mirror of
https://github.com/Z3Prover/z3
synced 2025-04-27 10:55:50 +00:00
Merge branch 'unstable' of https://git01.codeplex.com/z3 into unstable
This commit is contained in:
Nikolaj Bjorner
commit
36f7bad1da
8 changed files with 622 additions and 187 deletions
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@ -395,7 +395,6 @@ namespace pdr {
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lbool is_sat = m_solver.check_conjunction_as_assumptions(n.state());
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if (is_sat == l_true && core) {
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core->reset();
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model2cube(*model,*core);
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n.set_model(model);
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}
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return is_sat;
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@ -697,34 +696,6 @@ namespace pdr {
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}
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}
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void pred_transformer::model2cube(app* c, expr* val, expr_ref_vector& res) const {
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if (m.is_bool(val)) {
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res.push_back(m.is_true(val)?c:m.mk_not(c));
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}
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else {
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res.push_back(m.mk_eq(c, val));
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}
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}
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void pred_transformer::model2cube(const model_core& mdl, func_decl * d, expr_ref_vector& res) const {
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expr_ref interp(m);
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get_value_from_model(mdl, d, interp);
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app* c = m.mk_const(d);
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model2cube(c, interp, res);
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}
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void pred_transformer::model2cube(const model_core & mdl, expr_ref_vector & res) const {
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unsigned sz = mdl.get_num_constants();
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for (unsigned i = 0; i < sz; i++) {
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func_decl * d = mdl.get_constant(i);
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SASSERT(d->get_arity()==0);
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if (!m_solver.is_aux_symbol(d)) {
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model2cube(mdl, d, res);
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}
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}
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}
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// ----------------
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// model_node
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@ -1103,11 +1074,9 @@ namespace pdr {
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m_inductive_lvl(0),
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m_cancel(false)
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{
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m_use_model_generalizer = m_params.get_bool("use-model-generalizer", false);
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}
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context::~context() {
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reset_model_generalizers();
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reset_core_generalizers();
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reset();
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}
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@ -1169,7 +1138,6 @@ namespace pdr {
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void context::update_rules(datalog::rule_set& rules) {
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decl2rel rels;
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init_model_generalizers(rules);
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init_core_generalizers(rules);
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init_rules(rules, rels);
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decl2rel::iterator it = rels.begin(), end = rels.end();
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@ -1294,18 +1262,6 @@ namespace pdr {
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};
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void context::reset_model_generalizers() {
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std::for_each(m_model_generalizers.begin(), m_model_generalizers.end(), delete_proc<model_generalizer>());
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m_model_generalizers.reset();
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}
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void context::init_model_generalizers(datalog::rule_set& rules) {
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reset_model_generalizers();
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if (m_use_model_generalizer) {
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m_model_generalizers.push_back(alloc(model_evaluation_generalizer, *this, m));
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}
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}
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void context::reset_core_generalizers() {
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std::for_each(m_core_generalizers.begin(), m_core_generalizers.end(), delete_proc<core_generalizer>());
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m_core_generalizers.reset();
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@ -1552,11 +1508,7 @@ namespace pdr {
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}
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else {
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TRACE("pdr", tout << "node: " << &n << "\n";);
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for (unsigned i = 0; i < m_model_generalizers.size(); ++i) {
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(*m_model_generalizers[i])(n, cube);
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}
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create_children(n, m_pm.mk_and(cube));
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create_children(n);
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}
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break;
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case l_false: {
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@ -1627,45 +1579,6 @@ namespace pdr {
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}
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}
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// create children states from model cube.
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void context::create_children(model_node& n, expr* model) {
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if (!m_use_model_generalizer) {
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create_children2(n);
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return;
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}
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expr_ref_vector literals(m), sub_lits(m);
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expr_ref o_cube(m), n_cube(m);
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datalog::flatten_and(model, literals);
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ptr_vector<func_decl> preds;
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unsigned level = n.level();
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SASSERT(level > 0);
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n.pt().find_predecessors(n.model(), preds);
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n.pt().remove_predecessors(literals);
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TRACE("pdr",
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model_v2_pp(tout, n.model());
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tout << "Model cube\n";
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tout << mk_pp(model, m) << "\n";
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tout << "Predecessors\n";
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for (unsigned i = 0; i < preds.size(); ++i) {
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tout << preds[i]->get_name() << "\n";
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}
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);
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for (unsigned i = 0; i < preds.size(); ++i) {
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pred_transformer& pt = *m_rels.find(preds[i]);
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SASSERT(pt.head() == preds[i]);
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assign_ref_vector(sub_lits, literals);
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m_pm.filter_o_atoms(sub_lits, i);
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o_cube = m_pm.mk_and(sub_lits);
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m_pm.formula_o2n(o_cube, n_cube, i);
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model_node* child = alloc(model_node, &n, n_cube, pt, level-1);
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++m_stats.m_num_nodes;
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m_search.add_leaf(*child);
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}
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check_pre_closed(n);
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TRACE("pdr", m_search.display(tout););
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}
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/**
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\brief create children states from model cube.
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@ -1707,7 +1620,7 @@ namespace pdr {
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- Create sub-goals for L0 and L1.
