src/theory/bv/theory_bv.cpp

   1 /*********************                                                        */
   2 /*! \file theory_bv.cpp
   3  ** \verbatim
   4  ** Top contributors (to current version):
   5  **   Liana Hadarean, Andrew Reynolds, Aina Niemetz
   6  ** This file is part of the CVC4 project.
   7  ** Copyright (c) 2009-2018 by the authors listed in the file AUTHORS
   8  ** in the top-level source directory) and their institutional affiliations.
   9  ** All rights reserved.  See the file COPYING in the top-level source
  10  ** directory for licensing information.\endverbatim
  11  **
  12  ** [[ Add lengthier description here ]]
  13  ** \todo document this file
  14  **/
  15
  16 #include "theory/bv/theory_bv.h"
  17
  18 #include "options/bv_options.h"
  19 #include "options/smt_options.h"
  20 #include "proof/proof_manager.h"
  21 #include "proof/theory_proof.h"
  22 #include "smt/smt_statistics_registry.h"
  23 #include "theory/bv/abstraction.h"
  24 #include "theory/bv/bv_eager_solver.h"
  25 #include "theory/bv/bv_subtheory_algebraic.h"
  26 #include "theory/bv/bv_subtheory_bitblast.h"
  27 #include "theory/bv/bv_subtheory_core.h"
  28 #include "theory/bv/bv_subtheory_inequality.h"
  29 #include "theory/bv/slicer.h"
  30 #include "theory/bv/theory_bv_rewrite_rules_normalization.h"
  31 #include "theory/bv/theory_bv_rewrite_rules_simplification.h"
  32 #include "theory/bv/theory_bv_rewriter.h"
  33 #include "theory/bv/theory_bv_utils.h"
  34 #include "theory/ext_theory.h"
  35 #include "theory/theory_model.h"
  36 #include "theory/valuation.h"
  37
  38 using namespace CVC4::context;
  39 using namespace CVC4::theory::bv::utils;
  40 using namespace std;
  41
  42 namespace CVC4 {
  43 namespace theory {
  44 namespace bv {
  45
  46 TheoryBV::TheoryBV(context::Context* c, context::UserContext* u,
  47                    OutputChannel& out, Valuation valuation,
  48                    const LogicInfo& logicInfo, std::string name)
  49   : Theory(THEORY_BV, c, u, out, valuation, logicInfo, name),
  50     d_context(c),
  51     d_alreadyPropagatedSet(c),
  52     d_sharedTermsSet(c),
  53     d_subtheories(),
  54     d_subtheoryMap(),
  55     d_statistics(),
  56     d_staticLearnCache(),
  57     d_BVDivByZero(),
  58     d_BVRemByZero(),
  59     d_lemmasAdded(c, false),
  60     d_conflict(c, false),
  61     d_invalidateModelCache(c, true),
  62     d_literalsToPropagate(c),
  63     d_literalsToPropagateIndex(c, 0),
  64     d_propagatedBy(c),
  65     d_eagerSolver(NULL),
  66     d_abstractionModule(new AbstractionModule(getStatsPrefix(THEORY_BV))),
  67     d_isCoreTheory(false),
  68     d_calledPreregister(false),
  69     d_needsLastCallCheck(false),
  70     d_extf_range_infer(u),
  71     d_extf_collapse_infer(u)
  72 {
  73   setupExtTheory();
  74   getExtTheory()->addFunctionKind(kind::BITVECTOR_TO_NAT);
  75   getExtTheory()->addFunctionKind(kind::INT_TO_BITVECTOR);
  76   if (options::bitblastMode() == theory::bv::BITBLAST_MODE_EAGER) {
  77     d_eagerSolver = new EagerBitblastSolver(this);
  78     return;
  79   }
  80
  81   if (options::bitvectorEqualitySolver() && !options::proof())
  82   {
  83     SubtheorySolver* core_solver = new CoreSolver(c, this);
  84     d_subtheories.push_back(core_solver);
  85     d_subtheoryMap[SUB_CORE] = core_solver;
  86   }
  87
  88   if (options::bitvectorInequalitySolver() && !options::proof())
  89   {
  90     SubtheorySolver* ineq_solver = new InequalitySolver(c, u, this);
  91     d_subtheories.push_back(ineq_solver);
  92     d_subtheoryMap[SUB_INEQUALITY] = ineq_solver;
  93   }
  94
  95   if (options::bitvectorAlgebraicSolver() && !options::proof())
  96   {
  97     SubtheorySolver* alg_solver = new AlgebraicSolver(c, this);
  98     d_subtheories.push_back(alg_solver);
  99     d_subtheoryMap[SUB_ALGEBRAIC] = alg_solver;
 100   }
 101
 102   BitblastSolver* bb_solver = new BitblastSolver(c, this);
 103   if (options::bvAbstraction()) {
 104     bb_solver->setAbstraction(d_abstractionModule);
 105   }
 106   d_subtheories.push_back(bb_solver);
 107   d_subtheoryMap[SUB_BITBLAST] = bb_solver;
 108 }
 109
 110 TheoryBV::~TheoryBV() {
 111   if (d_eagerSolver) {
 112     delete d_eagerSolver;
 113   }
 114   for (unsigned i = 0; i < d_subtheories.size(); ++i) {
 115     delete d_subtheories[i];
 116   }
 117   delete d_abstractionModule;
 118 }
 119
 120 void TheoryBV::setMasterEqualityEngine(eq::EqualityEngine* eq) {
 121   if (options::bitblastMode() == theory::bv::BITBLAST_MODE_EAGER) {
 122     return;
 123   }
