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add rewrite for mod over negation, refine axioms for grobner quotients

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This commit is contained in:
Nikolaj Bjorner 2025-09-02 18:26:22 -07:00
parent e2235d81d3
commit a382ddbd8a
4 changed files with 95 additions and 66 deletions
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6
src/ast/rewriter/arith_rewriter.cpp
View file

@ -1419,6 +1419,12 @@ br_status arith_rewriter::mk_mod_core(expr * arg1, expr * arg2, expr_ref & resul
return BR_REWRITE1; return BR_REWRITE1;
} }
// mod x -y = mod x y
if (m_util.is_mul(arg2, t1, t2) && m_util.is_numeral(t1, v1) && v1 == -1) {
result = m_util.mk_mod(arg1, t2);
return BR_REWRITE1;
}
return BR_FAILED; return BR_FAILED;
} }

127
src/math/lp/nla_grobner.cpp
View file

@ -54,6 +54,7 @@ namespace nla {
if (m_delay > 0) { if (m_delay > 0) {
--m_delay; --m_delay;
TRACE(grobner, tout << "delay " << m_delay << "\n");
return; return;
} }
@ -71,20 +72,20 @@ namespace nla {
if (is_conflicting()) if (is_conflicting())
return; return;
if (propagate_eqs())
return;
if (propagate_factorization())
return;
if (propagate_linear_equations())
return;
if (propagate_quotients()) if (propagate_quotients())
return; return;
if (propagate_gcd_test()) if (propagate_gcd_test())
return; return;
if (propagate_eqs())
return;
if (propagate_factorization())
return;
if (propagate_linear_equations())
return;
} }
catch (...) { catch (...) {
@ -147,9 +148,10 @@ namespace nla {
ineq new_eq(v, llc::EQ, rational::zero()); ineq new_eq(v, llc::EQ, rational::zero());
if (c().ineq_holds(new_eq)) if (c().ineq_holds(new_eq))
return false; return false;
lemma_builder lemma(c(), "pdd-eq"); lemma_builder lemma(c(), "grobner-eq");
add_dependencies(lemma, eq); add_dependencies(lemma, eq);
lemma |= new_eq; lemma |= new_eq;
TRACE(grobner, lemma.display(tout););
return true; return true;
} }
if (p.is_offset()) { if (p.is_offset()) {
@ -164,9 +166,10 @@ namespace nla {
ineq new_eq(term(a, v), llc::EQ, b); ineq new_eq(term(a, v), llc::EQ, b);
if (c().ineq_holds(new_eq)) if (c().ineq_holds(new_eq))
return false; return false;
lemma_builder lemma(c(), "pdd-eq"); lemma_builder lemma(c(), "grobner-eq");
add_dependencies(lemma, eq); add_dependencies(lemma, eq);
lemma |= new_eq; lemma |= new_eq;
TRACE(grobner, lemma.display(tout););
return true; return true;
} }
@ -196,7 +199,7 @@ namespace nla {
if (c().ineq_holds(i)) if (c().ineq_holds(i))
return false; return false;
lemma_builder lemma(c(), "pdd-factored"); lemma_builder lemma(c(), "grobner-factored");
add_dependencies(lemma, eq); add_dependencies(lemma, eq);
for (auto const& i : ineqs) for (auto const& i : ineqs)
lemma |= i; lemma |= i;
@ -277,6 +280,8 @@ namespace nla {
}; };
for (auto [x, k] : m_powers) { for (auto [x, k] : m_powers) {
SASSERT(k > 1); SASSERT(k > 1);
if (k > 4) // cut off at larger exponents.
continue;
bool gcd_fail = true; bool gcd_fail = true;
dd::pdd kx = m.mk_var(x) * m.mk_val(k); dd::pdd kx = m.mk_var(x) * m.mk_val(k);
for (unsigned r = 0; gcd_fail && r < k; r++) { for (unsigned r = 0; gcd_fail && r < k; r++) {
@ -286,7 +291,7 @@ namespace nla {
gcd_fail = false; gcd_fail = false;
} }
if (gcd_fail) { if (gcd_fail) {
lemma_builder lemma(c(), "pdd-power"); lemma_builder lemma(c(), "grobner-gcd-test");
add_dependencies(lemma, eq); add_dependencies(lemma, eq);
return true; return true;
} }
@ -329,6 +334,7 @@ namespace nla {
eval.var2val() = [&](unsigned j) { return val(j); }; eval.var2val() = [&](unsigned j) { return val(j); };
if (eval(p) == 0) if (eval(p) == 0)
return false; return false;
TRACE(grobner, tout << "propagate_quotients " << p << "\n");
