mirror of
https://github.com/Z3Prover/z3
synced 2025-04-08 18:31:49 +00:00
working on pb
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
parent
8cb959127f
commit
50cc852112
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@ -332,6 +332,10 @@ namespace smt {
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return get_assignment(literal(v));
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}
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literal_vector const & assigned_literals() const {
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return m_assigned_literals;
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}
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lbool get_assignment(expr * n) const;
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// Similar to get_assignment, but returns l_undef if n is not internalized.
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@ -225,6 +225,7 @@ namespace smt {
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virtual proof * mk_proof(conflict_resolution & cr) = 0;
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virtual char const * get_name() const { return "simple"; }
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};
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class simple_theory_justification : public simple_justification {
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@ -274,6 +275,7 @@ namespace smt {
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virtual char const * get_name() const { return "theory-propagation"; }
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};
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class theory_conflict_justification : public simple_theory_justification {
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@ -37,6 +37,156 @@ namespace smt {
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SASSERT(well_formed());
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}
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void theory_pb::ineq::reset() {
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m_max_coeff = 0;
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m_watch_sz = 0;
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m_sum = 0;
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m_max_sum = 0;
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m_num_propagations = 0;
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m_compilation_threshold = UINT_MAX;
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m_compiled = l_false;
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m_args.reset();
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m_k = 0;
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}
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theory_pb::numeral theory_pb::ineq::gcd(numeral a, numeral b) {
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while (a != b) {
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if (a == 0) return b;
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if (b == 0) return a;
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SASSERT(a != 0 && b != 0);
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if (a < b) {
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b %= a;
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}
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else {
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a %= b;
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}
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}
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return a;
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}
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lbool theory_pb::ineq::normalize() {
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numeral& k = m_k;
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arg_t& args = m_args;
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// normalize first all literals to be positive:
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// then we can compare them more easily.
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for (unsigned i = 0; i < size(); ++i) {
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if (lit(i).sign()) {
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args[i].first.neg();
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k -= coeff(i);
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args[i].second = -coeff(i);
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}
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}
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// remove constants
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for (unsigned i = 0; i < size(); ++i) {
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if (lit(i) == true_literal) {
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k += coeff(i);
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std::swap(args[i], args[size()-1]);
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args.pop_back();
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}
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else if (lit(i) == false_literal) {
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std::swap(args[i], args[size()-1]);
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args.pop_back();
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}
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}
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// sort and coalesce arguments:
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std::sort(args.begin(), args.end());
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for (unsigned i = 0; i + 1 < size(); ++i) {
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if (lit(i) == args[i+1].first) {
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args[i].second += coeff(i+1);
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for (unsigned j = i+1; j + 1 < size(); ++j) {
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args[j] = args[j+1];
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}
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args.pop_back();
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}
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if (coeff(i) == 0) {
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for (unsigned j = i; j + 1 < size(); ++j) {
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args[j] = args[j+1];
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}
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args.pop_back();
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}
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}
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//
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// Ensure all coefficients are positive:
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// c*l + y >= k
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// <=>
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// c*(1-~l) + y >= k
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// <=>
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// c - c*~l + y >= k
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// <=>
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// -c*~l + y >= k - c
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//
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numeral sum = 0;
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for (unsigned i = 0; i < size(); ++i) {
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numeral c = coeff(i);
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if (c < 0) {
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args[i].second = -c;
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args[i].first = ~lit(i);
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k -= c;
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}
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sum += coeff(i);
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}
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// detect tautologies:
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if (k <= 0) {
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args.reset();
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return l_true;
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}
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// detect infeasible constraints:
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if (sum < k) {
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args.reset();
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return l_false;
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}
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// Ensure the largest coefficient is not larger than k:
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for (unsigned i = 0; i < size(); ++i) {
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numeral c = coeff(i);
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if (c > k) {
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args[i].second = k;
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}
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}
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SASSERT(!args.empty());
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// apply cutting plane reduction:
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numeral g = 0;
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for (unsigned i = 0; g != 1 && i < size(); ++i) {
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numeral c = coeff(i);
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if (c != k) {
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g = gcd(g, c);
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}
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}
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if (g == 0) {
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// all coefficients are equal to k.
