mirror of
https://github.com/Z3Prover/z3
synced 2025-04-24 17:45:32 +00:00
working on duality and quantified arithmetic in interpolation
This commit is contained in:
Ken McMillan
parent
8320144af0
commit
a93f8b04e5
10 changed files with 829 additions and 60 deletions
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@ -75,15 +75,16 @@ struct frame_reducer : public iz3mgr {
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}
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}
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void get_frames(const std::vector<ast> &z3_preds,
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void get_frames(const std::vector<std::vector<ast> >&z3_preds,
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const std::vector<int> &orig_parents,
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std::vector<ast> &assertions,
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std::vector<std::vector<ast> >&assertions,
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std::vector<int> &parents,
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z3pf proof){
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frames = z3_preds.size();
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orig_parents_copy = orig_parents;
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for(unsigned i = 0; i < z3_preds.size(); i++)
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frame_map[z3_preds[i]] = i;
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for(unsigned j = 0; j < z3_preds[i].size(); j++)
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frame_map[z3_preds[i][j]] = i;
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used_frames.resize(frames);
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hash_set<ast> memo;
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get_proof_assumptions_rec(proof,memo,used_frames);
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@ -202,7 +203,7 @@ public:
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}
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void proof_to_interpolant(z3pf proof,
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const std::vector<ast> &cnsts,
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const std::vector<std::vector<ast> > &cnsts,
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const std::vector<int> &parents,
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std::vector<ast> &interps,
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const std::vector<ast> &theory,
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@ -216,7 +217,7 @@ public:
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// get rid of frames not used in proof
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std::vector<ast> cnsts_vec;
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std::vector<std::vector<ast> > cnsts_vec;
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std::vector<int> parents_vec;
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frame_reducer fr(*this);
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fr.get_frames(cnsts,parents,cnsts_vec,parents_vec,proof);
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@ -235,10 +236,7 @@ public:
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#define BINARY_INTERPOLATION
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#ifndef BINARY_INTERPOLATION
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// create a translator
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std::vector<std::vector<ast> > cnsts_vec_vec(cnsts_vec.size());
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for(unsigned i = 0; i < cnsts_vec.size(); i++)
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cnsts_vec_vec[i].push_back(cnsts_vec[i]);
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iz3translation *tr = iz3translation::create(*this,sp,cnsts_vec_vec,parents_vec,theory);
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iz3translation *tr = iz3translation::create(*this,sp,cnsts_vec,parents_vec,theory);
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tr_killer.set(tr);
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// set the translation options, if needed
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@ -273,7 +271,8 @@ public:
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std::vector<std::vector<ast> > cnsts_vec_vec(2);
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for(unsigned j = 0; j < cnsts_vec.size(); j++){
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bool is_A = the_base.in_range(j,rng);
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cnsts_vec_vec[is_A ? 0 : 1].push_back(cnsts_vec[j]);
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for(unsigned k = 0; k < cnsts_vec[j].size(); k++)
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cnsts_vec_vec[is_A ? 0 : 1].push_back(cnsts_vec[j][k]);
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}
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killme<iz3translation> tr_killer_i;
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@ -308,6 +307,19 @@ public:
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}
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void proof_to_interpolant(z3pf proof,
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std::vector<ast> &cnsts,
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const std::vector<int> &parents,
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std::vector<ast> &interps,
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const std::vector<ast> &theory,
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interpolation_options_struct *options = 0
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){
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std::vector<std::vector<ast> > cnsts_vec(cnsts.size());
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for(unsigned i = 0; i < cnsts.size(); i++)
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cnsts_vec[i].push_back(cnsts[i]);
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proof_to_interpolant(proof,cnsts_vec,parents,interps,theory,options);
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}
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// same as above, but represents the tree using an ast
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void proof_to_interpolant(const z3pf &proof,
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@ -322,7 +334,6 @@ public:
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to_parents_vec_representation(_cnsts, tree, cnsts, parents, theory, pos_map);
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//use the parents vector representation to compute interpolant
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proof_to_interpolant(proof,cnsts,parents,interps,theory,options);
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@ -397,6 +408,35 @@ void iz3interpolate(ast_manager &_m_manager,
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interps[i] = itp.uncook(_interps[i]);
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}
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void iz3interpolate(ast_manager &_m_manager,
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ast *proof,
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const ::vector<ptr_vector<ast> > &cnsts,
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const ::vector<int> &parents,
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ptr_vector<ast> &interps,
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const ptr_vector<ast> &theory,
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interpolation_options_struct * options)
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{
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iz3interp itp(_m_manager);
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if(options)
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options->apply(itp);
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std::vector<std::vector<iz3mgr::ast> > _cnsts(cnsts.size());
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std::vector<int> _parents(parents.size());
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std::vector<iz3mgr::ast> _interps;
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std::vector<iz3mgr::ast> _theory(theory.size());
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for(unsigned i = 0; i < cnsts.size(); i++)
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for(unsigned j = 0; j < cnsts[i].size(); j++)
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_cnsts[i].push_back(itp.cook(cnsts[i][j]));
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for(unsigned i = 0; i < parents.size(); i++)
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_parents[i] = parents[i];
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for(unsigned i = 0; i < theory.size(); i++)
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_theory[i] = itp.cook(theory[i]);
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iz3mgr::ast _proof = itp.cook(proof);
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itp.proof_to_interpolant(_proof,_cnsts,_parents,_interps,_theory,options);
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interps.resize(_interps.size());
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for(unsigned i = 0; i < interps.size(); i++)
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interps[i] = itp.uncook(_interps[i]);
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}
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void iz3interpolate(ast_manager &_m_manager,
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ast *proof,
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const ptr_vector<ast> &cnsts,
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@ -56,6 +56,16 @@ void iz3interpolate(ast_manager &_m_manager,
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const ptr_vector<ast> &theory,
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interpolation_options_struct * options = 0);
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/* Same as above, but each constraint is a vector of formulas. */
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void iz3interpolate(ast_manager &_m_manager,
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ast *proof,
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const vector<ptr_vector<ast> > &cnsts,
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const ::vector<int> &parents,
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ptr_vector<ast> &interps,
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const ptr_vector<ast> &theory,
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interpolation_options_struct * options = 0);
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/* Compute an interpolant from a proof. This version uses the ast
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representation, for compatibility with the new API. */
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@ -815,6 +815,22 @@ iz3mgr::ast iz3mgr::subst(ast var, ast t, ast e){
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return subst(memo,var,t,e);
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}
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iz3mgr::ast iz3mgr::subst(stl_ext::hash_map<ast,ast> &subst_memo,ast e){
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std::pair<ast,ast> foo(e,ast());
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std::pair<hash_map<ast,ast>::iterator,bool> bar = subst_memo.insert(foo);
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ast &res = bar.first->second;
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if(bar.second){
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int nargs = num_args(e);
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std::vector<ast> args(nargs);
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for(int i = 0; i < nargs; i++)
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args[i] = subst(subst_memo,arg(e,i));
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opr f = op(e);
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if(f == Equal && args[0] == args[1]) res = mk_true();
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else res = clone(e,args);
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}
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return res;
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}
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// apply a quantifier to a formula, with some optimizations
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// 1) bound variable does not occur -> no quantifier
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// 2) bound variable must be equal to some term -> substitute
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@ -631,6 +631,9 @@ class iz3mgr {
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ast subst(ast var, ast t, ast e);
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// apply a substitution defined by a map
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ast subst(stl_ext::hash_map<ast,ast> &map, ast e);
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// apply a quantifier to a formula, with some optimizations
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// 1) bound variable does not occur -> no quantifier
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// 2) bound variable must be equal to some term -> substitute
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@ -118,6 +118,28 @@ class iz3proof_itp_impl : public iz3proof_itp {
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where t is an arbitrary term */
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symb rewrite_B;
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/* a normalization step is of the form (lhs=rhs) : proof, where "proof"
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is a proof of lhs=rhs and lhs is a mixed term. If rhs is a mixed term
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then it must have a greater index than lhs. */
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symb normal_step;
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/* A chain of normalization steps is either "true" (the null chain)
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or normal_chain(<step> <tail>), where step is a normalization step
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and tail is a normalization chain. The lhs of <step> must have
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a less term index than any lhs in the chain. Moreover, the rhs of
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<step> may not occur as the lhs of step in <tail>. If we wish to
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add lhs=rhs to the beginning of <tail> and rhs=rhs' occurs in <tail>
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we must apply transitivity, transforming <step> to lhs=rhs'. */
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symb normal_chain;
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/* If p is a proof of Q and c is a normalization chain, then normal(p,c)
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is a proof of Q(c) (that is, Q with all substitutions in c performed). */
