mirror of
https://github.com/Z3Prover/z3
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458 lines
19 KiB
C++
458 lines
19 KiB
C++
/*++
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Copyright (c) 2020 Microsoft Corporation
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Module Name:
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arith_solver.h
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Abstract:
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Theory plugin for arithmetic
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Author:
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Nikolaj Bjorner (nbjorner) 2020-09-08
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--*/
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#pragma once
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#include "util/obj_pair_set.h"
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#include "ast/ast_trail.h"
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#include "ast/arith_decl_plugin.h"
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#include "math/lp/lp_solver.h"
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#include "math/lp/lp_primal_simplex.h"
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#include "math/lp/lp_dual_simplex.h"
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#include "math/lp/indexed_value.h"
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#include "math/lp/lar_solver.h"
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#include "math/lp/nla_solver.h"
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#include "math/lp/lp_types.h"
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#include "math/lp/lp_api.h"
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#include "math/polynomial/algebraic_numbers.h"
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#include "math/polynomial/polynomial.h"
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#include "sat/smt/sat_th.h"
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namespace euf {
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class solver;
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}
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namespace arith {
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typedef ptr_vector<lp_api::bound<sat::literal>> lp_bounds;
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typedef lp::var_index lpvar;
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typedef euf::theory_var theory_var;
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typedef euf::theory_id theory_id;
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typedef euf::enode enode;
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typedef euf::enode_pair enode_pair;
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typedef sat::literal literal;
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typedef sat::bool_var bool_var;
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typedef sat::literal_vector literal_vector;
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typedef lp_api::bound<sat::literal> api_bound;
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class solver : public euf::th_euf_solver {
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struct scope {
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unsigned m_bounds_lim;
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unsigned m_idiv_lim;
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unsigned m_asserted_qhead;
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unsigned m_asserted_lim;
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unsigned m_underspecified_lim;
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expr* m_not_handled;
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};
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class resource_limit : public lp::lp_resource_limit {
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solver& m_imp;
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public:
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resource_limit(solver& i) : m_imp(i) { }
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bool get_cancel_flag() override { return !m_imp.m.inc(); }
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};
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struct var_value_eq {
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solver& m_th;
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var_value_eq(solver& th) :m_th(th) {}
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bool operator()(theory_var v1, theory_var v2) const {
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if (m_th.is_int(v1) != m_th.is_int(v2)) {
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return false;
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}
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return m_th.is_eq(v1, v2);
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}
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};
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struct var_value_hash {
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solver& m_th;
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var_value_hash(solver& th) :m_th(th) {}
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unsigned operator()(theory_var v) const {
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if (m_th.use_nra_model()) {
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return m_th.is_int(v);
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}
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else {
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return (unsigned)std::hash<lp::impq>()(m_th.get_ivalue(v));
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}
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}
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};
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int_hashtable<var_value_hash, var_value_eq> m_model_eqs;
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bool m_new_eq { false };
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// temporary values kept during internalization
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struct internalize_state {
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expr_ref_vector m_terms;
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vector<rational> m_coeffs;
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svector<theory_var> m_vars;
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rational m_offset;
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ptr_vector<expr> m_to_ensure_enode, m_to_ensure_var;
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internalize_state(ast_manager& m) : m_terms(m) {}
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void reset() {
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m_terms.reset();
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m_coeffs.reset();
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m_offset.reset();
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m_vars.reset();
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m_to_ensure_enode.reset();
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m_to_ensure_var.reset();
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}
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};
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scoped_ptr_vector<internalize_state> m_internalize_states;
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unsigned m_internalize_head = 0;
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class scoped_internalize_state {
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solver& m_imp;
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internalize_state& m_st;
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internalize_state& push_internalize(solver& i) {
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if (i.m_internalize_head == i.m_internalize_states.size()) {
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i.m_internalize_states.push_back(alloc(internalize_state, i.m));
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}
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internalize_state& st = *i.m_internalize_states[i.m_internalize_head++];
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st.reset();
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return st;
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}
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public:
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scoped_internalize_state(solver& i) : m_imp(i), m_st(push_internalize(i)) {}
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~scoped_internalize_state() { --m_imp.m_internalize_head; }
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expr_ref_vector& terms() { return m_st.m_terms; }
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vector<rational>& coeffs() { return m_st.m_coeffs; }
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svector<theory_var>& vars() { return m_st.m_vars; }
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rational& offset() { return m_st.m_offset; }
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ptr_vector<expr>& to_ensure_enode() { return m_st.m_to_ensure_enode; }
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ptr_vector<expr>& to_ensure_var() { return m_st.m_to_ensure_var; }
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void push(expr* e, rational c) { m_st.m_terms.push_back(e); m_st.m_coeffs.push_back(c); }
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void set_back(unsigned i) {
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if (terms().size() == i + 1) return;
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terms()[i] = terms().back();
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coeffs()[i] = coeffs().back();
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terms().pop_back();
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coeffs().pop_back();
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}
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};
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typedef vector<std::pair<rational, lpvar>> var_coeffs;
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vector<rational> m_columns;
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var_coeffs m_left_side; // constraint left side
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lpvar m_one_var = UINT_MAX;
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lpvar m_zero_var = UINT_MAX;
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lpvar m_rone_var = UINT_MAX;
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lpvar m_rzero_var = UINT_MAX;
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enum constraint_source {
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inequality_source,
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equality_source,
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definition_source,
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null_source
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};
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svector<constraint_source> m_constraint_sources;
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svector<literal> m_inequalities; // asserted rows corresponding to inequality literals.
