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z3/src/ast/simplifiers/euf_completion.cpp
Nikolaj Bjorner 423930dbad missing files
2025-06-10 16:31:13 -07:00

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C++

/*++
Copyright (c) 2022 Microsoft Corporation
Module Name:
euf_completion.cpp
Abstract:
Ground completion for equalities
Author:
Nikolaj Bjorner (nbjorner) 2022-10-30
Notes:
Create a congruence closure of E.
Select _simplest_ term in each equivalence class. A term is _simplest_
if it is smallest in a well-order, such as a ground Knuth-Bendix order.
A basic approach is terms that are of smallest depth, are values can be chosen as simplest.
Ties between equal-depth terms can be resolved arbitrarily.
Algorithm for extracting canonical form from an E-graph:
* Compute function canon(t) that maps every term in E to a canonical, least with respect to well-order relative to the congruence closure.
That is, terms that are equal modulo the congruence closure have the same canonical representative.
* Each f(t) = g(s) in E:
* add f(canon(t)) = canon(f(t)), g(canon(s)) = canon(g(s)) where canon(f(t)) = canon(g(s)) by construction.
* Each other g(t) in E:
* add g(canon(t)) to E.
* Note that canon(g(t)) = true because g(t) = true is added to congruence closure of E.
* We claim the new formula is equivalent.
* The dependencies for each rewrite can be computed by following the equality justification data-structure.
Conditional saturation:
- forall X . Body => Head
- propagate when (all assertions in) Body is merged with True
- insert expressions from Body into a watch list.
When elements of the watch list are merged by true/false
trigger rep-propagation with respect to body.
Mam optimization?
match(p, t, S) = suppose all variables in p are bound in S, check equality using canonization of p[S], otherwise prune instances from S.
--*/
#include "ast/ast_pp.h"
#include "ast/ast_util.h"
#include "ast/euf/euf_egraph.h"
#include "ast/rewriter/var_subst.h"
#include "ast/simplifiers/euf_completion.h"
#include "ast/shared_occs.h"
#include "params/smt_params_helper.hpp"
namespace euf {
completion::completion(ast_manager& m, dependent_expr_state& fmls) :
dependent_expr_simplifier(m, fmls),
m_egraph(m),
m_mam(mam::mk(*this, *this)),
m_canonical(m),
m_eargs(m),
m_deps(m),
m_rewriter(m) {
m_tt = m_egraph.mk(m.mk_true(), 0, 0, nullptr);
m_ff = m_egraph.mk(m.mk_false(), 0, 0, nullptr);
m_rewriter.set_order_eq(true);
m_rewriter.set_flat_and_or(false);
std::function<void(euf::enode*, euf::enode*)> _on_merge =
[&](euf::enode* root, euf::enode* other) {
m_mam->on_merge(root, other);
watch_rule(root, other);
};
std::function<void(euf::enode*)> _on_make =
[&](euf::enode* n) {
m_mam->add_node(n, false);
};
m_egraph.set_on_merge(_on_merge);
m_egraph.set_on_make(_on_make);
}
completion::~completion() {
}
bool completion::should_stop() {
return
!m.inc() ||
m_egraph.inconsistent() ||
m_fmls.inconsistent() ||
resource_limits_exceeded();
}
void completion::updt_params(params_ref const& p) {
smt_params_helper sp(p);
m_max_instantiations = sp.qi_max_instances();
}
struct completion::push_watch_rule : public trail {
vector<ptr_vector<conditional_rule>>& m_rules;
unsigned idx;
