mirror of
https://github.com/Z3Prover/z3
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551 lines
24 KiB
C++
551 lines
24 KiB
C++
/*++
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Copyright (c) 2021 Microsoft Corporation
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Module Name:
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polysat solver
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Abstract:
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Polynomial solver for modular arithmetic.
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Author:
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Nikolaj Bjorner (nbjorner) 2021-03-19
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Jakob Rath 2021-04-6
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--*/
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#pragma once
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#include "util/statistics.h"
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#include "util/params.h"
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#include "math/polysat/boolean.h"
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#include "math/polysat/conflict.h"
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#include "math/polysat/constraint.h"
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#include "math/polysat/constraint_manager.h"
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#include "math/polysat/clause_builder.h"
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#include "math/polysat/simplify_clause.h"
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#include "math/polysat/simplify.h"
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#include "math/polysat/restart.h"
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#include "math/polysat/ule_constraint.h"
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#include "math/polysat/justification.h"
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#include "math/polysat/linear_solver.h"
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#include "math/polysat/search_state.h"
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#include "math/polysat/assignment.h"
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#include "math/polysat/trail.h"
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#include "math/polysat/viable.h"
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#include "math/polysat/log.h"
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#include <limits>
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#include <optional>
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namespace polysat {
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struct config {
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uint64_t m_max_conflicts = std::numeric_limits<uint64_t>::max();
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uint64_t m_max_decisions = std::numeric_limits<uint64_t>::max();
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bool m_log_conflicts = false;
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};
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/**
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* A metric to evaluate lemmas from conflict analysis.
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* Lower is better.
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*
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* Comparison criterion:
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* - Lowest jump level has priority, because otherwise, some of the accumulated lemmas may still be false after backjumping.
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* - To break ties on jump level, choose clause with the fewest literals at its highest decision level;
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* to limit case splits.
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*/
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class lemma_score {
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unsigned m_jump_level;
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unsigned m_literals_at_max_level;
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public:
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lemma_score(unsigned jump_level, unsigned at_max_level)
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: m_jump_level(jump_level), m_literals_at_max_level(at_max_level)
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{ }
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unsigned jump_level() const { return m_jump_level; }
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unsigned literals_at_max_level() const { return m_literals_at_max_level; }
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static lemma_score max() {
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return {UINT_MAX, UINT_MAX};
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}
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bool operator==(lemma_score const& other) const {
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return m_jump_level == other.m_jump_level
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&& m_literals_at_max_level == other.m_literals_at_max_level;
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}
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bool operator!=(lemma_score const& other) const { return !operator==(other); }
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bool operator<(lemma_score const& other) const {
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return m_jump_level < other.m_jump_level
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|| (m_jump_level == other.m_jump_level && m_literals_at_max_level < other.m_literals_at_max_level);
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}
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bool operator>(lemma_score const& other) const { return other.operator<(*this); }
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bool operator<=(lemma_score const& other) const { return operator==(other) || operator<(other); }
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bool operator>=(lemma_score const& other) const { return operator==(other) || operator>(other); }
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std::ostream& display(std::ostream& out) const {
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return out << "jump_level=" << m_jump_level << " at_max_level=" << m_literals_at_max_level;
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}
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};
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inline std::ostream& operator<<(std::ostream& out, lemma_score const& ls) { return ls.display(out); }
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class solver {
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struct stats {
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unsigned m_num_iterations;
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unsigned m_num_decisions;
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unsigned m_num_propagations;
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unsigned m_num_conflicts;
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unsigned m_num_restarts;
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unsigned m_num_viable_fallback; ///< how often did we query the univariate solver
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void reset() { memset(this, 0, sizeof(*this)); }