tracked_uint_set nl_vars; tracked_uint_set nl_vars;
rational d(1); rational d(1);
for (auto const& m : p) { for (auto const& m : p) {
@ -339,6 +345,7 @@ namespace nla {
nl_vars.insert(j); nl_vars.insert(j);
} }
bool found_lemma = false;
for (auto v : nl_vars) { for (auto v : nl_vars) {
auto& m = p.manager(); auto& m = p.manager();
dd::pdd lc(m), r(m); dd::pdd lc(m), r(m);
@ -364,70 +371,87 @@ namespace nla {
continue; continue;
auto [t, offset] = linear_to_term(lc); auto [t, offset] = linear_to_term(lc);
auto [t2, offset2] = linear_to_term(r); auto [t2, offset2] = linear_to_term(r);
lemma_builder lemma(c(), "pdd-quotient"); lemma_builder lemma(c(), "grobner-quotient");
add_dependencies(lemma, eq); add_dependencies(lemma, eq);
// v = 0 or lc = 0 or r != 0 // v = 0 or lc = 0 or r != 0
lemma |= ineq(v, llc::EQ, rational::zero()); lemma |= ineq(v, llc::EQ, rational::zero());
lemma |= ineq(t, llc::EQ, -offset); lemma |= ineq(t, llc::EQ, -offset);
lemma |= ineq(t2, llc::NE, -offset2); lemma |= ineq(t2, llc::NE, -offset2);
return true; TRACE(grobner, lemma.display(tout << "quotient1\n"));
found_lemma = true;
continue;
} }
// r_value != 0 // r_value != 0
if (v_value == 0) { if (v_value == 0) {
// v = 0 => r = 0 // v = 0 => r = 0
lemma_builder lemma(c(), "pdd-quotient"); lemma_builder lemma(c(), "grobner-quotient");
add_dependencies(lemma, eq); add_dependencies(lemma, eq);
auto [t, offset] = linear_to_term(r); auto [t, offset] = linear_to_term(r);
lemma |= ineq(v, llc::NE, rational::zero()); lemma |= ineq(v, llc::NE, rational::zero());
lemma |= ineq(t, llc::EQ, -offset); lemma |= ineq(t, llc::EQ, -offset);
return true; TRACE(grobner, lemma.display(tout << "quotient2\n"));
found_lemma = true;
continue;
} }
if (lc_value == 0) { if (lc_value == 0) {
if (!lc.is_linear()) if (!lc.is_linear())
continue; continue;
// lc = 0 => r = 0 // lc = 0 => r = 0
lemma_builder lemma(c(), "pdd-quotient"); lemma_builder lemma(c(), "grobner-quotient");
add_dependencies(lemma, eq); add_dependencies(lemma, eq);
auto [t, offset] = linear_to_term(lc); auto [t, offset] = linear_to_term(lc);
auto [t2, offset2] = linear_to_term(r); auto [t2, offset2] = linear_to_term(r);
lemma |= ineq(t, llc::NE, -offset); lemma |= ineq(t, llc::NE, -offset);
lemma |= ineq(t2, llc::EQ, -offset2); lemma |= ineq(t2, llc::EQ, -offset2);
return true; TRACE(grobner, lemma.display(tout << "quotient3\n"));
found_lemma = true;
continue;
} }
if (divides(v_value, r_value)) if (divides(v_value, r_value))
continue; continue;
if (abs(v_value) > abs(r_value)) { if (abs(v_value) > abs(r_value)) {
// v*c + r = 0 & v > 0 => r >= v or -r >= v or r = 0 // v*c + r = 0 & v > 0 => r >= v or -r >= v or r = 0
lemma_builder lemma(c(), "pdd-quotient"); lemma_builder lemma(c(), "grobner-quotient");
auto [t, offset] = linear_to_term(r); auto [t, offset] = linear_to_term(r);
add_dependencies(lemma, eq); add_dependencies(lemma, eq);
if (v_value > 0) { if (v_value > 0 && r_value > 0) {
lemma |= ineq(v, llc::LE, rational::zero()); // v*c + t = 0 => v <= 0 or v <= t or t <= 0
lemma |= ineq(t, llc::EQ, -offset); lemma |= ineq(v, llc::LE, rational::zero()); // v <= 0
lemma |= ineq(t, llc::LE, -offset); // t <= 0
t.add_monomial(rational(-1), v); t.add_monomial(rational(-1), v);
lemma |= ineq(t, llc::GE, -offset); lemma |= ineq(t, llc::GE, -offset); // t - v >= 0
auto [t2, offset2] = linear_to_term(-r);
t2.add_monomial(rational(-1), v);
lemma |= ineq(t2, llc::GE, -offset2);
} }
else { else if (v_value > 0 && r_value < 0) {
// v*lc + r = 0 & v < 0 => r <= v or -r <= v or r = 0 // v*c + t = 0 => v <= 0 or v <= -t or t >= 0
