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https://github.com/Z3Prover/z3
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add some notes to regex
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
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@ -10,8 +10,8 @@ Abstract:
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Cube finder
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Author:
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Nikolaj Bjorner (nbjorner)
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Lev Nachmanson (levnach)
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Nikolaj Bjorner (nbjorner)
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Revision History:
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--*/
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@ -41,7 +41,7 @@ namespace lp {
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lp_status st = lra.find_feasible_solution();
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if (st != lp_status::FEASIBLE && st != lp_status::OPTIMAL) {
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TRACE("cube", tout << "cannot find a feasiblie solution";);
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TRACE("cube", tout << "cannot find a feasible solution";);
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lra.pop();
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lra.move_non_basic_columns_to_bounds();
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// it can happen that we found an integer solution here
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@ -34,7 +34,6 @@ namespace smt {
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arith_util& seq_regex::a() { return th.m_autil; }
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void seq_regex::rewrite(expr_ref& e) { th.m_rewrite(e); }
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bool seq_regex::propagate() {
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bool change = false;
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for (unsigned i = 0; !ctx.inconsistent() && i < m_to_propagate.size(); ++i) {
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@ -46,6 +45,23 @@ namespace smt {
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return change;
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}
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/**
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* is_string_equality holds of str.in_re s R, if R is of the form .* ++ x ++ .* ++ y ++ .* ++
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* s = fresh1 ++ x ++ fresh2 ++ y ++ fresh3
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*
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* example rewrite:
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* (str.in_re s .* ++ R) => s = x ++ y and (str.in_re y R)
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*
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* is_string_equality is currently placed under propagate_accept.
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* this allows extracting string equalities after processing regexes that are not
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* simple unions of simple concatentations. Though, it may produce different equations for
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* alternate values of the unfolding index.
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*/
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bool seq_regex::is_string_equality(literal lit) {
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return false;
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}
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/**
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* Propagate the atom (str.in.re s r)
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*
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@ -76,8 +92,12 @@ namespace smt {
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if (coallesce_in_re(lit))
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return;
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//
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// TBD s in R => R != {}
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// non-emptiness enforcement could instead of here,
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// be added to propagate_accept after some threshold is met.
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//
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if (false) {
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expr_ref is_empty(m.mk_eq(r, re().mk_empty(m.get_sort(s))), m);
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rewrite(is_empty);
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@ -135,7 +155,7 @@ namespace smt {
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* (accept s i r[if(c,r1,r2)]) & c => (accept s i r[r1])
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* (accept s i r[if(c,r1,r2)]) & ~c => (accept s i r[r2])
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* (accept s i r) & len(s) <= i => nullable(r)
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* (accept s r) & len(s) > i => (accept s (+ i 1) D(nth(s,i), r))
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* (accept s i r) & len(s) > i => (accept s (+ i 1) D(nth(s,i), r))
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*/
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bool seq_regex::propagate(literal lit) {
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@ -143,15 +163,15 @@ namespace smt {
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expr* s = nullptr, *i = nullptr, *r = nullptr;
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expr* e = ctx.bool_var2expr(lit.var());
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VERIFY(sk().is_accept(e, s, i, r));
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unsigned idx = 0;
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rational n;
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VERIFY(a().is_numeral(i, n));
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SASSERT(n.is_unsigned());
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idx = n.get_unsigned();
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VERIFY(sk().is_accept(e, s, i, idx, r));
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expr_ref is_nullable(m), d(r, m);
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TRACE("seq", tout << "propagate " << mk_pp(e, m) << "\n";);
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if (is_string_equality(lit))
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return true;
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if (block_unfolding(lit, idx))
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return true;
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@ -161,62 +181,46 @@ namespace smt {
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case l_undef:
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ctx.mark_as_relevant(len_s_le_i);
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return false;
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case l_true: {
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expr_ref is_nullable = seq_rw().is_nullable(r);
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case l_true:
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is_nullable = seq_rw().is_nullable(r);
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rewrite(is_nullable);
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th.add_axiom(~lit, ~len_s_le_i, th.mk_literal(is_nullable));
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return true;
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}
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case l_false:
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break;
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}
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expr_ref head(m), d(r, m), i_next(m);
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literal_vector conds;
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if (!unfold_cofactors(d, conds))
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return false;
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// s in R & len(s) > i => tail(s,i) in D(nth(s, i), R)
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head = th.mk_nth(s, i);
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i_next = a().mk_int(idx + 1);
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// (accept s i R) & len(s) > i => (accept s (+ i 1) D(nth(s, i), R)) or conds
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expr_ref head = th.mk_nth(s, i);
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d = seq_rw().derivative(head, d);
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if (!d)
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throw default_exception("unable to expand derivative");
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literal acc_next = th.mk_literal(sk().mk_accept(s, i_next, d));
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if (conds.empty()) {
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th.add_axiom(~lit, len_s_le_i, acc_next);
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}
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else {
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conds.push_back(~lit);
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conds.push_back(len_s_le_i);
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conds.push_back(acc_next);
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for (literal c : conds)
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ctx.mark_as_relevant(c);
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ctx.mk_th_axiom(th.get_id(), conds.size(), conds.c_ptr());
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}
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TRACE("seq", tout << "head " << head << "\n";
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tout << mk_pp(r, m) << "\n";);
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literal acc_next = th.mk_literal(sk().mk_accept(s, a().mk_int(idx + 1), d));
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conds.push_back(~lit);
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conds.push_back(len_s_le_i);
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conds.push_back(acc_next);
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th.add_axiom(conds);
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TRACE("seq", tout << "unfold " << head << "\n" << mk_pp(r, m) << "\n";);
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return true;
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}
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/**
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* Put a limit to the unfolding of s.
