src/theory/quantifiers/fmf/bounded_integers.cpp

   1 /*********************                                                        */
   2 /*! \file bounded_integers.cpp
   3  ** \verbatim
   4  ** Top contributors (to current version):
   5  **   Andrew Reynolds, Andres Noetzli, Mathias Preiner
   6  ** This file is part of the CVC4 project.
   7  ** Copyright (c) 2009-2020 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  ** \brief Bounded integers module
  13  **
  14  ** This class manages integer bounds for quantifiers
  15  **/
  16
  17 #include "theory/quantifiers/fmf/bounded_integers.h"
  18
  19 #include "expr/node_algorithm.h"
  20 #include "options/quantifiers_options.h"
  21 #include "theory/arith/arith_msum.h"
  22 #include "theory/datatypes/theory_datatypes_utils.h"
  23 #include "theory/quantifiers/first_order_model.h"
  24 #include "theory/quantifiers/fmf/model_engine.h"
  25 #include "theory/quantifiers/term_enumeration.h"
  26 #include "theory/quantifiers/term_util.h"
  27 #include "theory/quantifiers_engine.h"
  28 #include "theory/theory_engine.h"
  29
  30 using namespace CVC4;
  31 using namespace std;
  32 using namespace CVC4::theory;
  33 using namespace CVC4::theory::quantifiers;
  34 using namespace CVC4::kind;
  35
  36 BoundedIntegers::IntRangeDecisionHeuristic::IntRangeDecisionHeuristic(
  37     Node r,
  38     context::Context* c,
  39     context::Context* u,
  40     Valuation valuation,
  41     bool isProxy)
  42     : DecisionStrategyFmf(c, valuation), d_range(r), d_ranges_proxied(u)
  43 {
  44   if( options::fmfBoundLazy() ){
  45     d_proxy_range = isProxy ? r : NodeManager::currentNM()->mkSkolem( "pbir", r.getType() );
  46   }else{
  47     d_proxy_range = r;
  48   }
  49   if( !isProxy ){
  50     Trace("bound-int") << "Introduce proxy " << d_proxy_range << " for " << d_range << std::endl;
  51   }
  52 }
  53 Node BoundedIntegers::IntRangeDecisionHeuristic::mkLiteral(unsigned n)
  54 {
  55   NodeManager* nm = NodeManager::currentNM();
  56   Node cn = nm->mkConst(Rational(n == 0 ? 0 : n - 1));
  57   return nm->mkNode(n == 0 ? LT : LEQ, d_proxy_range, cn);
  58 }
  59
  60 Node BoundedIntegers::IntRangeDecisionHeuristic::proxyCurrentRangeLemma()
  61 {
  62   if (d_range == d_proxy_range)
  63   {
  64     return Node::null();
  65   }
  66   unsigned curr = 0;
  67   if (!getAssertedLiteralIndex(curr))
  68   {
  69     return Node::null();
  70   }
  71   if (d_ranges_proxied.find(curr) != d_ranges_proxied.end())
  72   {
  73     return Node::null();
  74   }
  75   d_ranges_proxied[curr] = true;
  76   NodeManager* nm = NodeManager::currentNM();
  77   Node currLit = getLiteral(curr);
  78   Node lem =
  79       nm->mkNode(EQUAL,
  80                  currLit,
  81                  nm->mkNode(curr == 0 ? LT : LEQ,
  82                             d_range,
  83                             nm->mkConst(Rational(curr == 0 ? 0 : curr - 1))));
  84   return lem;
  85 }
  86
  87 BoundedIntegers::BoundedIntegers(QuantifiersEngine* qe,
  88                                  QuantifiersState& qs,
  89                                  QuantifiersInferenceManager& qim)
  90     : QuantifiersModule(qs, qim, qe)
  91 {
  92 }
  93
  94 BoundedIntegers::~BoundedIntegers() {}
  95
  96 void BoundedIntegers::presolve() {
  97   d_bnd_it.clear();
  98 }
  99
 100 bool BoundedIntegers::hasNonBoundVar( Node f, Node b, std::map< Node, bool >& visited ) {
 101   if( visited.find( b )==visited.end() ){
 102     visited[b] = true;
 103     if( b.getKind()==BOUND_VARIABLE ){
 104       if( !isBound( f, b ) ){
 105         return true;
 106       }
 107     }else{
 108       for( unsigned i=0; i<b.getNumChildren(); i++ ){
 109         if( hasNonBoundVar( f, b[i], visited ) ){
 110           return true;
 111         }
 112       }
 113     }
 114   }
 115   return false;
 116 }
 117 bool BoundedIntegers::hasNonBoundVar( Node f, Node b ) {
 118   std::map< Node, bool > visited;
 119   return hasNonBoundVar( f, b, visited );
 120 }
 121
 122 bool BoundedIntegers::processEqDisjunct( Node q, Node n, Node& v, std::vector< Node >& v_cases ) {
 123   if( n.getKind()==EQUAL ){
 124     for( unsigned i=0; i<2; i++ ){