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*/
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void context::create_children2(model_node& n) {
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void context::create_children(model_node& n) {
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SASSERT(n.level() > 0);
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pred_transformer& pt = n.pt();
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@ -1723,12 +1636,17 @@ namespace pdr {
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verbose_stream() << "Phi:\n" << mk_pp(phi, m) << "\n";);
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model_evaluator mev(m);
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expr_ref_vector mdl(m), forms(m);
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expr_ref_vector mdl(m), forms(m), Phi(m);
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forms.push_back(T);
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forms.push_back(phi);
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datalog::flatten_and(forms);
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ptr_vector<expr> forms1(forms.size(), forms.c_ptr());
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expr_ref_vector Phi = mev.minimize_literals(forms1, M);
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if (m_params.get_bool(":use-model-generalizer", false)) {
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Phi.append(mev.minimize_model(forms1, M));
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}
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else {
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Phi.append(mev.minimize_literals(forms1, M));
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}
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ptr_vector<func_decl> preds;
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pt.find_predecessors(r, preds);
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pt.remove_predecessors(Phi);
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@ -1834,9 +1752,6 @@ namespace pdr {
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st.update("PDR max depth", m_stats.m_max_depth);
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m_pm.collect_statistics(st);
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for (unsigned i = 0; i < m_model_generalizers.size(); ++i) {
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m_model_generalizers[i]->collect_statistics(st);
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}
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for (unsigned i = 0; i < m_core_generalizers.size(); ++i) {
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m_core_generalizers[i]->collect_statistics(st);
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}
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@ -98,9 +98,6 @@ namespace pdr {
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void init_atom(decl2rel const& pts, app * atom, app_ref_vector& var_reprs, expr_ref_vector& conj, unsigned tail_idx);
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void ground_free_vars(expr* e, app_ref_vector& vars, ptr_vector<app>& aux_vars);
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void model2cube(const model_core& md, func_decl * d, expr_ref_vector& res) const;
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void model2cube(app* c, expr* val, expr_ref_vector& res) const;
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void simplify_formulas(tactic& tac, expr_ref_vector& fmls);
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// Debugging
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@ -157,8 +154,6 @@ namespace pdr {
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manager& get_pdr_manager() const { return pm; }
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ast_manager& get_manager() const { return m; }
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void model2cube(const model_core & mdl, expr_ref_vector & res) const;
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void add_premises(decl2rel const& pts, unsigned lvl, expr_ref_vector& r);
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void close(expr* e);
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@ -266,18 +261,6 @@ namespace pdr {
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class context;
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// 'state' is satisifiable with predecessor 'cube'.
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// Generalize predecessor still forcing satisfiability.
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class model_generalizer {
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protected:
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context& m_ctx;
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public:
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model_generalizer(context& ctx): m_ctx(ctx) {}
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virtual ~model_generalizer() {}
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virtual void operator()(model_node& n, expr_ref_vector& cube) = 0;
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virtual void collect_statistics(statistics& st) {}
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};
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// 'state' is unsatisfiable at 'level' with 'core'.
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// Minimize or weaken core.
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class core_generalizer {
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@ -317,9 +300,7 @@ namespace pdr {
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pred_transformer* m_query;
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model_search m_search;
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lbool m_last_result;
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bool m_use_model_generalizer;
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unsigned m_inductive_lvl;
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ptr_vector<model_generalizer> m_model_generalizers;
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ptr_vector<core_generalizer> m_core_generalizers;
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stats m_stats;
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volatile bool m_cancel;
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@ -336,8 +317,7 @@ namespace pdr {
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void check_pre_closed(model_node& n);
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void expand_node(model_node& n);
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lbool expand_state(model_node& n, expr_ref_vector& cube);
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void create_children(model_node& n, expr* model);
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void create_children2(model_node& n);
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void create_children(model_node& n);
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expr_ref mk_sat_answer() const;
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expr_ref mk_unsat_answer() const;
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@ -347,7 +327,6 @@ namespace pdr {
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// Initialization
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class classifier_proc;
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void init_model_generalizers(datalog::rule_set& rules);
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void init_core_generalizers(datalog::rule_set& rules);
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bool check_invariant(unsigned lvl);
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@ -359,7 +338,6 @@ namespace pdr {
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void simplify_formulas();
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void reset_model_generalizers();
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void reset_core_generalizers();
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public:
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@ -29,19 +29,6 @@ Revision History:
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namespace pdr {
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//
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// eliminate conjuncts from cube as long as state is satisfied.
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//
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void model_evaluation_generalizer::operator()(model_node& n, expr_ref_vector& cube) {
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expr_ref_vector forms(cube.get_manager());
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forms.push_back(n.state());
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forms.push_back(n.pt().transition());
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datalog::flatten_and(forms);
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ptr_vector<expr> forms1(forms.size(), forms.c_ptr());
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model_ref mdl = n.model_ptr();
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m_model_evaluator.minimize_model(forms1, mdl, cube);
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}
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//
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// main propositional induction generalizer.
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// drop literals one by one from the core and check if the core is still inductive.
