merging interpolation and duality changes into unstable

src/duality/duality.h

@@ -1184,7 +1184,13 @@ namespace Duality {
       hash_map<Edge *, Edge *> EdgeCloneMap;
       std::vector<expr> alit_stack;
       std::vector<unsigned> alit_stack_sizes;
-      hash_map<Edge *, uptr<LogicSolver> > edge_solvers;
+
+      // to let us use one solver per edge
+      struct edge_solver {
+	hash_map<ast,expr> AssumptionLits;
+	uptr<solver> slvr;
+      };
+      hash_map<Edge *, edge_solver > edge_solvers;
       
 #ifdef LIMIT_STACK_WEIGHT
       struct weight_counter {
@@ -1236,19 +1242,23 @@ namespace Duality {
 
       void GetTermTreeAssertionLiteralsRec(TermTree *assumptions);
 
-      LogicSolver *SolverForEdge(Edge *edge, bool models);
+      edge_solver &SolverForEdge(Edge *edge, bool models, bool axioms);
 
   public:
       struct scoped_solver_for_edge {
-	LogicSolver *orig_ls;
+	solver *orig_slvr;
 	RPFP_caching *rpfp;
-	scoped_solver_for_edge(RPFP_caching *_rpfp, Edge *edge, bool models = false){
+	edge_solver *es;
+	scoped_solver_for_edge(RPFP_caching *_rpfp, Edge *edge, bool models = false, bool axioms = false){
 	  rpfp = _rpfp;
-	  orig_ls = rpfp->ls;
-	  rpfp->ls = rpfp->SolverForEdge(edge,models);
+	  orig_slvr = rpfp->ls->slvr;
+	  es = &(rpfp->SolverForEdge(edge,models,axioms)); 
+	  rpfp->ls->slvr = es->slvr.get();
+	  rpfp->AssumptionLits.swap(es->AssumptionLits);
 	}
 	~scoped_solver_for_edge(){
-	  rpfp->ls = orig_ls;
+	  rpfp->ls->slvr = orig_slvr;
+	  rpfp->AssumptionLits.swap(es->AssumptionLits);
 	}
       };
 

src/duality/duality_rpfp.cpp

@@ -2711,10 +2711,12 @@ namespace Duality {
       const std::vector<expr> &theory = ls->get_axioms();
       for(unsigned i = 0; i < theory.size(); i++)
 	s.add(theory[i]);
-      if(s.check(lits.size(),&lits[0]) != unsat)
-	throw "should be unsat";
+      for(int k = 0; k < 100; k++) // keep trying, maybe MBQI will do something!
+	if(s.check(lits.size(),&lits[0]) == unsat)
+	  goto is_unsat;
+      throw "should be unsat";
     }
-    
+  is_unsat:
     for(unsigned i = 0; i < conjuncts.size(); ){
       std::swap(conjuncts[i],conjuncts.back());
       std::swap(lits[i],lits.back());
@@ -2747,8 +2749,20 @@ namespace Duality {
     
     // verify
     check_result res = CheckCore(lits,full_core);
-    if(res != unsat)
+    if(res != unsat){
+      // add the axioms in the off chance they are useful
+      const std::vector<expr> &theory = ls->get_axioms();
+      for(unsigned i = 0; i < theory.size(); i++)
+	GetAssumptionLits(theory[i],assumps);
+      lits = assumps; 
+      std::copy(core.begin(),core.end(),std::inserter(lits,lits.end()));
+      
+      for(int k = 0; k < 100; k++) // keep trying, maybe MBQI will do something!
+	if((res = CheckCore(lits,full_core)) == unsat)
+	  goto is_unsat;
       throw "should be unsat";
+    }
+  is_unsat:
     FilterCore(core,full_core);
     
     std::vector<expr> dummy;
@@ -2889,13 +2903,20 @@ namespace Duality {
     timer_stop("Generalize");
   }
 
-  RPFP::LogicSolver *RPFP_caching::SolverForEdge(Edge *edge, bool models){
-    uptr<LogicSolver> &p = edge_solvers[edge];
+  RPFP_caching::edge_solver &RPFP_caching::SolverForEdge(Edge *edge, bool models, bool axioms){
+    edge_solver &es = edge_solvers[edge];
+    uptr<solver> &p = es.slvr;
     if(!p.get()){
       scoped_no_proof no_proofs_please(ctx.m()); // no proofs
-      p.set(new iZ3LogicSolver(ctx,models)); // no models
+      p.set(new solver(ctx,true,models)); // no models
+      if(axioms){
+	RPFP::LogicSolver *ls = edge->owner->ls;
+	const std::vector<expr> &axs = ls->get_axioms();
+	for(unsigned i = 0; i < axs.size(); i++)
+	  p.get()->add(axs[i]);
+      }
     }
-    return p.get();
+    return es;
   }
 
 
@@ -3362,6 +3383,8 @@ namespace Duality {
       }
     }
 
+    bool some_labels = false;
+
     // create the edges
 
     for(unsigned i = 0; i < clauses.size(); i++){
@@ -3397,17 +3420,23 @@ namespace Duality {
       Term labeled = body;
       std::vector<label_struct > lbls;  // TODO: throw this away for now
       body = RemoveLabels(body,lbls);
+      if(!eq(labeled,body))
+	some_labels = true; // remember if there are labels, as we then can't do qe_lite
       // body = IneqToEq(body); // UFO converts x=y to (x<=y & x >= y). Undo this.
       body = body.simplify();
 
