mirror of
https://github.com/Z3Prover/z3
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1862 lines
65 KiB
C++
1862 lines
65 KiB
C++
/*++
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Copyright (c) 2011 Microsoft Corporation
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Module Name:
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pdr_context.cpp
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Abstract:
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PDR predicate transformers and search context.
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Author:
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Nikolaj Bjorner (nbjorner) 2011-11-20.
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Revision History:
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Based on pdr_dl.cpp by
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Krystof Hoder (t-khoder) 2011-9-19.
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Notes:
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--*/
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#include <sstream>
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#include "dl_util.h"
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#include "rewriter.h"
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#include "rewriter_def.h"
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#include "var_subst.h"
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#include "util.h"
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#include "pdr_prop_solver.h"
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#include "pdr_context.h"
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#include "pdr_generalizers.h"
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#include "datatype_decl_plugin.h"
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#include "for_each_expr.h"
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#include "model_v2_pp.h"
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#include "dl_rule_set.h"
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#include "unit_subsumption_tactic.h"
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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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static const unsigned infty_level = UINT_MAX;
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static bool is_infty_level(unsigned lvl) { return lvl == infty_level; }
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static unsigned next_level(unsigned lvl) { return is_infty_level(lvl)?lvl:(lvl+1); }
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// ----------------
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// pred_tansformer
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pred_transformer::pred_transformer(context& ctx, manager& pm, func_decl* head):
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ctx(ctx), pm(pm), m(pm.get_manager()), m_head(head, m),
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m_sig(m), m_solver(pm, head->get_name()),
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m_invariants(m), m_transition(m), m_initial_state(m),
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m_reachable(pm, pm.get_params()) {}
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pred_transformer::~pred_transformer() {
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qinst_map::iterator it = m_rule2qinst.begin(), end = m_rule2qinst.end();
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for (; it != end; ++it) {
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dealloc(it->m_value);
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}
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rule2inst::iterator it2 = m_rule2inst.begin(), end2 = m_rule2inst.end();
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for (; it2 != end2; ++it2) {
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dealloc(it2->m_value);
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}
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rule2expr::iterator it3 = m_rule2transition.begin(), end3 = m_rule2transition.end();
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for (; it3 != end3; ++it3) {
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m.dec_ref(it3->m_value);
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}
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}
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std::ostream& pred_transformer::display(std::ostream& out) const {
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if (!rules().empty()) out << "rules\n";
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for (unsigned i = 0; i < rules().size(); ++i) {
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rules()[i]->display_smt2(m, out) << "\n";
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}
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out << "transition\n" << mk_pp(transition(), m) << "\n";
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return out;
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}
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void pred_transformer::collect_statistics(statistics& st) const {
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m_solver.collect_statistics(st);
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m_reachable.collect_statistics(st);
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st.update("PDR num propagations", m_stats.m_num_propagations);
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unsigned np = m_invariants.size();
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for (unsigned i = 0; i < m_levels.size(); ++i) {
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np += m_levels[i].size();
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}
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st.update("PDR num properties", np);
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}
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void pred_transformer::init_sig() {
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if (m_sig.empty()) {
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for (unsigned i = 0; i < m_head->get_arity(); ++i) {
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sort * arg_sort = m_head->get_domain(i);
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std::stringstream name_stm;
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name_stm << m_head->get_name() << '_' << i;
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func_decl_ref stm(m);
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stm = m.mk_func_decl(symbol(name_stm.str().c_str()), 0, (sort*const*)0, arg_sort);
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m_sig.push_back(pm.get_o_pred(stm, 0));
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}
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}
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}
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void pred_transformer::ensure_level(unsigned level) {
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if (is_infty_level(level)) {
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return;
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}
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while (m_levels.size() <= level) {
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m_solver.add_level();
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m_levels.push_back(expr_ref_vector(m));
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}
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}
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bool pred_transformer::is_reachable(expr* state) {
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return m_reachable.is_reachable(state);
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}
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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_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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if (it->m_value) it->m_value->display_smt2(m, tout) << "\n";
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}
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);
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it = m_tag2rule.begin();
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if (m_tag2rule.size() == 1) {
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return *it->m_value;
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}
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expr_ref vl(m);
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for (; it != end; ++it) {
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expr* pred = it->m_key;
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TRACE("pdr", tout << mk_pp(pred, m) << "\n";);
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if (model.eval(to_app(pred)->get_decl(), vl) && m.is_true(vl)) {
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return *it->m_value;
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}
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}
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UNREACHABLE();
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return *((datalog::rule*)0);
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}
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void pred_transformer::find_predecessors(datalog::rule const& r, ptr_vector<func_decl>& preds) const {
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preds.reset();
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unsigned tail_sz = r.get_uninterpreted_tail_size();
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for (unsigned ti = 0; ti < tail_sz; ti++) {
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preds.push_back(r.get_tail(ti)->get_decl());
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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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for (unsigned i = 0; i < literals.size(); ) {
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expr* l = literals[i].get();
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m.is_not(l, l);
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if (m_tag2rule.contains(l)) {
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literals[i] = literals.back();
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literals.pop_back();
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}
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else {
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++i;
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}
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}
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}
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void pred_transformer::simplify_formulas(tactic& tac, expr_ref_vector& v) {
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goal_ref g(alloc(goal, m, false, false, false));
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for (unsigned j = 0; j < v.size(); ++j) g->assert_expr(v[j].get());
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model_converter_ref mc;
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proof_converter_ref pc;
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expr_dependency_ref core(m);
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goal_ref_buffer result;
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tac(g, result, mc, pc, core);
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SASSERT(result.size() == 1);
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goal* r = result[0];
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v.reset();
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for (unsigned j = 0; j < r->size(); ++j) v.push_back(r->form(j));
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}
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void pred_transformer::simplify_formulas() {
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tactic_ref us = mk_unit_subsumption_tactic(m);
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simplify_formulas(*us, m_invariants);
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for (unsigned i = 0; i < m_levels.size(); ++i) {
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expr_ref_vector& v = m_levels[i];
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simplify_formulas(*us, m_levels[i]);
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}
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}
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expr_ref pred_transformer::get_formulas(unsigned level, bool add_axioms) {
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expr_ref_vector res(m);
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if (add_axioms) {
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res.push_back(pm.get_background());
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res.push_back((level == 0)?initial_state():transition());
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}
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res.append(m_invariants);
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for (unsigned i = level; i < m_levels.size(); ++i) {
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res.append(m_levels[i]);
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}
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return pm.mk_and(res);
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}
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expr_ref pred_transformer::get_propagation_formula(decl2rel const& pts, unsigned level) {
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expr_ref result(m), tmp1(m), tmp2(m);
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expr_ref_vector conj(m);
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if (level == 0) {
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conj.push_back(initial_state());
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}
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else {
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conj.push_back(transition());
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}
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conj.push_back(get_formulas(level, true));
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obj_map<expr, datalog::rule const*>::iterator it = m_tag2rule.begin(), end = m_tag2rule.end();
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for (; level > 0 && it != end; ++it) {
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expr* tag = it->m_key;
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datalog::rule const* r = it->m_value;
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if (!r) continue;
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find_predecessors(*r, m_predicates);
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for (unsigned i = 0; i < m_predicates.size(); ++i) {
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func_decl* d = m_predicates[i];
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pred_transformer & pt = *pts.find(d);
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tmp1 = pt.get_formulas(level-1, false);
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TRACE("pdr", tout << mk_pp(tmp1, m) << "\n";);
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pm.formula_n2o(tmp1, tmp2, i, false);
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conj.push_back(m.mk_implies(tag, tmp2));
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}
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}
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return pm.mk_and(conj);
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}
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bool pred_transformer::propagate_to_next_level(unsigned src_level) {
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unsigned tgt_level = next_level(src_level);
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ensure_level(next_level(tgt_level));
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expr_ref_vector& src = m_levels[src_level];
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CTRACE("pdr", !src.empty(),
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tout << "propagating " << src_level << " to " << tgt_level;
