mirror of
https://github.com/Z3Prover/z3
synced 2025-04-06 17:44:08 +00:00
Merge branch 'unstable' of https://git01.codeplex.com/z3 into unstable
This commit is contained in:
Leonardo de Moura
commit
472b8caa41
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@ -832,6 +832,7 @@ inline bool is_app(ast const * n) { return n->get_kind() == AST_APP; }
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inline bool is_var(ast const * n) { return n->get_kind() == AST_VAR; }
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inline bool is_quantifier(ast const * n) { return n->get_kind() == AST_QUANTIFIER; }
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inline bool is_forall(ast const * n) { return is_quantifier(n) && static_cast<quantifier const *>(n)->is_forall(); }
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inline bool is_exists(ast const * n) { return is_quantifier(n) && static_cast<quantifier const *>(n)->is_exists(); }
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// -----------------------------------
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//
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@ -20,8 +20,8 @@ Notes:
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Implements proof rule of the form:
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a(x) & q(x) -> p(x) b(y) & q(y) -> p(y)
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---------------------------------------------
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a(x) & q(x) -> p(x), b(y) & q(y) -> p(y)
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----------------------------------------------
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(a(z) \/ b(z)) & q(z) -> p(z)
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@ -754,6 +754,7 @@
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<ClCompile Include="qe_bv_plugin.cpp" />
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<ClCompile Include="qe_datatype_plugin.cpp" />
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<ClCompile Include="qe_dl_plugin.cpp" />
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<ClCompile Include="qe_lite.cpp" />
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<ClCompile Include="qe_sat_tactic.cpp" />
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<ClCompile Include="qe_tactic.cpp" />
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<ClCompile Include="qffpa_tactic.cpp" />
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@ -1161,6 +1162,7 @@
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<ClInclude Include="pull_ite_tree.h" />
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<ClInclude Include="pull_quant.h" />
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<ClInclude Include="push_app_ite.h" />
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<ClInclude Include="qe_lite.h" />
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<ClInclude Include="qe_sat_tactic.h" />
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<ClInclude Include="qfnra_sign.h" />
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<ClInclude Include="qfuf_strategy.h" />
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@ -41,6 +41,7 @@ Notes:
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#include "model_smt2_pp.h"
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#include "dl_mk_rule_inliner.h"
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#include "ast_smt2_pp.h"
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#include "qe_lite.h"
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namespace pdr {
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@ -124,7 +125,7 @@ namespace pdr {
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datalog::rule const& pred_transformer::find_rule(model_core const& model) const {
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obj_map<expr, datalog::rule const*>::iterator it = m_tag2rule.begin(), end = m_tag2rule.end();
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TRACE("pdr",
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TRACE("pdr_verbose",
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for (; it != end; ++it) {
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expr* pred = it->m_key;
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tout << mk_pp(pred, m) << ":\n";
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@ -394,7 +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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@ -522,6 +522,7 @@ namespace pdr {
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expr_ref_vector conj(m);
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app_ref_vector& var_reprs = *(alloc(app_ref_vector, m));
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qinst* qi = 0;
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ptr_vector<app> aux_vars;
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unsigned ut_size = rule.get_uninterpreted_tail_size();
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unsigned t_size = rule.get_tail_size();
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@ -534,7 +535,7 @@ namespace pdr {
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init_atom(pts, rule.get_tail(i), var_reprs, conj, i);
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}
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for (unsigned i = ut_size; i < t_size; ++i) {
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ground_free_vars(rule.get_tail(i), var_reprs);
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ground_free_vars(rule.get_tail(i), var_reprs, aux_vars);
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}
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SASSERT(check_filled(var_reprs));
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expr_ref_vector tail(m);
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@ -585,6 +586,7 @@ namespace pdr {
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m_rule2qinst.insert(&rule, qi);
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}
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m_rule2inst.insert(&rule,&var_reprs);
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m_rule2vars.insert(&rule, aux_vars);
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}
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bool pred_transformer::check_filled(app_ref_vector const& v) const {
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@ -595,7 +597,7 @@ namespace pdr {
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}
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// create constants for free variables in tail.
