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internalize arithmetic sub-terms #5753

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Nikolaj Bjorner 2022-01-13 15:34:04 -08:00
parent e816946ddc
commit 2363bfc132
2 changed files with 698 additions and 1 deletions
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/*++
Copyright (c) 2020 Microsoft Corporation
Module Name:
arith_internalize.cpp
Abstract:
Theory plugin for arithmetic
Author:
Nikolaj Bjorner (nbjorner) 2020-09-08
--*/
#include "sat/smt/euf_solver.h"
#include "sat/smt/arith_solver.h"
namespace arith {
sat::literal solver::internalize(expr* e, bool sign, bool root, bool learned) {
init_internalize();
flet<bool> _is_learned(m_is_redundant, learned);
internalize_atom(e);
literal lit = ctx.expr2literal(e);
if (sign)
lit.neg();
return lit;
}
void solver::internalize(expr* e, bool redundant) {
init_internalize();
flet<bool> _is_learned(m_is_redundant, redundant);
if (m.is_bool(e))
internalize_atom(e);
else
internalize_term(e);
}
void solver::init_internalize() {
force_push();
// initialize 0, 1 variables:
if (!m_internalize_initialized) {
get_one(true);
get_one(false);
get_zero(true);
get_zero(false);
ctx.push(value_trail<bool>(m_internalize_initialized));
m_internalize_initialized = true;
}
}
lpvar solver::get_one(bool is_int) {
return add_const(1, is_int ? m_one_var : m_rone_var, is_int);
}
lpvar solver::get_zero(bool is_int) {
return add_const(0, is_int ? m_zero_var : m_rzero_var, is_int);
}
void solver::ensure_nla() {
if (!m_nla) {
m_nla = alloc(nla::solver, *m_solver.get(), m.limit());
for (auto const& _s : m_scopes) {
(void)_s;
m_nla->push();
}
smt_params_helper prms(s().params());
m_nla->settings().run_order() = prms.arith_nl_order();
m_nla->settings().run_tangents() = prms.arith_nl_tangents();
m_nla->settings().run_horner() = prms.arith_nl_horner();
m_nla->settings().horner_subs_fixed() = prms.arith_nl_horner_subs_fixed();
m_nla->settings().horner_frequency() = prms.arith_nl_horner_frequency();
m_nla->settings().horner_row_length_limit() = prms.arith_nl_horner_row_length_limit();
m_nla->settings().run_grobner() = prms.arith_nl_grobner();
m_nla->settings().run_nra() = prms.arith_nl_nra();
m_nla->settings().grobner_subs_fixed() = prms.arith_nl_grobner_subs_fixed();
m_nla->settings().grobner_eqs_growth() = prms.arith_nl_grobner_eqs_growth();
m_nla->settings().grobner_expr_size_growth() = prms.arith_nl_grobner_expr_size_growth();
m_nla->settings().grobner_expr_degree_growth() = prms.arith_nl_grobner_expr_degree_growth();
m_nla->settings().grobner_max_simplified() = prms.arith_nl_grobner_max_simplified();
m_nla->settings().grobner_number_of_conflicts_to_report() = prms.arith_nl_grobner_cnfl_to_report();
m_nla->settings().grobner_quota() = prms.arith_nl_gr_q();
m_nla->settings().grobner_frequency() = prms.arith_nl_grobner_frequency();
m_nla->settings().expensive_patching() = prms.arith_nl_expp();
}
}
void solver::found_unsupported(expr* n) {
ctx.push(value_trail<expr*>(m_not_handled));
