mirror of
https://github.com/Z3Prover/z3
synced 2025-04-10 19:27:06 +00:00
working on duality and quantified arithmetic in interpolation
This commit is contained in:
Ken McMillan
parent
8320144af0
commit
a93f8b04e5
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@ -277,6 +277,7 @@ namespace Duality {
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public:
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std::list<Edge *> edges;
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std::list<Node *> nodes;
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std::list<Edge *> constraints;
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};
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@ -286,6 +287,8 @@ namespace Duality {
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literals dualLabels;
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std::list<stack_entry> stack;
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std::vector<Term> axioms; // only saved here for printing purposes
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solver aux_solver;
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public:
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@ -296,7 +299,7 @@ namespace Duality {
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inherit the axioms.
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*/
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RPFP(LogicSolver *_ls) : Z3User(*(_ls->ctx), *(_ls->slvr)), dualModel(*(_ls->ctx))
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RPFP(LogicSolver *_ls) : Z3User(*(_ls->ctx), *(_ls->slvr)), dualModel(*(_ls->ctx)), aux_solver(*(_ls->ctx))
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{
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ls = _ls;
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nodeCount = 0;
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@ -351,10 +354,10 @@ namespace Duality {
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bool SubsetEq(const Transformer &other){
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Term t = owner->SubstParams(other.IndParams,IndParams,other.Formula);
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expr test = Formula && !t;
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owner->slvr.push();
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owner->slvr.add(test);
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check_result res = owner->slvr.check();
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owner->slvr.pop(1);
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owner->aux_solver.push();
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owner->aux_solver.add(test);
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check_result res = owner->aux_solver.check();
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owner->aux_solver.pop(1);
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return res == unsat;
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}
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@ -444,6 +447,19 @@ namespace Duality {
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return n;
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}
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/** Delete a node. You can only do this if not connected to any edges.*/
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void DeleteNode(Node *node){
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if(node->Outgoing || !node->Incoming.empty())
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throw "cannot delete RPFP node";
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for(std::vector<Node *>::iterator it = nodes.end(), en = nodes.begin(); it != en;){
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if(*(--it) == node){
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nodes.erase(it);
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break;
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}
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}
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delete node;
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}
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/** This class represents a hyper-edge in the RPFP graph */
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class Edge
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@ -460,6 +476,7 @@ namespace Duality {
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hash_map<ast,Term> varMap;
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Edge *map;
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Term labeled;
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std::vector<Term> constraints;
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Edge(Node *_Parent, const Transformer &_F, const std::vector<Node *> &_Children, RPFP *_owner, int _number)
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: F(_F), Parent(_Parent), Children(_Children), dual(expr(_owner->ctx)) {
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@ -480,6 +497,29 @@ namespace Duality {
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return e;
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}
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/** Delete a hyper-edge and unlink it from any nodes. */
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void DeleteEdge(Edge *edge){
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if(edge->Parent)
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edge->Parent->Outgoing = 0;
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for(unsigned int i = 0; i < edge->Children.size(); i++){
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std::vector<Edge *> &ic = edge->Children[i]->Incoming;
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for(std::vector<Edge *>::iterator it = ic.begin(), en = ic.end(); it != en; ++it){
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if(*it == edge){
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ic.erase(it);
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break;
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}
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}
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}
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for(std::vector<Edge *>::iterator it = edges.end(), en = edges.begin(); it != en;){
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if(*(--it) == edge){
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edges.erase(it);
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break;
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}
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}
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delete edge;
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}
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/** Create an edge that lower-bounds its parent. */
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Edge *CreateLowerBoundEdge(Node *_Parent)
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{
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@ -494,13 +534,25 @@ namespace Duality {
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void AssertEdge(Edge *e, int persist = 0, bool with_children = false, bool underapprox = false);
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/* Constrain an edge by the annotation of one of its children. */
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void ConstrainParent(Edge *parent, Node *child);
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/** For incremental solving, asserts the negation of the upper bound associated
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* with a node.
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* */
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void AssertNode(Node *n);
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/** Assert a constraint on an edge in the SMT context.
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*/
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void ConstrainEdge(Edge *e, const Term &t);
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/** Fix the truth values of atomic propositions in the given
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edge to their values in the current assignment. */
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void FixCurrentState(Edge *root);
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/** Declare a constant in the background theory. */
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void DeclareConstant(const FuncDecl &f);
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@ -592,6 +644,9 @@ namespace Duality {
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Term ComputeUnderapprox(Node *root, int persist);
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/** Try to strengthen the annotation of a node by removing disjuncts. */
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void Generalize(Node *node);
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/** Push a scope. Assertions made after Push can be undone by Pop. */
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void Push();
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@ -803,7 +858,15 @@ namespace Duality {
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Term SubstBound(hash_map<int,Term> &subst, const Term &t);
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void ConstrainEdgeLocalized(Edge *e, const Term &t);
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void GreedyReduce(solver &s, std::vector<expr> &conjuncts);
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void NegateLits(std::vector<expr> &lits);
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expr SimplifyOr(std::vector<expr> &lits);
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void SetAnnotation(Node *root, const expr &t);
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};
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/** RPFP solver base class. */
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@ -283,7 +283,10 @@ namespace Duality {
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children[i] = ToTermTree(e->Children[i]);
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// Term top = ReducedDualEdge(e);
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Term top = e->dual.null() ? ctx.bool_val(true) : e->dual;
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return new TermTree(top, children);
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TermTree *res = new TermTree(top, children);
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for(unsigned i = 0; i < e->constraints.size(); i++)
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res->addTerm(e->constraints[i]);
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return res;
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}
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TermTree *RPFP::GetGoalTree(Node *root){
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@ -375,6 +378,19 @@ namespace Duality {
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x = x && y;
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}
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void RPFP::SetAnnotation(Node *root, const expr &t){
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hash_map<ast, Term> memo;
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Term b;
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std::vector<Term> v;
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RedVars(root, b, v);
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memo[b] = ctx.bool_val(true);
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for (unsigned i = 0; i < v.size(); i++)
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memo[v[i]] = root->Annotation.IndParams[i];
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Term annot = SubstRec(memo, t);
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// Strengthen(ref root.Annotation.Formula, annot);
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root->Annotation.Formula = annot;
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}
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void RPFP::DecodeTree(Node *root, TermTree *interp, int persist)
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{
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std::vector<TermTree *> &ic = interp->getChildren();
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@ -384,16 +400,7 @@ namespace Duality {
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for (unsigned i = 0; i < nc.size(); i++)
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DecodeTree(nc[i], ic[i], persist);
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}
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hash_map<ast, Term> memo;
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Term b;
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std::vector<Term> v;
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RedVars(root, b, v);
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memo[b] = ctx.bool_val(true);
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for (unsigned i = 0; i < v.size(); i++)
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memo[v[i]] = root->Annotation.IndParams[i];
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Term annot = SubstRec(memo, interp->getTerm());
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// Strengthen(ref root.Annotation.Formula, annot);
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root->Annotation.Formula = annot;
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SetAnnotation(root,interp->getTerm());
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#if 0
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if(persist != 0)
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Z3_persist_ast(ctx,root->Annotation.Formula,persist);
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@ -511,6 +518,10 @@ namespace Duality {
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timer_stop("solver add");
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}
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void RPFP::ConstrainParent(Edge *parent, Node *child){
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ConstrainEdgeLocalized(parent,GetAnnotation(child));
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}
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/** For incremental solving, asserts the negation of the upper bound associated
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* with a node.
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@ -526,6 +537,24 @@ namespace Duality {
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}
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}
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/** Assert a constraint on an edge in the SMT context.