 #ifdef USE_QE_LITE
       std::set<int> idxs;
-      for(unsigned j = 0; j < Indparams.size(); j++)
-	if(Indparams[j].is_var())
-	  idxs.insert(Indparams[j].get_index_value());
-      body = body.qe_lite(idxs,false);
+      if(!some_labels){ // can't do qe_lite if we have to reconstruct labels
+	for(unsigned j = 0; j < Indparams.size(); j++)
+	  if(Indparams[j].is_var())
+	    idxs.insert(Indparams[j].get_index_value());
+	body = body.qe_lite(idxs,false);
+      }
       hash_map<int,hash_map<ast,Term> > sb_memo;
       body = SubstBoundRec(sb_memo,substs[i],0,body);
+      if(some_labels)
+	labeled = SubstBoundRec(sb_memo,substs[i],0,labeled);
       for(unsigned j = 0; j < Indparams.size(); j++)
 	Indparams[j] = SubstBoundRec(sb_memo, substs[i], 0, Indparams[j]);
 #endif

src/duality/duality_solver.cpp

@@ -51,12 +51,17 @@ Revision History:
 // #define TOP_DOWN
 // #define EFFORT_BOUNDED_STRAT
 #define SKIP_UNDERAPPROX_NODES
-#define USE_RPFP_CLONE
 // #define KEEP_EXPANSIONS
 // #define USE_CACHING_RPFP
 // #define PROPAGATE_BEFORE_CHECK
+
+#define USE_RPFP_CLONE
 #define USE_NEW_GEN_CANDS
 
+//#define NO_PROPAGATE
+//#define NO_GENERALIZE
+//#define NO_DECISIONS
+
 namespace Duality {
 
   // TODO: must be a better place for this...
@@ -129,13 +134,11 @@ namespace Duality {
       {
 	scoped_no_proof no_proofs_please(ctx.m());
 #ifdef USE_RPFP_CLONE
-	clone_ls = new RPFP::iZ3LogicSolver(ctx, false); // no models needed for this one
-      clone_rpfp = new RPFP_caching(clone_ls);
+      clone_rpfp = new RPFP_caching(rpfp->ls);
       clone_rpfp->Clone(rpfp);
 #endif      
 #ifdef USE_NEW_GEN_CANDS
-      gen_cands_ls = new RPFP::iZ3LogicSolver(ctx);
-      gen_cands_rpfp = new RPFP_caching(gen_cands_ls);
+      gen_cands_rpfp = new RPFP_caching(rpfp->ls);
       gen_cands_rpfp->Clone(rpfp);
 #endif      
       }
@@ -144,20 +147,16 @@ namespace Duality {
     ~Duality(){
 #ifdef USE_RPFP_CLONE
       delete clone_rpfp;
-      delete clone_ls;
 #endif      
 #ifdef USE_NEW_GEN_CANDS
       delete gen_cands_rpfp;
-      delete gen_cands_ls;
 #endif
     }
 
 #ifdef USE_RPFP_CLONE
-    RPFP::LogicSolver *clone_ls;
     RPFP_caching *clone_rpfp;
 #endif      
 #ifdef USE_NEW_GEN_CANDS
-    RPFP::LogicSolver *gen_cands_ls;
     RPFP_caching *gen_cands_rpfp;
 #endif      
 
@@ -1255,7 +1254,7 @@ namespace Duality {
 	slvr.pop(1);
 	delete checker;
 #else
-	RPFP_caching::scoped_solver_for_edge(gen_cands_rpfp,edge,true /* models */);
+	RPFP_caching::scoped_solver_for_edge ssfe(gen_cands_rpfp,edge,true /* models */, true /*axioms*/);
 	gen_cands_rpfp->Push();
 	Node *root = CheckerForEdgeClone(edge,gen_cands_rpfp);
 	if(gen_cands_rpfp->Check(root) != unsat){
@@ -1940,11 +1939,15 @@ namespace Duality {
 	      for(unsigned i = 0; i < expansions.size(); i++){
 		Node *node = expansions[i];
 		tree->SolveSingleNode(top,node);
+#ifdef NO_GENERALIZE
+		node->Annotation.Formula = tree->RemoveRedundancy(node->Annotation.Formula).simplify();
+#else
 		if(expansions.size() == 1 && NodeTooComplicated(node))
 		  SimplifyNode(node);
 		else
 		  node->Annotation.Formula = tree->RemoveRedundancy(node->Annotation.Formula).simplify();
 		Generalize(node);
+#endif
 		if(RecordUpdate(node))
 		  update_count++;
 		else
@@ -1984,7 +1987,9 @@ namespace Duality {
 	      if(stack.size() == 1)break;
 	      if(prev_level_used){
 		Node *node = stack.back().expansions[0];
+#ifndef NO_PROPAGATE
 		if(!Propagate(node)) break;
+#endif
 		if(!RecordUpdate(node)) break; // shouldn't happen!
 		RemoveUpdateNodesAtCurrentLevel(); // this level is about to be deleted -- remove its children from update list
 		propagated = true;
@@ -2006,11 +2011,13 @@ namespace Duality {
 	  }
 	  else {
 	    was_sat = true;
-	    tree->Push();
+	    tree->Push();
 	    std::vector<Node *> &expansions = stack.back().expansions;
+#ifndef NO_DECISIONS
 	    for(unsigned i = 0; i < expansions.size(); i++){
 	      tree->FixCurrentState(expansions[i]->Outgoing);
 	    }
+#endif
 #if 0
 	    if(tree->slvr().check() == unsat)
 	      throw "help!";