TRACE("arith", tout << "unsupported " << mk_pp(n, m) << "\n";);
m_not_handled = n;
}
void solver::found_underspecified(expr* n) {
if (a.is_underspecified(n)) {
TRACE("arith", tout << "Unhandled: " << mk_pp(n, m) << "\n";);
m_underspecified.push_back(to_app(n));
}
expr* e = nullptr, * x = nullptr, * y = nullptr;
if (a.is_div(n, x, y)) {
e = a.mk_div0(x, y);
}
else if (a.is_idiv(n, x, y)) {
e = a.mk_idiv0(x, y);
}
else if (a.is_rem(n, x, y)) {
e = a.mk_rem0(x, y);
}
else if (a.is_mod(n, x, y)) {
e = a.mk_mod0(x, y);
}
else if (a.is_power(n, x, y)) {
e = a.mk_power0(x, y);
}
if (e) {
literal lit = eq_internalize(n, e);
add_unit(lit);
}
}
lpvar solver::add_const(int c, lpvar& var, bool is_int) {
if (var != UINT_MAX) {
return var;
}
ctx.push(value_trail<lpvar>(var));
app_ref cnst(a.mk_numeral(rational(c), is_int), m);
mk_enode(cnst);
theory_var v = mk_evar(cnst);
var = lp().add_var(v, is_int);
add_def_constraint_and_equality(var, lp::GE, rational(c));
add_def_constraint_and_equality(var, lp::LE, rational(c));
TRACE("arith", tout << "add " << cnst << ", var = " << var << "\n";);
return var;
}
lpvar solver::register_theory_var_in_lar_solver(theory_var v) {
lpvar lpv = lp().external_to_local(v);
if (lpv != lp::null_lpvar)
return lpv;
return lp().add_var(v, is_int(v));
}
void solver::linearize_term(expr* term, scoped_internalize_state& st) {
st.push(term, rational::one());
linearize(st);
}
void solver::linearize_ineq(expr* lhs, expr* rhs, scoped_internalize_state& st) {
st.push(lhs, rational::one());
st.push(rhs, rational::minus_one());
linearize(st);
}
void solver::linearize(scoped_internalize_state& st) {
expr_ref_vector& terms = st.terms();
svector<theory_var>& vars = st.vars();
vector<rational>& coeffs = st.coeffs();
rational& offset = st.offset();
rational r;
expr* n1, * n2;
unsigned index = 0;
while (index < terms.size()) {
SASSERT(index >= vars.size());
expr* n = terms.get(index);
st.to_ensure_enode().push_back(n);
if (a.is_add(n)) {
for (expr* arg : *to_app(n)) {
st.push(arg, coeffs[index]);
}
st.set_back(index);
}
else if (a.is_sub(n)) {
unsigned sz = to_app(n)->get_num_args();
terms[index] = to_app(n)->get_arg(0);
for (unsigned i = 1; i < sz; ++i) {
st.push(to_app(n)->get_arg(i), -coeffs[index]);
}
}
else if (a.is_mul(n, n1, n2) && a.is_extended_numeral(n1, r)) {
coeffs[index] *= r;
terms[index] = n2;
st.to_ensure_enode().push_back(n1);
}
else if (a.is_mul(n, n1, n2) && a.is_extended_numeral(n2, r)) {
coeffs[index] *= r;
terms[index] = n1;
st.to_ensure_enode().push_back(n2);
}
else if (a.is_mul(n)) {
theory_var v = internalize_mul(to_app(n));
coeffs[vars.size()] = coeffs[index];
vars.push_back(v);
++index;
}
else if (a.is_power(n, n1, n2) && is_app(n1) && a.is_extended_numeral(n2, r) && r.is_unsigned() && r <= 10) {
theory_var v = internalize_power(to_app(n), to_app(n1), r.get_unsigned());
coeffs[vars.size()] = coeffs[index];
vars.push_back(v);
++index;
}
else if (a.is_numeral(n, r)) {
offset += coeffs[index] * r;