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|
|
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@ -25,14 +25,6 @@ Revision History:
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namespace pdr {
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class model_evaluation_generalizer : public model_generalizer {
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model_evaluator m_model_evaluator;
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public:
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model_evaluation_generalizer(context& ctx, ast_manager& m) : model_generalizer(ctx), m_model_evaluator(m) {}
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virtual ~model_evaluation_generalizer() {}
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virtual void operator()(model_node& n, expr_ref_vector& cube);
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};
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class core_bool_inductive_generalizer : public core_generalizer {
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unsigned m_failure_limit;
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public:
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|
|
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@ -90,33 +90,6 @@ std::string pp_cube(unsigned sz, expr * const * lits, ast_manager& m) {
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//
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bool model_evaluator::get_assignment(expr* e, expr*& var, expr*& val) {
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if (m.is_eq(e, var, val)) {
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if (!is_uninterp(var)) {
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std::swap(var, val);
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}
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if (m.is_true(val) || m.is_false(val) || m_arith.is_numeral(val)) {
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return true;
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}
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TRACE("pdr_verbose", tout << "no value for " << mk_pp(val, m) << "\n";);
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return false;
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}
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else if (m.is_not(e, var)) {
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val = m.mk_false();
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return true;
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}
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else if (m.is_bool(e)) {
|
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val = m.mk_true();
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var = e;
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return true;
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}
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else {
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TRACE("pdr_verbose", tout << "no value set of " << mk_pp(e, m) << "\n";);
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return false;
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}
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}
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void model_evaluator::assign_value(expr* e, expr* val) {
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rational r;
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if (m.is_true(val)) {
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@ -166,7 +139,7 @@ void model_evaluator::reset() {
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m_model = 0;
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}
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void model_evaluator::minimize_model(ptr_vector<expr> const & formulas, model_ref& mdl, expr_ref_vector & model) {
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expr_ref_vector model_evaluator::minimize_model(ptr_vector<expr> const & formulas, model_ref& mdl) {
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setup_model(mdl);
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TRACE("pdr_verbose",
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@ -174,7 +147,7 @@ void model_evaluator::minimize_model(ptr_vector<expr> const & formulas, model_re
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for (unsigned i = 0; i < formulas.size(); ++i) tout << mk_pp(formulas[i], m) << "\n";
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);
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prune_by_cone_of_influence(formulas, model);
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expr_ref_vector model = prune_by_cone_of_influence(formulas);
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TRACE("pdr_verbose",
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tout << "pruned model:\n";
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for (unsigned i = 0; i < model.size(); ++i) tout << mk_pp(model[i].get(), m) << "\n";);
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|
@ -185,6 +158,8 @@ void model_evaluator::minimize_model(ptr_vector<expr> const & formulas, model_re
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setup_model(mdl);
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VERIFY(check_model(formulas));
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reset(););
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return model;
|
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}
|
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|
||||
expr_ref_vector model_evaluator::minimize_literals(ptr_vector<expr> const& formulas, model_ref& mdl) {
|
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|
|
@ -340,7 +315,7 @@ void model_evaluator::collect(ptr_vector<expr> const& formulas, ptr_vector<expr>
|
|||
m_visited.reset();
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||||
}
|
||||
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||||
void model_evaluator::prune_by_cone_of_influence(ptr_vector<expr> const & formulas, expr_ref_vector& model) {
|
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expr_ref_vector model_evaluator::prune_by_cone_of_influence(ptr_vector<expr> const & formulas) {
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||||
ptr_vector<expr> tocollect;
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collect(formulas, tocollect);
|
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m1.reset();
|
||||
|
|
@ -349,19 +324,23 @@ void model_evaluator::prune_by_cone_of_influence(ptr_vector<expr> const & formul
|
|||
TRACE("pdr_verbose", tout << "collect: " << mk_pp(tocollect[i], m) << "\n";);
|
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for_each_expr(*this, m_visited, tocollect[i]);
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||||
}
|
||||
unsigned sz1 = model.size();
|
||||
for (unsigned i = 0; i < model.size(); ++i) {
|
||||
expr* e = model[i].get(), *var, *val;
|
||||
if (get_assignment(e, var, val)) {
|
||||
if (!m_visited.is_marked(var)) {
|
||||
model[i] = model.back();
|
||||
model.pop_back();
|
||||
--i;
|
||||
}
|
||||
unsigned sz = m_model->get_num_constants();
|
||||
expr_ref e(m), eq(m);
|
||||
expr_ref_vector model(m);
|
||||
bool_rewriter rw(m);
|
||||
for (unsigned i = 0; i < sz; i++) {
|
||||
func_decl * d = m_model->get_constant(i);
|
||||
expr* val = m_model->get_const_interp(d);
|
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e = m.mk_const(d);
|
||||
if (m_visited.is_marked(e)) {
|
||||
rw.mk_eq(e, val, eq);
|
||||
model.push_back(eq);
|
||||
}
|
||||
}
|
||||
m_visited.reset();
|
||||
TRACE("pdr", tout << sz1 << " ==> " << model.size() << "\n";);
|
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TRACE("pdr", tout << sz << " ==> " << model.size() << "\n";);
|
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return model;
|
||||
|
||||
}
|
||||
|
||||
void model_evaluator::eval_arith(app* e) {
|
||||
|
|
|
|||
|
|
@ -194,10 +194,9 @@ class model_evaluator {
|
|||
void reset();
|
||||
void setup_model(model_ref& model);
|
||||
void assign_value(expr* e, expr* v);
|
||||
bool get_assignment(expr* e, expr*& var, expr*& val);
|
||||
void collect(ptr_vector<expr> const& formulas, ptr_vector<expr>& tocollect);
|
||||
void process_formula(app* e, ptr_vector<expr>& todo, ptr_vector<expr>& tocollect);
|
||||
void prune_by_cone_of_influence(ptr_vector<expr> const & formulas, expr_ref_vector& model);
|
||||
expr_ref_vector prune_by_cone_of_influence(ptr_vector<expr> const & formulas);
|
||||
void eval_arith(app* e);
|
||||
void eval_basic(app* e);
|
||||
void eval_iff(app* e, expr* arg1, expr* arg2);
|
||||
|
|
@ -230,7 +229,13 @@ protected:
|
|||
public:
|
||||
model_evaluator(ast_manager& m) : m(m), m_arith(m), m_bv(m), m_refs(m) {}
|
||||
|
||||
virtual void minimize_model(ptr_vector<expr> const & formulas, model_ref& mdl, expr_ref_vector& model);
|
||||
/**
|
||||
\brief extract equalities from model that suffice to satisfy formula.