 124   if (options::bitvectorEqualitySolver()) {
 125     dynamic_cast<CoreSolver*>(d_subtheoryMap[SUB_CORE])->setMasterEqualityEngine(eq);
 126   }
 127 }
 128
 129 void TheoryBV::spendResource(unsigned amount)
 130 {
 131   getOutputChannel().spendResource(amount);
 132 }
 133
 134 TheoryBV::Statistics::Statistics():
 135   d_avgConflictSize("theory::bv::AvgBVConflictSize"),
 136   d_solveSubstitutions("theory::bv::NumSolveSubstitutions", 0),
 137   d_solveTimer("theory::bv::solveTimer"),
 138   d_numCallsToCheckFullEffort("theory::bv::NumFullCheckCalls", 0),
 139   d_numCallsToCheckStandardEffort("theory::bv::NumStandardCheckCalls", 0),
 140   d_weightComputationTimer("theory::bv::weightComputationTimer"),
 141   d_numMultSlice("theory::bv::NumMultSliceApplied", 0)
 142 {
 143   smtStatisticsRegistry()->registerStat(&d_avgConflictSize);
 144   smtStatisticsRegistry()->registerStat(&d_solveSubstitutions);
 145   smtStatisticsRegistry()->registerStat(&d_solveTimer);
 146   smtStatisticsRegistry()->registerStat(&d_numCallsToCheckFullEffort);
 147   smtStatisticsRegistry()->registerStat(&d_numCallsToCheckStandardEffort);
 148   smtStatisticsRegistry()->registerStat(&d_weightComputationTimer);
 149   smtStatisticsRegistry()->registerStat(&d_numMultSlice);
 150 }
 151
 152 TheoryBV::Statistics::~Statistics() {
 153   smtStatisticsRegistry()->unregisterStat(&d_avgConflictSize);
 154   smtStatisticsRegistry()->unregisterStat(&d_solveSubstitutions);
 155   smtStatisticsRegistry()->unregisterStat(&d_solveTimer);
 156   smtStatisticsRegistry()->unregisterStat(&d_numCallsToCheckFullEffort);
 157   smtStatisticsRegistry()->unregisterStat(&d_numCallsToCheckStandardEffort);
 158   smtStatisticsRegistry()->unregisterStat(&d_weightComputationTimer);
 159   smtStatisticsRegistry()->unregisterStat(&d_numMultSlice);
 160 }
 161
 162 Node TheoryBV::getBVDivByZero(Kind k, unsigned width) {
 163   NodeManager* nm = NodeManager::currentNM();
 164   if (k == kind::BITVECTOR_UDIV) {
 165     if (d_BVDivByZero.find(width) == d_BVDivByZero.end()) {
 166       // lazily create the function symbols
 167       ostringstream os;
 168       os << "BVUDivByZero_" << width;
 169       Node divByZero = nm->mkSkolem(os.str(),
 170                                     nm->mkFunctionType(nm->mkBitVectorType(width), nm->mkBitVectorType(width)),
 171                                     "partial bvudiv", NodeManager::SKOLEM_EXACT_NAME);
 172       d_BVDivByZero[width] = divByZero;
 173     }
 174     return d_BVDivByZero[width];
 175   }
 176   else if (k == kind::BITVECTOR_UREM) {
 177     if (d_BVRemByZero.find(width) == d_BVRemByZero.end()) {
 178       ostringstream os;
 179       os << "BVURemByZero_" << width;
 180       Node divByZero = nm->mkSkolem(os.str(),
 181                                     nm->mkFunctionType(nm->mkBitVectorType(width), nm->mkBitVectorType(width)),
 182                                     "partial bvurem", NodeManager::SKOLEM_EXACT_NAME);
 183       d_BVRemByZero[width] = divByZero;
 184     }
 185     return d_BVRemByZero[width];
 186   }
 187
 188   Unreachable();
 189 }
 190
 191 void TheoryBV::finishInit()
 192 {
 193   // these kinds are semi-evaluated in getModelValue (applications of this
 194   // kind are treated as variables)
 195   TheoryModel* tm = d_valuation.getModel();
 196   Assert(tm != nullptr);
 197   tm->setSemiEvaluatedKind(kind::BITVECTOR_ACKERMANNIZE_UDIV);
 198   tm->setSemiEvaluatedKind(kind::BITVECTOR_ACKERMANNIZE_UREM);
 199 }
 200
 201 Node TheoryBV::expandDefinition(LogicRequest &logicRequest, Node node) {
 202   Debug("bitvector-expandDefinition") << "TheoryBV::expandDefinition(" << node << ")" << std::endl;
 203
 204   switch (node.getKind()) {
 205   case kind::BITVECTOR_SDIV:
 206   case kind::BITVECTOR_SREM:
 207   case kind::BITVECTOR_SMOD:
 208     return TheoryBVRewriter::eliminateBVSDiv(node);
 209     break;
 210
 211   case kind::BITVECTOR_UDIV:
 212   case kind::BITVECTOR_UREM: {
 213     NodeManager* nm = NodeManager::currentNM();
 214     unsigned width = node.getType().getBitVectorSize();
 215
 216     if (options::bitvectorDivByZeroConst()) {
 217       Kind kind = node.getKind() == kind::BITVECTOR_UDIV ? kind::BITVECTOR_UDIV_TOTAL : kind::BITVECTOR_UREM_TOTAL;
 218       return nm->mkNode(kind, node[0], node[1]);
 219     }
 220
 221     TNode num = node[0], den = node[1];
 222     Node den_eq_0 = nm->mkNode(kind::EQUAL, den, utils::mkZero(width));
 223     Node divTotalNumDen = nm->mkNode(node.getKind() == kind::BITVECTOR_UDIV ? kind::BITVECTOR_UDIV_TOTAL :
 224                                      kind::BITVECTOR_UREM_TOTAL, num, den);