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svector<euf::enode_pair> m_equalities; // asserted rows corresponding to equalities.
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svector<theory_var> m_definitions; // asserted rows corresponding to definitions
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svector<std::pair<euf::th_eq, bool>> m_delayed_eqs;
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literal_vector m_asserted;
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expr* m_not_handled{ nullptr };
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ptr_vector<app> m_underspecified;
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ptr_vector<expr> m_idiv_terms;
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vector<ptr_vector<api_bound> > m_use_list; // bounds where variables are used.
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// attributes for incremental version:
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u_map<api_bound*> m_bool_var2bound;
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vector<lp_bounds> m_bounds;
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unsigned_vector m_unassigned_bounds;
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unsigned_vector m_bounds_trail;
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unsigned m_asserted_qhead = 0;
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svector<std::pair<theory_var, theory_var> > m_assume_eq_candidates;
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unsigned m_assume_eq_head{ 0 };
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lp::u_set m_tmp_var_set;
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unsigned m_num_conflicts{ 0 };
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lp_api::stats m_stats;
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svector<scope> m_scopes;
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// non-linear arithmetic
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scoped_ptr<nla::solver> m_nla;
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scoped_ptr<scoped_anum> m_a1, m_a2;
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// integer arithmetic
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scoped_ptr<lp::int_solver> m_lia;
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scoped_ptr<lp::lar_solver> m_solver;
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resource_limit m_resource_limit;
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lp_bounds m_new_bounds;
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symbol m_farkas;
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lp::lp_bound_propagator<solver> m_bp;
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mutable vector<std::pair<lp::tv, rational>> m_todo_terms;
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// lemmas
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lp::explanation m_explanation;
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vector<nla::lemma> m_nla_lemma_vector;
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literal_vector m_core, m_core2;
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svector<enode_pair> m_eqs;
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vector<parameter> m_params;
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nla::lemma m_lemma;
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arith_util a;
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bool is_int(theory_var v) const { return is_int(var2enode(v)); }
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bool is_int(euf::enode* n) const { return a.is_int(n->get_expr()); }
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bool is_real(theory_var v) const { return is_real(var2enode(v)); }
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bool is_real(euf::enode* n) const { return a.is_real(n->get_expr()); }
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bool is_bool(theory_var v) const { return is_bool(var2enode(v)); }
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bool is_bool(euf::enode* n) const { return m.is_bool(n->get_expr()); }
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// internalize
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bool m_internalize_initialized { false };
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void init_internalize();
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lpvar add_const(int c, lpvar& var, bool is_int);
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lpvar get_one(bool is_int);
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lpvar get_zero(bool is_int);
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void ensure_nla();
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void found_unsupported(expr* n);
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void found_underspecified(expr* n);
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void linearize_term(expr* term, scoped_internalize_state& st);
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void linearize_ineq(expr* lhs, expr* rhs, scoped_internalize_state& st);
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void linearize(scoped_internalize_state& st);
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void add_eq_constraint(lp::constraint_index index, enode* n1, enode* n2);
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void add_ineq_constraint(lp::constraint_index index, literal lit);
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void add_def_constraint(lp::constraint_index index);
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void add_def_constraint(lp::constraint_index index, theory_var v);
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void add_def_constraint_and_equality(lpvar vi, lp::lconstraint_kind kind, const rational& bound);
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void internalize_args(app* t, bool force = false);
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theory_var internalize_power(app* t, app* n, unsigned p);
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theory_var internalize_mul(app* t);
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theory_var internalize_def(expr* term);
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theory_var internalize_def(expr* term, scoped_internalize_state& st);
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theory_var internalize_linearized_def(expr* term, scoped_internalize_state& st);
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void init_left_side(scoped_internalize_state& st);
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bool internalize_term(expr* term);
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bool internalize_atom(expr* atom);
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bool is_unit_var(scoped_internalize_state& st);
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bool is_one(scoped_internalize_state& st);
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bool is_zero(scoped_internalize_state& st);
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enode* mk_enode(expr* e);
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lpvar register_theory_var_in_lar_solver(theory_var v);
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theory_var mk_evar(expr* e);
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bool has_var(expr* e);
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bool reflect(expr* n) const;
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lpvar get_lpvar(theory_var v) const;
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lp::tv get_tv(theory_var v) const;
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// axioms
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void mk_div_axiom(expr* p, expr* q);
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void mk_to_int_axiom(app* n);
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void mk_is_int_axiom(expr* n);
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void mk_idiv_mod_axioms(expr* p, expr* q);