 125       Node t = n[i];
 126       if( !hasNonBoundVar( q, n[1-i] ) ){
 127         if( t==v ){
 128           v_cases.push_back( n[1-i] );
 129           return true;
 130         }else if( v.isNull() && t.getKind()==BOUND_VARIABLE ){
 131           v = t;
 132           v_cases.push_back( n[1-i] );
 133           return true;
 134         }
 135       }
 136     }
 137   }
 138   return false;
 139 }
 140
 141 void BoundedIntegers::processMatchBoundVars( Node q, Node n, std::vector< Node >& bvs, std::map< Node, bool >& visited ){
 142   if( visited.find( n )==visited.end() ){
 143     visited[n] = true;
 144     if( n.getKind()==BOUND_VARIABLE && !isBound( q, n ) ){
 145       bvs.push_back( n );
 146     //injective operators
 147     }else if( n.getKind()==kind::APPLY_CONSTRUCTOR ){
 148       for( unsigned i=0; i<n.getNumChildren(); i++ ){
 149         processMatchBoundVars( q, n[i], bvs, visited );
 150       }
 151     }
 152   }
 153 }
 154
 155 void BoundedIntegers::process( Node q, Node n, bool pol,
 156                                std::map< Node, unsigned >& bound_lit_type_map,
 157                                std::map< int, std::map< Node, Node > >& bound_lit_map,
 158                                std::map< int, std::map< Node, bool > >& bound_lit_pol_map,
 159                                std::map< int, std::map< Node, Node > >& bound_int_range_term,
 160                                std::map< Node, std::vector< Node > >& bound_fixed_set ){
 161   if( n.getKind()==OR || n.getKind()==AND ){
 162     if( (n.getKind()==OR)==pol ){
 163       for( unsigned i=0; i<n.getNumChildren(); i++) {
 164         process( q, n[i], pol, bound_lit_type_map, bound_lit_map, bound_lit_pol_map, bound_int_range_term, bound_fixed_set );
 165       }
 166     }else{
 167       //if we are ( x != t1 ^ ...^ x != tn ), then x can be bound to { t1...tn }
 168       Node conj = n;
 169       if( !pol ){
 170         conj = TermUtil::simpleNegate( conj );
 171       }
 172       Trace("bound-int-debug") << "Process possible finite disequality conjunction : " << conj << std::endl;
 173       Assert(conj.getKind() == AND);
 174       Node v;
 175       std::vector< Node > v_cases;
 176       bool success = true;
 177       for( unsigned i=0; i<conj.getNumChildren(); i++ ){
 178         if( conj[i].getKind()==NOT && processEqDisjunct( q, conj[i][0], v, v_cases ) ){
 179           //continue
 180         }else{
 181           Trace("bound-int-debug") << "...failed due to " << conj[i] << std::endl;
 182           success = false;
 183           break;
 184         }
 185       }
 186       if( success && !isBound( q, v ) ){
 187         Trace("bound-int-debug") << "Success with variable " << v << std::endl;
 188         bound_lit_type_map[v] = BOUND_FIXED_SET;
 189         bound_lit_map[3][v] = n;
 190         bound_lit_pol_map[3][v] = pol;
 191         bound_fixed_set[v].clear();
 192         bound_fixed_set[v].insert( bound_fixed_set[v].end(), v_cases.begin(), v_cases.end() );
 193       }
 194     }
 195   }else if( n.getKind()==EQUAL ){
 196     if( !pol ){
 197       // non-applied DER on x != t, x can be bound to { t }
 198       Node v;
 199       std::vector< Node > v_cases;
 200       if( processEqDisjunct( q, n, v, v_cases ) ){
 201         if( !isBound( q, v ) ){
 202           bound_lit_type_map[v] = BOUND_FIXED_SET;
 203           bound_lit_map[3][v] = n;
 204           bound_lit_pol_map[3][v] = pol;
 205           Assert(v_cases.size() == 1);
 206           bound_fixed_set[v].clear();
 207           bound_fixed_set[v].push_back( v_cases[0] );
 208         }
 209       }
 210     }
 211   }else if( n.getKind()==NOT ){
 212     process( q, n[0], !pol, bound_lit_type_map, bound_lit_map, bound_lit_pol_map, bound_int_range_term, bound_fixed_set );
 213   }else if( n.getKind()==GEQ ){
 214     if( n[0].getType().isInteger() ){
 215       std::map< Node, Node > msum;
 216       if (ArithMSum::getMonomialSumLit(n, msum))
 217       {
 218         Trace("bound-int-debug") << "literal (polarity = " << pol << ") " << n << " is monomial sum : " << std::endl;
 219         ArithMSum::debugPrintMonomialSum(msum, "bound-int-debug");