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*/
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void RPFP::ConstrainEdge(Edge *e, const Term &t)
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{
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Term tl = Localize(e, t);
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ConstrainEdgeLocalized(e,tl);
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}
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void RPFP::ConstrainEdgeLocalized(Edge *e, const Term &tl)
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{
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e->constraints.push_back(tl);
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stack.back().constraints.push_back(e);
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slvr.add(tl);
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}
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/** Declare a constant in the background theory. */
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void RPFP::DeclareConstant(const FuncDecl &f){
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@ -1064,7 +1093,7 @@ namespace Duality {
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}
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}
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/* Unreachable! */
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throw "error in RPFP::ImplicantRed";
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std::cerr << "error in RPFP::ImplicantRed";
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goto done;
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}
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else if(k == Not) {
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@ -1671,6 +1700,17 @@ namespace Duality {
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return eu;
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}
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void RPFP::FixCurrentState(Edge *edge){
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hash_set<ast> dont_cares;
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resolve_ite_memo.clear();
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timer_start("UnderapproxFormula");
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Term dual = edge->dual.null() ? ctx.bool_val(true) : edge->dual;
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Term eu = UnderapproxFormula(dual,dont_cares);
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timer_stop("UnderapproxFormula");
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ConstrainEdgeLocalized(edge,eu);
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}
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RPFP::Term RPFP::ModelValueAsConstraint(const Term &t){
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if(t.is_array()){
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@ -1714,6 +1754,69 @@ namespace Duality {
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res = CreateRelation(p->Annotation.IndParams,funder);
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}
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void RPFP::GreedyReduce(solver &s, std::vector<expr> &conjuncts){
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// verify
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s.push();
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expr conj = ctx.make(And,conjuncts);
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s.add(conj);
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check_result res = s.check();
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s.pop(1);
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if(res != unsat)
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throw "should be unsat";
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for(unsigned i = 0; i < conjuncts.size(); ){
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std::swap(conjuncts[i],conjuncts.back());
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expr save = conjuncts.back();
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conjuncts.pop_back();
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s.push();
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expr conj = ctx.make(And,conjuncts);
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s.add(conj);
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check_result res = s.check();
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s.pop(1);
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if(res != unsat){
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conjuncts.push_back(save);
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std::swap(conjuncts[i],conjuncts.back());
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i++;
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}
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}
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}
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void RPFP::NegateLits(std::vector<expr> &lits){
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for(unsigned i = 0; i < lits.size(); i++){
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expr &f = lits[i];
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if(f.is_app() && f.decl().get_decl_kind() == Not)
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f = f.arg(0);
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else
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f = !f;
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}
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}
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expr RPFP::SimplifyOr(std::vector<expr> &lits){
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if(lits.size() == 0)
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return ctx.bool_val(false);
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if(lits.size() == 1)
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return lits[0];
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return ctx.make(Or,lits);
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}
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void RPFP::Generalize(Node *node){
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std::vector<expr> conjuncts;
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expr fmla = GetAnnotation(node);
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CollectConjuncts(fmla,conjuncts,false);
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// try to remove conjuncts one at a tme
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aux_solver.push();
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Edge *edge = node->Outgoing;
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if(!edge->dual.null())
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aux_solver.add(edge->dual);
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for(unsigned i = 0; i < edge->constraints.size(); i++){
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expr tl = edge->constraints[i];
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aux_solver.add(tl);
