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https://github.com/Z3Prover/z3
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internalize arithmetic sub-terms #5753
This commit is contained in:
Nikolaj Bjorner
parent
e816946ddc
commit
2363bfc132
2 changed files with 698 additions and 1 deletions
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@ -0,0 +1,697 @@
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/*++
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Copyright (c) 2020 Microsoft Corporation
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Module Name:
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arith_internalize.cpp
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Abstract:
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Theory plugin for arithmetic
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Author:
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Nikolaj Bjorner (nbjorner) 2020-09-08
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--*/
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#include "sat/smt/euf_solver.h"
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#include "sat/smt/arith_solver.h"
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namespace arith {
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sat::literal solver::internalize(expr* e, bool sign, bool root, bool learned) {
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init_internalize();
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flet<bool> _is_learned(m_is_redundant, learned);
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internalize_atom(e);
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literal lit = ctx.expr2literal(e);
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if (sign)
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lit.neg();
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return lit;
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}
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void solver::internalize(expr* e, bool redundant) {
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init_internalize();
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flet<bool> _is_learned(m_is_redundant, redundant);
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if (m.is_bool(e))
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internalize_atom(e);
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else
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internalize_term(e);
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}
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void solver::init_internalize() {
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force_push();
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// initialize 0, 1 variables:
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if (!m_internalize_initialized) {
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get_one(true);
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get_one(false);
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get_zero(true);
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get_zero(false);
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ctx.push(value_trail<bool>(m_internalize_initialized));
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m_internalize_initialized = true;
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}
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}
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lpvar solver::get_one(bool is_int) {
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return add_const(1, is_int ? m_one_var : m_rone_var, is_int);
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}
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lpvar solver::get_zero(bool is_int) {
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return add_const(0, is_int ? m_zero_var : m_rzero_var, is_int);
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}
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void solver::ensure_nla() {
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if (!m_nla) {
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m_nla = alloc(nla::solver, *m_solver.get(), m.limit());
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for (auto const& _s : m_scopes) {
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(void)_s;
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m_nla->push();
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}
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smt_params_helper prms(s().params());
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m_nla->settings().run_order() = prms.arith_nl_order();
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m_nla->settings().run_tangents() = prms.arith_nl_tangents();
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m_nla->settings().run_horner() = prms.arith_nl_horner();
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m_nla->settings().horner_subs_fixed() = prms.arith_nl_horner_subs_fixed();
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m_nla->settings().horner_frequency() = prms.arith_nl_horner_frequency();
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m_nla->settings().horner_row_length_limit() = prms.arith_nl_horner_row_length_limit();
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m_nla->settings().run_grobner() = prms.arith_nl_grobner();
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m_nla->settings().run_nra() = prms.arith_nl_nra();
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m_nla->settings().grobner_subs_fixed() = prms.arith_nl_grobner_subs_fixed();
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m_nla->settings().grobner_eqs_growth() = prms.arith_nl_grobner_eqs_growth();
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m_nla->settings().grobner_expr_size_growth() = prms.arith_nl_grobner_expr_size_growth();
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m_nla->settings().grobner_expr_degree_growth() = prms.arith_nl_grobner_expr_degree_growth();
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m_nla->settings().grobner_max_simplified() = prms.arith_nl_grobner_max_simplified();
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m_nla->settings().grobner_number_of_conflicts_to_report() = prms.arith_nl_grobner_cnfl_to_report();
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m_nla->settings().grobner_quota() = prms.arith_nl_gr_q();
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m_nla->settings().grobner_frequency() = prms.arith_nl_grobner_frequency();
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m_nla->settings().expensive_patching() = prms.arith_nl_expp();
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}
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}
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void solver::found_unsupported(expr* n) {
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ctx.push(value_trail<expr*>(m_not_handled));
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TRACE("arith", tout << "unsupported " << mk_pp(n, m) << "\n";);
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m_not_handled = n;
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}
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void solver::found_underspecified(expr* n) {
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if (a.is_underspecified(n)) {
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TRACE("arith", tout << "Unhandled: " << mk_pp(n, m) << "\n";);
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m_underspecified.push_back(to_app(n));
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}