 220         for( std::map< Node, Node >::iterator it = msum.begin(); it != msum.end(); ++it ){
 221           if ( !it->first.isNull() && it->first.getKind()==BOUND_VARIABLE && !isBound( q, it->first ) ){
 222             //if not bound in another way
 223             if( bound_lit_type_map.find( it->first )==bound_lit_type_map.end() || bound_lit_type_map[it->first] == BOUND_INT_RANGE ){
 224               Node veq;
 225               if (ArithMSum::isolate(it->first, msum, veq, GEQ) != 0)
 226               {
 227                 Node n1 = veq[0];
 228                 Node n2 = veq[1];
 229                 if(pol){
 230                   //flip
 231                   n1 = veq[1];
 232                   n2 = veq[0];
 233                   if( n1.getKind()==BOUND_VARIABLE ){
 234                     n2 = ArithMSum::offset(n2, 1);
 235                   }else{
 236                     n1 = ArithMSum::offset(n1, -1);
 237                   }
 238                   veq = NodeManager::currentNM()->mkNode( GEQ, n1, n2 );
 239                 }
 240                 Trace("bound-int-debug") << "Isolated for " << it->first << " : (" << n1 << " >= " << n2 << ")" << std::endl;
 241                 Node t = n1==it->first ? n2 : n1;
 242                 if( !hasNonBoundVar( q, t ) ) {
 243                   Trace("bound-int-debug") << "The bound is relevant." << std::endl;
 244                   int loru = n1==it->first ? 0 : 1;
 245                   bound_lit_type_map[it->first] = BOUND_INT_RANGE;
 246                   bound_int_range_term[loru][it->first] = t;
 247                   bound_lit_map[loru][it->first] = n;
 248                   bound_lit_pol_map[loru][it->first] = pol;
 249                 }else{
 250                   Trace("bound-int-debug") << "The term " << t << " has non-bound variable." << std::endl;
 251                 }
 252               }
 253             }
 254           }
 255         }
 256       }
 257     }
 258   }else if( n.getKind()==MEMBER ){
 259     if( !pol && !hasNonBoundVar( q, n[1] ) ){
 260       std::vector< Node > bound_vars;
 261       std::map< Node, bool > visited;
 262       processMatchBoundVars( q, n[0], bound_vars, visited );
 263       for( unsigned i=0; i<bound_vars.size(); i++ ){
 264         Node v = bound_vars[i];
 265         Trace("bound-int-debug") << "literal (polarity = " << pol << ") " << n << " is membership." << std::endl;
 266         bound_lit_type_map[v] = BOUND_SET_MEMBER;
 267         bound_lit_map[2][v] = n;
 268         bound_lit_pol_map[2][v] = pol;
 269       }
 270     }
 271   }else{
 272     Assert(n.getKind() != LEQ && n.getKind() != LT && n.getKind() != GT);
 273   }
 274 }
 275
 276 bool BoundedIntegers::needsCheck( Theory::Effort e ) {
 277   return e==Theory::EFFORT_LAST_CALL;
 278 }
 279
 280 void BoundedIntegers::check(Theory::Effort e, QEffort quant_e)
 281 {
 282   if (quant_e != QEFFORT_STANDARD)
 283   {
 284     return;
 285   }
 286   Trace("bint-engine") << "---Bounded Integers---" << std::endl;
 287   bool addedLemma = false;
 288   // make sure proxies are up-to-date with range
 289   for (const Node& r : d_ranges)
 290   {
 291     Node prangeLem = d_rms[r]->proxyCurrentRangeLemma();
 292     if (!prangeLem.isNull())
 293     {
 294       Trace("bound-int-lemma")
 295           << "*** bound int : proxy lemma : " << prangeLem << std::endl;
 296       d_quantEngine->addLemma(prangeLem);
 297       addedLemma = true;
 298     }
 299   }
 300   Trace("bint-engine") << "   addedLemma = " << addedLemma << std::endl;
 301 }
 302 void BoundedIntegers::setBoundedVar(Node q, Node v, BoundVarType bound_type)
 303 {
 304   d_bound_type[q][v] = bound_type;
 305   d_set_nums[q][v] = d_set[q].size();
 306   d_set[q].push_back( v );
 307   Trace("bound-int-var") << "Bound variable #" << d_set_nums[q][v] << " : " << v
 308                          << std::endl;
 309 }
 310
 311 void BoundedIntegers::checkOwnership(Node f)
 312 {
 313   //this needs to be done at preregister since it affects e.g. QuantDSplit's preregister
 314   Trace("bound-int") << "check ownership quantifier " << f << std::endl;
 315   NodeManager* nm = NodeManager::currentNM();
 316
 317   bool success;
 318   do{
 319     std::map< Node, unsigned > bound_lit_type_map;
