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add start of self-contained proof checker for arithmetic

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2022-06-03 09:11:02 -07:00
parent 93a0322cac
commit 3d1e03e00a
2 changed files with 311 additions and 70 deletions
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92
src/shell/drat_frontend.cpp
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@ -17,6 +17,8 @@ Copyright (c) 2020 Microsoft Corporation
#include "cmd_context/cmd_context.h"
#include "ast/proofs/proof_checker.h"
#include "ast/rewriter/th_rewriter.h"
#include "sat/smt/arith_proof_checker.h"
class smt_checker {
ast_manager& m;
@ -162,92 +164,40 @@ public:
bool validate_hint(expr_ref_vector const& exprs, sat::literal_vector const& lits, sat::proof_hint const& hint) {
// return; // remove when testing this
proof_checker pc(m);
arith_util autil(m);
arith::proof_checker achecker(m);
switch (hint.m_ty) {
case sat::hint_type::null_h:
break;
case sat::hint_type::cut_h:
case sat::hint_type::bound_h:
case sat::hint_type::farkas_h: {
expr_ref sum(m), last_sum(m);
bool is_strict = false;
vector<rational> coeffs;
rational lc(1);
for (auto const& [coeff, a, b]: hint.m_eqs) {
coeffs.push_back(coeff);
lc = lcm(lc, denominator(coeff));
}
for (auto const& [coeff, lit] : hint.m_literals) {
coeffs.push_back(coeff);
lc = lcm(lc, denominator(coeff));
}
if (!lc.is_one())
for (auto& coeff : coeffs)
coeff *= lc;
unsigned i = 0;
achecker.reset();
for (auto const& [coeff, a, b]: hint.m_eqs) {
expr* x = exprs[a];
expr* y = exprs[b];
coeffs.push_back(coeff);
app_ref e(m.mk_eq(x, y), m);
if (!pc.check_arith_literal(true, e, coeffs[i], sum, is_strict)) {
std::cout << "p failed checking hint " << e << "\n";
return false;
}
++i;
achecker.add_eq(x, y);
}
for (auto const& [coeff, lit] : hint.m_literals) {
last_sum = sum;
unsigned sz = hint.m_literals.size();
for (unsigned i = 0; i < sz; ++i) {
auto const& [coeff, lit] = hint.m_literals[i];
app_ref e(to_app(m_b2e[lit.var()]), m);
if (!pc.check_arith_literal(!lit.sign(), e, coeffs[i], sum, is_strict)) {
std::cout << "p failed checking hint " << e << "\n";
return false;
}
++i;
}
if (!sum.get()) {
std::cout << "p no summation\n";
return false;
}
th_rewriter rw(m);
if (sat::hint_type::bound_h == hint.m_ty) {
rw(last_sum);
sum = last_sum;
auto const& [coeff, lit] = hint.m_literals.back();
rational last_coeff = coeff, r;
expr* x, *y, *z;
if (autil.is_add(sum)) {
x = to_app(sum)->get_arg(1);
if (autil.is_mul(x, y, z) && autil.is_numeral(y, r)) {
last_coeff = r;
if (i + 1 == sz && sat::hint_type::bound_h == hint.m_ty) {
if (!achecker.add_conseq(coeff, e, lit.sign())) {
std::cout << "p failed checking hint " << e << "\n";
return false;
}
}
else if (!achecker.add_ineq(coeff, e, lit.sign())) {
std::cout << "p failed checking hint " << e << "\n";
return false;
}
app_ref e(to_app(m_b2e[lit.var()]), m);
VERIFY(pc.check_arith_literal(!lit.sign(), e, last_coeff, sum, is_strict));
}
if (is_strict)
sum = autil.mk_lt(sum, autil.mk_numeral(rational(0), sum->get_sort()));
else
sum = autil.mk_le(sum, autil.mk_numeral(rational(0), sum->get_sort()));
rw(sum);
if (!m.is_false(sum)) {
// check hint:
std::cout << "p hint not verified " << sum << "\n";
auto const& [coeff, lit] = hint.m_literals.back();
expr_ref sum1(m);
bool is_strict1 = false;
app_ref e(to_app(m_b2e[lit.var()]), m);
rational coeffb = coeffs.back();
VERIFY(pc.check_arith_literal(!lit.sign(), e, coeffb, sum1, is_strict1));
std::cout << last_sum << " => ~" << sum1 << "\n";
bool ok = achecker.check();
if (!ok) {
for (auto const& [coeff, a, b]: hint.m_eqs) {
expr* x = exprs[a];
expr* y = exprs[b];
@ -261,6 +211,8 @@ public:
}
return false;
}
std::cout << "p hint verified\n";
break;
}