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stats() { reset(); }
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};
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friend class assignment;
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friend class constraint;
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friend class ule_constraint;
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friend class umul_ovfl_constraint;
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friend class smul_fl_constraint;
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friend class op_constraint;
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friend class signed_constraint;
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friend class clause;
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friend class clause_builder;
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friend class conflict;
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friend class conflict_explainer;
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friend class simplify_clause;
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friend class simplify;
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friend class restart;
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friend class explainer;
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friend class inference_engine;
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friend class file_inference_logger;
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friend class forbidden_intervals;
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friend class linear_solver;
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friend class viable;
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friend class viable_fallback;
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friend class search_state;
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friend class num_pp;
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friend class lit_pp;
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friend class assignment_pp;
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friend class assignments_pp;
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friend class ex_polynomial_superposition;
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friend class free_variable_elimination;
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friend class saturation;
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friend class constraint_manager;
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friend class scoped_solverv;
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friend class test_polysat;
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friend class test_fi;
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friend struct inf_resolve_with_assignment;
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reslimit& m_lim;
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params_ref m_params;
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mutable scoped_ptr_vector<dd::pdd_manager> m_pdd;
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viable m_viable; // viable sets per variable
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viable_fallback m_viable_fallback; // fallback for viable, using bitblasting over univariate constraints
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linear_solver m_linear_solver;
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conflict m_conflict;
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simplify_clause m_simplify_clause;
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simplify m_simplify;
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restart m_restart;
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bool_var_manager m_bvars; // Map boolean variables to constraints
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var_queue m_free_pvars; // free poly vars
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stats m_stats;
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config m_config;
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// Per constraint state
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constraint_manager m_constraints;
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// Per variable information
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vector<rational> m_value; // assigned value
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vector<justification> m_justification; // justification for variable assignment
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vector<constraints> m_pwatch; // watch list datastructure into constraints.
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#ifndef NDEBUG
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std::optional<pvar> m_locked_wlist; // restrict watch list modification while it is being propagated
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bool m_is_propagating = false; // set to true during propagation
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bool m_is_solving = false; // set to true during solving
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#endif
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unsigned_vector m_activity;
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vector<pdd> m_vars;
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unsigned_vector m_size; // store size of variables (bit width)
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search_state m_search;
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unsigned m_qhead = 0; // next item to propagate (index into m_search)
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unsigned m_level = 0;
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svector<trail_instr_t> m_trail;
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unsigned_vector m_qhead_trail;
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constraints m_pwatch_queue;
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#if 0
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constraints m_pwatch_trail;
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#endif
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ptr_vector<clause> m_lemmas; ///< the non-asserting lemmas
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unsigned m_lemmas_qhead = 0;
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unsigned_vector m_base_levels; // External clients can push/pop scope.
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void push_qhead() {
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m_trail.push_back(trail_instr_t::qhead_i);
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m_qhead_trail.push_back(m_qhead);
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}
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void pop_qhead() {
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m_qhead = m_qhead_trail.back();
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m_qhead_trail.pop_back();
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}
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unsigned size(pvar v) const { return m_size[v]; }
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/**
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* undo trail operations for backtracking.
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* Each struct is a subclass of trail and implements undo().