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tout << " for relation " << head()->get_name() << "\n";);
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for (unsigned i = 0; i < src.size(); ) {
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expr * curr = src[i].get();
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unsigned stored_lvl;
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VERIFY(m_prop2level.find(curr, stored_lvl));
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SASSERT(stored_lvl >= src_level);
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bool assumes_level;
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if (stored_lvl > src_level) {
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TRACE("pdr", tout << "at level: "<< stored_lvl << " " << mk_pp(curr, m) << "\n";);
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src[i] = src.back();
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src.pop_back();
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}
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else if (is_invariant(tgt_level, curr, false, assumes_level)) {
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add_property(curr, tgt_level); // assumes_level?tgt_level:infty_level
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TRACE("pdr", tout << "is invariant: "<< tgt_level << " " << mk_pp(curr, m) << "\n";);
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src[i] = src.back();
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src.pop_back();
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++m_stats.m_num_propagations;
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}
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else {
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TRACE("pdr", tout << "not propagated: " << mk_pp(curr, m) << "\n";);
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++i;
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}
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}
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IF_VERBOSE(2, verbose_stream() << "propagate: ";
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if (is_infty_level(src_level)) {
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verbose_stream() << "infty";
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}
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else verbose_stream() << src_level;
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for (unsigned i = 0; i < src.size(); ++i) {
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verbose_stream() << mk_pp(src[i].get(), m) << "\n";
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});
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return src.empty();
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}
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bool pred_transformer::add_property1(expr * lemma, unsigned lvl) {
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if (is_infty_level(lvl)) {
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if (m.is_false(lemma)) {
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return false;
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}
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if (!m_invariants.contains(lemma)) {
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TRACE("pdr", tout << "property1: " << head()->get_name() << " " << mk_pp(lemma, m) << "\n";);
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m_invariants.push_back(lemma);
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m_solver.add_formula(lemma);
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return true;
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}
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else {
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TRACE("pdr", tout << "already contained: " << head()->get_name() << " " << mk_pp(lemma, m) << "\n";);
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return false;
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}
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}
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ensure_level(lvl);
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unsigned old_level;
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if (!m_prop2level.find(lemma, old_level) || old_level < lvl) {
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TRACE("pdr", tout << "property1: " << lvl << " " << head()->get_name() << " " << mk_pp(lemma, m) << "\n";);
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m_levels[lvl].push_back(lemma);
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m_prop2level.insert(lemma, lvl);
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m_solver.add_level_formula(lemma, lvl);
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return true;
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}
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else {
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TRACE("pdr", tout << "old-level: " << old_level << " " << head()->get_name() << " " << mk_pp(lemma, m) << "\n";);
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return false;
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}
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}
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void pred_transformer::add_child_property(pred_transformer& child, expr* lemma, unsigned lvl) {
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ensure_level(lvl);
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expr_ref_vector fmls(m);
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mk_assumptions(child.head(), lemma, fmls);
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for (unsigned i = 0; i < fmls.size(); ++i) {
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TRACE("pdr", tout << "child property: " << mk_pp(fmls[i].get(), m) << "\n";);
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if (is_infty_level(lvl)) {
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m_solver.add_formula(fmls[i].get());
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}
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else {
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m_solver.add_level_formula(fmls[i].get(), lvl);
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}
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}
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}
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void pred_transformer::add_property(expr* lemma, unsigned lvl) {
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expr_ref_vector lemmas(m);
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datalog::flatten_and(lemma, lemmas);
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for (unsigned i = 0; i < lemmas.size(); ++i) {
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expr* lemma_i = lemmas[i].get();
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if (add_property1(lemma_i, lvl)) {
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IF_VERBOSE(2, verbose_stream() << lvl << " " << mk_pp(lemma_i, m) << "\n";);
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for (unsigned j = 0; j < m_use.size(); ++j) {
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m_use[j]->add_child_property(*this, lemma_i, next_level(lvl));
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}
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}
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}
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}
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expr_ref pred_transformer::get_cover_delta(int level) {
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expr_ref result(m.mk_true(), m), v(m), c(m);
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if (level == -1) {
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result = pm.mk_and(m_invariants);
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}
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else if ((unsigned)level < m_levels.size()) {
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result = pm.mk_and(m_levels[level]);
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}
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// replace local constants by bound variables.
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expr_substitution sub(m);
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for (unsigned i = 0; i < m_sig.size(); ++i) {
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c = m.mk_const(pm.o2n(sig(i), 0));
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v = m.mk_var(i, sig(i)->get_range());
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sub.insert(c, v);
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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)(result);
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return result;
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}
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void pred_transformer::add_cover(unsigned level, expr* property) {
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// replace bound variables by local constants.
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expr_ref result(property, m), v(m), c(m);
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expr_substitution sub(m);
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for (unsigned i = 0; i < m_sig.size(); ++i) {
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c = m.mk_const(pm.o2n(sig(i), 0));
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v = m.mk_var(i, sig(i)->get_range());
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sub.insert(v, c);
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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)(result);
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TRACE("pdr", tout << "cover:\n" << mk_pp(result, m) << "\n";);
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// add the property.
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add_property(result, level);
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}
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lbool pred_transformer::is_reachable(model_node& n, expr_ref_vector* core) {
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TRACE("pdr",
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tout << "is-reachable: " << head()->get_name() << " level: " << n.level() << "\n";
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tout << mk_pp(n.state(), m) << "\n";);
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ensure_level(n.level());
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model_ref model;
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prop_solver::scoped_level _sl(m_solver, n.level());
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m_solver.set_core(core);
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m_solver.set_model(&model);
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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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n.set_model(model);
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}
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return is_sat;
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}
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bool pred_transformer::is_invariant(unsigned level, expr* states, bool inductive, bool& assumes_level, expr_ref_vector* core) {
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expr_ref_vector conj(m);
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expr_ref tmp(m);
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conj.push_back(m.mk_not(states));
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if (inductive) {
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mk_assumptions(head(), states, conj);
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}
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tmp = pm.mk_and(conj);
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prop_solver::scoped_level _sl(m_solver, level);
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m_solver.set_core(core);
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lbool r = m_solver.check_conjunction_as_assumptions(tmp);
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if (r == l_false) {
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assumes_level = m_solver.assumes_level();
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}
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return r == l_false;
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}
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bool pred_transformer::check_inductive(unsigned level, expr_ref_vector& lits, bool& assumes_level) {
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manager& pm = get_pdr_manager();
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expr_ref_vector conj(m), core(m);
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expr_ref fml(m), states(m);
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states = m.mk_not(pm.mk_and(lits));
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mk_assumptions(head(), states, conj);
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fml = pm.mk_and(conj);
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prop_solver::scoped_level _sl(m_solver, level);
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m_solver.set_core(&core);
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m_solver.set_subset_based_core(true);
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lbool res = m_solver.check_assumptions_and_formula(lits, fml);
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if (res == l_false) {
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lits.reset();
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lits.append(core);
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assumes_level = m_solver.assumes_level();
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}
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return res == l_false;
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}
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void pred_transformer::mk_assumptions(func_decl* head, expr* fml, expr_ref_vector& result) {
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expr_ref tmp1(m), tmp2(m);
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obj_map<expr, datalog::rule const*>::iterator it = m_tag2rule.begin(), end = m_tag2rule.end();
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for (; it != end; ++it) {
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expr* pred = it->m_key;
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datalog::rule const* r = it->m_value;
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if (!r) continue;
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find_predecessors(*r, m_predicates);
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|
for (unsigned i = 0; i < m_predicates.size(); i++) {
|
|
func_decl* d = m_predicates[i];
|
|
if (d == head) {
|
|
tmp1 = m.mk_implies(pred, fml);
|
|
pm.formula_n2o(tmp1, tmp2, i);
|
|
result.push_back(tmp2);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void pred_transformer::initialize(decl2rel const& pts) {
|
|
m_initial_state = m.mk_false();
|
|
m_transition = m.mk_true();
|
|
init_rules(pts, m_initial_state, m_transition);
|
|
th_rewriter rw(m);
|
|
rw(m_transition);
|
|
rw(m_initial_state);
|
|
if (ctx.is_dl()) {
|
|
hoist_non_bool_if(m_transition);
|
|
hoist_non_bool_if(m_initial_state);
|
|
}
|
|
m_solver.add_formula(m_transition);
|
|
m_solver.add_level_formula(m_initial_state, 0);
|
|
TRACE("pdr",
|
|
tout << "Initial state: " << mk_pp(m_initial_state, m) << "\n";
|
|
tout << "Transition: " << mk_pp(m_transition, m) << "\n";);
|
|
SASSERT(is_app(m_initial_state));
|
|
m_reachable.add_init(to_app(m_initial_state));
|
|
}
|
|
|
|
void pred_transformer::init_rules(decl2rel const& pts, expr_ref& init, expr_ref& transition) {
|
|
expr_ref_vector transitions(m);
|
|
ptr_vector<datalog::rule const> tr_rules;
|
|
datalog::rule const* rule;
|
|
expr_ref_vector disj(m);
|
|
app_ref pred(m);
|
|
for (unsigned i = 0; i < rules().size(); ++i) {
|
|
init_rule(pts, *rules()[i], init, tr_rules, transitions);
|
|
}
|
|
switch(transitions.size()) {
|
|
case 0:
|
|
transition = m.mk_false();
|
|
break;
|
|
case 1:
|
|
// create a dummy tag.