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for (unsigned i = 0; i < size(); ++i) {
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SASSERT(coeff(i) == k);
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args[i].second = 1;
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}
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k = 1;
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}
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else if (g > 1) {
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//
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// Example 5x + 5y + 2z + 2u >= 5
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// becomes 3x + 3y + z + u >= 3
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//
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numeral k_new = k / g;
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if ((k % g) != 0) { // k_new is the ceiling of k / g.
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k_new++;
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}
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for (unsigned i = 0; i < size(); ++i) {
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numeral c = coeff(i);
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if (c == k) {
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c = k_new;
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}
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else {
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c = c / g;
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}
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args[i].second = c;
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}
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k = k_new;
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}
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SASSERT(well_formed());
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return l_undef;
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}
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bool theory_pb::ineq::well_formed() const {
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SASSERT(k() > 0);
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uint_set vars;
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@ -57,7 +207,8 @@ namespace smt {
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theory_pb::theory_pb(ast_manager& m):
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theory(m.mk_family_id("card")),
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m_util(m)
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m_util(m),
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m_lemma(null_literal)
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{}
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theory_pb::~theory_pb() {
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@ -101,7 +252,7 @@ namespace smt {
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args[i].second = -args[i].second;
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}
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k = -k;
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lbool is_true = normalize_ineq(args, k);
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lbool is_true = c->normalize();
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literal lit(abv);
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switch(is_true) {
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@ -138,8 +289,9 @@ namespace smt {
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++log;
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n *= 2;
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}
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c->m_compilation_threshold = args.size()*log;
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TRACE("card", tout << "compilation threshold: " << (args.size()*log) << "\n";);
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unsigned th = 10*args.size()*log;
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c->m_compilation_threshold = th;
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TRACE("card", tout << "compilation threshold: " << th << "\n";);
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}
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else {
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c->m_compilation_threshold = UINT_MAX;
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@ -167,10 +319,34 @@ namespace smt {
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ctx.set_var_theory(bv, get_id());
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}
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has_bv = (ctx.get_var_theory(bv) == get_id());
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#if 0
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TBD:
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if (!has_bv) {
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if (!ctx.e_internalized(arg)) {
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ctx.internalize(arg, false);
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SASSERT(ctx.e_internalized(arg));
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}
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enode* n = ctx.get_enode(arg);
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theory_var v = mk_var(n);
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ctx.attach_th_var(n, this, v);
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}
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#endif
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}
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else if (m.is_true(arg)) {
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bv = true_bool_var;
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has_bv = true;
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}
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else if (m.is_false(arg)) {
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bv = true_bool_var;
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has_bv = true;
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negate = !negate;
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}
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// pre-processing should better remove negations under cardinality.
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// assumes relevancy level = 2 or 0.
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// TBD: should should have been like an uninterpreted
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// function intenalize, where enodes for each argument
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// is available.
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if (!has_bv) {
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expr_ref tmp(m), fml(m);
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tmp = m.mk_fresh_const("card_proxy",m.mk_bool_sort());
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ineqs->push_back(&c);
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}
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theory_pb::numeral theory_pb::gcd(numeral a, numeral b) {
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while (a != b) {
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if (a == 0) return b;
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if (b == 0) return a;
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SASSERT(a != 0 && b != 0);
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if (a < b) {
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b %= a;
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}
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else {
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a %= b;
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}
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}
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return a;
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}
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lbool theory_pb::normalize_ineq(arg_t& args, numeral& k) {
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// normalize first all literals to be positive:
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// then we can compare them more easily.
