/*++ Copyright (c) 2021 Microsoft Corporation Module Name: Polysat core saturation Author: Nikolaj Bjorner (nbjorner) 2021-03-19 Jakob Rath 2021-04-6 --*/ #pragma once #include "math/polysat/clause_builder.h" #include "math/polysat/conflict.h" #include "math/polysat/variable_elimination.h" namespace polysat { /** * Introduce lemmas that derive new (simpler) constraints from the current conflict and partial model. */ class saturation { friend class parity_tracker; friend class conflict_resolver; solver& s; clause_builder m_lemma; char const* m_rule = nullptr; parity_tracker m_parity_tracker; unsigned_vector m_occ; unsigned_vector m_occ_cnt; void set_rule(char const* r) { m_rule = r; } bool is_non_overflow(pdd const& x, pdd const& y, signed_constraint& c); signed_constraint ineq(bool strict, pdd const& lhs, pdd const& rhs); void log_lemma(pvar v, conflict& core); bool propagate(pvar v, conflict& core, signed_constraint crit1, signed_constraint c); bool propagate(pvar v, conflict& core, inequality const& crit1, signed_constraint c); bool propagate(pvar v, conflict& core, signed_constraint c); bool add_conflict(pvar v, conflict& core, inequality const& crit1, signed_constraint c); bool add_conflict(pvar v, conflict& core, inequality const& crit1, inequality const& crit2, signed_constraint c); bool try_ugt_x(pvar v, conflict& core, inequality const& c); bool try_ugt_y(pvar v, conflict& core, inequality const& c); bool try_ugt_y(pvar v, conflict& core, inequality const& l_y, inequality const& yx_l_zx, pdd const& x, pdd const& z); bool try_y_l_ax_and_x_l_z(pvar x, conflict& core, inequality const& c); bool try_y_l_ax_and_x_l_z(pvar x, conflict& core, inequality const& x_l_z, inequality const& y_l_ax, pdd const& a, pdd const& y); bool try_ugt_z(pvar z, conflict& core, inequality const& c); bool try_ugt_z(pvar z, conflict& core, inequality const& x_l_z0, inequality const& yz_l_xz, pdd const& y, pdd const& x); bool try_parity(pvar x, conflict& core, inequality const& axb_l_y); bool try_parity_diseq(pvar x, conflict& core, inequality const& axb_l_y); bool try_mul_bounds(pvar x, conflict& core, inequality const& axb_l_y); bool try_factor_equality(pvar x, conflict& core, inequality const& a_l_b); bool try_infer_equality(pvar x, conflict& core, inequality const& a_l_b); bool try_mul_eq_1(pvar x, conflict& core, inequality const& axb_l_y); bool try_mul_odd(pvar x, conflict& core, inequality const& axb_l_y); bool try_mul_eq_bound(pvar x, conflict& core, inequality const& axb_l_y); bool try_transitivity(pvar x, conflict& core, inequality const& axb_l_y); bool try_tangent(pvar v, conflict& core, inequality const& c); bool try_add_overflow_bound(pvar x, conflict& core, inequality const& axb_l_y); bool try_add_mul_bound(pvar x, conflict& core, inequality const& axb_l_y); bool try_add_mul_bound2(pvar x, conflict& core, inequality const& axb_l_y); bool try_infer_parity_equality(pvar x, conflict& core, inequality const& a_l_b); bool try_div_monotonicity(conflict& core); rational round(rational const& M, rational const& x); bool eval_round(rational const& M, pdd const& p, rational& r); bool extract_linear_form(pdd const& q, pvar& y, rational& a, rational& b); bool extract_bilinear_form(pvar x, pdd const& p, pvar& y, rational& a, rational& b, rational& c, rational& d); bool adjust_bound(rational const& x_min, rational const& x_max, rational const& y0, rational const& M, rational const& a, rational const& b, rational const& c, rational& d, rational* x_split); bool update_min(rational& y_min, rational const& x_min, rational const& x_max, rational const& a, rational const& b, rational const& c, rational const& d); bool update_max(rational& y_max, rational const& x_min, rational const& x_max, rational const& a, rational const& b, rational const& c, rational const& d); bool update_bounds_for_xs(rational const& x_min, rational const& x_max, rational& y_min, rational& y_max, rational const& y0, rational const& a1, rational const& b1, rational const& c1, rational const& d1, rational const& a2, rational const& b2, rational const& c2, rational const& d2, rational const& M, inequality const& a_l_b); void fix_values(pvar x, pvar y, pdd const& p); void fix_values(pvar y, pdd const& p); // c := lhs ~ v // where ~ is < or <= bool is_l_v(pvar v, inequality const& c); // c := v ~ rhs bool is_g_v(pvar v, inequality const& c); // c := x ~ Y bool is_x_l_Y(pvar x, inequality const& i, pdd& y); // c := Y ~ x bool is_Y_l_x(pvar x, inequality const& i, pdd& y); // c := X*y ~ X*Z bool is_Xy_l_XZ(pvar y, inequality const& c, pdd& x, pdd& z); bool verify_Xy_l_XZ(pvar y, inequality const& c, pdd const& x, pdd const& z); // c := Y ~ Ax bool is_Y_l_Ax(pvar x, inequality const& c, pdd& a, pdd& y); bool verify_Y_l_Ax(pvar x, inequality const& c, pdd const& a, pdd const& y); // c := Ax ~ Y bool is_Ax_l_Y(pvar x, inequality const& c, pdd& a, pdd& y); bool verify_Ax_l_Y(pvar x, inequality const& c, pdd const& a, pdd const& y); // c := Ax + B ~ Y bool is_AxB_l_Y(pvar x, inequality const& c, pdd& a, pdd& b, pdd& y); bool verify_AxB_l_Y(pvar x, inequality const& c, pdd const& a, pdd const& b, pdd const& y); // c := Y ~ Ax + B bool is_Y_l_AxB(pvar x, inequality const& c, pdd& y, pdd& a, pdd& b); bool verify_Y_l_AxB(pvar x, inequality const& c, pdd const& y, pdd const& a, pdd& b); // c := Ax + B ~ Y, val(Y) = 0 bool is_AxB_eq_0(pvar x, inequality const& c, pdd& a, pdd& b, pdd& y); bool verify_AxB_eq_0(pvar x, inequality const& c, pdd const& a, pdd const& b, pdd const& y); // c := Ax + B != Y, val(Y) = 0 bool is_AxB_diseq_0(pvar x, inequality const& c, pdd& a, pdd& b, pdd& y); // c := Y*X ~ z*X bool is_YX_l_zX(pvar z, inequality const& c, pdd& x, pdd& y); bool verify_YX_l_zX(pvar z, inequality const& c, pdd const& x, pdd const& y); // c := xY <= xZ bool is_xY_l_xZ(pvar x, inequality const& c, pdd& y, pdd& z); // xy := x * Y bool is_xY(pvar x, pdd const& xy, pdd& y); // a * b does not overflow bool is_non_overflow(pdd const& a, pdd const& b); // p := coeff*x*y where coeff_x = coeff*x, x a variable bool is_coeffxY(pdd const& coeff_x, pdd const& p, pdd& y); bool is_add_overflow(pvar x, inequality const& i, pdd& y, bool& is_minus); bool has_upper_bound(pvar x, conflict& core, rational& bound, vector& x_ge_bound); bool has_lower_bound(pvar x, conflict& core, rational& bound, vector& x_le_bound); // determine min/max parity of polynomial unsigned min_parity(pdd const& p, vector& explain); unsigned max_parity(pdd const& p, vector& explain); unsigned min_parity(pdd const& p) { vector ex; return min_parity(p, ex); } unsigned max_parity(pdd const& p) { vector ex; return max_parity(p, ex); } lbool get_multiple(const pdd& p1, const pdd& p2, pdd& out); bool is_forced_eq(pdd const& p, rational const& val); bool is_forced_eq(pdd const& p, int i) { return is_forced_eq(p, rational(i)); } bool is_forced_diseq(pdd const& p, int i, signed_constraint& c); bool is_forced_odd(pdd const& p, signed_constraint& c); bool is_forced_false(signed_constraint const& sc); bool is_forced_true(signed_constraint const& sc); bool try_inequality(pvar v, inequality const& i, conflict& core); bool try_umul_ovfl(pvar v, signed_constraint c, conflict& core); bool try_umul_ovfl_noovfl(pvar v, signed_constraint c, conflict& core); bool try_umul_noovfl_lo(pvar v, signed_constraint c, conflict& core); bool try_umul_noovfl_bounds(pvar v, signed_constraint c, conflict& core); bool try_umul_ovfl_bounds(pvar v, signed_constraint c, conflict& core); bool try_op(pvar v, signed_constraint c, conflict& core); public: saturation(solver& s); void perform(pvar v, conflict& core); bool perform(pvar v, signed_constraint sc, conflict& core); }; /* * TODO: we could resolve constraints in cjust[v] against each other to * obtain stronger propagation. Example: * (x + 1)*P = 0 and (x + 1)*Q = 0, where gcd(P,Q) = 1, then we have x + 1 = 0. * We refer to this process as narrowing. * In general form it can rely on factoring. * Root finding can further prune viable. */ }