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https://github.com/Z3Prover/z3
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fix bug in proof generation for PDR, add more features for handling quantifiers
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
2d1a6bf270
commit
a813c384a6
8 changed files with 356 additions and 40 deletions
33
src/muz_qe/equiv_proof_converter.cpp
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33
src/muz_qe/equiv_proof_converter.cpp
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@ -0,0 +1,33 @@
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/*++
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Copyright (c) 2012 Microsoft Corporation
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Module Name:
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equiv_proof_converter.cpp
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Abstract:
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Proof converter that applies equivalence rule to leaves.
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Author:
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Nikolaj Bjorner (nbjorner) 2012-11-23
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Revision History:
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--*/
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#include "equiv_proof_converter.h"
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#include "ast_pp.h"
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#include "dl_util.h"
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void equiv_proof_converter::insert(expr* fml1, expr* fml2) {
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datalog::scoped_fine_proof _sp(m);
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proof_ref p1(m), p2(m), p3(m);
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p1 = m.mk_asserted(fml1);
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p2 = m.mk_rewrite(fml1, fml2);
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p3 = m.mk_modus_ponens(p1, p2);
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TRACE("proof_converter", tout << mk_pp(p3.get(), m) << "\n";);
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SASSERT(m.has_fact(p3));
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m_replace.insert(p3);
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}
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@ -43,13 +43,7 @@ public:
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return m_replace.translate(translator);
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}
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void insert(expr* fml1, expr* fml2) {
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proof_ref p1(m), p2(m), p3(m);
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p1 = m.mk_asserted(fml1);
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p2 = m.mk_rewrite(fml1, fml2);
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p3 = m.mk_modus_ponens(p1, p2);
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m_replace.insert(p3);
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}
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void insert(expr* fml1, expr* fml2);
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ast_manager& get_manager() { return m; }
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@ -162,9 +162,6 @@ namespace pdr {
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}
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}
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void pred_transformer::find_predecessors(model_core const& model, ptr_vector<func_decl>& preds) const {
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find_predecessors(find_rule(model), preds);
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}
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void pred_transformer::remove_predecessors(expr_ref_vector& literals) {
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// remove tags
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@ -740,6 +737,44 @@ namespace pdr {
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return expr_ref(m.mk_app(f, args.size(), args.c_ptr()), m);
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}
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static bool is_ini(datalog::rule const& r) {
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return r.get_uninterpreted_tail_size() == 0;
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}
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datalog::rule* model_node::get_rule() {
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if (m_rule) {
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return const_cast<datalog::rule*>(m_rule);
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}
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// only initial states are not set by the PDR search.
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datalog::rule const& rl1 = pt().find_rule(*m_model);
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if (is_ini(rl1)) {
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set_rule(&rl1);
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return const_cast<datalog::rule*>(m_rule);
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}
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ast_manager& m = pt().get_manager();
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// otherwise, the initial state is reachable.
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ptr_vector<datalog::rule> const& rules = pt().rules();
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ptr_vector<datalog::rule> ini_rules;
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expr_ref_vector tags(m);
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expr_ref ini_tags(m), ini_state(m);
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for (unsigned i = 0; i < rules.size(); ++i) {
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datalog::rule* rl = rules[i];
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if (is_ini(*rl)) {
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tags.push_back(pt().rule2tag(rl));
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}
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}
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SASSERT(!tags.empty());
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ini_tags = m.mk_or(tags.size(), tags.c_ptr());
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ini_state = m.mk_and(ini_tags, pt().initial_state(), state());