++index;
}
else if (a.is_uminus(n, n1)) {
coeffs[index].neg();
terms[index] = n1;
}
else if (a.is_to_real(n, n1)) {
terms[index] = n1;
if (!ctx.get_enode(n)) {
app* t = to_app(n);
VERIFY(internalize_term(to_app(n1)));
mk_enode(t);
theory_var v = mk_evar(n);
theory_var w = mk_evar(n1);
lpvar vj = register_theory_var_in_lar_solver(v);
lpvar wj = register_theory_var_in_lar_solver(w);
auto lu_constraints = lp().add_equality(vj, wj);
add_def_constraint(lu_constraints.first);
add_def_constraint(lu_constraints.second);
}
}
else if (is_app(n) && a.get_family_id() == to_app(n)->get_family_id()) {
bool is_first = nullptr == ctx.get_enode(n);
app* t = to_app(n);
internalize_args(t);
mk_enode(t);
theory_var v = mk_evar(n);
coeffs[vars.size()] = coeffs[index];
vars.push_back(v);
++index;
if (!is_first) {
// skip recursive internalization
}
else if (a.is_to_int(n, n1))
mk_to_int_axiom(t);
else if (a.is_abs(n))
mk_abs_axiom(t);
else if (a.is_idiv(n, n1, n2)) {
if (!a.is_numeral(n2, r) || r.is_zero()) found_underspecified(n);
m_idiv_terms.push_back(n);
app_ref mod(a.mk_mod(n1, n2), m);
internalize(mod, m_is_redundant);
st.to_ensure_var().push_back(n1);
st.to_ensure_var().push_back(n2);
}
else if (a.is_mod(n, n1, n2)) {
if (!a.is_numeral(n2, r) || r.is_zero()) found_underspecified(n);
mk_idiv_mod_axioms(n1, n2);
st.to_ensure_var().push_back(n1);
st.to_ensure_var().push_back(n2);
}
else if (a.is_rem(n, n1, n2)) {
if (!a.is_numeral(n2, r) || r.is_zero()) found_underspecified(n);
mk_rem_axiom(n1, n2);
st.to_ensure_var().push_back(n1);
st.to_ensure_var().push_back(n2);
}
else if (a.is_div(n, n1, n2)) {
if (!a.is_numeral(n2, r) || r.is_zero()) found_underspecified(n);
mk_div_axiom(n1, n2);
st.to_ensure_var().push_back(n1);
st.to_ensure_var().push_back(n2);
}
else if (!a.is_div0(n) && !a.is_mod0(n) && !a.is_idiv0(n) && !a.is_rem0(n) && !a.is_power0(n)) {
found_unsupported(n);
}
else {
// no-op
}
}
else {
if (is_app(n)) {
internalize_args(to_app(n));
for (expr* arg : *to_app(n))
if ((a.is_real(arg) || a.is_int(arg)) && !m.is_bool(arg))
internalize_term(arg);
}
theory_var v = mk_evar(n);
coeffs[vars.size()] = coeffs[index];
vars.push_back(v);
++index;
}
}
for (unsigned i = st.to_ensure_enode().size(); i-- > 0; ) {
expr* n = st.to_ensure_enode()[i];
if (is_app(n)) {
mk_enode(to_app(n));
}
}
st.to_ensure_enode().reset();
for (unsigned i = st.to_ensure_var().size(); i-- > 0; ) {
expr* n = st.to_ensure_var()[i];
if (is_app(n))
internalize_term(to_app(n));
}
st.to_ensure_var().reset();
}
void solver::eq_internalized(enode* n) {
internalize_term(n->get_arg(0)->get_expr());
internalize_term(n->get_arg(1)->get_expr());
}
bool solver::internalize_atom(expr* atom) {
TRACE("arith", tout << mk_pp(atom, m) << "\n";);
expr* n1, *n2;
rational r;
lp_api::bound_kind k;
theory_var v = euf::null_theory_var;
bool_var bv = ctx.get_si().add_bool_var(atom);
m_bool_var2bound.erase(bv);
literal lit(bv, false);
ctx.attach_lit(lit, atom);
if (a.is_le(atom, n1, n2) && a.is_extended_numeral(n2, r)) {