 320     std::map< int, std::map< Node, Node > > bound_lit_map;
 321     std::map< int, std::map< Node, bool > > bound_lit_pol_map;
 322     std::map< int, std::map< Node, Node > > bound_int_range_term;
 323     std::map< Node, std::vector< Node > > bound_fixed_set;
 324     success = false;
 325     process( f, f[1], true, bound_lit_type_map, bound_lit_map, bound_lit_pol_map, bound_int_range_term, bound_fixed_set );
 326     //for( std::map< Node, Node >::iterator it = d_bounds[0][f].begin(); it != d_bounds[0][f].end(); ++it ){
 327     for( std::map< Node, unsigned >::iterator it = bound_lit_type_map.begin(); it != bound_lit_type_map.end(); ++it ){
 328       Node v = it->first;
 329       if( !isBound( f, v ) ){
 330         bool setBoundVar = false;
 331         if( it->second==BOUND_INT_RANGE ){
 332           //must have both
 333           std::map<Node, Node>& blm0 = bound_lit_map[0];
 334           std::map<Node, Node>& blm1 = bound_lit_map[1];
 335           if (blm0.find(v) != blm0.end() && blm1.find(v) != blm1.end())
 336           {
 337             setBoundedVar( f, v, BOUND_INT_RANGE );
 338             setBoundVar = true;
 339             for( unsigned b=0; b<2; b++ ){
 340               //set the bounds
 341               Assert(bound_int_range_term[b].find(v)
 342                      != bound_int_range_term[b].end());
 343               d_bounds[b][f][v] = bound_int_range_term[b][v];
 344             }
 345             Node r = nm->mkNode(MINUS, d_bounds[1][f][v], d_bounds[0][f][v]);
 346             d_range[f][v] = Rewriter::rewrite(r);
 347             Trace("bound-int") << "Variable " << v << " is bound because of int range literals " << bound_lit_map[0][v] << " and " << bound_lit_map[1][v] << std::endl;
 348           }
 349         }else if( it->second==BOUND_SET_MEMBER ){
 350           // only handles infinite element types currently (cardinality is not
 351           // supported for finite element types #1123). Regardless, this is
 352           // typically not a limitation since this variable can be bound in a
 353           // standard way below since its type is finite.
 354           if (!v.getType().isInterpretedFinite())
 355           {
 356             setBoundedVar(f, v, BOUND_SET_MEMBER);
 357             setBoundVar = true;
 358             d_setm_range[f][v] = bound_lit_map[2][v][1];
 359             d_setm_range_lit[f][v] = bound_lit_map[2][v];
 360             d_range[f][v] = nm->mkNode(CARD, d_setm_range[f][v]);
 361             Trace("bound-int") << "Variable " << v
 362                                << " is bound because of set membership literal "
 363                                << bound_lit_map[2][v] << std::endl;
 364           }
 365         }else if( it->second==BOUND_FIXED_SET ){
 366           setBoundedVar(f, v, BOUND_FIXED_SET);
 367           setBoundVar = true;
 368           for (unsigned i = 0; i < bound_fixed_set[v].size(); i++)
 369           {
 370             Node t = bound_fixed_set[v][i];
 371             if (expr::hasBoundVar(t))
 372             {
 373               d_fixed_set_ngr_range[f][v].push_back(t);
 374             }
 375             else
 376             {
 377               d_fixed_set_gr_range[f][v].push_back(t);
 378             }
 379           }
 380           Trace("bound-int") << "Variable " << v
 381                              << " is bound because of disequality conjunction "
 382                              << bound_lit_map[3][v] << std::endl;
 383         }
 384         if( setBoundVar ){
 385           success = true;
 386           //set Attributes on literals
 387           for( unsigned b=0; b<2; b++ ){
 388             std::map<Node, Node>& blm = bound_lit_map[b];
 389             if (blm.find(v) != blm.end())
 390             {
 391               std::map<Node, bool>& blmp = bound_lit_pol_map[b];
 392               // WARNING_CANDIDATE:
 393               // This assertion may fail. We intentionally do not enable this in
 394               // production as it is considered safe for this to fail. We fail
 395               // the assertion in debug mode to have this instance raised to
 396               // our attention.