src/interp/iz3mgr.cpp

@@ -249,6 +249,9 @@ iz3mgr::ast iz3mgr::clone(const ast &t, const std::vector<ast> &_args){
 
 
 void iz3mgr::show(ast t){
+  if(t.null()){
+    std::cout  << "(null)" << std::endl;
+  }
   params_ref p;
   p.set_bool("flat_assoc",false);
   std::cout  << mk_pp(t.raw(), m(), p) << std::endl;
@@ -693,10 +696,13 @@ void iz3mgr::linear_comb(ast &P, const ast &c, const ast &Q, bool round_off){
       throw "not an inequality";
     }
   }
-  Qrhs = make(Times,c,Qrhs);
-  bool pstrict = op(P) == Lt, strict = pstrict || qstrict;
-  if(pstrict && qstrict && round_off)
+  bool pstrict = op(P) == Lt;
+  if(qstrict && round_off && (pstrict || !(c == make_int(rational(1))))){
     Qrhs = make(Sub,Qrhs,make_int(rational(1)));
+    qstrict = false;
+  }
+  Qrhs = make(Times,c,Qrhs);
+  bool strict = pstrict || qstrict;
   if(strict)
     P = make(Lt,arg(P,0),make(Plus,arg(P,1),Qrhs));
   else
@@ -881,3 +887,14 @@ iz3mgr::ast iz3mgr::apply_quant(opr quantifier, ast var, ast e){
   std::vector<ast> bvs; bvs.push_back(var);
   return make_quant(quantifier,bvs,e);
 }
+
+#if 0
+void iz3mgr::get_bound_substitutes(stl_ext::hash_map<ast,bool> &memo, const ast &e, const ast &var, std::vector<ast> &substs){
+  std::pair<ast,bool> foo(e,false);
+  std::pair<hash_map<ast,bool>::iterator,bool> bar = memo.insert(foo);
+  if(bar.second){
+    if(op(e) == 
+  }
+ 
+}
+#endif

src/interp/iz3proof_itp.cpp

@@ -579,18 +579,36 @@ class iz3proof_itp_impl : public iz3proof_itp {
     return is_ineq(ineq);
   }
 
+  ast destruct_cond_ineq(const ast &ineq, ast &Aproves, ast &Bproves){
+    ast res = ineq;
+    opr o = op(res);
+    if(o == And){
+      Aproves = my_and(Aproves,arg(res,0));
+      res = arg(res,1);
+      o = op(res);
+    }
+    if(o == Implies){
+      Bproves = my_and(Bproves,arg(res,0));
+      res = arg(res,1);
+    }
+    return res;
+  }
+
   ast simplify_sum(std::vector<ast> &args){
     ast Aproves = mk_true(), Bproves = mk_true();
-    ast ineq = args[0];
+    ast ineq = destruct_cond_ineq(args[0],Aproves,Bproves);
     if(!is_normal_ineq(ineq)) throw cannot_simplify();
     sum_cond_ineq(ineq,args[1],args[2],Aproves,Bproves);
     return my_and(Aproves,my_implies(Bproves,ineq));
   }
 
   ast simplify_rotate_sum(const ast &pl, const ast &pf){
-    ast cond = mk_true();
+    ast Aproves = mk_true(), Bproves = mk_true();
     ast ineq = make(Leq,make_int("0"),make_int("0"));
-    return rotate_sum_rec(pl,pf,cond,ineq);
+    ineq = rotate_sum_rec(pl,pf,Aproves,Bproves,ineq);
+    if(is_true(Aproves) && is_true(Bproves))
+      return ineq;
+    return my_and(Aproves,my_implies(Bproves,ineq));
   }
 
   bool is_rewrite_chain(const ast &chain){
@@ -623,7 +641,11 @@ class iz3proof_itp_impl : public iz3proof_itp {
 
   void sum_cond_ineq(ast &ineq, const ast &coeff2, const ast &ineq2, ast &Aproves, ast &Bproves){
     opr o = op(ineq2);
-    if(o == Implies){
+    if(o == And){
+      sum_cond_ineq(ineq,coeff2,arg(ineq2,1),Aproves,Bproves);
+      Aproves = my_and(Aproves,arg(ineq2,0));
+    }
+    else if(o == Implies){
       sum_cond_ineq(ineq,coeff2,arg(ineq2,1),Aproves,Bproves);
       Bproves = my_and(Bproves,arg(ineq2,0));
     }
@@ -683,23 +705,20 @@ class iz3proof_itp_impl : public iz3proof_itp {
     return make(op(ineq),mk_idiv(arg(ineq,0),divisor),mk_idiv(arg(ineq,1),divisor));
   }
   
-  ast rotate_sum_rec(const ast &pl, const ast &pf, ast &Bproves, ast &ineq){
-    if(pf == pl)
-      return my_implies(Bproves,simplify_ineq(ineq));
+  ast rotate_sum_rec(const ast &pl, const ast &pf, ast &Aproves, ast &Bproves, ast &ineq){
+    if(pf == pl){
+      if(sym(ineq) == normal)
+	return ineq;
+      return simplify_ineq(ineq);
+    }
     if(op(pf) == Uninterpreted && sym(pf) == sum){
       if(arg(pf,2) == pl){
-	ast Aproves = mk_true();
 	sum_cond_ineq(ineq,make_int("1"),arg(pf,0),Aproves,Bproves);
-	if(!is_true(Aproves))
-	  throw "help!";
 	ineq = idiv_ineq(ineq,arg(pf,1));
-	return my_implies(Bproves,ineq);
+	return ineq;
       }
-      ast Aproves = mk_true();
       sum_cond_ineq(ineq,arg(pf,1),arg(pf,2),Aproves,Bproves);
-      if(!is_true(Aproves))
-	throw "help!";
-      return rotate_sum_rec(pl,arg(pf,0),Bproves,ineq);
+      return rotate_sum_rec(pl,arg(pf,0),Aproves,Bproves,ineq);
     }
     throw cannot_simplify();
   }
@@ -749,6 +768,28 @@ class iz3proof_itp_impl : public iz3proof_itp {
     return res;
   }
 
+  ast unmixed_eq2ineq(const ast &lhs, const ast &rhs, opr comp_op, const ast &equa, ast &cond){
+    ast ineqs= chain_ineqs(comp_op,LitA,equa,lhs,rhs); // chain must be from lhs to rhs
+    cond = my_and(cond,chain_conditions(LitA,equa)); 
+    ast Bconds = z3_simplify(chain_conditions(LitB,equa)); 
+    if(is_true(Bconds) && op(ineqs) != And)
+      return my_implies(cond,ineqs);
+    if(op(ineqs) != And)
+      return my_and(Bconds,my_implies(cond,ineqs));
+    throw "help!";
+  }
+
+  ast add_mixed_eq2ineq(const ast &lhs, const ast &rhs, const ast &equa, const ast &itp){
+    if(is_true(equa))
+      return itp;
+     std::vector<ast> args(3);
+     args[0] = itp;
+     args[1] = make_int("1");
+     ast ineq = make(Leq,make_int(rational(0)),make_int(rational(0)));
+     args[2] = make_normal(ineq,cons_normal(fix_normal(lhs,rhs,equa),mk_true()));
+     return simplify_sum(args);
+  }
+
   ast simplify_rotate_eq2leq(const ast &pl, const ast &neg_equality, const ast &pf){
     if(pl == arg(pf,1)){
       ast cond = mk_true();
@@ -756,20 +797,21 @@ class iz3proof_itp_impl : public iz3proof_itp {
       if(is_equivrel_chain(equa)){
 	ast lhs,rhs; eq_from_ineq(arg(neg_equality,0),lhs,rhs); // get inequality we need to prove
 	LitType lhst = get_term_type(lhs), rhst = get_term_type(rhs);
-	if(lhst != LitMixed && rhst != LitMixed){
-	  ast ineqs= chain_ineqs(op(arg(neg_equality,0)),LitA,equa,lhs,rhs); // chain must be from lhs to rhs
-	  cond = my_and(cond,chain_conditions(LitA,equa)); 
-	  ast Bconds = z3_simplify(chain_conditions(LitB,equa)); 
-	  if(is_true(Bconds) && op(ineqs) != And)
-	    return my_implies(cond,ineqs);
-	}
+	if(lhst != LitMixed && rhst != LitMixed)
+	  return unmixed_eq2ineq(lhs, rhs, op(arg(neg_equality,0)), equa, cond);
 	else {
-	  ast itp = make(Leq,make_int(rational(0)),make_int(rational(0)));
-	  return make_normal(itp,cons_normal(fix_normal(lhs,rhs,equa),mk_true()));
+	  ast left, left_term, middle, right_term, right;
+	  left = get_left_movers(equa,lhs,middle,left_term);
+	  middle = get_right_movers(middle,rhs,right,right_term);
+	  ast itp = unmixed_eq2ineq(left_term, right_term, op(arg(neg_equality,0)), middle, cond);
+	  // itp = my_implies(cond,itp);
+	  itp = add_mixed_eq2ineq(lhs, left_term, left, itp);
+	  itp = add_mixed_eq2ineq(right_term, rhs, right, itp);
+	  return itp;
 	}
       }
     }
-    throw cannot_simplify();
+    throw "help!";
   }
 
   void reverse_modpon(std::vector<ast> &args){
@@ -836,6 +878,8 @@ class iz3proof_itp_impl : public iz3proof_itp {
     ast equa = sep_cond(args[0],cond);
     if(is_equivrel_chain(equa))
       return my_implies(cond,reverse_chain(equa));
+    if(is_negation_chain(equa))
+      return commute_negation_chain(equa);
     throw cannot_simplify();
   }
 