 225     Node divByZero = getBVDivByZero(node.getKind(), width);
 226     Node divByZeroNum = nm->mkNode(kind::APPLY_UF, divByZero, num);
 227     node = nm->mkNode(kind::ITE, den_eq_0, divByZeroNum, divTotalNumDen);
 228     logicRequest.widenLogic(THEORY_UF);
 229     return node;
 230   }
 231     break;
 232
 233   default:
 234     return node;
 235     break;
 236   }
 237
 238   Unreachable();
 239 }
 240
 241
 242 void TheoryBV::preRegisterTerm(TNode node) {
 243   d_calledPreregister = true;
 244   Debug("bitvector-preregister") << "TheoryBV::preRegister(" << node << ")" << std::endl;
 245
 246   if (options::bitblastMode() == theory::bv::BITBLAST_MODE_EAGER) {
 247     // the aig bit-blaster option is set heuristically
 248     // if bv abstraction is not used
 249     if (!d_eagerSolver->isInitialized()) {
 250       d_eagerSolver->initialize();
 251     }
 252
 253     if (node.getKind() == kind::BITVECTOR_EAGER_ATOM) {
 254       Node formula = node[0];
 255       d_eagerSolver->assertFormula(formula);
 256     }
 257     // nothing to do for the other terms
 258     return;
 259   }
 260
 261   for (unsigned i = 0; i < d_subtheories.size(); ++i) {
 262     d_subtheories[i]->preRegister(node);
 263   }
 264
 265   // AJR : equality solver currently registers all terms to ExtTheory, if we want a lazy reduction without the bv equality solver, need to call this
 266   //getExtTheory()->registerTermRec( node );
 267 }
 268
 269 void TheoryBV::sendConflict() {
 270   Assert(d_conflict);
 271   if (d_conflictNode.isNull()) {
 272     return;
 273   } else {
 274     Debug("bitvector") << indent() << "TheoryBV::check(): conflict " << d_conflictNode << std::endl;
 275     d_out->conflict(d_conflictNode);
 276     d_statistics.d_avgConflictSize.addEntry(d_conflictNode.getNumChildren());
 277     d_conflictNode = Node::null();
 278   }
 279 }
 280
 281 void TheoryBV::checkForLemma(TNode fact)
 282 {
 283   if (fact.getKind() == kind::EQUAL)
 284   {
 285     NodeManager* nm = NodeManager::currentNM();
 286     if (fact[0].getKind() == kind::BITVECTOR_UREM_TOTAL)
 287     {
 288       TNode urem = fact[0];
 289       TNode result = fact[1];
 290       TNode divisor = urem[1];
 291       Node result_ult_div = nm->mkNode(kind::BITVECTOR_ULT, result, divisor);
 292       Node divisor_eq_0 =
 293           nm->mkNode(kind::EQUAL, divisor, mkZero(getSize(divisor)));
 294       Node split = nm->mkNode(
 295           kind::OR, divisor_eq_0, nm->mkNode(kind::NOT, fact), result_ult_div);
 296       lemma(split);
 297     }
 298     if (fact[1].getKind() == kind::BITVECTOR_UREM_TOTAL)
 299     {
 300       TNode urem = fact[1];
 301       TNode result = fact[0];
 302       TNode divisor = urem[1];
 303       Node result_ult_div = nm->mkNode(kind::BITVECTOR_ULT, result, divisor);
 304       Node divisor_eq_0 =
 305           nm->mkNode(kind::EQUAL, divisor, mkZero(getSize(divisor)));
 306       Node split = nm->mkNode(
 307           kind::OR, divisor_eq_0, nm->mkNode(kind::NOT, fact), result_ult_div);
 308       lemma(split);
 309     }
 310   }
 311 }
 312
 313 void TheoryBV::check(Effort e)
 314 {
 315   if (done() && e<Theory::EFFORT_FULL) {
 316     return;
 317   }
 318
 319   //last call : do reductions on extended bitvector functions
 320   if (e == Theory::EFFORT_LAST_CALL) {
 321     std::vector<Node> nred = getExtTheory()->getActive();
 322     doExtfReductions(nred);
 323     return;
 324   }
 325
 326   TimerStat::CodeTimer checkTimer(d_checkTime);
 327   Debug("bitvector") << "TheoryBV::check(" << e << ")" << std::endl;
 328   TimerStat::CodeTimer codeTimer(d_statistics.d_solveTimer);
 329   // we may be getting new assertions so the model cache may not be sound
 330   d_invalidateModelCache.set(true);
 331   // if we are using the eager solver
 332   if (options::bitblastMode() == theory::bv::BITBLAST_MODE_EAGER) {
 333     // this can only happen on an empty benchmark
 334     if (!d_eagerSolver->isInitialized()) {
 335       d_eagerSolver->initialize();
 336     }
 337     if (!Theory::fullEffort(e))
 338       return;
 339
 340     std::vector<TNode> assertions;
 341     while (!done()) {
 342       TNode fact = get().assertion;
 343       Assert (fact.getKind() == kind::BITVECTOR_EAGER_ATOM);
 344       assertions.push_back(fact);
 345     }
 346     Assert (d_eagerSolver->hasAssertions(assertions));
 347
 348     bool ok = d_eagerSolver->checkSat();
 349     if (!ok) {
 350       if (assertions.size() == 1) {
 351         d_out->conflict(assertions[0]);
 352         return;
 353       }
