Copyright (c) 2017 Microsoft Corporation
Module Name:
sat_drat.cpp
Abstract:
Produce DRAT proofs.
Check them using a very simple forward checker
that interacts with external plugins.
Author:
Nikolaj Bjorner (nbjorner) 2017-2-3
Notes:
--*/
#include "sat_solver.h"
#include "sat_drat.h"
namespace sat {
drat::drat(solver& s) :
s(s),
m_out(nullptr),
m_bout(nullptr),
m_inconsistent(false),
m_check_unsat(false),
m_check_sat(false),
m_check(false),
m_activity(false)
{
if (s.get_config().m_drat && s.get_config().m_drat_file.is_non_empty_string()) {
auto mode = s.get_config().m_drat_binary ? (std::ios_base::binary | std::ios_base::out | std::ios_base::trunc) : std::ios_base::out;
m_out = alloc(std::ofstream, s.get_config().m_drat_file.str(), mode);
if (s.get_config().m_drat_binary) {
std::swap(m_out, m_bout);
}
}
}
drat::~drat() {
if (m_out) m_out->flush();
if (m_bout) m_bout->flush();
dealloc(m_out);
dealloc(m_bout);
for (unsigned i = 0; i < m_proof.size(); ++i) {
clause* c = m_proof[i];
if (c) {
m_alloc.del_clause(c);
}
}
m_proof.reset();
m_out = nullptr;
m_bout = nullptr;
}
void drat::updt_config() {
m_check_unsat = s.get_config().m_drat_check_unsat;
m_check_sat = s.get_config().m_drat_check_sat;
m_check = m_check_unsat || m_check_sat;
m_activity = s.get_config().m_drat_activity;
}
std::ostream& drat::pp(std::ostream& out, status st) const {
if (st.is_redundant())
out << "l";
else if (st.is_deleted())
out << "d";
else if (st.is_asserted())
out << "a";
else if (st.is_input())
out << "i";
if (!st.is_sat())
out << " " << m_theory[st.get_th()];
return out;
}
void drat::dump(unsigned n, literal const* c, status st) {
if (st.is_asserted() && !s.m_ext)
return;
if (m_activity && ((m_stats.m_num_add % 1000) == 0))
dump_activity();
char buffer[10000];
char digits[20];
char* lastd = digits + sizeof(digits);
unsigned len = 0;
if (st.is_deleted()) {
buffer[len++] = 'd';
buffer[len++] = ' ';
}
else if (st.is_input()) {
buffer[len++] = 'i';
buffer[len++] = ' ';
}
else if (!st.is_sat()) {
if (st.is_redundant()) {
buffer[len++] = 'r';
buffer[len++] = ' ';
}
else if (st.is_asserted()) {
buffer[len++] = 'a';
buffer[len++] = ' ';
}
}
if (!st.is_sat()) {
for (char ch : m_theory[st.get_th()])
buffer[len++] = ch;
buffer[len++] = ' ';
}
for (unsigned i = 0; i < n; ++i) {
literal lit = c[i];
unsigned v = lit.var();
if (lit.sign()) buffer[len++] = '-';
char* d = lastd;
SASSERT(v > 0);
while (v > 0) {
d--;
*d = (v % 10) + '0';
v /= 10;
SASSERT(d > digits);
}
SASSERT(len + lastd < sizeof(buffer) + d);
memcpy(buffer + len, d, lastd - d);
len += static_cast<unsigned>(lastd - d);
buffer[len++] = ' ';
if (len + 50 > sizeof(buffer)) {
m_out->write(buffer, len);
len = 0;
}
}
buffer[len++] = '0';
buffer[len++] = '\n';
m_out->write(buffer, len);
}
void drat::dump_activity() {
(*m_out) << "c activity ";
for (unsigned v = 0; v < s.num_vars(); ++v) {
(*m_out) << s.m_activity[v] << " ";
}
(*m_out) << "\n";
}
void drat::bdump(unsigned n, literal const* c, status st) {
unsigned char ch = 0;
if (st.is_redundant())
ch = 'a';
else if (st.is_deleted())
ch = 'd';
else return;
char buffer[10000];
int len = 0;
buffer[len++] = ch;
for (unsigned i = 0; i < n; ++i) {
literal lit = c[i];
