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https://github.com/Z3Prover/z3
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special case branching
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
ed1a5797fb
commit
c454b81b2c
3 changed files with 201 additions and 50 deletions
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@ -3212,7 +3212,8 @@ namespace smt {
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template<typename Ext>
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bool theory_arith<Ext>::get_value(enode * n, expr_ref & r) {
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theory_var v = n->get_th_var(get_id());
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return v != null_theory_var && to_expr(get_value(v), is_int(v), r);
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inf_numeral val;
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return v != null_theory_var && (val = get_value(v), (!is_int(v) || val.is_int())) && to_expr(val, is_int(v), r);
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}
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template<typename Ext>
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@ -257,7 +257,7 @@ final_check_status theory_seq::final_check_eh() {
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TRACE("seq", tout << ">>fixed_length\n";);
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return FC_CONTINUE;
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}
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if (reduce_length_eq() || branch_variable_mb() || branch_variable()) {
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if (reduce_length_eq() || branch_unit_variable() || branch_binary_variable() || branch_variable_mb() || branch_variable()) {
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++m_stats.m_branch_variable;
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TRACE("seq", tout << ">>branch_variable\n";);
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return FC_CONTINUE;
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@ -305,40 +305,184 @@ bool theory_seq::reduce_length_eq() {
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return false;
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}
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bool theory_seq::branch_binary_variable() {
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unsigned sz = m_eqs.size();
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for (unsigned i = 0; i < sz; ++i) {
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eq const& e = m_eqs[i];
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if (branch_binary_variable(e)) {
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return true;
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}
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}
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return false;
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}
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bool theory_seq::branch_binary_variable(eq const& e) {
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if (is_complex(e)) {
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return false;
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}
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ptr_vector<expr> xs, ys;
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expr* x, *y;
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bool is_binary = is_binary_eq(e.ls(), e.rs(), x, xs, ys, y);
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if (!is_binary) {
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is_binary = is_binary_eq(e.rs(), e.ls(), x, xs, ys, y);
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}
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if (!is_binary) {
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return false;
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}
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if (x == y) {
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return false;
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}
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// Equation is of the form x ++ xs = ys ++ y
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// where xs, ys are units.
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// x is either a prefix of ys, all of ys ++ y or ys ++ y1, such that y = y1 ++ y2, y2 = xs
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rational lenX, lenY;
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context& ctx = get_context();
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if (branch_variable(e)) {
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return true;
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}
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if (!get_length(x, lenX)) {
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enforce_length(ensure_enode(x));
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return true;
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}
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if (!get_length(y, lenY)) {
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enforce_length(ensure_enode(y));
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return true;
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}
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if (lenX + rational(xs.size()) != lenY + rational(ys.size())) {
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// |x| - |y| = |ys| - |xs|
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expr_ref a(mk_sub(m_util.str.mk_length(x), m_util.str.mk_length(y)), m);
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expr_ref b(m_autil.mk_int(ys.size()-xs.size()), m);
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propagate_lit(e.dep(), 0, 0, mk_eq(a, b, false));
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return true;
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}
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if (lenX <= rational(ys.size())) {
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expr_ref_vector Ys(m);
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Ys.append(ys.size(), ys.c_ptr());
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branch_unit_variable(e.dep(), x, Ys);
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return true;
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}
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expr_ref le(m_autil.mk_le(m_util.str.mk_length(x), m_autil.mk_int(ys.size())), m);
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literal lit = mk_literal(le);
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if (l_false == ctx.get_assignment(lit)) {
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// |x| > |ys| => x = ys ++ y1, y = y1 ++ y2, y2 = xs
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expr_ref Y1(mk_skolem(symbol("seq.left"), x, y), m);
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expr_ref Y2(mk_skolem(symbol("seq.right"), x, y), m);
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ys.push_back(Y1);
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expr_ref ysY1(m_util.str.mk_concat(ys.size(), ys.c_ptr()), m);
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expr_ref xsE(m_util.str.mk_concat(xs.size(), xs.c_ptr()), m);
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expr_ref Y1Y2(m_util.str.mk_concat(Y1, Y2), m);
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literal_vector lits;
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lits.push_back(~lit);
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dependency* dep = e.dep();
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propagate_eq(dep, lits, x, ysY1, true);
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propagate_eq(dep, lits, y, Y1Y2, true);
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propagate_eq(dep, lits, Y2, xsE, true);
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}
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else {
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ctx.mark_as_relevant(lit);
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}
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return true;
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}
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bool theory_seq::branch_unit_variable() {
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unsigned sz = m_eqs.size();
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for (unsigned i = 0; i < sz; ++i) {
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eq const& e = m_eqs[i];
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if (is_unit_eq(e.ls(), e.rs())) {
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branch_unit_variable(e.dep(), e.ls()[0], e.rs());
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return true;
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}
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else if (is_unit_eq(e.rs(), e.ls())) {
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branch_unit_variable(e.dep(), e.rs()[0], e.ls());
