src/theory/sort_inference.cpp

   1 /*********************                                                        */
   2 /*! \file sort_inference.cpp
   3  ** \verbatim
   4  ** Top contributors (to current version):
   5  **   Andrew Reynolds, Paul Meng, Kshitij Bansal
   6  ** This file is part of the CVC4 project.
   7  ** Copyright (c) 2009-2019 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 Sort inference module
  13  **
  14  ** This class implements sort inference, based on a simple algorithm:
  15  ** First, we assume all functions and predicates have distinct uninterpreted types.
  16  ** One pass is made through the input assertions, while a union-find data structure
  17  ** maintains necessary information regarding constraints on these types.
  18  **/
  19
  20 #include "theory/sort_inference.h"
  21
  22 #include <vector>
  23
  24 #include "options/quantifiers_options.h"
  25 #include "options/smt_options.h"
  26 #include "options/uf_options.h"
  27 #include "proof/proof_manager.h"
  28 #include "theory/rewriter.h"
  29 #include "theory/quantifiers/quant_util.h"
  30
  31 using namespace CVC4;
  32 using namespace std;
  33
  34 namespace CVC4 {
  35
  36 void SortInference::UnionFind::print(const char * c){
  37   for( std::map< int, int >::iterator it = d_eqc.begin(); it != d_eqc.end(); ++it ){
  38     Trace(c) << "s_" << it->first << " = s_" << it->second << ", ";
  39   }
  40   for( unsigned i=0; i<d_deq.size(); i++ ){
  41     Trace(c) << "s_" << d_deq[i].first << " != s_" << d_deq[i].second << ", ";
  42   }
  43   Trace(c) << std::endl;
  44 }
  45 void SortInference::UnionFind::set( UnionFind& c ) {
  46   clear();
  47   for( std::map< int, int >::iterator it = c.d_eqc.begin(); it != c.d_eqc.end(); ++it ){
  48     d_eqc[ it->first ] = it->second;
  49   }
  50   d_deq.insert( d_deq.end(), c.d_deq.begin(), c.d_deq.end() );
  51 }
  52 int SortInference::UnionFind::getRepresentative( int t ){
  53   std::map< int, int >::iterator it = d_eqc.find( t );
  54   if( it==d_eqc.end() || it->second==t ){
  55     return t;
  56   }else{
  57     int rt = getRepresentative( it->second );
  58     d_eqc[t] = rt;
  59     return rt;
  60   }
  61 }
  62 void SortInference::UnionFind::setEqual( int t1, int t2 ){
  63   if( t1!=t2 ){
  64     int rt1 = getRepresentative( t1 );
  65     int rt2 = getRepresentative( t2 );
  66     if( rt1>rt2 ){
  67       d_eqc[rt1] = rt2;
  68     }else{
  69       d_eqc[rt2] = rt1;
  70     }
  71   }
  72 }
  73 bool SortInference::UnionFind::isValid() {
  74   for( unsigned i=0; i<d_deq.size(); i++ ){
  75     if( areEqual( d_deq[i].first, d_deq[i].second ) ){
  76       return false;
  77     }
  78   }
  79   return true;
  80 }
  81
  82
  83 void SortInference::recordSubsort( TypeNode tn, int s ){
  84   s = d_type_union_find.getRepresentative( s );
  85   if( std::find( d_sub_sorts.begin(), d_sub_sorts.end(), s )==d_sub_sorts.end() ){
  86     d_sub_sorts.push_back( s );
  87     d_type_sub_sorts[tn].push_back( s );
  88   }
  89 }
  90
  91 void SortInference::printSort( const char* c, int t ){
  92   int rt = d_type_union_find.getRepresentative( t );
  93   if( d_type_types.find( rt )!=d_type_types.end() ){
  94     Trace(c) << d_type_types[rt];
  95   }else{
  96     Trace(c) << "s_" << rt;
  97   }
  98 }
  99
 100 void SortInference::reset() {
 101   d_sub_sorts.clear();
 102   d_non_monotonic_sorts.clear();
 103   d_type_sub_sorts.clear();
 104   //reset info
 105   d_sortCount = 1;
 106   d_type_union_find.clear();
 107   d_type_types.clear();
 108   d_id_for_types.clear();
 109   d_op_return_types.clear();
 110   d_op_arg_types.clear();
 111   d_var_types.clear();
 112   //for rewriting
 113   d_symbol_map.clear();
 114   d_const_map.clear();
 115 }
 116
 117 void SortInference::initialize(const std::vector<Node>& assertions)
 118 {
 119   Trace("sort-inference-proc") << "Calculating sort inference..." << std::endl;
 120   // process all assertions
 121   std::map<Node, int> visited;
 122   NodeManager * nm = NodeManager::currentNM();
 123   int btId = getIdForType( nm->booleanType() );
 124   for (const Node& a : assertions)
 125   {
 126     Trace("sort-inference-debug") << "Process " << a << std::endl;
 127     std::map<Node, Node> var_bound;
 128     int pid = process(a, var_bound, visited);
 129     // the type of the topmost term must be Boolean
 130     setEqual( pid, btId );
 131   }
 132   Trace("sort-inference-proc") << "...done" << std::endl;
 133   for (const std::pair<const Node, int>& rt : d_op_return_types)
 134   {
 135     Trace("sort-inference") << rt.first << " : ";
 136     TypeNode retTn = rt.first.getType();
 137     if (!d_op_arg_types[rt.first].empty())
 138     {
 139       Trace("sort-inference") << "( ";