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expr* e = nullptr, * x = nullptr, * y = nullptr;
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if (a.is_div(n, x, y)) {
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e = a.mk_div0(x, y);
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}
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else if (a.is_idiv(n, x, y)) {
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e = a.mk_idiv0(x, y);
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}
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else if (a.is_rem(n, x, y)) {
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e = a.mk_rem0(x, y);
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}
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else if (a.is_mod(n, x, y)) {
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e = a.mk_mod0(x, y);
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}
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else if (a.is_power(n, x, y)) {
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e = a.mk_power0(x, y);
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}
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if (e) {
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literal lit = eq_internalize(n, e);
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add_unit(lit);
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}
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}
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lpvar solver::add_const(int c, lpvar& var, bool is_int) {
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if (var != UINT_MAX) {
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return var;
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}
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ctx.push(value_trail<lpvar>(var));
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app_ref cnst(a.mk_numeral(rational(c), is_int), m);
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mk_enode(cnst);
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theory_var v = mk_evar(cnst);
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var = lp().add_var(v, is_int);
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add_def_constraint_and_equality(var, lp::GE, rational(c));
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add_def_constraint_and_equality(var, lp::LE, rational(c));
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TRACE("arith", tout << "add " << cnst << ", var = " << var << "\n";);
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return var;
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}
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lpvar solver::register_theory_var_in_lar_solver(theory_var v) {
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lpvar lpv = lp().external_to_local(v);
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if (lpv != lp::null_lpvar)
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return lpv;
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return lp().add_var(v, is_int(v));
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}
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void solver::linearize_term(expr* term, scoped_internalize_state& st) {
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st.push(term, rational::one());
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linearize(st);
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}
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void solver::linearize_ineq(expr* lhs, expr* rhs, scoped_internalize_state& st) {
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st.push(lhs, rational::one());
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st.push(rhs, rational::minus_one());
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linearize(st);
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}
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void solver::linearize(scoped_internalize_state& st) {
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expr_ref_vector& terms = st.terms();
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svector<theory_var>& vars = st.vars();
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vector<rational>& coeffs = st.coeffs();
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rational& offset = st.offset();
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rational r;
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expr* n1, * n2;
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unsigned index = 0;
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while (index < terms.size()) {
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SASSERT(index >= vars.size());
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expr* n = terms.get(index);
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st.to_ensure_enode().push_back(n);
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if (a.is_add(n)) {
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for (expr* arg : *to_app(n)) {
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st.push(arg, coeffs[index]);
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}
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st.set_back(index);
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}
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else if (a.is_sub(n)) {
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unsigned sz = to_app(n)->get_num_args();
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terms[index] = to_app(n)->get_arg(0);
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for (unsigned i = 1; i < sz; ++i) {
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st.push(to_app(n)->get_arg(i), -coeffs[index]);
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}
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}
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else if (a.is_mul(n, n1, n2) && a.is_extended_numeral(n1, r)) {
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coeffs[index] *= r;
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terms[index] = n2;
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st.to_ensure_enode().push_back(n1);
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}
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else if (a.is_mul(n, n1, n2) && a.is_extended_numeral(n2, r)) {
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coeffs[index] *= r;
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terms[index] = n1;
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st.to_ensure_enode().push_back(n2);
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}
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else if (a.is_mul(n)) {
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theory_var v = internalize_mul(to_app(n));
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coeffs[vars.size()] = coeffs[index];
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vars.push_back(v);
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++index;
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}
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else if (a.is_power(n, n1, n2) && is_app(n1) && a.is_extended_numeral(n2, r) && r.is_unsigned() && r <= 10) {
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theory_var v = internalize_power(to_app(n), to_app(n1), r.get_unsigned());
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coeffs[vars.size()] = coeffs[index];
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vars.push_back(v);
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++index;
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}
