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https://github.com/Z3Prover/z3
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20c54048f7
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@ -18,6 +18,7 @@ namespace nra {
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typedef nla::mon_eq mon_eq;
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typedef nla::variable_map_type variable_map_type;
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struct solver::imp {
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lp::lar_solver& lra;
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reslimit& m_limit;
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@ -68,12 +69,12 @@ struct solver::imp {
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}
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}
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for (auto const& m : m_nla_core.m_to_refine)
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todo.push_back(m);
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for (auto const& m : m_nla_core.m_to_refine)
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todo.push_back(m);
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for (unsigned i = 0; i < todo.size(); ++i) {
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auto v = todo[i];
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if (visited.contains(v))
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if (visited.contains(v))
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continue;
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visited.insert(v);
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var2occurs.reserve(v + 1);
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@ -82,22 +83,22 @@ struct solver::imp {
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auto const& c = lra.constraints()[ci];
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for (auto const& [coeff, w] : c.coeffs())
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todo.push_back(w);
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}
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}
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for (auto w : var2occurs[v].monics)
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todo.push_back(w);
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if (lra.column_corresponds_to_term(v)) {
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m_term_set.insert(v);
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lp::tv ti = lp::tv::raw(lra.column_to_reported_index(v));
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for (auto kv : lra.get_term(ti))
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todo.push_back(kv.column().index());
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for (auto kv : lra.get_term(ti))
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todo.push_back(kv.column().index());
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}
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if (m_nla_core.is_monic_var(v)) {
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m_mon_set.insert(v);
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for (auto w : m_nla_core.emons()[v])
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todo.push_back(w);
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}
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}
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}
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}
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@ -112,7 +113,7 @@ struct solver::imp {
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TBD: use partial model from lra_solver to prime the state of nlsat_solver.
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TBD: explore more incremental ways of applying nlsat (using assumptions)
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*/
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lbool check() {
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lbool check() {
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SASSERT(need_check());
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m_values = nullptr;
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m_nlsat = alloc(nlsat::solver, m_limit, m_params, false);
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@ -125,18 +126,18 @@ struct solver::imp {
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// add linear inequalities from lra_solver
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for (auto ci : m_constraint_set)
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add_constraint(ci);
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// add polynomial definitions.
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for (auto const& m : m_mon_set)
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add_monic_eq(m_nla_core.emons()[m]);
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for (auto const& m : m_mon_set)
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add_monic_eq(m_nla_core.emons()[m]);
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// add term definitions.
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for (unsigned i : m_term_set)
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for (unsigned i : m_term_set)
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add_term(i);
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lbool r = l_undef;
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try {
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r = m_nlsat->check();
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r = m_nlsat->check();
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}
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catch (z3_exception&) {
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if (m_limit.is_canceled()) {
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@ -146,30 +147,31 @@ struct solver::imp {
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throw;
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}
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}
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TRACE("nra",
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#if 0
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TRACE("nra",
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m_nlsat->display(tout << r << "\n");
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display(tout);
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for (auto [j, x] : m_lp2nl) tout << "j" << j << " := x" << x << "\n";
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);
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display(tout);
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for (auto [j, x] : m_lp2nl) tout << "j" << j << " := x" << x << "\n";);
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#endif
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switch (r) {
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case l_true:
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case l_true:
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m_nla_core.set_use_nra_model(true);
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lra.init_model();
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for (lp::constraint_index ci : lra.constraints().indices())
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if (!check_constraint(ci)) {
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IF_VERBOSE(0, verbose_stream() << "constraint " << ci << " violated\n";
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lra.constraints().display(verbose_stream()));
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UNREACHABLE();
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return l_undef;
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}
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for (auto const& m : m_nla_core.emons()) {
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if (!check_monic(m)) {
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IF_VERBOSE(0, verbose_stream() << "monic " << m << " violated\n";
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lra.constraints().display(verbose_stream()));
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UNREACHABLE();
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return l_undef;
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}
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lra.init_model();
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for (lp::constraint_index ci : lra.constraints().indices())
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if (!check_constraint(ci)) {
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IF_VERBOSE(0, verbose_stream() << "constraint " << ci << " violated\n";