 140       for (size_t i = 0; i < d_op_arg_types[rt.first].size(); i++)
 141       {
 142         recordSubsort(retTn[i], d_op_arg_types[rt.first][i]);
 143         printSort("sort-inference", d_op_arg_types[rt.first][i]);
 144         Trace("sort-inference") << " ";
 145       }
 146       Trace("sort-inference") << ") -> ";
 147       retTn = retTn[(int)retTn.getNumChildren() - 1];
 148     }
 149     recordSubsort(retTn, rt.second);
 150     printSort("sort-inference", rt.second);
 151     Trace("sort-inference") << std::endl;
 152   }
 153   for (std::pair<const Node, std::map<Node, int> >& vt : d_var_types)
 154   {
 155     Trace("sort-inference")
 156         << "Quantified formula : " << vt.first << " : " << std::endl;
 157     for (const Node& v : vt.first[0])
 158     {
 159       recordSubsort(v.getType(), vt.second[v]);
 160       printSort("sort-inference", vt.second[v]);
 161       Trace("sort-inference") << std::endl;
 162     }
 163     Trace("sort-inference") << std::endl;
 164   }
 165
 166   // determine monotonicity of sorts
 167   Trace("sort-inference-proc")
 168       << "Calculating monotonicty for subsorts..." << std::endl;
 169   std::map<Node, std::map<int, bool> > visitedm;
 170   for (const Node& a : assertions)
 171   {
 172     Trace("sort-inference-debug")
 173         << "Process monotonicity for " << a << std::endl;
 174     std::map<Node, Node> var_bound;
 175     processMonotonic(a, true, true, var_bound, visitedm);
 176   }
 177   Trace("sort-inference-proc") << "...done" << std::endl;
 178
 179   Trace("sort-inference") << "We have " << d_sub_sorts.size()
 180                           << " sub-sorts : " << std::endl;
 181   for (unsigned i = 0, size = d_sub_sorts.size(); i < size; i++)
 182   {
 183     printSort("sort-inference", d_sub_sorts[i]);
 184     if (d_type_types.find(d_sub_sorts[i]) != d_type_types.end())
 185     {
 186       Trace("sort-inference") << " is interpreted." << std::endl;
 187     }
 188     else if (d_non_monotonic_sorts.find(d_sub_sorts[i])
 189              == d_non_monotonic_sorts.end())
 190     {
 191       Trace("sort-inference") << " is monotonic." << std::endl;
 192     }
 193     else
 194     {
 195       Trace("sort-inference") << " is not monotonic." << std::endl;
 196     }
 197   }
 198 }
 199
 200 Node SortInference::simplify(Node n,
 201                              std::map<Node, Node>& model_replace_f,
 202                              std::map<Node, std::map<TypeNode, Node> >& visited)
 203 {
 204   Trace("sort-inference-debug") << "Simplify " << n << std::endl;
 205   std::map<Node, Node> var_bound;
 206   TypeNode tnn;
 207   Node ret = simplifyNode(n, var_bound, tnn, model_replace_f, visited);
 208   ret = theory::Rewriter::rewrite(ret);
 209   return ret;
 210 }
 211
 212 void SortInference::getNewAssertions(std::vector<Node>& new_asserts)
 213 {
 214   NodeManager* nm = NodeManager::currentNM();
 215   // now, ensure constants are distinct
 216   for (const std::pair<const TypeNode, std::map<Node, Node> >& cm : d_const_map)
 217   {
 218     std::vector<Node> consts;
 219     for (const std::pair<const Node, Node>& c : cm.second)
 220     {
 221       Assert(c.first.isConst());
 222       consts.push_back(c.second);
 223     }
 224     // add lemma enforcing introduced constants to be distinct
 225     if (consts.size() > 1)
 226     {
 227       Node distinct_const = nm->mkNode(kind::DISTINCT, consts);
 228       Trace("sort-inference-rewrite")
 229           << "Add the constant distinctness lemma: " << std::endl;
 230       Trace("sort-inference-rewrite") << "  " << distinct_const << std::endl;
 231       new_asserts.push_back(distinct_const);
 232     }
 233   }
 234
 235   // enforce constraints based on monotonicity
 236   Trace("sort-inference-proc") << "Enforce monotonicity..." << std::endl;
 237
 238   for (const std::pair<const TypeNode, std::vector<int> >& tss :
 239        d_type_sub_sorts)
 240   {
 241     int nmonSort = -1;
 242     unsigned nsorts = tss.second.size();
 243     for (unsigned i = 0; i < nsorts; i++)
 244     {
 245       if (d_non_monotonic_sorts.find(tss.second[i])
 246           != d_non_monotonic_sorts.end())
 247       {
 248         nmonSort = tss.second[i];
 249         break;
 250       }
 251     }
 252     if (nmonSort != -1)
 253     {
 254       std::vector<Node> injections;
 255       TypeNode base_tn = getOrCreateTypeForId(nmonSort, tss.first);
 256       for (unsigned i = 0; i < nsorts; i++)
 257       {
 258         if (tss.second[i] != nmonSort)
 259         {
 260           TypeNode new_tn = getOrCreateTypeForId(tss.second[i], tss.first);
 261           // make injection to nmonSort
 262           Node a1 = mkInjection(new_tn, base_tn);