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void pred_transformer::ground_free_vars(expr* e, app_ref_vector& vars) {
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void pred_transformer::ground_free_vars(expr* e, app_ref_vector& vars, ptr_vector<app>& aux_vars) {
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ptr_vector<sort> sorts;
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get_free_vars(e, sorts);
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while (vars.size() < sorts.size()) {
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@ -604,6 +606,7 @@ namespace pdr {
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for (unsigned i = 0; i < sorts.size(); ++i) {
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if (sorts[i] && !vars[i].get()) {
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vars[i] = m.mk_fresh_const("aux", sorts[i]);
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aux_vars.push_back(vars[i].get());
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}
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}
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}
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@ -693,34 +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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@ -1102,7 +1077,6 @@ namespace pdr {
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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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@ -1164,7 +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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@ -1289,25 +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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classifier_proc classify(m, rules);
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if (classify.is_bool_arith()) {
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m_model_generalizers.push_back(alloc(bool_model_evaluation_generalizer, *this, m));
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}
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else {
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m_model_generalizers.push_back(alloc(model_evaluation_generalizer, *this, m));
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}
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if (m_params.get_bool(":use-precondition-generalizer", false)) {
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m_model_generalizers.push_back(alloc(model_precond_generalizer, *this));
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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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@ -1553,13 +1507,8 @@ namespace pdr {
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close_node(n);
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}
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else {
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TRACE("pdr", tout << "node: " << &n << "\n";
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expr_ref cb(m.mk_and(cube.size(),cube.c_ptr()), m);
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tout << mk_pp(cb.get(), m) << "\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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TRACE("pdr", tout << "node: " << &n << "\n";);
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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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@ -1630,40 +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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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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@ -1713,35 +1628,126 @@ 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, expr* psi) {
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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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model_core const& M = n.model();
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datalog::rule const& r = pt.find_rule(M);
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model_ref M = n.model_ptr();
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datalog::rule const& r = pt.find_rule(*M);
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expr* T = pt.get_transition(r);
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expr* phi = n.state();
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ternary_model_evaluator tmev(m);
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expr_ref_vector mdl(m);
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ptr_vector<expr> forms;
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IF_VERBOSE(2, verbose_stream() << "Model:\n";
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model_smt2_pp(verbose_stream(), m, *M, 0);
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verbose_stream() << "\n";
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verbose_stream() << "Transition:\n" << mk_pp(T, m) << "\n";
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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), 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(psi, mdl);
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expr_ref_vector Phi = tmev.minimize_literals(forms, mdl);
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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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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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expr_ref_vector vars(m);
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app_ref_vector vars(m);
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unsigned sig_size = pt.head()->get_arity();
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for (unsigned i = 0; i < sig_size; ++i) {
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vars.push_back(m.mk_const(m_pm.o2n(pt.sig(i), 0)));
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}
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// TBD: reduce_vars(vars, Phi);
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ptr_vector<app> aux_vars;
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pt.get_aux_vars(r, aux_vars);
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vars.append(aux_vars.size(), aux_vars.c_ptr());
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qe_lite qe(m);
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expr_ref phi1 = m_pm.mk_and(Phi);
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qe(vars, phi1);
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IF_VERBOSE(2,
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verbose_stream() << "Vars:\n";
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for (unsigned i = 0; i < vars.size(); ++i) {
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verbose_stream() << mk_pp(vars[i].get(), m) << "\n";
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}
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verbose_stream() << "Literals\n";
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verbose_stream() << mk_pp(m_pm.mk_and(Phi), m) << "\n";
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verbose_stream() << "Reduced\n" << mk_pp(phi1, m) << "\n";);
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if (!vars.empty()) {
|
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// also fresh names for auxiliary variables in body?
|
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expr_substitution sub(m);
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expr_ref tmp(m);
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proof_ref pr(m);
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pr = m.mk_asserted(m.mk_true());
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for (unsigned i = 0; i < vars.size(); ++i) {
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M->eval(vars[i]->get_decl(), tmp);
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sub.insert(vars[i].get(), tmp, pr);
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}
|
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scoped_ptr<expr_replacer> rep = mk_default_expr_replacer(m);
|
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rep->set_substitution(&sub);
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(*rep)(phi1);
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IF_VERBOSE(2, verbose_stream() << "Projected:\n" << mk_pp(phi1, m) << "\n";);
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}
|
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Phi.reset();
|
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datalog::flatten_and(phi1, Phi);
|
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unsigned_vector indices;
|
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vector<expr_ref_vector> child_states;
|
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child_states.resize(preds.size(), expr_ref_vector(m));
|
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for (unsigned i = 0; i < Phi.size(); ++i) {
|
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m_pm.collect_indices(Phi[i].get(), indices);
|
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if (indices.size() == 0) {
|
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IF_VERBOSE(2, verbose_stream() << "Skipping " << mk_pp(Phi[i].get(), m) << "\n";);
|
||||
}
|
||||
else if (indices.size() == 1) {
|
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child_states[indices.back()].push_back(Phi[i].get());
|
||||
}
|
||||
else {
|
||||
expr_substitution sub(m);
|
||||
expr_ref tmp(m);
|
||||
proof_ref pr(m);
|
||||
pr = m.mk_asserted(m.mk_true());
|
||||
vector<ptr_vector<app> > vars;
|
||||
m_pm.collect_variables(Phi[i].get(), vars);
|
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SASSERT(vars.size() == indices.back()+1);
|
||||
for (unsigned j = 1; j < indices.size(); ++j) {
|
||||
ptr_vector<app> const& vs = vars[indices[j]];
|
||||
for (unsigned k = 0; k < vs.size(); ++k) {
|
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M->eval(vs[k]->get_decl(), tmp);
|
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sub.insert(vs[k], tmp, pr);
|
||||
child_states[indices[j]].push_back(m.mk_eq(vs[k], tmp));
|
||||
}
|
||||
}
|
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tmp = Phi[i].get();
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||||
scoped_ptr<expr_replacer> rep = mk_default_expr_replacer(m);
|
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rep->set_substitution(&sub);
|
||||
(*rep)(tmp);
|
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child_states[indices[0]].push_back(tmp);
|
||||
}
|
||||
}
|
||||
|
||||
expr_ref n_cube(m);
|
||||
for (unsigned i = 0; i < preds.size(); ++i) {
|
||||
pred_transformer& pt = *m_rels.find(preds[i]);
|
||||
SASSERT(pt.head() == preds[i]);
|
||||
expr_ref o_cube = m_pm.mk_and(child_states[i]);
|
||||
m_pm.formula_o2n(o_cube, n_cube, i);
|
||||
model_node* child = alloc(model_node, &n, n_cube, pt, n.level()-1);
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++m_stats.m_num_nodes;
|
||||
m_search.add_leaf(*child);
|
||||
IF_VERBOSE(2, verbose_stream() << "Predecessor: " << mk_pp(o_cube, m) << "\n";);
|
||||
}
|
||||
check_pre_closed(n);
|
||||
|
||||
|
||||
// TBD ...