 397               Assert(blmp.find(v) != blmp.end());
 398               BoundIntLitAttribute bila;
 399               bound_lit_map[b][v].setAttribute(bila, blmp[v] ? 1 : 0);
 400             }
 401             else
 402             {
 403               Assert(it->second != BOUND_INT_RANGE);
 404             }
 405           }
 406         }
 407       }
 408     }
 409     if( !success ){
 410       //resort to setting a finite bound on a variable
 411       for( unsigned i=0; i<f[0].getNumChildren(); i++) {
 412         if( d_bound_type[f].find( f[0][i] )==d_bound_type[f].end() ){
 413           TypeNode tn = f[0][i].getType();
 414           if ((tn.isSort() && tn.isInterpretedFinite())
 415               || d_quantEngine->getTermEnumeration()->mayComplete(tn))
 416           {
 417             success = true;
 418             setBoundedVar( f, f[0][i], BOUND_FINITE );
 419             break;
 420           }
 421         }
 422       }
 423     }
 424   }while( success );
 425
 426   if( Trace.isOn("bound-int") ){
 427     Trace("bound-int") << "Bounds are : " << std::endl;
 428     for( unsigned i=0; i<f[0].getNumChildren(); i++) {
 429       Node v = f[0][i];
 430       if( std::find( d_set[f].begin(), d_set[f].end(), v )!=d_set[f].end() ){
 431         Assert(d_bound_type[f].find(v) != d_bound_type[f].end());
 432         if( d_bound_type[f][v]==BOUND_INT_RANGE ){
 433           Trace("bound-int") << "  " << d_bounds[0][f][v] << " <= " << v << " <= " << d_bounds[1][f][v] << " (range is " << d_range[f][v] << ")" << std::endl;
 434         }else if( d_bound_type[f][v]==BOUND_SET_MEMBER ){
 435           if( d_setm_range_lit[f][v][0]==v ){
 436             Trace("bound-int") << "  " << v << " in " << d_setm_range[f][v] << std::endl;
 437           }else{
 438             Trace("bound-int") << "  " << v << " unifiable in " << d_setm_range_lit[f][v] << std::endl;
 439           }
 440         }else if( d_bound_type[f][v]==BOUND_FIXED_SET ){
 441           Trace("bound-int") << "  " << v << " in { ";
 442           for (TNode fnr : d_fixed_set_ngr_range[f][v])
 443           {
 444             Trace("bound-int") << fnr << " ";
 445           }
 446           for (TNode fgr : d_fixed_set_gr_range[f][v])
 447           {
 448             Trace("bound-int") << fgr << " ";
 449           }
 450           Trace("bound-int") << "}" << std::endl;
 451         }else if( d_bound_type[f][v]==BOUND_FINITE ){
 452           Trace("bound-int") << "  " << v << " has small finite type." << std::endl;
 453         }else{
 454           Trace("bound-int") << "  " << v << " has unknown bound." << std::endl;
 455           Assert(false);
 456         }
 457       }else{
 458         Trace("bound-int") << "  " << "*** " << v << " is unbounded." << std::endl;
 459       }
 460     }
 461   }
 462
 463   bool bound_success = true;
 464   for( unsigned i=0; i<f[0].getNumChildren(); i++) {
 465     if( d_bound_type[f].find( f[0][i] )==d_bound_type[f].end() ){
 466       Trace("bound-int-warn") << "Warning : Bounded Integers : Due to quantification on " << f[0][i] << ", could not find bounds for " << f << std::endl;
 467       bound_success = false;
 468       break;
 469     }
 470   }
 471
 472   if( bound_success ){
 473     d_bound_quants.push_back( f );
 474     for( unsigned i=0; i<d_set[f].size(); i++) {
 475       Node v = d_set[f][i];
 476       std::map< Node, Node >::iterator itr = d_range[f].find( v );
 477       if( itr != d_range[f].end() ){
 478         Node r = itr->second;
 479         Assert(!r.isNull());
 480         bool isProxy = false;
 481         if (expr::hasBoundVar(r))
 482         {
 483           // introduce a new bound
 484           Node new_range = NodeManager::currentNM()->mkSkolem(
 485               "bir", r.getType(), "bound for term");
 486           d_nground_range[f][v] = r;
 487           d_range[f][v] = new_range;
 488           r = new_range;
 489           isProxy = true;
 490         }
 491         if( !r.isConst() ){
 492           if (d_rms.find(r) == d_rms.end())
 493           {
 494             Trace("bound-int") << "For " << v << ", bounded Integer Module will try to minimize : " << r << std::endl;
 495             d_ranges.push_back( r );
 496             d_rms[r].reset(
 497                 new IntRangeDecisionHeuristic(r,
 498                                               d_qstate.getSatContext(),
 499                                               d_qstate.getUserContext(),
 500                                               d_quantEngine->getValuation(),
 501                                               isProxy));
 502             d_quantEngine->getTheoryEngine()
 503                 ->getDecisionManager()
 504                 ->registerStrategy(DecisionManager::STRAT_QUANT_BOUND_INT_SIZE,
 505                                    d_rms[r].get());
 506           }
 507         }
 508       }
 509     }
 510   }
 511 }
 512
 513 bool BoundedIntegers::isBound(Node q, Node v) const
 514 {
 515   std::map<Node, std::vector<Node> >::const_iterator its = d_set.find(q);
 516   if (its == d_set.end())
 517   {
 518     return false;
 519   }
 520   return std::find(its->second.begin(), its->second.end(), v)
 521          != its->second.end();
 522 }
 523
 524 BoundVarType BoundedIntegers::getBoundVarType(Node q, Node v) const
 525 {
 526   std::map<Node, std::map<Node, BoundVarType> >::const_iterator itb =
 527       d_bound_type.find(q);
 528   if (itb == d_bound_type.end())
 529   {
 530     return BOUND_NONE;
 531   }