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*/
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void del_var();
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dd::pdd_manager& sz2pdd(unsigned sz) const;
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dd::pdd_manager& var2pdd(pvar v) const;
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assignment const& assignment() const { return m_search.assignment(); }
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void push_level();
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void pop_levels(unsigned num_levels);
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void try_assign_eval(signed_constraint c);
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void assign_propagate(sat::literal lit, clause& reason);
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void assign_decision(sat::literal lit);
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void assign_eval(sat::literal lit);
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void activate_constraint(signed_constraint c);
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unsigned level(sat::literal lit, clause const& cl);
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void assign_propagate(pvar v, rational const& val);
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void assign_verify(pvar v, rational val, justification j);
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void assign_core(pvar v, rational const& val, justification const& j);
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bool is_assigned(pvar v) const { return !m_justification[v].is_unassigned(); }
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bool is_decision(pvar v) const { return m_justification[v].is_decision(); }
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bool should_search();
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void propagate(sat::literal lit);
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void propagate(pvar v);
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bool propagate(pvar v, constraint* c);
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bool propagate(sat::literal lit, clause& cl);
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void enqueue_pwatch(constraint* c);
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bool should_add_pwatch() const;
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void add_pwatch();
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void add_pwatch(constraint* c);
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void add_pwatch(constraint* c, pvar v);
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void erase_pwatch(pvar v, constraint* c);
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void erase_pwatch(constraint* c);
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void set_conflict_at_base_level() { m_conflict.init_at_base_level(); }
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void set_conflict(signed_constraint c) { m_conflict.init(c); }
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void set_conflict(clause& cl) { m_conflict.init(cl); }
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void set_conflict(pvar v, bool by_viable_fallback) { m_conflict.init(v, by_viable_fallback); }
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bool can_decide() const;
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bool can_bdecide() const;
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bool can_pdecide() const;
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void decide();
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void bdecide();
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void pdecide(pvar v);
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void linear_propagate();
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bool is_conflict() const { return !m_conflict.empty(); }
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bool at_base_level() const;
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unsigned base_level() const;
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void resolve_conflict();
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void revert_decision(pvar v);
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void revert_bool_decision(sat::literal lit);
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void backjump_and_learn(unsigned jump_level, clause& lemma);
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void backjump_and_learn(unsigned max_jump_level);
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std::optional<lemma_score> compute_lemma_score(clause const& lemma);
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// activity of variables based on standard VSIDS
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unsigned m_activity_inc = 128;
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unsigned m_variable_decay = 110;
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void inc_activity(pvar v);
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void decay_activity();
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void rescale_activity();
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void report_unsat();
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void learn_lemma(clause& lemma);
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void backjump(unsigned new_level);
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void add_clause(clause& clause);
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void add_clause(signed_constraint c1, bool is_redundant);
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void add_clause(signed_constraint c1, signed_constraint c2, bool is_redundant);
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void add_clause(signed_constraint c1, signed_constraint c2, signed_constraint c3, bool is_redundant);
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void add_clause(signed_constraint c1, signed_constraint c2, signed_constraint c3, signed_constraint c4, bool is_redundant);
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void add_clause(std::initializer_list<signed_constraint> cs, bool is_redundant);
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void add_clause(unsigned n, signed_constraint const* cs, bool is_redundant);
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// Create a clause without adding it to the solver.
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clause_ref mk_clause(signed_constraint c1, bool is_redundant);
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clause_ref mk_clause(signed_constraint c1, signed_constraint c2, bool is_redundant);
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clause_ref mk_clause(signed_constraint c1, signed_constraint c2, signed_constraint c3, bool is_redundant);
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clause_ref mk_clause(signed_constraint c1, signed_constraint c2, signed_constraint c3, signed_constraint c4, bool is_redundant);
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clause_ref mk_clause(signed_constraint c1, signed_constraint c2, signed_constraint c3, signed_constraint c4, signed_constraint c5, bool is_redundant);
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clause_ref mk_clause(std::initializer_list<signed_constraint> cs, bool is_redundant);
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clause_ref mk_clause(unsigned n, signed_constraint const* cs, bool is_redundant);
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signed_constraint lit2cnstr(sat::literal lit) const { return m_constraints.lookup(lit); }
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bool inc() { return m_lim.inc(); }
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bool invariant();
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static bool invariant(signed_constraints const& cs);
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bool wlist_invariant();
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bool assignment_invariant();
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bool verify_sat();
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bool can_propagate();
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void propagate();
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public:
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/**
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* to share chronology we pass an external trail stack.
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* every update to the solver is going to be retractable
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* by pushing an undo action on the trail stack.
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*/
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solver(reslimit& lim);
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~solver();
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/**
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* End-game satisfiability checker.
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*
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* Returns l_undef if the search cannot proceed.
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* Possible reasons:
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* - Resource limits are exhausted.
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*/
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lbool check_sat();
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/**
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* retrieve unsat core dependencies
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*/
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void unsat_core(dependency_vector& deps);
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/**
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* Return value / level of v in the current model (only meaningful if check_sat() returned l_true).