|
||||
TRACE("pdr", m_search.display(tout););
|
||||
}
|
||||
|
||||
|
|
@ -1754,9 +1760,6 @@ namespace pdr {
|
|||
st.update("PDR max depth", m_stats.m_max_depth);
|
||||
m_pm.collect_statistics(st);
|
||||
|
||||
for (unsigned i = 0; i < m_model_generalizers.size(); ++i) {
|
||||
m_model_generalizers[i]->collect_statistics(st);
|
||||
}
|
||||
for (unsigned i = 0; i < m_core_generalizers.size(); ++i) {
|
||||
m_core_generalizers[i]->collect_statistics(st);
|
||||
}
|
||||
|
|
|
|||
|
|
@ -60,6 +60,7 @@ namespace pdr {
|
|||
};
|
||||
|
||||
typedef obj_map<datalog::rule const, expr*> rule2expr;
|
||||
typedef obj_map<datalog::rule const, ptr_vector<app> > rule2apps;
|
||||
|
||||
manager& pm; // pdr-manager
|
||||
ast_manager& m; // manager
|
||||
|
|
@ -77,6 +78,7 @@ namespace pdr {
|
|||
qinst_map m_rule2qinst; // map tag to quantifier instantiation.
|
||||
rule2inst m_rule2inst; // map rules to instantiations of indices
|
||||
rule2expr m_rule2transition; // map rules to transition
|
||||
rule2apps m_rule2vars; // map rule to auxiliary variables
|
||||
expr_ref m_transition; // transition relation.
|
||||
expr_ref m_initial_state; // initial state.
|
||||
reachable_cache m_reachable;
|
||||
|
|
@ -94,10 +96,7 @@ namespace pdr {
|
|||
void init_rule(decl2rel const& pts, datalog::rule const& rule, expr_ref& init,
|
||||
ptr_vector<datalog::rule const>& rules, expr_ref_vector& transition);
|
||||
void init_atom(decl2rel const& pts, app * atom, app_ref_vector& var_reprs, expr_ref_vector& conj, unsigned tail_idx);
|
||||
void ground_free_vars(expr* e, app_ref_vector& vars);
|
||||
|
||||
void model2cube(const model_core& md, func_decl * d, expr_ref_vector& res) const;
|
||||
void model2cube(app* c, expr* val, expr_ref_vector& res) const;
|
||||
void ground_free_vars(expr* e, app_ref_vector& vars, ptr_vector<app>& aux_vars);
|
||||
|
||||
void simplify_formulas(tactic& tac, expr_ref_vector& fmls);
|
||||
|
||||
|
|
@ -137,6 +136,7 @@ namespace pdr {
|
|||
void find_predecessors(model_core const& model, ptr_vector<func_decl>& preds) const;
|
||||
datalog::rule const& find_rule(model_core const& model) const;
|
||||
expr* get_transition(datalog::rule const& r) { return m_rule2transition.find(&r); }
|
||||
void get_aux_vars(datalog::rule const& r, ptr_vector<app>& vs) { m_rule2vars.find(&r, vs); }
|
||||
|
||||
bool propagate_to_next_level(unsigned level);
|
||||
void add_property(expr * lemma, unsigned lvl); // add property 'p' to state at level.
