z3-z3-4.13.0.src.sat.smt.array_model.cpp Maven / Gradle / Ivy
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/*++
Copyright (c) 2020 Microsoft Corporation
Module Name:
array_model.cpp
Abstract:
Theory plugin for arrays
Author:
Nikolaj Bjorner (nbjorner) 2020-09-08
--*/
#include "model/array_factory.h"
#include "sat/smt/array_solver.h"
#include "sat/smt/euf_solver.h"
namespace array {
void solver::init_model() {
collect_defaults();
collect_selects();
}
void solver::finalize_model(model& mdl) {
std::for_each(m_selects_range.begin(), m_selects_range.end(), delete_proc());
}
bool solver::add_dep(euf::enode* n, top_sort& dep) {
if (!a.is_array(n->get_expr())) {
dep.insert(n, nullptr);
return true;
}
if (a.is_array(n->get_expr())) {
for (euf::enode* p : euf::enode_parents(n->get_root()))
if (a.is_default(p->get_expr()))
dep.add(n, p);
for (euf::enode* p : *get_select_set(n)) {
dep.add(n, p);
for (unsigned i = 1; i < p->num_args(); ++i)
dep.add(n, p->get_arg(i));
}
}
for (euf::enode* k : euf::enode_class(n))
if (a.is_const(k->get_expr()))
dep.add(n, k->get_arg(0));
theory_var v = get_th_var(n);
euf::enode* d = get_default(v);
if (d)
dep.add(n, d);
if (!dep.contains_dep(n))
dep.insert(n, nullptr);
return true;
}
void solver::add_value(euf::enode* n, model& mdl, expr_ref_vector& values) {
SASSERT(a.is_array(n->get_expr()));
ptr_vector args;
sort* srt = n->get_sort();
n = n->get_root();
if (a.is_as_array(n->get_expr())) {
values.set(n->get_expr_id(), n->get_expr());
return;
}
theory_var v = get_th_var(n);
euf::enode* d = get_default(v);
if (a.is_const(n->get_expr())) {
expr* val = values.get(d->get_root_id());
SASSERT(val);
values.set(n->get_expr_id(), a.mk_const_array(n->get_sort(), val));
return;
}
unsigned arity = get_array_arity(srt);
func_decl * f = mk_aux_decl_for_array_sort(m, srt);
func_interp * fi = alloc(func_interp, m, arity);
mdl.register_decl(f, fi);
if (d && !fi->get_else())
fi->set_else(values.get(d->get_root_id()));
if (!fi->get_else() && get_else(v))
fi->set_else(get_else(v));
if (!fi->get_else()) {
expr* else_value = nullptr;
unsigned max_occ_num = 0;
obj_map num_occ;
for (euf::enode* p : euf::enode_parents(n->get_root())) {
if (a.is_select(p->get_expr()) && p->get_arg(0)->get_root() == n->get_root()) {
expr* v = values.get(p->get_root_id(), nullptr);
if (!v)
continue;
unsigned no = 0;
num_occ.find(v, no);
++no;
num_occ.insert(v, no);
if (no > max_occ_num) {
else_value = v;
max_occ_num = no;
}
}
}
if (else_value)
fi->set_else(else_value);
}
if (!get_else(v) && fi->get_else())
set_else(v, fi->get_else());
if (!get_else(v)) {
expr* else_value = mdl.get_some_value(get_array_range(srt));
fi->set_else(else_value);
set_else(v, else_value);
}
for (euf::enode* p : *get_select_set(n)) {
expr* value = values.get(p->get_root_id(), nullptr);
if (!value || value == fi->get_else())
continue;
args.reset();
for (unsigned i = 1; i < p->num_args(); ++i) {
if (!values.get(p->get_arg(i)->get_root_id())) {
TRACE("array", tout << ctx.bpp(p->get_arg(i)) << "\n");
}
SASSERT(values.get(p->get_arg(i)->get_root_id()));
}
for (unsigned i = 1; i < p->num_args(); ++i)
args.push_back(values.get(p->get_arg(i)->get_root_id()));
fi->insert_entry(args.data(), value);
}
TRACE("array", tout << "array-as-function " << ctx.bpp(n) << " := " << mk_pp(f, m) << "\n" << "default " << mk_pp(fi->get_else(), m) << "\n";);
parameter p(f);
values.set(n->get_expr_id(), m.mk_app(get_id(), OP_AS_ARRAY, 1, &p));
}
bool solver::must_have_different_model_values(theory_var v1, theory_var v2) {
euf::enode* else1 = nullptr, * else2 = nullptr;
euf::enode* n1 = var2enode(v1);
expr* e1 = n1->get_expr();
if (!a.is_array(e1))
return true;
else1 = get_default(v1);
else2 = get_default(v2);
if (else1 && else2 && else1->get_root() != else2->get_root() && has_large_domain(e1))
return true;
return false;
}
unsigned solver::sel_hash::operator()(euf::enode * n) const {
return get_composite_hash(n, n->num_args() - 1, sel_khasher(), sel_chasher());
}
bool solver::sel_eq::operator()(euf::enode * n1, euf::enode * n2) const {
SASSERT(n1->num_args() == n2->num_args());
unsigned num_args = n1->num_args();
for (unsigned i = 1; i < num_args; i++)
if (n1->get_arg(i)->get_root() != n2->get_arg(i)->get_root())
return false;
return true;
}
void solver::collect_selects() {
int num_vars = get_num_vars();
m_selects.reset();