 532   std::map<Node, BoundVarType>::const_iterator it = itb->second.find(v);
 533   if (it == itb->second.end())
 534   {
 535     return BOUND_NONE;
 536   }
 537   return it->second;
 538 }
 539
 540 void BoundedIntegers::getBoundVarIndices(Node q,
 541                                          std::vector<unsigned>& indices) const
 542 {
 543   std::map<Node, std::vector<Node> >::const_iterator it = d_set.find(q);
 544   if (it != d_set.end())
 545   {
 546     for (const Node& v : it->second)
 547     {
 548       indices.push_back(d_quantEngine->getTermUtil()->getVariableNum(q, v));
 549     }
 550   }
 551 }
 552
 553 void BoundedIntegers::getBounds( Node f, Node v, RepSetIterator * rsi, Node & l, Node & u ) {
 554   l = d_bounds[0][f][v];
 555   u = d_bounds[1][f][v];
 556   if( d_nground_range[f].find(v)!=d_nground_range[f].end() ){
 557     //get the substitution
 558     std::vector< Node > vars;
 559     std::vector< Node > subs;
 560     if( getRsiSubsitution( f, v, vars, subs, rsi ) ){
 561       u = u.substitute( vars.begin(), vars.end(), subs.begin(), subs.end() );
 562       l = l.substitute( vars.begin(), vars.end(), subs.begin(), subs.end() );
 563     }else{
 564       u = Node::null();
 565       l = Node::null();
 566     }
 567   }
 568 }
 569
 570 void BoundedIntegers::getBoundValues( Node f, Node v, RepSetIterator * rsi, Node & l, Node & u ) {
 571   getBounds( f, v, rsi, l, u );
 572   Trace("bound-int-rsi") << "Get value in model for..." << l << " and " << u << std::endl;
 573   if( !l.isNull() ){
 574     l = d_quantEngine->getModel()->getValue( l );
 575   }
 576   if( !u.isNull() ){
 577     u = d_quantEngine->getModel()->getValue( u );
 578   }
 579   Trace("bound-int-rsi") << "Value is " << l << " ... " << u << std::endl;
 580   return;
 581 }
 582
 583 bool BoundedIntegers::isGroundRange(Node q, Node v)
 584 {
 585   if (isBound(q, v))
 586   {
 587     if (d_bound_type[q][v] == BOUND_INT_RANGE)
 588     {
 589       return !expr::hasBoundVar(getLowerBound(q, v))
 590              && !expr::hasBoundVar(getUpperBound(q, v));
 591     }
 592     else if (d_bound_type[q][v] == BOUND_SET_MEMBER)
 593     {
 594       return !expr::hasBoundVar(d_setm_range[q][v]);
 595     }
 596     else if (d_bound_type[q][v] == BOUND_FIXED_SET)
 597     {
 598       return !d_fixed_set_ngr_range[q][v].empty();
 599     }
 600   }
 601   return false;
 602 }
 603
 604 Node BoundedIntegers::getSetRange( Node q, Node v, RepSetIterator * rsi ) {
 605   Node sr = d_setm_range[q][v];
 606   if( d_nground_range[q].find(v)!=d_nground_range[q].end() ){
 607     Trace("bound-int-rsi-debug")
 608         << sr << " is non-ground, apply substitution..." << std::endl;
 609     //get the substitution
 610     std::vector< Node > vars;
 611     std::vector< Node > subs;
 612     if( getRsiSubsitution( q, v, vars, subs, rsi ) ){
 613       Trace("bound-int-rsi-debug")
 614           << "  apply " << vars << " -> " << subs << std::endl;
 615       sr = sr.substitute( vars.begin(), vars.end(), subs.begin(), subs.end() );
 616     }else{
 617       sr = Node::null();
 618     }
 619   }
 620   return sr;
 621 }
 622
 623 Node BoundedIntegers::getSetRangeValue( Node q, Node v, RepSetIterator * rsi ) {
 624   Node sr = getSetRange( q, v, rsi );
 625   if (sr.isNull())
 626   {
 627     return sr;
 628   }
 629   Trace("bound-int-rsi") << "Get value in model for..." << sr << std::endl;
 630   Assert(!expr::hasFreeVar(sr));
 631   Node sro = sr;
 632   sr = d_quantEngine->getModel()->getValue(sr);
 633   // if non-constant, then sr does not occur in the model, we fail
 634   if (!sr.isConst())
 635   {
 636     return Node::null();
 637   }
 638   Trace("bound-int-rsi") << "Value is " << sr << std::endl;
 639   if (sr.getKind() == EMPTYSET)
 640   {
 641     return sr;
 642   }
 643   NodeManager* nm = NodeManager::currentNM();
 644   Node nsr;
 645   TypeNode tne = sr.getType().getSetElementType();
 646
 647   // we can use choice functions for canonical symbolic instantiations
 648   unsigned srCard = 0;
 649   while (sr.getKind() == UNION)
 650   {
 651     srCard++;
 652     sr = sr[0];
 653   }
 654   Assert(sr.getKind() == SINGLETON);
 655   srCard++;
 656   // choices[i] stores the canonical symbolic representation of the (i+1)^th
 657   // element of sro
 658   std::vector<Node> choices;
 659   Node srCardN = nm->mkNode(CARD, sro);
 660   Node choice_i;
 661   for (unsigned i = 0; i < srCard; i++)
 662   {
 663     if (i == d_setm_choice[sro].size())
 664     {
 665       choice_i = nm->mkBoundVar(tne);
 666       choices.push_back(choice_i);
 667       Node cBody = nm->mkNode(MEMBER, choice_i, sro);
 668       if (choices.size() > 1)
 669       {
 670         cBody = nm->mkNode(AND, cBody, nm->mkNode(DISTINCT, choices));
 671       }
 672       choices.pop_back();
 673       Node bvl = nm->mkNode(BOUND_VAR_LIST, choice_i);
 674       Node cMinCard = nm->mkNode(LEQ, srCardN, nm->mkConst(Rational(i)));
 675       choice_i = nm->mkNode(WITNESS, bvl, nm->mkNode(OR, cMinCard, cBody));
 676       d_setm_choice[sro].push_back(choice_i);
 677     }
 678     Assert(i < d_setm_choice[sro].size());
 679     choice_i = d_setm_choice[sro][i];
 680     choices.push_back(choice_i);
 681     Node sChoiceI = nm->mkSingleton(choice_i.getType(), choice_i);
 682     if (nsr.isNull())
 683     {
 684       nsr = sChoiceI;
 685     }
 686     else
 687     {
 688       nsr = nm->mkNode(UNION, nsr, sChoiceI);
 689     }
 690   }
 691   // turns the concrete model value of sro into a canonical representation
 692   //   e.g.