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model_ref mdl;
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pt().get_solver().set_model(&mdl);
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VERIFY(l_true == pt().get_solver().check_conjunction_as_assumptions(ini_state));
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datalog::rule const& rl2 = pt().find_rule(*mdl);
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SASSERT(is_ini(rl2));
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set_rule(&rl2);
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return const_cast<datalog::rule*>(m_rule);
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}
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void model_node::mk_instantiate(datalog::rule_ref& r0, datalog::rule_ref& r1, expr_ref_vector& binding) {
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ast_manager& m = pt().get_manager();
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@ -763,7 +798,7 @@ namespace pdr {
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model.insert(e, m.mk_true());
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}
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}
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r0 = const_cast<datalog::rule*>(&pt().find_rule(*m_model.get()));
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r0 = get_rule();
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app_ref_vector& inst = pt().get_inst(r0);
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TRACE("pdr", tout << mk_pp(state(), m) << " instance: " << inst.size() << "\n";);
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for (unsigned i = 0; i < inst.size(); ++i) {
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@ -1644,7 +1679,7 @@ namespace pdr {
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switch (expand_state(n, cube, uses_level)) {
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case l_true:
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if (n.level() == 0) {
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TRACE("pdr", tout << "reachable\n";);
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TRACE("pdr", tout << "reachable at level 0\n";);
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close_node(n);
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}
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else {
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@ -1772,6 +1807,8 @@ namespace pdr {
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expr* T = pt.get_transition(r);
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expr* phi = n.state();
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n.set_rule(&r);
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IF_VERBOSE(3, 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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@ -132,7 +132,6 @@ namespace pdr {
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bool is_reachable(expr* state);
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void remove_predecessors(expr_ref_vector& literals);
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void find_predecessors(datalog::rule const& r, ptr_vector<func_decl>& predicates) const;
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void find_predecessors(model_core const& model, ptr_vector<func_decl>& preds) const;
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datalog::rule const& find_rule(model_core const& model) const;
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expr* get_transition(datalog::rule const& r) { return m_rule2transition.find(&r); }
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ptr_vector<app>& get_aux_vars(datalog::rule const& r) { return m_rule2vars.find(&r); }
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@ -163,6 +162,8 @@ namespace pdr {
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void ground_free_vars(expr* e, app_ref_vector& vars, ptr_vector<app>& aux_vars);
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prop_solver& get_solver() { return m_solver; }
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};
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@ -177,10 +178,11 @@ namespace pdr {
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unsigned m_orig_level;
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unsigned m_depth;
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bool m_closed;
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datalog::rule const* m_rule;
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public:
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model_node(model_node* parent, expr_ref& state, pred_transformer& pt, unsigned level):
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m_parent(parent), m_pt(pt), m_state(state), m_model(0),
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m_level(level), m_orig_level(level), m_depth(0), m_closed(false) {
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m_level(level), m_orig_level(level), m_depth(0), m_closed(false), m_rule(0) {
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if (m_parent) {
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m_parent->m_children.push_back(this);
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SASSERT(m_parent->m_level == level+1);
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@ -217,6 +219,9 @@ namespace pdr {
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void set_pre_closed() { m_closed = true; }
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void reset() { m_children.reset(); }
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void set_rule(datalog::rule const* r) { m_rule = r; }
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datalog::rule* get_rule();
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expr_ref get_trace() const;
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void mk_instantiate(datalog::rule_ref& r0, datalog::rule_ref& r1, expr_ref_vector& binding);
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@ -105,7 +105,11 @@ namespace pdr {
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}
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void quantifier_model_checker::add_binding(quantifier* q, expr_ref_vector& binding) {
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void quantifier_model_checker::add_binding(quantifier* q, expr_ref_vector& binding) {
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if (binding.size() != q->get_num_decls()) {
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// not a full binding. It may happen that the quantifier got simplified.