 354       Node conflict = utils::mkAnd(assertions);
 355       d_out->conflict(conflict);
 356       return;
 357     }
 358     return;
 359   }
 360
 361
 362   if (Theory::fullEffort(e)) {
 363     ++(d_statistics.d_numCallsToCheckFullEffort);
 364   } else {
 365     ++(d_statistics.d_numCallsToCheckStandardEffort);
 366   }
 367   // if we are already in conflict just return the conflict
 368   if (inConflict()) {
 369     sendConflict();
 370     return;
 371   }
 372
 373   while (!done()) {
 374     TNode fact = get().assertion;
 375
 376     checkForLemma(fact);
 377
 378     for (unsigned i = 0; i < d_subtheories.size(); ++i) {
 379       d_subtheories[i]->assertFact(fact);
 380     }
 381   }
 382
 383   bool ok = true;
 384   bool complete = false;
 385   for (unsigned i = 0; i < d_subtheories.size(); ++i) {
 386     Assert (!inConflict());
 387     ok = d_subtheories[i]->check(e);
 388     complete = d_subtheories[i]->isComplete();
 389
 390     if (!ok) {
 391       // if we are in a conflict no need to check with other theories
 392       Assert (inConflict());
 393       sendConflict();
 394       return;
 395     }
 396     if (complete) {
 397       // if the last subtheory was complete we stop
 398       break;
 399     }
 400   }
 401
 402   //check extended functions
 403   if (Theory::fullEffort(e)) {
 404     //do inferences (adds external lemmas)  TODO: this can be improved to add internal inferences
 405     std::vector< Node > nred;
 406     if( getExtTheory()->doInferences( 0, nred ) ){
 407       return;
 408     }
 409     d_needsLastCallCheck = false;
 410     if( !nred.empty() ){
 411       //other inferences involving bv2nat, int2bv
 412       if( options::bvAlgExtf() ){
 413         if( doExtfInferences( nred ) ){
 414           return;
 415         }
 416       }
 417       if( !options::bvLazyReduceExtf() ){
 418         if( doExtfReductions( nred ) ){
 419           return;
 420         }
 421       }else{
 422         d_needsLastCallCheck = true;
 423       }
 424     }
 425   }
 426 }
 427
 428 bool TheoryBV::doExtfInferences(std::vector<Node>& terms)
 429 {
 430   NodeManager* nm = NodeManager::currentNM();
 431   bool sentLemma = false;
 432   eq::EqualityEngine* ee = getEqualityEngine();
 433   std::map<Node, Node> op_map;
 434   for (unsigned j = 0; j < terms.size(); j++)
 435   {
 436     TNode n = terms[j];
 437     Assert(n.getKind() == kind::BITVECTOR_TO_NAT
 438            || n.getKind() == kind::INT_TO_BITVECTOR);
 439     if (n.getKind() == kind::BITVECTOR_TO_NAT)
 440     {
 441       // range lemmas
 442       if (d_extf_range_infer.find(n) == d_extf_range_infer.end())
 443       {
 444         d_extf_range_infer.insert(n);
 445         unsigned bvs = n[0].getType().getBitVectorSize();
 446         Node min = nm->mkConst(Rational(0));
 447         Node max = nm->mkConst(Rational(Integer(1).multiplyByPow2(bvs)));
 448         Node lem = nm->mkNode(kind::AND,
 449                               nm->mkNode(kind::GEQ, n, min),
 450                               nm->mkNode(kind::LT, n, max));
 451         Trace("bv-extf-lemma")
 452             << "BV extf lemma (range) : " << lem << std::endl;
 453         d_out->lemma(lem);
 454         sentLemma = true;
 455       }
 456     }
 457     Node r = (ee && ee->hasTerm(n[0])) ? ee->getRepresentative(n[0]) : n[0];
 458     op_map[r] = n;
 459   }
 460   for (unsigned j = 0; j < terms.size(); j++)
 461   {
 462     TNode n = terms[j];
 463     Node r = (ee && ee->hasTerm(n[0])) ? ee->getRepresentative(n) : n;
 464     std::map<Node, Node>::iterator it = op_map.find(r);
 465     if (it != op_map.end())
 466     {
 467       Node parent = it->second;
 468       // Node cterm = parent[0]==n ? parent : nm->mkNode( parent.getOperator(),
 469       // n );
 470       Node cterm = parent[0].eqNode(n);
 471       Trace("bv-extf-lemma-debug")
 472           << "BV extf collapse based on : " << cterm << std::endl;
 473       if (d_extf_collapse_infer.find(cterm) == d_extf_collapse_infer.end())
 474       {
 475         d_extf_collapse_infer.insert(cterm);
 476
 477         Node t = n[0];
 478         if (n.getKind() == kind::INT_TO_BITVECTOR)
 479         {
 480           Assert(t.getType().isInteger());
 481           // congruent modulo 2^( bv width )
 482           unsigned bvs = n.getType().getBitVectorSize();
 483           Node coeff = nm->mkConst(Rational(Integer(1).multiplyByPow2(bvs)));
 484           Node k = nm->mkSkolem(
 485               "int_bv_cong", t.getType(), "for int2bv/bv2nat congruence");
 486           t = nm->mkNode(kind::PLUS, t, nm->mkNode(kind::MULT, coeff, k));