@@ -909,7 +953,9 @@ class iz3proof_itp_impl : public iz3proof_itp {
     get_subterm_normals(ineq1,ineq2,tail,nc,top_pos,memo, Aproves, Bproves);
     ast itp;
     if(is_rewrite_side(LitA,head)){
-      itp = ineq1;
+      itp = make(Leq,make_int("0"),make_int("0"));
+      linear_comb(itp,make_int("1"),ineq1); // make sure it is normal form
+      //itp = ineq1;
       ast mc = z3_simplify(chain_side_proves(LitB,pref));
       Bproves = my_and(Bproves,mc);
     }
@@ -951,7 +997,7 @@ class iz3proof_itp_impl : public iz3proof_itp {
   ast simplify_modpon(const std::vector<ast> &args){
     ast Aproves = mk_true(), Bproves = mk_true();
     ast chain = simplify_modpon_fwd(args,Bproves);
-    ast Q2 = sep_cond(args[2],Bproves);
+    ast Q2 = destruct_cond_ineq(args[2],Aproves,Bproves);
     ast interp;
     if(is_normal_ineq(Q2)){ // inequalities are special
       ast nQ2 = rewrite_chain_to_normal_ineq(chain,Aproves,Bproves);
@@ -1450,6 +1496,50 @@ class iz3proof_itp_impl : public iz3proof_itp {
     return is_negation_chain(rest);
   }
 
+  ast commute_negation_chain(const ast &chain){
+    if(is_true(chain))
+      return chain;
+    ast last = chain_last(chain);
+    ast rest = chain_rest(chain);
+    if(is_true(rest)){
+      ast old = rewrite_rhs(last);
+      if(!(op(old) == Not))
+	throw "bad negative equality chain";
+      ast equ = arg(old,0);
+      if(!is_equivrel(equ))
+	throw "bad negative equality chain";
+      last = rewrite_update_rhs(last,top_pos,make(Not,make(op(equ),arg(equ,1),arg(equ,0))),make(True));
+      return chain_cons(rest,last);
+    }
+    ast pos = rewrite_pos(last);
+    if(pos == top_pos)
+      throw "bad negative equality chain";
+    int idx = pos_arg(pos);
+    if(idx != 0)
+      throw "bad negative equality chain";
+    pos = arg(pos,1);
+    if(pos == top_pos){
+      ast lhs = rewrite_lhs(last);
+      ast rhs = rewrite_rhs(last);
+      if(op(lhs) != Equal || op(rhs) != Equal)
+	throw "bad negative equality chain";
+      last = make_rewrite(rewrite_side(last),rewrite_pos(last),rewrite_cond(last),
+			  make(Iff,make(Equal,arg(lhs,1),arg(lhs,0)),make(Equal,arg(rhs,1),arg(rhs,0))));
+    }
+    else {
+      idx = pos_arg(pos);
+      if(idx == 0)
+	idx = 1;
+      else if(idx == 1)
+	idx = 0;
+      else
+	throw "bad negative equality chain";
+      pos = pos_add(0,pos_add(idx,arg(pos,1)));
+      last = make_rewrite(rewrite_side(last),pos,rewrite_cond(last),rewrite_equ(last));
+    }
+    return chain_cons(commute_negation_chain(rest),last);
+  }
+
   // split a rewrite chain into head and tail at last top-level rewrite
   ast get_head_chain(const ast &chain, ast &tail, bool is_not = true){
     ast last = chain_last(chain);
@@ -1466,6 +1556,47 @@ class iz3proof_itp_impl : public iz3proof_itp {
     return head;
   }
 
+  // split a rewrite chain into head and tail at last non-mixed term
+  ast get_right_movers(const ast &chain, const ast &rhs, ast &tail, ast &mid){
+    if(is_true(chain) || get_term_type(rhs) != LitMixed){
+      mid = rhs;
+      tail = mk_true();
+      return chain;
+    }
+    ast last = chain_last(chain);
+    ast rest = chain_rest(chain);
+    ast mm = subst_in_pos(rhs,rewrite_pos(last),rewrite_lhs(last));
+    ast res = get_right_movers(rest,mm,tail,mid);
+    tail = chain_cons(tail,last);
+    return res;
+  }
+  
+  // split a rewrite chain into head and tail at first non-mixed term
+  ast get_left_movers(const ast &chain, const ast &lhs, ast &tail, ast &mid){
+    if(is_true(chain)){
+      mid = lhs; 
+      if(get_term_type(lhs) != LitMixed){
+	tail = mk_true();
+	return chain;
+      }
+      return ast();
+    }
+    ast last = chain_last(chain);
+    ast rest = chain_rest(chain);
+    ast res = get_left_movers(rest,lhs,tail,mid);
+    if(res.null()){
+      mid = subst_in_pos(mid,rewrite_pos(last),rewrite_rhs(last));
+      if(get_term_type(mid) != LitMixed){
+	tail = mk_true();
+	return chain;
+      }
+      return ast();
+    }      
+    tail = chain_cons(tail,last);
+    return res;
+  }
+
+
   struct cannot_split {};
 