|
||||
|
|
@ -154,8 +154,6 @@ namespace pdr {
|
|||
manager& get_pdr_manager() const { return pm; }
|
||||
ast_manager& get_manager() const { return m; }
|
||||
|
||||
void model2cube(const model_core & mdl, expr_ref_vector & res) const;
|
||||
|
||||
void add_premises(decl2rel const& pts, unsigned lvl, expr_ref_vector& r);
|
||||
|
||||
void close(expr* e);
|
||||
|
|
@ -194,7 +192,8 @@ namespace pdr {
|
|||
ptr_vector<model_node> const& children() { return m_children; }
|
||||
pred_transformer& pt() const { return m_pt; }
|
||||
model_node* parent() const { return m_parent; }
|
||||
model_core const& model() const { return *m_model; }
|
||||
model* model_ptr() const { return m_model.get(); }
|
||||
model const& model() const { return *m_model; }
|
||||
unsigned index() const;
|
||||
|
||||
bool is_closed() const { return m_closed; }
|
||||
|
|
@ -262,18 +261,6 @@ namespace pdr {
|
|||
|
||||
class context;
|
||||
|
||||
// 'state' is satisifiable with predecessor 'cube'.
|
||||
// Generalize predecessor still forcing satisfiability.
|
||||
class model_generalizer {
|
||||
protected:
|
||||
context& m_ctx;
|
||||
public:
|
||||
model_generalizer(context& ctx): m_ctx(ctx) {}
|
||||
virtual ~model_generalizer() {}
|
||||
virtual void operator()(model_node& n, expr_ref_vector& cube) = 0;
|
||||
virtual void collect_statistics(statistics& st) {}
|
||||
};
|
||||
|
||||
// 'state' is unsatisfiable at 'level' with 'core'.
|
||||
// Minimize or weaken core.
|
||||
class core_generalizer {
|
||||
|
|
@ -301,7 +288,6 @@ namespace pdr {
|
|||
stats() { reset(); }
|
||||
void reset() { memset(this, 0, sizeof(*this)); }
|
||||
};
|
||||
|
||||
|
||||
front_end_params& m_fparams;
|
||||
params_ref const& m_params;
|
||||
|
|
@ -315,7 +301,6 @@ namespace pdr {
|
|||
model_search m_search;
|
||||
lbool m_last_result;
|
||||
unsigned m_inductive_lvl;
|
||||
ptr_vector<model_generalizer> m_model_generalizers;
|
||||
ptr_vector<core_generalizer> m_core_generalizers;
|
||||
stats m_stats;
|
||||
volatile bool m_cancel;
|
||||
|
|
@ -332,8 +317,7 @@ namespace pdr {
|
|||
void check_pre_closed(model_node& n);
|
||||
void expand_node(model_node& n);
|
||||
lbool expand_state(model_node& n, expr_ref_vector& cube);
|
||||
void create_children(model_node& n, expr* cube);
|
||||
void create_children2(model_node& n, expr* cube);
|
||||
void create_children(model_node& n);
|
||||
expr_ref mk_sat_answer() const;
|
||||
expr_ref mk_unsat_answer() const;
|
||||
|
||||
|
|
@ -343,7 +327,6 @@ namespace pdr {
|
|||
|
||||
// Initialization
|
||||
class classifier_proc;
|
||||
void init_model_generalizers(datalog::rule_set& rules);
|
||||
void init_core_generalizers(datalog::rule_set& rules);
|
||||
|
||||
bool check_invariant(unsigned lvl);
|
||||
|
|
@ -355,7 +338,6 @@ namespace pdr {
|
|||
|
||||
void simplify_formulas();
|
||||
|
||||
void reset_model_generalizers();
|
||||
void reset_core_generalizers();
|
||||
|
||||
public:
|
||||
|
|
|
|||
|
|
@ -202,7 +202,7 @@ void dl_interface::collect_params(param_descrs& p) {
|
|||
p.insert(":inline-proofs", CPK_BOOL, "PDR: (default true) run PDR with proof mode turned on and extract Farkas coefficients directly (instead of creating a separate proof object when extracting coefficients)");
|
||||
p.insert(":flexible-trace", CPK_BOOL, "PDR: (default false) allow PDR generate long counter-examples by extending candidate trace within search area");
|
||||
p.insert(":unfold-rules", CPK_UINT, "PDR: (default 0) unfold rules statically using iterative squarring");
|
||||
PRIVATE_PARAMS(p.insert(":use-precondition-generalizer", CPK_BOOL, "PDR: (default false) enable generalizations from weakest pre-conditions"););
|
||||
p.insert(":use-model-generalizer", CPK_BOOL, "PDR: (default false) use model for backwards propagation (instead of symbolic simulation)");
|
||||
PRIVATE_PARAMS(p.insert(":use-multicore-generalizer", CPK_BOOL, "PDR: (default false) extract multiple cores for blocking states"););
|
||||
PRIVATE_PARAMS(p.insert(":use-inductive-generalizer", CPK_BOOL, "PDR: (default true) generalize lemmas using induction strengthening"););
|
||||
PRIVATE_PARAMS(p.insert(":use-interpolants", CPK_BOOL, "PDR: (default false) use iZ3 interpolation for lemma generation"););
|
||||
|
|
|
|||
|
|
@ -28,66 +28,6 @@ Revision History:
|
|||
|
||||
namespace pdr {
|
||||
|
||||
static void solve_for_next_vars(expr_ref& F, model_node& n, expr_substitution& sub) {
|
||||
ast_manager& m = F.get_manager();
|
||||
manager& pm = n.pt().get_pdr_manager();
|
||||
const model_core & mdl = n.model();
|
||||
unsigned sz = mdl.get_num_constants();
|
||||
expr_ref_vector refs(m);
|
||||
|
||||
for (unsigned i = 0; i < sz; i++) {
|
||||
func_decl * d = mdl.get_constant(i);
|
||||
expr_ref interp(m);
|
||||
ptr_vector<app> cs;
|
||||
if (m.is_bool(d->get_range())) {
|
||||
get_value_from_model(mdl, d, interp);
|
||||
app* c = m.mk_const(d);
|
||||
refs.push_back(c);
|
||||
refs.push_back(interp);
|
||||
sub.insert(c, interp);
|
||||
}
|
||||
}
|
||||
scoped_ptr<expr_replacer> rep = mk_default_expr_replacer(m);
|
||||
rep->set_substitution(&sub);
|
||||
(*rep)(F);
|
||||
th_rewriter rw(m);
|
||||
rw(F);
|
||||
ptr_vector<expr> todo;
|
||||
todo.push_back(F);
|
||||
expr* e1, *e2;
|
||||
while (!todo.empty()) {
|
||||
expr* e = todo.back();
|
||||
todo.pop_back();
|
||||
if (m.is_and(e)) {
|
||||
todo.append(to_app(e)->get_num_args(), to_app(e)->get_args());
|
||||
}
|
||||
else if ((m.is_eq(e, e1, e2) && pm.is_n(e1) && pm.is_o_formula(e2)) ||
|
||||
(m.is_eq(e, e2, e1) && pm.is_n(e1) && pm.is_o_formula(e2))) {
|
||||
sub.insert(e1, e2);
|
||||
TRACE("pdr", tout << mk_pp(e1, m) << " |-> " << mk_pp(e2, m) << "\n";);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
//
|
||||
// eliminate conjuncts from cube as long as state is satisfied.
|
||||
//
|
||||
void model_evaluation_generalizer::operator()(model_node& n, expr_ref_vector& cube) {
|
||||
ptr_vector<expr> forms;
|
||||
forms.push_back(n.state());
|
||||
forms.push_back(n.pt().transition());
|
||||
m_model_evaluator.minimize_model(forms, cube);
|
||||
}
|
||||
|
||||
//
|
||||
// eliminate conjuncts from cube as long as state is satisfied.
|
||||
//
|
||||
void bool_model_evaluation_generalizer::operator()(model_node& n, expr_ref_vector& cube) {
|
||||
ptr_vector<expr> forms;
|
||||
forms.push_back(n.state());
|
||||
forms.push_back(n.pt().transition());
|
||||
m_model_evaluator.minimize_model(forms, cube);
|
||||
}
|
||||
|
||||
//
|
||||
// main propositional induction generalizer.
|
||||
|
|
@ -203,31 +143,6 @@ namespace pdr {
|
|||
m_farkas_learner.collect_statistics(st);
|
||||
}
|
||||
|
||||
void model_precond_generalizer::operator()(model_node& n, expr_ref_vector& cube) {
|
||||
ast_manager& m = n.pt().get_manager();
|
||||
manager& pm = n.pt().get_pdr_manager();
|
||||
expr_ref A(m), state(m);
|
||||
expr_ref_vector states(m);
|
||||
A = n.pt().get_formulas(n.level(), true);
|
||||
|
||||
// extract substitution for next-state variables.
|
||||
expr_substitution sub(m);
|
||||
solve_for_next_vars(A, n, sub);
|
||||
scoped_ptr<expr_replacer> rep = mk_default_expr_replacer(m);
|
||||
rep->set_substitution(&sub);
|
||||
A = m.mk_and(A, n.state());
|
||||
(*rep)(A);
|
||||
|
||||
datalog::flatten_and(A, states);
|
||||
|
||||
for (unsigned i = 0; i < states.size(); ++i) {
|
||||
expr* s = states[i].get();
|
||||
if (pm.is_o_formula(s) && pm.is_homogenous_formula(s)) {
|
||||
cube.push_back(s);
|
||||
}
|
||||
}
|
||||
TRACE("pdr", for (unsigned i = 0; i < cube.size(); ++i) tout << mk_pp(cube[i].get(), m) << "\n";);
|
||||
}
|
||||
|
||||
/**
|
||||
< F, phi, i + 1 >
|
||||
|
|
|
|||
|
|
@ -25,14 +25,6 @@ Revision History:
|
|||
|
||||
namespace pdr {
|
||||
|
||||
class bool_model_evaluation_generalizer : public model_generalizer {
|
||||
ternary_model_evaluator m_model_evaluator;
|
||||
public:
|
||||
bool_model_evaluation_generalizer(context& ctx, ast_manager& m) : model_generalizer(ctx), m_model_evaluator(m) {}
|
||||
virtual ~bool_model_evaluation_generalizer() {}
|
||||
virtual void operator()(model_node& n, expr_ref_vector& cube);
|
||||
};
|
||||
|
||||
class core_bool_inductive_generalizer : public core_generalizer {
|
||||
unsigned m_failure_limit;
|
||||
public:
|
||||
|
|
@ -50,21 +42,6 @@ namespace pdr {
|
|||
virtual void collect_statistics(statistics& st) const;
|
||||
};
|
||||
|
||||
class model_precond_generalizer : public model_generalizer {
|
||||
public:
|
||||
model_precond_generalizer(context& ctx): model_generalizer(ctx) {}
|
||||
virtual ~model_precond_generalizer() {}
|
||||
virtual void operator()(model_node& n, expr_ref_vector& cube);
|
||||
};
|
||||
|
||||
class model_evaluation_generalizer : public model_generalizer {
|
||||
th_rewriter_model_evaluator m_model_evaluator;
|
||||
public:
|
||||
model_evaluation_generalizer(context& ctx, ast_manager& m) : model_generalizer(ctx), m_model_evaluator(m) {}
|
||||
virtual ~model_evaluation_generalizer() {}
|
||||
virtual void operator()(model_node& n, expr_ref_vector& cube);
|
||||
};
|
||||
|
||||
class core_multi_generalizer : public core_generalizer {
|
||||
core_bool_inductive_generalizer m_gen;
|
||||
public:
|
||||
|
|
|
|||
|
|
@ -223,6 +223,20 @@ namespace pdr {
|
|||
bool is_homogenous_formula(expr * e) const {
|
||||
return m_mux.is_homogenous_formula(e);
|
||||
}
|
||||
|
||||
/**
|
||||
Collect indices used in expression.
|
||||
*/
|
||||
void collect_indices(expr* e, unsigned_vector& indices) const {
|
||||
m_mux.collect_indices(e, indices);
|
||||
}
|
||||
|
||||
/**
|
||||
Collect used variables of each index.
|
||||
*/
|
||||
void collect_variables(expr* e, vector<ptr_vector<app> >& vars) const {
|
||||
m_mux.collect_variables(e, vars);
|
||||
}
|
||||
|
||||
/**
|
||||
Return true iff both s1 and s2 are either "n" or "o" of the same index.
|
||||
|
|
@ -275,8 +289,6 @@ namespace pdr {
|
|||
bool try_get_state_and_value_from_atom(expr * atom, app *& state, app_ref& value);
|
||||
bool try_get_state_decl_from_atom(expr * atom, func_decl *& state);
|
||||
|
||||
void get_state_cube_from_model(const model_core & mdl, expr_ref_vector & cube) const
|
||||
{ return m_mux.get_muxed_cube_from_model(mdl, cube); }
|
||||
|
||||
std::string pp_model(const model_core & mdl) const
|
||||
{ return m_mux.pp_model(mdl); }
|
||||
|
|
|
|||
|
|
@ -228,6 +228,76 @@ bool sym_mux::is_homogenous(const expr_ref_vector & vect, unsigned idx) const
|
|||
return true;
|
||||
}
|
||||
|
||||
class sym_mux::index_collector {
|
||||
sym_mux const& m_parent;
|
||||
svector<bool> m_indices;
|
||||
public:
|
||||
index_collector(sym_mux const& s):
|
||||
m_parent(s) {}
|
||||
|
||||
void operator()(expr * e) {
|
||||
if (is_app(e)) {