|
||||
|
||||
\pre model satisfies formulas
|
||||
*/
|
||||
|
||||
expr_ref_vector minimize_model(ptr_vector<expr> const & formulas, model_ref& mdl);
|
||||
|
||||
/**
|
||||
\brief extract literals from formulas that satisfy formulas.
|
||||
|
|
@ -239,12 +244,6 @@ public:
|
|||
*/
|
||||
expr_ref_vector minimize_literals(ptr_vector<expr> const & formulas, model_ref& mdl);
|
||||
|
||||
/**
|
||||
\brief extract literals from formulas that satisfy formulas.
|
||||
|
||||
\pre model satisfies formulas
|
||||
*/
|
||||
expr_ref_vector minimize_literals(ptr_vector<expr> const & formulas, expr_ref_vector const & model);
|
||||
|
||||
// for_each_expr visitor.
|
||||
void operator()(expr* e) {}
|
||||
|
|
|
|||
536
lib/qe_lite.cpp
Normal file
536
lib/qe_lite.cpp
Normal file
|
|
@ -0,0 +1,536 @@
|
|||
/*++
|
||||
Copyright (c) 2012 Microsoft Corporation
|
||||
|
||||
Module Name:
|
||||
|
||||
qe_lite.cpp
|
||||
|
||||
Abstract:
|
||||
|
||||
Light weight partial quantifier-elimination procedure
|
||||
|
||||
Author:
|
||||
|
||||
Nikolaj Bjorner (nbjorner) 2012-10-17
|
||||
|
||||
Revision History:
|
||||
|
||||
- TBD: integrate Fourier Motzkin elimination
|
||||
integrate Gaussean elimination
|
||||
|
||||
--*/
|
||||
#include "qe_lite.h"
|
||||
#include "expr_abstract.h"
|
||||
#include "used_vars.h"
|
||||
#include"occurs.h"
|
||||
#include"for_each_expr.h"
|
||||
#include"rewriter_def.h"
|
||||
#include"ast_pp.h"
|
||||
#include"ast_ll_pp.h"
|
||||
#include"ast_smt2_pp.h"
|
||||
#include"tactical.h"
|
||||
#include"bool_rewriter.h"
|
||||
#include"var_subst.h"
|
||||
|
||||
class der2 {
|
||||
ast_manager & m;
|
||||
var_subst m_subst;
|
||||
expr_ref_buffer m_new_exprs;
|
||||
|
||||
ptr_vector<expr> m_map;
|
||||
int_vector m_pos2var;
|
||||
ptr_vector<var> m_inx2var;
|
||||
unsigned_vector m_order;
|
||||
expr_ref_vector m_subst_map;
|
||||
expr_ref_buffer m_new_args;
|
||||
|
||||
/**
|
||||
\brief Return true if e can be viewed as a variable disequality.
|
||||
Store the variable id in v and the definition in t.
|
||||
For example:
|
||||
|
||||
if e is (not (= (VAR 1) T)), then v assigned to 1, and t to T.
|
||||
if e is (iff (VAR 2) T), then v is assigned to 2, and t to (not T).
|
||||
(not T) is used because this formula is equivalent to (not (iff (VAR 2) (not T))),
|
||||
and can be viewed as a disequality.
|
||||
*/
|
||||
bool is_var_diseq(expr * e, unsigned num_decls, var *& v, expr_ref & t);
|
||||
|
||||
/**
|
||||
\brief Return true if e can be viewed as a variable equality.