   /** Split a chain of rewrites two chains, operating on positions 0 and 1.
@@ -1668,11 +1799,13 @@ class iz3proof_itp_impl : public iz3proof_itp {
   }
 
   ast fix_normal(const ast &lhs, const ast &rhs, const ast &proof){
+    LitType lhst = get_term_type(lhs);
     LitType rhst = get_term_type(rhs);
-    if(rhst != LitMixed || ast_id(lhs) < ast_id(rhs))
+    if(lhst == LitMixed && (rhst != LitMixed || ast_id(lhs) < ast_id(rhs)))
       return make_normal_step(lhs,rhs,proof);
-    else
+    if(rhst == LitMixed && (lhst != LitMixed || ast_id(rhs) < ast_id(lhs)))
       return make_normal_step(rhs,lhs,reverse_chain(proof));
+    throw "help!";
   }
 
   ast chain_side_proves(LitType side, const ast &chain){
@@ -1692,8 +1825,10 @@ class iz3proof_itp_impl : public iz3proof_itp {
     ast lhs2 = normal_lhs(f2);
     int id1 = ast_id(lhs1);
     int id2 = ast_id(lhs2);
-    if(id1 < id2) return cons_normal(f1,merge_normal_chains_rec(normal_rest(chain1),chain2,trans,Aproves,Bproves));
-    if(id2 < id1) return cons_normal(f2,merge_normal_chains_rec(chain1,normal_rest(chain2),trans,Aproves,Bproves));
+    if(id1 < id2)
+      return cons_normal(f1,merge_normal_chains_rec(normal_rest(chain1),chain2,trans,Aproves,Bproves));
+    if(id2 < id1)
+      return cons_normal(f2,merge_normal_chains_rec(chain1,normal_rest(chain2),trans,Aproves,Bproves));
     ast rhs1 = normal_rhs(f1);
     ast rhs2 = normal_rhs(f2);
     LitType t1 = get_term_type(rhs1);
@@ -1719,9 +1854,13 @@ class iz3proof_itp_impl : public iz3proof_itp {
       Aproves = my_and(Aproves,mcB);
       ast rep = apply_rewrite_chain(rhs1,Aproof);
       new_proof = concat_rewrite_chain(pf1,Aproof);
-      new_normal = make_normal_step(rhs1,rep,new_proof);
+      new_normal = make_normal_step(lhs1,rep,new_proof);
+      ast A_normal = make_normal_step(rhs1,rep,Aproof);
+      ast res = cons_normal(new_normal,merge_normal_chains_rec(normal_rest(chain1),normal_rest(chain2),trans,Aproves,Bproves));
+      res = merge_normal_chains_rec(res,cons_normal(A_normal,make(True)),trans,Aproves,Bproves);
+      return res;
     }
-    else if(t1 == LitA && t2 == LitB)
+    else if(t1 == LitB && t2 == LitA)
       return merge_normal_chains_rec(chain2,chain1,trans,Aproves,Bproves);
     else if(t1 == LitA) {
       ast new_proof = concat_rewrite_chain(reverse_chain(pf1),pf2);
@@ -1743,17 +1882,20 @@ class iz3proof_itp_impl : public iz3proof_itp {
       return chain;
     ast f = normal_first(chain);
     ast r = normal_rest(chain);
+    r = trans_normal_chain(r,trans);
     ast rhs = normal_rhs(f);
     hash_map<ast,ast>::iterator it = trans.find(rhs);
     ast new_normal;
-    if(it != trans.end()){
+    if(it != trans.end() && get_term_type(normal_lhs(f)) == LitMixed){
       const ast &f2 = it->second;
       ast pf = concat_rewrite_chain(normal_proof(f),normal_proof(f2));
       new_normal = make_normal_step(normal_lhs(f),normal_rhs(f2),pf);
     }
     else
       new_normal = f;
-    return cons_normal(new_normal,trans_normal_chain(r,trans));
+    if(get_term_type(normal_lhs(f)) == LitMixed)
+      trans[normal_lhs(f)] = new_normal;
+    return cons_normal(new_normal,r);
   }
 
   ast merge_normal_chains(const ast &chain1, const ast &chain2, ast &Aproves, ast &Bproves){
@@ -2011,8 +2153,14 @@ class iz3proof_itp_impl : public iz3proof_itp {
   /** Make a Reflexivity node. This rule produces |- x = x */
   
   virtual node make_reflexivity(ast con){
-    throw proof_error();
-}
+    if(get_term_type(con) == LitA)
+      return mk_false();
+    if(get_term_type(con) == LitB)
+      return mk_true();
+    ast itp = make(And,make(contra,no_proof,mk_false()),
+		   make(contra,mk_true(),mk_not(con)));
+    return itp;
+  }
   
   /** Make a Symmetry node. This takes a derivation of |- x = y and
       produces | y = x. Ditto for ~(x=y) */
@@ -2247,10 +2395,19 @@ class iz3proof_itp_impl : public iz3proof_itp {
 	throw proof_error();
       }
     }
-    Qrhs = make(Times,c,Qrhs);
+#if 0
     bool pstrict = op(P) == Lt, strict = pstrict || qstrict;
     if(pstrict && qstrict && round_off)
       Qrhs = make(Sub,Qrhs,make_int(rational(1)));
+#else
+    bool pstrict = op(P) == Lt;
+    if(qstrict && round_off && (pstrict || !(c == make_int(rational(1))))){
+      Qrhs = make(Sub,Qrhs,make_int(rational(1)));
+      qstrict = false;
+    }
+    Qrhs = make(Times,c,Qrhs);
+    bool strict = pstrict || qstrict;
+#endif
     if(strict)
       P = make(Lt,arg(P,0),make(Plus,arg(P,1),Qrhs));
     else
@@ -2269,8 +2426,14 @@ class iz3proof_itp_impl : public iz3proof_itp {
       itp =  mk_true();
       break;
     default: { // mixed equality
-      if(get_term_type(x) == LitMixed || get_term_type(y) == LitMixed)
-	std::cerr << "WARNING: mixed term in leq2eq\n"; 
+      if(get_term_type(x) == LitMixed || get_term_type(y) == LitMixed){
+	// std::cerr << "WARNING: mixed term in leq2eq\n"; 
+	std::vector<ast> lits;
+	lits.push_back(con);
+	lits.push_back(make(Not,xleqy));
+	lits.push_back(make(Not,yleqx));
+	return make_axiom(lits);
+      }
       std::vector<ast> conjs; conjs.resize(3);
       conjs[0] = mk_not(con);
       conjs[1] = xleqy;
@@ -2405,7 +2568,15 @@ class iz3proof_itp_impl : public iz3proof_itp {
 	    frng = srng; // this term will be localized
 	}
 	else if(o == Plus || o == Times){ // don't want bound variables inside arith ops
-	  frng = erng; // this term will be localized
+	  // std::cout << "WARNING: non-local arithmetic\n";
+	  //	  frng = erng; // this term will be localized
+	}
+	else if(o == Select){ // treat the array term like a function symbol
+	  prover::range srng = pv->ast_scope(arg(e,0)); 
+	  if(!(srng.lo > srng.hi) &&  pv->ranges_intersect(srng,rng)) // localize to desired range if possible
+	    frng = pv->range_glb(srng,rng);
+	  else
+	    frng = srng; // this term will be localized
 	}
 	std::vector<ast> largs(nargs);
 	std::vector<ast> eqs;
@@ -2434,7 +2605,7 @@ class iz3proof_itp_impl : public iz3proof_itp {
       return e; // this term occurs in range, so it's O.K.
 
     if(is_array_type(get_type(e)))
-      throw "help!";
+      std::cerr << "WARNING: array quantifier\n";
 
     // choose a frame for the constraint that is close to range
     int frame = pv->range_near(pv->ast_scope(e),rng);

src/interp/iz3translate.cpp

@@ -188,6 +188,15 @@ public:
       get_Z3_lits(con, lits);
       iproof->make_axiom(lits);
     }
+#ifdef LOCALIZATION_KLUDGE
+    else if(dk == PR_MODUS_PONENS && pr(prem(proof,0)) == PR_QUANT_INST
+	    && get_locality_rec(prem(proof,1)) == INT_MAX){
+      std::vector<ast> lits;
+      ast con = conc(proof);
+      get_Z3_lits(con, lits);
+      iproof->make_axiom(lits);
+    }
+#endif
     else {
       unsigned nprems = num_prems(proof);
       for(unsigned i = 0; i < nprems; i++){
@@ -1271,6 +1280,84 @@ public:
     return make(Plus,args);
   }
 