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*/
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rational get_value(pvar v) const { SASSERT(is_assigned(v)); return m_value[v]; }
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unsigned get_level(pvar v) const { SASSERT(is_assigned(v)); return m_justification[v].level(); }
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/**
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* Evaluate term under the current assignment.
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*/
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bool try_eval(pdd const& p, rational& out_value) const;
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/**
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* Add variable with bit-size.
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*/
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pvar add_var(unsigned sz);
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/**
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* Create polynomial terms
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*/
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pdd var(pvar v) { return m_vars[v]; }
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/**
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* Create terms for unsigned quot-rem
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*
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* Return tuple (quot, rem)
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*
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* The following properties are enforced:
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* b*quot + rem = a
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* ~ovfl(b*quot)
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* rem < b or b = 0
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*/
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std::pair<pdd, pdd> quot_rem(pdd const& a, pdd const& b) { return m_constraints.quot_rem(a, b); }
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/** Create expression for the logical right shift of p by q. */
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pdd lshr(pdd const& p, pdd const& q) { return m_constraints.lshr(p, q); }
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/** Create expression for the logical left shift of p by q. */
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pdd shl(pdd const& p, pdd const& q) { return m_constraints.shl(p, q); }
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/** Create expression for the bit-wise negation of p. */
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pdd bnot(pdd const& p) { return m_constraints.bnot(p); }
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/** Create expression for bit-wise and of p, q. */
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pdd band(pdd const& p, pdd const& q) { return m_constraints.band(p, q); }
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/** Create expression for bit-wise or of p, q. */
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pdd bor(pdd const& p, pdd const& q) { return m_constraints.bor(p, q); }
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/** Create expression for bit-wise xor of p, q. */
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pdd bxor(pdd const& p, pdd const& q) { return m_constraints.bxor(p, q); }
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/** Create expression for bit-wise nand of p, q. */
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pdd bnand(pdd const& p, pdd const& q) { return m_constraints.bnand(p, q); }
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/** Create expression for bit-wise nor of p, q. */
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pdd bnor(pdd const& p, pdd const& q) { return m_constraints.bnor(p, q); }
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/**
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* Create polynomial constant.
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*/
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pdd value(rational const& v, unsigned sz);
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/**
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* Apply current substitution to p.
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*/
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pdd subst(pdd const& p) const;
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/** Create constraints */
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signed_constraint eq(pdd const& p) { return m_constraints.eq(p); }
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signed_constraint diseq(pdd const& p) { return ~m_constraints.eq(p); }
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signed_constraint eq(pdd const& p, pdd const& q) { return eq(p - q); }
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signed_constraint diseq(pdd const& p, pdd const& q) { return diseq(p - q); }
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signed_constraint eq(pdd const& p, rational const& q) { return eq(p - q); }
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signed_constraint eq(pdd const& p, unsigned q) { return eq(p - q); }
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signed_constraint odd(pdd const& p) { return ~even(p); }
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signed_constraint even(pdd const& p) { return parity(p, 1); }
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signed_constraint parity(pdd const& p, unsigned k) { return eq(p*rational::power_of_two(p.manager().power_of_2() - k)); }
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signed_constraint diseq(pdd const& p, rational const& q) { return diseq(p - q); }
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signed_constraint diseq(pdd const& p, unsigned q) { return diseq(p - q); }
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signed_constraint ule(pdd const& p, pdd const& q) { return m_constraints.ule(p, q); }
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signed_constraint ule(pdd const& p, rational const& q) { return ule(p, p.manager().mk_val(q)); }
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signed_constraint ule(rational const& p, pdd const& q) { return ule(q.manager().mk_val(p), q); }