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}
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GreedyReduce(aux_solver,conjuncts);
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aux_solver.pop(1);
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NegateLits(conjuncts);
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SetAnnotation(node,SimplifyOr(conjuncts));
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}
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/** Push a scope. Assertions made after Push can be undone by Pop. */
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@ -1735,6 +1838,8 @@ namespace Duality {
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(*it)->dual = expr(ctx,NULL);
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for(std::list<Node *>::iterator it = back.nodes.begin(), en = back.nodes.end(); it != en; ++it)
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(*it)->dual = expr(ctx,NULL);
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for(std::list<Edge *>::iterator it = back.constraints.begin(), en = back.constraints.end(); it != en; ++it)
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(*it)->constraints.pop_back();
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stack.pop_back();
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}
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}
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@ -1270,18 +1270,24 @@ namespace Duality {
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}
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}
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bool UpdateNodeToNode(Node *node, Node *top){
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if(!node->Annotation.SubsetEq(top->Annotation)){
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reporter->Update(node,top->Annotation);
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indset->Update(node,top->Annotation);
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updated_nodes.insert(node->map);
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node->Annotation.IntersectWith(top->Annotation);
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return true;
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}
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return false;
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}
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/** Update the unwinding solution, using an interpolant for the
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derivation tree. */
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void UpdateWithInterpolant(Node *node, RPFP *tree, Node *top){
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if(top->Outgoing)
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for(unsigned i = 0; i < top->Outgoing->Children.size(); i++)
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UpdateWithInterpolant(node->Outgoing->Children[i],tree,top->Outgoing->Children[i]);
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if(!node->Annotation.SubsetEq(top->Annotation)){
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reporter->Update(node,top->Annotation);
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indset->Update(node,top->Annotation);
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updated_nodes.insert(node->map);
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node->Annotation.IntersectWith(top->Annotation);
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}
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UpdateNodeToNode(node, top);
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heuristic->Update(node);
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}
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@ -1305,7 +1311,8 @@ namespace Duality {
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if(node->Bound.IsFull()) return true;
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reporter->Bound(node);
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int start_decs = rpfp->CumulativeDecisions();
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DerivationTree dt(this,unwinding,reporter,heuristic,FullExpand);
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DerivationTree *dtp = new DerivationTreeSlow(this,unwinding,reporter,heuristic,FullExpand);
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DerivationTree &dt = *dtp;
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bool res = dt.Derive(unwinding,node,UseUnderapprox);
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int end_decs = rpfp->CumulativeDecisions();
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// std::cout << "decisions: " << (end_decs - start_decs) << std::endl;
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@ -1321,6 +1328,7 @@ namespace Duality {
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UpdateWithInterpolant(node,dt.tree,dt.top);
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delete dt.tree;
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}
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delete dtp;
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return !res;
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}
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@ -1491,7 +1499,7 @@ namespace Duality {
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return res != unsat;
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}
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bool Build(){
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virtual bool Build(){
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#ifdef EFFORT_BOUNDED_STRAT
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start_decs = tree->CumulativeDecisions();
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#endif
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@ -1545,7 +1553,7 @@ namespace Duality {
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}
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}
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void ExpandNode(RPFP::Node *p){
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virtual void ExpandNode(RPFP::Node *p){
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// tree->RemoveEdge(p->Outgoing);
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Edge *edge = duality->GetNodeOutgoing(p->map,last_decs);
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std::vector<RPFP::Node *> &cs = edge->Children;
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@ -1573,6 +1581,7 @@ namespace Duality {
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}
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#else
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#if 0
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void ExpansionChoices(std::set<Node *> &best){
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std::vector <Node *> unused_set, used_set;
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std::set<Node *> choices;
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@ -1668,7 +1677,7 @@ namespace Duality {