 487         }
 488         Node lem = parent.eqNode(t);
 489
 490         if (parent[0] != n)
 491         {
 492           Assert(ee->areEqual(parent[0], n));
 493           lem = nm->mkNode(kind::IMPLIES, parent[0].eqNode(n), lem);
 494         }
 495         Trace("bv-extf-lemma")
 496             << "BV extf lemma (collapse) : " << lem << std::endl;
 497         d_out->lemma(lem);
 498         sentLemma = true;
 499       }
 500     }
 501   }
 502   return sentLemma;
 503 }
 504
 505 bool TheoryBV::doExtfReductions( std::vector< Node >& terms ) {
 506   std::vector< Node > nredr;
 507   if( getExtTheory()->doReductions( 0, terms, nredr ) ){
 508     return true;
 509   }
 510   Assert( nredr.empty() );
 511   return false;
 512 }
 513
 514 bool TheoryBV::needsCheckLastEffort() {
 515   return d_needsLastCallCheck;
 516 }
 517 bool TheoryBV::collectModelInfo(TheoryModel* m)
 518 {
 519   Assert(!inConflict());
 520   if (options::bitblastMode() == theory::bv::BITBLAST_MODE_EAGER) {
 521     if (!d_eagerSolver->collectModelInfo(m, true))
 522     {
 523       return false;
 524     }
 525   }
 526   for (unsigned i = 0; i < d_subtheories.size(); ++i) {
 527     if (d_subtheories[i]->isComplete()) {
 528       return d_subtheories[i]->collectModelInfo(m, true);
 529     }
 530   }
 531   return true;
 532 }
 533
 534 Node TheoryBV::getModelValue(TNode var) {
 535   Assert(!inConflict());
 536   for (unsigned i = 0; i < d_subtheories.size(); ++i) {
 537     if (d_subtheories[i]->isComplete()) {
 538       return d_subtheories[i]->getModelValue(var);
 539     }
 540   }
 541   Unreachable();
 542 }
 543
 544 void TheoryBV::propagate(Effort e) {
 545   Debug("bitvector") << indent() << "TheoryBV::propagate()" << std::endl;
 546   if (options::bitblastMode() == theory::bv::BITBLAST_MODE_EAGER) {
 547     return;
 548   }
 549
 550   if (inConflict()) {
 551     return;
 552   }
 553
 554   // go through stored propagations
 555   bool ok = true;
 556   for (; d_literalsToPropagateIndex < d_literalsToPropagate.size() && ok; d_literalsToPropagateIndex = d_literalsToPropagateIndex + 1) {
 557     TNode literal = d_literalsToPropagate[d_literalsToPropagateIndex];
 558     // temporary fix for incremental bit-blasting
 559     if (d_valuation.isSatLiteral(literal)) {
 560       Debug("bitvector::propagate") << "TheoryBV:: propagating " << literal <<"\n";
 561       ok = d_out->propagate(literal);
 562     }
 563   }
 564
 565   if (!ok) {
 566     Debug("bitvector::propagate") << indent() << "TheoryBV::propagate(): conflict from theory engine" << std::endl;
 567     setConflict();
 568   }
 569 }
 570
 571
 572 eq::EqualityEngine * TheoryBV::getEqualityEngine() {
 573   CoreSolver* core = (CoreSolver*)d_subtheoryMap[SUB_CORE];
 574   if( core ){
 575     return core->getEqualityEngine();
 576   }else{
 577     return NULL;
 578   }
 579 }
 580
 581 bool TheoryBV::getCurrentSubstitution( int effort, std::vector< Node >& vars, std::vector< Node >& subs, std::map< Node, std::vector< Node > >& exp ) {
 582   eq::EqualityEngine * ee = getEqualityEngine();
 583   if( ee ){
 584     //get the constant equivalence classes
 585     bool retVal = false;
 586     for( unsigned i=0; i<vars.size(); i++ ){
 587       Node n = vars[i];
 588       if( ee->hasTerm( n ) ){
 589         Node nr = ee->getRepresentative( n );
 590         if( nr.isConst() ){
 591           subs.push_back( nr );
 592           exp[n].push_back( n.eqNode( nr ) );
 593           retVal = true;
 594         }else{
 595           subs.push_back( n );
 596         }
 597       }else{
 598         subs.push_back( n );
 599       }
 600     }
 601     //return true if the substitution is non-trivial
 602     return retVal;
 603   }
 604   return false;
 605 }
 606
 607 int TheoryBV::getReduction(int effort, Node n, Node& nr)
 608 {
 609   Trace("bv-ext") << "TheoryBV::checkExt : non-reduced : " << n << std::endl;
 610   NodeManager* const nm = NodeManager::currentNM();
 611   if (n.getKind() == kind::BITVECTOR_TO_NAT)
 612   {
 613     // taken from rewrite code
 614     const unsigned size = utils::getSize(n[0]);
 615     const Node z = nm->mkConst(Rational(0));
 616     const Node bvone = utils::mkOne(1);
 617     NodeBuilder<> result(kind::PLUS);
 618     Integer i = 1;
 619     for (unsigned bit = 0; bit < size; ++bit, i *= 2)
 620     {
 621       Node cond =
 622           nm->mkNode(kind::EQUAL,
 623                      nm->mkNode(nm->mkConst(BitVectorExtract(bit, bit)), n[0]),
 624                      bvone);
 625       result << nm->mkNode(kind::ITE, cond, nm->mkConst(Rational(i)), z);