v = internalize_def(n1);
k = lp_api::upper_t;
}
else if (a.is_ge(atom, n1, n2) && a.is_extended_numeral(n2, r)) {
v = internalize_def(n1);
k = lp_api::lower_t;
}
else if (a.is_le(atom, n1, n2) && a.is_extended_numeral(n1, r)) {
v = internalize_def(n2);
k = lp_api::lower_t;
}
else if (a.is_ge(atom, n1, n2) && a.is_extended_numeral(n1, r)) {
v = internalize_def(n2);
k = lp_api::upper_t;
}
else if (a.is_le(atom, n1, n2)) {
expr_ref n3(a.mk_sub(n1, n2), m);
v = internalize_def(n3);
k = lp_api::upper_t;
r = 0;
}
else if (a.is_ge(atom, n1, n2)) {
expr_ref n3(a.mk_sub(n1, n2), m);
v = internalize_def(n3);
k = lp_api::lower_t;
r = 0;
}
else if (a.is_lt(atom, n1, n2)) {
expr_ref n3(a.mk_sub(n1, n2), m);
v = internalize_def(n3);
k = lp_api::lower_t;
r = 0;
lit.neg();
}
else if (a.is_gt(atom, n1, n2)) {
expr_ref n3(a.mk_sub(n1, n2), m);
v = internalize_def(n3);
k = lp_api::upper_t;
r = 0;
lit.neg();
}
else if (a.is_is_int(atom)) {
mk_is_int_axiom(atom);
return true;
}
else {
TRACE("arith", tout << "Could not internalize " << mk_pp(atom, m) << "\n";);
found_unsupported(atom);
return true;
}
enode* n = ctx.get_enode(atom);
theory_var w = mk_var(n);
ctx.attach_th_var(n, this, w);
ctx.get_egraph().set_merge_enabled(n, false);
if (is_int(v) && !r.is_int())
r = (k == lp_api::upper_t) ? floor(r) : ceil(r);
api_bound* b = mk_var_bound(lit, v, k, r);
m_bounds[v].push_back(b);
updt_unassigned_bounds(v, +1);
m_bounds_trail.push_back(v);
m_bool_var2bound.insert(bv, b);
TRACE("arith_verbose", tout << "Internalized " << lit << ": " << mk_pp(atom, m) << " " << *b << "\n";);
m_new_bounds.push_back(b);
//add_use_lists(b);
return true;
}
bool solver::internalize_term(expr* term) {
if (!has_var(term))
register_theory_var_in_lar_solver(internalize_def(term));
return true;
}
theory_var solver::internalize_def(expr* term, scoped_internalize_state& st) {
TRACE("arith", tout << expr_ref(term, m) << "\n";);
if (ctx.get_enode(term))
return mk_evar(term);
linearize_term(term, st);
if (is_unit_var(st))
return st.vars()[0];
theory_var v = mk_evar(term);
SASSERT(euf::null_theory_var != v);
st.coeffs().resize(st.vars().size() + 1);
st.coeffs()[st.vars().size()] = rational::minus_one();
st.vars().push_back(v);
return v;
}
// term - v = 0
theory_var solver::internalize_def(expr* term) {
scoped_internalize_state st(*this);
linearize_term(term, st);
return internalize_linearized_def(term, st);
}
void solver::internalize_args(app* t, bool force) {
SASSERT(!m.is_bool(t));
TRACE("arith", tout << mk_pp(t, m) << " " << force << " " << reflect(t) << "\n";);
if (!force && !reflect(t))
return;
for (expr* arg : *t)
e_internalize(arg);
}
theory_var solver::internalize_power(app* t, app* n, unsigned p) {
internalize_args(t, true);
bool _has_var = has_var(t);
mk_enode(t);
theory_var v = mk_evar(t);
if (_has_var)
return v;
internalize_term(n);
theory_var w = mk_evar(n);
if (p == 0) {
mk_power0_axioms(t, n);
}
else {
svector<lpvar> vars;
for (unsigned i = 0; i < p; ++i)