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#endif
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#endif
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bool ExpandSomeNodes(bool high_priority = false){
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bool ExpandSomeNodes(bool high_priority = false, int max = INT_MAX){
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#ifdef EFFORT_BOUNDED_STRAT
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last_decs = tree->CumulativeDecisions() - start_decs;
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#endif
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@ -1679,17 +1688,194 @@ namespace Duality {
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timer_stop("ExpansionChoices");
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std::list<RPFP::Node *> leaves_copy = leaves; // copy so can modify orig
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leaves.clear();
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int count = 0;
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for(std::list<RPFP::Node *>::iterator it = leaves_copy.begin(), en = leaves_copy.end(); it != en; ++it){
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if(choices.find(*it) != choices.end())
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if(choices.find(*it) != choices.end() && count < max){
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count++;
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ExpandNode(*it);
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}
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else leaves.push_back(*it);
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}
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timer_stop("ExpandSomeNodes");
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return !choices.empty();
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}
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void RemoveExpansion(RPFP::Node *p){
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Edge *edge = p->Outgoing;
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Node *parent = edge->Parent;
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std::vector<RPFP::Node *> cs = edge->Children;
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tree->DeleteEdge(edge);
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for(unsigned i = 0; i < cs.size(); i++)
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tree->DeleteNode(cs[i]);
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leaves.push_back(parent);
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}
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};
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class DerivationTreeSlow : public DerivationTree {
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public:
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struct stack_entry {
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unsigned level; // SMT solver stack level
|
||||
std::vector<Node *> expansions;
|
||||
};
|
||||
|
||||
std::vector<stack_entry> stack;
|
||||
|
||||
hash_map<Node *, expr> updates;
|
||||
|
||||
DerivationTreeSlow(Duality *_duality, RPFP *rpfp, Reporter *_reporter, Heuristic *_heuristic, bool _full_expand)
|
||||
: DerivationTree(_duality, rpfp, _reporter, _heuristic, _full_expand) {
|
||||
stack.push_back(stack_entry());
|
||||
}
|
||||
|
||||
virtual bool Build(){
|
||||
|
||||
stack.back().level = tree->slvr.get_scope_level();
|
||||
|
||||
while (true)
|
||||
{
|
||||
lbool res;
|
||||
|
||||
unsigned slvr_level = tree->slvr.get_scope_level();
|
||||
if(slvr_level != stack.back().level)
|
||||
throw "stacks out of sync!";
|
||||
|
||||
res = tree->Solve(top, 1); // incremental solve, keep interpolants for one pop
|
||||
|
||||
if (res == l_false) {
|
||||
if (stack.empty()) // should never happen
|
||||
return false;
|
||||
|
||||
std::vector<Node *> &expansions = stack.back().expansions;
|
||||
int update_count = 0;
|
||||
for(unsigned i = 0; i < expansions.size(); i++){
|
||||
tree->Generalize(expansions[i]);
|
||||
if(RecordUpdate(expansions[i]))
|
||||
update_count++;
|
||||
}
|
||||
if(update_count == 0)
|
||||
std::cout << "backtracked without learning\n";
|
||||
tree->Pop(1);
|
||||
hash_set<Node *> leaves_to_remove;
|
||||
for(unsigned i = 0; i < expansions.size(); i++){
|
||||
Node *node = expansions[i];
|
||||
// if(node != top)
|
||||
// tree->ConstrainParent(node->Incoming[0],node);
|
||||
std::vector<Node *> &cs = node->Outgoing->Children;
|
||||
for(unsigned i = 0; i < cs.size(); i++){
|
||||
leaves_to_remove.insert(cs[i]);
|
||||
UnmapNode(cs[i]);
|
||||
if(std::find(updated_nodes.begin(),updated_nodes.end(),cs[i]) != updated_nodes.end())
|
||||
throw "help!";
|
||||
}
|
||||
RemoveExpansion(node);
|
||||
}
|
||||
RemoveLeaves(leaves_to_remove);
|
||||
stack.pop_back();
|
||||
HandleUpdatedNodes();
|
||||
if(stack.size() == 1)
|
||||
return false;
|
||||
}
|
||||
else {
|
||||
tree->Push();
|
||||
std::vector<Node *> &expansions = stack.back().expansions;
|
||||
for(unsigned i = 0; i < expansions.size(); i++){
|
||||
tree->FixCurrentState(expansions[i]->Outgoing);
|
||||
}
|
||||
if(tree->slvr.check() == unsat)
|
||||
throw "help!";
|
||||
stack.push_back(stack_entry());
|
||||
stack.back().level = tree->slvr.get_scope_level();
|
||||
if(ExpandSomeNodes(false,1)){
|
||||
continue;
|
||||
}
|
||||
while(stack.size() > 1){
|
||||
tree->Pop(1);
|
||||
stack.pop_back();
|
||||
}
|
||||
return true;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void RemoveLeaves(hash_set<Node *> &leaves_to_remove){
|
||||
std::list<RPFP::Node *> leaves_copy;
|
||||
leaves_copy.swap(leaves);
|
||||
for(std::list<RPFP::Node *>::iterator it = leaves_copy.begin(), en = leaves_copy.end(); it != en; ++it){
|
||||
if(leaves_to_remove.find(*it) == leaves_to_remove.end())
|
||||
leaves.push_back(*it);
|
||||
}
|
||||
}
|
||||
|
||||
hash_map<Node *, std::vector<Node *> > node_map;
|
||||
std::list<Node *> updated_nodes;
|
||||
|
||||
virtual void ExpandNode(RPFP::Node *p){
|
||||
stack.back().expansions.push_back(p);
|
||||
DerivationTree::ExpandNode(p);
|
||||
std::vector<Node *> &new_nodes = p->Outgoing->Children;
|
||||
for(unsigned i = 0; i < new_nodes.size(); i++){
|
||||
Node *n = new_nodes[i];
|
||||
node_map[n->map].push_back(n);
|
||||
}
|
||||
}
|
||||
|
||||
bool RecordUpdate(Node *node){
|
||||
bool res = duality->UpdateNodeToNode(node->map,node);
|
||||
if(res){
|
||||
std::vector<Node *> to_update = node_map[node->map];
|
||||
for(unsigned i = 0; i < to_update.size(); i++){
|
||||
Node *node2 = to_update[i];
|
||||
// maintain invariant that no nodes on updated list are created at current stack level
|
||||
if(node2 == node || !(node->Incoming.size() > 0 && AtCurrentStackLevel(node2->Incoming[0]->Parent))){
|
||||
updated_nodes.push_back(node2);
|
||||
if(node2 != node)
|
||||
node2->Annotation = node->Annotation;
|
||||
}
|
||||
}
|
||||
}
|
||||
return res;
|
||||
}
|
||||
|
||||
void HandleUpdatedNodes(){
|
||||
for(std::list<Node *>::iterator it = updated_nodes.begin(), en = updated_nodes.end(); it != en;){
|
||||
Node *node = *it;
|
||||
node->Annotation = node->map->Annotation;
|
||||