unsigned v = 2 * lit.var() + (lit.sign() ? 1 : 0);
do {
ch = static_cast<unsigned char>(v & 255);
v >>= 7;
if (v) ch |= 128;
buffer[len++] = ch;
if (len == sizeof(buffer)) {
m_bout->write(buffer, len);
len = 0;
}
} while (v);
}
buffer[len++] = 0;
m_bout->write(buffer, len);
}
bool drat::is_cleaned(clause& c) const {
literal last = null_literal;
unsigned n = c.size();
for (unsigned i = 0; i < n; ++i) {
if (c[i] == last) return true;
last = c[i];
}
return false;
}
void drat::trace(std::ostream& out, unsigned n, literal const* c, status st) {
pp(out, st) << " ";
literal last = null_literal;
for (unsigned i = 0; i < n; ++i) {
if (c[i] != last) {
out << c[i] << " ";
last = c[i];
}
}
out << "\n";
}
void drat::append(literal l, status st) {
TRACE("sat_drat", pp(tout, st) << " " << l << "\n";);
declare(l);
IF_VERBOSE(20, trace(verbose_stream(), 1, &l, st););
if (st.is_redundant() && st.is_sat()) {
verify(1, &l);
}
if (st.is_deleted()) {
return;
}
if (m_check_unsat) {
assign_propagate(l);
}
m_units.push_back(l);
}
void drat::append(literal l1, literal l2, status st) {
TRACE("sat_drat", pp(tout, st) << " " << l1 << " " << l2 << "\n";);
declare(l1);
declare(l2);
literal lits[2] = { l1, l2 };
IF_VERBOSE(20, trace(verbose_stream(), 2, lits, st););
if (st.is_deleted()) {
}
else {
if (st.is_redundant() && st.is_sat()) {
verify(2, lits);
}
clause* c = m_alloc.mk_clause(2, lits, st.is_redundant());
m_proof.push_back(c);
m_status.push_back(st);
if (!m_check_unsat) return;
unsigned idx = m_watched_clauses.size();
m_watched_clauses.push_back(watched_clause(c, l1, l2));
m_watches[(~l1).index()].push_back(idx);
m_watches[(~l2).index()].push_back(idx);
if (value(l1) == l_false && value(l2) == l_false) {
m_inconsistent = true;
}
else if (value(l1) == l_false) {
assign_propagate(l2);
}
else if (value(l2) == l_false) {
assign_propagate(l1);
}
}
}
void drat::bool_def(bool_var v, unsigned n) {
if (m_out)
(*m_out) << "b " << v << " " << n << " 0\n";
}
void drat::def_begin(char id, unsigned n, std::string const& name) {
if (m_out)
(*m_out) << id << " " << n << " " << name;
}
void drat::def_add_arg(unsigned arg) {
if (m_out)
(*m_out) << " " << arg;
}
void drat::def_end() {
if (m_out)
(*m_out) << " 0\n";
}
void drat::log_adhoc(std::function<void(std::ostream&)>& fn) {
if (m_out)
fn(*m_out);
}
#if 0
bool drat::is_clause(clause& c, literal l1, literal l2, literal l3, drat::status st1, drat::status st2) {
if (c.size() != 3) return false;
if (l1 == c[0]) {
if (l2 == c[1] && l3 == c[2]) return true;
if (l2 == c[2] && l3 == c[1]) return true;
}
if (l2 == c[0]) {
if (l1 == c[1] && l3 == c[2]) return true;
if (l1 == c[2] && l3 == c[1]) return true;
}
if (l3 == c[0]) {
if (l1 == c[1] && l2 == c[2]) return true;
if (l1 == c[2] && l2 == c[1]) return true;
}
return false;
}
#endif
void drat::append(clause& c, status st) {
TRACE("sat_drat", pp(tout, st) << " " << c << "\n";);
for (literal lit : c) declare(lit);
unsigned n = c.size();
IF_VERBOSE(20, trace(verbose_stream(), n, c.begin(), st););
if (st.is_redundant() && st.is_sat()) {
verify(c);
}
m_status.push_back(st);
m_proof.push_back(&c);
if (st.is_deleted()) {
if (n > 0) del_watch(c, c[0]);
if (n > 1) del_watch(c, c[1]);
return;
}
unsigned num_watch = 0;
