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z3-z3-4.12.6.src.sat.smt.array_solver.h Maven / Gradle / Ivy
/*++
Copyright (c) 2020 Microsoft Corporation
Module Name:
array_solver.h
Abstract:
Theory plugin for arrays
Author:
Nikolaj Bjorner (nbjorner) 2020-09-08
--*/
#pragma once
#include "ast/ast_trail.h"
#include "sat/smt/sat_th.h"
#include "ast/array_decl_plugin.h"
namespace euf {
class solver;
}
namespace array {
class solver : public euf::th_euf_solver {
typedef euf::theory_var theory_var;
typedef euf::theory_id theory_id;
typedef sat::literal literal;
typedef sat::bool_var bool_var;
typedef sat::literal_vector literal_vector;
typedef union_find array_union_find;
struct stats {
unsigned m_num_store_axiom, m_num_extensionality_axiom;
unsigned m_num_eq_splits, m_num_congruence_axiom;
unsigned m_num_select_store_axiom, m_num_select_as_array_axiom, m_num_select_map_axiom;
unsigned m_num_select_const_axiom, m_num_select_store_axiom_delayed;
unsigned m_num_default_store_axiom, m_num_default_map_axiom;
unsigned m_num_default_const_axiom, m_num_default_as_array_axiom;
unsigned m_num_select_lambda_axiom;
void reset() { memset(this, 0, sizeof(*this)); }
stats() { reset(); }
};
// void log_drat(array_justification const& c);
struct var_data {
bool m_prop_upward = false ;
bool m_has_default = false;
euf::enode_vector m_lambdas; // equivalent nodes that have beta reduction properties
euf::enode_vector m_parent_lambdas; // parents that have beta reduction properties
euf::enode_vector m_parent_selects; // parents that use array in select position
};
array_util a;
stats m_stats;
scoped_ptr_vector m_var_data;
ast2ast_trailmap m_sort2epsilon;
ast2ast_trailmap m_sort2diag;
obj_map m_sort2diff;
array_union_find m_find;
theory_var find(theory_var v) { return m_find.find(v); }
theory_var find(euf::enode* n) { return find(n->get_th_var(get_id())); }
func_decl_ref_vector const& sort2diff(sort* s);
// internalize
bool visit(expr* e) override;
bool visited(expr* e) override;
bool post_visit(expr* e, bool sign, bool root) override;
void ensure_var(euf::enode* n);
void internalize_eh(euf::enode* n);
void internalize_lambda_eh(euf::enode* n);
// axioms
struct axiom_record {
enum class kind_t {
is_store,
is_select,
is_extensionality,
is_default,
is_congruence
};
enum class state_t {
is_new,
is_delayed,
is_applied
};
kind_t m_kind;
state_t m_state = state_t::is_new;
euf::enode* n;
euf::enode* select;
axiom_record(kind_t k, euf::enode* n, euf::enode* select = nullptr) : m_kind(k), n(n), select(select) {}
bool is_delayed() const { return m_state == state_t::is_delayed; }
bool is_applied() const { return m_state == state_t::is_applied; }
void set_new() { m_state = state_t::is_new; }
void set_applied() { m_state = state_t::is_applied; }
void set_delayed() { m_state = state_t::is_delayed; }
struct hash {
solver& s;
hash(solver& s) :s(s) {}
unsigned hash_select(axiom_record const& r) const {
unsigned h = mk_mix(r.n->get_expr_id(), (unsigned)r.m_kind, r.select->get_arg(1)->get_expr_id());
for (unsigned i = 2; i < r.select->num_args(); ++i)
h = mk_mix(h, h, r.select->get_arg(i)->get_expr_id());
return h;
}
unsigned operator()(unsigned idx) const {
auto const& r = s.m_axiom_trail[idx];
if (r.m_kind == kind_t::is_select)
return hash_select(r);
return mk_mix(r.n->get_expr_id(), (unsigned)r.m_kind, r.select ? r.select->get_expr_id() : 1);
}
};
struct eq {
solver& s;
eq(solver& s) :s(s) {}
bool eq_select(axiom_record const& p, axiom_record const& r) const {
if (p.m_kind != r.m_kind || p.n != r.n)
return false;
for (unsigned i = p.select->num_args(); i-- > 1; )
if (p.select->get_arg(i) != r.select->get_arg(i))
return false;