+
+  ast replace_summands_with_fresh_vars(const ast &t, hash_map<ast,ast> &map){
+    if(op(t) == Plus){
+      int nargs = num_args(t);
+      std::vector<ast> args(nargs);
+      for(int i = 0; i < nargs; i++)
+	args[i] = replace_summands_with_fresh_vars(arg(t,i),map);
+      return make(Plus,args);
+    }
+    if(op(t) == Times)
+      return make(Times,arg(t,0),replace_summands_with_fresh_vars(arg(t,1),map));
+    if(map.find(t) == map.end())
+      map[t] =  mk_fresh_constant("@s",get_type(t));
+    return map[t];
+  }
+
+  ast painfully_normalize_ineq(const ast &ineq, hash_map<ast,ast> &map){
+    ast res = normalize_inequality(ineq);
+    ast lhs = arg(res,0);
+    lhs = replace_summands_with_fresh_vars(lhs,map);
+    res = make(op(res),SortSum(lhs),arg(res,1));
+    return res;
+  }
+
+  Iproof::node painfully_reconstruct_farkas(const std::vector<ast> &prems, const std::vector<Iproof::node> &pfs, const ast &con){
+    int nprems = prems.size();
+    std::vector<ast> pcons(nprems),npcons(nprems);
+    hash_map<ast,ast> pcon_to_pf, npcon_to_pcon, pain_map;
+    for(int i = 0; i < nprems; i++){
+      pcons[i] = conc(prems[i]);
+      npcons[i] = painfully_normalize_ineq(pcons[i],pain_map);
+      pcon_to_pf[npcons[i]] = pfs[i];
+      npcon_to_pcon[npcons[i]] = pcons[i];
+    }
+    // ast leq = make(Leq,arg(con,0),arg(con,1));
+    ast ncon = painfully_normalize_ineq(mk_not(con),pain_map);
+    pcons.push_back(mk_not(con));
+    npcons.push_back(ncon);
+    // ast assumps = make(And,pcons);
+    ast new_proof;
+    if(is_sat(npcons,new_proof))
+      throw "Proof error!";
+    pfrule dk = pr(new_proof);
+    int nnp = num_prems(new_proof);
+    std::vector<Iproof::node> my_prems;
+    std::vector<ast> farkas_coeffs, my_pcons;
+
+    if(dk == PR_TH_LEMMA 
+       && get_theory_lemma_theory(new_proof) == ArithTheory
+       && get_theory_lemma_kind(new_proof) == FarkasKind)
+      get_farkas_coeffs(new_proof,farkas_coeffs);
+    else if(dk == PR_UNIT_RESOLUTION && nnp == 2){
+      for(int i = 0; i < nprems; i++)
+	farkas_coeffs.push_back(make_int(rational(1)));
+    }
+    else
+      throw "cannot reconstruct farkas proof";
+
+    for(int i = 0; i < nnp; i++){
+      ast p = conc(prem(new_proof,i));
+      p = really_normalize_ineq(p);
+      if(pcon_to_pf.find(p) != pcon_to_pf.end()){
+	my_prems.push_back(pcon_to_pf[p]);
+	my_pcons.push_back(npcon_to_pcon[p]);
+      }
+      else if(p == ncon){
+	my_prems.push_back(iproof->make_hypothesis(mk_not(con)));
+	my_pcons.push_back(mk_not(con));
+      }
+      else
+	throw "cannot reconstruct farkas proof";
+    }
+    Iproof::node res = iproof->make_farkas(mk_false(),my_prems,my_pcons,farkas_coeffs);
+    return res;
+  }
+
+
+
   ast really_normalize_ineq(const ast &ineq){
     ast res = normalize_inequality(ineq);
     res = make(op(res),SortSum(arg(res,0)),arg(res,1));
@@ -1309,7 +1396,7 @@ public:
 	farkas_coeffs.push_back(make_int(rational(1)));
     }
     else
-      throw "cannot reconstruct farkas proof";
+      return painfully_reconstruct_farkas(prems,pfs,con);
 
     for(int i = 0; i < nnp; i++){
       ast p = conc(prem(new_proof,i));
@@ -1452,9 +1539,11 @@ public:
 	lits.push_back(from_ast(con));
 
       // pattern match some idioms
-      if(dk == PR_MODUS_PONENS && pr(prem(proof,0)) == PR_QUANT_INST && pr(prem(proof,1)) == PR_REWRITE ) {
-	res = iproof->make_axiom(lits);
-	return res;
+      if(dk == PR_MODUS_PONENS && pr(prem(proof,0)) == PR_QUANT_INST){
+	if(get_locality_rec(prem(proof,1)) == INT_MAX) {
+	  res = iproof->make_axiom(lits);
+	  return res;
+	}
       }
       if(dk == PR_MODUS_PONENS && expect_clause && op(con) == Or){
 	Iproof::node clause = translate_main(prem(proof,0),true);
@@ -1465,12 +1554,20 @@ public:
       if(dk == PR_MODUS_PONENS && expect_clause && op(con) == Or)
 	std::cout << "foo!\n";
 
+#if 0
       if(1 && dk == PR_TRANSITIVITY && pr(prem(proof,1)) == PR_COMMUTATIVITY){
 	Iproof::node clause = translate_main(prem(proof,0),true);
 	res = make(commute,clause,conc(prem(proof,0))); // HACK -- we depend on Iproof::node being same as ast.
 	return res;
       }
       
+      if(1 && dk == PR_TRANSITIVITY && pr(prem(proof,0)) == PR_COMMUTATIVITY){
+	Iproof::node clause = translate_main(prem(proof,1),true);
+	res = make(commute,clause,conc(prem(proof,1))); // HACK -- we depend on Iproof::node being same as ast.
+	return res;
+      }
+#endif
+
       if(dk == PR_TRANSITIVITY && is_eq_propagate(prem(proof,1))){
 	try {
 	  res = CombineEqPropagate(proof);
@@ -1627,9 +1724,10 @@ public:
 	  break;
 	case ArrayTheory: {// nothing fancy for this
 	  ast store_array;
-	  if(!get_store_array(con,store_array))
-	    throw unsupported();
-	  res = iproof->make_axiom(lits,ast_scope(store_array));
+	  if(get_store_array(con,store_array))
+	    res = iproof->make_axiom(lits,ast_scope(store_array));
+	  else
+	    res = iproof->make_axiom(lits); // for array extensionality axiom
 	  break;
 	}
 	default:
@@ -1653,6 +1751,12 @@ public:
 	res = args[0];
 	break;
       }
+      case PR_COMMUTATIVITY: {
+	ast comm_equiv = make(op(con),arg(con,0),arg(con,0));
+	ast pf = iproof->make_reflexivity(comm_equiv);
+	res = make(commute,pf,comm_equiv);
+	break;
+      }
       default:
 	assert(0 && "translate_main: unsupported proof rule");
 	throw unsupported();