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for (unsigned i = 0; i < args.size(); ++i) {
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if (args[i].first.sign()) {
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args[i].first.neg();
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k -= args[i].second;
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args[i].second = -args[i].second;
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}
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}
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// remove constants
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for (unsigned i = 0; i < args.size(); ++i) {
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if (args[i].first == true_literal) {
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k += args[i].second;
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std::swap(args[i], args[args.size()-1]);
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args.pop_back();
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}
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else if (args[i].first == false_literal) {
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std::swap(args[i], args[args.size()-1]);
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args.pop_back();
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}
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}
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// sort and coalesce arguments:
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std::sort(args.begin(), args.end());
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for (unsigned i = 0; i + 1 < args.size(); ++i) {
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if (args[i].first == args[i+1].first) {
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args[i].second += args[i+1].second;
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for (unsigned j = i+1; j + 1 < args.size(); ++j) {
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args[j] = args[j+1];
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}
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args.resize(args.size()-1);
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}
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if (args[i].second == 0) {
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for (unsigned j = i; j + 1 < args.size(); ++j) {
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args[j] = args[j+1];
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}
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args.resize(args.size()-1);
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}
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}
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//
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// Ensure all coefficients are positive:
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// c*l + y >= k
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// <=>
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// c*(1-~l) + y >= k
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// <=>
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// c - c*~l + y >= k
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// <=>
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// -c*~l + y >= k - c
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//
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numeral sum = 0;
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for (unsigned i = 0; i < args.size(); ++i) {
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numeral c = args[i].second;
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if (c < 0) {
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args[i].second = -c;
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args[i].first = ~args[i].first;
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k -= c;
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}
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sum += args[i].second;
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}
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// detect tautologies:
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if (k <= 0) {
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args.reset();
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return l_true;
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}
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// detect infeasible constraints:
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if (sum < k) {
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args.reset();
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return l_false;
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}
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// Ensure the largest coefficient is not larger than k:
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for (unsigned i = 0; i < args.size(); ++i) {
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numeral c = args[i].second;
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if (c > k) {
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args[i].second = k;
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}
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}
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SASSERT(!args.empty());
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// apply cutting plane reduction:
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numeral g = 0;
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for (unsigned i = 0; g != 1 && i < args.size(); ++i) {
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numeral c = args[i].second;
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if (c != k) {
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g = gcd(g, c);
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}
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}
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if (g == 0) {
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// all coefficients are equal to k.
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for (unsigned i = 0; i < args.size(); ++i) {
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SASSERT(args[i].second == k);
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args[i].second = 1;
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}
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k = 1;
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}
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else if (g > 1) {
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//
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// Example 5x + 5y + 2z + 2u >= 5
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// becomes 3x + 3y + z + u >= 3
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//
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numeral k_new = k / g;
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if ((k % g) != 0) { // k_new is the ceiling of k / g.
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k_new++;
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}
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for (unsigned i = 0; i < args.size(); ++i) {
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numeral c = args[i].second;
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if (c == k) {
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c = k_new;
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}
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else {
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c = c / g;
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}
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args[i].second = c;
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}
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k = k_new;
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}
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return l_undef;
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}
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void theory_pb::collect_statistics(::statistics& st) const {
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st.update("pb axioms", m_stats.m_num_axioms);
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st.update("pb propagations", m_stats.m_num_propagations);
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@ -384,6 +426,10 @@ namespace smt {
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m_to_compile.reset();
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}
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void theory_pb::new_eq_eh(theory_var v1, theory_var v2) {
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IF_VERBOSE(0, verbose_stream() << v1 << " = " << v2 << "\n";);
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}
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void theory_pb::assign_eh(bool_var v, bool is_true) {
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context& ctx = get_context();
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ptr_vector<ineq>* ineqs = 0;
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@ -461,7 +507,7 @@ namespace smt {
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if (maxsum < c.k()) {
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literal_vector& lits = get_unhelpful_literals(c, true);
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lits.push_back(~c.lit());
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add_clause(c, lits);
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add_clause(c, c.lit(), lits);
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return;
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}
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@ -514,7 +560,7 @@ namespace smt {
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//
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literal_vector& lits = get_unhelpful_literals(c, false);
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lits.push_back(~c.lit());
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add_clause(c, lits);
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add_clause(c, literal(v, !is_true), lits);
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}
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else if (c.max_sum() < k + c.max_coeff()) {
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//
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@ -804,9 +850,14 @@ namespace smt {
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std::ostream& theory_pb::display(std::ostream& out, ineq& c) const {
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ast_manager& m = get_manager();
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context& ctx = get_context();
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expr_ref tmp(m);
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ctx.literal2expr(c.lit(), tmp);
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out << tmp << "\n";
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if (c.lit() != null_literal) {
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expr_ref tmp(m);
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ctx.literal2expr(c.lit(), tmp);
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out << tmp << "\n";
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}
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else {
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out << "null\n";
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}
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for (unsigned i = 0; i < c.size(); ++i) {
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out << c.coeff(i) << "*" << c.lit(i);
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if (i + 1 < c.size()) {
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@ -829,6 +880,17 @@ namespace smt {
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return m_literals;
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}
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class theory_pb::pb_justification : public theory_propagation_justification {
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ineq& m_ineq;
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public:
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pb_justification(ineq& c, family_id fid, region & r,
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unsigned num_lits, literal const * lits, literal consequent):
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theory_propagation_justification(fid, r, num_lits, lits, consequent),
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m_ineq(c)
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{}
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ineq& get_ineq() { return m_ineq; }
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};
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void theory_pb::add_assign(ineq& c, literal_vector const& lits, literal l) {
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inc_propagations(c);
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m_stats.m_num_propagations++;
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@ -841,13 +903,13 @@ namespace smt {
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display(tout, c););
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ctx.assign(l, ctx.mk_justification(
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theory_propagation_justification(
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get_id(), ctx.get_region(), lits.size(), lits.c_ptr(), l)));
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pb_justification(
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c, get_id(), ctx.get_region(), lits.size(), lits.c_ptr(), l)));
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}
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|
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void theory_pb::add_clause(ineq& c, literal_vector const& lits) {
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void theory_pb::add_clause(ineq& c, literal conseq, literal_vector const& lits) {
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inc_propagations(c);
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m_stats.m_num_axioms++;
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context& ctx = get_context();
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|
@ -857,11 +919,139 @@ namespace smt {
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}
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tout << "\n";
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display(tout, c););
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// DEBUG_CODE(resolve_conflict(conseq, c););
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justification* js = 0;
|
||||
ctx.mk_clause(lits.size(), lits.c_ptr(), js, CLS_AUX_LEMMA, 0);
|
||||
IF_VERBOSE(2, ctx.display_literals_verbose(verbose_stream(),
|
||||
lits.size(), lits.c_ptr());
|
||||
verbose_stream() << "\n";);
|
||||
// ctx.mk_th_axiom(get_id(), lits.size(), lits.c_ptr());
|
||||
|
||||
}
|
||||
|
||||
void theory_pb::process_antecedent(literal l, numeral coeff) {
|
||||
context& ctx = get_context();
|
||||
bool_var v = l.var();
|
||||
unsigned lvl = ctx.get_assign_level(v);
|
||||
IF_VERBOSE(0, verbose_stream() << l << "*" << coeff << " marked: " << ctx.is_marked(v) << " lvl: " << lvl << "\n";);
|
||||
if (!ctx.is_marked(v) && lvl > ctx.get_base_level()) {
|
||||
ctx.set_mark(v);
|
||||
if (lvl == m_conflict_lvl) {
|
||||
++m_num_marks;
|
||||
}
|
||||
else {
|
||||
m_lemma.m_args.push_back(std::make_pair(l, coeff));
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void theory_pb::process_ineq(ineq& c) {
|
||||
// TBD: create CUT.
|
||||
context& ctx = get_context();
|
||||
for (unsigned i = 0; i < c.size(); ++i) {
|
||||
process_antecedent(c.lit(i), c.coeff(i));
|
||||
}
|
||||
process_antecedent(~c.lit(), 1);
|
||||
}
|
||||
|
||||
//
|
||||
// modeled after sat_solver/smt_context
|
||||
//
|
||||
void theory_pb::resolve_conflict(literal conseq, ineq& c) {
|
||||
|
||||
bool_var v;
|
||||
context& ctx = get_context();
|
||||
unsigned& lvl = m_conflict_lvl = ctx.get_assign_level(c.lit());
|
||||
for (unsigned i = 0; i < c.size(); ++i) {
|
||||
IF_VERBOSE(0, verbose_stream() << "conflict level: " << m_conflict_lvl << "\n";);
|
||||
v = c.lit(i).var();
|
||||
if (ctx.get_assignment(v) != l_undef) {
|
||||
lvl = std::max(lvl, ctx.get_assign_level(v));
|
||||
}
|
||||
}
|
||||
|
||||
if (lvl == ctx.get_base_level()) {
|
||||
return;
|
||||
}
|
||||
|
||||
b_justification js(ctx.mk_justification(
|
||||
pb_justification(c, get_id(), ctx.get_region(),
|
||||
0, 0, c.lit())));
|
||||
m_lemma.reset();
|
||||
m_num_marks = 0;
|
||||
|
||||
// point into stack of assigned literals
|
||||
literal_vector const& lits = ctx.assigned_literals();
|
||||
SASSERT(!lits.empty());
|
||||
unsigned idx = lits.size()-1;
|
||||
|
||||
do {
|
||||
//
|
||||
// Resolve selected conseq with antecedents.
|
||||
//
|
||||
switch(js.get_kind()) {
|
||||
case b_justification::CLAUSE: {
|
||||
clause* cls = js.get_clause();
|
||||
unsigned num_lits = cls->get_num_literals();
|
||||
for (unsigned i = 0; i < num_lits; ++i) {
|
||||
process_antecedent(cls->get_literal(i), 1);
|
||||
}
|
||||
justification* cjs = cls->get_justification();
|
||||
if (cjs) {
|
||||
// TBD
|
||||
NOT_IMPLEMENTED_YET();
|
||||
}
|
||||
break;
|
||||
}
|
||||
case b_justification::BIN_CLAUSE:
|
||||
SASSERT(conseq.var() != js.get_literal().var());
|
||||
process_antecedent(~js.get_literal(), 1);
|
||||
break;
|
||||
case b_justification::AXIOM:
|
||||
break;
|
||||
case b_justification::JUSTIFICATION: {
|
||||
justification& j = *js.get_justification();
|
||||
// only process pb justifications.
|
||||
if (j.get_from_theory() != get_id()) break;
|
||||
pb_justification& pbj = dynamic_cast<pb_justification&>(j);
|
||||
// weaken the lemma and resolve.
|
||||
process_ineq(pbj.get_ineq());
|
||||
break;
|
||||
}
|
||||
default:
|
||||
UNREACHABLE();
|
||||
}
|
||||
//
|
||||
// find the next marked variable in the assignment stack
|
||||
//
|
||||
SASSERT(idx > 0);
|
||||
SASSERT(m_num_marks > 0);
|
||||
do {
|
||||
conseq = lits[idx];
|
||||
v = conseq.var();
|
||||
--idx;
|
||||
}
|
||||
while (!ctx.is_marked(v));
|
||||
|
||||
js = ctx.get_justification(v);
|
||||
--m_num_marks;
|
||||
ctx.unset_mark(v);
|
||||
IF_VERBOSE(0, verbose_stream() << "unmark: " << v << "\n";);
|
||||
}
|
||||
while (m_num_marks > 0);
|
||||
|
||||
// unset the marks on lemmas
|
||||
for (unsigned i = 0; i < m_lemma.size(); ++i) {
|
||||
bool_var v = m_lemma.lit(i).var();
|
||||
if (ctx.is_marked(v)) {
|
||||
IF_VERBOSE(0, verbose_stream() << "unmark: " << v << "\n";);
|
||||
ctx.unset_mark(v);
|
||||
}
|
||||
}
|
||||
|
||||
TRACE("card", display(tout, m_lemma););
|
||||
|
||||
IF_VERBOSE(1, display(verbose_stream(), m_lemma););
|
||||
}
|
||||
}
|
||||
|
|
|
@ -28,6 +28,7 @@ namespace smt {
|
|||
class theory_pb : public theory {
|
||||
|
||||
struct sort_expr;
|
||||
class pb_justification;
|
||||
typedef int64 numeral;
|
||||
typedef svector<std::pair<literal, numeral> > arg_t;
|
||||
|
||||
|
@ -57,16 +58,9 @@ namespace smt {
|
|||
unsigned m_compilation_threshold;
|
||||
lbool m_compiled;
|
||||
|
||||
ineq(literal l):
|
||||
m_lit(l),
|
||||
m_max_coeff(0),
|
||||
m_watch_sz(0),
|
||||
m_sum(0),
|
||||
m_max_sum(0),
|
||||
m_num_propagations(0),
|
||||
m_compilation_threshold(UINT_MAX),
|
||||
m_compiled(l_false)
|
||||
{}
|
||||
ineq(literal l) : m_lit(l) {
|
||||
reset();
|
||||
}
|
||||
|
||||
literal lit() const { return m_lit; }
|
||||
numeral const & k() const { return m_k; }
|
||||
|
@ -90,9 +84,16 @@ namespace smt {
|
|||
return begin;
|
||||
}
|
||||
|
||||
void reset();
|
||||
|
||||
void negate();
|
||||
|
||||
lbool normalize();
|
||||
|
||||
bool well_formed() const;
|
||||
|
||||
static numeral gcd(numeral a, numeral b);
|
||||
|
||||
};
|
||||
|
||||
typedef ptr_vector<ineq> watch_list;
|
||||
|
@ -109,8 +110,6 @@ namespace smt {
|
|||
ptr_vector<ineq> m_to_compile; // inequalities to compile.
|
||||
|
||||
// internalize_atom:
|
||||
lbool normalize_ineq(arg_t& args, numeral& k);
|
||||
static numeral gcd(numeral a, numeral b);
|
||||
literal compile_arg(expr* arg);
|
||||
void add_watch(ineq& c, unsigned index);
|
||||
void del_watch(watch_list& watch, unsigned index, ineq& c, unsigned ineq_index);
|
||||
|
@ -120,7 +119,7 @@ namespace smt {
|
|||
std::ostream& display(std::ostream& out, ineq& c) const;
|
||||
virtual void display(std::ostream& out) const;
|
||||
|
||||
void add_clause(ineq& c, literal_vector const& lits);
|
||||
void add_clause(ineq& c, literal conseq, literal_vector const& lits);
|
||||
void add_assign(ineq& c, literal_vector const& lits, literal l);
|
||||
literal_vector& get_lits();
|
||||
|
||||
|
@ -134,6 +133,16 @@ namespace smt {
|
|||
void compile_ineq(ineq& c);
|
||||
void inc_propagations(ineq& c);
|
||||
unsigned get_compilation_threshold(ineq& c);
|
||||
|
||||
//
|
||||
// Conflict resolution, cutting plane derivation.
|
||||
//
|
||||
unsigned m_num_marks;
|
||||
unsigned m_conflict_lvl;
|
||||
ineq m_lemma;
|
||||
void resolve_conflict(literal conseq, ineq& c);
|
||||
void process_antecedent(literal l, numeral coeff);
|
||||
void process_ineq(ineq& c);
|
||||
public:
|
||||
theory_pb(ast_manager& m);
|
||||
|
||||
|
@ -142,7 +151,7 @@ namespace smt {
|
|||
virtual theory * mk_fresh(context * new_ctx);
|
||||
virtual bool internalize_atom(app * atom, bool gate_ctx);
|
||||
virtual bool internalize_term(app * term) { UNREACHABLE(); return false; }
|
||||
virtual void new_eq_eh(theory_var v1, theory_var v2) { }
|
||||
virtual void new_eq_eh(theory_var v1, theory_var v2);
|
||||
virtual void new_diseq_eh(theory_var v1, theory_var v2) { }
|
||||
virtual bool use_diseqs() const { return false; }
|
||||
virtual bool build_models() const { return false; }
|
||||
|
|
Loading…
Reference in a new issue