mirror of
https://github.com/Z3Prover/z3
synced 2025-04-23 17:15:31 +00:00
nra to nla
Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson
parent
bd0180925b
commit
7a79397769
6 changed files with 312 additions and 416 deletions
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@ -24,6 +24,8 @@
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#include "math/lp/horner.h"
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#include "math/lp/nla_intervals.h"
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#include "math/grobner/pdd_solver.h"
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#include "math/lp/nla_lemma.h"
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#include "nlsat/nlsat_solver.h"
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namespace nla {
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@ -66,18 +68,6 @@ public:
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const rational& rs() const { return m_rs; };
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};
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class lemma {
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vector<ineq> m_ineqs;
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lp::explanation m_expl;
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public:
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void push_back(const ineq& i) { m_ineqs.push_back(i);}
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size_t size() const { return m_ineqs.size() + m_expl.size(); }
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const vector<ineq>& ineqs() const { return m_ineqs; }
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vector<ineq>& ineqs() { return m_ineqs; }
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lp::explanation& expl() { return m_expl; }
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const lp::explanation& expl() const { return m_expl; }
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bool is_conflict() const { return m_ineqs.empty() && !m_expl.empty(); }
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};
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class core;
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//
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@ -12,8 +12,12 @@
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#include "math/lp/var_eqs.h"
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#include "math/lp/factorization.h"
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#include "math/lp/nla_solver.h"
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#include "math/lp/nla_core.h"
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namespace nla {
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nla_settings& solver::settings() { return m_core->m_nla_settings; }
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void solver::add_monic(lpvar v, unsigned sz, lpvar const* vs) {
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m_core->add_monic(v, sz, vs);
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}
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@ -36,7 +40,8 @@ void solver::pop(unsigned n) {
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m_core->pop(n);
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}
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solver::solver(lp::lar_solver& s): m_core(alloc(core, s, m_res_limit)) {
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solver::solver(lp::lar_solver& s): m_core(alloc(core, s, m_res_limit)),
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m_nra(s, m_res_limit, *m_core) {
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}
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bool solver::influences_nl_var(lpvar j) const {
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@ -11,23 +11,27 @@ Author:
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#include "math/lp/lp_settings.h"
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#include "util/rlimit.h"
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#include "util/params.h"
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#include "nlsat/nlsat_solver.h"
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#include "math/lp/lar_solver.h"
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#include "math/lp/monic.h"
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#include "math/lp/nla_core.h"
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#include "math/lp/nla_settings.h"
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#include "math/lp/nla_lemma.h"
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namespace nra {
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class solver;
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}
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namespace nla {
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class core;
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// nonlinear integer incremental linear solver
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class solver {
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reslimit m_res_limit;
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core* m_core;
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nra::solver m_nra;
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public:
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void add_monic(lpvar v, unsigned sz, lpvar const* vs);
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solver(lp::lar_solver& s);
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~solver();
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nla_settings& settings() { return m_core->m_nla_settings; }
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nla_settings& settings();
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void push();
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void pop(unsigned scopes);
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bool need_check();
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@ -9,272 +9,273 @@
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#include "math/polynomial/polynomial.h"
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#include "math/polynomial/algebraic_numbers.h"
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#include "util/map.h"
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#include "math/lp/monic.h"
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#include "math/lp/nla_core.h"
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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& s;
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reslimit& m_limit;
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params_ref m_params;
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u_map<polynomial::var> m_lp2nl; // map from lar_solver variables to nlsat::solver variables
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scoped_ptr<nlsat::solver> m_nlsat;
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scoped_ptr<scoped_anum> m_zero;
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vector<mon_eq> m_monics;
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unsigned_vector m_monics_lim;
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mutable variable_map_type m_variable_values; // current model
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struct solver::imp {
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lp::lar_solver& s;
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reslimit& m_limit;
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params_ref m_params;
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u_map<polynomial::var> m_lp2nl; // map from lar_solver variables to nlsat::solver variables
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scoped_ptr<nlsat::solver> m_nlsat;
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scoped_ptr<scoped_anum> m_zero;
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vector<mon_eq> m_monics;
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unsigned_vector m_monics_lim;
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mutable variable_map_type m_variable_values; // current model
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nla::core& m_nla_core;
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imp(lp::lar_solver& s, reslimit& lim, params_ref const& p, nla::core& nla_core):
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s(s),
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m_limit(lim),
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m_params(p),
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m_nla_core(nla_core) {}
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imp(lp::lar_solver& s, reslimit& lim, params_ref const& p):
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s(s),
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m_limit(lim),
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m_params(p) {
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}
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bool need_check() {
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return !m_monics.empty() && !check_assignments(m_monics, s, m_variable_values);
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}
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bool need_check() {