if(node->Incoming.size() > 0)
|
||||
tree->ConstrainParent(node->Incoming[0],node);
|
||||
if(AtCurrentStackLevel(node->Incoming[0]->Parent)){
|
||||
std::list<Node *>::iterator victim = it;
|
||||
++it;
|
||||
updated_nodes.erase(victim);
|
||||
}
|
||||
else
|
||||
++it;
|
||||
}
|
||||
}
|
||||
|
||||
bool AtCurrentStackLevel(Node *node){
|
||||
std::vector<Node *> vec = stack.back().expansions;
|
||||
for(unsigned i = 0; i < vec.size(); i++)
|
||||
if(vec[i] == node)
|
||||
return true;
|
||||
return false;
|
||||
}
|
||||
|
||||
void UnmapNode(Node *node){
|
||||
std::vector<Node *> &vec = node_map[node->map];
|
||||
for(unsigned i = 0; i < vec.size(); i++){
|
||||
if(vec[i] == node){
|
||||
std::swap(vec[i],vec.back());
|
||||
vec.pop_back();
|
||||
return;
|
||||
}
|
||||
}
|
||||
throw "can't unmap node";
|
||||
}
|
||||
|
||||
};
|
||||
|
||||
|
||||
class Covering {
|
||||
|
||||
struct cover_info {
|
||||
|
|
|
|||
|
|
@ -425,15 +425,18 @@ expr context::make_quant(decl_kind op, const std::vector<sort> &_sorts, const st
|
|||
|
||||
static int linearize_assumptions(int num,
|
||||
TermTree *assumptions,
|
||||
std::vector<expr> &linear_assumptions,
|
||||
std::vector<std::vector <expr> > &linear_assumptions,
|
||||
std::vector<int> &parents){
|
||||
for(unsigned i = 0; i < assumptions->getChildren().size(); i++)
|
||||
num = linearize_assumptions(num, assumptions->getChildren()[i], linear_assumptions, parents);
|
||||
linear_assumptions[num] = assumptions->getTerm();
|
||||
// linear_assumptions[num].push_back(assumptions->getTerm());
|
||||
for(unsigned i = 0; i < assumptions->getChildren().size(); i++)
|
||||
parents[assumptions->getChildren()[i]->getNumber()] = num;
|
||||
parents[num] = SHRT_MAX; // in case we have no parent
|
||||
linear_assumptions[num] = assumptions->getTerm();
|
||||
linear_assumptions[num].push_back(assumptions->getTerm());
|
||||
std::vector<expr> &ts = assumptions->getTerms();
|
||||
for(unsigned i = 0; i < ts.size(); i++)
|
||||
linear_assumptions[num].push_back(ts[i]);
|
||||
return num + 1;
|
||||
}
|
||||
|
||||
|
|
@ -462,14 +465,15 @@ expr context::make_quant(decl_kind op, const std::vector<sort> &_sorts, const st
|
|||
|
||||
{
|
||||
int size = assumptions->number(0);
|
||||
std::vector<expr> linear_assumptions(size);
|
||||
std::vector<std::vector<expr> > linear_assumptions(size);
|
||||
std::vector<int> parents(size);
|
||||
linearize_assumptions(0,assumptions,linear_assumptions,parents);
|
||||
|
||||
ptr_vector< ::ast> _interpolants(size-1);
|
||||
ptr_vector< ::ast>_assumptions(size);
|
||||
vector<ptr_vector< ::ast> >_assumptions(size);
|
||||
for(int i = 0; i < size; i++)
|
||||
_assumptions[i] = linear_assumptions[i];
|
||||
for(unsigned j = 0; j < linear_assumptions[i].size(); j++)
|
||||
_assumptions[i].push_back(linear_assumptions[i][j]);
|
||||
::vector<int> _parents; _parents.resize(parents.size());
|
||||
for(unsigned i = 0; i < parents.size(); i++)
|
||||
_parents[i] = parents[i];
|
||||
|
|
@ -481,7 +485,8 @@ expr context::make_quant(decl_kind op, const std::vector<sort> &_sorts, const st
|
|||
|
||||
if(!incremental){
|
||||
for(unsigned i = 0; i < linear_assumptions.size(); i++)
|
||||
add(linear_assumptions[i]);
|
||||
for(unsigned j = 0; j < linear_assumptions[i].size(); j++)
|
||||
add(linear_assumptions[i][j]);
|
||||
}
|
||||
|
||||
check_result res = check();
|
||||
|
|
|
|||
|
|
@ -867,6 +867,9 @@ namespace Duality {
|
|||
if(m_solver)
|
||||
m_solver->cancel();
|
||||
}
|
||||
|
||||
unsigned get_scope_level(){return m_solver->get_scope_level();}
|
||||
|
||||
};
|
||||
|
||||
#if 0
|
||||
|
|
@ -1199,6 +1202,8 @@ namespace Duality {
|
|||
|
||||
inline expr getTerm(){return term;}
|
||||
|
||||
inline std::vector<expr> &getTerms(){return terms;}
|
||||
|
||||
inline std::vector<TermTree *> &getChildren(){
|
||||
return children;
|
||||
}
|
||||
|
|
@ -1215,6 +1220,8 @@ namespace Duality {
|
|||
}
|
||||
|
||||
inline void setTerm(expr t){term = t;}
|
||||
|
||||
inline void addTerm(expr t){terms.push_back(t);}
|
||||
|
||||
inline void setChildren(const std::vector<TermTree *> & _children){
|
||||
children = _children;
|
||||
|
|
@ -1231,6 +1238,7 @@ namespace Duality {
|
|||
|
||||
private:
|
||||
expr term;
|
||||
std::vector<expr> terms;
|
||||
std::vector<TermTree *> children;
|
||||
int num;
|
||||
};
|
||||
|
|
|
|||
|
|
@ -75,15 +75,16 @@ struct frame_reducer : public iz3mgr {
|
|||
}
|
||||
}
|
||||
|
||||
void get_frames(const std::vector<ast> &z3_preds,
|
||||
void get_frames(const std::vector<std::vector<ast> >&z3_preds,
|
||||
const std::vector<int> &orig_parents,
|
||||
std::vector<ast> &assertions,
|
||||
std::vector<std::vector<ast> >&assertions,
|
||||
std::vector<int> &parents,
|
||||
z3pf proof){
|
||||
frames = z3_preds.size();
|
||||
orig_parents_copy = orig_parents;
|
||||
for(unsigned i = 0; i < z3_preds.size(); i++)
|
||||
frame_map[z3_preds[i]] = i;
|
||||
for(unsigned j = 0; j < z3_preds[i].size(); j++)
|
||||
frame_map[z3_preds[i][j]] = i;
|
||||
used_frames.resize(frames);
|
||||
hash_set<ast> memo;
|
||||
get_proof_assumptions_rec(proof,memo,used_frames);
|
||||
|
|
@ -202,7 +203,7 @@ public:
|
|||
}
|
||||
|
||||
void proof_to_interpolant(z3pf proof,
|
||||
const std::vector<ast> &cnsts,
|
||||
const std::vector<std::vector<ast> > &cnsts,
|
||||
const std::vector<int> &parents,
|
||||
std::vector<ast> &interps,
|
||||
const std::vector<ast> &theory,
|
||||
|
|
@ -216,7 +217,7 @@ public:
|
|||
|
||||
// get rid of frames not used in proof
|
||||
|
||||
std::vector<ast> cnsts_vec;
|
||||
std::vector<std::vector<ast> > cnsts_vec;
|
||||
std::vector<int> parents_vec;
|
||||
frame_reducer fr(*this);
|
||||
fr.get_frames(cnsts,parents,cnsts_vec,parents_vec,proof);
|
||||
|
|
@ -235,10 +236,7 @@ public:
|
|||
#define BINARY_INTERPOLATION
|
||||
#ifndef BINARY_INTERPOLATION
|
||||
// create a translator
|
||||
std::vector<std::vector<ast> > cnsts_vec_vec(cnsts_vec.size());
|
||||
for(unsigned i = 0; i < cnsts_vec.size(); i++)
|
||||
cnsts_vec_vec[i].push_back(cnsts_vec[i]);
|
||||
iz3translation *tr = iz3translation::create(*this,sp,cnsts_vec_vec,parents_vec,theory);
|
||||
iz3translation *tr = iz3translation::create(*this,sp,cnsts_vec,parents_vec,theory);
|
||||
tr_killer.set(tr);
|
||||
|
||||
// set the translation options, if needed
|
||||
|
|
@ -273,7 +271,8 @@ public:
|
|||
std::vector<std::vector<ast> > cnsts_vec_vec(2);
|
||||
for(unsigned j = 0; j < cnsts_vec.size(); j++){
|
||||
bool is_A = the_base.in_range(j,rng);
|
||||
cnsts_vec_vec[is_A ? 0 : 1].push_back(cnsts_vec[j]);
|
||||
for(unsigned k = 0; k < cnsts_vec[j].size(); k++)
|
||||
cnsts_vec_vec[is_A ? 0 : 1].push_back(cnsts_vec[j][k]);
|
||||
}
|
||||
|
||||
killme<iz3translation> tr_killer_i;
|
||||
|
|
@ -308,6 +307,19 @@ public:
|
|||
}
|
||||
|
||||
|
||||
void proof_to_interpolant(z3pf proof,
|
||||
std::vector<ast> &cnsts,
|
||||
const std::vector<int> &parents,
|
||||
std::vector<ast> &interps,
|
||||
const std::vector<ast> &theory,
|
||||
interpolation_options_struct *options = 0
|
||||
){
|
||||
std::vector<std::vector<ast> > cnsts_vec(cnsts.size());
|
||||
for(unsigned i = 0; i < cnsts.size(); i++)
|
||||
cnsts_vec[i].push_back(cnsts[i]);
|
||||
proof_to_interpolant(proof,cnsts_vec,parents,interps,theory,options);