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void mk_rem_axiom(expr* dividend, expr* divisor);
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void mk_bound_axioms(api_bound& b);
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void mk_bound_axiom(api_bound& b1, api_bound& b2);
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void mk_power0_axioms(app* t, app* n);
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void flush_bound_axioms();
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// bounds
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struct compare_bounds {
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bool operator()(api_bound* a1, api_bound* a2) const { return a1->get_value() < a2->get_value(); }
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};
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typedef lp_bounds::iterator iterator;
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lp_bounds::iterator first(
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lp_api::bound_kind kind,
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iterator it,
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iterator end);
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lp_bounds::iterator next_inf(
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api_bound* a1,
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lp_api::bound_kind kind,
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iterator it,
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iterator end,
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bool& found_compatible);
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lp_bounds::iterator next_sup(
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api_bound* a1,
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lp_api::bound_kind kind,
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iterator it,
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iterator end,
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bool& found_compatible);
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void propagate_eqs(lp::tv t, lp::constraint_index ci, lp::lconstraint_kind k, api_bound& b, rational const& value);
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void propagate_basic_bounds(unsigned qhead);
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void propagate_bounds_with_lp_solver();
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void propagate_bound(literal lit, api_bound& b);
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void propagate_lp_solver_bound(const lp::implied_bound& be);
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void refine_bound(theory_var v, const lp::implied_bound& be);
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literal is_bound_implied(lp::lconstraint_kind k, rational const& value, api_bound const& b) const;
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void assert_bound(bool is_true, api_bound& b);
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void mk_eq_axiom(bool is_eq, euf::th_eq const& eq);
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void mk_diseq_axiom(euf::th_eq const& eq);
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void assert_idiv_mod_axioms(theory_var u, theory_var v, theory_var w, rational const& r);
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api_bound* mk_var_bound(sat::literal lit, theory_var v, lp_api::bound_kind bk, rational const& bound);
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lp::lconstraint_kind bound2constraint_kind(bool is_int, lp_api::bound_kind bk, bool is_true);
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void fixed_var_eh(theory_var v1, lp::constraint_index ci1, lp::constraint_index ci2, rational const& bound);
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bool set_upper_bound(lp::tv t, lp::constraint_index ci, rational const& v) { return set_bound(t, ci, v, false); }
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bool set_lower_bound(lp::tv t, lp::constraint_index ci, rational const& v) { return set_bound(t, ci, v, true); }
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bool set_bound(lp::tv tv, lp::constraint_index ci, rational const& v, bool is_lower);
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typedef std::pair<lp::constraint_index, rational> constraint_bound;
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vector<constraint_bound> m_lower_terms;
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vector<constraint_bound> m_upper_terms;
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vector<constraint_bound> m_history;
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bool can_get_value(theory_var v) const {
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return is_registered_var(v) && m_model_is_initialized;
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}
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vector<rational> m_fixed_values;
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map<rational, theory_var, rational::hash_proc, rational::eq_proc> m_value2var;
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struct undo_value;
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void register_fixed_var(theory_var v, rational const& value);
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// solving
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void report_equality_of_fixed_vars(unsigned vi1, unsigned vi2);
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void reserve_bounds(theory_var v);
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void updt_unassigned_bounds(theory_var v, int inc);
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void pop_core(unsigned n) override;
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void push_core() override;
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void del_bounds(unsigned old_size);
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bool all_zeros(vector<rational> const& v) const;
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bound_prop_mode propagation_mode() const;
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bool is_registered_var(theory_var v) const;
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void ensure_column(theory_var v);
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lp::impq get_ivalue(theory_var v) const;
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rational get_value(theory_var v) const;
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void random_update();
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bool assume_eqs();
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bool delayed_assume_eqs();
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bool is_eq(theory_var v1, theory_var v2);
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bool use_nra_model();
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lbool make_feasible();
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bool check_delayed_eqs();
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lbool check_lia();
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lbool check_nla();
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bool is_infeasible() const;
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nlsat::anum const& nl_value(theory_var v, scoped_anum& r) const;
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bool has_bound(lpvar vi, lp::constraint_index& ci, rational const& bound, bool is_lower);
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bool has_lower_bound(lpvar vi, lp::constraint_index& ci, rational const& bound);
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bool has_upper_bound(lpvar vi, lp::constraint_index& ci, rational const& bound);
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/*
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* Facility to put a small box around integer variables used in branch and bounds.