return true;
}
unsigned operator()(unsigned a, unsigned b) const {
auto const& p = s.m_axiom_trail[a];
auto const& r = s.m_axiom_trail[b];
if (p.m_kind == kind_t::is_select)
return eq_select(p, r);
return p.m_kind == r.m_kind && p.n == r.n && p.select == r.select;
}
};
};
typedef hashtable axiom_table_t;
axiom_record::hash m_hash;
axiom_record::eq m_eq;
axiom_table_t m_axioms;
svector m_axiom_trail;
unsigned m_qhead = 0;
unsigned m_delay_qhead = 0;
bool m_enable_delay = true;
struct reset_new;
void push_axiom(axiom_record const& r);
bool propagate_axiom(unsigned idx);
bool assert_axiom(unsigned idx);
bool assert_select(unsigned idx, axiom_record & r);
bool assert_default(axiom_record & r);
void set_applied(unsigned idx) { m_axiom_trail[idx].set_applied(); }
bool is_applied(unsigned idx) const { return m_axiom_trail[idx].is_applied(); }
bool is_delayed(unsigned idx) const { return m_axiom_trail[idx].is_delayed(); }
axiom_record select_axiom(euf::enode* s, euf::enode* n) { return axiom_record(axiom_record::kind_t::is_select, n, s); }
axiom_record default_axiom(euf::enode* n) { return axiom_record(axiom_record::kind_t::is_default, n); }
axiom_record store_axiom(euf::enode* n) { return axiom_record(axiom_record::kind_t::is_store, n); }
axiom_record extensionality_axiom(euf::enode* x, euf::enode* y) { return axiom_record(axiom_record::kind_t::is_extensionality, x, y); }
axiom_record congruence_axiom(euf::enode* a, euf::enode* b) { return axiom_record(axiom_record::kind_t::is_congruence, a, b); }
scoped_ptr m_constraint;
sat::ext_justification_idx array_axiom() { return m_constraint->to_index(); }
bool assert_store_axiom(app* _e);
bool assert_select_store_axiom(app* select, app* store);
bool assert_select_const_axiom(app* select, app* cnst);
bool assert_select_as_array_axiom(app* select, app* arr);
bool assert_select_map_axiom(app* select, app* map);
bool assert_select_lambda_axiom(app* select, expr* lambda);
bool assert_extensionality(expr* e1, expr* e2);
bool assert_default_map_axiom(app* map);
bool assert_default_const_axiom(app* cnst);
bool assert_default_store_axiom(app* store);
bool assert_congruent_axiom(expr* e1, expr* e2);
bool add_delayed_axioms();
bool add_as_array_eqs(euf::enode* n);
expr_ref apply_map(app* map, unsigned n, expr* const* args);
bool is_map_combinator(expr* e) const;
bool has_unitary_domain(app* array_term);
bool has_large_domain(expr* array_term);
std::pair mk_epsilon(sort* s);
void collect_shared_vars(sbuffer& roots);
bool add_interface_equalities();
bool is_shared_arg(euf::enode* r);
bool is_array(euf::enode* n) const { return a.is_array(n->get_expr()); }
// solving
void add_parent_select(theory_var v_child, euf::enode* select);
void add_parent_default(theory_var v_child);
void add_lambda(theory_var v, euf::enode* lambda);
void add_parent_lambda(theory_var v_child, euf::enode* lambda);
void propagate_select_axioms(var_data const& d, euf::enode* a);
void propagate_parent_select_axioms(theory_var v);
void propagate_parent_default(theory_var v);
void set_prop_upward(theory_var v);
void set_prop_upward(var_data& d);
void set_prop_upward_store(euf::enode* n);
unsigned get_lambda_equiv_size(var_data const& d) const;
bool should_set_prop_upward(var_data const& d) const;
bool should_prop_upward(var_data const& d) const;
bool can_beta_reduce(euf::enode* n) const { return can_beta_reduce(n->get_expr()); }
bool can_beta_reduce(expr* e) const;
bool check_lambdas();
var_data& get_var_data(euf::enode* n) { return get_var_data(n->get_th_var(get_id())); }
var_data& get_var_data(theory_var v) { return *m_var_data[v]; }
var_data const& get_var_data(theory_var v) const { return *m_var_data[v]; }