 263           injections.push_back(a1);
 264           if (d_non_monotonic_sorts.find(tss.second[i])
 265               != d_non_monotonic_sorts.end())
 266           {
 267             // also must make injection from nmonSort to this
 268             Node a2 = mkInjection(base_tn, new_tn);
 269             injections.push_back(a2);
 270           }
 271         }
 272       }
 273       if (Trace.isOn("sort-inference-rewrite"))
 274       {
 275         Trace("sort-inference-rewrite")
 276             << "Add the following injections for " << tss.first
 277             << " to ensure consistency wrt non-monotonic sorts : " << std::endl;
 278         for (const Node& i : injections)
 279         {
 280           Trace("sort-inference-rewrite") << "   " << i << std::endl;
 281         }
 282       }
 283       new_asserts.insert(
 284           new_asserts.end(), injections.begin(), injections.end());
 285     }
 286   }
 287   Trace("sort-inference-proc") << "...done" << std::endl;
 288   // no sub-sort information is stored
 289   reset();
 290   Trace("sort-inference-debug") << "Finished sort inference" << std::endl;
 291 }
 292
 293 void SortInference::computeMonotonicity(const std::vector<Node>& assertions)
 294 {
 295   std::map<Node, std::map<int, bool> > visitedmt;
 296   Trace("sort-inference-proc")
 297       << "Calculating monotonicty for types..." << std::endl;
 298   for (const Node& a : assertions)
 299   {
 300     Trace("sort-inference-debug")
 301         << "Process type monotonicity for " << a << std::endl;
 302     std::map<Node, Node> var_bound;
 303     processMonotonic(a, true, true, var_bound, visitedmt, true);
 304   }
 305   Trace("sort-inference-proc") << "...done" << std::endl;
 306 }
 307
 308 void SortInference::setEqual( int t1, int t2 ){
 309   if( t1!=t2 ){
 310     int rt1 = d_type_union_find.getRepresentative( t1 );
 311     int rt2 = d_type_union_find.getRepresentative( t2 );
 312     if( rt1!=rt2 ){
 313       Trace("sort-inference-debug") << "Set equal : ";
 314       printSort( "sort-inference-debug", rt1 );
 315       Trace("sort-inference-debug") << " ";
 316       printSort( "sort-inference-debug", rt2 );
 317       Trace("sort-inference-debug") << std::endl;
 318       /*
 319       d_type_eq_class[rt1].insert( d_type_eq_class[rt1].end(), d_type_eq_class[rt2].begin(), d_type_eq_class[rt2].end() );
 320       d_type_eq_class[rt2].clear();
 321       Trace("sort-inference-debug") << "EqClass : { ";
 322       for( int i=0; i<(int)d_type_eq_class[rt1].size(); i++ ){
 323         Trace("sort-inference-debug") << d_type_eq_class[rt1][i] << ", ";
 324       }
 325       Trace("sort-inference-debug") << "}" << std::endl;
 326       */
 327       if( rt2>rt1 ){
 328         //swap
 329         int swap = rt1;
 330         rt1 = rt2;
 331         rt2 = swap;
 332       }
 333       std::map< int, TypeNode >::iterator it1 = d_type_types.find( rt1 );
 334       if( it1!=d_type_types.end() ){
 335         if( d_type_types.find( rt2 )==d_type_types.end() ){
 336           d_type_types[rt2] = it1->second;
 337           d_type_types.erase( rt1 );
 338         }else{
 339           Trace("sort-inference-debug") << "...fail : associated with types " << d_type_types[rt1] << " and " << d_type_types[rt2] << std::endl;
 340           return;
 341         }
 342       }
 343       d_type_union_find.d_eqc[rt1] = rt2;
 344     }
 345   }
 346 }
 347
 348 int SortInference::getIdForType( TypeNode tn ){
 349   //register the return type
 350   std::map< TypeNode, int >::iterator it = d_id_for_types.find( tn );
 351   if( it==d_id_for_types.end() ){
 352     int sc = d_sortCount;
 353     d_type_types[d_sortCount] = tn;
 354     d_id_for_types[tn] = d_sortCount;
 355     d_sortCount++;
 356     return sc;
 357   }else{
 358     return it->second;
 359   }
 360 }
 361
 362 int SortInference::process( Node n, std::map< Node, Node >& var_bound, std::map< Node, int >& visited ){
 363   std::map< Node, int >::iterator itv = visited.find( n );
 364   if( itv!=visited.end() ){
 365     return itv->second;
 366   }else{
 367     //add to variable bindings
 368     bool use_new_visited = false;
 369     std::map< Node, int > new_visited;
 370     if( n.getKind()==kind::FORALL || n.getKind()==kind::EXISTS ){
 371       if( d_var_types.find( n )!=d_var_types.end() ){
 372         return getIdForType( n.getType() );
 373       }else{
 374         //apply sort inference to quantified variables
 375         for( size_t i=0; i<n[0].getNumChildren(); i++ ){
 376           TypeNode nitn = n[0][i].getType();
 377           if( !nitn.isSort() )
 378           {
 379             // If the variable is of an interpreted sort, we assume the
 380             // the sort of the variable will stay the same sort.