|
||||
*/
|
||||
bool is_var_eq(expr * e, unsigned num_decls, var *& v, expr_ref & t);
|
||||
|
||||
bool is_var_def(bool check_eq, expr* e, unsigned num_decls, var*& v, expr_ref& t);
|
||||
|
||||
void get_elimination_order();
|
||||
void create_substitution(unsigned sz);
|
||||
void apply_substitution(quantifier * q, expr_ref & r);
|
||||
void reduce_quantifier1(quantifier * q, expr_ref & r, proof_ref & pr);
|
||||
void elim_unused_vars(expr_ref& r, proof_ref &pr);
|
||||
|
||||
public:
|
||||
der2(ast_manager & m):m(m),m_subst(m),m_new_exprs(m),m_subst_map(m),m_new_args(m) {}
|
||||
void operator()(quantifier * q, expr_ref & r, proof_ref & pr);
|
||||
void reduce_quantifier(quantifier * q, expr_ref & r, proof_ref & pr);
|
||||
ast_manager& get_manager() const { return m; }
|
||||
};
|
||||
|
||||
static bool is_var(expr * e, unsigned num_decls) {
|
||||
return is_var(e) && to_var(e)->get_idx() < num_decls;
|
||||
}
|
||||
|
||||
static bool is_neg_var(ast_manager & m, expr * e, unsigned num_decls) {
|
||||
expr* e1;
|
||||
return m.is_not(e, e1) && is_var(e1, num_decls);
|
||||
}
|
||||
|
||||
bool der2::is_var_def(bool check_eq, expr* e, unsigned num_decls, var*& v, expr_ref& t) {
|
||||
if (check_eq) {
|
||||
return is_var_eq(e, num_decls, v, t);
|
||||
}
|
||||
else {
|
||||
return is_var_diseq(e, num_decls, v, t);
|
||||
}
|
||||
}
|
||||
|
||||
bool der2::is_var_eq(expr * e, unsigned num_decls, var * & v, expr_ref & t) {
|
||||
expr* lhs, *rhs;
|
||||
|
||||
// (= VAR t), (iff VAR t), (iff (not VAR) t), (iff t (not VAR)) cases
|
||||
if (m.is_eq(e, lhs, rhs) || m.is_iff(e, lhs, rhs)) {
|
||||
// (iff (not VAR) t) (iff t (not VAR)) cases
|
||||
if (!is_var(lhs, num_decls) && !is_var(rhs, num_decls) && m.is_bool(lhs)) {
|
||||
if (!is_neg_var(m, lhs, num_decls)) {
|
||||
std::swap(lhs, rhs);
|
||||
}
|
||||
if (!is_neg_var(m, lhs, num_decls)) {
|
||||
return false;
|
||||
}
|
||||
v = to_var(lhs);
|
||||
t = m.mk_not(rhs);
|
||||
m_new_exprs.push_back(t);
|
||||
TRACE("der", tout << mk_pp(e, m) << "\n";);
|
||||
return true;
|
||||
}
|
||||
if (!is_var(lhs, num_decls))
|
||||
std::swap(lhs, rhs);
|
||||
if (!is_var(lhs, num_decls))
|
||||
return false;
|
||||
v = to_var(lhs);
|
||||
t = rhs;
|
||||
TRACE("der", tout << mk_pp(e, m) << "\n";);
|
||||
return true;
|
||||
}
|
||||
|
||||
// (ite cond (= VAR t) (= VAR t2)) case
|
||||
expr* cond, *e2, *e3;
|
||||
if (m.is_ite(e, cond, e2, e3)) {
|
||||
if (is_var_eq(e2, num_decls, v, t)) {
|
||||
expr_ref t2(m);
|
||||
var* v2;
|
||||
if (is_var_eq(e3, num_decls, v2, t2) && v2 == v) {
|
||||
t = m.mk_ite(cond, t, t2);
|
||||
m_new_exprs.push_back(t);
|
||||
return true;
|
||||
}
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
// VAR = true case
|
||||
if (is_var(e, num_decls)) {
|
||||
t = m.mk_true();
|
||||
v = to_var(e);
|
||||
TRACE("der", tout << mk_pp(e, m) << "\n";);
|
||||
return true;
|
||||
}
|
||||
|
||||
// VAR = false case
|
||||
if (is_neg_var(m, e, num_decls)) {
|
||||
t = m.mk_false();
|
||||
v = to_var(to_app(e)->get_arg(0));
|
||||
TRACE("der", tout << mk_pp(e, m) << "\n";);
|
||||
return true;
|
||||
}
|
||||
|
||||
return false;
|
||||
}
|
||||
|
||||
/**
|
||||
\brief Return true if \c e is of the form (not (= VAR t)) or (not (iff VAR t)) or
|
||||
(iff VAR t) or (iff (not VAR) t) or (VAR IDX) or (not (VAR IDX)).
|
||||
The last case can be viewed
|
||||
*/
|
||||
bool der2::is_var_diseq(expr * e, unsigned num_decls, var * & v, expr_ref & t) {
|
||||
expr* e1;
|
||||
if (m.is_not(e, e1)) {
|
||||
return is_var_eq(e, num_decls, v, t);
|
||||
}
|
||||
else if (is_var_eq(e, num_decls, v, t) && m.is_bool(v)) {
|
||||
bool_rewriter(m).mk_not(t, t);
|
||||
m_new_exprs.push_back(t);
|
||||
return true;
|
||||
}
|
||||
else {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
|
||||
void der2::elim_unused_vars(expr_ref& r, proof_ref& pr) {
|
||||
if (is_quantifier(r)) {
|
||||
quantifier * q = to_quantifier(r);
|
||||
::elim_unused_vars(m, q, r);
|
||||
if (m.proofs_enabled()) {
|
||||
proof * p1 = m.mk_elim_unused_vars(q, r);
|
||||
pr = m.mk_transitivity(pr, p1);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
Reduce the set of definitions in quantifier.