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else if (a.is_numeral(n, r)) {
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offset += coeffs[index] * r;
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++index;
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}
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else if (a.is_uminus(n, n1)) {
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coeffs[index].neg();
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terms[index] = n1;
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}
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else if (a.is_to_real(n, n1)) {
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terms[index] = n1;
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if (!ctx.get_enode(n)) {
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app* t = to_app(n);
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VERIFY(internalize_term(to_app(n1)));
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mk_enode(t);
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theory_var v = mk_evar(n);
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theory_var w = mk_evar(n1);
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lpvar vj = register_theory_var_in_lar_solver(v);
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lpvar wj = register_theory_var_in_lar_solver(w);
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auto lu_constraints = lp().add_equality(vj, wj);
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add_def_constraint(lu_constraints.first);
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add_def_constraint(lu_constraints.second);
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}
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}
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else if (is_app(n) && a.get_family_id() == to_app(n)->get_family_id()) {
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bool is_first = nullptr == ctx.get_enode(n);
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app* t = to_app(n);
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internalize_args(t);
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mk_enode(t);
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theory_var v = mk_evar(n);
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coeffs[vars.size()] = coeffs[index];
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vars.push_back(v);
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++index;
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if (!is_first) {
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// skip recursive internalization
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}
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else if (a.is_to_int(n, n1))
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mk_to_int_axiom(t);
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else if (a.is_abs(n))
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mk_abs_axiom(t);
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else if (a.is_idiv(n, n1, n2)) {
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if (!a.is_numeral(n2, r) || r.is_zero()) found_underspecified(n);
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m_idiv_terms.push_back(n);
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app_ref mod(a.mk_mod(n1, n2), m);
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internalize(mod, m_is_redundant);
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st.to_ensure_var().push_back(n1);
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st.to_ensure_var().push_back(n2);
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}
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else if (a.is_mod(n, n1, n2)) {
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if (!a.is_numeral(n2, r) || r.is_zero()) found_underspecified(n);
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mk_idiv_mod_axioms(n1, n2);
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st.to_ensure_var().push_back(n1);
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st.to_ensure_var().push_back(n2);
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}
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else if (a.is_rem(n, n1, n2)) {
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if (!a.is_numeral(n2, r) || r.is_zero()) found_underspecified(n);
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mk_rem_axiom(n1, n2);
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st.to_ensure_var().push_back(n1);
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st.to_ensure_var().push_back(n2);
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}
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else if (a.is_div(n, n1, n2)) {
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if (!a.is_numeral(n2, r) || r.is_zero()) found_underspecified(n);
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mk_div_axiom(n1, n2);
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st.to_ensure_var().push_back(n1);
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st.to_ensure_var().push_back(n2);
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}
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else if (!a.is_div0(n) && !a.is_mod0(n) && !a.is_idiv0(n) && !a.is_rem0(n) && !a.is_power0(n)) {
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found_unsupported(n);
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}
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else {
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// no-op
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}
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}
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else {
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if (is_app(n)) {
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internalize_args(to_app(n));
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for (expr* arg : *to_app(n))
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if ((a.is_real(arg) || a.is_int(arg)) && !m.is_bool(arg))
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internalize_term(arg);
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}
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theory_var v = mk_evar(n);
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coeffs[vars.size()] = coeffs[index];
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vars.push_back(v);
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++index;
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}
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}
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for (unsigned i = st.to_ensure_enode().size(); i-- > 0; ) {
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expr* n = st.to_ensure_enode()[i];
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if (is_app(n)) {
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mk_enode(to_app(n));
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}
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}
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st.to_ensure_enode().reset();
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for (unsigned i = st.to_ensure_var().size(); i-- > 0; ) {
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expr* n = st.to_ensure_var()[i];
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if (is_app(n))
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internalize_term(to_app(n));
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}
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st.to_ensure_var().reset();
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}