|
|
pred = m.mk_fresh_const(head()->get_name().str().c_str(), m.mk_bool_sort());
|
|
rule = tr_rules[0];
|
|
m_tag2rule.insert(pred, rule);
|
|
m_rule2tag.insert(rule, pred.get());
|
|
transitions.push_back(pred);
|
|
transition = pm.mk_and(transitions);
|
|
break;
|
|
default:
|
|
for (unsigned i = 0; i < transitions.size(); ++i) {
|
|
pred = m.mk_fresh_const(head()->get_name().str().c_str(), m.mk_bool_sort());
|
|
rule = tr_rules[i];
|
|
m_tag2rule.insert(pred, rule);
|
|
m_rule2tag.insert(rule, pred);
|
|
disj.push_back(pred);
|
|
transitions[i] = m.mk_implies(pred, transitions[i].get());
|
|
}
|
|
transitions.push_back(m.mk_or(disj.size(), disj.c_ptr()));
|
|
transition = pm.mk_and(transitions);
|
|
break;
|
|
}
|
|
}
|
|
|
|
void pred_transformer::init_rule(
|
|
decl2rel const& pts,
|
|
datalog::rule const& rule,
|
|
expr_ref& init,
|
|
ptr_vector<datalog::rule const>& rules,
|
|
expr_ref_vector& transitions)
|
|
{
|
|
// Predicates that are variable representatives. Other predicates at
|
|
// positions the variables occur are made equivalent with these.
|
|
expr_ref_vector conj(m);
|
|
app_ref_vector& var_reprs = *(alloc(app_ref_vector, m));
|
|
qinst* qi = 0;
|
|
ptr_vector<app> aux_vars;
|
|
|
|
unsigned ut_size = rule.get_uninterpreted_tail_size();
|
|
unsigned t_size = rule.get_tail_size();
|
|
SASSERT(ut_size <= t_size);
|
|
init_atom(pts, rule.get_head(), var_reprs, conj, UINT_MAX);
|
|
for (unsigned i = 0; i < ut_size; ++i) {
|
|
if (rule.is_neg_tail(i)) {
|
|
throw default_exception("PDR does not support negated predicates in rule tails");
|
|
}
|
|
init_atom(pts, rule.get_tail(i), var_reprs, conj, i);
|
|
}
|
|
for (unsigned i = ut_size; i < t_size; ++i) {
|
|
ground_free_vars(rule.get_tail(i), var_reprs, aux_vars);
|
|
}
|
|
SASSERT(check_filled(var_reprs));
|
|
expr_ref_vector tail(m);
|
|
for (unsigned i = ut_size; i < t_size; ++i) {
|
|
tail.push_back(rule.get_tail(i));
|
|
}
|
|
datalog::flatten_and(tail);
|
|
for (unsigned i = 0; i < tail.size(); ++i) {
|
|
expr_ref tmp(m);
|
|
var_subst(m, false)(tail[i].get(), var_reprs.size(), (expr*const*)var_reprs.c_ptr(), tmp);
|
|
quantifier* q;
|
|
if (datalog::rule_manager::is_forall(m, tmp, q)) {
|
|
|
|
if (!qi) {
|
|
qi = alloc(qinst, m);
|
|
}
|
|
//
|
|
// The contract is to instantiate q with
|
|
// sufficient witnesses to validate body.
|
|
//
|
|
qi->quantifiers.push_back(q);
|
|
tmp = m.mk_true();
|
|
}
|
|
conj.push_back(tmp);
|
|
TRACE("pdr", tout << mk_pp(tail[i].get(), m) << "\n" << mk_pp(tmp, m) << "\n";);
|
|
SASSERT(is_ground(tmp));
|
|
}
|
|
expr_ref fml = pm.mk_and(conj);
|
|
th_rewriter rw(m);
|
|
rw(fml);
|
|
TRACE("pdr", tout << mk_pp(fml, m) << "\n";);
|
|
SASSERT(is_ground(fml));
|
|
if (m.is_false(fml)) {
|
|
dealloc(qi);
|
|
qi = 0;
|
|
// no-op.
|
|
}
|
|
else {
|
|
if (ut_size == 0 && !qi) {
|
|
init = m.mk_or(init, fml);
|
|
}
|
|
transitions.push_back(fml);
|
|
m.inc_ref(fml);
|
|
m_rule2transition.insert(&rule, fml.get());
|
|
rules.push_back(&rule);
|
|
}
|
|
if (qi) {
|
|
m_rule2qinst.insert(&rule, qi);
|
|
}
|
|
m_rule2inst.insert(&rule,&var_reprs);
|
|
m_rule2vars.insert(&rule, aux_vars);
|
|
}
|
|
|
|
bool pred_transformer::check_filled(app_ref_vector const& v) const {
|
|
for (unsigned i = 0; i < v.size(); ++i) {
|
|
if (!v[i]) return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
// create constants for free variables in tail.
|
|
void pred_transformer::ground_free_vars(expr* e, app_ref_vector& vars, ptr_vector<app>& aux_vars) {
|
|
ptr_vector<sort> sorts;
|
|
get_free_vars(e, sorts);
|
|
while (vars.size() < sorts.size()) {
|
|
vars.push_back(0);
|
|
}
|
|
for (unsigned i = 0; i < sorts.size(); ++i) {
|
|
if (sorts[i] && !vars[i].get()) {
|
|
vars[i] = m.mk_fresh_const("aux", sorts[i]);
|
|
aux_vars.push_back(vars[i].get());
|
|
}
|
|
}
|
|
}
|
|
|
|
// create names for variables used in relations.
|
|
void pred_transformer::init_atom(
|
|
decl2rel const& pts,
|
|
app * atom,
|
|
app_ref_vector& var_reprs,
|
|
expr_ref_vector& conj,
|
|
unsigned tail_idx
|
|
)
|
|
{
|
|
unsigned arity = atom->get_num_args();
|
|
func_decl* head = atom->get_decl();
|
|
pred_transformer& pt = *pts.find(head);
|
|
for (unsigned i = 0; i < arity; i++) {
|
|
app_ref rep(m);
|
|
|
|
if (tail_idx == UINT_MAX) {
|
|
rep = m.mk_const(pm.o2n(pt.sig(i), 0));
|
|
}
|
|
else {
|
|
rep = m.mk_const(pm.o2o(pt.sig(i), 0, tail_idx));
|
|
}
|
|
|
|
expr * arg = atom->get_arg(i);
|
|
if (is_var(arg)) {
|
|
var * v = to_var(arg);
|
|
unsigned var_idx = v->get_idx();
|
|
if (var_idx >= var_reprs.size()) {
|
|
var_reprs.resize(var_idx+1);
|
|
}
|
|
expr * repr = var_reprs[var_idx].get();
|
|
if (repr) {
|
|
conj.push_back(m.mk_eq(rep, repr));
|
|
}
|
|
else {
|
|
var_reprs[var_idx] = rep;
|
|
}
|
|
}
|
|
else {
|
|
SASSERT(is_app(arg));
|
|
conj.push_back(m.mk_eq(rep, arg));
|
|
}
|
|
}
|
|
}
|
|
|
|
void pred_transformer::add_premises(decl2rel const& pts, unsigned lvl, expr_ref_vector& r) {
|
|
r.push_back(pm.get_background());
|
|
r.push_back((lvl == 0)?initial_state():transition());
|
|
for (unsigned i = 0; i < rules().size(); ++i) {
|
|
add_premises(pts, lvl, *rules()[i], r);
|
|
}
|
|
}
|
|
|
|
void pred_transformer::close(expr* e) {
|
|
m_reachable.add_reachable(e);
|
|
}
|
|
|
|
void pred_transformer::add_premises(decl2rel const& pts, unsigned lvl, datalog::rule& rule, expr_ref_vector& r) {
|
|
find_predecessors(rule, m_predicates);
|
|
for (unsigned i = 0; i < m_predicates.size(); ++i) {
|
|
expr_ref tmp(m);
|
|
func_decl* head = m_predicates[i];
|
|
pred_transformer& pt = *pts.find(head);
|
|
expr_ref inv = pt.get_formulas(lvl, false);
|
|
if (!m.is_true(inv)) {
|
|
pm.formula_n2o(inv, tmp, i, true);
|
|
r.push_back(tmp);
|
|
}
|
|
}
|
|
}
|
|
|
|
void pred_transformer::inherit_properties(pred_transformer& other) {
|
|
SASSERT(m_head == other.m_head);
|
|
obj_map<expr, unsigned>::iterator it = other.m_prop2level.begin();
|
|
obj_map<expr, unsigned>::iterator end = other.m_prop2level.end();
|
|
|
|
for (; it != end; ++it) {
|
|
add_property(it->m_key, it->m_value);
|
|
}
|
|
for (unsigned i = 0; i < other.m_invariants.size(); ++i) {
|
|
expr* e = other.m_invariants[i].get();
|
|
m_invariants.push_back(e);
|
|
m_solver.add_formula(e);
|
|
}
|
|
}
|
|
|
|
// ----------------
|
|
// model_node
|
|
|
|
void model_node::set_closed() {
|
|
pt().close(state());
|
|
m_closed = true;
|
|
}
|
|
|
|
expr_ref model_node::get_trace() const {
|
|
pred_transformer& p = pt();
|
|
ast_manager& m = p.get_manager();
|
|
manager& pm = p.get_pdr_manager();
|
|
TRACE("pdr", model_v2_pp(tout, model()););
|
|
func_decl* f = p.head();
|
|
unsigned arity = f->get_arity();
|
|
expr_ref_vector args(m);
|
|
func_decl_ref v(m);
|
|
for (unsigned i = 0; i < arity; ++i) {
|
|
v = pm.o2n(p.sig(i),0);
|
|
expr* e = model().get_const_interp(v);
|
|
if (e) {
|
|
args.push_back(e);
|
|
}
|
|
else {
|
|