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return !m_monics.empty() && !check_assignments(m_monics, s, m_variable_values);
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}
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void add(lp::var_index v, unsigned sz, lp::var_index const* vs) {
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m_monics.push_back(mon_eq(v, sz, vs));
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}
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void add(lp::var_index v, unsigned sz, lp::var_index const* vs) {
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m_monics.push_back(mon_eq(v, sz, vs));
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}
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void push() {
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m_monics_lim.push_back(m_monics.size());
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}
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void push() {
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m_monics_lim.push_back(m_monics.size());
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}
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void pop(unsigned n) {
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if (n == 0) return;
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m_monics.shrink(m_monics_lim[m_monics_lim.size() - n]);
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m_monics_lim.shrink(m_monics_lim.size() - n);
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}
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void pop(unsigned n) {
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if (n == 0) return;
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m_monics.shrink(m_monics_lim[m_monics_lim.size() - n]);
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m_monics_lim.shrink(m_monics_lim.size() - n);
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}
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/*
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\brief Check if polynomials are well defined.
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multiply values for vs and check if they are equal to value for v.
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epsilon has been computed.
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*/
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/* bool check_assignment(mon_eq const& m) const {
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rational r1 = m_variable_values[m.m_v];
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rational r2(1);
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for (auto w : m.vars()) {
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r2 *= m_variable_values[w];
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}
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return r1 == r2;
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}
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/*
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\brief Check if polynomials are well defined.
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multiply values for vs and check if they are equal to value for v.
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epsilon has been computed.
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*/
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/* bool check_assignment(mon_eq const& m) const {
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rational r1 = m_variable_values[m.m_v];
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rational r2(1);
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for (auto w : m.vars()) {
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r2 *= m_variable_values[w];
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}
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return r1 == r2;
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}
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bool check_assignments() const {
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s.get_model(m_variable_values);
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for (auto const& m : m_monics) {
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if (!check_assignment(m)) return false;
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}
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return true;
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}
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*/
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/**
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\brief one-shot nlsat check.
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A one shot checker is the least functionality that can
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enable non-linear reasoning.
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In addition to checking satisfiability we would also need
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to identify equalities in the model that should be assumed
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with the remaining solver.
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bool check_assignments() const {
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s.get_model(m_variable_values);
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for (auto const& m : m_monics) {
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if (!check_assignment(m)) return false;
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}
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return true;
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}
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*/
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/**
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\brief one-shot nlsat check.
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A one shot checker is the least functionality that can
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enable non-linear reasoning.
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In addition to checking satisfiability we would also need
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to identify equalities in the model that should be assumed
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with the remaining solver.
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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(lp::explanation& ex) {
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SASSERT(need_check());
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m_nlsat = alloc(nlsat::solver, m_limit, m_params, false);
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m_zero = alloc(scoped_anum, am());
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m_lp2nl.reset();
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vector<nlsat::assumption, false> core;
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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(lp::explanation& ex) {
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SASSERT(need_check());
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m_nlsat = alloc(nlsat::solver, m_limit, m_params, false);
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m_zero = alloc(scoped_anum, am());
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m_lp2nl.reset();
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vector<nlsat::assumption, false> core;
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// add linear inequalities from lra_solver
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for (lp::constraint_index ci : s.constraints().indices()) {
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add_constraint(ci);
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// add linear inequalities from lra_solver
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for (lp::constraint_index ci : s.constraints().indices()) {
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add_constraint(ci);
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}
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// add polynomial definitions.
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for (auto const& m : m_monics) {
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add_monic_eq(m);
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}
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// TBD: add variable bounds?
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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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}
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catch (z3_exception&) {
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if (m_limit.get_cancel_flag()) {
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r = l_undef;
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}
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// add polynomial definitions.
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for (auto const& m : m_monics) {
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add_monic_eq(m);
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else {
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throw;
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}
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// TBD: add variable bounds?