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return true;
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}
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}
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return false;
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}
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/**
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\brief ls := X... == rs := abcdef
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*/
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bool theory_seq::is_unit_eq(expr_ref_vector const& ls, expr_ref_vector const& rs) {
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if (ls.empty() || !is_var(ls[0])) {
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return false;
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}
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for (unsigned i = 0; i < rs.size(); ++i) {
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if (!m_util.str.is_unit(rs[i])) {
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return false;
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}
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}
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return true;
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}
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void theory_seq::branch_unit_variable(dependency* dep, expr* X, expr_ref_vector const& units) {
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SASSERT(is_var(X));
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context& ctx = get_context();
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rational lenX;
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if (!get_length(X, lenX)) {
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enforce_length(ensure_enode(X));
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return;
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}
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if (lenX > rational(units.size())) {
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expr_ref le(m_autil.mk_le(m_util.str.mk_length(X), m_autil.mk_int(units.size())), m);
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propagate_lit(dep, 0, 0, mk_literal(le));
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return;
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}
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SASSERT(lenX.is_unsigned());
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unsigned lX = lenX.get_unsigned();
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if (lX == 0) {
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set_empty(X);
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}
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else {
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literal lit = mk_eq(m_autil.mk_int(lX), m_util.str.mk_length(X), false);
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if (l_true == ctx.get_assignment(lit)) {
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expr_ref R(m_util.str.mk_concat(lX, units.c_ptr()), m);
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literal_vector lits;
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lits.push_back(lit);
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propagate_eq(dep, lits, X, R, true);
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}
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else {
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ctx.mark_as_relevant(lit);
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ctx.force_phase(lit);
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}
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}
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}
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bool theory_seq::branch_variable_mb() {
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context& ctx = get_context();
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unsigned sz = m_eqs.size();
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int start = ctx.get_random_value();
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bool change = false;
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for (unsigned i = 0; i < sz; ++i) {
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unsigned k = (i + start) % sz;
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for (unsigned i = 0; i < m_eqs.size(); ++i) {
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eq const& e = m_eqs[i];
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vector<rational> len1, len2;
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if (!is_complex(e)) {
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continue;
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}
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if (!enforce_length(e.ls(), len1) || !enforce_length(e.rs(), len2)) {
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change = true;
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continue;
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}
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if (e.ls().empty() || e.rs().empty() ||
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(!is_var(e.ls()[0]) && !is_var(e.rs()[0]))) {
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continue;
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}
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if (!enforce_length(e.ls(), len1) || !enforce_length(e.rs(), len2)) {
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change = true;
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continue;
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}
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rational l1, l2;
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for (unsigned i = 0; i < len1.size(); ++i) l1 += len1[i];
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for (unsigned i = 0; i < len2.size(); ++i) l2 += len2[i];
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for (unsigned j = 0; j < len1.size(); ++j) l1 += len1[j];
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for (unsigned j = 0; j < len2.size(); ++j) l2 += len2[j];
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if (l1 != l2) {
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TRACE("seq", tout << "lengths are not compatible\n";);
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expr_ref l = mk_concat(e.ls().size(), e.ls().c_ptr());
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expr_ref r = mk_concat(e.rs().size(), e.rs().c_ptr());
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expr_ref lnl(m_util.str.mk_length(l), m), lnr(m_util.str.mk_length(r), m);
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add_axiom(~mk_eq(l, r, false), mk_eq(lnl, lnr, false));
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literal_vector lits;
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propagate_eq(e.dep(), lits, lnl, lnr, false);
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change = true;
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continue;
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}
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if (split_lengths(e.dep(), e.ls(), e.rs(), len1, len2)) {
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TRACE("seq", display_equation(tout, e););
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TRACE("seq", tout << "split lengths\n";);
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return true;
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}
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}
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@ -417,42 +561,38 @@ bool theory_seq::split_lengths(dependency* dep,
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b = mk_concat(bs, m.get_sort(X));
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SASSERT(X != Y);
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expr_ref split_pred = mk_skolem(symbol("seq.split"), X, b, Y, m.mk_bool_sort());
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literal split_predl = mk_literal(split_pred);
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lbool is_split = ctx.get_assignment(split_predl);
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if (is_split != l_true) {
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// split_pred <=> |b| < |X| <= |b| + |Y|
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expr_ref lenX(m_util.str.mk_length(X), m);
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expr_ref lenY(m_util.str.mk_length(Y), m);
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expr_ref lenb(m_util.str.mk_length(b), m);
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expr_ref le1(m_autil.mk_le(mk_sub(lenX, lenb), m_autil.mk_int(0)), m);
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expr_ref le2(m_autil.mk_le(mk_sub(mk_sub(lenX, lenb), lenY),
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m_autil.mk_int(0)), m);
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literal lit1(~mk_literal(le1));