void pop_core(unsigned n) override;
// models
// I need a set of select enodes where select(A,i) = select(B,j) if i->get_root() == j->get_root()
struct sel_khasher {
unsigned operator()(euf::enode const * n) const { return 0; }
};
struct sel_chasher {
unsigned operator()(euf::enode const * n, unsigned idx) const {
return n->get_arg(idx+1)->get_root()->hash();
}
};
struct sel_hash {
unsigned operator()(euf::enode * n) const;
};
struct sel_eq {
bool operator()(euf::enode * n1, euf::enode * n2) const;
};
typedef ptr_hashtable select_set;
euf::enode_vector m_defaults; // temporary field for model construction
ptr_vector m_else_values; //
svector m_parents; // temporary field for model construction
obj_map m_selects; // mapping from array -> relevant selects
ptr_vector m_selects_domain;
ptr_vector m_selects_range;
bool must_have_different_model_values(theory_var v1, theory_var v2);
select_set* get_select_set(euf::enode* n);
void collect_defaults();
void collect_selects(); // mapping from array -> relevant selects
void propagate_select_to_store_parents(euf::enode* r, euf::enode* sel, euf::enode_pair_vector& todo);
void mg_merge(theory_var u, theory_var v);
theory_var mg_find(theory_var n);
void set_default(theory_var v, euf::enode* n);
euf::enode* get_default(theory_var v);
void set_else(theory_var v, expr* e);
expr* get_else(theory_var v);
// diagnostics
std::ostream& display_info(std::ostream& out, char const* id, euf::enode_vector const& v) const;
std::ostream& display(std::ostream& out, axiom_record const& r) const;
void validate_check() const;
void validate_select_store(euf::enode* n) const;
void validate_extensionality(euf::enode* s, euf::enode* t) const;
public:
solver(euf::solver& ctx, theory_id id);
~solver() override;
bool is_external(bool_var v) override { return false; }
void get_antecedents(literal l, sat::ext_justification_idx idx, literal_vector& r, bool probing) override {}
void asserted(literal l) override {}
sat::check_result check() override;
std::ostream& display(std::ostream& out) const override;
std::ostream& display_justification(std::ostream& out, sat::ext_justification_idx idx) const override;
std::ostream& display_constraint(std::ostream& out, sat::ext_constraint_idx idx) const override;
void collect_statistics(statistics& st) const override;
euf::th_solver* clone(euf::solver& ctx) override;
void new_eq_eh(euf::th_eq const& eq) override;
bool use_diseqs() const override { return true; }
void new_diseq_eh(euf::th_eq const& eq) override;
bool unit_propagate() override;
void init_model() override;
void finalize_model(model& mdl) override;
bool include_func_interp(func_decl* f) const override { return a.is_ext(f); }
void add_value(euf::enode* n, model& mdl, expr_ref_vector& values) override;
bool add_dep(euf::enode* n, top_sort& dep) override;
sat::literal internalize(expr* e, bool sign, bool root) override;
void internalize(expr* e) override;
euf::theory_var mk_var(euf::enode* n) override;
void apply_sort_cnstr(euf::enode* n, sort* s) override;
bool is_shared(theory_var v) const override;
bool is_beta_redex(euf::enode* p, euf::enode* n) const override;
bool enable_self_propagate() const override { return true; }
void relevant_eh(euf::enode* n) override;
bool enable_ackerman_axioms(euf::enode* n) const override { return !a.is_array(n->get_sort()); }
void merge_eh(theory_var, theory_var, theory_var v1, theory_var v2);
void after_merge_eh(theory_var r1, theory_var r2, theory_var v1, theory_var v2) {}
void unmerge_eh(theory_var v1, theory_var v2) {}
euf::enode_vector const& parent_selects(euf::enode* n) { return m_var_data[find(n->get_th_var(get_id()))]->m_parent_selects; }
};
}