|
||||
Then eliminate variables that have become unused
|
||||
*/
|
||||
void der2::operator()(quantifier * q, expr_ref & r, proof_ref & pr) {
|
||||
TRACE("der", tout << mk_pp(q, m) << "\n";);
|
||||
pr = 0;
|
||||
r = q;
|
||||
reduce_quantifier(q, r, pr);
|
||||
if (r != q) {
|
||||
elim_unused_vars(r, pr);
|
||||
}
|
||||
}
|
||||
|
||||
void der2::reduce_quantifier(quantifier * q, expr_ref & r, proof_ref & pr) {
|
||||
r = q;
|
||||
// Keep applying reduce_quantifier1 until r doesn't change anymore
|
||||
do {
|
||||
proof_ref curr_pr(m);
|
||||
q = to_quantifier(r);
|
||||
reduce_quantifier1(q, r, curr_pr);
|
||||
if (m.proofs_enabled()) {
|
||||
pr = m.mk_transitivity(pr, curr_pr);
|
||||
}
|
||||
} while (q != r && is_quantifier(r));
|
||||
|
||||
m_new_exprs.reset();
|
||||
}
|
||||
|
||||
void der2::reduce_quantifier1(quantifier * q, expr_ref & r, proof_ref & pr) {
|
||||
expr * e = q->get_expr();
|
||||
unsigned num_decls = q->get_num_decls();
|
||||
var * v = 0;
|
||||
expr_ref t(m);
|
||||
unsigned num_args = 1;
|
||||
expr* const* args = &e;
|
||||
if ((q->is_forall() && m.is_or(e)) ||
|
||||
(q->is_exists() && m.is_and(e))) {
|
||||
num_args = to_app(e)->get_num_args();
|
||||
args = to_app(e)->get_args();
|
||||
}
|
||||
|
||||
unsigned def_count = 0;
|
||||
unsigned largest_vinx = 0;
|
||||
|
||||
m_map.reset();
|
||||
m_pos2var.reset();
|
||||
m_inx2var.reset();
|
||||
m_pos2var.reserve(num_args, -1);
|
||||
|
||||
// Find all definitions
|
||||
for (unsigned i = 0; i < num_args; i++) {
|
||||
if (is_var_def(q->is_exists(), args[i], num_decls, v, t)) {
|
||||
unsigned idx = v->get_idx();
|
||||
if(m_map.get(idx, 0) == 0) {
|
||||
m_map.reserve(idx + 1, 0);
|
||||
m_inx2var.reserve(idx + 1, 0);
|
||||
m_map[idx] = t;
|
||||
m_inx2var[idx] = v;
|
||||
m_pos2var[i] = idx;
|
||||
def_count++;
|
||||
largest_vinx = std::max(idx, largest_vinx);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
if (def_count > 0) {
|
||||
get_elimination_order();
|
||||
SASSERT(m_order.size() <= def_count); // some might be missing because of cycles
|
||||
|
||||
if (!m_order.empty()) {
|
||||
create_substitution(largest_vinx + 1);
|
||||
apply_substitution(q, r);
|
||||
}
|
||||
else {
|
||||
r = q;
|
||||
}
|
||||
}
|
||||
else {
|
||||
TRACE("der_bug", tout << "Did not find any diseq\n" << mk_pp(q, m) << "\n";);
|
||||
r = q;
|
||||
}
|
||||
|
||||
if (m.proofs_enabled()) {
|
||||
pr = r == q ? 0 : m.mk_der(q, r);
|
||||
}
|
||||
}
|
||||
|
||||
static void der_sort_vars(ptr_vector<var> & vars, ptr_vector<expr> & definitions, unsigned_vector & order) {
|
||||
order.reset();
|
||||
|
||||
// eliminate self loops, and definitions containing quantifiers.
|
||||
bool found = false;
|
||||
for (unsigned i = 0; i < definitions.size(); i++) {
|
||||
var * v = vars[i];
|
||||
expr * t = definitions[i];
|
||||
if (t == 0 || has_quantifiers(t) || occurs(v, t))
|
||||
definitions[i] = 0;
|
||||
else
|
||||
found = true; // found at least one candidate
|
||||
}
|
||||
|
||||
if (!found)
|
||||
return;
|
||||
|
||||
typedef std::pair<expr *, unsigned> frame;
|
||||
svector<frame> todo;
|
||||
|
||||
expr_fast_mark1 visiting;
|
||||
expr_fast_mark2 done;
|
||||
|
||||
unsigned vidx, num;
|
||||
|
||||
for (unsigned i = 0; i < definitions.size(); i++) {
|
||||
if (definitions[i] == 0)
|
||||
continue;
|
||||
var * v = vars[i];
|
||||
SASSERT(v->get_idx() == i);
|
||||
SASSERT(todo.empty());
|
||||
todo.push_back(frame(v, 0));
|
||||
while (!todo.empty()) {
|
||||
start:
|
||||
frame & fr = todo.back();
|
||||
expr * t = fr.first;
|
||||
if (t->get_ref_count() > 1 && done.is_marked(t)) {
|
||||
todo.pop_back();
|
||||
continue;
|
||||
}
|
||||
switch (t->get_kind()) {
|
||||
case AST_VAR:
|
||||
vidx = to_var(t)->get_idx();
|
||||
if (fr.second == 0) {
|
||||
CTRACE("der_bug", vidx >= definitions.size(), tout << "vidx: " << vidx << "\n";);
|
||||
// Remark: The size of definitions may be smaller than the number of variables occuring in the quantified formula.