vars.push_back(register_theory_var_in_lar_solver(w));
ensure_nla();
m_solver->register_existing_terms();
m_nla->add_monic(register_theory_var_in_lar_solver(v), vars.size(), vars.data());
}
return v;
}
theory_var solver::internalize_mul(app* t) {
SASSERT(a.is_mul(t));
internalize_args(t, true);
bool _has_var = has_var(t);
mk_enode(t);
theory_var v = mk_evar(t);
if (!_has_var) {
svector<lpvar> vars;
for (expr* n : *t) {
if (is_app(n)) VERIFY(internalize_term(to_app(n)));
SASSERT(ctx.get_enode(n));
theory_var v = mk_evar(n);
vars.push_back(register_theory_var_in_lar_solver(v));
}
TRACE("arith", tout << "v" << v << " := " << mk_pp(t, m) << "\n" << vars << "\n";);
m_solver->register_existing_terms();
ensure_nla();
m_nla->add_monic(register_theory_var_in_lar_solver(v), vars.size(), vars.data());
}
return v;
}
theory_var solver::internalize_linearized_def(expr* term, scoped_internalize_state& st) {
theory_var v = mk_evar(term);
TRACE("arith", tout << mk_bounded_pp(term, m) << " v" << v << "\n";);
if (is_unit_var(st) && v == st.vars()[0]) {
return st.vars()[0];
}
else if (is_one(st) && a.is_numeral(term)) {
return lp().local_to_external(get_one(a.is_int(term)));
}
else if (is_zero(st) && a.is_numeral(term)) {
return lp().local_to_external(get_zero(a.is_int(term)));
}
else {
init_left_side(st);
lpvar vi = get_lpvar(v);
if (vi == UINT_MAX) {
if (m_left_side.empty()) {
vi = lp().add_var(v, a.is_int(term));
add_def_constraint_and_equality(vi, lp::GE, st.offset());
add_def_constraint_and_equality(vi, lp::LE, st.offset());
register_fixed_var(v, st.offset());
return v;
}
if (!st.offset().is_zero()) {
m_left_side.push_back(std::make_pair(st.offset(), get_one(a.is_int(term))));
}
if (m_left_side.empty()) {
vi = lp().add_var(v, a.is_int(term));
add_def_constraint_and_equality(vi, lp::GE, rational(0));
add_def_constraint_and_equality(vi, lp::LE, rational(0));
}
else {
vi = lp().add_term(m_left_side, v);
SASSERT(lp::tv::is_term(vi));
TRACE("arith_verbose",
tout << "v" << v << " := " << mk_pp(term, m)
<< " slack: " << vi << " scopes: " << m_scopes.size() << "\n";
lp().print_term(lp().get_term(lp::tv::raw(vi)), tout) << "\n";);
}
}
return v;
}
}
bool solver::is_unit_var(scoped_internalize_state& st) {
return st.offset().is_zero() && st.vars().size() == 1 && st.coeffs()[0].is_one();
}
bool solver::is_one(scoped_internalize_state& st) {
return st.offset().is_one() && st.vars().empty();
}
bool solver::is_zero(scoped_internalize_state& st) {
return st.offset().is_zero() && st.vars().empty();
}
void solver::init_left_side(scoped_internalize_state& st) {
SASSERT(all_zeros(m_columns));
svector<theory_var> const& vars = st.vars();
vector<rational> const& coeffs = st.coeffs();
for (unsigned i = 0; i < vars.size(); ++i) {
theory_var var = vars[i];
rational const& coeff = coeffs[i];
if (m_columns.size() <= static_cast<unsigned>(var)) {
m_columns.setx(var, coeff, rational::zero());
}
else {
m_columns[var] += coeff;
}
}
m_left_side.clear();
// reset the coefficients after they have been used.