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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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}
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TRACE("arith", display(tout); m_nlsat->display(tout << r << "\n"););
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switch (r) {
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case l_true:
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break;
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case l_false:
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ex.clear();
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m_nlsat->get_core(core);
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for (auto c : core) {
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unsigned idx = static_cast<unsigned>(static_cast<imp*>(c) - this);
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ex.push_justification(idx, rational(1));
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TRACE("arith", tout << "ex: " << idx << "\n";);
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}
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catch (z3_exception&) {
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if (m_limit.get_cancel_flag()) {
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r = l_undef;
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}
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else {
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throw;
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}
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}
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TRACE("arith", display(tout); m_nlsat->display(tout << r << "\n"););
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switch (r) {
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case l_true:
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break;
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case l_false:
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ex.clear();
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m_nlsat->get_core(core);
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for (auto c : core) {
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unsigned idx = static_cast<unsigned>(static_cast<imp*>(c) - this);
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ex.push_justification(idx, rational(1));
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TRACE("arith", tout << "ex: " << idx << "\n";);
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}
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break;
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break;
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case l_undef:
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break;
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}
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return r;
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}
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case l_undef:
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break;
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}
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return r;
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}
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void add_monic_eq(mon_eq const& m) {
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polynomial::manager& pm = m_nlsat->pm();
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svector<polynomial::var> vars;
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void add_monic_eq(mon_eq const& m) {
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polynomial::manager& pm = m_nlsat->pm();
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svector<polynomial::var> vars;
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for (auto v : m.vars()) {
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vars.push_back(lp2nl(v));
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}
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polynomial::monomial_ref m1(pm.mk_monomial(vars.size(), vars.c_ptr()), pm);
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polynomial::monomial_ref m2(pm.mk_monomial(lp2nl(m.var()), 1), pm);
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polynomial::monomial * mls[2] = { m1, m2 };
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polynomial::scoped_numeral_vector coeffs(pm.m());
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coeffs.push_back(mpz(1));
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coeffs.push_back(mpz(-1));
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polynomial::polynomial_ref p(pm.mk_polynomial(2, coeffs.c_ptr(), mls), pm);
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polynomial::polynomial* ps[1] = { p };
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bool even[1] = { false };
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nlsat::literal lit = m_nlsat->mk_ineq_literal(nlsat::atom::kind::EQ, 1, ps, even);
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m_nlsat->mk_clause(1, &lit, nullptr);
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}
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void add_constraint(unsigned idx) {
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auto& c = s.constraints()[idx];
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auto& pm = m_nlsat->pm();
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auto k = c.kind();
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auto rhs = c.rhs();
