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https://github.com/Z3Prover/z3
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fixes for qe_arith
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
4af4466821
commit
196aed785e
2 changed files with 51 additions and 88 deletions
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@ -23,6 +23,7 @@ Revision History:
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#include "arith_decl_plugin.h"
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#include "ast_pp.h"
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#include "th_rewriter.h"
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#include "expr_functors.h"
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namespace qe {
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@ -33,61 +34,39 @@ namespace qe {
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expr_ref_vector m_ineq_terms;
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vector<rational> m_ineq_coeffs;
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svector<bool> m_ineq_strict;
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scoped_ptr<contains_app> m_var;
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struct cant_project {};
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// TBD: replace by "contains_x" class.
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bool contains(app* var, expr* t) const {
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ast_mark mark;
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ptr_vector<expr> todo;
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todo.push_back(t);
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while (!todo.empty()) {
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t = todo.back();
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todo.pop_back();
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if (mark.is_marked(t)) {
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continue;
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}
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mark.mark(t, true);
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if (var == t) {
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return true;
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}
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SASSERT(is_app(t));
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app* ap = to_app(t);
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todo.append(ap->get_num_args(), ap->get_args());
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}
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return false;
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}
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void is_linear(app* var, rational const& mul, expr* t, rational& c, expr_ref_vector& ts) {
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void is_linear(rational const& mul, expr* t, rational& c, expr_ref_vector& ts) {
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expr* t1, *t2;
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rational mul1;
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if (t == var) {
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if (t == m_var->x()) {
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c += mul;
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}
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else if (a.is_mul(t, t1, t2) && a.is_numeral(t1, mul1)) {
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is_linear(var, mul* mul1, t2, c, ts);
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is_linear(mul* mul1, t2, c, ts);
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}
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else if (a.is_mul(t, t1, t2) && a.is_numeral(t2, mul1)) {
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is_linear(var, mul* mul1, t1, c, ts);
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is_linear(mul* mul1, t1, c, ts);
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}
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else if (a.is_add(t)) {
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app* ap = to_app(t);
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for (unsigned i = 0; i < ap->get_num_args(); ++i) {
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is_linear(var, mul, ap->get_arg(i), c, ts);
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is_linear(mul, ap->get_arg(i), c, ts);
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}
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}
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else if (a.is_sub(t, t1, t2)) {
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is_linear(var, mul, t1, c, ts);
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is_linear(var, -mul, t2, c, ts);
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is_linear(mul, t1, c, ts);
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is_linear(-mul, t2, c, ts);
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}
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else if (a.is_uminus(t, t1)) {
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is_linear(var, -mul, t1, c, ts);
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is_linear(-mul, t1, c, ts);
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}
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else if (a.is_numeral(t, mul1)) {
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ts.push_back(a.mk_numeral(mul*mul1, m.get_sort(t)));
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}
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else if (contains(var, t)) {
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else if ((*m_var)(t)) {
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IF_VERBOSE(1, verbose_stream() << mk_pp(t, m) << "\n";);
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throw cant_project();
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}
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@ -99,8 +78,8 @@ namespace qe {
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}
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}
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bool is_linear(app* var, expr* lit, rational& c, expr_ref& t, bool& is_strict) {
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if (!contains(var, lit)) {
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bool is_linear(expr* lit, rational& c, expr_ref& t, bool& is_strict) {
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if (!(*m_var)(lit)) {
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return false;
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}
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expr* e1, *e2;
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@ -114,20 +93,20 @@ namespace qe {
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}
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SASSERT(!m.is_not(lit));
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if (a.is_le(lit, e1, e2) || a.is_ge(lit, e2, e1)) {
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is_linear(var, mul, e1, c, ts);
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is_linear(var, -mul, e2, c, ts);
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is_linear( mul, e1, c, ts);
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is_linear(-mul, e2, c, ts);
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s = m.get_sort(e1);
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is_strict = is_not;
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}
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else if (a.is_lt(lit, e1, e2) || a.is_gt(lit, e2, e1)) {
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is_linear(var, mul, e1, c, ts);
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is_linear(var, -mul, e2, c, ts);
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is_linear( mul, e1, c, ts);
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is_linear(-mul, e2, c, ts);
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s = m.get_sort(e1);
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is_strict = !is_not;
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}
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else if (m.is_eq(lit, e1, e2) && !is_not) {
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is_linear(var, mul, e1, c, ts);
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is_linear(var, -mul, e2, c, ts);
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is_linear( mul, e1, c, ts);
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is_linear(-mul, e2, c, ts);
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s = m.get_sort(e1);
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is_strict = false;
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}
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@ -143,14 +122,15 @@ namespace qe {
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return true;
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}
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void project(model& model, app* var, expr_ref_vector& lits) {
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unsigned num_pos = 0, num_neg = 0;
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void project(model& model, expr_ref_vector& lits) {
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unsigned num_pos = 0;
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unsigned num_neg = 0;
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expr_ref_vector new_lits(m);
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for (unsigned i = 0; i < lits.size(); ++i) {
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rational c(0);
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expr_ref t(m);
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bool is_strict;
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if (is_linear(var, lits[i].get(), c, t, is_strict)) {
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if (is_linear(lits[i].get(), c, t, is_strict)) {
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m_ineq_coeffs.push_back(c);
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m_ineq_terms.push_back(t);