|
||||
if (definitions.get(vidx, 0) != 0) {
|
||||
if (visiting.is_marked(t)) {
|
||||
// cycle detected: remove t
|
||||
visiting.reset_mark(t);
|
||||
definitions[vidx] = 0;
|
||||
}
|
||||
else {
|
||||
visiting.mark(t);
|
||||
fr.second = 1;
|
||||
todo.push_back(frame(definitions[vidx], 0));
|
||||
goto start;
|
||||
}
|
||||
}
|
||||
}
|
||||
else {
|
||||
SASSERT(fr.second == 1);
|
||||
if (definitions.get(vidx, 0) != 0) {
|
||||
visiting.reset_mark(t);
|
||||
order.push_back(vidx);
|
||||
}
|
||||
else {
|
||||
// var was removed from the list of candidate vars to elim cycle
|
||||
// do nothing
|
||||
}
|
||||
}
|
||||
if (t->get_ref_count() > 1)
|
||||
done.mark(t);
|
||||
todo.pop_back();
|
||||
break;
|
||||
case AST_QUANTIFIER:
|
||||
UNREACHABLE();
|
||||
todo.pop_back();
|
||||
break;
|
||||
case AST_APP:
|
||||
num = to_app(t)->get_num_args();
|
||||
while (fr.second < num) {
|
||||
expr * arg = to_app(t)->get_arg(fr.second);
|
||||
fr.second++;
|
||||
if (arg->get_ref_count() > 1 && done.is_marked(arg))
|
||||
continue;
|
||||
todo.push_back(frame(arg, 0));
|
||||
goto start;
|
||||
}
|
||||
if (t->get_ref_count() > 1)
|
||||
done.mark(t);
|
||||
todo.pop_back();
|
||||
break;
|
||||
default:
|
||||
UNREACHABLE();
|
||||
todo.pop_back();
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void der2::get_elimination_order() {
|
||||
m_order.reset();
|
||||
|
||||
TRACE("top_sort",
|
||||
tout << "DEFINITIONS: " << std::endl;
|
||||
for(unsigned i = 0; i < m_map.size(); i++)
|
||||
if(m_map[i]) tout << "VAR " << i << " = " << mk_pp(m_map[i], m) << std::endl;
|
||||
);
|
||||
|
||||
// der2::top_sort ts(m);
|
||||
der_sort_vars(m_inx2var, m_map, m_order);
|
||||
|
||||
TRACE("der",
|
||||
tout << "Elimination m_order:" << std::endl;
|
||||
for(unsigned i=0; i<m_order.size(); i++)
|
||||
{
|
||||
if (i != 0) tout << ",";
|
||||
tout << m_order[i];
|
||||
}
|
||||
tout << std::endl;
|
||||
);
|
||||
}
|
||||
|
||||
void der2::create_substitution(unsigned sz) {
|
||||
m_subst_map.reset();
|
||||
m_subst_map.resize(sz, 0);
|
||||
|
||||
for(unsigned i = 0; i < m_order.size(); i++) {
|
||||
expr_ref cur(m_map[m_order[i]], m);
|
||||
|
||||
// do all the previous substitutions before inserting
|
||||
expr_ref r(m);
|
||||
m_subst(cur, m_subst_map.size(), m_subst_map.c_ptr(), r);
|
||||
|
||||
unsigned inx = sz - m_order[i]- 1;
|
||||
SASSERT(m_subst_map[inx]==0);
|
||||
m_subst_map[inx] = r;
|
||||
}
|
||||
}
|
||||
|
||||
void der2::apply_substitution(quantifier * q, expr_ref & r) {
|
||||
expr * e = q->get_expr();
|
||||
unsigned num_args=to_app(e)->get_num_args();
|
||||
bool_rewriter rw(m);
|
||||
|
||||
// get a new expression
|
||||
m_new_args.reset();
|
||||
for(unsigned i = 0; i < num_args; i++) {
|
||||
int x = m_pos2var[i];
|
||||
if (x != -1 && m_map[x] != 0)
|
||||
continue; // this is a disequality with definition (vanishes)
|
||||
|
||||
m_new_args.push_back(to_app(e)->get_arg(i));
|
||||
}
|
||||
|
||||
expr_ref t(m);
|
||||
if (q->is_forall()) {
|
||||
rw.mk_or(m_new_args.size(), m_new_args.c_ptr(), t);
|
||||
}
|
||||
else {
|
||||
rw.mk_and(m_new_args.size(), m_new_args.c_ptr(), t);
|
||||
}
|
||||
expr_ref new_e(m);
|
||||
m_subst(t, m_subst_map.size(), m_subst_map.c_ptr(), new_e);
|
||||
|
||||
// don't forget to update the quantifier patterns
|
||||
expr_ref_buffer new_patterns(m);
|
||||
expr_ref_buffer new_no_patterns(m);
|
||||
for (unsigned j = 0; j < q->get_num_patterns(); j++) {
|
||||
expr_ref new_pat(m);
|
||||
m_subst(q->get_pattern(j), m_subst_map.size(), m_subst_map.c_ptr(), new_pat);
|
||||
new_patterns.push_back(new_pat);
|
||||
}
|
||||
|
||||