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lra.constraints().display(verbose_stream()));
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UNREACHABLE();
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return l_undef;
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}
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for (auto const& m : m_nla_core.emons()) {
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if (!check_monic(m)) {
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IF_VERBOSE(0, verbose_stream() << "monic " << m << " violated\n";
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lra.constraints().display(verbose_stream()));
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UNREACHABLE();
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return l_undef;
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}
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}
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break;
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case l_false: {
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lp::explanation ex;
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@ -186,9 +188,9 @@ struct solver::imp {
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}
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case l_undef:
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break;
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}
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}
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return r;
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}
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}
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void add_monic_eq_bound(mon_eq const& m) {
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if (!lra.column_has_lower_bound(m.var()) &&
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@ -322,22 +324,22 @@ struct solver::imp {
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m_lp2nl.reset();
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m_term_set.reset();
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for (auto const& eq : eqs)
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add_eq(*eq);
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for (auto const& m : m_nla_core.emons())
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if (any_of(m.vars(), [&](lp::lpvar v) { return m_lp2nl.contains(v); }))
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add_monic_eq_bound(m);
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for (unsigned i : m_term_set)
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add_term(i);
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add_eq(*eq);
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for (auto const& m : m_nla_core.emons())
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if (any_of(m.vars(), [&](lp::lpvar v) { return m_lp2nl.contains(v); }))
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add_monic_eq_bound(m);
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for (unsigned i : m_term_set)
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add_term(i);
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for (auto const& [v, w] : m_lp2nl) {
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if (lra.column_has_lower_bound(v))
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add_lb(lra.get_lower_bound(v), w, lra.get_column_lower_bound_witness(v));
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if (lra.column_has_upper_bound(v))
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add_ub(lra.get_upper_bound(v), w, lra.get_column_upper_bound_witness(v));
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if (lra.column_has_lower_bound(v))
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add_lb(lra.get_lower_bound(v), w, lra.get_column_lower_bound_witness(v));
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if (lra.column_has_upper_bound(v))
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add_ub(lra.get_upper_bound(v), w, lra.get_column_upper_bound_witness(v));
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}
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lbool r = l_undef;
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try {
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r = m_nlsat->check();
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r = m_nlsat->check();
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}
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catch (z3_exception&) {
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if (m_limit.is_canceled()) {
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@ -349,13 +351,13 @@ struct solver::imp {
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}
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switch (r) {
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case l_true:
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case l_true:
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m_nla_core.set_use_nra_model(true);
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lra.init_model();
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for (lp::constraint_index ci : lra.constraints().indices())
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for (lp::constraint_index ci : lra.constraints().indices())
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if (!check_constraint(ci))
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return l_undef;
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for (auto const& m : m_nla_core.emons()) {
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return l_undef;
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for (auto const& m : m_nla_core.emons())
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if (!check_monic(m))
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return l_undef;
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break;
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@ -365,7 +367,7 @@ struct solver::imp {
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m_nlsat->get_core(core);
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u_dependency_manager dm;
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vector<unsigned, false> lv;
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for (auto c : core)
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for (auto c : core)
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dm.linearize(static_cast<u_dependency*>(c), lv);
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for (auto ci : lv)
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ex.push_back(ci);
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@ -375,8 +377,7 @@ struct solver::imp {
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}
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case l_undef:
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break;
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}
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}
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return r;
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}
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@ -388,18 +389,18 @@ struct solver::imp {
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m_term_set.reset();
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for (auto const& eq : eqs)
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add_eq(eq);
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for (auto const& m : m_nla_core.emons())
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add_monic_eq(m);
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for (auto const& m : m_nla_core.emons())
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add_monic_eq(m);
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for (auto const& [v, w] : m_lp2nl) {
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if (lra.column_has_lower_bound(v))
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add_lb(lra.get_lower_bound(v), w);
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if (lra.column_has_upper_bound(v))
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add_ub(lra.get_upper_bound(v), w);
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}
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lbool r = l_undef;
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try {
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r = m_nlsat->check();
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r = m_nlsat->check();
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}
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catch (z3_exception&) {
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if (m_limit.is_canceled()) {