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m_ineq_strict.push_back(is_strict);
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@ -158,7 +138,7 @@ namespace qe {
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++num_pos;
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}
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else {
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--num_neg;
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++num_neg;
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}
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}
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else {
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@ -170,69 +150,39 @@ namespace qe {
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if (num_pos == 0 || num_neg == 0) {
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return;
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}
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if (num_pos < num_neg) {
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unsigned max_t = find_max(model);
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for (unsigned i = 0; i < m_ineq_terms.size(); ++i) {
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if (i != max_t) {
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if (m_ineq_coeffs[i].is_pos()) {
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lits.push_back(mk_le(i, max_t));
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}
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else {
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lits.push_back(mk_lt(i, max_t));
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}
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bool use_pos = num_pos < num_neg;
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unsigned max_t = find_max(model, use_pos);
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for (unsigned i = 0; i < m_ineq_terms.size(); ++i) {
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if (i != max_t) {
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if (m_ineq_coeffs[i].is_pos() == use_pos) {
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lits.push_back(mk_le(i, max_t));
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}
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}
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}
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else {
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unsigned min_t = find_min(model);
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for (unsigned i = 0; i < m_ineq_terms.size(); ++i) {
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if (i != min_t) {
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if (m_ineq_coeffs[i].is_neg()) {
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lits.push_back(mk_le(min_t, i));
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}
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else {
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lits.push_back(mk_lt(min_t, i));
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}
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else {
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lits.push_back(mk_lt(i, max_t));
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}
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}
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}
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}
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unsigned find_max(model& mdl) {
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return find_min_max(mdl, true);
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}
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unsigned find_min(model& mdl) {
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return find_min_max(mdl, false);
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}
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unsigned find_min_max(model& mdl, bool do_max) {
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unsigned find_max(model& mdl, bool do_pos) {
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unsigned result;
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bool found = false;
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rational found_val(0), r;
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expr_ref val(m);
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for (unsigned i = 0; i < m_ineq_terms.size(); ++i) {
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rational const& ac = m_ineq_coeffs[i];
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if (ac.is_pos() && do_max) {
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if (ac.is_pos() == do_pos) {
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VERIFY(mdl.eval(m_ineq_terms[i].get(), val));
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VERIFY(a.is_numeral(val, r));
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r /= ac;
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r /= abs(ac);
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IF_VERBOSE(1, verbose_stream() << "max: " << mk_pp(m_ineq_terms[i].get(), m) << " " << r << " " << (!found || r > found_val) << "\n";);
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if (!found || r > found_val) {
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result = i;
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found_val = r;
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found = true;
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}
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}
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else if (ac.is_neg() && !do_max) {
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VERIFY(mdl.eval(m_ineq_terms[i].get(), val));
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VERIFY(a.is_numeral(val, r));
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r /= abs(ac); //// review.
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if (!found || r < found_val) {
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result = i;
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found_val = r;
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found = true;
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}
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}
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}
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SASSERT(found);
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return result;
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@ -300,11 +250,19 @@ namespace qe {
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m(m), a(m), m_rw(m), m_ineq_terms(m) {}
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expr_ref operator()(model& model, app_ref_vector& vars, expr_ref_vector const& lits) {
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app_ref_vector new_vars(m);
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expr_ref_vector result(lits);
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for (unsigned i = 0; i < vars.size(); ++i) {
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project(model, vars[i].get(), result);
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m_var = alloc(contains_app, m, vars[i].get());
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try {
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project(model, result);
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}
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catch (cant_project) {
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new_vars.push_back(vars[i].get());
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}
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}
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vars.reset();
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vars.append(new_vars);
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expr_ref res1(m);
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expr_ref tmp = qe::mk_and(result);
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m_rw(tmp, res1);
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@ -17,6 +17,9 @@ static expr_ref parse_fml(ast_manager& m, char const* str) {
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buffer << "(declare-const x Real)\n"
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<< "(declare-const y Real)\n"
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<< "(declare-const z Real)\n"
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<< "(declare-const u Real)\n"
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<< "(declare-const v Real)\n"
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<< "(declare-const t Real)\n"
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<< "(declare-const a Real)\n"
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<< "(declare-const b Real)\n"
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<< "(assert " << str << ")\n";
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@ -31,6 +34,7 @@ static char const* example1 = "(and (<= x 3.0) (<= (* 3.0 x) y) (<= z y))";
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static char const* example2 = "(and (<= z x) (<= x 3.0) (<= (* 3.0 x) y) (<= z y))";
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static char const* example3 = "(and (<= z x) (<= x 3.0) (< (* 3.0 x) y) (<= z y))";
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static char const* example4 = "(and (<= z x) (<= x 3.0) (not (>= (* 3.0 x) y)) (<= z y))";
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static char const* example5 = "(and (<= y x) (<= z x) (<= x u) (<= x v) (<= x t))";
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static void test(char const *ex) {
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smt_params params;
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@ -61,4 +65,5 @@ void tst_qe_arith() {
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test(example2);
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test(example3);
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test(example4);
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test(example5);
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}
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