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*/
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struct bound_info {
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rational m_offset;
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unsigned m_range;
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bound_info() {}
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bound_info(rational const& o, unsigned r) :m_offset(o), m_range(r) {}
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};
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unsigned m_bounded_range_idx; // current size of bounded range.
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literal m_bounded_range_lit; // current bounded range literal
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expr_ref_vector m_bound_terms; // predicates used for bounds
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expr_ref m_bound_predicate;
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obj_map<expr, expr*> m_predicate2term;
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obj_map<expr, bound_info> m_term2bound_info;
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bool m_model_is_initialized = false;
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unsigned small_lemma_size() const { return get_config().m_arith_small_lemma_size; }
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bool propagate_eqs() const { return get_config().m_arith_propagate_eqs && m_num_conflicts < get_config().m_arith_propagation_threshold; }
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bool should_propagate() const { return bound_prop_mode::BP_NONE != propagation_mode(); }
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bool should_refine_bounds() const { return bound_prop_mode::BP_REFINE == propagation_mode() && s().at_search_lvl(); }
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unsigned init_range() const { return 5; }
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unsigned max_range() const { return 20; }
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void reset_evidence();
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bool check_idiv_bounds();
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bool is_bounded(expr* n);
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app_ref mk_bound(lp::lar_term const& term, rational const& k, bool lower_bound);
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app_ref mk_bound(lp::lar_term const& term, rational const& k, bool lower_bound, rational& offset, expr_ref& t);
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literal mk_eq(lp::lar_term const& term, rational const& offset);
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rational gcd_reduce(u_map<rational>& coeffs);
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app_ref mk_term(lp::lar_term const& term, bool is_int);
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app_ref coeffs2app(u_map<rational> const& coeffs, rational const& offset, bool is_int);
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void term2coeffs(lp::lar_term const& term, u_map<rational>& coeffs, rational const& coeff);
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void term2coeffs(lp::lar_term const& term, u_map<rational>& coeffs);
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void get_infeasibility_explanation_and_set_conflict();
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void set_conflict();
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void set_conflict_or_lemma(literal_vector const& core, bool is_conflict);
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void set_evidence(lp::constraint_index idx, literal_vector& core, svector<enode_pair>& eqs);
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void assign(literal lit, literal_vector const& core, svector<enode_pair> const& eqs, vector<parameter> const& params);
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void false_case_of_check_nla(const nla::lemma& l);
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void dbg_finalize_model(model& mdl);
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public:
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solver(euf::solver& ctx, theory_id id);
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~solver() override;
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bool is_external(bool_var v) override { return false; }
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void get_antecedents(literal l, sat::ext_justification_idx idx, literal_vector& r, bool probing) override;
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void asserted(literal l) override;
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sat::check_result check() override;
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std::ostream& display(std::ostream& out) const override;
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std::ostream& display_justification(std::ostream& out, sat::ext_justification_idx idx) const override;
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std::ostream& display_constraint(std::ostream& out, sat::ext_constraint_idx idx) const override;
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void collect_statistics(statistics& st) const override;
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euf::th_solver* clone(euf::solver& ctx) override;
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bool use_diseqs() const override { return true; }
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void new_eq_eh(euf::th_eq const& eq) override;
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void new_diseq_eh(euf::th_eq const& de) override;
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bool unit_propagate() override;
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void init_model() override;
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void finalize_model(model& mdl) override { DEBUG_CODE(dbg_finalize_model(mdl);); }
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void add_value(euf::enode* n, model& mdl, expr_ref_vector& values) override;
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bool add_dep(euf::enode* n, top_sort<euf::enode>& dep) override;
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sat::literal internalize(expr* e, bool sign, bool root, bool learned) override;
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void internalize(expr* e, bool redundant) override;
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void eq_internalized(euf::enode* n) override;
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void apply_sort_cnstr(euf::enode* n, sort* s) override {}
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bool is_shared(theory_var v) const override;
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lbool get_phase(bool_var v) override;
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bool include_func_interp(func_decl* f) const override;
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bool enable_ackerman_axioms(euf::enode* n) const override { return !a.is_add(n->get_expr()); }
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// bounds and equality propagation callbacks
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lp::lar_solver& lp() { return *m_solver; }
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lp::lar_solver const& lp() const { return *m_solver; }
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bool is_equal(theory_var x, theory_var y) const;
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bool add_eq(lpvar u, lpvar v, lp::explanation const& e, bool is_fixed);
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void consume(rational const& v, lp::constraint_index j);
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bool bound_is_interesting(unsigned vi, lp::lconstraint_kind kind, const rational& bval) const;
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};
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}
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