 381             d_var_types[n][n[0][i]] = getIdForType( nitn );
 382           }
 383           else
 384           {
 385             // If it is of an uninterpreted sort, infer subsorts.
 386             d_var_types[n][n[0][i]] = d_sortCount;
 387             d_sortCount++;
 388           }
 389           var_bound[ n[0][i] ] = n;
 390         }
 391       }
 392       use_new_visited = true;
 393     }
 394
 395     //process children
 396     std::vector< Node > children;
 397     std::vector< int > child_types;
 398     for( size_t i=0; i<n.getNumChildren(); i++ ){
 399       bool processChild = true;
 400       if( n.getKind()==kind::FORALL || n.getKind()==kind::EXISTS ){
 401         processChild =
 402             options::userPatternsQuant() == options::UserPatMode::IGNORE
 403                 ? i == 1
 404                 : i >= 1;
 405       }
 406       if( processChild ){
 407         children.push_back( n[i] );
 408         child_types.push_back( process( n[i], var_bound, use_new_visited ? new_visited : visited ) );
 409       }
 410     }
 411
 412     //remove from variable bindings
 413     if( n.getKind()==kind::FORALL || n.getKind()==kind::EXISTS ){
 414       //erase from variable bound
 415       for( size_t i=0; i<n[0].getNumChildren(); i++ ){
 416         var_bound.erase( n[0][i] );
 417       }
 418     }
 419     Trace("sort-inference-debug") << "...Process " << n << std::endl;
 420
 421     int retType;
 422     if( n.getKind()==kind::EQUAL && !n[0].getType().isBoolean() ){
 423       Trace("sort-inference-debug") << "For equality " << n << ", set equal types from : " << n[0].getType() << " " << n[1].getType() << std::endl;
 424       //if original types are mixed (e.g. Int/Real), don't commit type equality in either direction
 425       if( n[0].getType()!=n[1].getType() ){
 426         //for now, assume the original types
 427         for( unsigned i=0; i<2; i++ ){
 428           int ct = getIdForType( n[i].getType() );
 429           setEqual( child_types[i], ct );
 430         }
 431       }else{
 432         //we only require that the left and right hand side must be equal
 433         setEqual( child_types[0], child_types[1] );
 434       }
 435       d_equality_types[n] = child_types[0];
 436       retType = getIdForType( n.getType() );
 437     }else if( n.getKind()==kind::APPLY_UF ){
 438       Node op = n.getOperator();
 439       TypeNode tn_op = op.getType();
 440       if( d_op_return_types.find( op )==d_op_return_types.end() ){
 441         if( n.getType().isBoolean() ){
 442           //use booleans
 443           d_op_return_types[op] = getIdForType( n.getType() );
 444         }else{
 445           //assign arbitrary sort for return type
 446           d_op_return_types[op] = d_sortCount;
 447           d_sortCount++;
 448         }
 449         // d_type_eq_class[d_sortCount].push_back( op );
 450         // assign arbitrary sort for argument types
 451         for( size_t i=0; i<n.getNumChildren(); i++ ){
 452           d_op_arg_types[op].push_back(d_sortCount);
 453           d_sortCount++;
 454         }
 455       }
 456       for( size_t i=0; i<n.getNumChildren(); i++ ){
 457         //the argument of the operator must match the return type of the subterm
 458         if( n[i].getType()!=tn_op[i] ){
 459           //if type mismatch, assume original types
 460           Trace("sort-inference-debug") << "Argument " << i << " of " << op << " " << n[i] << " has type " << n[i].getType();
 461           Trace("sort-inference-debug") << ", while operator arg has type " << tn_op[i] << std::endl;
 462           int ct1 = getIdForType( n[i].getType() );
 463           setEqual( child_types[i], ct1 );
 464           int ct2 = getIdForType( tn_op[i] );
 465           setEqual( d_op_arg_types[op][i], ct2 );
 466         }else{
 467           setEqual( child_types[i], d_op_arg_types[op][i] );
 468         }
 469       }
 470       //return type is the return type
 471       retType = d_op_return_types[op];
 472     }else{
 473       std::map< Node, Node >::iterator it = var_bound.find( n );
 474       if( it!=var_bound.end() ){
 475         Trace("sort-inference-debug") << n << " is a bound variable." << std::endl;
 476         //the return type was specified while binding
 477         retType = d_var_types[it->second][n];
 478       }else if( n.isVar() ){
 479         Trace("sort-inference-debug") << n << " is a variable." << std::endl;
 480         if( d_op_return_types.find( n )==d_op_return_types.end() ){
 481           //assign arbitrary sort
 482           d_op_return_types[n] = d_sortCount;
 483           d_sortCount++;
 484           // d_type_eq_class[d_sortCount].push_back( n );
 485         }
 486         retType = d_op_return_types[n];
 487       }else if( n.isConst() ){
 488         Trace("sort-inference-debug") << n << " is a constant." << std::endl;
 489         //can be any type we want
 490         retType = d_sortCount;
 491         d_sortCount++;
 492       }else{
 493         Trace("sort-inference-debug") << n << " is a interpreted symbol." << std::endl;
 494         //it is an interpreted term
 495         for( size_t i=0; i<children.size(); i++ ){
 496           Trace("sort-inference-debug") << children[i] << " forced to have " << children[i].getType() << std::endl;
 497           //must enforce the actual type of the operator on the children
 498           int ct = getIdForType( children[i].getType() );
 499           setEqual( child_types[i], ct );
 500         }
 501         //return type must be the actual return type
 502         retType = getIdForType( n.getType() );
 503       }
 504     }
 505     Trace("sort-inference-debug") << "...Type( " << n << " ) = ";
 506     printSort("sort-inference-debug", retType );
 507     Trace("sort-inference-debug") << std::endl;
 508     visited[n] = retType;
 509     return retType;
 510   }
 511 }
 512
 513 void SortInference::processMonotonic( Node n, bool pol, bool hasPol, std::map< Node, Node >& var_bound, std::map< Node, std::map< int, bool > >& visited, bool typeMode ) {
 514   int pindex = hasPol ? ( pol ? 1 : -1 ) : 0;
 515   if( visited[n].find( pindex )==visited[n].end() ){
 516     visited[n][pindex] = true;
 517     Trace("sort-inference-debug") << "...Process monotonic " << pol << " " << hasPol << " " << n << std::endl;
 518     if( n.getKind()==kind::FORALL ){
 519       //only consider variables universally if it is possible this quantified formula is asserted positively
 520       if( !hasPol || pol ){
 521         for( unsigned i=0; i<n[0].getNumChildren(); i++ ){
 522           var_bound[n[0][i]] = n;
 523         }
 524       }
 525       processMonotonic( n[1], pol, hasPol, var_bound, visited, typeMode );
 526       if( !hasPol || pol ){
 527         for( unsigned i=0; i<n[0].getNumChildren(); i++ ){
 528           var_bound.erase( n[0][i] );
 529         }
 530       }
 531       return;
 532     }else if( n.getKind()==kind::EQUAL ){
 533       if( !hasPol || pol ){
 534         for( unsigned i=0; i<2; i++ ){
 535           if( var_bound.find( n[i] )!=var_bound.end() ){
 536             if( !typeMode ){
 537               int sid = getSortId( var_bound[n[i]], n[i] );
 538               d_non_monotonic_sorts[sid] = true;
 539             }else{
 540               d_non_monotonic_sorts_orig[n[i].getType()] = true;
 541             }
 542             break;
 543           }
 544         }
 545       }
 546     }
 547     for( unsigned i=0; i<n.getNumChildren(); i++ ){
 548       bool npol;
 549       bool nhasPol;
 550       theory::QuantPhaseReq::getPolarity( n, i, hasPol, pol, nhasPol, npol );
 551       processMonotonic( n[i], npol, nhasPol, var_bound, visited, typeMode );
 552     }
 553   }
 554 }
 555
 556
 557 TypeNode SortInference::getOrCreateTypeForId( int t, TypeNode pref ){
 558   int rt = d_type_union_find.getRepresentative( t );
 559   if( d_type_types.find( rt )!=d_type_types.end() ){
 560     return d_type_types[rt];
 561   }else{
 562     TypeNode retType;
 563     // See if we can assign pref. This is an optimization for reusing an
 564     // uninterpreted sort as the first subsort, so that fewer symbols needed
 565     // to be rewritten in the sort-inferred signature. Notice we only assign
 566     // pref here if it is an uninterpreted sort.