literal l1, l2;
for (unsigned i = 0; i < n; ++i) {
if (value(c[i]) != l_false) {
if (num_watch == 0) {
l1 = c[i];
++num_watch;
}
else {
l2 = c[i];
++num_watch;
break;
}
}
}
switch (num_watch) {
case 0:
m_inconsistent = true;
break;
case 1:
assign_propagate(l1);
break;
default: {
SASSERT(num_watch == 2);
unsigned idx = m_watched_clauses.size();
m_watched_clauses.push_back(watched_clause(&c, l1, l2));
m_watches[(~l1).index()].push_back(idx);
m_watches[(~l2).index()].push_back(idx);
break;
}
}
}
void drat::del_watch(clause& c, literal l) {
watch& w = m_watches[(~l).index()];
for (unsigned i = 0; i < w.size(); ++i) {
if (m_watched_clauses[w[i]].m_clause == &c) {
w[i] = w.back();
w.pop_back();
break;
}
}
}
void drat::declare(literal l) {
if (!m_check) return;
unsigned n = static_cast<unsigned>(l.var());
while (m_assignment.size() <= n) {
m_assignment.push_back(l_undef);
m_watches.push_back(watch());
m_watches.push_back(watch());
}
}
bool drat::is_drup(unsigned n, literal const* c, literal_vector& units) {
if (m_inconsistent)
return true;
if (n == 0)
return false;
unsigned num_units = m_units.size();
for (unsigned i = 0; !m_inconsistent && i < n; ++i) {
declare(c[i]);
assign_propagate(~c[i]);
}
for (unsigned i = num_units; i < m_units.size(); ++i) {
m_assignment[m_units[i].var()] = l_undef;
}
units.append(m_units.size() - num_units, m_units.data() + num_units);
m_units.shrink(num_units);
bool ok = m_inconsistent;
m_inconsistent = false;
return ok;
}
bool drat::is_drup(unsigned n, literal const* c) {
if (m_inconsistent)
return true;
if (n == 0)
return false;
unsigned num_units = m_units.size();
for (unsigned i = 0; !m_inconsistent && i < n; ++i) {
assign_propagate(~c[i]);
}
if (!m_inconsistent) {
DEBUG_CODE(validate_propagation(););
}
DEBUG_CODE(
for (literal u : m_units) {
SASSERT(m_assignment[u.var()] != l_undef);
});
#if 0
if (!m_inconsistent) {
literal_vector lits(n, c);
IF_VERBOSE(0, verbose_stream() << "not drup " << lits << "\n");
for (unsigned v = 0; v < m_assignment.size(); ++v) {
lbool val = m_assignment[v];
if (val != l_undef) {
IF_VERBOSE(0, verbose_stream() << literal(v, false) << " |-> " << val << "\n");
}
}
for (clause* cp : s.m_clauses) {
clause& cl = *cp;
bool found = false;
for (literal l : cl) {
if (m_assignment[l.var()] != (l.sign() ? l_true : l_false)) {
found = true;
break;
}
}
if (!found) {
IF_VERBOSE(0, verbose_stream() << "Clause is false under assignment: " << cl << "\n");
}
}
for (clause* cp : s.m_learned) {
clause& cl = *cp;
bool found = false;
for (literal l : cl) {
if (m_assignment[l.var()] != (l.sign() ? l_true : l_false)) {
found = true;
break;
}
}
if (!found) {
IF_VERBOSE(0, verbose_stream() << "Clause is false under assignment: " << cl << "\n");
}
}
svector<sat::solver::bin_clause> bin;
s.collect_bin_clauses(bin, true);
for (auto& b : bin) {
bool found = false;
if (m_assignment[b.first.var()] != (b.first.sign() ? l_true : l_false)) found = true;
if (m_assignment[b.second.var()] != (b.second.sign() ? l_true : l_false)) found = true;
if (!found) {
IF_VERBOSE(0, verbose_stream() << "Bin clause is false under assignment: " << b.first << " " << b.second << "\n");
}
}
IF_VERBOSE(0, s.display(verbose_stream()));
exit(0);
}
#endif