args.push_back(m.mk_const(v));
|
|
}
|
|
}
|
|
return expr_ref(m.mk_app(f, args.size(), args.c_ptr()), m);
|
|
}
|
|
|
|
|
|
void model_node::mk_instantiate(datalog::rule_ref& r0, datalog::rule_ref& r1, expr_ref_vector& binding) {
|
|
ast_manager& m = pt().get_manager();
|
|
expr_ref_vector conjs(m);
|
|
obj_map<expr,expr*> model;
|
|
datalog::flatten_and(state(), conjs);
|
|
for (unsigned i = 0; i < conjs.size(); ++i) {
|
|
expr* e = conjs[i].get(), *e1, *e2;
|
|
if (m.is_eq(e, e1, e2) || m.is_iff(e, e1, e2)) {
|
|
if (m.is_value(e2)) {
|
|
model.insert(e1, e2);
|
|
}
|
|
else if (m.is_value(e1)) {
|
|
model.insert(e2, e1);
|
|
}
|
|
}
|
|
else if (m.is_not(e, e1)) {
|
|
model.insert(e1, m.mk_false());
|
|
}
|
|
else {
|
|
model.insert(e, m.mk_true());
|
|
}
|
|
}
|
|
r0 = const_cast<datalog::rule*>(&pt().find_rule(*m_model.get()));
|
|
app_ref_vector& inst = pt().get_inst(r0);
|
|
TRACE("pdr", tout << mk_pp(state(), m) << "\n";);
|
|
for (unsigned i = 0; i < inst.size(); ++i) {
|
|
expr* v;
|
|
if (model.find(inst[i].get(), v)) {
|
|
binding.push_back(v);
|
|
}
|
|
else {
|
|
binding.push_back(m.mk_var(i, m.get_sort(inst[i].get())));
|
|
}
|
|
}
|
|
r1 = r0;
|
|
if (!inst.empty()) {
|
|
r1.get_manager().substitute(r1, binding.size(), binding.c_ptr());
|
|
}
|
|
}
|
|
|
|
|
|
|
|
std::ostream& model_node::display(std::ostream& out, unsigned indent) {
|
|
for (unsigned i = 0; i < indent; ++i) out << " ";
|
|
out << m_level << " " << m_pt.head()->get_name() << " " << (m_closed?"closed":"open") << "\n";
|
|
for (unsigned i = 0; i < indent; ++i) out << " ";
|
|
out << " " << mk_pp(m_state, m_state.get_manager(), indent) << "\n";
|
|
for (unsigned i = 0; i < children().size(); ++i) {
|
|
children()[i]->display(out, indent + 1);
|
|
}
|
|
return out;
|
|
}
|
|
|
|
unsigned model_node::index() const {
|
|
model_node* p = parent();
|
|
if (!p) return 0;
|
|
for (unsigned i = 0; i < p->children().size(); ++i) {
|
|
if (this == p->children()[i]) return i;
|
|
}
|
|
UNREACHABLE();
|
|
return 0;
|
|
}
|
|
|
|
|
|
// ----------------
|
|
// model_search
|
|
|
|
model_node* model_search::next() {
|
|
if (m_leaves.empty()) {
|
|
return 0;
|
|
}
|
|
model_node* result = m_leaves.back();
|
|
m_leaves.pop_back();
|
|
return result;
|
|
}
|
|
|
|
bool model_search::is_repeated(model_node& n) const {
|
|
model_node* p = n.parent();
|
|
while (p) {
|
|
if (p->state() == n.state()) {
|
|
return true;
|
|
}
|
|
p = p->parent();
|
|
}
|
|
return false;
|
|
}
|
|
|
|
void model_search::add_leaf(model_node& n) {
|
|
unsigned& count = cache(n).insert_if_not_there2(n.state(), 0)->get_data().m_value;
|
|
++count;
|
|
if (count == 1 || is_repeated(n)) {
|
|
set_leaf(n);
|
|
}
|
|
else {
|
|
n.set_pre_closed();
|
|
}
|
|
}
|
|
|
|
void model_search::set_leaf(model_node& n) {
|
|
erase_children(n);
|
|
SASSERT(n.is_open());
|
|
if (m_bfs) {
|
|
m_leaves.push_front(&n);
|
|
}
|
|
else {
|
|
m_leaves.push_back(&n);
|
|
}
|
|
}
|
|
|
|
void model_search::set_root(model_node* root) {
|
|
reset();
|
|
m_root = root;
|
|
SASSERT(cache(*root).empty());
|
|
cache(*root).insert(root->state(), 1);
|
|
set_leaf(*root);
|
|
}
|
|
|
|
obj_map<expr, unsigned>& model_search::cache(model_node const& n) {
|
|
unsigned l = n.orig_level();
|
|
if (l >= m_cache.size()) {
|
|
m_cache.resize(l + 1);
|
|
}
|
|
return m_cache[l];
|
|
}
|
|
|
|
void model_search::erase_children(model_node& n) {
|
|
ptr_vector<model_node> todo, nodes;
|
|
todo.append(n.children());
|
|
erase_leaf(n);
|
|
n.reset();
|
|
while (!todo.empty()) {
|
|
model_node* m = todo.back();
|
|
todo.pop_back();
|
|
nodes.push_back(m);
|
|
todo.append(m->children());
|
|
erase_leaf(*m);
|
|
remove_node(*m);
|
|
}
|
|
std::for_each(nodes.begin(), nodes.end(), delete_proc<model_node>());
|
|
}
|
|
|
|
void model_search::remove_node(model_node& n) {
|
|
if (0 == --cache(n).find(n.state())) {
|
|
cache(n).remove(n.state());
|
|
}
|
|
}
|
|
|
|
void model_search::erase_leaf(model_node& n) {
|
|
if (n.children().empty() && n.is_open()) {
|
|
std::deque<model_node*>::iterator
|
|
it = m_leaves.begin(),
|
|
end = m_leaves.end();
|
|
for (; it != end; ++it) {
|
|
if (*it == &n) {
|
|
m_leaves.erase(it);
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
std::ostream& model_search::display(std::ostream& out) const {
|
|
if (m_root) {
|
|
m_root->display(out, 0);
|
|
}
|
|
out << "goals\n";
|
|
std::deque<model_node*>::const_iterator
|
|
it = m_leaves.begin(),
|
|
end = m_leaves.end();
|
|
for (; it != end; ++it) {
|
|
(*it)->display(out, 1);
|
|
}
|
|
return out;
|
|
}
|
|
|
|
expr_ref model_search::get_trace() const {
|
|
pred_transformer& pt = get_root().pt();
|
|
ast_manager& m = pt.get_manager();
|
|
manager& pm = pt.get_pdr_manager();
|
|
expr_ref result(m.mk_true(),m);
|
|
expr_ref_vector rules(m);
|
|
ptr_vector<model_node> nodes;
|
|
nodes.push_back(m_root);
|
|
while (!nodes.empty()) {
|
|
model_node* current = nodes.back();
|
|
nodes.pop_back();
|
|
rules.push_back(current->get_trace());
|
|
nodes.append(current->children());
|
|
}
|
|
return pm.mk_and(rules);
|
|
}
|
|
|
|
proof_ref model_search::get_proof_trace(context const& ctx) const {
|
|
pred_transformer& pt = get_root().pt();
|
|
ast_manager& m = pt.get_manager();
|
|
datalog::context& dctx = ctx.get_context();
|
|
datalog::rule_manager& rm = dctx.get_rule_manager();
|
|
datalog::rule_unifier unifier(dctx);
|
|
datalog::dl_decl_util util(m);
|
|
datalog::rule_ref r0(rm), r1(rm);
|
|
obj_map<expr, proof*> cache;
|
|
obj_map<expr, datalog::rule*> rules;
|
|
ptr_vector<model_node> todo;
|
|
proof_ref_vector trail(m);
|
|
datalog::rule_ref_vector rules_trail(rm);
|
|
proof* pr = 0;
|
|
todo.push_back(m_root);
|
|
while (!todo.empty()) {
|
|
model_node* n = todo.back();
|
|
if (cache.find(n->state(), pr)) {
|
|
todo.pop_back();
|
|
continue;
|
|
}
|
|
ptr_vector<proof> pfs;
|
|
ptr_vector<datalog::rule> rls;
|
|
ptr_vector<model_node> const& chs = n->children();
|
|
pfs.push_back(0);
|
|
rls.push_back(0);
|
|
for (unsigned i = 0; i < chs.size(); ++i) {
|
|
if (cache.find(chs[i]->state(), pr)) {
|
|
pfs.push_back(pr);
|
|
rls.push_back(rules.find(chs[i]->state()));
|
|
}
|
|
else {
|
|
todo.push_back(chs[i]);
|
|
}
|
|
}
|
|
if (pfs.size() != 1 + chs.size()) {
|
|
continue;
|
|
}
|
|
proof_ref rl(m);
|
|
expr_ref fml0(m);
|
|
expr_ref_vector binding(m);
|
|
n->mk_instantiate(r0, r1, binding);
|
|
r0->to_formula(fml0);
|
|
proof_ref p1(m), p2(m);
|
|
p1 = m.mk_asserted(fml0);
|
|
pfs[0] = p1;
|
|
rls[0] = r1;
|
|
TRACE("pdr",
|
|
tout << "root: " << mk_pp(p1.get(), m) << "\n";
|
|
for (unsigned i = 0; i < binding.size(); ++i) {
|
|
tout << mk_pp(binding[i].get(), m) << "\n";
|
|
}
|
|
for (unsigned i = 1; i < pfs.size(); ++i) {
|
|
tout << mk_pp(pfs[i], m) << "\n";
|
|
}
|
|
);
|
|
datalog::rule_ref reduced_rule(rm), r3(rm);
|
|
reduced_rule = rls[0];
|
|
// check if binding is identity.
|
|
bool binding_is_id = true;
|
|
for (unsigned i = 0; binding_is_id && i < binding.size(); ++i) {
|
|
expr* v = binding[i].get();
|
|
binding_is_id = is_var(v) && to_var(v)->get_idx() == i;
|
|
}
|
|
if (rls.size() > 1 || !binding_is_id) {
|
|
vector<expr_ref_vector> substs;
|
|
svector<std::pair<unsigned,unsigned> > positions;
|
|
substs.push_back(binding); // TODO base substitution.
|
|
for (unsigned i = 1; i < rls.size(); ++i) {
|
|
datalog::rule& src = *rls[i];
|
|
bool unified = unifier.unify_rules(*reduced_rule, 0, src);
|
|
if (!unified) {
|
|
std::cout << "Could not unify rules: ";
|
|
reduced_rule->display(dctx, std::cout);
|
|
src.display(dctx, std::cout);
|
|
}
|
|
expr_ref_vector sub1 = unifier.get_rule_subst(*reduced_rule, true);
|
|
TRACE("pdr",
|
|
for (unsigned k = 0; k < sub1.size(); ++k) {
|
|
tout << mk_pp(sub1[k].get(), m) << " ";
|
|
}
|
|
tout << "\n";
|
|
);
|
|
for (unsigned j = 0; j < substs.size(); ++j) {
|
|
// TODO. apply sub1 to subst.
|
|
}
|
|
|
|
positions.push_back(std::make_pair(i,0));
|
|
substs.push_back(unifier.get_rule_subst(src, false));
|
|
VERIFY(unifier.apply(*reduced_rule.get(), 0, src, r3));
|
|
reduced_rule = r3;
|
|
}
|
|
expr_ref fml_concl(m);
|
|
reduced_rule->to_formula(fml_concl);
|
|
p1 = m.mk_hyper_resolve(pfs.size(), pfs.c_ptr(), fml_concl, positions, substs);
|
|
}
|
|
cache.insert(n->state(), p1);
|
|
rules.insert(n->state(), reduced_rule);
|
|
trail.push_back(p1);
|
|
rules_trail.push_back(reduced_rule);
|
|
todo.pop_back();
|
|
}
|
|
return proof_ref(cache.find(m_root->state()), m);
|
|
}
|
|
|
|
model_search::~model_search() {
|
|
TRACE("pdr", tout << "\n";);
|
|
reset();
|
|
}
|
|
|
|
void model_search::reset() {
|
|
if (m_root) {
|
|
erase_children(*m_root);
|
|
remove_node(*m_root);
|
|
dealloc(m_root);
|
|
m_root = 0;
|
|
}
|
|
}
|
|
|
|
void model_search::backtrack_level(bool uses_level, model_node& n) {
|
|
SASSERT(m_root);
|
|
if (uses_level && m_root->level() > n.level()) {
|
|
IF_VERBOSE(2, verbose_stream() << "Increase level " << n.level() << "\n";);
|
|
n.increase_level();
|
|
m_leaves.push_back(&n);
|
|
}
|
|
else {
|
|
model_node* p = n.parent();
|
|
if (p) {
|
|
set_leaf(*p);
|
|
}
|
|
}
|
|
}
|
|
|
|
// ----------------
|
|
// context
|
|
|
|
context::context(
|
|
front_end_params& fparams,
|
|
params_ref const& params,
|
|
ast_manager& m
|
|
)
|
|
: m_fparams(fparams),
|
|
m_params(params),
|
|
m(m),
|
|
m_context(0),
|
|
m_quantifier_inst(*this, m),
|
|
m_pm(m_fparams, m_params, m),
|
|
m_query_pred(m),
|
|
m_query(0),
|
|
m_search(m_params.get_bool(":bfs-model-search", true)),
|
|
m_last_result(l_undef),
|
|
m_inductive_lvl(0),
|
|
m_cancel(false),
|
|
m_is_dl(false)
|
|
{
|
|
}
|
|
|
|
context::~context() {
|
|
reset_core_generalizers();
|
|
reset();
|
|
}
|
|
|
|
void context::reset() {
|
|
TRACE("pdr", tout << "\n";);
|
|
cleanup();
|
|
decl2rel::iterator it = m_rels.begin(), end = m_rels.end();
|
|
for (; it != end; ++it) {
|
|
dealloc(it->m_value);
|
|
}
|
|
m_rels.reset();
|
|
m_search.reset();
|
|
m_query = 0;
|
|
m_last_result = l_undef;
|
|
m_inductive_lvl = 0;
|
|
}
|
|
|
|
void context::init_rules(datalog::rule_set& rules, decl2rel& rels) {
|
|
m_context = &rules.get_context();
|
|
// Allocate collection of predicate transformers
|
|
datalog::rule_set::decl2rules::iterator dit = rules.begin_grouped_rules(), dend = rules.end_grouped_rules();
|
|
decl2rel::obj_map_entry* e;
|
|
for (; dit != dend; ++dit) {
|
|
func_decl* pred = dit->m_key;
|
|
TRACE("pdr", tout << mk_pp(pred, m) << "\n";);
|
|
SASSERT(!rels.contains(pred));
|
|
e = rels.insert_if_not_there2(pred, alloc(pred_transformer, *this, get_pdr_manager(), pred));
|
|
datalog::rule_vector const& pred_rules = *dit->m_value;
|
|
for (unsigned i = 0; i < pred_rules.size(); ++i) {
|
|
e->get_data().m_value->add_rule(pred_rules[i]);
|
|
}
|
|
}
|
|
// Initialize use list dependencies
|
|
decl2rel::iterator it = rels.begin(), end = rels.end();
|
|
for (; it != end; ++it) {
|
|
func_decl* pred = it->m_key;
|
|
pred_transformer* pt = it->m_value, *pt_user;
|
|
obj_hashtable<func_decl> const& deps = rules.get_dependencies().get_deps(pred);
|
|
obj_hashtable<func_decl>::iterator itf = deps.begin(), endf = deps.end();
|
|
for (; itf != endf; ++itf) {
|
|
TRACE("pdr", tout << mk_pp(pred, m) << " " << mk_pp(*itf, m) << "\n";);
|
|
if (!rels.find(*itf, pt_user)) {
|
|
pt_user = alloc(pred_transformer, *this, get_pdr_manager(), *itf);
|
|
rels.insert(*itf, pt_user);
|
|
}
|
|
pt_user->add_use(pt);
|
|
}
|
|
}
|
|
|
|
// Initialize the predicate transformers.
|
|
it = rels.begin(), end = rels.end();
|
|
for (; it != end; ++it) {
|
|
pred_transformer& rel = *it->m_value;
|
|
rel.initialize(rels);
|
|
TRACE("pdr", rel.display(tout); );
|
|
}
|
|
}
|
|
|
|
void context::update_rules(datalog::rule_set& rules) {
|
|
decl2rel rels;
|
|
init_core_generalizers(rules);
|
|
init_rules(rules, rels);
|
|
decl2rel::iterator it = rels.begin(), end = rels.end();
|
|
for (; it != end; ++it) {
|
|
pred_transformer* pt = 0;
|
|
if (m_rels.find(it->m_key, pt)) {
|
|
it->m_value->inherit_properties(*pt);
|
|
}
|
|
}
|
|
reset();
|
|
it = rels.begin(), end = rels.end();
|
|
for (; it != end; ++it) {
|
|
m_rels.insert(it->m_key, it->m_value);
|
|
}
|
|
}
|
|
|
|
unsigned context::get_num_levels(func_decl* p) {
|
|
pred_transformer* pt = 0;
|
|
if (m_rels.find(p, pt)) {
|
|
return pt->get_num_levels();
|
|
}
|
|
else {
|
|
IF_VERBOSE(10, verbose_stream() << "did not find predicate " << p->get_name() << "\n";);
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
expr_ref context::get_cover_delta(int level, func_decl* p) {
|
|
pred_transformer* pt = 0;
|
|
if (m_rels.find(p, pt)) {
|
|
return pt->get_cover_delta(level);
|
|
}
|
|
else {
|
|
IF_VERBOSE(10, verbose_stream() << "did not find predicate " << p->get_name() << "\n";);
|
|
return expr_ref(m.mk_true(), m);
|
|
}
|
|
}
|
|
|
|
void context::add_cover(int level, func_decl* p, expr* property) {
|
|
pred_transformer* pt = 0;
|
|
if (!m_rels.find(p, pt)) {
|
|
pt = alloc(pred_transformer, *this, get_pdr_manager(), p);
|
|
m_rels.insert(p, pt);
|
|
IF_VERBOSE(10, verbose_stream() << "did not find predicate " << p->get_name() << "\n";);
|
|
}
|
|
unsigned lvl = (level == -1)?infty_level:((unsigned)level);
|
|
pt->add_cover(lvl, property);
|
|
}
|
|
|
|
class context::classifier_proc {
|
|
ast_manager& m;
|
|
arith_util a;
|
|
bool m_is_bool;
|
|
bool m_is_bool_arith;
|
|
bool m_has_arith;
|
|
bool m_is_dl;
|
|
public:
|
|
classifier_proc(ast_manager& m, datalog::rule_set& rules):
|
|
m(m), a(m), m_is_bool(true), m_is_bool_arith(true), m_has_arith(false), m_is_dl(false) {
|
|
classify(rules);
|
|
}
|
|
void operator()(expr* e) {
|
|
if (m_is_bool) {
|
|
if (!m.is_bool(e)) {
|
|
m_is_bool = false;
|
|
}
|
|
else if (is_var(e)) {
|
|
// no-op.
|
|
}
|
|
else if (!is_app(e)) {
|
|
m_is_bool = false;
|
|
}
|
|
else if (to_app(e)->get_num_args() > 0 &&
|
|
to_app(e)->get_family_id() != m.get_basic_family_id()) {
|
|
m_is_bool = false;
|
|
}
|
|
}
|
|
|
|
m_has_arith = m_has_arith || a.is_int_real(e);
|
|
|
|
if (m_is_bool_arith) {
|
|
if (!m.is_bool(e) && !a.is_int_real(e)) {
|
|
m_is_bool_arith = false;
|
|
}
|
|
else if (is_var(e)) {
|
|
// no-op
|
|
}
|
|
else if (!is_app(e)) {
|
|
m_is_bool_arith = false;
|
|
}
|
|
else if (to_app(e)->get_num_args() > 0 &&
|
|
to_app(e)->get_family_id() != m.get_basic_family_id() &&
|
|
to_app(e)->get_family_id() != a.get_family_id()) {
|
|
m_is_bool_arith = false;
|
|
}
|
|
}
|
|
}
|
|
|
|
bool is_bool() const { return m_is_bool; }
|
|
|
|
bool is_bool_arith() const { return m_is_bool_arith; }
|
|
|
|
bool is_dl() const { return m_is_dl; }
|
|
|
|
|
|
private:
|
|
|
|
void classify(datalog::rule_set& rules) {
|
|
expr_fast_mark1 mark;
|
|
datalog::rule_set::iterator it = rules.begin(), end = rules.end();
|
|
for (; it != end; ++it) {
|
|
datalog::rule& r = *(*it);
|
|
classify_pred(mark, r.get_head());
|
|
unsigned utsz = r.get_uninterpreted_tail_size();
|
|
for (unsigned i = 0; i < utsz; ++i) {
|
|
classify_pred(mark, r.get_tail(i));
|
|
}
|
|
for (unsigned i = utsz; i < r.get_tail_size(); ++i) {
|
|
quick_for_each_expr(*this, mark, r.get_tail(i));
|
|
}
|
|
}
|
|
mark.reset();
|
|
|
|
m_is_dl = false;
|
|
if (m_has_arith) {
|
|
ptr_vector<expr> forms;
|
|
for (it = rules.begin(); it != end; ++it) {
|
|
datalog::rule& r = *(*it);
|
|
unsigned utsz = r.get_uninterpreted_tail_size();
|
|
for (unsigned i = utsz; i < r.get_tail_size(); ++i) {
|
|
forms.push_back(r.get_tail(i));
|
|
}
|
|
}
|
|
m_is_dl = is_difference_logic(m, forms.size(), forms.c_ptr());
|
|
}
|
|
}
|
|
|
|
void classify_pred(expr_fast_mark1& mark, app* pred) {
|
|
for (unsigned i = 0; i < pred->get_num_args(); ++i) {
|
|
quick_for_each_expr(*this, mark, pred->get_arg(i));
|
|
}
|
|
}
|
|
};
|
|
|
|
|
|
void context::reset_core_generalizers() {
|
|
std::for_each(m_core_generalizers.begin(), m_core_generalizers.end(), delete_proc<core_generalizer>());
|
|
m_core_generalizers.reset();
|
|
}
|
|
|
|
void context::init_core_generalizers(datalog::rule_set& rules) {
|
|
reset_core_generalizers();
|
|
classifier_proc classify(m, rules);
|
|
m_is_dl = false;
|
|
bool use_mc = m_params.get_bool(":use-multicore-generalizer", false);
|
|
if (use_mc) {
|
|
m_core_generalizers.push_back(alloc(core_multi_generalizer, *this, 0));
|
|
}
|
|
if (m_params.get_bool(":use-farkas", true) && !classify.is_bool()) {
|
|
if (m_params.get_bool(":inline-proof-mode", true)) {
|
|
m.toggle_proof_mode(PGM_FINE);
|
|
m_fparams.m_proof_mode = PGM_FINE;
|
|
m_fparams.m_arith_bound_prop = BP_NONE;
|
|
m_fparams.m_arith_auto_config_simplex = true;
|
|
m_fparams.m_arith_propagate_eqs = false;
|
|
m_fparams.m_arith_eager_eq_axioms = false;
|
|
if (classify.is_dl()) {
|
|
m_fparams.m_arith_mode = AS_DIFF_LOGIC;
|
|
m_fparams.m_arith_expand_eqs = true;
|
|
m_is_dl = true;
|
|
}
|
|
}
|
|
else {
|
|
m_core_generalizers.push_back(alloc(core_farkas_generalizer, *this, m, m_fparams));
|
|
}
|
|
}
|
|
if (!use_mc && m_params.get_bool(":use-inductive-generalizer", true)) {
|
|
m_core_generalizers.push_back(alloc(core_bool_inductive_generalizer, *this, 0));
|
|
}
|
|
if (m_params.get_bool(":use-interpolants", false)) {
|
|
m_core_generalizers.push_back(alloc(core_interpolant_generalizer, *this));
|
|
}
|
|
if (m_params.get_bool(":inductive-reachability-check", false)) {
|
|
m_core_generalizers.push_back(alloc(core_induction_generalizer, *this));
|
|
}
|
|
}
|
|
|
|
void context::get_level_property(unsigned lvl, expr_ref_vector& res, vector<relation_info>& rs) const {
|
|
decl2rel::iterator it = m_rels.begin(), end = m_rels.end();
|
|
for (; it != end; ++it) {
|
|
pred_transformer* r = it->m_value;
|
|
if (r->head() == m_query_pred) {
|
|
continue;
|
|
}
|
|
expr_ref conj = r->get_formulas(lvl, false);
|
|
m_pm.formula_n2o(0, false, conj);
|
|
res.push_back(conj);
|
|
ptr_vector<func_decl> sig(r->head()->get_arity(), r->sig());
|
|
rs.push_back(relation_info(m, r->head(), sig, conj));
|
|
}
|
|
}
|
|
|
|
void context::simplify_formulas() {
|
|
decl2rel::iterator it = m_rels.begin(), end = m_rels.end();
|
|
for (; it != end; ++it) {
|
|
pred_transformer* r = it->m_value;
|
|
r->simplify_formulas();
|
|
}
|
|
}
|
|
|
|
lbool context::solve() {
|
|
m_last_result = l_undef;
|
|
try {
|
|
solve_impl();
|
|
UNREACHABLE();
|
|
}
|
|
catch (model_exception) {
|
|
check_quantifiers();
|
|
IF_VERBOSE(1, verbose_stream() << "\n"; m_search.display(verbose_stream()););
|
|
m_last_result = l_true;
|
|
return l_true;
|
|
}
|
|
catch (inductive_exception) {
|
|
simplify_formulas();
|
|
m_last_result = l_false;
|
|
TRACE("pdr", display_certificate(tout););
|
|
IF_VERBOSE(1, display_certificate(verbose_stream()););
|
|
return l_false;
|
|
}
|
|
catch (unknown_exception) {
|
|
return l_undef;
|
|
}
|
|
return l_undef;
|
|
}
|
|
|
|
void context::cancel() {
|
|
m_cancel = true;
|
|
}
|
|
|
|
void context::cleanup() {
|
|
m_cancel = false;
|
|
}
|
|
|
|
void context::checkpoint() {
|
|
if (m_cancel) {
|
|
throw default_exception("pdr canceled");
|
|
}
|
|
}
|
|
|
|
/**
|
|
\brief retrieve answer.
|
|
*/
|
|
expr_ref context::get_answer() {
|
|
switch(m_last_result) {
|
|
case l_true: return mk_sat_answer();
|
|
case l_false: return mk_unsat_answer();
|
|
default: return expr_ref(m.mk_true(), m);
|
|
}
|
|
}
|
|
|
|
void context::get_model(model_ref& md) {
|
|
SASSERT(m_last_result == l_false);
|
|
expr_ref_vector refs(m);
|
|
vector<relation_info> rs;
|
|
get_level_property(m_inductive_lvl, refs, rs);
|
|
inductive_property ex(m, m_mc, rs);
|
|
ex.to_model(md);
|
|
}
|
|
|
|
proof_ref context::get_proof() const {
|
|
datalog::scoped_coarse_proof _sc(m);
|
|
proof_ref proof(m);
|
|
SASSERT(m_last_result == l_true);
|
|
proof = m_search.get_proof_trace(*this);
|
|
apply(m, m_pc.get(), proof);
|
|
return proof;
|
|
}
|
|
|
|
|
|
/**
|
|
\brief Retrieve satisfying assignment with explanation.
|
|
*/
|
|
expr_ref context::mk_sat_answer() const {
|
|
if (m_params.get_bool(":generate-proof-trace", false)) {
|
|
proof_ref pr = get_proof();
|
|
return expr_ref(pr.get(), m);
|
|
}
|
|
return m_search.get_trace();
|
|
}
|
|
|
|
expr_ref context::mk_unsat_answer() const {
|
|
expr_ref_vector refs(m);
|
|
vector<relation_info> rs;
|
|
get_level_property(m_inductive_lvl, refs, rs);
|
|
inductive_property ex(m, const_cast<model_converter_ref&>(m_mc), rs);
|
|
return ex.to_expr();
|
|
}
|
|
|
|
void context::solve_impl() {
|
|
if (!m_rels.find(m_query_pred, m_query)) {
|
|
throw inductive_exception();
|
|
}
|
|
unsigned lvl = 0;
|
|
bool reachable;
|
|
while (true) {
|
|
checkpoint();
|
|
reachable = check_reachability(lvl);
|
|
if (reachable) {
|
|
throw model_exception();
|
|
}
|
|
if (lvl != 0) {
|
|
propagate(lvl);
|
|
}
|
|
lvl++;
|
|
m_stats.m_max_depth = std::max(m_stats.m_max_depth, lvl);
|
|
IF_VERBOSE(1,verbose_stream() << "Entering level "<<lvl << "\n";);
|
|
}
|
|
}
|
|
|
|
//
|
|
// Check that quantifiers are satisfied in the produced model.
|
|
//
|
|
void context::check_quantifiers() {
|
|
if (has_quantifiers()) {
|
|
m_quantifier_inst.model_check(m_search.get_root());
|
|
}
|
|
}
|
|
|
|
bool context::has_quantifiers() const {
|
|
decl2rel const& dr = get_pred_transformers();
|
|
decl2rel::iterator it = dr.begin(), end = dr.end();
|
|
for (; it != end; ++it) {
|
|
pred_transformer* pt = it->m_value;
|
|
if (pt->has_quantifiers()) return true;
|
|
}
|
|
return false;
|
|
}
|
|
|
|
//
|
|
// Pick a potential counter example state.
|
|
// Initialize a search tree using that counter-example.
|
|
// If the counter-example expands to a full model, then
|
|
// the search tree is a model, otherwise obtain the next
|
|
// query state.
|
|
//
|
|
bool context::check_reachability(unsigned level) {
|
|
expr_ref state(m.mk_true(), m);
|
|
model_node* root = alloc(model_node, 0, state, *m_query, level);
|
|
m_search.set_root(root);
|
|
|
|
while (model_node* node = m_search.next()) {
|
|
IF_VERBOSE(2, verbose_stream() << "Expand node: " << node->level() << "\n";);
|
|
checkpoint();
|
|
expand_node(*node);
|
|
}
|
|
return root->is_closed();
|
|
}
|
|
|
|
void context::close_node(model_node& n) {
|
|
n.set_closed();
|
|
model_node* p = n.parent();
|
|
while (p && p->is_1closed()) {
|
|
p->set_closed();
|
|
p = p->parent();
|
|
}
|
|
}
|
|
|
|
void context::check_pre_closed(model_node& n) {
|
|
for (unsigned i = 0; i < n.children().size(); ++i) {
|
|
if (!n.children()[i]->is_closed()) return;
|
|
}
|
|
n.set_pre_closed();
|
|
model_node* p = n.parent();
|
|
while (p && p->is_1closed()) {
|
|
p->set_pre_closed();
|
|
p = p->parent();
|
|
}
|
|
}
|
|
|
|
void context::expand_node(model_node& n) {
|
|
SASSERT(n.is_open());
|
|
expr_ref_vector cube(m);
|
|
|
|
if (n.pt().is_reachable(n.state())) {
|
|
TRACE("pdr", tout << "reachable\n";);
|
|
close_node(n);
|
|
}
|
|
else {
|
|
switch (expand_state(n, cube)) {
|
|
case l_true:
|
|
if (n.level() == 0) {
|
|
TRACE("pdr", tout << "reachable\n";);
|
|
close_node(n);
|
|
}
|
|
else {
|
|
TRACE("pdr", tout << "node: " << &n << "\n";);
|
|
create_children(n);
|
|
}
|
|
break;
|
|
case l_false: {
|
|
core_generalizer::cores cores;
|
|
cores.push_back(std::make_pair(cube, true));
|
|
|
|
for (unsigned i = 0; !cores.empty() && i < m_core_generalizers.size(); ++i) {
|
|
core_generalizer::cores new_cores;
|
|
for (unsigned j = 0; j < cores.size(); ++j) {
|
|
(*m_core_generalizers[i])(n, cores[j].first, cores[j].second, new_cores);
|
|
}
|
|
cores.reset();
|
|
cores.append(new_cores);
|
|
}
|
|
bool found_invariant = false;
|
|
for (unsigned i = 0; i < cores.size(); ++i) {
|
|
expr_ref_vector const& core = cores[i].first;
|
|
bool uses_level = cores[i].second;
|
|
found_invariant = !uses_level || found_invariant;
|
|
expr_ref ncore(m_pm.mk_not_and(core), m);
|
|
TRACE("pdr", tout << "invariant state: " << (uses_level?"":"(inductive) ") << mk_pp(ncore, m) << "\n";);
|
|
n.pt().add_property(ncore, uses_level?n.level():infty_level);
|
|
}
|
|
CASSERT("pdr",n.level() == 0 || check_invariant(n.level()-1));
|
|
m_search.backtrack_level(!found_invariant && m_params.get_bool(":flexible-trace", false), n);
|
|
break;
|
|
}
|
|
case l_undef: {
|
|
TRACE("pdr", tout << "unknown state: " << mk_pp(m_pm.mk_and(cube), m) << "\n";);
|
|
throw unknown_exception();
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
//
|
|
// check if predicate transformer has a satisfiable predecessor state.
|
|
// returns either a satisfiable predecessor state or
|
|
// return a property that blocks state and is implied by the
|
|
// predicate transformer (or some unfolding of it).
|
|
//
|
|
lbool context::expand_state(model_node& n, expr_ref_vector& result) {
|
|
return n.pt().is_reachable(n, &result);
|
|
}
|
|
|
|
void context::propagate(unsigned max_prop_lvl) {
|
|
if (m_params.get_bool(":simplify-formulas-pre", false)) {
|
|
simplify_formulas();
|
|
}
|
|
for (unsigned lvl = 0; lvl <= max_prop_lvl; lvl++) {
|
|
checkpoint();
|
|
bool all_propagated = true;
|
|
decl2rel::iterator it = m_rels.begin(), end = m_rels.end();
|
|
for (; it != end; ++it) {
|
|
checkpoint();
|
|
pred_transformer& r = *it->m_value;
|
|
all_propagated = r.propagate_to_next_level(lvl) && all_propagated;
|
|
}
|
|
CASSERT("pdr", check_invariant(lvl));
|
|
|
|
if (all_propagated && lvl == max_prop_lvl) {
|
|
m_inductive_lvl = lvl;
|
|
throw inductive_exception();
|
|
}
|
|
}
|
|
if (m_params.get_bool(":simplify-formulas-post", false)) {
|
|
simplify_formulas();
|
|
}
|
|
}
|
|
|
|
|
|
/**
|
|
\brief create children states from model cube.
|
|
|
|
Introduce the shorthands:
|
|
|
|
- T(x0,x1,x) for transition
|
|
- phi(x) for n.state()
|
|
- psi(x0,x1,x) for psi
|
|
- M(x0,x1,x) for n.model()
|
|
|
|
Assumptions:
|
|
M => psi
|
|
psi => phi & T
|
|
psi & M agree on which rules are taken.