|
||||
func_decl * sym = to_app(e)->get_decl();
|
||||
unsigned idx;
|
||||
if (m_parent.try_get_index(sym, idx)) {
|
||||
SASSERT(idx > 0);
|
||||
--idx;
|
||||
if (m_indices.size() <= idx) {
|
||||
m_indices.resize(idx+1, false);
|
||||
}
|
||||
m_indices[idx] = true;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void extract(unsigned_vector& indices) {
|
||||
for (unsigned i = 0; i < m_indices.size(); ++i) {
|
||||
if (m_indices[i]) {
|
||||
indices.push_back(i);
|
||||
}
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
|
||||
|
||||
void sym_mux::collect_indices(expr* e, unsigned_vector& indices) const {
|
||||
indices.reset();
|
||||
index_collector collector(*this);
|
||||
for_each_expr(collector, m_visited, e);
|
||||
m_visited.reset();
|
||||
collector.extract(indices);
|
||||
}
|
||||
|
||||
class sym_mux::variable_collector {
|
||||
sym_mux const& m_parent;
|
||||
vector<ptr_vector<app> >& m_vars;
|
||||
public:
|
||||
variable_collector(sym_mux const& s, vector<ptr_vector<app> >& vars):
|
||||
m_parent(s), m_vars(vars) {}
|
||||
|
||||
void operator()(expr * e) {
|
||||
if (is_app(e)) {
|
||||
func_decl * sym = to_app(e)->get_decl();
|
||||
unsigned idx;
|
||||
if (m_parent.try_get_index(sym, idx)) {
|
||||
SASSERT(idx > 0);
|
||||
--idx;
|
||||
if (m_vars.size() <= idx) {
|
||||
m_vars.resize(idx+1, ptr_vector<app>());
|
||||
}
|
||||
m_vars[idx].push_back(to_app(e));
|
||||
}
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
void sym_mux::collect_variables(expr* e, vector<ptr_vector<app> >& vars) const {
|
||||
vars.reset();
|
||||
variable_collector collector(*this, vars);
|
||||
for_each_expr(collector, m_visited, e);
|
||||
m_visited.reset();
|
||||
}
|
||||
|
||||
class sym_mux::hmg_checker {
|
||||
const sym_mux & m_parent;
|
||||
|
|
@ -445,38 +515,6 @@ void sym_mux::filter_non_model_lits(expr_ref_vector & vect) const {
|
|||
}
|
||||
}
|
||||
|
||||
void sym_mux::get_muxed_cube_from_model(const model_core & mdl, expr_ref_vector & res) const
|
||||
{
|
||||
res.reset();
|
||||
unsigned sz = mdl.get_num_constants();
|
||||
for (unsigned i = 0; i < sz; i++) {
|
||||
func_decl * d = mdl.get_constant(i);
|
||||
|
||||
if(!is_muxed(d) || m_non_model_syms.contains(get_primary(d))) { continue; }
|
||||
|
||||
SASSERT(d->get_arity()==0);
|
||||
expr_ref interp(m);
|
||||
get_value_from_model(mdl, d, interp);
|
||||
|
||||
app_ref constant(m.mk_const(d), m);
|
||||
app_ref lit(m);
|
||||
if(m.is_bool(d->get_range())) {
|
||||
if(m.is_true(interp)) {
|
||||
lit = constant;
|
||||
}
|
||||
else {
|
||||
SASSERT(m.is_false(interp));
|
||||
lit = m.mk_not(constant);
|
||||
}
|
||||
}
|
||||
else {
|
||||
lit = m.mk_eq(constant, interp);
|
||||
}
|
||||
res.push_back(lit);
|
||||
}
|
||||
//LOGV(5, " got cube "<<pp_cube(res, m));
|
||||
}
|
||||
|
||||
class sym_mux::decl_idx_comparator
|
||||
{
|
||||
const sym_mux & m_parent;
|
||||
|
|
|
|||
|
|
@ -86,6 +86,8 @@ private:
|
|||
class hmg_checker;
|
||||
class nonmodel_sym_checker;
|
||||
class index_renamer_cfg;
|
||||
class index_collector;
|
||||
class variable_collector;
|
||||
|
||||
std::string get_suffix(unsigned i) const;
|
||||
void ensure_tuple_size(func_decl * prim, unsigned sz) const;
|
||||
|
|
@ -184,6 +186,15 @@ public:
|
|||
*/
|
||||
bool contains(expr * e, unsigned idx) const;
|
||||
|
||||
/**
|
||||
Collect indices used in expression.
|
||||
*/
|
||||
void collect_indices(expr* e, unsigned_vector& indices) const;
|
||||
|
||||
/**
|
||||
Collect used variables of each index.
|
||||
*/
|
||||
void collect_variables(expr* e, vector<ptr_vector<app> >& vars) const;
|
||||
|
||||
/**
|
||||
Convert symbol sym which has to be of src_idx variant into variant tgt_idx.
|
||||
|
|
|
|||
1108
lib/pdr_util.cpp
1108
lib/pdr_util.cpp
File diff suppressed because it is too large
Load diff
|
|
@ -170,34 +170,15 @@ void vect_set_union(ref_vector<Type,Mgr> & tgt, ref_vector<Type,Mgr> & src, Comp
|
|||
}
|
||||
|
||||
|
||||
class model_evaluator_base {
|
||||
protected:
|
||||
virtual void check_model(ptr_vector<expr> const & formulas,
|
||||
expr_ref_vector & model, bool & has_unknown, bool & has_false) = 0;
|
||||
public:
|
||||
virtual void minimize_model(ptr_vector<expr> const & formulas, expr_ref_vector & model);
|
||||
};
|
||||
|
||||
class th_rewriter_model_evaluator : public model_evaluator_base {
|
||||
class expr_rewriter_cfg;
|
||||
ast_manager& m;
|
||||
th_rewriter m_rewriter;
|
||||
|
||||
void setup_assignment(expr_ref_vector const& model, obj_map<expr,expr*>& assignment);
|
||||
|
||||
protected:
|
||||
virtual void check_model(ptr_vector<expr> const & formulas,
|
||||
expr_ref_vector & model, bool & has_unknown,
|
||||
bool & has_false);
|
||||
public:
|
||||
th_rewriter_model_evaluator(ast_manager& m) : m(m), m_rewriter(m) {}
|
||||
};
|
||||
|
||||
class ternary_model_evaluator : public model_evaluator_base {
|
||||
class model_evaluator {
|
||||
ast_manager& m;
|
||||
arith_util m_arith;
|
||||
bv_util m_bv;
|
||||
obj_map<expr,rational> m_values;
|
||||
obj_map<expr,rational> m_numbers;
|
||||
expr_ref_vector m_refs;
|
||||
obj_map<expr, expr*> m_values;
|
||||
model_ref m_model;
|
||||
|
||||
//00 -- non-visited
|
||||
//01 -- X
|
||||
|
|
@ -209,16 +190,17 @@ class ternary_model_evaluator : public model_evaluator_base {
|
|||
unsigned m_level2;
|
||||
expr_mark m_visited;
|
||||
|
||||
void setup_model(expr_ref_vector const& model);
|
||||
void add_model(expr* e);
|
||||
void del_model(expr* e);
|
||||
|
||||
bool get_assignment(expr* e, expr*& var, expr*& val);
|
||||
|
||||
void reset();
|
||||
void setup_model(model_ref& model);
|
||||
void assign_value(expr* e, expr* v);
|
||||
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);
|
||||
void prune_by_probing(ptr_vector<expr> const & formulas, expr_ref_vector& model);
|
||||
void process_formula(app* e, ptr_vector<expr>& todo, ptr_vector<expr>& tocollect);
|
||||
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);
|
||||
void inherit_value(expr* e, expr* v);
|
||||
|
||||
//00 -- non-visited
|
||||
//01 -- X
|
||||
|
|
@ -234,27 +216,34 @@ class ternary_model_evaluator : public model_evaluator_base {
|
|||
inline void set_false(expr* x) { SASSERT(is_unknown(x)); m1.mark(x); }
|
||||
inline void set_true(expr* x) { SASSERT(is_unknown(x)); m1.mark(x); m2.mark(x); }
|
||||
inline void set_bool(expr* x, bool v) { if (v) { set_true(x); } else { set_false(x); } }
|
||||
inline rational const& get_value(expr* x) const { return m_values.find(x); }
|
||||
inline void set_value(expr* x, rational const& v) { set_v(x); TRACE("pdr_verbose", tout << mk_pp(x,m) << " " << v << "\n";); m_values.insert(x,v); }
|
||||
|
||||
inline rational const& get_number(expr* x) const { return m_numbers.find(x); }
|
||||
inline void set_number(expr* x, rational const& v) { set_v(x); TRACE("pdr_verbose", tout << mk_pp(x,m) << " " << v << "\n";); m_numbers.insert(x,v); }
|
||||
inline expr* get_value(expr* x) { return m_values.find(x); }
|
||||
inline void set_value(expr* x, expr* v) { set_v(x); m_refs.push_back(v); m_values.insert(x, v); }
|
||||
|
||||
|
||||
protected:
|
||||
|
||||
bool check_model(ptr_vector<expr> const & formulas);
|
||||
virtual void check_model(ptr_vector<expr> const & formulas, expr_ref_vector & model,
|
||||
bool & has_unknown, bool & has_false) {
|
||||
UNREACHABLE();
|
||||
}
|
||||
|
||||
public:
|
||||
ternary_model_evaluator(ast_manager& m) : m(m), m_arith(m), m_bv(m) {}
|
||||
virtual void minimize_model(ptr_vector<expr> const & formulas, expr_ref_vector & model);
|
||||
model_evaluator(ast_manager& m) : m(m), m_arith(m), m_bv(m), m_refs(m) {}
|
||||
|
||||
/**
|
||||
\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.
|
||||
|
||||
\pre model satisfies formulas
|
||||
*/
|
||||
expr_ref_vector minimize_literals(ptr_vector<expr> const & formulas, expr_ref_vector const & model);
|
||||
expr_ref_vector minimize_literals(ptr_vector<expr> const & formulas, model_ref& mdl);
|
||||
|
||||
|
||||
// for_each_expr visitor.
|
||||
void operator()(expr* e) {}
|
||||
|
|
@ -262,11 +251,6 @@ public:
|
|||
|
||||
void get_value_from_model(const model_core & mdl, func_decl * f, expr_ref& res);
|
||||
|
||||
/**
|
||||
If the solver argument is non-zero, we will exclude its auxiliary symbols from the generated cube.
|
||||
*/
|
||||
void get_cube_from_model(const model_core & mdl, expr_ref_vector & res, pdr::prop_solver& solver);
|
||||
|
||||
}
|
||||
|
||||
#endif
|
||||
|
|
|
|||
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…
Reference in a new issue