push_watch_rule(vector<ptr_vector<conditional_rule>>& r, unsigned i) : m_rules(r), idx(i) {}
void undo() override {
m_rules[idx].pop_back();
}
};
struct completion::scoped_generation {
completion& c;
unsigned m_generation = 0;
scoped_generation(completion& c, unsigned g): c(c) {
m_generation = c.m_generation;
c.m_generation = g;
}
~scoped_generation() {
c.m_generation = m_generation;
}
};
void completion::push() {
if (m_side_condition_solver)
m_side_condition_solver->push();
m_egraph.push();
dependent_expr_simplifier::push();
}
void completion::pop(unsigned n) {
clear_propagation_queue();
dependent_expr_simplifier::pop(n);
m_egraph.pop(n);
if (m_side_condition_solver)
m_side_condition_solver->pop(n);
}
void completion::clear_propagation_queue() {
for (auto r : m_propagation_queue)
r->m_in_queue = false;
m_propagation_queue.reset();
}
void completion::watch_rule(enode* root, enode* other) {
auto oid = other->get_id();
if (oid >= m_rule_watch.size())
return;
if (m_rule_watch[oid].empty())
return;
auto is_true_or_false = m.is_true(root->get_expr()) || m.is_false(root->get_expr());
if (is_true_or_false) {
for (auto r : m_rule_watch[oid])
if (!r->m_in_queue)
r->m_in_queue = true,
m_propagation_queue.push_back(r);
}
else {
// root is not true or false, use root to watch rules
auto rid = root->get_id();
m_rule_watch.reserve(rid + 1);
for (auto r : m_rule_watch[oid]) {
m_rule_watch[rid].push_back(r);
get_trail().push(push_watch_rule(m_rule_watch, rid));
}
}
}
void completion::reduce() {
m_has_new_eq = true;
for (unsigned rounds = 0; m_has_new_eq && rounds <= 3 && !should_stop(); ++rounds) {
++m_epoch;
m_has_new_eq = false;
add_egraph();
map_canonical();
read_egraph();
IF_VERBOSE(11, verbose_stream() << "(euf.completion :rounds " << rounds << ")\n");
}
}
void completion::add_egraph() {
m_nodes_to_canonize.reset();
unsigned sz = qtail();
for (unsigned i = qhead(); i < sz; ++i) {
auto [f, p, d] = m_fmls[i]();
add_constraint(f, p, d);
}
m_should_propagate = true;
while (m_should_propagate && !should_stop()) {
m_should_propagate = false;
m_egraph.propagate();
m_mam->propagate();
propagate_rules();
IF_VERBOSE(11, verbose_stream() << "propagate " << m_stats.m_num_instances << "\n");
if (!m_should_propagate)
propagate_all_rules();
}
}
void completion::add_constraint(expr* f, proof* pr, expr_dependency* d) {
if (m_egraph.inconsistent())
return;
auto add_children = [&](enode* n) {
for (auto* ch : enode_args(n))
m_nodes_to_canonize.push_back(ch);
};
expr* x, * y;
if (m.is_eq(f, x, y)) {
enode* a = mk_enode(x);
enode* b = mk_enode(y);
m_egraph.merge(a, b, d);
add_children(a);
add_children(b);
}
else if (m.is_not(f, f)) {
enode* n = mk_enode(f);
m_egraph.merge(n, m_ff, d);
add_children(n);
}
else {
enode* n = mk_enode(f);
m_egraph.merge(n, m_tt, d);
add_children(n);
if (is_forall(f)) {
quantifier* q = to_quantifier(f);
ptr_vector<app> ground;
for (unsigned i = 0; i < q->get_num_patterns(); ++i) {
auto p = to_app(q->get_pattern(i));
mam::ground_subterms(p, ground);
for (expr* g : ground)
mk_enode(g);
m_mam->add_pattern(q, p);
}
auto pq = get_dependency(q);
m_q2dep.insert(q, pq);
get_trail().push(insert_obj_map(m_q2dep, q));
}
add_rule(f, pr, d);
}
if (m_side_condition_solver)