 693   // singleton(0) union singleton(1)
 694   //   becomes
 695   // C1 union ( witness y. card(S)<=1 OR ( y in S AND distinct( y, C1 ) ) )
 696   // where C1 = ( witness x. card(S)<=0 OR x in S ).
 697   Trace("bound-int-rsi") << "...reconstructed " << nsr << std::endl;
 698   return nsr;
 699 }
 700
 701 bool BoundedIntegers::getRsiSubsitution( Node q, Node v, std::vector< Node >& vars, std::vector< Node >& subs, RepSetIterator * rsi ) {
 702
 703   Trace("bound-int-rsi") << "Get bound value in model of variable " << v << std::endl;
 704   Assert(d_set_nums[q].find(v) != d_set_nums[q].end());
 705   int vindex = d_set_nums[q][v];
 706   Assert(d_set_nums[q][v] == vindex);
 707   Trace("bound-int-rsi-debug") << "  index order is " << vindex << std::endl;
 708   //must take substitution for all variables that are iterating at higher level
 709   for( int i=0; i<vindex; i++) {
 710     Assert(d_set_nums[q][d_set[q][i]] == i);
 711     Trace("bound-int-rsi") << "Look up the value for " << d_set[q][i] << " " << i << std::endl;
 712     int vo = rsi->getVariableOrder(i);
 713     Assert(q[0][vo] == d_set[q][i]);
 714     Node t = rsi->getCurrentTerm(vo, true);
 715     Trace("bound-int-rsi") << "term : " << t << std::endl;
 716     vars.push_back( d_set[q][i] );
 717     subs.push_back( t );
 718   }
 719
 720   //check if it has been instantiated
 721   if( !vars.empty() && !d_bnd_it[q][v].hasInstantiated(subs) ){
 722     if( d_bound_type[q][v]==BOUND_INT_RANGE || d_bound_type[q][v]==BOUND_SET_MEMBER ){
 723       //must add the lemma
 724       Node nn = d_nground_range[q][v];
 725       nn = nn.substitute( vars.begin(), vars.end(), subs.begin(), subs.end() );
 726       Node lem = NodeManager::currentNM()->mkNode( LEQ, nn, d_range[q][v] );
 727       Trace("bound-int-lemma") << "*** Add lemma to minimize instantiated non-ground term " << lem << std::endl;
 728       d_quantEngine->getOutputChannel().lemma(lem);
 729     }
 730     return false;
 731   }else{
 732     return true;
 733   }
 734 }
 735
 736 Node BoundedIntegers::matchBoundVar( Node v, Node t, Node e ){
 737   if( t==v ){
 738     return e;
 739   }else if( t.getKind()==kind::APPLY_CONSTRUCTOR ){
 740     if( e.getKind()==kind::APPLY_CONSTRUCTOR ){
 741       if( t.getOperator() != e.getOperator() ) {
 742         return Node::null();
 743       }
 744     }
 745     NodeManager* nm = NodeManager::currentNM();
 746     const DType& dt = datatypes::utils::datatypeOf(t.getOperator());
 747     unsigned index = datatypes::utils::indexOf(t.getOperator());
 748     for( unsigned i=0; i<t.getNumChildren(); i++ ){
 749       Node u;
 750       if( e.getKind()==kind::APPLY_CONSTRUCTOR ){
 751         u = matchBoundVar( v, t[i], e[i] );
 752       }else{
 753         Node se = nm->mkNode(APPLY_SELECTOR_TOTAL,
 754                              dt[index].getSelectorInternal(e.getType(), i),
 755                              e);
 756         u = matchBoundVar( v, t[i], se );
 757       }
 758       if( !u.isNull() ){
 759         return u;
 760       }
 761     }
 762   }
 763   return Node::null();
 764 }
 765
 766 bool BoundedIntegers::getBoundElements( RepSetIterator * rsi, bool initial, Node q, Node v, std::vector< Node >& elements ) {
 767   if( initial || !isGroundRange( q, v ) ){
 768     elements.clear();
 769     BoundVarType bvt = getBoundVarType(q, v);
 770     if( bvt==BOUND_INT_RANGE ){
 771       Node l, u;
 772       getBoundValues( q, v, rsi, l, u );
 773       if( l.isNull() || u.isNull() ){
 774         Trace("bound-int-warn") << "WARNING: Could not find integer bounds in model for " << v << " in " << q << std::endl;
 775         //failed, abort the iterator
 776         return false;
 777       }else{
 778         Trace("bound-int-rsi") << "Can limit bounds of " << v << " to " << l << "..." << u << std::endl;