 626     }
 627     nr = Node(result);
 628     return -1;
 629   }
 630   else if (n.getKind() == kind::INT_TO_BITVECTOR)
 631   {
 632     // taken from rewrite code
 633     const unsigned size = n.getOperator().getConst<IntToBitVector>().size;
 634     const Node bvzero = utils::mkZero(1);
 635     const Node bvone = utils::mkOne(1);
 636     std::vector<Node> v;
 637     Integer i = 2;
 638     while (v.size() < size)
 639     {
 640       Node cond = nm->mkNode(
 641           kind::GEQ,
 642           nm->mkNode(kind::INTS_MODULUS_TOTAL, n[0], nm->mkConst(Rational(i))),
 643           nm->mkConst(Rational(i, 2)));
 644       cond = Rewriter::rewrite(cond);
 645       v.push_back(nm->mkNode(kind::ITE, cond, bvone, bvzero));
 646       i *= 2;
 647     }
 648     NodeBuilder<> result(kind::BITVECTOR_CONCAT);
 649     result.append(v.rbegin(), v.rend());
 650     nr = Node(result);
 651     return -1;
 652   }
 653   return 0;
 654 }
 655
 656 Theory::PPAssertStatus TheoryBV::ppAssert(TNode in,
 657                                           SubstitutionMap& outSubstitutions)
 658 {
 659   switch (in.getKind())
 660   {
 661     case kind::EQUAL:
 662     {
 663       if (in[0].isVar() && !in[1].hasSubterm(in[0]))
 664       {
 665         ++(d_statistics.d_solveSubstitutions);
 666         outSubstitutions.addSubstitution(in[0], in[1]);
 667         return PP_ASSERT_STATUS_SOLVED;
 668       }
 669       if (in[1].isVar() && !in[0].hasSubterm(in[1]))
 670       {
 671         ++(d_statistics.d_solveSubstitutions);
 672         outSubstitutions.addSubstitution(in[1], in[0]);
 673         return PP_ASSERT_STATUS_SOLVED;
 674       }
 675       Node node = Rewriter::rewrite(in);
 676       if ((node[0].getKind() == kind::BITVECTOR_EXTRACT && node[1].isConst())
 677           || (node[1].getKind() == kind::BITVECTOR_EXTRACT
 678               && node[0].isConst()))
 679       {
 680         Node extract = node[0].isConst() ? node[1] : node[0];
 681         if (extract[0].getKind() == kind::VARIABLE)
 682         {
 683           Node c = node[0].isConst() ? node[0] : node[1];
 684
 685           unsigned high = utils::getExtractHigh(extract);
 686           unsigned low = utils::getExtractLow(extract);
 687           unsigned var_bitwidth = utils::getSize(extract[0]);
 688           std::vector<Node> children;
 689
 690           if (low == 0)
 691           {
 692             Assert(high != var_bitwidth - 1);
 693             unsigned skolem_size = var_bitwidth - high - 1;
 694             Node skolem = utils::mkVar(skolem_size);
 695             children.push_back(skolem);
 696             children.push_back(c);
 697           }
 698           else if (high == var_bitwidth - 1)
 699           {
 700             unsigned skolem_size = low;
 701             Node skolem = utils::mkVar(skolem_size);
 702             children.push_back(c);
 703             children.push_back(skolem);
 704           }
 705           else
 706           {
 707             unsigned skolem1_size = low;
 708             unsigned skolem2_size = var_bitwidth - high - 1;
 709             Node skolem1 = utils::mkVar(skolem1_size);
 710             Node skolem2 = utils::mkVar(skolem2_size);
 711             children.push_back(skolem2);
 712             children.push_back(c);
 713             children.push_back(skolem1);
 714           }
 715           Node concat = utils::mkConcat(children);
 716           Assert(utils::getSize(concat) == utils::getSize(extract[0]));
 717           outSubstitutions.addSubstitution(extract[0], concat);
 718           return PP_ASSERT_STATUS_SOLVED;
 719         }
 720       }
 721     }
 722     break;
 723     case kind::BITVECTOR_ULT:
 724     case kind::BITVECTOR_SLT:
 725     case kind::BITVECTOR_ULE:
 726     case kind::BITVECTOR_SLE:
 727
 728     default:
 729       // TODO other predicates
 730       break;
 731   }
 732   return PP_ASSERT_STATUS_UNSOLVED;
 733 }
 734
 735 Node TheoryBV::ppRewrite(TNode t)
 736 {
 737   Debug("bv-pp-rewrite") << "TheoryBV::ppRewrite " << t << "\n";
 738   Node res = t;
 739   if (RewriteRule<BitwiseEq>::applies(t)) {
 740     Node result = RewriteRule<BitwiseEq>::run<false>(t);
 741     res = Rewriter::rewrite(result);
 742   } else if (d_isCoreTheory && t.getKind() == kind::EQUAL) {
 743     std::vector<Node> equalities;
 744     Slicer::splitEqualities(t, equalities);
 745     res = utils::mkAnd(equalities);
 746   } else if (RewriteRule<UltPlusOne>::applies(t)) {
 747     Node result = RewriteRule<UltPlusOne>::run<false>(t);
 748     res = Rewriter::rewrite(result);