m_side_condition_solver->add_constraint(f, pr, d);
}
lbool completion::eval_cond(expr* f, proof_ref& pr, expr_dependency*& d) {
auto n = mk_enode(f);
if (m.is_true(n->get_root()->get_expr())) {
d = m.mk_join(d, explain_eq(n, n->get_root()));
// TODO update pr
return l_true;
}
if (m.is_false(n->get_root()->get_expr()))
return l_false;
expr* g = nullptr;
if (m.is_not(f, g)) {
n = mk_enode(g);
if (m.is_false(n->get_root()->get_expr())) {
d = m.mk_join(d, explain_eq(n, n->get_root()));
// TODO update pr
return l_true;
}
if (m.is_true(n->get_root()->get_expr()))
return l_false;
}
if (m_side_condition_solver) {
expr_dependency* sd = nullptr;
if (m_side_condition_solver->is_true(f, pr, sd)) {
add_constraint(f, pr, sd);
d = m.mk_join(d, sd);
return l_true;
}
}
return l_undef;
}
void completion::add_rule(expr* f, proof* pr, expr_dependency* d) {
expr* x = nullptr, * y = nullptr;
if (!m.is_implies(f, x, y))
return;
expr_ref_vector body(m);
proof_ref pr_i(m), pr0(m);
proof_ref_vector prs(m);
expr_ref head(y, m);
body.push_back(x);
flatten_and(body);
unsigned j = 0;
for (auto f : body) {
switch (eval_cond(f, pr_i, d)) {
case l_true:
if (m.proofs_enabled())
prs.push_back(pr_i);
break;
case l_false:
return;
case l_undef:
body[j++] = f;
break;
}
}
body.shrink(j);
if (m.proofs_enabled()) {
// TODO
}
if (body.empty())
add_constraint(head, pr0, d);
else {
euf::enode_vector _body;
for (auto* f : body)
_body.push_back(m_egraph.find(f)->get_root());
auto r = alloc(conditional_rule, _body, head, pr0, d);
m_rules.push_back(r);
get_trail().push(new_obj_trail(r));
get_trail().push(push_back_vector(m_rules));
insert_watch(_body[0], r);
}
}
void completion::insert_watch(enode* n, conditional_rule* r) {
n = n->get_root();
if (m.is_not(n->get_expr()))
n = n->get_arg(0)->get_root();
m_rule_watch.reserve(n->get_id() + 1);
m_rule_watch[n->get_id()].push_back(r);
get_trail().push(push_watch_rule(m_rule_watch, n->get_id()));
}
void completion::propagate_all_rules() {
for (auto* r : m_rules)
if (!r->m_in_queue)
r->m_in_queue = true,
m_propagation_queue.push_back(r);
propagate_rules();
}
void completion::propagate_rules() {
for (unsigned i = 0; i < m_propagation_queue.size() && !should_stop(); ++i) {
auto r = m_propagation_queue[i];
r->m_in_queue = false;
propagate_rule(*r);
}
clear_propagation_queue();
}
void completion::propagate_rule(conditional_rule& r) {
if (!r.m_active)
return;
for (unsigned i = r.m_watch_index; i < r.m_body.size(); ++i) {
auto* f = r.m_body.get(i);
proof_ref pr(m);
switch (eval_cond(f->get_expr(), pr, r.m_dep)) {
case l_true:
get_trail().push(value_trail(r.m_watch_index));
++r.m_watch_index;
// TODO accumulate proof in r?
break;
case l_false:
get_trail().push(value_trail(r.m_active));
r.m_active = false;
return;
default:
insert_watch(f, &r);
return;
}
}
if (r.m_body.empty()) {
add_constraint(r.m_head, r.m_proof, r.m_dep);
get_trail().push(value_trail(r.m_active));
r.m_active = false;
}
}
// callback when mam finds a binding
void completion::on_binding(quantifier* q, app* pat, enode* const* binding, unsigned mg, unsigned ming, unsigned mx) {
if (m_egraph.inconsistent())
return;
var_subst subst(m);
expr_ref_vector _binding(m);
unsigned max_generation = 0;
for (unsigned i = 0; i < q->get_num_decls(); ++i) {
_binding.push_back(binding[i]->get_expr());
max_generation = std::max(max_generation, binding[i]->generation());
}
expr_ref r = subst(q->get_expr(), _binding);
IF_VERBOSE(12, verbose_stream() << "add " << r << "\n");
IF_VERBOSE(1, verbose_stream() << max_generation << "\n");
scoped_generation sg(*this, max_generation + 1);
auto [pr, d] = get_dependency(q);
add_constraint(r, pr, d);
propagate_rules();
m_should_propagate = true;
++m_stats.m_num_instances;
}
void completion::read_egraph() {
if (m_egraph.inconsistent()) {
auto* d = explain_conflict();
dependent_expr de(m, m.mk_false(), nullptr, d);
m_fmls.update(0, de);
return;
}
unsigned sz = qtail();
for (unsigned i = qhead(); i < sz; ++i) {
auto [f, p, d] = m_fmls[i]();
expr_dependency_ref dep(d, m);
expr_ref g = canonize_fml(f, dep);
if (g != f) {
m_fmls.update(i, dependent_expr(m, g, nullptr, dep));
m_stats.m_num_rewrites++;
IF_VERBOSE(11, verbose_stream() << mk_bounded_pp(f, m, 3) << " -> " << mk_bounded_pp(g, m, 3) << "\n");
update_has_new_eq(g);
}
CTRACE(euf_completion, g != f, tout << mk_bounded_pp(f, m) << " -> " << mk_bounded_pp(g, m) << "\n");
}
}
bool completion::is_new_eq(expr* a, expr* b) {
enode* na = m_egraph.find(a);
enode* nb = m_egraph.find(b);
if (!na)
IF_VERBOSE(11, verbose_stream() << "not internalied " << mk_bounded_pp(a, m) << "\n");
if (!nb)
IF_VERBOSE(11, verbose_stream() << "not internalied " << mk_bounded_pp(b, m) << "\n");
if (na && nb && na->get_root() != nb->get_root())
IF_VERBOSE(11, verbose_stream() << m_egraph.bpp(na) << " " << m_egraph.bpp(nb) << "\n");
return !na || !nb || na->get_root() != nb->get_root();
}
void completion::update_has_new_eq(expr* g) {
expr* x, * y;
if (m_has_new_eq)
return;
else if (m.is_eq(g, x, y))
m_has_new_eq |= is_new_eq(x, y);
else if (m.is_and(g)) {
for (expr* arg : *to_app(g))
update_has_new_eq(arg);
}
else if (m.is_not(g, g))
m_has_new_eq |= is_new_eq(g, m.mk_false());
else
m_has_new_eq |= is_new_eq(g, m.mk_true());
}
enode* completion::mk_enode(expr* e) {
m_todo.push_back(e);
enode* n;
while (!m_todo.empty()) {
e = m_todo.back();
if (m_egraph.find(e)) {
m_todo.pop_back();
continue;
}
if (!is_app(e)) {
m_nodes_to_canonize.push_back(m_egraph.mk(e, m_generation, 0, nullptr));
m_todo.pop_back();
continue;
}
m_args.reset();
unsigned sz = m_todo.size();
for (expr* arg : *to_app(e)) {
n = m_egraph.find(arg);
if (n)
m_args.push_back(n);
else
m_todo.push_back(arg);
}
if (sz == m_todo.size()) {
m_nodes_to_canonize.push_back(m_egraph.mk(e, m_generation, m_args.size(), m_args.data()));
m_todo.pop_back();
}
}
return m_egraph.find(e);
}
expr_ref completion::canonize_fml(expr* f, expr_dependency_ref& d) {
auto is_nullary = [&](expr* e) {
return is_app(e) && to_app(e)->get_num_args() == 0;
};
expr* x, * y;
if (m.is_eq(f, x, y)) {
expr_ref x1 = canonize(x, d);
expr_ref y1 = canonize(y, d);
if (is_nullary(x)) {
SASSERT(x1 == x);
x1 = get_canonical(x, d);
}
if (is_nullary(y)) {
SASSERT(y1 == y);
y1 = get_canonical(y, d);
}
if (x == y)
return expr_ref(m.mk_true(), m);
if (x == x1 && y == y1)
return m_rewriter.mk_eq(x, y);
if (is_nullary(x) && is_nullary(y))
return mk_and(m_rewriter.mk_eq(x, x1), m_rewriter.mk_eq(y, x1));
if (x == x1 && is_nullary(x))
return m_rewriter.mk_eq(y1, x1);
if (y == y1 && is_nullary(y))
return m_rewriter.mk_eq(x1, y1);
if (is_nullary(x))
return mk_and(m_rewriter.mk_eq(x, x1), m_rewriter.mk_eq(y1, x1));
if (is_nullary(y))
return mk_and(m_rewriter.mk_eq(y, y1), m_rewriter.mk_eq(x1, y1));
if (x1 == y1)
return expr_ref(m.mk_true(), m);
else {
expr* c = get_canonical(x, d);
if (c == x1)
return m_rewriter.mk_eq(y1, c);
else if (c == y1)
return m_rewriter.mk_eq(x1, c);
else
return mk_and(m_rewriter.mk_eq(x1, c), m_rewriter.mk_eq(y1, c));
}
}
if (m.is_not(f, x)) {
expr_ref x1 = canonize(x, d);
return expr_ref(mk_not(m, x1), m);
}
return canonize(f, d);
}
expr_ref completion::mk_and(expr* a, expr* b) {
if (m.is_true(a))
return expr_ref(b, m);
if (m.is_true(b))
return expr_ref(a, m);
return expr_ref(m.mk_and(a, b), m);
}
expr_ref completion::canonize(expr* f, expr_dependency_ref& d) {
if (!is_app(f))
return expr_ref(f, m); // todo could normalize ground expressions under quantifiers
m_eargs.reset();
bool change = false;
for (expr* arg : *to_app(f)) {
m_eargs.push_back(get_canonical(arg, d));
change |= arg != m_eargs.back();
}
if (m.is_eq(f))
return m_rewriter.mk_eq(m_eargs.get(0), m_eargs.get(1));
if (!change)
return expr_ref(f, m);
else
return expr_ref(m_rewriter.mk_app(to_app(f)->get_decl(), m_eargs.size(), m_eargs.data()), m);
}
expr* completion::get_canonical(expr* f, expr_dependency_ref& d) {
enode* n = m_egraph.find(f);
enode* r = n->get_root();
d = m.mk_join(d, explain_eq(n, r));
d = m.mk_join(d, m_deps.get(r->get_id(), nullptr));
SASSERT(m_canonical.get(r->get_id()));
return m_canonical.get(r->get_id());
}
expr* completion::get_canonical(enode* n) {
if (m_epochs.get(n->get_id(), 0) == m_epoch)
return m_canonical.get(n->get_id());
else
return nullptr;
}
void completion::set_canonical(enode* n, expr* e) {
class vtrail : public trail {
expr_ref_vector& c;
unsigned idx;
expr_ref old_value;
public:
vtrail(expr_ref_vector& c, unsigned idx) :
c(c), idx(idx), old_value(c.get(idx), c.m()) {
}
void undo() override {
c[idx] = old_value;
old_value = nullptr;
}
};
SASSERT(e);
if (num_scopes() > 0 && m_canonical.size() > n->get_id())
m_trail.push(vtrail(m_canonical, n->get_id()));
m_canonical.setx(n->get_id(), e);
m_epochs.setx(n->get_id(), m_epoch, 0);
}
expr_dependency* completion::explain_eq(enode* a, enode* b) {
if (a == b)
return nullptr;
ptr_vector<expr_dependency> just;
m_egraph.begin_explain();
m_egraph.explain_eq(just, nullptr, a, b);
m_egraph.end_explain();
expr_dependency* d = nullptr;
for (expr_dependency* d2 : just)
d = m.mk_join(d, d2);
return d;
}
expr_dependency* completion::explain_conflict() {
ptr_vector<expr_dependency> just;
m_egraph.begin_explain();
m_egraph.explain(just, nullptr);
m_egraph.end_explain();
expr_dependency* d = nullptr;
for (expr_dependency* d2 : just)
d = m.mk_join(d, d2);
return d;
}
void completion::collect_statistics(statistics& st) const {
st.update("euf-completion-rewrites", m_stats.m_num_rewrites);
st.update("euf-completion-instances", m_stats.m_num_instances);
}
bool completion::is_gt(expr* lhs, expr* rhs) const {
if (lhs == rhs)
return false;
// values are always less in ordering than non-values.
bool v1 = m.is_value(lhs);
bool v2 = m.is_value(rhs);
if (!v1 && v2)
return true;
if (v1 && !v2)
return false;
if (get_depth(lhs) > get_depth(rhs))
return true;
if (get_depth(lhs) < get_depth(rhs))
return false;
// slow path
auto n1 = get_num_exprs(lhs);
auto n2 = get_num_exprs(rhs);
if (n1 > n2)
return true;
if (n1 < n2)
return false;
if (is_app(lhs) && is_app(rhs)) {
app* l = to_app(lhs);
app* r = to_app(rhs);
if (l->get_decl()->get_id() != r->get_decl()->get_id())
return l->get_decl()->get_id() > r->get_decl()->get_id();
if (l->get_num_args() != r->get_num_args())
return l->get_num_args() > r->get_num_args();
for (unsigned i = 0; i < l->get_num_args(); ++i)
if (l->get_arg(i) != r->get_arg(i))
return is_gt(l->get_arg(i), r->get_arg(i));
UNREACHABLE();
}
if (is_quantifier(lhs) && is_quantifier(rhs)) {
expr* l = to_quantifier(lhs)->get_expr();
expr* r = to_quantifier(rhs)->get_expr();
return is_gt(l, r);
}
if (is_quantifier(lhs))
return true;
return false;
}
void completion::map_canonical() {
m_todo.reset();
enode_vector roots;
if (m_nodes_to_canonize.empty())
return;
for (unsigned i = 0; i < m_nodes_to_canonize.size(); ++i) {
enode* n = m_nodes_to_canonize[i]->get_root();
if (n->is_marked1())
continue;
n->mark1();
roots.push_back(n);
enode* rep = nullptr;
for (enode* k : enode_class(n))
if (!rep || m.is_value(k->get_expr()) || is_gt(rep->get_expr(), k->get_expr()))
rep = k;
// IF_VERBOSE(0, verbose_stream() << m_egraph.bpp(n) << " ->\n" << m_egraph.bpp(rep) << "\n";);
m_reps.setx(n->get_id(), rep, nullptr);
TRACE(euf_completion, tout << "rep " << m_egraph.bpp(n) << " -> " << m_egraph.bpp(rep) << "\n";
for (enode* k : enode_class(n)) tout << m_egraph.bpp(k) << "\n";);
m_todo.push_back(n->get_expr());
for (enode* arg : enode_args(n)) {
arg = arg->get_root();
if (!arg->is_marked1())
m_nodes_to_canonize.push_back(arg);
}
}
for (enode* r : roots)
r->unmark1();
// explain dependencies when no nodes are marked.
// explain_eq uses both mark1 and mark2 on e-nodes so
// we cannot call it inside the previous loop where mark1 is used
// to track which roots have been processed.
for (enode* r : roots) {
enode* rep = m_reps[r->get_id()];
auto* d = explain_eq(r, rep);
m_deps.setx(r->get_id(), d);
}
expr_ref new_expr(m);
while (!m_todo.empty()) {
expr* e = m_todo.back();
enode* n = m_egraph.find(e);
SASSERT(n->is_root());
enode* rep = m_reps[n->get_id()];
if (get_canonical(n))
m_todo.pop_back();
else if (get_depth(rep->get_expr()) == 0 || !is_app(rep->get_expr())) {
set_canonical(n, rep->get_expr());
m_todo.pop_back();
}
else {
m_eargs.reset();
unsigned sz = m_todo.size();
bool new_arg = false;
expr_dependency* d = m_deps.get(n->get_id(), nullptr);
for (enode* arg : enode_args(rep)) {
enode* rarg = arg->get_root();
expr* c = get_canonical(rarg);
if (c) {
m_eargs.push_back(c);
new_arg |= c != arg->get_expr();
d = m.mk_join(d, m_deps.get(rarg->get_id(), nullptr));
}
else
m_todo.push_back(rarg->get_expr());
}
if (sz == m_todo.size()) {
m_todo.pop_back();
if (new_arg)
new_expr = m_rewriter.mk_app(to_app(rep->get_expr())->get_decl(), m_eargs.size(), m_eargs.data());
else
new_expr = rep->get_expr();
set_canonical(n, new_expr);
m_deps.setx(n->get_id(), d);
}
}
}
}
}