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symb normal;
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ast get_placeholder(ast t){
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hash_map<ast,ast>::iterator it = placeholders.find(t);
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@ -521,10 +543,16 @@ class iz3proof_itp_impl : public iz3proof_itp {
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throw cannot_simplify();
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}
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bool is_normal_ineq(const ast &ineq){
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if(sym(ineq) == normal)
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return is_ineq(arg(ineq,0));
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return is_ineq(ineq);
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}
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ast simplify_sum(std::vector<ast> &args){
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ast cond = mk_true();
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ast ineq = args[0];
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if(!is_ineq(ineq)) throw cannot_simplify();
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if(!is_normal_ineq(ineq)) throw cannot_simplify();
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sum_cond_ineq(ineq,cond,args[1],args[2]);
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return my_implies(cond,ineq);
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}
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@ -540,6 +568,8 @@ class iz3proof_itp_impl : public iz3proof_itp {
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}
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ast ineq_from_chain(const ast &chain, ast &cond){
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if(sym(chain) == normal)
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throw "normalized inequalities not supported here";
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if(is_rewrite_chain(chain)){
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ast last = chain_last(chain);
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ast rest = chain_rest(chain);
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@ -561,6 +591,13 @@ class iz3proof_itp_impl : public iz3proof_itp {
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cond = my_and(cond,arg(ineq2,0));
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}
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else {
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if(sym(ineq) == normal || sym(ineq2) == normal){
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ast Aproves = mk_true();
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sum_normal_ineq(ineq,coeff2,ineq2,Aproves,cond);
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if(!is_true(Aproves))
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throw "Aproves not handled in sum_cond_ineq";
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return;
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}
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ast the_ineq = ineq_from_chain(ineq2,cond);
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if(is_ineq(the_ineq))
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linear_comb(ineq,coeff2,the_ineq);
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@ -569,6 +606,27 @@ class iz3proof_itp_impl : public iz3proof_itp {
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}
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}
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void destruct_normal(const ast &pf, ast &p, ast &n){
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if(sym(pf) == normal){
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p = arg(pf,0);
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n = arg(pf,1);
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}
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else {
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p = pf;
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n = mk_true();
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}
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}
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void sum_normal_ineq(ast &ineq, const ast &coeff2, const ast &ineq2, ast &Aproves, ast &Bproves){
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ast in1,in2,n1,n2;
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destruct_normal(ineq,in1,n1);
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destruct_normal(ineq2,in2,n2);
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ast dummy;
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sum_cond_ineq(in1,dummy,coeff2,in2);
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n1 = merge_normal_chains(n1,n2, Aproves, Bproves);
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ineq = make(normal,in1,n1);
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}
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bool is_ineq(const ast &ineq){
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opr o = op(ineq);
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if(o == Not) o = op(arg(ineq,0));
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@ -577,6 +635,12 @@ class iz3proof_itp_impl : public iz3proof_itp {
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// divide both sides of inequality by a non-negative integer divisor
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ast idiv_ineq(const ast &ineq1, const ast &divisor){
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if(sym(ineq1) == normal){
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ast in1,n1;
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destruct_normal(ineq1,in1,n1);
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in1 = idiv_ineq(in1,divisor);
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return make(normal,in1,n1);
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}
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if(divisor == make_int(rational(1)))
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return ineq1;
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ast ineq = ineq1;
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@ -649,11 +713,18 @@ class iz3proof_itp_impl : public iz3proof_itp {
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ast equa = sep_cond(arg(pf,0),cond);
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if(is_equivrel_chain(equa)){
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ast lhs,rhs; eq_from_ineq(arg(neg_equality,0),lhs,rhs); // get inequality we need to prove
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ast ineqs= chain_ineqs(op(arg(neg_equality,0)),LitA,equa,lhs,rhs); // chain must be from lhs to rhs
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cond = my_and(cond,chain_conditions(LitA,equa));
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ast Bconds = chain_conditions(LitB,equa);
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if(is_true(Bconds) && op(ineqs) != And)
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return my_implies(cond,ineqs);
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LitType lhst = get_term_type(lhs), rhst = get_term_type(rhs);
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if(lhst != LitMixed && rhst != LitMixed){
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ast ineqs= chain_ineqs(op(arg(neg_equality,0)),LitA,equa,lhs,rhs); // chain must be from lhs to rhs
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cond = my_and(cond,chain_conditions(LitA,equa));
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ast Bconds = z3_simplify(chain_conditions(LitB,equa));
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if(is_true(Bconds) && op(ineqs) != And)
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return my_implies(cond,ineqs);
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}
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else {
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ast itp = make(Leq,make_int(rational(0)),make_int(rational(0)));
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return make(normal,itp,cons_normal(fix_normal(lhs,rhs,equa),mk_true()));
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}
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}
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}
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throw cannot_simplify();
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@ -757,11 +828,57 @@ class iz3proof_itp_impl : public iz3proof_itp {
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chain = concat_rewrite_chain(chain,split[1]);
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}
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}
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else // if not an equivalence, must be of form T <-> pred
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else { // if not an equivalence, must be of form T <-> pred
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chain = concat_rewrite_chain(P,PeqQ);
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}
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return chain;
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}
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void get_subterm_normals(const ast &ineq1, const ast &ineq2, const ast &chain, ast &normals,
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const ast &pos, hash_set<ast> &memo, ast &Aproves, ast &Bproves){
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opr o1 = op(ineq1);
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opr o2 = op(ineq2);
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if(o1 == Not || o1 == Leq || o1 == Lt || o1 == Geq || o1 == Gt || o1 == Plus || o1 == Times){
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int n = num_args(ineq1);
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if(o2 != o1 || num_args(ineq2) != n)
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throw "bad inequality rewriting";
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for(int i = 0; i < n; i++){
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ast new_pos = add_pos_to_end(pos,i);
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get_subterm_normals(arg(ineq1,i), arg(ineq2,i), chain, normals, new_pos, memo, Aproves, Bproves);
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}
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}
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else if(get_term_type(ineq2) == LitMixed && memo.find(ineq2) == memo.end()){
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memo.insert(ineq2);
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ast sub_chain = extract_rewrites(chain,pos);
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if(is_true(sub_chain))
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throw "bad inequality rewriting";
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ast new_normal = make_normal(ineq2,ineq1,reverse_chain(sub_chain));
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normals = merge_normal_chains(normals,cons_normal(new_normal,mk_true()), Aproves, Bproves);
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}
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}
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ast rewrite_chain_to_normal_ineq(const ast &chain, ast &Aproves, ast &Bproves){
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ast tail, pref = get_head_chain(chain,tail,false); // pref is x=y, tail is x=y -> x'=y'
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ast head = chain_last(pref);
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ast ineq1 = rewrite_rhs(head);
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ast ineq2 = apply_rewrite_chain(ineq1,tail);
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ast nc = mk_true();
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hash_set<ast> memo;
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get_subterm_normals(ineq1,ineq2,tail,nc,top_pos,memo, Aproves, Bproves);
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ast itp;
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if(is_rewrite_side(LitA,head)){
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itp = ineq1;
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ast mc = z3_simplify(chain_side_proves(LitB,pref));
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Bproves = my_and(Bproves,mc);
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}
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else {
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itp = make(Leq,make_int(rational(0)),make_int(rational(0)));
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ast mc = z3_simplify(chain_side_proves(LitA,pref));
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Aproves = my_and(Aproves,mc);
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}
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return make(normal,itp,nc);
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}
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/* Given a chain rewrite chain deriving not P and a rewrite chain deriving P, return an interpolant. */
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ast contra_chain(const ast &neg_chain, const ast &pos_chain){
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// equality is a special case. we use the derivation of x=y to rewrite not(x=y) to not(y=y)
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@ -790,11 +907,18 @@ class iz3proof_itp_impl : public iz3proof_itp {
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}
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ast simplify_modpon(const std::vector<ast> &args){
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ast cond = mk_true();
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ast chain = simplify_modpon_fwd(args,cond);
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ast Q2 = sep_cond(args[2],cond);
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ast interp = is_negation_chain(chain) ? contra_chain(chain,Q2) : contra_chain(Q2,chain);
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return my_implies(cond,interp);
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ast Aproves = mk_true(), Bproves = mk_true();
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ast chain = simplify_modpon_fwd(args,Bproves);
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ast Q2 = sep_cond(args[2],Bproves);
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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);
|
||||
new_proof = concat_rewrite_chain(pf1,Aproof);
|
||||
new_normal = make_normal(rhs1,rep,new_proof);
|
||||
}
|
||||
else if(t1 == LitA && t2 == LitB)
|
||||
return merge_normal_chains_rec(chain2,chain1,trans,Aproves,Bproves);
|
||||
else if(t1 == LitA) {
|
||||
ast new_proof = concat_rewrite_chain(reverse_chain(pf1),pf2);
|
||||
ast mc = chain_side_proves(LitB,new_proof);
|
||||
Bproves = my_and(Bproves,mc);
|
||||
new_normal = f1; // choice is arbitrary
|
||||
}
|
||||
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…
Add table
Add a link
Reference in a new issue