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signed_constraint ule(pdd const& p, int n) { return ule(p, rational(n)); }
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signed_constraint ule(int n, pdd const& p) { return ule(rational(n), p); }
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signed_constraint uge(pdd const& p, pdd const& q) { return ule(q, p); }
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signed_constraint uge(pdd const& p, rational const& q) { return ule(q, p); }
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signed_constraint ult(pdd const& p, pdd const& q) { return m_constraints.ult(p, q); }
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signed_constraint ult(pdd const& p, rational const& q) { return ult(p, p.manager().mk_val(q)); }
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signed_constraint ult(rational const& p, pdd const& q) { return ult(q.manager().mk_val(p), q); }
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signed_constraint ult(int p, pdd const& q) { return ult(rational(p), q); }
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signed_constraint ult(pdd const& p, int q) { return ult(p, rational(q)); }
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signed_constraint sle(pdd const& p, pdd const& q) { return m_constraints.sle(p, q); }
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signed_constraint slt(pdd const& p, pdd const& q) { return m_constraints.slt(p, q); }
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signed_constraint slt(pdd const& p, rational const& q) { return slt(p, p.manager().mk_val(q)); }
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signed_constraint slt(rational const& p, pdd const& q) { return slt(q.manager().mk_val(p), q); }
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signed_constraint slt(pdd const& p, int n) { return slt(p, rational(n)); }
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signed_constraint slt(int n, pdd const& p) { return slt(rational(n), p); }
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signed_constraint sgt(pdd const& p, pdd const& q) { return slt(q, p); }
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signed_constraint sgt(pdd const& p, int n) { return slt(n, p); }
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signed_constraint sgt(int n, pdd const& p) { return slt(p, n); }
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signed_constraint umul_ovfl(pdd const& p, pdd const& q) { return m_constraints.umul_ovfl(p, q); }
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signed_constraint umul_ovfl(rational const& p, pdd const& q) { return umul_ovfl(q.manager().mk_val(p), q); }
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signed_constraint smul_ovfl(pdd const& p, pdd const& q) { return m_constraints.smul_ovfl(p, q); }
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signed_constraint smul_udfl(pdd const& p, pdd const& q) { return m_constraints.smul_udfl(p, q); }
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signed_constraint bit(pdd const& p, unsigned i) { return m_constraints.bit(p, i); }
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/** Create and activate constraints */
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void add_eq(pdd const& p, dependency dep = null_dependency) { assign_eh(eq(p), dep); }
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void add_eq(pdd const& p, pdd const& q, dependency dep = null_dependency) { assign_eh(eq(p, q), dep); }
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void add_eq(pdd const& p, rational const& q, dependency dep = null_dependency) { assign_eh(eq(p, q), dep); }
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void add_eq(pdd const& p, unsigned q, dependency dep = null_dependency) { assign_eh(eq(p, q), dep); }
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void add_diseq(pdd const& p, dependency dep = null_dependency) { assign_eh(diseq(p), dep); }
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void add_diseq(pdd const& p, pdd const& q, dependency dep = null_dependency) { assign_eh(diseq(p, q), dep); }
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void add_diseq(pdd const& p, rational const& q, dependency dep = null_dependency) { assign_eh(diseq(p, q), dep); }
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void add_diseq(pdd const& p, unsigned q, dependency dep = null_dependency) { assign_eh(diseq(p, q), dep); }
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void add_ule(pdd const& p, pdd const& q, dependency dep = null_dependency) { assign_eh(ule(p, q), dep); }
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void add_ult(pdd const& p, pdd const& q, dependency dep = null_dependency) { assign_eh(ult(p, q), dep); }
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void add_sle(pdd const& p, pdd const& q, dependency dep = null_dependency) { assign_eh(sle(p, q), dep); }
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void add_slt(pdd const& p, pdd const& q, dependency dep = null_dependency) { assign_eh(slt(p, q), dep); }
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void add_umul_noovfl(pdd const& p, pdd const& q, dependency dep = null_dependency) { assign_eh(~umul_ovfl(p, q), dep); }
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void add_umul_ovfl(pdd const& p, pdd const& q, dependency dep = null_dependency) { assign_eh(umul_ovfl(p, q), dep); }
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void add_ule(pdd const& p, rational const& q, dependency dep = null_dependency) { add_ule(p, p.manager().mk_val(q), dep); }
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void add_ule(rational const& p, pdd const& q, dependency dep = null_dependency) { add_ule(q.manager().mk_val(p), q, dep); }
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void add_ule(pdd const& p, unsigned q, dependency dep = null_dependency) { add_ule(p, rational(q), dep); }
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void add_ule(unsigned p, pdd const& q, dependency dep = null_dependency) { add_ule(rational(p), q, dep); }
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void add_ult(pdd const& p, rational const& q, dependency dep = null_dependency) { add_ult(p, p.manager().mk_val(q), dep); }
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void add_ult(rational const& p, pdd const& q, dependency dep = null_dependency) { add_ult(q.manager().mk_val(p), q, dep); }