for (theory_var var : vars) {
rational const& r = m_columns[var];
if (!r.is_zero()) {
auto vi = register_theory_var_in_lar_solver(var);
if (lp::tv::is_term(vi))
vi = lp().map_term_index_to_column_index(vi);
m_left_side.push_back(std::make_pair(r, vi));
m_columns[var].reset();
}
}
SASSERT(all_zeros(m_columns));
}
enode* solver::mk_enode(expr* e) {
TRACE("arith", tout << expr_ref(e, m) << "\n";);
enode* n = ctx.get_enode(e);
if (n)
return n;
if (!a.is_arith_expr(e))
n = e_internalize(e);
else {
ptr_buffer<enode> args;
if (reflect(e))
for (expr* arg : *to_app(e))
args.push_back(e_internalize(arg));
n = ctx.mk_enode(e, args.size(), args.data());
ctx.attach_node(n);
}
return n;
}
theory_var solver::mk_evar(expr* n) {
enode* e = mk_enode(n);
if (e->is_attached_to(get_id()))
return e->get_th_var(get_id());
theory_var v = mk_var(e);
TRACE("arith_verbose", tout << "v" << v << " " << mk_pp(n, m) << "\n";);
SASSERT(m_bounds.size() <= static_cast<unsigned>(v) || m_bounds[v].empty());
reserve_bounds(v);
ctx.attach_th_var(e, this, v);
SASSERT(euf::null_theory_var != v);
return v;
}
bool solver::has_var(expr* e) {
enode* n = ctx.get_enode(e);
return n && n->is_attached_to(get_id());
}
void solver::add_eq_constraint(lp::constraint_index index, enode* n1, enode* n2) {
m_constraint_sources.setx(index, equality_source, null_source);
m_equalities.setx(index, enode_pair(n1, n2), enode_pair(nullptr, nullptr));
}
void solver::add_ineq_constraint(lp::constraint_index index, literal lit) {
m_constraint_sources.setx(index, inequality_source, null_source);
m_inequalities.setx(index, lit, sat::null_literal);
}
void solver::add_def_constraint(lp::constraint_index index) {
m_constraint_sources.setx(index, definition_source, null_source);
m_definitions.setx(index, euf::null_theory_var, euf::null_theory_var);
}
void solver::add_def_constraint(lp::constraint_index index, theory_var v) {
m_constraint_sources.setx(index, definition_source, null_source);
m_definitions.setx(index, v, euf::null_theory_var);
}
void solver::add_def_constraint_and_equality(lpvar vi, lp::lconstraint_kind kind,
const rational& bound) {
lpvar vi_equal;
lp::constraint_index ci = lp().add_var_bound_check_on_equal(vi, kind, bound, vi_equal);
add_def_constraint(ci);
if (vi_equal != lp::null_lpvar)
report_equality_of_fixed_vars(vi, vi_equal);
m_new_eq = true;
}
bool solver::reflect(expr* n) const {
return get_config().m_arith_reflect || a.is_underspecified(n) || !a.is_arith_expr(n);
}
lpvar solver::get_lpvar(theory_var v) const {
return lp().external_to_local(v);
}
lp::tv solver::get_tv(theory_var v) const {
return lp::tv::raw(get_lpvar(v));
}
/**
\brief We must redefine this method, because theory of arithmetic contains
underspecified operators such as division by 0.
(/ a b) is essentially an uninterpreted function when b = 0.
Thus, 'a' must be considered a shared var if it is the child of an underspecified operator.
if merge(a / b, x + y) and a / b is root, then x + y become shared and all z + u in equivalence class of x + y.
TBD: when the set of underspecified subterms is small, compute the shared variables below it.
Recompute the set if there are merges that invalidate it.
Use the set to determine if a variable is shared.
*/
bool solver::is_shared(theory_var v) const {
if (m_underspecified.empty()) {
return false;
}
enode* n = var2enode(v);
enode* r = n->get_root();
unsigned usz = m_underspecified.size();
if (r->num_parents() > 2 * usz) {
for (unsigned i = 0; i < usz; ++i) {
app* u = m_underspecified[i];
unsigned sz = u->get_num_args();
for (unsigned j = 0; j < sz; ++j)
if (expr2enode(u->get_arg(j))->get_root() == r)
return true;
}
}
else {
for (enode* parent : euf::enode_parents(r))
if (a.is_underspecified(parent->get_expr()))
return true;
}
return false;
}
struct solver::undo_value : public trail {
solver& s;
undo_value(solver& s):s(s) {}
void undo() override {
s.m_value2var.erase(s.m_fixed_values.back());
s.m_fixed_values.pop_back();
}
};
void solver::register_fixed_var(theory_var v, rational const& value) {
if (m_value2var.contains(value))
return;
m_fixed_values.push_back(value);
m_value2var.insert(value, v);
ctx.push(undo_value(*this));
}
}

2
src/sat/smt/arith_internalize.cpp
View file

@ -278,7 +278,7 @@ namespace arith {
if (is_app(n)) {
internalize_args(to_app(n));
for (expr* arg : *to_app(n))
if (a.is_arith_expr(arg) && !m.is_bool(arg))
if (a.is_real(arg) || a.is_int(arg))
internalize_term(arg);
}
theory_var v = mk_evar(n);