for (unsigned i = num_units; i < m_units.size(); ++i) {
m_assignment[m_units[i].var()] = l_undef;
}
m_units.shrink(num_units);
bool ok = m_inconsistent;
m_inconsistent = false;
return ok;
}
bool drat::is_drat(unsigned n, literal const* c) {
return false;
if (m_inconsistent || n == 0)
return true;
for (unsigned i = 0; i < n; ++i)
if (is_drat(n, c, i))
return true;
return false;
}
void drat::validate_propagation() const {
for (unsigned i = 0; i < m_proof.size(); ++i) {
status st = m_status[i];
if (m_proof[i] && m_proof[i]->size() > 1 && !st.is_deleted()) {
clause& c = *m_proof[i];
unsigned num_undef = 0, num_true = 0;
for (unsigned j = 0; j < c.size(); ++j) {
switch (value(c[j])) {
case l_false: break;
case l_true: num_true++; break;
case l_undef: num_undef++; break;
}
}
CTRACE("sat_drat", num_true == 0 && num_undef == 1, display(tout););
SASSERT(num_true != 0 || num_undef != 1);
}
}
}
bool drat::is_drat(unsigned n, literal const* c, unsigned pos) {
SASSERT(pos < n);
literal l = c[pos];
literal_vector lits(n, c);
SASSERT(lits.size() == n);
for (unsigned i = 0; i < m_proof.size(); ++i) {
status st = m_status[i];
if (m_proof[i] && m_proof[i]->size() > 1 && st.is_asserted()) {
clause& c = *m_proof[i];
unsigned j = 0;
for (; j < c.size() && c[j] != ~l; ++j) {}
if (j != c.size()) {
lits.append(j, c.begin());
lits.append(c.size() - j - 1, c.begin() + j + 1);
if (!is_drup(lits.size(), lits.data()))
return false;
lits.resize(n);
}
}
}
return true;
}
void drat::verify(unsigned n, literal const* c) {
if (!m_check_unsat) {
return;
}
for (unsigned i = 0; i < n; ++i) {
declare(c[i]);
}
if (is_drup(n, c)) {
++m_stats.m_num_drup;
return;
}
if (is_drat(n, c)) {
++m_stats.m_num_drat;
return;
}
literal_vector lits(n, c);
IF_VERBOSE(0, verbose_stream() << "Verification of " << lits << " failed\n");
std::string line;
std::getline(std::cin, line);
exit(0);
#if 0
SASSERT(false);
INVOKE_DEBUGGER();
exit(0);
UNREACHABLE();
TRACE("sat_drat",
tout << literal_vector(n, c) << "\n";
display(tout);
s.display(tout););
UNREACHABLE();
#endif
}
bool drat::contains(literal c, justification const& j) {
if (!m_check_sat) {
return true;
}
switch (j.get_kind()) {
case justification::NONE:
return m_units.contains(c);
case justification::BINARY:
return contains(c, j.get_literal());
case justification::TERNARY:
return contains(c, j.get_literal1(), j.get_literal2());
case justification::CLAUSE:
return contains(s.get_clause(j));
default:
return true;
}
}
bool drat::contains(unsigned n, literal const* lits) {
if (!m_check) return true;
unsigned num_add = 0;
unsigned num_del = 0;
for (unsigned i = m_proof.size(); i-- > 0; ) {
clause& c = *m_proof[i];
status st = m_status[i];
if (match(n, lits, c)) {
if (st.is_deleted()) {
num_del++;
}
else {
num_add++;
}
}
}
return num_add > num_del;
}
bool drat::match(unsigned n, literal const* lits, clause const& c) const {
if (n == c.size()) {
for (unsigned i = 0; i < n; ++i) {
literal lit1 = lits[i];
bool found = false;
for (literal lit2 : c) {
if (lit1 == lit2) {
found = true;
break;
}
}
if (!found) {
return false;
}
}
return true;
}
return false;
}
void drat::display(std::ostream& out) const {
out << "units: " << m_units << "\n";
for (unsigned i = 0; i < m_assignment.size(); ++i) {