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return;
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}
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apply_binding(q, binding);
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vector<expr_ref_vector> bindings;
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generalize_binding(binding, bindings);
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@ -126,15 +130,18 @@ namespace pdr {
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inst.append(var_inst.size(), (expr*const*)var_inst.c_ptr());
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inst.reverse();
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expr_abstract(m, 0, inst.size(), inst.c_ptr(), e, e);
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if (m_instantiations.contains(to_app(e))) {
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return;
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}
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m_instantiated_rules.push_back(m_current_rule);
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m_instantiations.push_back(to_app(e));
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TRACE("pdr", tout << mk_pp(q, m) << "\n";
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tout << "binding\n";
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tout << "binding: ";
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for (unsigned i = 0; i < binding.size(); ++i) {
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tout << mk_pp(binding[i].get(), m) << " ";
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}
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tout << "\n";
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tout << "inst\n";
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tout << "inst: ";
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for (unsigned i = 0; i < var_inst.size(); ++i) {
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tout << mk_pp(var_inst[i].get(), m) << " ";
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}
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@ -361,6 +368,7 @@ namespace pdr {
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scoped_ptr<expr_replacer> rep = mk_default_expr_replacer(m);
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for (unsigned j = 0; j < qis.size(); ++j) {
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q = qis[j].get();
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SASSERT(is_forall(q));
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app_ref_vector& inst = pt.get_inst(m_current_rule);
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TRACE("pdr",
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tout << "q:\n" << mk_pp(q, m) << "\n";
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@ -433,11 +441,16 @@ namespace pdr {
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unsigned t_size = r.get_tail_size();
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var_subst vs(m, false);
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sort_ref_vector vars(m);
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uint_set empty_index_set;
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qe_lite qe(m);
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r.get_vars(vars);
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#if 1
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if (qis) {
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quantifier_ref_vector const& qi = *qis;
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for (unsigned i = 0; i < qi.size(); ++i) {
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fml = qi[i]->get_expr();
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quantifier* q = qi[i];
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fml = q->get_expr();
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a = to_app(fml);
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p = a->get_decl();
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expr* p_reach = get_reachable(p);
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@ -448,9 +461,17 @@ namespace pdr {
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sub.insert(v, a->get_arg(j));
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}
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sub(p_reach, fml);
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body.push_back(m.update_quantifier(qi[i], fml));
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uint_set is;
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for (unsigned j = 0; j < q->get_num_decls(); ++j) {
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is.insert(j);
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}
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fml = m.mk_not(fml);
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qe(is, true, fml);
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fml = m.mk_not(fml);
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body.push_back(m.update_quantifier(q, fml));
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}
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}
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#endif
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a = r.get_head();
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for (unsigned i = 0; i < a->get_num_args(); ++i) {
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v = m.mk_var(vars.size()+i, m.get_sort(a->get_arg(i)));
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@ -489,8 +510,6 @@ namespace pdr {
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SASSERT(is_well_sorted(m, fml));
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if (!vars.empty()) {
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fml = to_quantifier(fml)->get_expr();
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uint_set empty_index_set;
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qe_lite qe(m);
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qe(empty_index_set, false, fml);
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fml = m.mk_exists(vars.size(), vars.c_ptr(), names.c_ptr(), fml);
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SASSERT(is_well_sorted(m, fml));
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@ -498,7 +517,7 @@ namespace pdr {
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}
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SASSERT(is_well_sorted(m, fml));
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IF_VERBOSE(0, verbose_stream() << "instantiate to\n:" << mk_pp(fml, m) << "\n";);
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IF_VERBOSE(0, verbose_stream() << "instantiate to:\n" << mk_pp(fml, m) << "\n";);
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return fml;
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}
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@ -386,13 +386,12 @@ namespace pdr {
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for_each_expr(*this, m_visited, tocollect[i]);
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}
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unsigned sz = m_model->get_num_constants();
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expr_ref e(m), eq(m);
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expr_ref e(m), eq(m), val(m);
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expr_ref_vector model(m);
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for (unsigned i = 0; i < sz; i++) {
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func_decl * d = m_model->get_constant(i);
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expr* val = m_model->get_const_interp(d);
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e = m.mk_const(d);
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e = m.mk_const(m_model->get_constant(i));
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if (m_visited.is_marked(e)) {
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val = eval(m_model, e);
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eq = m.mk_eq(e, val);
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model.push_back(eq);
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}
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@ -923,6 +922,20 @@ namespace pdr {
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return !has_x;
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}
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expr_ref model_evaluator::eval(model_ref& model, func_decl* d) {
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SASSERT(d->get_arity() == 0);
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expr_ref result(m);
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if (m_array.is_array(d->get_range())) {
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expr_ref e(m);
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e = m.mk_const(d);
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result = eval(model, e);
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}
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else {
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result = model->get_const_interp(d);
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}
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return result;
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}
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expr_ref model_evaluator::eval(model_ref& model, expr* e) {
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expr_ref result(m);
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m_model = model;
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@ -129,6 +129,8 @@ namespace pdr {
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void operator()(expr* e) {}
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expr_ref eval(model_ref& mdl, expr* e);
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expr_ref eval(model_ref& mdl, func_decl* d);
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};
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/**
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@ -33,6 +33,8 @@ Revision History:
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#include "dl_util.h"
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#include "th_rewriter.h"
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#include "dl_util.h"
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#include "for_each_expr.h"
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#include "expr_safe_replace.h"
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class is_variable_proc {
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@ -77,9 +79,10 @@ public:
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namespace eq {
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class der {
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ast_manager & m;
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arith_util a;
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is_variable_proc* m_is_variable;
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var_subst m_subst;
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expr_ref_buffer m_new_exprs;
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expr_ref_vector m_new_exprs;
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ptr_vector<expr> m_map;
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int_vector m_pos2var;
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@ -225,7 +228,81 @@ namespace eq {
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return false;
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}
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}
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bool solve_arith_core(app * lhs, expr * rhs, expr * eq, var* & var, expr_ref & def) {
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SASSERT(a.is_add(lhs));
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bool is_int = a.is_int(lhs);
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expr * a1;
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expr * v;
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rational a_val;
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unsigned num = lhs->get_num_args();
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unsigned i;
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for (i = 0; i < num; i++) {
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expr * arg = lhs->get_arg(i);
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if (is_variable(arg)) {
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a_val = rational(1);
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v = arg;
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break;
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}
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else if (a.is_mul(arg, a1, v) &&
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is_variable(v) &&
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a.is_numeral(a1, a_val) &&
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!a_val.is_zero() &&
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(!is_int || a_val.is_minus_one())) {
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break;
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}
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}
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if (i == num)
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return false;
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var = to_var(v);
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expr_ref inv_a(m);
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if (!a_val.is_one()) {
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inv_a = a.mk_numeral(rational(1)/a_val, is_int);
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rhs = a.mk_mul(inv_a, rhs);
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}
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ptr_buffer<expr> other_args;
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for (unsigned j = 0; j < num; j++) {
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if (i != j) {
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if (inv_a)
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other_args.push_back(a.mk_mul(inv_a, lhs->get_arg(j)));
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else
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other_args.push_back(lhs->get_arg(j));
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}
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}
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switch (other_args.size()) {
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case 0:
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def = rhs;
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break;
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case 1:
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def = a.mk_sub(rhs, other_args[0]);
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break;
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default:
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def = a.mk_sub(rhs, a.mk_add(other_args.size(), other_args.c_ptr()));
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break;
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}
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m_new_exprs.push_back(def);
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return true;
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}
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bool arith_solve(expr * lhs, expr * rhs, expr * eq, var* & var, expr_ref & t) {
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return
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(a.is_add(lhs) && solve_arith_core(to_app(lhs), rhs, eq, var, t)) ||
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(a.is_add(rhs) && solve_arith_core(to_app(rhs), lhs, eq, var, t));
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}
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bool trival_solve(expr* lhs, expr* rhs, expr* eq, var* & v, expr_ref& t) {
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if (!is_variable(lhs)) {
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std::swap(lhs, rhs);
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}
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if (!is_variable(lhs)) {
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return false;
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||||
}
|
||||
v = to_var(lhs);
|
||||
t = rhs;
|
||||
TRACE("der", tout << mk_pp(eq, m) << "\n";);
|
||||
return true;
|
||||
}
|
||||
|
||||
|
||||
/**
|
||||
|
|
@ -251,14 +328,13 @@ namespace eq {
|
|||
TRACE("der", tout << mk_pp(e, m) << "\n";);
|
||||
return true;
|
||||
}
|
||||
if (!is_variable(lhs))
|
||||
std::swap(lhs, rhs);
|
||||
if (!is_variable(lhs))
|
||||
return false;
|
||||
v = to_var(lhs);
|
||||
t = rhs;
|
||||
TRACE("der", tout << mk_pp(e, m) << "\n";);
|
||||
return true;
|
||||
if (trival_solve(lhs, rhs, e, v, t)) {
|
||||
return true;
|
||||
}
|
||||
if (arith_solve(lhs, rhs, e, v, t)) {
|
||||
return true;
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
// (ite cond (= VAR t) (= VAR t2)) case
|
||||
|
|
@ -494,7 +570,7 @@ namespace eq {
|
|||
}
|
||||
|
||||
public:
|
||||
der(ast_manager & m): m(m), m_is_variable(0), m_subst(m), m_new_exprs(m), m_subst_map(m), m_new_args(m), m_rewriter(m) {}
|
||||
der(ast_manager & m): m(m), a(m), m_is_variable(0), m_subst(m), m_new_exprs(m), m_subst_map(m), m_new_args(m), m_rewriter(m) {}
|
||||
|
||||
void set_is_variable_proc(is_variable_proc& proc) { m_is_variable = &proc;}
|
||||
|
||||
|
|
@ -538,20 +614,129 @@ namespace eq {
|
|||
namespace ar {
|
||||
class der {
|
||||
ast_manager& m;
|
||||
array_util a;
|
||||
is_variable_proc* m_is_variable;
|
||||
ptr_vector<expr> m_todo;
|
||||
expr_mark m_visited;
|
||||
|
||||
bool is_variable(expr * e) const {
|
||||
return (*m_is_variable)(e);
|
||||
}
|
||||
|
||||
void mark_all(expr* e) {
|
||||
for_each_expr(*this, m_visited, e);
|
||||
}
|
||||
|
||||
void mark_all(expr_ref_vector const& fmls, unsigned j) {
|
||||
for (unsigned i = 0; i < fmls.size(); ++i) {
|
||||
if (i != j) {
|
||||
mark_all(fmls[i]);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
Ex A. A[x] = t & Phi where x \not\in A, t.
|
||||
=>
|
||||
Ex A. Phi[store(A,x,t)]
|
||||
*/
|
||||
|
||||
bool solve_select(expr_ref_vector& conjs, unsigned i, expr* e1, expr* e2) {
|
||||
if (a.is_select(e1)) {
|
||||
app* a1 = to_app(e1);
|
||||
expr* A = a1->get_arg(0);
|
||||
if (!is_variable(A)) {
|
||||
return false;
|
||||
}
|
||||
m_visited.reset();
|
||||
for (unsigned j = 1; j < a1->get_num_args(); ++j) {
|
||||
mark_all(a1->get_arg(j));
|
||||
}
|
||||
mark_all(e2);
|
||||
if (m_visited.is_marked(A)) {
|
||||
return false;
|
||||
}
|
||||
ptr_vector<expr> args;
|
||||
args.push_back(A);
|
||||
args.append(a1->get_num_args()-1, a1->get_args()+1);
|
||||
args.push_back(e2);
|
||||
expr* B = a.mk_store(args.size(), args.c_ptr());
|
||||
expr_safe_replace rep(m);
|
||||
rep.insert(A, B);
|
||||
expr_ref tmp(m);
|
||||
for (unsigned j = 0; j < conjs.size(); ++j) {
|
||||
if (i == j) {
|
||||
conjs[j] = m.mk_true();
|
||||
}
|
||||
else {
|
||||
rep(conjs[j].get(), tmp);
|
||||
conjs[j] = tmp;
|
||||
}
|
||||
}
|
||||
return true;
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
bool solve_select(expr_ref_vector& conjs, unsigned i, expr* e) {
|
||||
expr* e1, *e2;
|
||||
return
|
||||
m.is_eq(e, e1, e2) &&
|
||||
(solve_select(conjs, i, e1, e2) ||
|
||||
solve_select(conjs, i, e2, e1));
|
||||
}
|
||||
|
||||
/**
|
||||
Ex x. A[x] != B[x] & Phi where x \not\in A, B, Phi
|
||||
=>
|
||||
A != B & Phi
|
||||
*/
|
||||
bool solve_neq_select(expr_ref_vector& conjs, unsigned i, expr* e) {
|
||||
expr* e1, *a1, *a2;
|
||||
if (m.is_not(e, e1) && m.is_eq(e1, a1, a2)) {
|
||||
if (a.is_select(a1) &&
|
||||
a.is_select(a2) &&
|
||||
to_app(a1)->get_num_args() == to_app(a2)->get_num_args()) {
|
||||
expr* e1 = to_app(a1)->get_arg(0);
|
||||
expr* e2 = to_app(a2)->get_arg(0);
|
||||
m_visited.reset();
|
||||
mark_all(conjs, i);
|
||||
mark_all(e1);
|
||||
mark_all(e2);
|
||||
for (unsigned j = 1; j < to_app(a1)->get_num_args(); ++j) {
|
||||
expr* x = to_app(a1)->get_arg(j);
|
||||
expr* y = to_app(a2)->get_arg(j);
|
||||
if (!is_variable(x)) {
|
||||
return false;
|
||||
}
|
||||
if (x != y) {
|
||||
return false;
|
||||
}
|
||||
if (m_visited.is_marked(x)) {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
conjs[i] = m.mk_not(m.mk_eq(e1, e2));
|
||||
return true;
|
||||
}
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
|
||||
public:
|
||||
|
||||
der(ast_manager& m): m(m), m_is_variable(0) {}
|
||||
der(ast_manager& m): m(m), a(m), m_is_variable(0) {}
|
||||
|
||||
void operator()(expr_ref_vector& fmls) {
|
||||
IF_VERBOSE(1, verbose_stream() << "Todo: eliminate arrays\n";);
|
||||
for (unsigned i = 0; i < fmls.size(); ++i) {
|
||||
solve_select(fmls, i, fmls[i].get());
|
||||
solve_neq_select(fmls, i, fmls[i].get());
|
||||
}
|
||||
}
|
||||
|
||||
void operator()(expr* e) {}
|
||||
|
||||
void set_is_variable_proc(is_variable_proc& proc) { m_is_variable = &proc;}
|
||||
|
||||
};
|
||||
|
|
@ -1904,6 +2089,22 @@ class qe_lite::impl {
|
|||
fm::fm m_fm;
|
||||
ar::der m_array_der;
|
||||
|
||||
bool has_unique_non_ground(expr_ref_vector const& fmls, unsigned& index) {
|
||||
index = fmls.size();
|
||||
if (index <= 1) {
|
||||
return false;
|
||||
}
|
||||
for (unsigned i = 0; i < fmls.size(); ++i) {
|
||||
if (!is_ground(fmls[i])) {
|
||||
if (index != fmls.size()) {
|
||||
return false;
|
||||
}
|
||||
index = i;
|
||||
}
|
||||
}
|
||||
return index < fmls.size();
|
||||
}
|
||||
|
||||
public:
|
||||
impl(ast_manager& m): m(m), m_der(m), m_fm(m, m_params), m_array_der(m) {}
|
||||
|
||||
|
|
@ -1970,9 +2171,21 @@ public:
|
|||
|
||||
void operator()(uint_set const& index_set, bool index_of_bound, expr_ref_vector& fmls) {
|
||||
datalog::flatten_and(fmls);
|
||||
unsigned index;
|
||||
if (has_unique_non_ground(fmls, index)) {
|
||||
expr_ref fml(m);
|
||||
fml = fmls[index].get();
|
||||
(*this)(index_set, index_of_bound, fml);
|
||||
fmls[index] = fml;
|
||||
return;
|
||||
}
|
||||
TRACE("qe_lite", for (unsigned i = 0; i < fmls.size(); ++i) {
|
||||
tout << mk_pp(fmls[i].get(), m) << "\n";
|
||||
});
|
||||
IF_VERBOSE(3, for (unsigned i = 0; i < fmls.size(); ++i) {
|
||||
verbose_stream() << mk_pp(fmls[i].get(), m) << "\n";
|
||||
});
|
||||
is_variable_test is_var(index_set, index_of_bound);
|
||||
TRACE("qe_lite", for (unsigned i = 0; i < fmls.size(); ++i) tout << mk_pp(fmls[i].get(), m) << "\n";);
|
||||
IF_VERBOSE(3, for (unsigned i = 0; i < fmls.size(); ++i) verbose_stream() << mk_pp(fmls[i].get(), m) << "\n";);
|
||||
m_der.set_is_variable_proc(is_var);
|
||||
m_fm.set_is_variable_proc(is_var);
|
||||
m_array_der.set_is_variable_proc(is_var);
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue