src/theory/bv/theory_bv.cpp

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