|
||||
}
|
||||
|
||||
// same as above, but represents the tree using an ast
|
||||
|
||||
void proof_to_interpolant(const z3pf &proof,
|
||||
|
|
@ -322,7 +334,6 @@ public:
|
|||
|
||||
to_parents_vec_representation(_cnsts, tree, cnsts, parents, theory, pos_map);
|
||||
|
||||
|
||||
//use the parents vector representation to compute interpolant
|
||||
proof_to_interpolant(proof,cnsts,parents,interps,theory,options);
|
||||
|
||||
|
|
@ -397,6 +408,35 @@ void iz3interpolate(ast_manager &_m_manager,
|
|||
interps[i] = itp.uncook(_interps[i]);
|
||||
}
|
||||
|
||||
void iz3interpolate(ast_manager &_m_manager,
|
||||
ast *proof,
|
||||
const ::vector<ptr_vector<ast> > &cnsts,
|
||||
const ::vector<int> &parents,
|
||||
ptr_vector<ast> &interps,
|
||||
const ptr_vector<ast> &theory,
|
||||
interpolation_options_struct * options)
|
||||
{
|
||||
iz3interp itp(_m_manager);
|
||||
if(options)
|
||||
options->apply(itp);
|
||||
std::vector<std::vector<iz3mgr::ast> > _cnsts(cnsts.size());
|
||||
std::vector<int> _parents(parents.size());
|
||||
std::vector<iz3mgr::ast> _interps;
|
||||
std::vector<iz3mgr::ast> _theory(theory.size());
|
||||
for(unsigned i = 0; i < cnsts.size(); i++)
|
||||
for(unsigned j = 0; j < cnsts[i].size(); j++)
|
||||
_cnsts[i].push_back(itp.cook(cnsts[i][j]));
|
||||
for(unsigned i = 0; i < parents.size(); i++)
|
||||
_parents[i] = parents[i];
|
||||
for(unsigned i = 0; i < theory.size(); i++)
|
||||
_theory[i] = itp.cook(theory[i]);
|
||||
iz3mgr::ast _proof = itp.cook(proof);
|
||||
itp.proof_to_interpolant(_proof,_cnsts,_parents,_interps,_theory,options);
|
||||
interps.resize(_interps.size());
|
||||
for(unsigned i = 0; i < interps.size(); i++)
|
||||
interps[i] = itp.uncook(_interps[i]);
|
||||
}
|
||||
|
||||
void iz3interpolate(ast_manager &_m_manager,
|
||||
ast *proof,
|
||||
const ptr_vector<ast> &cnsts,
|
||||
|
|
|
|||
|
|
@ -56,6 +56,16 @@ void iz3interpolate(ast_manager &_m_manager,
|
|||
const ptr_vector<ast> &theory,
|
||||
interpolation_options_struct * options = 0);
|
||||
|
||||
/* Same as above, but each constraint is a vector of formulas. */
|
||||
|
||||
void iz3interpolate(ast_manager &_m_manager,
|
||||
ast *proof,
|
||||
const vector<ptr_vector<ast> > &cnsts,
|
||||
const ::vector<int> &parents,
|
||||
ptr_vector<ast> &interps,
|
||||
const ptr_vector<ast> &theory,
|
||||
interpolation_options_struct * options = 0);
|
||||
|
||||
/* Compute an interpolant from a proof. This version uses the ast
|
||||
representation, for compatibility with the new API. */
|
||||
|
||||
|
|
|
|||
|
|
@ -815,6 +815,22 @@ iz3mgr::ast iz3mgr::subst(ast var, ast t, ast e){
|
|||
return subst(memo,var,t,e);
|
||||
}
|
||||
|
||||
iz3mgr::ast iz3mgr::subst(stl_ext::hash_map<ast,ast> &subst_memo,ast e){
|
||||
std::pair<ast,ast> foo(e,ast());
|
||||
std::pair<hash_map<ast,ast>::iterator,bool> bar = subst_memo.insert(foo);
|
||||
ast &res = bar.first->second;
|
||||
if(bar.second){
|
||||
int nargs = num_args(e);
|
||||
std::vector<ast> args(nargs);
|
||||
for(int i = 0; i < nargs; i++)
|
||||
args[i] = subst(subst_memo,arg(e,i));
|
||||
opr f = op(e);
|
||||
if(f == Equal && args[0] == args[1]) res = mk_true();
|
||||
else res = clone(e,args);
|
||||
}
|
||||
return res;
|
||||
}
|
||||
|
||||
// apply a quantifier to a formula, with some optimizations
|
||||
// 1) bound variable does not occur -> no quantifier
|
||||
// 2) bound variable must be equal to some term -> substitute
|
||||
|
|
|
|||
|
|
@ -631,6 +631,9 @@ class iz3mgr {
|
|||
|
||||
ast subst(ast var, ast t, ast e);
|
||||
|
||||
// apply a substitution defined by a map
|
||||
ast subst(stl_ext::hash_map<ast,ast> &map, ast e);
|
||||
|
||||
// apply a quantifier to a formula, with some optimizations
|
||||
// 1) bound variable does not occur -> no quantifier
|
||||
// 2) bound variable must be equal to some term -> substitute
|
||||
|
|
|
|||
|
|
@ -118,6 +118,28 @@ class iz3proof_itp_impl : public iz3proof_itp {
|
|||
where t is an arbitrary term */
|
||||
symb rewrite_B;
|
||||
|
||||
/* a normalization step is of the form (lhs=rhs) : proof, where "proof"
|
||||
is a proof of lhs=rhs and lhs is a mixed term. If rhs is a mixed term
|
||||
then it must have a greater index than lhs. */
|
||||
symb normal_step;
|
||||
|
||||
/* A chain of normalization steps is either "true" (the null chain)
|
||||
or normal_chain(<step> <tail>), where step is a normalization step
|
||||
and tail is a normalization chain. The lhs of <step> must have
|
||||
a less term index than any lhs in the chain. Moreover, the rhs of
|
||||
<step> may not occur as the lhs of step in <tail>. If we wish to
|
||||
add lhs=rhs to the beginning of <tail> and rhs=rhs' occurs in <tail>
|
||||
we must apply transitivity, transforming <step> to lhs=rhs'. */
|
||||
|
||||
symb normal_chain;
|
||||
|
||||
/* If p is a proof of Q and c is a normalization chain, then normal(p,c)
|
||||
is a proof of Q(c) (that is, Q with all substitutions in c performed). */
|
||||
|
||||
symb normal;
|
||||
|
||||
|
||||
|
||||
|
||||
ast get_placeholder(ast t){
|
||||
hash_map<ast,ast>::iterator it = placeholders.find(t);
|
||||
|
|
@ -521,10 +543,16 @@ class iz3proof_itp_impl : public iz3proof_itp {
|
|||
throw cannot_simplify();
|
||||
}
|
||||
|
||||
bool is_normal_ineq(const ast &ineq){
|
||||
if(sym(ineq) == normal)
|
||||
return is_ineq(arg(ineq,0));
|
||||
return is_ineq(ineq);
|
||||
}
|
||||
|
||||
ast simplify_sum(std::vector<ast> &args){
|
||||
ast cond = mk_true();
|
||||
ast ineq = args[0];
|
||||
if(!is_ineq(ineq)) throw cannot_simplify();
|
||||
if(!is_normal_ineq(ineq)) throw cannot_simplify();
|
||||
sum_cond_ineq(ineq,cond,args[1],args[2]);
|
||||
return my_implies(cond,ineq);
|
||||
}
|
||||
|
|
@ -540,6 +568,8 @@ class iz3proof_itp_impl : public iz3proof_itp {
|
|||
}
|
||||
|
||||
ast ineq_from_chain(const ast &chain, ast &cond){
|
||||
if(sym(chain) == normal)
|
||||
throw "normalized inequalities not supported here";
|
||||
if(is_rewrite_chain(chain)){
|
||||
ast last = chain_last(chain);
|
||||
ast rest = chain_rest(chain);
|
||||
|
|
@ -561,6 +591,13 @@ class iz3proof_itp_impl : public iz3proof_itp {
|
|||
cond = my_and(cond,arg(ineq2,0));
|
||||
}
|
||||
else {
|
||||
if(sym(ineq) == normal || sym(ineq2) == normal){
|
||||
ast Aproves = mk_true();
|
||||
sum_normal_ineq(ineq,coeff2,ineq2,Aproves,cond);
|
||||
if(!is_true(Aproves))
|
||||
throw "Aproves not handled in sum_cond_ineq";
|
||||
return;
|
||||
}
|
||||
ast the_ineq = ineq_from_chain(ineq2,cond);
|
||||
if(is_ineq(the_ineq))
|
||||
linear_comb(ineq,coeff2,the_ineq);
|
||||
|
|
@ -569,6 +606,27 @@ class iz3proof_itp_impl : public iz3proof_itp {
|
|||
}
|
||||
}
|
||||
|
||||
void destruct_normal(const ast &pf, ast &p, ast &n){
|
||||
if(sym(pf) == normal){
|
||||
p = arg(pf,0);
|
||||
n = arg(pf,1);
|
||||
}
|
||||
else {
|
||||
p = pf;
|
||||
n = mk_true();
|
||||
}
|
||||
}
|
||||
|
||||
void sum_normal_ineq(ast &ineq, const ast &coeff2, const ast &ineq2, ast &Aproves, ast &Bproves){
|
||||
ast in1,in2,n1,n2;
|
||||
destruct_normal(ineq,in1,n1);
|
||||
destruct_normal(ineq2,in2,n2);
|
||||
ast dummy;
|
||||
sum_cond_ineq(in1,dummy,coeff2,in2);
|
||||
n1 = merge_normal_chains(n1,n2, Aproves, Bproves);