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void solver::eq_internalized(enode* n) {
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internalize_term(n->get_arg(0)->get_expr());
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internalize_term(n->get_arg(1)->get_expr());
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}
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bool solver::internalize_atom(expr* atom) {
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TRACE("arith", tout << mk_pp(atom, m) << "\n";);
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expr* n1, *n2;
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rational r;
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lp_api::bound_kind k;
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theory_var v = euf::null_theory_var;
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bool_var bv = ctx.get_si().add_bool_var(atom);
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m_bool_var2bound.erase(bv);
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literal lit(bv, false);
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ctx.attach_lit(lit, atom);
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if (a.is_le(atom, n1, n2) && a.is_extended_numeral(n2, r)) {
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v = internalize_def(n1);
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k = lp_api::upper_t;
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}
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else if (a.is_ge(atom, n1, n2) && a.is_extended_numeral(n2, r)) {
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v = internalize_def(n1);
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k = lp_api::lower_t;
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}
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else if (a.is_le(atom, n1, n2) && a.is_extended_numeral(n1, r)) {
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v = internalize_def(n2);
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k = lp_api::lower_t;
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}
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else if (a.is_ge(atom, n1, n2) && a.is_extended_numeral(n1, r)) {
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v = internalize_def(n2);
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k = lp_api::upper_t;
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}
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else if (a.is_le(atom, n1, n2)) {
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expr_ref n3(a.mk_sub(n1, n2), m);
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v = internalize_def(n3);
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k = lp_api::upper_t;
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r = 0;
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}
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else if (a.is_ge(atom, n1, n2)) {
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expr_ref n3(a.mk_sub(n1, n2), m);
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v = internalize_def(n3);
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k = lp_api::lower_t;
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r = 0;
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}
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else if (a.is_lt(atom, n1, n2)) {
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expr_ref n3(a.mk_sub(n1, n2), m);
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v = internalize_def(n3);
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k = lp_api::lower_t;
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r = 0;
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lit.neg();
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}
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else if (a.is_gt(atom, n1, n2)) {
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expr_ref n3(a.mk_sub(n1, n2), m);
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v = internalize_def(n3);
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k = lp_api::upper_t;
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r = 0;
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lit.neg();
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}
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else if (a.is_is_int(atom)) {
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mk_is_int_axiom(atom);
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return true;
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}
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else {
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TRACE("arith", tout << "Could not internalize " << mk_pp(atom, m) << "\n";);
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found_unsupported(atom);
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return true;
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}
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enode* n = ctx.get_enode(atom);
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theory_var w = mk_var(n);
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ctx.attach_th_var(n, this, w);
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ctx.get_egraph().set_merge_enabled(n, false);
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if (is_int(v) && !r.is_int())
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r = (k == lp_api::upper_t) ? floor(r) : ceil(r);
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api_bound* b = mk_var_bound(lit, v, k, r);
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m_bounds[v].push_back(b);
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updt_unassigned_bounds(v, +1);
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m_bounds_trail.push_back(v);
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m_bool_var2bound.insert(bv, b);
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TRACE("arith_verbose", tout << "Internalized " << lit << ": " << mk_pp(atom, m) << " " << *b << "\n";);
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m_new_bounds.push_back(b);
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//add_use_lists(b);
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return true;
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}
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bool solver::internalize_term(expr* term) {
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if (!has_var(term))
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register_theory_var_in_lar_solver(internalize_def(term));
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return true;
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}
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theory_var solver::internalize_def(expr* term, scoped_internalize_state& st) {
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TRACE("arith", tout << expr_ref(term, m) << "\n";);
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if (ctx.get_enode(term))
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return mk_evar(term);
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linearize_term(term, st);
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if (is_unit_var(st))
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return st.vars()[0];
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theory_var v = mk_evar(term);
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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));
|
||||
}
|
||||
|
||||
|
||||
}
|
||||
|
||||
|
|
@ -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);
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue