |
|
for (size_t i = 0; i < 2; i++) |
480 |
|
{ |
481 |
|
if (children[0][i].getKind() == SEQ_UNIT) |
482 |
|
{ |
483 |
|
t[i] = children[0][i][0]; |
484 |
|
} |
485 |
|
else if (children[0][i].isConst()) |
486 |
|
{ |
487 |
|
// notice that Word::getChars is not the right call here, since it |
488 |
|
// gets a vector of sequences of length one. We actually need to |
489 |
|
// extract the character, which is a sequence-specific operation. |
490 |
|
const Sequence& sx = children[0][i].getConst<Sequence>(); |
491 |
|
const std::vector<Node>& vec = sx.getVec(); |
492 |
|
if (vec.size() == 1) |
493 |
|
{ |
494 |
|
// the character of the single character sequence |
495 |
|
t[i] = vec[0]; |
496 |
|
} |
497 |
|
} |
498 |
|
if (t[i].isNull()) |
499 |
|
{ |
500 |
|
return Node::null(); |
501 |
|
} |
502 |
|
} |
503 |
|
Trace("strings-pfcheck-debug") |
504 |
|
<< "STRING_SEQ_UNIT_INJ: " << children[0] << " => " << t[0] |
505 |
|
<< " == " << t[1] << std::endl; |
506 |
|
AlwaysAssert(t[0].getType() == t[1].getType()); |
507 |
|
return t[0].eqNode(t[1]); |
508 |
|
} |
509 |
|
else if (id == PfRule::STRING_INFERENCE) |
510 |
|
{ |
511 |
|
Assert(args.size() >= 3); |
512 |
|
return args[0]; |
513 |
|
} |
514 |
|
return Node::null(); |
515 |
|
} |
516 |
|
|
517 |
|
} // namespace strings |
518 |
|
} // namespace theory |
519 |
22746 |
} // namespace cvc5 |