lbool v = value(literal(i, false));
if (v != l_undef) out << i << ": " << v << "\n";
}
for (unsigned i = 0; i < m_proof.size(); ++i) {
clause* c = m_proof[i];
if (!m_status[i].is_deleted() && c) {
unsigned num_true = 0;
unsigned num_undef = 0;
for (unsigned j = 0; j < c->size(); ++j) {
switch (value((*c)[j])) {
case l_true: num_true++; break;
case l_undef: num_undef++; break;
default: break;
}
}
if (num_true == 0 && num_undef == 0) {
out << "False ";
}
if (num_true == 0 && num_undef == 1) {
out << "Unit ";
}
pp(out, m_status[i]) << " " << i << ": " << *c << "\n";
}
}
for (unsigned i = 0; i < m_assignment.size(); ++i) {
watch const& w1 = m_watches[2 * i];
watch const& w2 = m_watches[2 * i + 1];
if (!w1.empty()) {
out << i << " |-> ";
for (unsigned i = 0; i < w1.size(); ++i) out << *(m_watched_clauses[w1[i]].m_clause) << " ";
out << "\n";
}
if (!w2.empty()) {
out << "-" << i << " |-> ";
for (unsigned i = 0; i < w2.size(); ++i) out << *(m_watched_clauses[w2[i]].m_clause) << " ";
out << "\n";
}
}
}
lbool drat::value(literal l) const {
lbool val = m_assignment.get(l.var(), l_undef);
return val == l_undef || !l.sign() ? val : ~val;
}
void drat::assign(literal l) {
lbool new_value = l.sign() ? l_false : l_true;
lbool old_value = value(l);
switch (old_value) {
case l_false:
m_inconsistent = true;
break;
case l_true:
break;
case l_undef:
m_assignment.setx(l.var(), new_value, l_undef);
m_units.push_back(l);
break;
}
}
void drat::assign_propagate(literal l) {
unsigned num_units = m_units.size();
assign(l);
for (unsigned i = num_units; !m_inconsistent && i < m_units.size(); ++i) {
propagate(m_units[i]);
}
}
void drat::propagate(literal l) {
watch& clauses = m_watches[l.index()];
watch::iterator it = clauses.begin();
watch::iterator it2 = it;
watch::iterator end = clauses.end();
for (; it != end; ++it) {
unsigned idx = *it;
watched_clause& wc = m_watched_clauses[idx];
clause& c = *wc.m_clause;
if (wc.m_l1 == ~l) {
std::swap(wc.m_l1, wc.m_l2);
}
SASSERT(wc.m_l2 == ~l);
if (value(wc.m_l1) == l_true) {
*it2 = *it;
it2++;
}
else {
bool done = false;
for (unsigned i = 0; !done && i < c.size(); ++i) {
literal lit = c[i];
if (lit != wc.m_l1 && lit != wc.m_l2 && value(lit) != l_false) {
wc.m_l2 = lit;
m_watches[(~lit).index()].push_back(idx);
done = true;
}
}
if (done) {
continue;
}
else if (value(wc.m_l1) == l_false) {
m_inconsistent = true;
goto end_process_watch;
}
else {
*it2 = *it;
it2++;
assign(wc.m_l1);
}
}
}
end_process_watch:
for (; it != end; ++it, ++it2)
*it2 = *it;
clauses.set_end(it2);
}
status drat::get_status(bool learned) const {
if (learned || s.m_searching)
return status::redundant();
return status::asserted();
}
void drat::add() {
++m_stats.m_num_add;
if (m_out) (*m_out) << "0\n";
if (m_bout) bdump(0, nullptr, status::redundant());
if (m_check_unsat) {
verify(0, nullptr);
SASSERT(m_inconsistent);
}
}
void drat::add(literal l, bool learned) {
++m_stats.m_num_add;
status st = get_status(learned);
if (m_out) dump(1, &l, st);
if (m_bout) bdump(1, &l, st);
if (m_check) append(l, st);
}
void drat::add(literal l1, literal l2, status st) {
if (st.is_deleted())
++m_stats.m_num_del;
else
++m_stats.m_num_add;
literal ls[2] = { l1, l2 };