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auto lhs = c.coeffs();
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auto sz = lhs.size();
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svector<polynomial::var> vars;
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rational den = denominator(rhs);
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for (auto kv : lhs) {
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vars.push_back(lp2nl(kv.second));
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den = lcm(den, denominator(kv.first));
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}
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vector<rational> coeffs;
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for (auto kv : lhs) {
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coeffs.push_back(den * kv.first);
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}
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rhs *= den;
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polynomial::polynomial_ref p(pm.mk_linear(sz, coeffs.c_ptr(), vars.c_ptr(), -rhs), 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;
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nlsat::assumption a = this + idx;
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switch (k) {
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case lp::lconstraint_kind::LE:
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lit = ~m_nlsat->mk_ineq_literal(nlsat::atom::kind::GT, 1, ps, is_even);
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break;
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case lp::lconstraint_kind::GE:
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lit = ~m_nlsat->mk_ineq_literal(nlsat::atom::kind::LT, 1, ps, is_even);
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break;
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case lp::lconstraint_kind::LT:
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lit = m_nlsat->mk_ineq_literal(nlsat::atom::kind::LT, 1, ps, is_even);
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break;
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case lp::lconstraint_kind::GT:
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lit = m_nlsat->mk_ineq_literal(nlsat::atom::kind::GT, 1, ps, is_even);
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break;
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case lp::lconstraint_kind::EQ:
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lit = m_nlsat->mk_ineq_literal(nlsat::atom::kind::EQ, 1, ps, is_even);
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break;
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default:
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lp_assert(false); // unreachable
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}
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m_nlsat->mk_clause(1, &lit, a);
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}
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bool is_int(lp::var_index v) {
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return s.var_is_int(v);
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}
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polynomial::var lp2nl(lp::var_index v) {
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polynomial::var r;
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if (!m_lp2nl.find(v, r)) {
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r = m_nlsat->mk_var(is_int(v));
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m_lp2nl.insert(v, r);
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TRACE("arith", tout << "j" << v << " := x" << r << "\n";);
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}
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return r;
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}
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nlsat::anum const& value(lp::var_index v) const {
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polynomial::var pv;
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if (m_lp2nl.find(v, pv))
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return m_nlsat->value(pv);
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else
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return *m_zero;
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}
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nlsat::anum_manager& am() {
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return m_nlsat->am();
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}
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std::ostream& display(std::ostream& out) const {
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for (auto m : m_monics) {
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out << "j" << m.var() << " = ";
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for (auto v : m.vars()) {
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vars.push_back(lp2nl(v));
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out << "j" << v << " ";
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}
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polynomial::monomial_ref m1(pm.mk_monomial(vars.size(), vars.c_ptr()), pm);
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polynomial::monomial_ref m2(pm.mk_monomial(lp2nl(m.var()), 1), pm);
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polynomial::monomial * mls[2] = { m1, m2 };
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polynomial::scoped_numeral_vector coeffs(pm.m());
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coeffs.push_back(mpz(1));
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coeffs.push_back(mpz(-1));
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polynomial::polynomial_ref p(pm.mk_polynomial(2, coeffs.c_ptr(), mls), pm);
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polynomial::polynomial* ps[1] = { p };
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bool even[1] = { false };
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nlsat::literal lit = m_nlsat->mk_ineq_literal(nlsat::atom::kind::EQ, 1, ps, even);
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m_nlsat->mk_clause(1, &lit, nullptr);
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out << "\n";
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}
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void add_constraint(unsigned idx) {
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||||
auto& c = s.constraints()[idx];
|
||||
auto& pm = m_nlsat->pm();
|
||||
auto k = c.kind();
|
||||
auto rhs = c.rhs();
|
||||
auto lhs = c.coeffs();
|
||||
auto sz = lhs.size();
|
||||
svector<polynomial::var> vars;
|
||||
rational den = denominator(rhs);
|
||||
for (auto kv : lhs) {
|
||||
vars.push_back(lp2nl(kv.second));
|
||||
den = lcm(den, denominator(kv.first));
|
||||
}
|
||||
vector<rational> coeffs;
|
||||
for (auto kv : lhs) {
|
||||
coeffs.push_back(den * kv.first);
|
||||
}
|
||||
rhs *= den;
|
||||
polynomial::polynomial_ref p(pm.mk_linear(sz, coeffs.c_ptr(), vars.c_ptr(), -rhs), pm);
|
||||
polynomial::polynomial* ps[1] = { p };
|
||||
bool is_even[1] = { false };
|
||||
nlsat::literal lit;
|
||||
nlsat::assumption a = this + idx;
|
||||
switch (k) {
|
||||
case lp::lconstraint_kind::LE:
|
||||
lit = ~m_nlsat->mk_ineq_literal(nlsat::atom::kind::GT, 1, ps, is_even);
|
||||
break;
|
||||
case lp::lconstraint_kind::GE:
|
||||
lit = ~m_nlsat->mk_ineq_literal(nlsat::atom::kind::LT, 1, ps, is_even);
|
||||
break;
|
||||
case lp::lconstraint_kind::LT:
|
||||
lit = m_nlsat->mk_ineq_literal(nlsat::atom::kind::LT, 1, ps, is_even);
|
||||
break;
|
||||
case lp::lconstraint_kind::GT:
|
||||
lit = m_nlsat->mk_ineq_literal(nlsat::atom::kind::GT, 1, ps, is_even);
|
||||
break;
|
||||
case lp::lconstraint_kind::EQ:
|
||||
lit = m_nlsat->mk_ineq_literal(nlsat::atom::kind::EQ, 1, ps, is_even);
|
||||
break;
|
||||
default:
|
||||
lp_assert(false); // unreachable
|
||||
}
|
||||
m_nlsat->mk_clause(1, &lit, a);
|
||||
}
|
||||
|
||||
bool is_int(lp::var_index v) {
|
||||
return s.var_is_int(v);
|
||||
}
|
||||
|
||||
|
||||
polynomial::var lp2nl(lp::var_index v) {
|
||||
polynomial::var r;
|
||||
if (!m_lp2nl.find(v, r)) {
|
||||
r = m_nlsat->mk_var(is_int(v));
|
||||
m_lp2nl.insert(v, r);
|
||||
TRACE("arith", tout << "j" << v << " := x" << r << "\n";);
|
||||
}
|
||||
return r;
|
||||
}
|
||||
|
||||
nlsat::anum const& value(lp::var_index v) const {
|
||||
polynomial::var pv;
|
||||
if (m_lp2nl.find(v, pv))
|
||||
return m_nlsat->value(pv);
|
||||
else
|
||||
return *m_zero;
|
||||
}
|
||||
|
||||
nlsat::anum_manager& am() {
|
||||
return m_nlsat->am();
|
||||
}
|
||||
|
||||
std::ostream& display(std::ostream& out) const {
|
||||
for (auto m : m_monics) {
|
||||
out << "j" << m.var() << " = ";
|
||||
for (auto v : m.vars()) {
|
||||
out << "j" << v << " ";
|
||||
}
|
||||
out << "\n";
|
||||
}
|
||||
return out;
|
||||
}
|
||||
};
|
||||
|
||||
solver::solver(lp::lar_solver& s, reslimit& lim, params_ref const& p) {
|
||||
m_imp = alloc(imp, s, lim, p);
|
||||
return out;
|
||||
}
|
||||
};
|
||||
|
||||
solver::~solver() {
|
||||
dealloc(m_imp);
|
||||
}
|
||||
solver::solver(lp::lar_solver& s, reslimit& lim, nla::core & nla_core, params_ref const& p) {
|
||||
m_imp = alloc(imp, s, lim, p, nla_core);
|
||||
}
|
||||
|
||||
void solver::add_monic(lp::var_index v, unsigned sz, lp::var_index const* vs) {
|
||||
m_imp->add(v, sz, vs);
|
||||
}
|
||||
solver::~solver() {
|
||||
dealloc(m_imp);
|
||||
}
|
||||
|
||||
lbool solver::check(lp::explanation& ex) {
|
||||
return m_imp->check(ex);
|
||||
}
|
||||
void solver::add_monic(lp::var_index v, unsigned sz, lp::var_index const* vs) {
|
||||
m_imp->add(v, sz, vs);
|
||||
}
|
||||
|
||||
bool solver::need_check() {
|
||||
return m_imp->need_check();
|
||||
}
|
||||
lbool solver::check(lp::explanation& ex) {
|
||||
return m_imp->check(ex);
|
||||
}
|
||||
|
||||
void solver::push() {
|
||||
m_imp->push();
|
||||
}
|
||||
bool solver::need_check() {
|
||||
return m_imp->need_check();
|
||||
}
|
||||
|
||||
void solver::pop(unsigned n) {
|
||||
m_imp->pop(n);
|
||||
}
|
||||
void solver::push() {
|
||||
m_imp->push();
|
||||
}
|
||||
|
||||
std::ostream& solver::display(std::ostream& out) const {
|
||||
return m_imp->display(out);
|
||||
}
|
||||
void solver::pop(unsigned n) {
|
||||
m_imp->pop(n);
|
||||
}
|
||||
|
||||
nlsat::anum const& solver::value(lp::var_index v) const {
|
||||
return m_imp->value(v);
|
||||
}
|
||||
std::ostream& solver::display(std::ostream& out) const {
|
||||
return m_imp->display(out);
|
||||
}
|
||||
|
||||
nlsat::anum_manager& solver::am() {
|
||||
return m_imp->am();
|
||||
}
|
||||
nlsat::anum const& solver::value(lp::var_index v) const {
|
||||
return m_imp->value(v);
|
||||
}
|
||||
|
||||
nlsat::anum_manager& solver::am() {
|
||||
return m_imp->am();
|
||||
}
|
||||
|
||||
}
|
||||
|
|
|
|||
|
|
@ -25,7 +25,7 @@ namespace nra {
|
|||
|
||||
public:
|
||||
|
||||
solver(lp::lar_solver& s, reslimit& lim, params_ref const& p = params_ref());
|
||||
solver(lp::lar_solver& s, reslimit& lim, nla::core & nla_core, params_ref const& p = params_ref());
|
||||
|
||||
~solver();
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue