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z3-z3-4.12.6.src.smt.dyn_ack.cpp Maven / Gradle / Ivy
/*++
Copyright (c) 2006 Microsoft Corporation
Module Name:
dyn_ack.cpp
Abstract:
Dynamic Ackermann's reduction
Author:
Leonardo de Moura (leonardo) 2007-04-24.
Revision History:
--*/
#include "smt/smt_context.h"
#include "smt/dyn_ack.h"
#include "ast/ast_pp.h"
namespace smt {
/**
\brief Justification for dynamic ackermann clause
*/
class dyn_ack_cc_justification : public justification {
app * m_app1;
app * m_app2;
public:
dyn_ack_cc_justification(app * n1, app * n2):
justification(false), // dyn_ack_cc_justifications are not stored in regions.
m_app1(n1),
m_app2(n2) {
SASSERT(m_app1->get_num_args() == m_app2->get_num_args());
SASSERT(m_app1->get_decl() == m_app2->get_decl());
SASSERT(m_app1->get_num_args() > 0);
SASSERT(m_app1->get_id() < m_app2->get_id());
}
char const * get_name() const override { return "dyn-ack"; }
void get_antecedents(conflict_resolution & cr) override {}
void display_debug_info(conflict_resolution & cr, std::ostream & out) override {
ast_manager & m = cr.get_manager();
out << "m_app1:\n" << mk_pp(m_app1, m) << "\n";
out << "m_app2:\n" << mk_pp(m_app2, m) << "\n";
}
/**
\brief Make a hypothesis (= lhs rhs) for the given equality.
The arguments of the given equality eq may have been swapped. That is, \c eq is of the form (= rhs lhs).
In this case, we also apply a symmetry rule.
\remark if negate == true, then the hypothesis is actually (not (= lhs rhs))
*/
proof * mk_hypothesis(ast_manager & m, app * eq, bool negate, expr * lhs, expr * rhs) {
SASSERT(m.is_eq(eq));
SASSERT((eq->get_arg(0) == lhs && eq->get_arg(1) == rhs) ||
(eq->get_arg(0) == rhs && eq->get_arg(1) == lhs));
app * h = negate ? m.mk_not(eq) : eq;
if (eq->get_arg(0) == lhs && eq->get_arg(1) == rhs) {
return m.mk_hypothesis(h);
}
else {
return m.mk_symmetry(m.mk_hypothesis(h));
}
}
proof * mk_proof(conflict_resolution & cr) override {
ast_manager & m = cr.get_manager();
unsigned num_args = m_app1->get_num_args();
proof_ref_vector prs(m);
expr_ref_vector lits(m);
for (unsigned i = 0; i < num_args; i++) {
expr * arg1 = m_app1->get_arg(i);
expr * arg2 = m_app2->get_arg(i);
if (arg1 != arg2) {
app * eq = m.mk_eq(arg1, arg2);
app_ref neq(m.mk_not(eq), m);
if (std::find(lits.begin(), lits.end(), neq.get()) == lits.end()) {
lits.push_back(neq);
prs.push_back(mk_hypothesis(m, eq, false, arg1, arg2));
}
}
}
app_ref eq(m.mk_eq(m_app1, m_app2), m);
proof_ref a1(m.mk_congruence(m_app1, m_app2, prs.size(), prs.data()), m);
proof_ref a2(mk_hypothesis(m, eq, true, m_app1, m_app2), m);
proof * antecedents[2] = { a1.get(), a2.get() };
proof_ref false_pr(m.mk_unit_resolution(2, antecedents), m);
lits.push_back(eq);
SASSERT(lits.size() >= 2);
app_ref lemma(m.mk_or(lits), m);
TRACE("dyn_ack", tout << lemma << "\n";);
TRACE("dyn_ack", tout << false_pr << "\n";);
return m.mk_lemma(false_pr, lemma);
}
};
class dyn_ack_eq_justification : public justification {
app * m_app1;
app * m_app2;
app * m_r;
app * m_eq1;
app * m_eq2;
app * m_eq3;
public:
dyn_ack_eq_justification(app * n1, app * n2, app* r, app* eq1, app* eq2, app* eq3):
justification(false), // dyn_ack_cc_justifications are not stored in regions.
m_app1(n1),
m_app2(n2),
m_r(r),
m_eq1(eq1),
m_eq2(eq2),
m_eq3(eq3) {
}
char const * get_name() const override { return "dyn-ack-eq"; }
void get_antecedents(conflict_resolution & cr) override {}
void display_debug_info(conflict_resolution & cr, std::ostream & out) override {
ast_manager & m = cr.get_manager();
out << mk_pp(m_eq1, m) << " " << mk_pp(m_eq2, m) << " => " << mk_pp(m_eq3, m) << "\n";
}
/**
* Create a proof of (or ~eq1 ~eq2 eq3)
* eq1 := app1 = r or symmetric
* eq2 := app2 = r or symmetric
* eq3 := app1 = app2 or symmetric
*
* p1: trans: hyp(eq1), hyp(eq2) |- eq3
* p2: unit-resolution: p1, hyp(~eq3) |- false
* p3: lemma: (or ~eq1 ~eq2 eq3)
*/
proof * mk_proof(conflict_resolution & cr) override {
ast_manager & m = cr.get_manager();
proof* p1, *p2, *p3, *p4, *p5, *p6;
expr* x = nullptr, *y = nullptr;
(void)x; (void)y;
p1 = m.mk_hypothesis(m_eq1);
if (m_eq1->get_arg(1) == m_app1) p1 = m.mk_symmetry(p1);
p2 = m.mk_hypothesis(m_eq2);
if (m_eq2->get_arg(0) == m_app2) p2 = m.mk_symmetry(p2);
(void)m_r;
SASSERT(m.is_eq(m.get_fact(p1), x, y) && x == m_app1 && y == m_r);
SASSERT(m.is_eq(m.get_fact(p2), x, y) && x == m_r && y == m_app2);
p3 = m.mk_transitivity(p1, p2);
SASSERT(m.is_eq(m.get_fact(p3), x, y) && x == m_app1 && y == m_app2);
if (m.get_fact(p3) != m_eq3) p3 = m.mk_symmetry(p3);
SASSERT(m.get_fact(p3) == m_eq3);
p4 = m.mk_hypothesis(m.mk_not(m_eq3));
proof* ps[2] = { p3, p4 };
p5 = m.mk_unit_resolution(2, ps);
SASSERT(m.get_fact(p5) == m.mk_false());
expr* eqs[3] = { m.mk_not(m_eq1), m.mk_not(m_eq2), m_eq3 };
expr_ref conclusion(m.mk_or(3, eqs), m);
p6 = m.mk_lemma(p5, conclusion);
return p6;
}
};
dyn_ack_manager::dyn_ack_manager(context & ctx, dyn_ack_params & p):
m_context(ctx),
m(ctx.get_manager()),
m_params(p) {
}
dyn_ack_manager::~dyn_ack_manager() {
reset_app_pairs();
reset_app_triples();
}
void dyn_ack_manager::reset_app_pairs() {
for (app_pair& p : m_app_pairs) {
m.dec_ref(p.first);
m.dec_ref(p.second);
}
m_app_pairs.reset();
}
void dyn_ack_manager::init_search_eh() {
m_app_pair2num_occs.reset();
reset_app_pairs();
m_to_instantiate.reset();
m_qhead = 0;
m_num_instances = 0;
m_num_propagations_since_last_gc = 0;
m_triple.m_app2num_occs.reset();
reset_app_triples();
m_triple.m_to_instantiate.reset();
m_triple.m_qhead = 0;
}
void dyn_ack_manager::cg_eh(app * n1, app * n2) {
SASSERT(n1->get_decl() == n2->get_decl());
SASSERT(n1->get_num_args() == n2->get_num_args());
SASSERT(n1 != n2);
if (m.is_eq(n1)) {
return;
}
if (n1->get_id() > n2->get_id())
std::swap(n1,n2);
app_pair p(n1, n2);
if (m_instantiated.contains(p)) {
return;
}
unsigned num_occs = 0;
if (m_app_pair2num_occs.find(n1, n2, num_occs)) {
TRACE("dyn_ack", tout << "used_cg_eh:\n" << mk_pp(n1, m) << "\n" << mk_pp(n2, m) << "\nnum_occs: " << num_occs << "\n";);
num_occs++;
}
else {
num_occs = 1;
m.inc_ref(n1);
m.inc_ref(n2);
m_app_pairs.push_back(p);
}
SASSERT(num_occs > 0);
m_app_pair2num_occs.insert(n1, n2, num_occs);
#ifdef Z3DEBUG
unsigned num_occs2 = 0;
SASSERT(m_app_pair2num_occs.find(n1, n2, num_occs2) && num_occs == num_occs2);
#endif
if (num_occs == m_params.m_dack_threshold) {
TRACE("dyn_ack", tout << "found candidate:\n" << mk_pp(n1, m) << "\n" << mk_pp(n2, m) << "\nnum_occs: " << num_occs << "\n";);
m_to_instantiate.push_back(p);
}
}
void dyn_ack_manager::eq_eh(app * n1, app * n2, app* r) {
if (n1 == n2 || r == n1 || r == n2 || m.is_bool(n1)) {
return;
}
if (n1->get_id() > n2->get_id())
std::swap(n1,n2);
TRACE("dyn_ack",
tout << mk_pp(n1, m) << " = " << mk_pp(n2, m) << " = " << mk_pp(r, m) << "\n";);
app_triple tr(n1, n2, r);
if (m_triple.m_instantiated.contains(tr)) {
return;
}
unsigned num_occs = 0;
if (m_triple.m_app2num_occs.find(n1, n2, r, num_occs)) {
TRACE("dyn_ack", tout << mk_pp(n1, m) << "\n" << mk_pp(n2, m) << "\n"
<< mk_pp(r, m) << "\n" << "\nnum_occs: " << num_occs << "\n";);
num_occs++;
}
else {
num_occs = 1;
m.inc_ref(n1);
m.inc_ref(n2);
m.inc_ref(r);
m_triple.m_apps.push_back(tr);
}
SASSERT(num_occs > 0);
m_triple.m_app2num_occs.insert(n1, n2, r, num_occs);
#ifdef Z3DEBUG
unsigned num_occs2 = 0;
SASSERT(m_triple.m_app2num_occs.find(n1, n2, r, num_occs2) && num_occs == num_occs2);
#endif
if (num_occs == m_params.m_dack_threshold) {
TRACE("dyn_ack", tout << "found candidate:\n" << mk_pp(n1, m) << "\n" << mk_pp(n2, m)
<< "\n" << mk_pp(r, m)
<< "\nnum_occs: " << num_occs << "\n";);
m_triple.m_to_instantiate.push_back(tr);
}
}
struct app_pair_lt {
typedef std::pair app_pair;
typedef obj_pair_map app_pair2num_occs;
app_pair2num_occs & m_app_pair2num_occs;
app_pair_lt(app_pair2num_occs & m):
m_app_pair2num_occs(m) {
}
bool operator()(app_pair const & p1, app_pair const & p2) const {
unsigned n1 = 0;
unsigned n2 = 0;
m_app_pair2num_occs.find(p1.first, p1.second, n1);
m_app_pair2num_occs.find(p2.first, p2.second, n2);
SASSERT(n1 > 0);
SASSERT(n2 > 0);
return n1 > n2;
}
};
void dyn_ack_manager::gc() {
TRACE("dyn_ack", tout << "dyn_ack GC\n";);
unsigned num_deleted = 0;
m_to_instantiate.reset();
m_qhead = 0;
svector::iterator it = m_app_pairs.begin();
svector::iterator end = m_app_pairs.end();
svector::iterator it2 = it;
for (; it != end; ++it) {
app_pair & p = *it;
if (m_instantiated.contains(p)) {
TRACE("dyn_ack", tout << "1) erasing:\n" << mk_pp(p.first, m) << "\n" << mk_pp(p.second, m) << "\n";);
m.dec_ref(p.first);
m.dec_ref(p.second);
SASSERT(!m_app_pair2num_occs.contains(p.first, p.second));
continue;
}
unsigned num_occs = 0;
m_app_pair2num_occs.find(p.first, p.second, num_occs);
// The following invariant is not true. p.first and
// p.second may have been instantiated, and removed from
// m_app_pair2num_occs, but not from m_app_pairs.
//
// SASSERT(num_occs > 0);
num_occs = static_cast(num_occs * m_params.m_dack_gc_inv_decay);
if (num_occs <= 1) {
num_deleted++;
TRACE("dyn_ack", tout << "2) erasing:\n" << mk_pp(p.first, m) << "\n" << mk_pp(p.second, m) << "\n";);
m_app_pair2num_occs.erase(p.first, p.second);
m.dec_ref(p.first);
m.dec_ref(p.second);
continue;
}
*it2 = p;
++it2;
SASSERT(num_occs > 0);
m_app_pair2num_occs.insert(p.first, p.second, num_occs);
if (num_occs >= m_params.m_dack_threshold)
m_to_instantiate.push_back(p);
}
m_app_pairs.set_end(it2);
app_pair_lt f(m_app_pair2num_occs);
// app_pair_lt is not a total order on pairs of expressions.
// So, we should use stable_sort to avoid different behavior in different platforms.
std::stable_sort(m_to_instantiate.begin(), m_to_instantiate.end(), f);
// IF_VERBOSE(10, if (num_deleted > 0) verbose_stream() << "dynamic ackermann GC: " << num_deleted << "\n";);
}
class dyn_ack_clause_del_eh : public clause_del_eh {
dyn_ack_manager & m;
public:
dyn_ack_clause_del_eh(dyn_ack_manager & m):
m(m) {
}
void operator()(ast_manager & _m, clause * cls) override {
m.del_clause_eh(cls);
dealloc(this);
}
};
void dyn_ack_manager::del_clause_eh(clause * cls) {
m_context.m_stats.m_num_del_dyn_ack++;
app_pair p((app*)nullptr,(app*)nullptr);
if (m_clause2app_pair.find(cls, p)) {
SASSERT(p.first && p.second);
m_instantiated.erase(p);
m_clause2app_pair.erase(cls);
SASSERT(!m_app_pair2num_occs.contains(p.first, p.second));
return;
}
app_triple tr(0,0,0);
if (m_triple.m_clause2apps.find(cls, tr)) {
SASSERT(tr.first && tr.second && tr.third);
m_triple.m_instantiated.erase(tr);
m_triple.m_clause2apps.erase(cls);
SASSERT(!m_triple.m_app2num_occs.contains(tr.first, tr.second, tr.third));
return;
}
}
void dyn_ack_manager::propagate_eh() {
if (m_params.m_dack == dyn_ack_strategy::DACK_DISABLED)
return;
m_num_propagations_since_last_gc++;
if (m_num_propagations_since_last_gc > m_params.m_dack_gc) {
gc();
m_num_propagations_since_last_gc = 0;
}
unsigned max_instances = static_cast(m_context.get_num_conflicts() * m_params.m_dack_factor);
while (m_num_instances < max_instances && m_qhead < m_to_instantiate.size()) {
app_pair & p = m_to_instantiate[m_qhead];
m_qhead++;
m_num_instances++;
instantiate(p.first, p.second);
}
while (m_num_instances < max_instances && m_triple.m_qhead < m_triple.m_to_instantiate.size()) {
app_triple & p = m_triple.m_to_instantiate[m_triple.m_qhead];
m_triple.m_qhead++;
m_num_instances++;
instantiate(p.first, p.second, p.third);
}
}
literal dyn_ack_manager::mk_eq(expr * n1, expr * n2) {
app_ref eq(m.mk_eq(n1, n2), m);
m_context.internalize(eq, true);
literal l = m_context.get_literal(eq);
TRACE("dyn_ack", tout << "eq:\n" << mk_pp(eq, m) << "\nliteral: ";
m_context.display_literal(tout, l); tout << "\n";);
return l;
}
void dyn_ack_manager::instantiate(app * n1, app * n2) {
SASSERT(m_params.m_dack != dyn_ack_strategy::DACK_DISABLED);
SASSERT(n1->get_decl() == n2->get_decl());
SASSERT(n1->get_num_args() == n2->get_num_args());
SASSERT(n1 != n2);
m_context.m_stats.m_num_dyn_ack++;
TRACE("dyn_ack_inst", tout << "dyn_ack: " << n1->get_id() << " " << n2->get_id() << "\n";);
TRACE("dyn_ack", tout << "expanding Ackermann's rule for:\n" << mk_pp(n1, m) << "\n" << mk_pp(n2, m) << "\n";);
unsigned num_args = n1->get_num_args();
literal_buffer lits;
for (unsigned i = 0; i < num_args; i++) {
expr * arg1 = n1->get_arg(i);
expr * arg2 = n2->get_arg(i);
if (arg1 != arg2)
lits.push_back(~mk_eq(arg1, arg2));
}
app_pair p(n1, n2);
SASSERT(m_app_pair2num_occs.contains(n1, n2));
m_app_pair2num_occs.erase(n1, n2);
// pair n1,n2 is still in m_app_pairs
m_instantiated.insert(p);
lits.push_back(mk_eq(n1, n2));
clause_del_eh * del_eh = alloc(dyn_ack_clause_del_eh, *this);
justification * js = nullptr;
if (m.proofs_enabled())
js = alloc(dyn_ack_cc_justification, n1, n2);
clause * cls = m_context.mk_clause(lits.size(), lits.data(), js, CLS_TH_LEMMA, del_eh);
if (!cls) {
dealloc(del_eh);
return;
}
TRACE("dyn_ack_clause", tout << "new clause:\n"; m_context.display_clause_detail(tout, cls); tout << "\n";);
m_clause2app_pair.insert(cls, p);
}
void dyn_ack_manager::reset() {
init_search_eh();
m_instantiated.reset();
m_clause2app_pair.reset();
m_triple.m_instantiated.reset();
m_triple.m_clause2apps.reset();
}
void dyn_ack_manager::reset_app_triples() {
for (app_triple& p : m_triple.m_apps) {
m.dec_ref(p.first);
m.dec_ref(p.second);
m.dec_ref(p.third);
}
m_triple.m_apps.reset();
}
void dyn_ack_manager::instantiate(app * n1, app * n2, app* r) {
context& ctx = m_context;
SASSERT(m_params.m_dack != dyn_ack_strategy::DACK_DISABLED);
SASSERT(n1 != n2 && n1 != r && n2 != r);
ctx.m_stats.m_num_dyn_ack++;
TRACE("dyn_ack_inst", tout << "dyn_ack: " << n1->get_id() << " " << n2->get_id() << " " << r->get_id() << "\n";);
TRACE("dyn_ack", tout << "expanding Ackermann's rule for:\n" << mk_pp(n1, m) << "\n"
<< mk_pp(n2, m) << "\n"
<< mk_pp(r, m) << "\n";
);
app_triple tr(n1, n2, r);
SASSERT(m_triple.m_app2num_occs.contains(n1, n2, r));
m_triple.m_app2num_occs.erase(n1, n2, r);
// pair n1,n2 is still in m_triple.m_apps
m_triple.m_instantiated.insert(tr);
literal_buffer lits;
literal eq1 = mk_eq(n1, r);
literal eq2 = mk_eq(n2, r);
literal eq3 = mk_eq(n1, n2);
lits.push_back(~eq1);
lits.push_back(~eq2);
lits.push_back(eq3);
clause_del_eh * del_eh = alloc(dyn_ack_clause_del_eh, *this);
justification * js = nullptr;
if (m.proofs_enabled()) {
js = alloc(dyn_ack_eq_justification, n1, n2, r,
m.mk_eq(n1, r),
m.mk_eq(n2, r),
m.mk_eq(n1, n2));
}
clause * cls = ctx.mk_clause(lits.size(), lits.data(), js, CLS_TH_LEMMA, del_eh);
if (!cls) {
dealloc(del_eh);
return;
}
TRACE("dyn_ack_clause", ctx.display_clause_detail(tout << "new clause:\n", cls); tout << "\n";);
m_triple.m_clause2apps.insert(cls, tr);
}
struct app_triple_lt {
typedef triple app_triple;
typedef obj_triple_map app_triple2num_occs;
app_triple2num_occs & m_app_triple2num_occs;
app_triple_lt(app_triple2num_occs & m):
m_app_triple2num_occs(m) {
}
bool operator()(app_triple const & p1, app_triple const & p2) const {
unsigned n1 = 0;
unsigned n2 = 0;
m_app_triple2num_occs.find(p1.first, p1.second, p1.third, n1);
m_app_triple2num_occs.find(p2.first, p2.second, p2.third, n2);
SASSERT(n1 > 0);
SASSERT(n2 > 0);
return n1 > n2;
}
};
void dyn_ack_manager::gc_triples() {
TRACE("dyn_ack", tout << "dyn_ack GC\n";);
unsigned num_deleted = 0;
m_triple.m_to_instantiate.reset();
m_triple.m_qhead = 0;
svector::iterator it = m_triple.m_apps.begin();
svector::iterator end = m_triple.m_apps.end();
svector::iterator it2 = it;
for (; it != end; ++it) {
app_triple & p = *it;
if (m_triple.m_instantiated.contains(p)) {
TRACE("dyn_ack", tout << "1) erasing:\n" << mk_pp(p.first, m) << "\n" << mk_pp(p.second, m) << "\n";);
m.dec_ref(p.first);
m.dec_ref(p.second);
m.dec_ref(p.third);
SASSERT(!m_triple.m_app2num_occs.contains(p.first, p.second, p.third));
continue;
}
unsigned num_occs = 0;
m_triple.m_app2num_occs.find(p.first, p.second, p.third, num_occs);
// The following invariant is not true. p.first and
// p.second may have been instantiated, and removed from
// m_app_triple2num_occs, but not from m_app_triples.
//
// SASSERT(num_occs > 0);
num_occs = static_cast(num_occs * m_params.m_dack_gc_inv_decay);
if (num_occs <= 1) {
num_deleted++;
TRACE("dyn_ack", tout << "2) erasing:\n" << mk_pp(p.first, m) << "\n" << mk_pp(p.second, m) << "\n";);
m_triple.m_app2num_occs.erase(p.first, p.second, p.third);
m.dec_ref(p.first);
m.dec_ref(p.second);
m.dec_ref(p.third);
continue;
}
*it2 = p;
++it2;
SASSERT(num_occs > 0);
m_triple.m_app2num_occs.insert(p.first, p.second, p.third, num_occs);
if (num_occs >= m_params.m_dack_threshold)
m_triple.m_to_instantiate.push_back(p);
}
m_triple.m_apps.set_end(it2);
app_triple_lt f(m_triple.m_app2num_occs);
// app_triple_lt is not a total order
std::stable_sort(m_triple.m_to_instantiate.begin(), m_triple.m_to_instantiate.end(), f);
// IF_VERBOSE(10, if (num_deleted > 0) verbose_stream() << "dynamic ackermann GC: " << num_deleted << "\n";);
}
#ifdef Z3DEBUG
bool dyn_ack_manager::check_invariant() const {
for (auto const& kv : m_clause2app_pair) {
app_pair const & p = kv.get_value();
SASSERT(m_instantiated.contains(p));
SASSERT(!m_app_pair2num_occs.contains(p.first, p.second));
}
return true;
}
#endif
};