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if (r == l_true)
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return r;
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IF_VERBOSE(0, verbose_stream() << "check-nra " << r << "\n";
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m_nlsat->display(verbose_stream());
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for (auto const& [v, w] : m_lp2nl) {
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verbose_stream() << "x" << w << " >= " << lra.get_lower_bound(v) << "\n";
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if (lra.column_has_upper_bound(v))
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verbose_stream() << "x" << w << " <= " << lra.get_upper_bound(v) << "\n";
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});
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});
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return r;
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}
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void add_eq(dd::solver::equation const& eq) {
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add_eq(eq.poly(), eq.dep());
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}
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void add_eq(dd::pdd const& eq, nlsat::assumption a = nullptr) {
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dd::pdd normeq = eq;
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rational lc(1);
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for (auto const& [c, m] : eq)
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for (auto const& [c, m] : eq)
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lc = lcm(denominator(c), lc);
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if (lc != 1)
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normeq *= lc;
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polynomial::manager& pm = m_nlsat->pm();
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polynomial::polynomial_ref p(pdd2polynomial(normeq), pm);
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bool is_even[1] = { false };
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polynomial::polynomial* ps[1] = { p };
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nlsat::literal lit = m_nlsat->mk_ineq_literal(nlsat::atom::kind::EQ, 1, ps, is_even);
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bool is_even[1] = {false};
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polynomial::polynomial* ps[1] = {p};
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nlsat::literal lit = m_nlsat->mk_ineq_literal(nlsat::atom::kind::EQ, 1, ps, is_even);
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m_nlsat->mk_clause(1, &lit, a);
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}
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void add_lb(lp::impq const& b, unsigned w, nlsat::assumption a = nullptr) {
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polynomial::manager& pm = m_nlsat->pm();
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polynomial::polynomial_ref p(pm.mk_polynomial(w), pm);
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add_lb(b, p, a);
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}
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void add_ub(lp::impq const& b, unsigned w, nlsat::assumption a = nullptr) {
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polynomial::manager& pm = m_nlsat->pm();
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polynomial::polynomial_ref p(pm.mk_polynomial(w), pm);
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polynomial::manager& pm = m_nlsat->pm();
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polynomial::polynomial_ref p2(pm.mk_const(bound), pm);
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polynomial::polynomial_ref p(pm.sub(p1, p2), pm);
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polynomial::polynomial* ps[1] = { p };
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bool is_even[1] = { false };
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polynomial::polynomial* ps[1] = {p};
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bool is_even[1] = {false};
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nlsat::literal lit = m_nlsat->mk_ineq_literal(k, 1, ps, is_even);
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if (neg)
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lit.neg();
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polynomial::polynomial_ref p1(pm.mk_polynomial(w), pm);
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add_bound(bound, p1, neg, k, a);
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}
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polynomial::polynomial* pdd2polynomial(dd::pdd const& p) {
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polynomial::manager& pm = m_nlsat->pm();
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if (p.is_val())
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if (p.is_val())
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return pm.mk_const(p.val());
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polynomial::polynomial_ref lo(pdd2polynomial(p.lo()), pm);
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polynomial::polynomial_ref hi(pdd2polynomial(p.hi()), pm);
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@ -502,7 +501,9 @@ struct solver::imp {
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polynomial::polynomial_ref mp(pm.mul(vp, hi), pm);
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return pm.add(lo, mp);
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}
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bool is_int(lp::var_index v) {
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return lra.var_is_int(v);
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}
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@ -521,7 +522,7 @@ struct solver::imp {
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//
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void add_term(unsigned term_column) {
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lp::tv ti = lp::tv::raw(lra.column_to_reported_index(term_column));
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const lp::lar_term& t = lra.get_term(ti);
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const lp::lar_term& t = lra.get_term(ti);
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// code that creates a polynomial equality between the linear coefficients and
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// variable representing the term.
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svector<polynomial::var> vars;
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@ -531,7 +532,7 @@ struct solver::imp {
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den = lcm(den, denominator(kv.coeff()));
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}
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vars.push_back(lp2nl(term_column));
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vector<rational> coeffs;
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for (auto kv : t) {
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coeffs.push_back(den * kv.coeff());
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coeffs.push_back(-den);
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polynomial::manager& pm = m_nlsat->pm();
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polynomial::polynomial_ref p(pm.mk_linear(coeffs.size(), coeffs.data(), vars.data(), rational(0)), pm);
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polynomial::polynomial* ps[1] = { p };
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bool is_even[1] = { false };
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nlsat::literal lit = m_nlsat->mk_ineq_literal(nlsat::atom::kind::EQ, 1, ps, is_even);
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polynomial::polynomial* ps[1] = {p};
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bool is_even[1] = {false};
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nlsat::literal lit = m_nlsat->mk_ineq_literal(nlsat::atom::kind::EQ, 1, ps, is_even);
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m_nlsat->mk_clause(1, &lit, nullptr);
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}
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@ -19,8 +19,6 @@ namespace lp {
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namespace nra {
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class solver {
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struct imp;
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imp* m_imp;
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