for (unsigned j = 0; j < q->get_num_no_patterns(); j++) {
|
||||
expr_ref new_nopat(m);
|
||||
m_subst(q->get_no_pattern(j), m_subst_map.size(), m_subst_map.c_ptr(), new_nopat);
|
||||
new_no_patterns.push_back(new_nopat);
|
||||
}
|
||||
|
||||
r = m.update_quantifier(q, new_patterns.size(), new_patterns.c_ptr(),
|
||||
new_no_patterns.size(), new_no_patterns.c_ptr(), new_e);
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
class qe_lite::impl {
|
||||
ast_manager& m;
|
||||
der2 m_der;
|
||||
|
||||
public:
|
||||
impl(ast_manager& m): m(m), m_der(m) {}
|
||||
|
||||
void operator()(app_ref_vector& vars, expr_ref& fml) {
|
||||
expr_ref tmp(fml);
|
||||
quantifier_ref q(m);
|
||||
proof_ref pr(m);
|
||||
symbol qe_lite("QE");
|
||||
expr_abstract(m, 0, vars.size(), (expr*const*)vars.c_ptr(), fml, tmp);
|
||||
ptr_vector<sort> sorts;
|
||||
svector<symbol> names;
|
||||
for (unsigned i = 0; i < vars.size(); ++i) {
|
||||
sorts.push_back(m.get_sort(vars[i].get()));
|
||||
names.push_back(vars[i]->get_decl()->get_name());
|
||||
}
|
||||
q = m.mk_exists(vars.size(), sorts.c_ptr(), names.c_ptr(), tmp, 1, qe_lite);
|
||||
m_der.reduce_quantifier(q, tmp, pr);
|
||||
// assumes m_der just updates the quantifier and does not change things more.
|
||||
if (is_exists(tmp) && to_quantifier(tmp)->get_qid() == qe_lite) {
|
||||
used_vars used;
|
||||
tmp = to_quantifier(tmp)->get_expr();
|
||||
used.process(tmp);
|
||||
var_subst vs(m, true);
|
||||
vs(tmp, vars.size(), (expr*const*)vars.c_ptr(), fml);
|
||||
// collect set of variables that were used.
|
||||
unsigned j = 0;
|
||||
for (unsigned i = 0; i < vars.size(); ++i) {
|
||||
if (used.contains(vars.size()-i-1)) {
|
||||
vars[j] = vars[i];
|
||||
++j;
|
||||
}
|
||||
}
|
||||
vars.resize(j);
|
||||
}
|
||||
else {
|
||||
fml = tmp;
|
||||
}
|
||||
}
|
||||
|
||||
void operator()(expr_ref& fml, proof_ref& pr) {
|
||||
// TODO apply der everywhere as a rewriting rule.
|
||||
// TODO add cancel method.
|
||||
if (is_quantifier(fml)) {
|
||||
m_der(to_quantifier(fml), fml, pr);
|
||||
}
|
||||
}
|
||||
|
||||
};
|
||||
|
||||
qe_lite::qe_lite(ast_manager& m) {
|
||||
m_impl = alloc(impl, m);
|
||||
}
|
||||
|
||||
qe_lite::~qe_lite() {
|
||||
dealloc(m_impl);
|
||||
}
|
||||
|
||||
void qe_lite::operator()(app_ref_vector& vars, expr_ref& fml) {
|
||||
(*m_impl)(vars, fml);
|
||||
}
|
||||
|
||||
void qe_lite::operator()(expr_ref& fml, proof_ref& pr) {
|
||||
(*m_impl)(fml, pr);
|
||||
}
|
||||
49
lib/qe_lite.h
Normal file
49
lib/qe_lite.h
Normal file
|
|
@ -0,0 +1,49 @@
|
|||
/*++
|
||||
Copyright (c) 2010 Microsoft Corporation
|
||||
|
||||
Module Name:
|
||||
|
||||
qe_lite.h
|
||||
|
||||
Abstract:
|
||||
|
||||
Light weight partial quantifier-elimination procedures
|
||||
|
||||
Author:
|
||||
|
||||
Nikolaj Bjorner (nbjorner) 2012-10-17
|
||||
|
||||
Revision History:
|
||||
|
||||
|
||||
--*/
|
||||
|
||||
#ifndef __QE_LITE_H__
|
||||
#define __QE_LITE_H__
|
||||
|
||||
#include "ast.h"
|
||||
|
||||
class qe_lite {
|
||||
class impl;
|
||||
impl * m_impl;
|
||||
public:
|
||||
qe_lite(ast_manager& m);
|
||||
|
||||
~qe_lite();
|
||||
|
||||
/**
|
||||
\brief
|
||||
Apply light-weight quantifier elimination
|
||||
on constants provided as vector of variables.
|
||||
Return the updated formula and updated set of variables that were not eliminated.
|
||||
|
||||
*/
|
||||
void operator()(app_ref_vector& vars, expr_ref& fml);
|
||||
|
||||
/**
|
||||
\brief full rewriting based light-weight quantifier elimination round.
|
||||
*/
|
||||
void operator()(expr_ref& fml, proof_ref& pr);
|
||||
};
|
||||
|
||||
#endif __QE_LITE_H__
|
||||
Loading…
Add table
Add a link
Reference in a new issue