lemma |= ineq(v, llc::GE, rational::zero()); lemma |= ineq(v, llc::LE, rational::zero()); // v <= 0
lemma |= ineq(t, llc::EQ, -offset); lemma |= ineq(t, llc::GE, -offset); // t >= 0
t.add_monomial(rational(1), v);
lemma |= ineq(t, llc::LE, -offset); // t + v <= 0
}
else if (v_value < 0 && r_value > 0) {
// v*c + t = 0 => v >= 0 or -v <= t or t <= 0
lemma |= ineq(v, llc::GE, rational::zero()); // v >= 0
lemma |= ineq(t, llc::LE, -offset); // t <= 0
t.add_monomial(rational(1), v);
lemma |= ineq(t, llc::GE, -offset); // t + v >= 0
}
else if (v_value < 0 && r_value < 0) {
// v*c + t = 0 => v >= 0 or v >= t or t >= 0
lemma |= ineq(v, llc::GE, rational::zero()); // v >= 0
lemma |= ineq(t, llc::GE, -offset); // t >= 0
t.add_monomial(rational(-1), v); t.add_monomial(rational(-1), v);
lemma |= ineq(t, llc::LE, -offset); lemma |= ineq(t, llc::LE, -offset); // t - v <= 0
auto [t2, offset2] = linear_to_term(-r);
t2.add_monomial(rational(-1), v);
lemma |= ineq(t2, llc::LE, -offset2);
} }
return true; TRACE(grobner, lemma.display(tout << "quotient4\n"));
found_lemma = true;
continue;
} }
// other division lemmas are possible. // other division lemmas are possible.
// also extend to non-linear r, non-linear lc // also extend to non-linear r, non-linear lc
} }
CTRACE(grobner, !found_lemma, tout << "no lemmas found for " << p << "\n");
return false; return found_lemma;
} }
void grobner::explain(dd::solver::equation const& eq, lp::explanation& exp) { void grobner::explain(dd::solver::equation const& eq, lp::explanation& exp) {
@ -542,24 +566,11 @@ namespace nla {
}; };
scoped_dep_interval i(di), i_wd(di); scoped_dep_interval i(di), i_wd(di);
evali.get_interval<dd::w_dep::without_deps>(e.poly(), i); evali.get_interval<dd::w_dep::without_deps>(e.poly(), i);
if (!di.separated_from_zero(i)) { if (!di.separated_from_zero(i)) {
TRACE(grobner, m_solver.display(tout << "not separated from 0 ", e) << "\n"; if (add_horner_conflict(e)) {
evali.get_interval_distributed<dd::w_dep::without_deps>(e.poly(), i); TRACE(grobner, m_solver.display(tout << "horner conflict ", e) << "\n");
tout << "separated from 0: " << di.separated_from_zero(i) << "\n";
for (auto j : e.poly().free_vars()) {
scoped_dep_interval a(di);
c().m_intervals.set_var_interval<dd::w_dep::without_deps>(j, a);
c().m_intervals.display(tout << "j" << j << " ", a); tout << " ";
}
tout << "\n");
if (add_horner_conflict(e))
return true; return true;
#if 0 }
if (add_nla_conflict(e))
return true;
#endif
return false; return false;
} }
evali.get_interval<dd::w_dep::with_deps>(e.poly(), i_wd); evali.get_interval<dd::w_dep::with_deps>(e.poly(), i_wd);
@ -572,10 +583,6 @@ namespace nla {
return true; return true;
} }
else { else {
#if 0
if (add_nla_conflict(e))
return true;
#endif
TRACE(grobner, m_solver.display(tout << "no conflict ", e) << "\n"); TRACE(grobner, m_solver.display(tout << "no conflict ", e) << "\n");
return false; return false;
} }
@ -662,7 +669,7 @@ namespace nla {
if (!lra.var_is_int(k)) if (!lra.var_is_int(k))
continue; continue;
// free integer columns are ignored unless m_add_all_eqs is set or we are doing gcd test. // free integer columns are ignored unless m_add_all_eqs is set or we are doing gcd test.
if (!m_add_all_eqs && !m_config.m_gcd_test) if (!m_add_all_eqs && !m_config.m_gcd_test && !m_config.m_propagate_quotients)
continue; continue;
// a free integer column with integer coefficients can be assigned. // a free integer column with integer coefficients can be assigned.
if (!m_add_all_eqs && all_of(c().lra.get_row(row), [&](auto& ri) { return ri.coeff().is_int();})) if (!m_add_all_eqs && all_of(c().lra.get_row(row), [&](auto& ri) { return ri.coeff().is_int();}))

1
src/math/lp/nla_grobner.h
View file

@ -88,6 +88,5 @@ namespace nla {
grobner(core *core); grobner(core *core);
void operator()(); void operator()();
void updt_params(params_ref const& p); void updt_params(params_ref const& p);
// dd::solver::equation_vector const& core_equations(bool all_eqs);
}; };
} }

27
src/smt/theory_lra.cpp
View file

@ -601,6 +601,12 @@ class theory_lra::imp {
ctx().mk_th_axiom(get_id(), l1, l2, l3, num_params, params); ctx().mk_th_axiom(get_id(), l1, l2, l3, num_params, params);
} }
void mk_clause(literal l1, literal l2, literal l3, literal l4, unsigned num_params, parameter* params) {
literal clause[4] = { l1, l2, l3, l4 };
TRACE(arith, ctx().display_literals_smt2(tout, 4, clause); tout << "\n";);
ctx().mk_th_axiom(get_id(), 4, clause, num_params, params);
}
bool reflect(app* n) const { bool reflect(app* n) const {
return params().m_arith_reflect || a.is_underspecified(n); return params().m_arith_reflect || a.is_underspecified(n);
@ -1288,6 +1294,7 @@ public:
else { else {
expr_ref mone(a.mk_int(-1), m); expr_ref mone(a.mk_int(-1), m);
expr_ref minus_q(a.mk_mul(mone, q), m);
literal eqz = mk_literal(m.mk_eq(q, zero)); literal eqz = mk_literal(m.mk_eq(q, zero));
literal mod_ge_0 = mk_literal(a.mk_ge(mod, zero)); literal mod_ge_0 = mk_literal(a.mk_ge(mod, zero));
@ -1296,12 +1303,13 @@ public:
// q = 0 or (p mod q) >= 0 // q = 0 or (p mod q) >= 0
// q >= 0 or (p mod q) + q <= -1 // q >= 0 or (p mod q) + q <= -1
// q <= 0 or (p mod q) - q <= -1 // q <= 0 or (p mod q) - q <= -1
// (p mod q) = (p mod -q)
mk_axiom(eqz, eq); mk_axiom(eqz, eq);
mk_axiom(eqz, mod_ge_0); mk_axiom(eqz, mod_ge_0);
mk_axiom(mk_literal(a.mk_le(q, zero)), mk_literal(a.mk_le(a.mk_add(mod, a.mk_mul(mone, q)), mone))); mk_axiom(mk_literal(a.mk_le(q, zero)), mk_literal(a.mk_le(a.mk_add(mod, minus_q), mone)));
mk_axiom(mk_literal(a.mk_ge(q, zero)), mk_literal(a.mk_le(a.mk_add(mod, q), mone))); mk_axiom(mk_literal(a.mk_ge(q, zero)), mk_literal(a.mk_le(a.mk_add(mod, q), mone)));
expr* x = nullptr, * y = nullptr; expr* x = nullptr, * y = nullptr;
if (false && !(a.is_mul(q, x, y) && mone == x)) if (false && !(a.is_mul(q, x, y) && mone == x))
mk_axiom(mk_literal(m.mk_eq(mod, a.mk_mod(p, a.mk_mul(mone, q))))); mk_axiom(mk_literal(m.mk_eq(mod, a.mk_mod(p, a.mk_mul(mone, q)))));
@ -1420,12 +1428,21 @@ public:
} }
} }
void mk_axiom(literal l1, literal l2, literal l3, literal l4) {
mk_clause(l1, l2, l3, l4, 0, nullptr);
if (ctx().relevancy()) {
ctx().mark_as_relevant(l1);
ctx().mark_as_relevant(l2);
ctx().mark_as_relevant(l3);
ctx().mark_as_relevant(l4);
}
}
literal mk_literal(expr* e) { literal mk_literal(expr* e) {
expr_ref pinned(e, m); expr_ref pinned(e, m);
TRACE(mk_bool_var, tout << pinned << " " << pinned->get_id() << "\n";); TRACE(mk_bool_var, tout << pinned << " " << pinned->get_id() << "\n";);
if (!ctx().e_internalized(e)) { if (!ctx().e_internalized(e))
ctx().internalize(e, false); ctx().internalize(e, false);
}
return ctx().get_literal(e); return ctx().get_literal(e);
} }