|
||||
ineq = make(normal,in1,n1);
|
||||
}
|
||||
|
||||
bool is_ineq(const ast &ineq){
|
||||
opr o = op(ineq);
|
||||
if(o == Not) o = op(arg(ineq,0));
|
||||
|
|
@ -577,6 +635,12 @@ class iz3proof_itp_impl : public iz3proof_itp {
|
|||
|
||||
// divide both sides of inequality by a non-negative integer divisor
|
||||
ast idiv_ineq(const ast &ineq1, const ast &divisor){
|
||||
if(sym(ineq1) == normal){
|
||||
ast in1,n1;
|
||||
destruct_normal(ineq1,in1,n1);
|
||||
in1 = idiv_ineq(in1,divisor);
|
||||
return make(normal,in1,n1);
|
||||
}
|
||||
if(divisor == make_int(rational(1)))
|
||||
return ineq1;
|
||||
ast ineq = ineq1;
|
||||
|
|
@ -649,11 +713,18 @@ class iz3proof_itp_impl : public iz3proof_itp {
|
|||
ast equa = sep_cond(arg(pf,0),cond);
|
||||
if(is_equivrel_chain(equa)){
|
||||
ast lhs,rhs; eq_from_ineq(arg(neg_equality,0),lhs,rhs); // get inequality we need to prove
|
||||
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 = chain_conditions(LitB,equa);
|
||||
if(is_true(Bconds) && op(ineqs) != And)
|
||||
return my_implies(cond,ineqs);
|
||||
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);
|
||||
}
|
||||
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()));
|
||||
}
|
||||
}
|
||||
}
|
||||
throw cannot_simplify();
|
||||
|
|
@ -757,11 +828,57 @@ class iz3proof_itp_impl : public iz3proof_itp {
|
|||
chain = concat_rewrite_chain(chain,split[1]);
|
||||
}
|
||||
}
|
||||
else // if not an equivalence, must be of form T <-> pred
|
||||
else { // if not an equivalence, must be of form T <-> pred
|
||||
chain = concat_rewrite_chain(P,PeqQ);
|
||||
}
|
||||
return chain;
|
||||
}
|
||||
|
||||
void get_subterm_normals(const ast &ineq1, const ast &ineq2, const ast &chain, ast &normals,
|
||||
const ast &pos, hash_set<ast> &memo, ast &Aproves, ast &Bproves){
|
||||
opr o1 = op(ineq1);
|
||||
opr o2 = op(ineq2);
|
||||
if(o1 == Not || o1 == Leq || o1 == Lt || o1 == Geq || o1 == Gt || o1 == Plus || o1 == Times){
|
||||
int n = num_args(ineq1);
|
||||
if(o2 != o1 || num_args(ineq2) != n)
|
||||
throw "bad inequality rewriting";
|
||||
for(int i = 0; i < n; i++){
|
||||
ast new_pos = add_pos_to_end(pos,i);
|
||||
get_subterm_normals(arg(ineq1,i), arg(ineq2,i), chain, normals, new_pos, memo, Aproves, Bproves);
|
||||
}
|
||||
}
|
||||
else if(get_term_type(ineq2) == LitMixed && memo.find(ineq2) == memo.end()){
|
||||
memo.insert(ineq2);
|
||||
ast sub_chain = extract_rewrites(chain,pos);
|
||||
if(is_true(sub_chain))
|
||||
throw "bad inequality rewriting";
|
||||
ast new_normal = make_normal(ineq2,ineq1,reverse_chain(sub_chain));
|
||||
normals = merge_normal_chains(normals,cons_normal(new_normal,mk_true()), Aproves, Bproves);
|
||||
}
|
||||
}
|
||||
|
||||
ast rewrite_chain_to_normal_ineq(const ast &chain, ast &Aproves, ast &Bproves){
|
||||
ast tail, pref = get_head_chain(chain,tail,false); // pref is x=y, tail is x=y -> x'=y'
|
||||
ast head = chain_last(pref);
|
||||
ast ineq1 = rewrite_rhs(head);
|
||||
ast ineq2 = apply_rewrite_chain(ineq1,tail);
|
||||
ast nc = mk_true();
|
||||
hash_set<ast> memo;
|
||||
get_subterm_normals(ineq1,ineq2,tail,nc,top_pos,memo, Aproves, Bproves);
|
||||
ast itp;
|
||||
if(is_rewrite_side(LitA,head)){
|
||||
itp = ineq1;
|
||||
ast mc = z3_simplify(chain_side_proves(LitB,pref));
|
||||
Bproves = my_and(Bproves,mc);
|
||||
}
|
||||
else {
|
||||
itp = make(Leq,make_int(rational(0)),make_int(rational(0)));
|
||||
ast mc = z3_simplify(chain_side_proves(LitA,pref));
|
||||
Aproves = my_and(Aproves,mc);
|
||||
}
|
||||
return make(normal,itp,nc);
|
||||
}
|
||||
|
||||
/* Given a chain rewrite chain deriving not P and a rewrite chain deriving P, return an interpolant. */
|
||||
ast contra_chain(const ast &neg_chain, const ast &pos_chain){
|
||||
// equality is a special case. we use the derivation of x=y to rewrite not(x=y) to not(y=y)
|
||||
|
|
@ -790,11 +907,18 @@ class iz3proof_itp_impl : public iz3proof_itp {
|
|||
}
|
||||
|
||||
ast simplify_modpon(const std::vector<ast> &args){
|
||||
ast cond = mk_true();
|
||||
ast chain = simplify_modpon_fwd(args,cond);
|
||||
ast Q2 = sep_cond(args[2],cond);
|
||||
ast interp = is_negation_chain(chain) ? contra_chain(chain,Q2) : contra_chain(Q2,chain);
|
||||
return my_implies(cond,interp);
|
||||
ast Aproves = mk_true(), Bproves = mk_true();
|
||||
ast chain = simplify_modpon_fwd(args,Bproves);
|
||||
ast Q2 = sep_cond(args[2],Bproves);
|
||||
ast interp;
|
||||
if(is_normal_ineq(Q2)){ // inequalities are special
|
||||
ast nQ2 = rewrite_chain_to_normal_ineq(chain,Aproves,Bproves);
|
||||
sum_cond_ineq(nQ2,Bproves,make_int(rational(1)),Q2);
|
||||
interp = normalize(nQ2);
|
||||
}
|
||||
else
|
||||
interp = is_negation_chain(chain) ? contra_chain(chain,Q2) : contra_chain(Q2,chain);
|
||||
return my_and(Aproves,my_implies(Bproves,interp));
|
||||
}
|
||||
|
||||
|
||||
|
|
@ -1035,6 +1159,12 @@ class iz3proof_itp_impl : public iz3proof_itp {
|
|||
return make(add_pos,make_int(rational(arg)),pos);
|
||||
}
|
||||
|
||||
ast add_pos_to_end(const ast &pos, int i){
|
||||
if(pos == top_pos)
|
||||
return pos_add(i,pos);
|
||||
return make(add_pos,arg(pos,0),add_pos_to_end(arg(pos,1),i));
|
||||
}
|
||||
|
||||
/* return the argument number of position, if not top */
|
||||
int pos_arg(const ast &pos){
|
||||
rational r;
|
||||
|
|
@ -1170,6 +1300,10 @@ class iz3proof_itp_impl : public iz3proof_itp {
|
|||
return make(sym(rew),pos_add(apos,arg(rew,0)),arg(rew,1),arg(rew,2));
|
||||
}
|
||||
|
||||
ast rewrite_pos_set(const ast &pos, const ast &rew){
|
||||
return make(sym(rew),pos,arg(rew,1),arg(rew,2));
|
||||
}
|
||||
|
||||
ast rewrite_up(const ast &rew){
|
||||
return make(sym(rew),arg(arg(rew,0),1),arg(rew,1),arg(rew,2));
|
||||
}
|
||||
|
|
@ -1317,6 +1451,28 @@ class iz3proof_itp_impl : public iz3proof_itp {
|
|||
split_chain_rec(chain,res);
|
||||
}
|
||||
|
||||
ast extract_rewrites(const ast &chain, const ast &pos){
|
||||
if(is_true(chain))
|
||||
return chain;
|
||||
ast last = chain_last(chain);
|
||||
ast rest = chain_rest(chain);
|
||||
ast new_rest = extract_rewrites(rest,pos);
|
||||
ast p1 = rewrite_pos(last);
|
||||
ast diff;
|
||||
switch(pos_diff(p1,pos,diff)){
|
||||
case -1: {
|
||||
ast new_last = rewrite_pos_set(diff, last);
|
||||
return chain_cons(new_rest,new_last);
|
||||
}
|
||||
case 1:
|
||||
if(rewrite_lhs(last) != rewrite_rhs(last))
|
||||
throw "bad rewrite chain";
|
||||
break;
|
||||
default:;
|
||||
}
|
||||
return new_rest;
|
||||
}
|
||||
|
||||
ast down_chain(const ast &chain){
|
||||
ast split[2];
|
||||
split_chain(chain,split);
|
||||
|
|
@ -1381,7 +1537,7 @@ class iz3proof_itp_impl : public iz3proof_itp {
|
|||
// ast s = ineq_to_lhs(ineq);
|
||||
// ast srhs = arg(s,1);
|
||||
ast srhs = arg(ineq,0);
|
||||
if(op(srhs) == Plus && num_args(srhs) == 2){
|
||||
if(op(srhs) == Plus && num_args(srhs) == 2 && arg(ineq,1) == make_int(rational(0))){
|
||||
lhs = arg(srhs,0);
|
||||
rhs = arg(srhs,1);
|
||||
// if(op(lhs) == Times)
|
||||
|
|
@ -1393,6 +1549,11 @@ class iz3proof_itp_impl : public iz3proof_itp {
|
|||
return;
|
||||
}
|
||||
}
|
||||
if(op(ineq) == Leq){
|
||||
lhs = srhs;
|
||||
rhs = arg(ineq,1);
|
||||
return;
|
||||
}
|
||||
throw "bad ineq";
|
||||
}
|
||||
|
||||
|
|