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void add_ult(pdd const& p, unsigned q, dependency dep = null_dependency) { add_ult(p, rational(q), dep); }
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void add_ult(unsigned p, pdd const& q, dependency dep = null_dependency) { add_ult(rational(p), q, dep); }
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void add_umul_noovfl(pdd const& p, rational const& q, dependency dep = null_dependency) { add_umul_noovfl(p, p.manager().mk_val(q), dep); }
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void add_umul_noovfl(rational const& p, pdd const& q, dependency dep = null_dependency) { add_umul_noovfl(q, p, dep); }
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void add_umul_noovfl(pdd const& p, unsigned q, dependency dep = null_dependency) { add_umul_noovfl(p, rational(q), dep); }
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void add_umul_noovfl(unsigned p, pdd const& q, dependency dep = null_dependency) { add_umul_noovfl(q, p, dep); }
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/**
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* Activate the constraint corresponding to the given boolean variable.
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* Note: to deactivate, use push/pop.
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*/
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void assign_eh(signed_constraint c, dependency dep);
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/**
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* Unit propagation accessible over API.
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*/
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lbool unit_propagate();
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/**
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* External context managment.
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* Adds so-called user-scope.
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*/
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void push();
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void pop(unsigned num_scopes = 1);
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std::ostream& display(std::ostream& out) const;
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void collect_statistics(statistics& st) const;
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params_ref const & params() const { return m_params; }
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void updt_params(params_ref const& p);
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config const& get_config() const { return m_config; }
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}; // class solver
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class assignments_pp { // TODO: can probably remove this now.
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solver const& s;
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public:
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assignments_pp(solver const& s): s(s) {}
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std::ostream& display(std::ostream& out) const;
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};
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class assignment_pp {
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solver const& s;
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pvar var;
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rational const& val;
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bool with_justification;
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public:
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assignment_pp(solver const& s, pvar var, rational const& val, bool with_justification = false): s(s), var(var), val(val), with_justification(with_justification) {}
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std::ostream& display(std::ostream& out) const;
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};
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class lit_pp {
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solver const& s;
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sat::literal lit;
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public:
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lit_pp(solver const& s, signed_constraint c): s(s), lit(c ? c.blit() : sat::null_literal) {}
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lit_pp(solver const& s, sat::literal lit): s(s), lit(lit) {}
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std::ostream& display(std::ostream& out) const;
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};
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/** Format value 'val' as member of the domain of 'var' */
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class num_pp {
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solver const& s;
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pvar var;
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rational const& val;
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public:
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num_pp(solver const& s, pvar var, rational const& val): s(s), var(var), val(val) {}
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std::ostream& display(std::ostream& out) const;
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};
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inline std::ostream& operator<<(std::ostream& out, solver const& s) { return s.display(out); }
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inline std::ostream& operator<<(std::ostream& out, num_pp const& v) { return v.display(out); }
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inline std::ostream& operator<<(std::ostream& out, lit_pp const& l) { return l.display(out); }
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inline std::ostream& operator<<(std::ostream& out, assignment_pp const& p) { return p.display(out); }
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inline std::ostream& operator<<(std::ostream& out, assignments_pp const& a) { return a.display(out); }
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}
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