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https://github.com/Z3Prover/z3
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add shortcuts for concatenation and equality propagation
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
c8d9be0bbf
commit
faebbc5384
3 changed files with 32 additions and 190 deletions
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@ -886,174 +886,6 @@ namespace qe {
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tactic * translate(ast_manager & m) {
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return alloc(nlqsat, m, m_mode, m_params);
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}
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#if 0
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/**
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Algorithm:
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I := true
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while there is M, such that M |= ~B & I:
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find P, such that M => P => exists y . ~B & I
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; forall y B => ~P
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C := core of P with respect to A
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; A => ~ C => ~ P
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I := I & ~C
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Alternative Algorithm:
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R := false
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while there is M, such that M |= A & ~R:
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find I, such that M => I => forall y . B
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R := R | I
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*/
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lbool interpolate(expr* a, expr* b, expr_ref& result) {
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SASSERT(m_mode == interp_t);
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reset();
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app_ref enableA(m), enableB(m);
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expr_ref A(m), B(m), fml(m);
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expr_ref_vector fmls(m), answer(m);
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// varsB are private to B.
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nlsat::var_vector vars;
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uint_set fvars;
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private_vars(a, b, vars, fvars);
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enableA = m.mk_const(symbol("#A"), m.mk_bool_sort());
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enableB = m.mk_not(enableA);
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A = m.mk_implies(enableA, a);
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B = m.mk_implies(enableB, m.mk_not(b));
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fml = m.mk_and(A, B);
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hoist(fml);
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nlsat::literal _enableB = nlsat::literal(m_a2b.to_var(enableB), false);
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nlsat::literal _enableA = ~_enableB;
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while (true) {
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m_mode = qsat_t;
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// enable B
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m_assumptions.reset();
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m_assumptions.push_back(_enableB);
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lbool is_sat = check_sat();
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switch (is_sat) {
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case l_undef:
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return l_undef;
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case l_true:
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break;
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case l_false:
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result = mk_and(answer);
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return l_true;
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}
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// disable B, enable A
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m_assumptions.reset();
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m_assumptions.push_back(_enableA);
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// add blocking clause to solver.
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nlsat::scoped_literal_vector core(m_solver);
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m_mode = elim_t;
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mbp(vars, fvars, core);
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// minimize core.
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nlsat::literal_vector _core(core.size(), core.c_ptr());
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_core.push_back(_enableA);
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is_sat = m_solver.check(_core); // TBD: only for quantifier-free A. Generalize output of elim_t to be a core.
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switch (is_sat) {
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case l_undef:
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return l_undef;
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case l_true:
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UNREACHABLE();
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case l_false:
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core.reset();
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core.append(_core.size(), _core.c_ptr());
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break;
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}
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negate_clause(core);
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// keep polarity of enableA, such that clause is only
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// used when checking satisfiability of B.
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for (unsigned i = 0; i < core.size(); ++i) {
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if (core[i].var() == _enableA.var()) core.set(i, ~core[i]);
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}
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add_clause(core); // Invariant is added as assumption for B.
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answer.push_back(clause2fml(core)); // TBD: remove answer literal.
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}
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}
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/**
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\brief extract variables that are private to a (not used in b).
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vars cover the real variables, and fvars cover the Boolean variables.
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TBD: We want fvars to be the complement such that returned core contains
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Shared boolean variables, but not the ones private to B.
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*/
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void private_vars(expr* a, expr* b, nlsat::var_vector& vars, uint_set& fvars) {
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app_ref_vector varsA(m), varsB(m);
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obj_hashtable<expr> varsAS;
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pred_abs abs(m);
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abs.get_free_vars(a, varsA);
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abs.get_free_vars(b, varsB);
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insert_set(varsAS, varsA);
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for (unsigned i = 0; i < varsB.size(); ++i) {
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if (varsAS.contains(varsB[i].get())) {
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varsB[i] = varsB.back();
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varsB.pop_back();
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--i;
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}
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}
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for (unsigned j = 0; j < varsB.size(); ++j) {
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app* v = varsB[j].get();
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if (m_a2b.is_var(v)) {
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fvars.insert(m_a2b.to_var(v));
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}
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else if (m_t2x.is_var(v)) {
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vars.push_back(m_t2x.to_var(v));
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}
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}
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}
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lbool maximize(app* _x, expr* _fml, scoped_anum& result, bool& unbounded) {
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expr_ref fml(_fml, m);
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reset();
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hoist(fml);
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nlsat::literal_vector lits;
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lbool is_sat = l_true;
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nlsat::var x = m_t2x.to_var(_x);
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m_mode = qsat_t;
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while (is_sat == l_true) {
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is_sat = check_sat();
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if (is_sat == l_true) {
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// m_asms is minimized set of literals that satisfy formula.
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nlsat::explain& ex = m_solver.get_explain();
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polynomial::manager& pm = m_solver.pm();
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anum_manager& am = m_solver.am();
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ex.maximize(x, m_asms.size(), m_asms.c_ptr(), result, unbounded);
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if (unbounded) {
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break;
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}
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// TBD: assert the new bound on x using the result.
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bool is_even = false;
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polynomial::polynomial_ref pr(pm);
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pr = pm.mk_polynomial(x);
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rational r;
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am.get_upper(result, r);
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// result is algebraic numeral, but polynomials are not defined over extension field.
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polynomial::polynomial* p = pr;
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nlsat::bool_var b = m_solver.mk_ineq_atom(nlsat::atom::GT, 1, &p, &is_even);
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nlsat::literal bound(b, false);
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m_solver.mk_clause(1, &bound);
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}
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}
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return is_sat;
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}
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#endif
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};
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};
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@ -397,15 +397,13 @@ bool theory_seq::branch_binary_variable(eq const& e) {
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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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expr_ref ysY1(mk_concat(ys));
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expr_ref xsE(mk_concat(xs));
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expr_ref Y1Y2(mk_concat(Y1, Y2));
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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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propagate_eq(dep, ~lit, x, ysY1);
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propagate_eq(dep, ~lit, y, Y1Y2);
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propagate_eq(dep, ~lit, Y2, xsE);
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}
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else {
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ctx.mark_as_relevant(lit);
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@ -471,9 +469,7 @@ void theory_seq::branch_unit_variable(dependency* dep, expr* X, expr_ref_vector
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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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propagate_eq(dep, lit, X, R);
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TRACE("seq", tout << "propagate " << mk_pp(X, m) << " " << R << "\n";);
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}
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else {
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@ -506,11 +502,10 @@ bool theory_seq::branch_variable_mb() {
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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 l = mk_concat(e.ls());
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expr_ref r = mk_concat(e.rs());
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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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literal_vector lits;
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propagate_eq(e.dep(), lits, lnl, lnr, false);
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propagate_eq(e.dep(), lnl, lnr, false);
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change = true;
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continue;
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}
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@ -626,8 +621,8 @@ bool theory_seq::split_lengths(dependency* dep,
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SASSERT(is_var(Y));
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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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expr_ref bY1 = mk_concat(b, Y1);
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expr_ref Y1Y2 = mk_concat(Y1, Y2);
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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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@ -1317,6 +1312,18 @@ void theory_seq::propagate_eq(dependency* dep, enode* n1, enode* n2) {
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enforce_length_coherence(n1, n2);
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}
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void theory_seq::propagate_eq(dependency* dep, expr* e1, expr* e2, bool add_eq) {
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literal_vector lits;
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propagate_eq(dep, lits, e1, e2, add_eq);
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}
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void theory_seq::propagate_eq(dependency* dep, literal lit, expr* e1, expr* e2, bool add_to_eqs) {
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literal_vector lits;
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lits.push_back(lit);
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propagate_eq(dep, lits, e1, e2, add_to_eqs);
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}
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void theory_seq::enforce_length_coherence(enode* n1, enode* n2) {
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expr* o1 = n1->get_owner();
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expr* o2 = n2->get_owner();
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@ -1662,19 +1669,18 @@ bool theory_seq::reduce_length(unsigned i, unsigned j, bool front, expr_ref_vect
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}
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SASSERT(0 < l1 && l1 < ls.size());
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SASSERT(0 < r1 && r1 < rs.size());
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expr_ref l(m_util.str.mk_concat(l1, ls1), m);
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expr_ref r(m_util.str.mk_concat(r1, rs1), m);
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expr_ref l = mk_concat(l1, ls1);
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expr_ref r = mk_concat(r1, rs1);
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expr_ref lenl(m_util.str.mk_length(l), m);
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expr_ref lenr(m_util.str.mk_length(r), m);
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literal lit = mk_eq(lenl, lenr, false);
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if (ctx.get_assignment(lit) == l_true) {
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literal_vector lits;
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expr_ref_vector lhs(m), rhs(m);
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lhs.append(l2, ls2);
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rhs.append(r2, rs2);
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deps = mk_join(deps, lit);
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m_eqs.push_back(eq(m_eq_id++, lhs, rhs, deps));
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propagate_eq(deps, lits, l, r, true);
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propagate_eq(deps, l, r, true);
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TRACE("seq", tout << "propagate eq\nlhs: " << lhs << "\nrhs: " << rhs << "\n";);
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return true;
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}
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@ -410,6 +410,8 @@ namespace smt {
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expr_ref mk_empty(sort* s) { return expr_ref(m_util.str.mk_empty(s), m); }
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expr_ref mk_concat(unsigned n, expr*const* es) { return expr_ref(m_util.str.mk_concat(n, es), m); }
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expr_ref mk_concat(expr_ref_vector const& es, sort* s) { if (es.empty()) return mk_empty(s); return mk_concat(es.size(), es.c_ptr()); }
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expr_ref mk_concat(expr_ref_vector const& es) { SASSERT(!es.empty()); return mk_concat(es.size(), es.c_ptr()); }
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expr_ref mk_concat(ptr_vector<expr> const& es) { SASSERT(!es.empty()); return mk_concat(es.size(), es.c_ptr()); }
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expr_ref mk_concat(expr* e1, expr* e2) { return expr_ref(m_util.str.mk_concat(e1, e2), m); }
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expr_ref mk_concat(expr* e1, expr* e2, expr* e3) { return expr_ref(m_util.str.mk_concat(e1, e2, e3), m); }
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bool solve_nqs(unsigned i);
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@ -436,7 +438,9 @@ namespace smt {
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void propagate_lit(dependency* dep, unsigned n, literal const* lits, literal lit);
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void propagate_eq(dependency* dep, enode* n1, enode* n2);
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void propagate_eq(literal lit, expr* e1, expr* e2, bool add_to_eqs);
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void propagate_eq(dependency* dep, literal_vector const& lits, expr* e1, expr* e2, bool add_to_eqs);
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void propagate_eq(dependency* dep, literal_vector const& lits, expr* e1, expr* e2, bool add_to_eqs = true);
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void propagate_eq(dependency* dep, expr* e1, expr* e2, bool add_to_eqs = true);
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void propagate_eq(dependency* dep, literal lit, expr* e1, expr* e2, bool add_to_eqs = true);
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void set_conflict(dependency* dep, literal_vector const& lits = literal_vector());
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u_map<unsigned> m_branch_start;
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