m_selects_domain.reset();
m_selects_range.reset();
for (theory_var v = 0; v < num_vars; ++v) {
euf::enode * r = var2enode(v)->get_root();
if (is_representative(v) && ctx.is_relevant(r)) {
for (euf::enode * parent : euf::enode_parents(r)) {
if (parent->get_cg() == parent &&
ctx.is_relevant(parent) &&
a.is_select(parent->get_expr()) &&
parent->get_arg(0)->get_root() == r) {
select_set * s = get_select_set(r);
SASSERT(!s->contains(parent) || (*(s->find(parent)))->get_root() == parent->get_root());
s->insert(parent);
}
}
}
}
euf::enode_pair_vector todo;
for (euf::enode * r : m_selects_domain)
for (euf::enode* sel : *get_select_set(r))
propagate_select_to_store_parents(r, sel, todo);
for (unsigned qhead = 0; qhead < todo.size(); qhead++) {
euf::enode_pair & pair = todo[qhead];
euf::enode * r = pair.first;
euf::enode * sel = pair.second;
propagate_select_to_store_parents(r, sel, todo);
}
}
void solver::propagate_select_to_store_parents(euf::enode* r, euf::enode* sel, euf::enode_pair_vector& todo) {
SASSERT(r->get_root() == r);
SASSERT(a.is_select(sel->get_expr()));
if (!ctx.is_relevant(r))
return;
for (euf::enode * parent : euf::enode_parents(r)) {
if (ctx.is_relevant(parent) &&
a.is_store(parent->get_expr()) &&
parent->get_arg(0)->get_root() == r) {
// propagate upward
select_set * parent_sel_set = get_select_set(parent);
euf::enode * parent_root = parent->get_root();
if (parent_sel_set->contains(sel))
continue;
SASSERT(sel->num_args() + 1 == parent->num_args());
// check whether the sel idx was overwritten by the store
unsigned num_args = sel->num_args();
unsigned i = 1;
for (; i < num_args; i++) {
if (sel->get_arg(i)->get_root() != parent->get_arg(i)->get_root())
break;
}
if (i < num_args) {
SASSERT(!parent_sel_set->contains(sel) || (*(parent_sel_set->find(sel)))->get_root() == sel->get_root());
parent_sel_set->insert(sel);
todo.push_back(std::make_pair(parent_root, sel));
}
}
}
}
solver::select_set* solver::get_select_set(euf::enode* n) {
euf::enode * r = n->get_root();
select_set * set = nullptr;
m_selects.find(r, set);
if (set == nullptr) {
set = alloc(select_set);
m_selects.insert(r, set);
m_selects_domain.push_back(r);
m_selects_range.push_back(set);
}
return set;
}
void solver::collect_defaults() {
unsigned num_vars = get_num_vars();
m_defaults.reset();
m_else_values.reset();
m_parents.reset();
m_parents.resize(num_vars, -1);
m_defaults.resize(num_vars);
m_else_values.resize(num_vars);
//
// Create equivalence classes for defaults.
//
for (unsigned v = 0; v < num_vars; ++v) {
euf::enode * n = var2enode(v);
expr* e = n->get_expr();
theory_var r = get_representative(v);
mg_merge(v, r);
if (a.is_const(e))
set_default(v, n->get_arg(0));
else if (a.is_store(e)) {
theory_var w = get_th_var(n->get_arg(0));
SASSERT(w != euf::null_theory_var);
mg_merge(v, get_representative(w));
TRACE("array", tout << "merge: " << ctx.bpp(n) << " " << v << " " << w << "\n";);
}
else if (a.is_default(e)) {
theory_var w = get_th_var(n->get_arg(0));
SASSERT(w != euf::null_theory_var);
set_default(w, n);
}
}
}
void solver::set_default(theory_var v, euf::enode* n) {
v = mg_find(v);
CTRACE("array", !m_defaults[v], tout << "set default: " << v << " " << ctx.bpp(n) << "\n";);
if (!m_defaults[v])
m_defaults[v] = n;
}
euf::enode* solver::get_default(theory_var v) {
return m_defaults[mg_find(v)];
}
void solver::set_else(theory_var v, expr* e) {
m_else_values[mg_find(v)] = e;
}
expr* solver::get_else(theory_var v) {
return m_else_values[mg_find(v)];
}
euf::theory_var solver::mg_find(theory_var n) {
if (m_parents[n] < 0)
return n;
theory_var n0 = n;
n = m_parents[n0];
if (m_parents[n] < -1)
return n;
while (m_parents[n] >= 0)
n = m_parents[n];
// compress path.
while (m_parents[n0] >= 0) {
theory_var n1 = m_parents[n0];
m_parents[n0] = n;
n0 = n1;
}
return n;
}
void solver::mg_merge(theory_var u, theory_var v) {
u = mg_find(u);
v = mg_find(v);
if (u != v) {
SASSERT(m_parents[u] < 0);
SASSERT(m_parents[v] < 0);
if (m_parents[u] > m_parents[v])
std::swap(u, v);
m_parents[u] += m_parents[v];
m_parents[v] = u;
if (!m_defaults[u])
m_defaults[u] = m_defaults[v];
CTRACE("array", m_defaults[v],
tout << ctx.bpp(m_defaults[v]->get_root()) << "\n";
tout << ctx.bpp(m_defaults[u]->get_root()) << "\n";
);
// NB. it may be the case that m_defaults[u] != m_defaults[v]
// when m and n are finite arrays.
}
}
}