 749   } else if( res.getKind() == kind::EQUAL &&
 750       ((res[0].getKind() == kind::BITVECTOR_PLUS &&
 751         RewriteRule<ConcatToMult>::applies(res[1])) ||
 752        (res[1].getKind() == kind::BITVECTOR_PLUS &&
 753         RewriteRule<ConcatToMult>::applies(res[0])))) {
 754     Node mult = RewriteRule<ConcatToMult>::applies(res[0])?
 755       RewriteRule<ConcatToMult>::run<false>(res[0]) :
 756       RewriteRule<ConcatToMult>::run<true>(res[1]);
 757     Node factor = mult[0];
 758     Node sum =  RewriteRule<ConcatToMult>::applies(res[0])? res[1] : res[0];
 759     Node new_eq = NodeManager::currentNM()->mkNode(kind::EQUAL, sum, mult);
 760     Node rewr_eq = RewriteRule<SolveEq>::run<true>(new_eq);
 761     if (rewr_eq[0].isVar() || rewr_eq[1].isVar()){
 762       res = Rewriter::rewrite(rewr_eq);
 763     } else {
 764       res = t;
 765     }
 766   } else if (RewriteRule<SignExtendEqConst>::applies(t)) {
 767     res = RewriteRule<SignExtendEqConst>::run<false>(t);
 768   } else if (RewriteRule<ZeroExtendEqConst>::applies(t)) {
 769     res = RewriteRule<ZeroExtendEqConst>::run<false>(t);
 770   }
 771   else if (RewriteRule<NormalizeEqPlusNeg>::applies(t))
 772   {
 773     res = RewriteRule<NormalizeEqPlusNeg>::run<false>(t);
 774   }
 775
 776   // if(t.getKind() == kind::EQUAL &&
 777   //    ((t[0].getKind() == kind::BITVECTOR_MULT && t[1].getKind() ==
 778   //    kind::BITVECTOR_PLUS) ||
 779   //     (t[1].getKind() == kind::BITVECTOR_MULT && t[0].getKind() ==
 780   //     kind::BITVECTOR_PLUS))) {
 781   //   // if we have an equality between a multiplication and addition
 782   //   // try to express multiplication in terms of addition
 783   //   Node mult = t[0].getKind() == kind::BITVECTOR_MULT? t[0] : t[1];
 784   //   Node add = t[0].getKind() == kind::BITVECTOR_PLUS? t[0] : t[1];
 785   //   if (RewriteRule<MultSlice>::applies(mult)) {
 786   //     Node new_mult = RewriteRule<MultSlice>::run<false>(mult);
 787   //     Node new_eq =
 788   //     Rewriter::rewrite(NodeManager::currentNM()->mkNode(kind::EQUAL,
 789   //     new_mult, add));
 790
 791   //     // the simplification can cause the formula to blow up
 792   //     // only apply if formula reduced
 793   //     if (d_subtheoryMap.find(SUB_BITBLAST) != d_subtheoryMap.end()) {
 794   //       BitblastSolver* bv = (BitblastSolver*)d_subtheoryMap[SUB_BITBLAST];
 795   //       uint64_t old_size = bv->computeAtomWeight(t);
 796   //       Assert (old_size);
 797   //       uint64_t new_size = bv->computeAtomWeight(new_eq);
 798   //       double ratio = ((double)new_size)/old_size;
 799   //       if (ratio <= 0.4) {
 800   //         ++(d_statistics.d_numMultSlice);
 801   //         return new_eq;
 802   //       }
 803   //     }
 804
 805   //     if (new_eq.getKind() == kind::CONST_BOOLEAN) {
 806   //       ++(d_statistics.d_numMultSlice);
 807   //       return new_eq;
 808   //     }
 809   //   }
 810   // }
 811
 812   if (options::bvAbstraction() && t.getType().isBoolean()) {
 813     d_abstractionModule->addInputAtom(res);
 814   }
 815   Debug("bv-pp-rewrite") << "to   " << res << "\n";
 816   return res;
 817 }
 818
 819 void TheoryBV::presolve() {
 820   Debug("bitvector") << "TheoryBV::presolve" << endl;
 821 }
 822
 823 static int prop_count = 0;
 824
 825 bool TheoryBV::storePropagation(TNode literal, SubTheory subtheory)
 826 {
 827   Debug("bitvector::propagate") << indent() << getSatContext()->getLevel() << " " << "TheoryBV::storePropagation(" << literal << ", " << subtheory << ")" << std::endl;
 828   prop_count++;
 829
 830   // If already in conflict, no more propagation
 831   if (d_conflict) {
 832     Debug("bitvector::propagate") << indent() << "TheoryBV::storePropagation(" << literal << ", " << subtheory << "): already in conflict" << std::endl;
 833     return false;
 834   }
 835
 836   // If propagated already, just skip
 837   PropagatedMap::const_iterator find = d_propagatedBy.find(literal);
 838   if (find != d_propagatedBy.end()) {
 839     return true;
 840   } else {
 841     bool polarity = literal.getKind() != kind::NOT;
 842     Node negatedLiteral = polarity ? literal.notNode() : (Node) literal[0];
 843     find = d_propagatedBy.find(negatedLiteral);
 844     if (find != d_propagatedBy.end() && (*find).second != subtheory) {
 845       // Safe to ignore this one, subtheory should produce a conflict
 846       return true;
 847     }
 848
 849     d_propagatedBy[literal] = subtheory;
 850   }
 851
 852   // Propagate differs depending on the subtheory
 853   // * bitblaster needs to be left alone until it's done, otherwise it doesn't know how to explain
 854   // * equality engine can propagate eagerly
 855   bool ok = true;
 856   if (subtheory == SUB_CORE) {
 857     d_out->propagate(literal);
 858     if (!ok) {
 859       setConflict();
 860     }
 861   } else {
 862     d_literalsToPropagate.push_back(literal);
 863   }
 864   return ok;
 865
 866 }/* TheoryBV::propagate(TNode) */
 867
 868
 869 void TheoryBV::explain(TNode literal, std::vector<TNode>& assumptions) {
 870   Assert (wasPropagatedBySubtheory(literal));
 871   SubTheory sub = getPropagatingSubtheory(literal);
 872   d_subtheoryMap[sub]->explain(literal, assumptions);
 873 }
 874
 875
 876 Node TheoryBV::explain(TNode node) {
 877   Debug("bitvector::explain") << "TheoryBV::explain(" << node << ")" << std::endl;
 878   std::vector<TNode> assumptions;
 879
 880   // Ask for the explanation
 881   explain(node, assumptions);
 882   // this means that it is something true at level 0
 883   if (assumptions.size() == 0) {
 884     return utils::mkTrue();
 885   }
 886   // return the explanation
 887   Node explanation = utils::mkAnd(assumptions);
 888   Debug("bitvector::explain") << "TheoryBV::explain(" << node << ") => " << explanation << std::endl;
 889   Debug("bitvector::explain") << "TheoryBV::explain done. \n";
 890   return explanation;
 891 }
 892
 893
 894 void TheoryBV::addSharedTerm(TNode t) {
 895   Debug("bitvector::sharing") << indent() << "TheoryBV::addSharedTerm(" << t << ")" << std::endl;
 896   d_sharedTermsSet.insert(t);
 897   if (options::bitvectorEqualitySolver()) {
 898     for (unsigned i = 0; i < d_subtheories.size(); ++i) {
 899       d_subtheories[i]->addSharedTerm(t);
 900     }
 901   }
 902 }
 903
 904
 905 EqualityStatus TheoryBV::getEqualityStatus(TNode a, TNode b)
 906 {
 907   if (options::bitblastMode() == theory::bv::BITBLAST_MODE_EAGER)
 908     return EQUALITY_UNKNOWN;
 909   Assert (options::bitblastMode() == theory::bv::BITBLAST_MODE_LAZY);
 910   for (unsigned i = 0; i < d_subtheories.size(); ++i) {
 911     EqualityStatus status = d_subtheories[i]->getEqualityStatus(a, b);
 912     if (status != EQUALITY_UNKNOWN) {
 913       return status;
 914     }
 915   }
 916   return EQUALITY_UNKNOWN; ;
 917 }
 918
 919
 920 void TheoryBV::enableCoreTheorySlicer() {
 921   Assert (!d_calledPreregister);
 922   d_isCoreTheory = true;
 923   if (d_subtheoryMap.find(SUB_CORE) != d_subtheoryMap.end()) {
 924     CoreSolver* core = (CoreSolver*)d_subtheoryMap[SUB_CORE];
 925     core->enableSlicer();
 926   }
 927 }
 928
 929
 930 void TheoryBV::ppStaticLearn(TNode in, NodeBuilder<>& learned) {
 931   if(d_staticLearnCache.find(in) != d_staticLearnCache.end()){
 932     return;
 933   }
 934   d_staticLearnCache.insert(in);
 935
 936   if (in.getKind() == kind::EQUAL) {
 937     if((in[0].getKind() == kind::BITVECTOR_PLUS && in[1].getKind() == kind::BITVECTOR_SHL) ||
 938        (in[1].getKind() == kind::BITVECTOR_PLUS && in[0].getKind() == kind::BITVECTOR_SHL)) {
 939       TNode p = in[0].getKind() == kind::BITVECTOR_PLUS ? in[0] : in[1];
 940       TNode s = in[0].getKind() == kind::BITVECTOR_PLUS ? in[1] : in[0];
 941
 942       if(p.getNumChildren() == 2
 943          && p[0].getKind()  == kind::BITVECTOR_SHL
 944          && p[1].getKind()  == kind::BITVECTOR_SHL ){
 945         unsigned size = utils::getSize(s);
 946         Node one = utils::mkConst(size, 1u);
 947         if(s[0] == one && p[0][0] == one && p[1][0] == one){
 948           Node zero = utils::mkConst(size, 0u);
 949           TNode b = p[0];
 950           TNode c = p[1];
 951           // (s : 1 << S) = (b : 1 << B) + (c : 1 << C)
 952           Node b_eq_0 = b.eqNode(zero);
 953           Node c_eq_0 = c.eqNode(zero);
 954           Node b_eq_c = b.eqNode(c);
 955
 956           Node dis = NodeManager::currentNM()->mkNode(
 957               kind::OR, b_eq_0, c_eq_0, b_eq_c);
 958           Node imp = in.impNode(dis);
 959           learned << imp;
 960         }
 961       }
 962     }
 963   }else if(in.getKind() == kind::AND){
 964     for(size_t i = 0, N = in.getNumChildren(); i < N; ++i){
 965       ppStaticLearn(in[i], learned);
 966     }
 967   }
 968 }
 969
 970 bool TheoryBV::applyAbstraction(const std::vector<Node>& assertions, std::vector<Node>& new_assertions) {
 971   bool changed = d_abstractionModule->applyAbstraction(assertions, new_assertions);
 972   if (changed &&
 973       options::bitblastMode() == theory::bv::BITBLAST_MODE_EAGER &&
 974       options::bitvectorAig()) {
 975     // disable AIG mode
 976     AlwaysAssert (!d_eagerSolver->isInitialized());
 977     d_eagerSolver->turnOffAig();
 978     d_eagerSolver->initialize();
 979   }
 980   return changed;
 981 }
 982
 983 void TheoryBV::setProofLog( BitVectorProof * bvp ) {
 984   if( options::bitblastMode() == theory::bv::BITBLAST_MODE_EAGER ){
 985     d_eagerSolver->setProofLog( bvp );
 986   }else{
 987     for( unsigned i=0; i< d_subtheories.size(); i++ ){
 988       d_subtheories[i]->setProofLog( bvp );
 989     }
 990   }
 991 }
 992
 993 void TheoryBV::setConflict(Node conflict)
 994 {
 995   if (options::bvAbstraction())
 996   {
 997     NodeManager* const nm = NodeManager::currentNM();
 998     Node new_conflict = d_abstractionModule->simplifyConflict(conflict);
 999
1000     std::vector<Node> lemmas;
1001     lemmas.push_back(new_conflict);
1002     d_abstractionModule->generalizeConflict(new_conflict, lemmas);
1003     for (unsigned i = 0; i < lemmas.size(); ++i)
1004     {
1005       lemma(nm->mkNode(kind::NOT, lemmas[i]));
1006     }
1007   }
1008   d_conflict = true;
1009   d_conflictNode = conflict;
1010 }
1011
1012 } /* namespace CVC4::theory::bv */
1013 } /* namespace CVC4::theory */
1014 } /* namespace CVC4 */