@ -1404,7 +1565,171 @@ class iz3proof_itp_impl : public iz3proof_itp {
|
|||
return chain_cons(rest,last);
|
||||
}
|
||||
|
||||
ast apply_rewrite_chain(const ast &t, const ast &chain){
|
||||
if(is_true(chain))
|
||||
return t;
|
||||
ast last = chain_last(chain);
|
||||
ast rest = chain_rest(chain);
|
||||
ast mid = apply_rewrite_chain(t,rest);
|
||||
ast res = subst_in_pos(mid,rewrite_pos(last),rewrite_rhs(last));
|
||||
return res;
|
||||
}
|
||||
|
||||
ast drop_rewrites(LitType t, const ast &chain, ast &remainder){
|
||||
if(!is_true(chain)){
|
||||
ast last = chain_last(chain);
|
||||
ast rest = chain_rest(chain);
|
||||
if(is_rewrite_side(t,last)){
|
||||
ast res = drop_rewrites(t,rest,remainder);
|
||||
remainder = chain_cons(remainder,last);
|
||||
return res;
|
||||
}
|
||||
}
|
||||
remainder = mk_true();
|
||||
return chain;
|
||||
}
|
||||
|
||||
// Normalization chains
|
||||
|
||||
ast cons_normal(const ast &first, const ast &rest){
|
||||
return make(normal_chain,first,rest);
|
||||
}
|
||||
|
||||
ast normal_first(const ast &t){
|
||||
return arg(t,0);
|
||||
}
|
||||
|
||||
ast normal_rest(const ast &t){
|
||||
return arg(t,1);
|
||||
}
|
||||
|
||||
ast normal_lhs(const ast &t){
|
||||
return arg(arg(t,0),1);
|
||||
}
|
||||
|
||||
ast normal_rhs(const ast &t){
|
||||
return arg(arg(t,0),1);
|
||||
}
|
||||
|
||||
ast normal_proof(const ast &t){
|
||||
return arg(t,1);
|
||||
}
|
||||
|
||||
ast make_normal(const ast &lhs, const ast &rhs, const ast &proof){
|
||||
return make(normal_step,make_equiv(lhs,rhs),proof);
|
||||
}
|
||||
|
||||
ast fix_normal(const ast &lhs, const ast &rhs, const ast &proof){
|
||||
LitType rhst = get_term_type(rhs);
|
||||
if(rhst != LitMixed || ast_id(lhs) < ast_id(rhs))
|
||||
return make_normal(lhs,rhs,proof);
|
||||
else
|
||||
return make_normal(rhs,lhs,reverse_chain(proof));
|
||||
}
|
||||
|
||||
ast chain_side_proves(LitType side, const ast &chain){
|
||||
LitType other_side = side == LitA ? LitB : LitA;
|
||||
return my_and(chain_conditions(other_side,chain),my_implies(chain_conditions(side,chain),chain_formulas(side,chain)));
|
||||
}
|
||||
|
||||
// Merge two normalization chains
|
||||
ast merge_normal_chains_rec(const ast &chain1, const ast &chain2, hash_map<ast,ast> &trans, ast &Aproves, ast &Bproves){
|
||||
if(is_true(chain1))
|
||||
return chain2;
|
||||
if(is_true(chain2))
|
||||
return chain1;
|
||||
ast f1 = normal_first(chain1);
|
||||
ast f2 = normal_first(chain2);
|
||||
ast lhs1 = normal_lhs(f1);
|
||||
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));
|
||||
ast rhs1 = normal_rhs(f1);
|
||||
ast rhs2 = normal_rhs(f2);
|
||||
LitType t1 = get_term_type(rhs1);
|
||||
LitType t2 = get_term_type(rhs2);
|
||||
int tid1 = ast_id(rhs1);
|
||||
int tid2 = ast_id(rhs2);
|
||||
ast pf1 = normal_proof(f1);
|
||||
ast pf2 = normal_proof(f2);
|
||||
ast new_normal;
|
||||
if(t1 == LitMixed && (t2 != LitMixed || tid2 > tid1)){
|
||||
ast new_proof = concat_rewrite_chain(reverse_chain(pf1),pf2);
|
||||
new_normal = f2;
|
||||
trans[rhs1] = make_normal(rhs1,rhs2,new_proof);
|
||||
}
|
||||
else if(t2 == LitMixed && (t1 != LitMixed || tid1 > tid2))
|
||||
return merge_normal_chains_rec(chain2,chain1,trans,Aproves,Bproves);
|
||||
else if(t1 == LitA && t2 == LitB){
|
||||
ast new_proof = concat_rewrite_chain(reverse_chain(pf1),pf2);
|
||||
ast Bproof, Aproof = drop_rewrites(LitB,new_proof,Bproof);
|
||||
ast mcA = chain_side_proves(LitB,Aproof);
|
||||
Bproves = my_and(Bproves,mcA);
|
||||
ast mcB = chain_side_proves(LitA,Bproof);
|
||||
Aproves = my_and(Aproves,mcB);
|
||||
ast rep = apply_rewrite_chain(rhs1,Aproof);
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new_proof = concat_rewrite_chain(pf1,Aproof);
|
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new_normal = make_normal(rhs1,rep,new_proof);
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}
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else if(t1 == LitA && t2 == LitB)
|
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return merge_normal_chains_rec(chain2,chain1,trans,Aproves,Bproves);
|
||||
else if(t1 == LitA) {
|
||||
ast new_proof = concat_rewrite_chain(reverse_chain(pf1),pf2);
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||||
ast mc = chain_side_proves(LitB,new_proof);
|
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Bproves = my_and(Bproves,mc);
|
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new_normal = f1; // choice is arbitrary
|
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}
|
||||
else { /* t1 = t2 = LitB */
|
||||
ast new_proof = concat_rewrite_chain(reverse_chain(pf1),pf2);
|
||||
ast mc = chain_side_proves(LitA,new_proof);
|
||||
Aproves = my_and(Aproves,mc);
|
||||
new_normal = f1; // choice is arbitrary
|
||||
}
|
||||
return cons_normal(new_normal,merge_normal_chains_rec(normal_rest(chain1),normal_rest(chain2),trans,Aproves,Bproves));
|
||||
}
|
||||
|
||||
ast trans_normal_chain(const ast &chain, hash_map<ast,ast> &trans){
|
||||
if(is_true(chain))
|
||||
return chain;
|
||||
ast f = normal_first(chain);
|
||||
ast r = normal_rest(chain);
|
||||
ast rhs = normal_rhs(f);
|
||||
hash_map<ast,ast>::iterator it = trans.find(rhs);
|
||||
ast new_normal;
|
||||
if(it != trans.end()){
|
||||
const ast &f2 = it->second;
|
||||
ast pf = concat_rewrite_chain(normal_proof(f),normal_proof(f2));
|
||||
new_normal = make_normal(normal_lhs(f),normal_rhs(f2),pf);
|
||||
}
|
||||
else
|
||||
new_normal = f;
|
||||
return cons_normal(new_normal,trans_normal_chain(r,trans));
|
||||
}
|
||||
|
||||
ast merge_normal_chains(const ast &chain1, const ast &chain2, ast &Aproves, ast &Bproves){
|
||||
hash_map<ast,ast> trans;
|
||||
ast res = merge_normal_chains_rec(chain1,chain2,trans,Aproves,Bproves);
|
||||
res = trans_normal_chain(res,trans);
|
||||
return res;
|
||||
}
|
||||
|
||||
ast normalize(const ast &t){
|
||||
if(sym(t) != normal)
|
||||
return t;
|
||||
ast chain = arg(t,1);
|
||||
hash_map<ast,ast> map;
|
||||
for(ast c = chain; !is_true(c); c = normal_rest(c)){
|
||||
ast first = normal_first(c);
|
||||
ast lhs = normal_lhs(first);
|
||||
ast rhs = normal_rhs(first);
|
||||
map[lhs] = rhs;
|
||||
}
|
||||
ast res = subst(map,arg(t,0));
|
||||
return res;
|
||||
}
|
||||
|
||||
/** Make an assumption node. The given clause is assumed in the given frame. */
|
||||
virtual node make_assumption(int frame, const std::vector<ast> &assumption){
|
||||
if(!weak){
|
||||
|
|
@ -1939,6 +2264,8 @@ class iz3proof_itp_impl : public iz3proof_itp {
|
|||
*/
|
||||
|
||||
ast make_refl(const ast &e){
|
||||
if(get_term_type(e) == LitA)
|
||||
return mk_false();
|
||||
return mk_true(); // TODO: is this right?
|
||||
}
|
||||
|
||||
|
|
@ -2141,6 +2468,12 @@ public:
|
|||
m().inc_ref(rewrite_A);
|
||||
rewrite_B = function("@rewrite_B",3,boolboolbooldom,bool_type());
|
||||
m().inc_ref(rewrite_B);
|
||||
normal_step = function("@normal_step",2,boolbooldom,bool_type());
|
||||
m().inc_ref(normal_step);
|
||||
normal_chain = function("@normal_chain",2,boolbooldom,bool_type());
|
||||
m().inc_ref(normal_chain);
|
||||
normal = function("@normal",2,boolbooldom,bool_type());
|
||||
m().inc_ref(normal);
|
||||
}
|
||||
|
||||
~iz3proof_itp_impl(){
|
||||
|
|
|
|||
Loading…
Reference in a new issue