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literal lit2(mk_literal(le2));
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add_axiom(~split_predl, lit1);
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add_axiom(~split_predl, lit2);
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add_axiom(split_predl, ~lit1, ~lit2);
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// |b| < |X| <= |b| + |Y| => x = bY1, Y = Y1Y2
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expr_ref lenXE(m_util.str.mk_length(X), m);
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expr_ref lenYE(m_util.str.mk_length(Y), m);
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expr_ref lenb(m_util.str.mk_length(b), m);
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expr_ref le1(m_autil.mk_le(mk_sub(lenXE, lenb), m_autil.mk_int(0)), m);
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expr_ref le2(m_autil.mk_le(mk_sub(mk_sub(lenXE, lenb), lenYE),
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m_autil.mk_int(0)), m);
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literal lit1(~mk_literal(le1));
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literal lit2(mk_literal(le2));
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literal_vector lits;
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lits.push_back(lit1);
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lits.push_back(lit2);
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if (ctx.get_assignment(lit1) != l_true ||
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ctx.get_assignment(lit2) != l_true) {
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ctx.mark_as_relevant(lit1);
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ctx.mark_as_relevant(lit2);
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}
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else if (m_util.str.is_unit(Y)) {
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SASSERT(lenB == lenX);
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SASSERT(is_split == l_true);
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bs.push_back(Y);
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expr_ref bY(m_util.str.mk_concat(bs), m);
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literal_vector lits;
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lits.push_back(split_predl);
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propagate_eq(dep, lits, X, bY, true);
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}
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else {
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SASSERT(is_var(Y));
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// split_pred => X = bY1, Y = Y1Y2
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SASSERT(is_split == l_true);
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expr_ref Y1(mk_skolem(symbol("seq.left"), X, b, Y), m);
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expr_ref Y2(mk_skolem(symbol("seq.right"), X, b, Y), m);
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expr_ref bY1(m_util.str.mk_concat(b, Y1), m);
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expr_ref Y1Y2(m_util.str.mk_concat(Y1, Y2), m);
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literal_vector lits;
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lits.push_back(split_predl);
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propagate_eq(dep, lits, X, bY1, true);
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propagate_eq(dep, lits, Y, Y1Y2, true);
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}
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@ -495,23 +635,11 @@ bool theory_seq::branch_variable() {
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unsigned sz = m_eqs.size();
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int start = ctx.get_random_value();
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unsigned s = 0;
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for (unsigned i = 0; i < sz; ++i) {
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unsigned k = (i + start) % sz;
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eq const& e = m_eqs[k];
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unsigned id = e.id();
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s = find_branch_start(2*id);
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TRACE("seq", tout << s << " " << id << ": " << e.ls() << " = " << e.rs() << "\n";);
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bool found = find_branch_candidate(s, e.dep(), e.ls(), e.rs());
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insert_branch_start(2*id, s);
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if (found) {
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return true;
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}
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s = find_branch_start(2*id + 1);
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found = find_branch_candidate(s, e.dep(), e.rs(), e.ls());
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insert_branch_start(2*id + 1, s);
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if (found) {
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if (branch_variable(e)) {
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return true;
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}
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@ -527,6 +655,22 @@ bool theory_seq::branch_variable() {
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return ctx.inconsistent();
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}
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bool theory_seq::branch_variable(eq const& e) {
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unsigned id = e.id();
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unsigned s = find_branch_start(2*id);
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TRACE("seq", tout << s << " " << id << ": " << e.ls() << " = " << e.rs() << "\n";);
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bool found = find_branch_candidate(s, e.dep(), e.ls(), e.rs());
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insert_branch_start(2*id, s);
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if (found) {
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return true;
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}
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s = find_branch_start(2*id + 1);
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found = find_branch_candidate(s, e.dep(), e.rs(), e.ls());
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insert_branch_start(2*id + 1, s);
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return found;
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}
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void theory_seq::insert_branch_start(unsigned k, unsigned s) {
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m_branch_start.insert(k, s);
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m_trail_stack.push(pop_branch(k));
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@ -359,6 +359,8 @@ namespace smt {
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// final check
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bool simplify_and_solve_eqs(); // solve unitary equalities
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bool reduce_length_eq();
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bool branch_unit_variable(); // branch on XYZ = abcdef
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bool branch_binary_variable(); // branch on abcX = Ydefg
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bool branch_variable_mb(); // branch on a variable, model based on length
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bool branch_variable(); // branch on a variable
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bool split_variable(); // split a variable
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@ -368,6 +370,10 @@ namespace smt {
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bool check_length_coherence(expr* e);
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bool fixed_length();
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bool fixed_length(expr* e);
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void branch_unit_variable(dependency* dep, expr* X, expr_ref_vector const& units);
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bool branch_variable(eq const& e);
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bool branch_binary_variable(eq const& e);
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bool is_unit_eq(expr_ref_vector const& ls, expr_ref_vector const& rs);
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bool propagate_length_coherence(expr* e);
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bool split_lengths(dependency* dep,
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expr_ref_vector const& ls, expr_ref_vector const& rs,
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