if (m_out) dump(2, ls, st);
if (m_bout) bdump(2, ls, st);
if (m_check) append(l1, l2, st);
}
void drat::add(clause& c, status st) {
if (st.is_deleted())
++m_stats.m_num_del;
else
++m_stats.m_num_add;
if (m_out) dump(c.size(), c.begin(), st);
if (m_bout) bdump(c.size(), c.begin(), st);
if (m_check) {
clause* cl = m_alloc.mk_clause(c.size(), c.begin(), st.is_redundant());
append(*cl, st);
}
}
void drat::add(literal_vector const& lits, status st) {
add(lits.size(), lits.data(), st);
}
void drat::add(unsigned sz, literal const* lits, status st) {
if (st.is_deleted())
++m_stats.m_num_del;
else
++m_stats.m_num_add;
if (m_check) {
switch (sz) {
case 0: add(); break;
case 1: append(lits[0], st); break;
default: {
clause* c = m_alloc.mk_clause(sz, lits, st.is_redundant());
append(*c, st);
break;
}
}
}
if (m_out)
dump(sz, lits, st);
}
void drat::add(literal_vector const& c) {
++m_stats.m_num_add;
if (m_out) dump(c.size(), c.begin(), status::redundant());
if (m_bout) bdump(c.size(), c.begin(), status::redundant());
if (m_check) {
for (literal lit : c) declare(lit);
switch (c.size()) {
case 0: add(); break;
case 1: append(c[0], status::redundant()); break;
default: {
verify(c.size(), c.begin());
clause* cl = m_alloc.mk_clause(c.size(), c.data(), true);
append(*cl, status::redundant());
break;
}
}
}
}
void drat::del(literal l) {
++m_stats.m_num_del;
if (m_out) dump(1, &l, status::deleted());
if (m_bout) bdump(1, &l, status::deleted());
if (m_check_unsat) append(l, status::deleted());
}
void drat::del(literal l1, literal l2) {
++m_stats.m_num_del;
literal ls[2] = { l1, l2 };
if (m_out) dump(2, ls, status::deleted());
if (m_bout) bdump(2, ls, status::deleted());
if (m_check) append(l1, l2, status::deleted());
}
void drat::del(clause& c) {
#if 0
for (literal lit : c) {
VERIFY(!m_seen[lit.index()]);
m_seen[lit.index()] = true;
}
for (literal lit : c) {
m_seen[lit.index()] = false;
}
#endif
++m_stats.m_num_del;
if (m_out) dump(c.size(), c.begin(), status::deleted());
if (m_bout) bdump(c.size(), c.begin(), status::deleted());
if (m_check) {
clause* c1 = m_alloc.mk_clause(c.size(), c.begin(), c.is_learned());
append(*c1, status::deleted());
}
}
void drat::del(literal_vector const& c) {
++m_stats.m_num_del;
if (m_out) dump(c.size(), c.begin(), status::deleted());
if (m_bout) bdump(c.size(), c.begin(), status::deleted());
if (m_check) {
clause* c1 = m_alloc.mk_clause(c.size(), c.begin(), true);
append(*c1, status::deleted());
}
}
void drat::check_model(model const& m) {
}
void drat::collect_statistics(statistics& st) const {
st.update("num-drup", m_stats.m_num_drup);
st.update("num-drat", m_stats.m_num_drat);
st.update("num-add", m_stats.m_num_add);
st.update("num-del", m_stats.m_num_del);
}
std::ostream& operator<<(std::ostream& out, sat::status const& st) {
std::function<symbol(int)> th = [&](int id) { return symbol(id); };
return out << sat::status_pp(st, th);
}
std::ostream& operator<<(std::ostream& out, sat::status_pp const& p) {
auto st = p.st;
if (st.is_deleted())
out << "d";
else if (st.is_input())
out << "i";
else if (st.is_asserted())
out << "a";
else if (st.is_redundant() && !st.is_sat())
out << "r";
if (!st.is_sat())
out << " " << p.th(st.get_th());
return out;
}
}