 779         Node range = Rewriter::rewrite( NodeManager::currentNM()->mkNode( MINUS, u, l ) );
 780         Node ra = Rewriter::rewrite( NodeManager::currentNM()->mkNode( LEQ, range, NodeManager::currentNM()->mkConst( Rational( 9999 ) ) ) );
 781         Node tl = l;
 782         Node tu = u;
 783         getBounds( q, v, rsi, tl, tu );
 784         Assert(!tl.isNull() && !tu.isNull());
 785         if( ra==d_quantEngine->getTermUtil()->d_true ){
 786           long rr = range.getConst<Rational>().getNumerator().getLong()+1;
 787           Trace("bound-int-rsi")  << "Actual bound range is " << rr << std::endl;
 788           for( unsigned k=0; k<rr; k++ ){
 789             Node t = NodeManager::currentNM()->mkNode(PLUS, tl, NodeManager::currentNM()->mkConst( Rational(k) ) );
 790             t = Rewriter::rewrite( t );
 791             elements.push_back( t );
 792           }
 793           return true;
 794         }else{
 795           Trace("fmf-incomplete") << "Incomplete because of integer quantification, bounds are too big for " << v << "." << std::endl;
 796           return false;
 797         }
 798       }
 799     }else if( bvt==BOUND_SET_MEMBER  ){
 800       Node srv = getSetRangeValue( q, v, rsi );
 801       if( srv.isNull() ){
 802         Trace("bound-int-warn") << "WARNING: Could not find set bound in model for " << v << " in " << q << std::endl;
 803         return false;
 804       }else{
 805         Trace("bound-int-rsi") << "Bounded by set membership : " << srv << std::endl;
 806         if( srv.getKind()!=EMPTYSET ){
 807           //collect the elements
 808           while( srv.getKind()==UNION ){
 809             Assert(srv[1].getKind() == kind::SINGLETON);
 810             elements.push_back( srv[1][0] );
 811             srv = srv[0];
 812           }
 813           Assert(srv.getKind() == kind::SINGLETON);
 814           elements.push_back( srv[0] );
 815           //check if we need to do matching, for literals like ( tuple( v ) in S )
 816           Node t = d_setm_range_lit[q][v][0];
 817           if( t!=v ){
 818             std::vector< Node > elements_tmp;
 819             elements_tmp.insert( elements_tmp.end(), elements.begin(), elements.end() );
 820             elements.clear();
 821             for( unsigned i=0; i<elements_tmp.size(); i++ ){
 822               //do matching to determine v -> u
 823               Node u = matchBoundVar( v, t, elements_tmp[i] );
 824               Trace("bound-int-rsi-debug") << "  unification : " << elements_tmp[i] << " = " << t << " yields " << v << " -> " << u << std::endl;
 825               if( !u.isNull() ){
 826                 elements.push_back( u );
 827               }
 828             }
 829           }
 830         }
 831         return true;
 832       }
 833     }else if( bvt==BOUND_FIXED_SET ){
 834       std::map< Node, std::vector< Node > >::iterator it = d_fixed_set_gr_range[q].find( v );
 835       if( it!=d_fixed_set_gr_range[q].end() ){
 836         for( unsigned i=0; i<it->second.size(); i++ ){
 837           elements.push_back( it->second[i] );
 838         }
 839       }
 840       it = d_fixed_set_ngr_range[q].find( v );
 841       if( it!=d_fixed_set_ngr_range[q].end() ){
 842         std::vector< Node > vars;
 843         std::vector< Node > subs;
 844         if( getRsiSubsitution( q, v, vars, subs, rsi ) ){
 845           for( unsigned i=0; i<it->second.size(); i++ ){
 846             Node t = it->second[i].substitute( vars.begin(), vars.end(), subs.begin(), subs.end() );
 847             elements.push_back( t );
 848           }
 849           return true;
 850         }else{
 851           return false;
 852         }
 853       }else{
 854         return true;
 855       }
 856     }else{
 857       return false;
 858     }
 859   }else{
 860     //no change required
 861     return true;
 862   }
 863 }