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