|
|
|
|
In other words,
|
|
1. psi is a weakening of M
|
|
2. phi & T is implied by psi
|
|
|
|
Goal is to find phi0(x0), phi1(x1) such that:
|
|
|
|
phi(x) & phi0(x0) & phi1(x1) => psi(x0, x1, x)
|
|
|
|
or at least (ignoring psi alltogether):
|
|
|
|
phi(x) & phi0(x0) & phi1(x1) => T(x0, x1, x)
|
|
|
|
Strategy:
|
|
|
|
- Extract literals from T & phi using ternary simulation with M.
|
|
- resulting formula is Phi.
|
|
|
|
- perform cheap existential quantifier elimination on
|
|
Phi <- exists x . Phi(x0,x1,x)
|
|
(e.g., destructive equality resolution)
|
|
|
|
- Sub-strategy 1: rename remaining x to fresh variables.
|
|
- Sub-strategy 2: replace remaining x to M(x).
|
|
|
|
- For each literal L in result:
|
|
|
|
- if L is x0 pure, add L to L0
|
|
- if L is x1 pure, add L to L1
|
|
- if L mixes x0, x1, add x1 = M(x1) to L1, add L(x1 |-> M(x1)) to L0
|
|
|
|
- Create sub-goals for L0 and L1.
|
|
|
|
*/
|
|
void context::create_children(model_node& n) {
|
|
SASSERT(n.level() > 0);
|
|
bool use_model_generalizer = m_params.get_bool(":use-model-generalizer", false);
|
|
// use_model_generalizer = use_model_generalizer || is_dl();
|
|
|
|
pred_transformer& pt = n.pt();
|
|
model_ref M = n.model_ptr();
|
|
datalog::rule const& r = pt.find_rule(*M);
|
|
expr* T = pt.get_transition(r);
|
|
expr* phi = n.state();
|
|
|
|
IF_VERBOSE(3, verbose_stream() << "Model:\n";
|
|
model_smt2_pp(verbose_stream(), m, *M, 0);
|
|
verbose_stream() << "\n";
|
|
verbose_stream() << "Transition:\n" << mk_pp(T, m) << "\n";
|
|
verbose_stream() << "Phi:\n" << mk_pp(phi, m) << "\n";);
|
|
|
|
model_evaluator mev(m);
|
|
expr_ref_vector mdl(m), forms(m), Phi(m);
|
|
forms.push_back(T);
|
|
forms.push_back(phi);
|
|
datalog::flatten_and(forms);
|
|
ptr_vector<expr> forms1(forms.size(), forms.c_ptr());
|
|
if (use_model_generalizer) {
|
|
Phi.append(mev.minimize_model(forms1, M));
|
|
}
|
|
else {
|
|
Phi.append(mev.minimize_literals(forms1, M));
|
|
}
|
|
ptr_vector<func_decl> preds;
|
|
pt.find_predecessors(r, preds);
|
|
pt.remove_predecessors(Phi);
|
|
|
|
app_ref_vector vars(m);
|
|
unsigned sig_size = pt.head()->get_arity();
|
|
for (unsigned i = 0; i < sig_size; ++i) {
|
|
vars.push_back(m.mk_const(m_pm.o2n(pt.sig(i), 0)));
|
|
}
|
|
ptr_vector<app> aux_vars;
|
|
pt.get_aux_vars(r, aux_vars);
|
|
vars.append(aux_vars.size(), aux_vars.c_ptr());
|
|
|
|
qe_lite qe(m);
|
|
expr_ref phi1 = m_pm.mk_and(Phi);
|
|
qe(vars, phi1);
|
|
if (!use_model_generalizer) {
|
|
reduce_disequalities(*M, 3, phi1);
|
|
}
|
|
|
|
IF_VERBOSE(2,
|
|
verbose_stream() << "Vars:\n";
|
|
for (unsigned i = 0; i < vars.size(); ++i) {
|
|
verbose_stream() << mk_pp(vars[i].get(), m) << "\n";
|
|
}
|
|
verbose_stream() << "Literals\n";
|
|
verbose_stream() << mk_pp(m_pm.mk_and(Phi), m) << "\n";
|
|
verbose_stream() << "Reduced\n" << mk_pp(phi1, m) << "\n";);
|
|
|
|
if (!vars.empty()) {
|
|
// also fresh names for auxiliary variables in body?
|
|
expr_substitution sub(m);
|
|
expr_ref tmp(m);
|
|
proof_ref pr(m);
|
|
pr = m.mk_asserted(m.mk_true());
|
|
|
|
for (unsigned i = 0; i < vars.size(); ++i) {
|
|
M->eval(vars[i]->get_decl(), tmp);
|
|
sub.insert(vars[i].get(), tmp, pr);
|
|
}
|
|
scoped_ptr<expr_replacer> rep = mk_default_expr_replacer(m);
|
|
rep->set_substitution(&sub);
|
|
(*rep)(phi1);
|
|
IF_VERBOSE(2, verbose_stream() << "Projected:\n" << mk_pp(phi1, m) << "\n";);
|
|
}
|
|
Phi.reset();
|
|
datalog::flatten_and(phi1, Phi);
|
|
unsigned_vector indices;
|
|
vector<expr_ref_vector> child_states;
|
|
child_states.resize(preds.size(), expr_ref_vector(m));
|
|
for (unsigned i = 0; i < Phi.size(); ++i) {
|
|
m_pm.collect_indices(Phi[i].get(), indices);
|
|
if (indices.size() == 0) {
|
|
IF_VERBOSE(2, verbose_stream() << "Skipping " << mk_pp(Phi[i].get(), m) << "\n";);
|
|
}
|
|
else if (indices.size() == 1) {
|
|
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);
|
|
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) {
|
|
M->eval(vs[k]->get_decl(), tmp);
|
|
sub.insert(vs[k], tmp, pr);
|
|
child_states[indices[j]].push_back(m.mk_eq(vs[k], tmp));
|
|
}
|
|
}
|
|
tmp = Phi[i].get();
|
|
scoped_ptr<expr_replacer> rep = mk_default_expr_replacer(m);
|
|
rep->set_substitution(&sub);
|
|
(*rep)(tmp);
|
|
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);
|
|
++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);
|
|
|
|
|
|
TRACE("pdr", m_search.display(tout););
|
|
}
|
|
|
|
void context::collect_statistics(statistics& st) const {
|
|
decl2rel::iterator it = m_rels.begin(), end = m_rels.end();
|
|
for (it = m_rels.begin(); it != end; ++it) {
|
|
it->m_value->collect_statistics(st);
|
|
}
|
|
st.update("PDR num unfoldings", m_stats.m_num_nodes);
|
|
st.update("PDR max depth", m_stats.m_max_depth);
|
|
m_pm.collect_statistics(st);
|
|
|
|
for (unsigned i = 0; i < m_core_generalizers.size(); ++i) {
|
|
m_core_generalizers[i]->collect_statistics(st);
|
|
}
|
|
}
|
|
|
|
|
|
std::ostream& context::display(std::ostream& out) const {
|
|
decl2rel::iterator it = m_rels.begin(), end = m_rels.end();
|
|
for (; it != end; ++it) {
|
|
it->m_value->display(out);
|
|
}
|
|
m_search.display(out);
|
|
return out;
|
|
}
|
|
|
|
bool context::check_invariant(unsigned lvl) {
|
|
decl2rel::iterator it = m_rels.begin(), end = m_rels.end();
|
|
for (; it != end; ++it) {
|
|
checkpoint();
|
|
if (!check_invariant(lvl, it->m_key)) {
|
|
return false;
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
|
|
bool context::check_invariant(unsigned lvl, func_decl* fn) {
|
|
smt::solver ctx(m, m_fparams);
|
|
pred_transformer& pt = *m_rels.find(fn);
|
|
expr_ref_vector conj(m);
|
|
expr_ref inv = pt.get_formulas(next_level(lvl), false);
|
|
if (m.is_true(inv)) return true;
|
|
pt.add_premises(m_rels, lvl, conj);
|
|
conj.push_back(m.mk_not(inv));
|
|
expr_ref fml(m.mk_and(conj.size(), conj.c_ptr()), m);
|
|
ctx.assert_expr(fml);
|
|
lbool result = ctx.check();
|
|
TRACE("pdr", tout << "Check invariant level: " << lvl << " " << result << "\n" << mk_pp(fml, m) << "\n";);
|
|
return result == l_false;
|
|
}
|
|
|
|
void context::display_certificate(std::ostream& strm) const {
|
|
switch(m_last_result) {
|
|
case l_false: {
|
|
expr_ref_vector refs(m);
|
|
vector<relation_info> rs;
|
|
get_level_property(m_inductive_lvl, refs, rs);
|
|
inductive_property ex(m, const_cast<model_converter_ref&>(m_mc), rs);
|
|
strm << ex.to_string();
|
|
break;
|
|
}
|
|
case l_true: {
|
|
strm << mk_pp(mk_sat_answer(), m);
|
|
break;
|
|
}
|
|
case l_undef: {
|
|
strm << "unknown";
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
|
|
}
|