 567     if (!pref.isNull() && d_id_for_types.find(pref) == d_id_for_types.end()
 568         && pref.isSort())
 569     {
 570       retType = pref;
 571     }else{
 572       //must create new type
 573       std::stringstream ss;
 574       ss << "it_" << t << "_" << pref;
 575       retType = NodeManager::currentNM()->mkSort( ss.str() );
 576     }
 577     Trace("sort-inference") << "-> Make type " << retType << " to correspond to ";
 578     printSort("sort-inference", t );
 579     Trace("sort-inference") << std::endl;
 580     d_id_for_types[ retType ] = rt;
 581     d_type_types[ rt ] = retType;
 582     return retType;
 583   }
 584 }
 585
 586 TypeNode SortInference::getTypeForId( int t ){
 587   int rt = d_type_union_find.getRepresentative( t );
 588   if( d_type_types.find( rt )!=d_type_types.end() ){
 589     return d_type_types[rt];
 590   }else{
 591     return TypeNode::null();
 592   }
 593 }
 594
 595 Node SortInference::getNewSymbol( Node old, TypeNode tn ){
 596   // if no sort was inferred for this node, return original
 597   if( tn.isNull() || tn.isComparableTo( old.getType() ) ){
 598     return old;
 599   }else if( old.isConst() ){
 600     //must make constant of type tn
 601     if( d_const_map[tn].find( old )==d_const_map[tn].end() ){
 602       std::stringstream ss;
 603       ss << "ic_" << tn << "_" << old;
 604       d_const_map[tn][ old ] = NodeManager::currentNM()->mkSkolem( ss.str(), tn, "constant created during sort inference" );  //use mkConst???
 605     }
 606     return d_const_map[tn][ old ];
 607   }else if( old.getKind()==kind::BOUND_VARIABLE ){
 608     std::stringstream ss;
 609     ss << "b_" << old;
 610     return NodeManager::currentNM()->mkBoundVar( ss.str(), tn );
 611   }else{
 612     std::stringstream ss;
 613     ss << "i_" << old;
 614     return NodeManager::currentNM()->mkSkolem( ss.str(), tn, "created during sort inference" );
 615   }
 616 }
 617
 618 Node SortInference::simplifyNode(
 619     Node n,
 620     std::map<Node, Node>& var_bound,
 621     TypeNode tnn,
 622     std::map<Node, Node>& model_replace_f,
 623     std::map<Node, std::map<TypeNode, Node> >& visited)
 624 {
 625   std::map< TypeNode, Node >::iterator itv = visited[n].find( tnn );
 626   if( itv!=visited[n].end() ){
 627     return itv->second;
 628   }else{
 629     Trace("sort-inference-debug2") << "Simplify " << n << ", type context=" << tnn << std::endl;
 630     std::vector< Node > children;
 631     std::map< Node, std::map< TypeNode, Node > > new_visited;
 632     bool use_new_visited = false;
 633     if( n.getKind()==kind::FORALL || n.getKind()==kind::EXISTS ){
 634       //recreate based on types of variables
 635       std::vector< Node > new_children;
 636       for( size_t i=0; i<n[0].getNumChildren(); i++ ){
 637         TypeNode tn = getOrCreateTypeForId( d_var_types[n][ n[0][i] ], n[0][i].getType() );
 638         Node v = getNewSymbol( n[0][i], tn );
 639         Trace("sort-inference-debug2") << "Map variable " << n[0][i] << " to " << v << std::endl;
 640         new_children.push_back( v );
 641         var_bound[ n[0][i] ] = v;
 642       }
 643       children.push_back( NodeManager::currentNM()->mkNode( n[0].getKind(), new_children ) );
 644       use_new_visited = true;
 645     }
 646
 647     //process children
 648     if( n.getMetaKind() == kind::metakind::PARAMETERIZED ){
 649       children.push_back( n.getOperator() );
 650     }
 651     Node op;
 652     if( n.hasOperator() ){
 653       op = n.getOperator();
 654     }
 655     bool childChanged = false;
 656     TypeNode tnnc;
 657     for( size_t i=0; i<n.getNumChildren(); i++ ){
 658       bool processChild = true;
 659       if( n.getKind()==kind::FORALL || n.getKind()==kind::EXISTS ){
 660         processChild =
 661             options::userPatternsQuant() == options::UserPatMode::IGNORE
 662                 ? i == 1
 663                 : i >= 1;
 664       }
 665       if( processChild ){
 666         if( n.getKind()==kind::APPLY_UF ){
 667           Assert(d_op_arg_types.find(op) != d_op_arg_types.end());
 668           tnnc = getOrCreateTypeForId( d_op_arg_types[op][i], n[i].getType() );
 669           Assert(!tnnc.isNull());
 670         }
 671         else if (n.getKind() == kind::EQUAL && !n[0].getType().isBoolean()
 672                  && i == 0)
 673         {
 674           Assert(d_equality_types.find(n) != d_equality_types.end());
 675           tnnc = getOrCreateTypeForId( d_equality_types[n], n[0].getType() );
 676           Assert(!tnnc.isNull());
 677         }
 678         Node nc = simplifyNode(n[i],
 679                                var_bound,
 680                                tnnc,
 681                                model_replace_f,
 682                                use_new_visited ? new_visited : visited);
 683         Trace("sort-inference-debug2") << "Simplify " << i << " " << n[i] << " returned " << nc << std::endl;
 684         children.push_back( nc );
 685         childChanged = childChanged || nc!=n[i];
 686       }
 687     }
 688
 689     //remove from variable bindings
 690     Node ret;
 691     if( n.getKind()==kind::FORALL || n.getKind()==kind::EXISTS ){
 692       //erase from variable bound
 693       for( size_t i=0; i<n[0].getNumChildren(); i++ ){
 694         Trace("sort-inference-debug2") << "Remove bound for " << n[0][i] << std::endl;
 695         var_bound.erase( n[0][i] );
 696       }
 697       ret = NodeManager::currentNM()->mkNode( n.getKind(), children );
 698     }else if( n.getKind()==kind::EQUAL ){
 699       TypeNode tn1 = children[0].getType();
 700       TypeNode tn2 = children[1].getType();
 701       if( !tn1.isComparableTo( tn2 ) ){
 702         Trace("sort-inference-warn") << "Sort inference created bad equality: " << children[0] << " = " << children[1] << std::endl;
 703         Trace("sort-inference-warn") << "  Types : " << children[0].getType() << " " << children[1].getType() << std::endl;
 704         Assert(false);
 705       }
 706       ret = NodeManager::currentNM()->mkNode( kind::EQUAL, children );
 707     }else if( n.getKind()==kind::APPLY_UF ){
 708       if( d_symbol_map.find( op )==d_symbol_map.end() ){
 709         //make the new operator if necessary
 710         bool opChanged = false;
 711         std::vector< TypeNode > argTypes;
 712         for( size_t i=0; i<n.getNumChildren(); i++ ){
 713           TypeNode tn = getOrCreateTypeForId( d_op_arg_types[op][i], n[i].getType() );
 714           argTypes.push_back( tn );
 715           if( tn!=n[i].getType() ){
 716             opChanged = true;
 717           }
 718         }
 719         TypeNode retType = getOrCreateTypeForId( d_op_return_types[op], n.getType() );
 720         if( retType!=n.getType() ){
 721           opChanged = true;
 722         }
 723         if( opChanged ){
 724           std::stringstream ss;
 725           ss << "io_" << op;
 726           TypeNode typ = NodeManager::currentNM()->mkFunctionType( argTypes, retType );
 727           d_symbol_map[op] = NodeManager::currentNM()->mkSkolem( ss.str(), typ, "op created during sort inference" );
 728           Trace("setp-model") << "Function " << op << " is replaced with " << d_symbol_map[op] << std::endl;
 729           model_replace_f[op] = d_symbol_map[op];
 730         }else{
 731           d_symbol_map[op] = op;
 732         }
 733       }
 734       children[0] = d_symbol_map[op];
 735       // make sure all children have been given proper types
 736       for (size_t i = 0, size = n.getNumChildren(); i < size; i++)
 737       {
 738         TypeNode tn = children[i+1].getType();
 739         TypeNode tna = getTypeForId( d_op_arg_types[op][i] );
 740         if (!tn.isSubtypeOf(tna))
 741         {
 742           Trace("sort-inference-warn") << "Sort inference created bad child: " << n << " " << n[i] << " " << tn << " " << tna << std::endl;
 743           Assert(false);
 744         }
 745       }
 746       ret = NodeManager::currentNM()->mkNode( kind::APPLY_UF, children );
 747     }else{
 748       std::map< Node, Node >::iterator it = var_bound.find( n );
 749       if( it!=var_bound.end() ){
 750         ret = it->second;
 751       }else if( n.getKind() == kind::VARIABLE || n.getKind() == kind::SKOLEM ){
 752         if( d_symbol_map.find( n )==d_symbol_map.end() ){
 753           TypeNode tn = getOrCreateTypeForId( d_op_return_types[n], n.getType() );
 754           d_symbol_map[n] = getNewSymbol( n, tn );
 755         }
 756         ret = d_symbol_map[n];
 757       }else if( n.isConst() ){
 758         //type is determined by context
 759         ret = getNewSymbol( n, tnn );
 760       }else if( childChanged ){
 761         ret = NodeManager::currentNM()->mkNode( n.getKind(), children );
 762       }else{
 763         ret = n;
 764       }
 765     }
 766     visited[n][tnn] = ret;
 767     return ret;
 768   }
 769 }
 770
 771 Node SortInference::mkInjection( TypeNode tn1, TypeNode tn2 ) {
 772   std::vector< TypeNode > tns;
 773   tns.push_back( tn1 );
 774   TypeNode typ = NodeManager::currentNM()->mkFunctionType( tns, tn2 );
 775   Node f = NodeManager::currentNM()->mkSkolem( "inj", typ, "injection for monotonicity constraint" );
 776   Trace("sort-inference") << "-> Make injection " << f << " from " << tn1 << " to " << tn2 << std::endl;
 777   Node v1 = NodeManager::currentNM()->mkBoundVar( "?x", tn1 );
 778   Node v2 = NodeManager::currentNM()->mkBoundVar( "?y", tn1 );
 779   Node ret = NodeManager::currentNM()->mkNode( kind::FORALL,
 780                NodeManager::currentNM()->mkNode( kind::BOUND_VAR_LIST, v1, v2 ),
 781                NodeManager::currentNM()->mkNode( kind::OR,
 782                  NodeManager::currentNM()->mkNode( kind::APPLY_UF, f, v1 ).eqNode( NodeManager::currentNM()->mkNode( kind::APPLY_UF, f, v2 ) ).negate(),
 783                  v1.eqNode( v2 ) ) );
 784   ret = theory::Rewriter::rewrite( ret );
 785   return ret;
 786 }
 787
 788 int SortInference::getSortId( Node n ) {
 789   Node op = n.getKind()==kind::APPLY_UF ? n.getOperator() : n;
 790   if( d_op_return_types.find( op )!=d_op_return_types.end() ){
 791     return d_type_union_find.getRepresentative( d_op_return_types[op] );
 792   }else{
 793     return 0;
 794   }
 795 }
 796
 797 int SortInference::getSortId( Node f, Node v ) {
 798   if( d_var_types.find( f )!=d_var_types.end() ){
 799     return d_type_union_find.getRepresentative( d_var_types[f][v] );
 800   }else{
 801     return 0;
 802   }
 803 }
 804
 805 void SortInference::setSkolemVar( Node f, Node v, Node sk ){
 806   Trace("sort-inference-temp") << "Set skolem var for " << f << ", variable " << v << std::endl;
 807   if( isWellSortedFormula( f ) && d_var_types.find( f )==d_var_types.end() ){
 808     //calculate the sort for variables if not done so already
 809     std::map< Node, Node > var_bound;
 810     std::map< Node, int > visited;
 811     process( f, var_bound, visited );
 812   }
 813   d_op_return_types[sk] = getSortId( f, v );
 814   Trace("sort-inference-temp") << "Set skolem sort id for " << sk << " to " << d_op_return_types[sk] << std::endl;
 815 }
 816
 817 bool SortInference::isWellSortedFormula( Node n ) {
 818   if( n.getType().isBoolean() && n.getKind()!=kind::APPLY_UF ){
 819     for( unsigned i=0; i<n.getNumChildren(); i++ ){
 820       if( !isWellSortedFormula( n[i] ) ){
 821         return false;
 822       }
 823     }
 824     return true;
 825   }else{
 826     return isWellSorted( n );
 827   }
 828 }
 829
 830 bool SortInference::isWellSorted( Node n ) {
 831   if( getSortId( n )==0 ){
 832     return false;
 833   }else{
 834     if( n.getKind()==kind::APPLY_UF ){
 835       for( unsigned i=0; i<n.getNumChildren(); i++ ){
 836         int s1 = getSortId( n[i] );
 837         int s2 = d_type_union_find.getRepresentative( d_op_arg_types[ n.getOperator() ][i] );
 838         if( s1!=s2 ){
 839           return false;
 840         }
 841         if( !isWellSorted( n[i] ) ){
 842           return false;
 843         }
 844       }
 845     }
 846     return true;
 847   }
 848 }
 849
 850 void SortInference::getSortConstraints( Node n, UnionFind& uf ) {
 851   if( n.getKind()==kind::APPLY_UF ){
 852     for( unsigned i=0; i<n.getNumChildren(); i++ ){
 853       getSortConstraints( n[i], uf );
 854       uf.setEqual( getSortId( n[i] ), d_type_union_find.getRepresentative( d_op_arg_types[ n.getOperator() ][i] ) );
 855     }
 856   }
 857 }
 858
 859 bool SortInference::isMonotonic( TypeNode tn ) {
 860   Assert(tn.isSort());
 861   return d_non_monotonic_sorts_orig.find( tn )==d_non_monotonic_sorts_orig.end();
 862 }
 863
 864 }/* CVC4 namespace */