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*/
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bool seq_regex::block_unfolding(literal lit, unsigned i) {
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expr* s = nullptr, *idx = nullptr, *r = nullptr;
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expr* e = ctx.bool_var2expr(lit.var());
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VERIFY(sk().is_accept(e, s, idx, r));
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if (i > th.m_max_unfolding_depth &&
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return
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i > th.m_max_unfolding_depth &&
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th.m_max_unfolding_lit != null_literal &&
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ctx.get_assignment(th.m_max_unfolding_lit) == l_true &&
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!ctx.at_base_level()) {
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th.propagate_lit(nullptr, 1, &lit, ~th.m_max_unfolding_lit);
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return true;
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}
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return false;
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!ctx.at_base_level() &&
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(th.propagate_lit(nullptr, 1, &lit, ~th.m_max_unfolding_lit),
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true);
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}
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/**
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@ -263,7 +267,6 @@ namespace smt {
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return true;
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}
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void seq_regex::propagate_eq(expr* r1, expr* r2) {
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// the dual version of unroll_non_empty, but
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// skolem functions have to be eliminated or turned into
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@ -317,7 +320,14 @@ namespace smt {
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VERIFY(u().is_re(r, seq_sort));
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VERIFY(u().is_seq(seq_sort, elem_sort));
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return expr_ref(m.mk_fresh_const("re.first", elem_sort), m);
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// return sk().mk("re.first", r, elem_sort);
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// return sk().mk("re.first", r, elem_sort);
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// - for this to be effective, requires internalizer to skip skolem function internalization,
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// because of the regex argument r and we don't handle extensionality of regex well.
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// It is probably a good idea to skip internalization of all skolem expressions,
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// but requires some changes to theory_seq.
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// - it is more useful to eliminate quantifiers in he common case, so never have to
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// work with fresh expressions in the fist hand. This is possible for characters and
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// ranges (just equalities and inequalities with constant bounds).
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}
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expr_ref seq_regex::unroll_non_empty(expr* r, expr_mark& seen, unsigned depth) {
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@ -49,6 +49,8 @@ namespace smt {
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seq_skolem& sk();
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arith_util& a();
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bool is_string_equality(literal lit);
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void rewrite(expr_ref& e);
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bool coallesce_in_re(literal lit);
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void propagate_in_re(literal lit);
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// (accept s i r) means
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// the suffix of s after the first i characters is a member of r
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void propagate_accept(literal lit);
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void propagate_eq(expr* r1, expr* r2);
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@ -101,10 +101,11 @@ namespace smt {
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r = to_app(a)->get_arg(2), n = to_app(a)->get_arg(3),
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true);
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}
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bool is_accept(expr* a, expr*& s, expr*& i, expr*& r) const {
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return is_accept(a) && to_app(a)->get_num_args() == 3 &&
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(s = to_app(a)->get_arg(0), i = to_app(a)->get_arg(1),
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r = to_app(a)->get_arg(2), true);
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bool is_accept(expr* e, expr*& s, expr*& i, unsigned& idx, expr*& r) const {
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return is_accept(e) && to_app(e)->get_num_args() == 3 &&
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(s = to_app(e)->get_arg(0), i = to_app(e)->get_arg(1),
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r = to_app(e)->get_arg(2), true) &&
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a.is_unsigned(i, idx);
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}
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bool is_post(expr* e, expr*& s, expr*& start);
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bool is_pre(expr* e, expr*& s, expr*& i);
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@ -2917,14 +2917,21 @@ literal theory_seq::mk_eq_empty(expr* _e, bool phase) {
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void theory_seq::add_axiom(literal l1, literal l2, literal l3, literal l4, literal l5) {
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literal_vector lits;
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if (l1 == true_literal || l2 == true_literal || l3 == true_literal || l4 == true_literal || l5 == true_literal) return;
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if (l1 != null_literal && l1 != false_literal) { ctx.mark_as_relevant(l1); lits.push_back(l1); }
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if (l2 != null_literal && l2 != false_literal) { ctx.mark_as_relevant(l2); lits.push_back(l2); }
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if (l3 != null_literal && l3 != false_literal) { ctx.mark_as_relevant(l3); lits.push_back(l3); }
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if (l4 != null_literal && l4 != false_literal) { ctx.mark_as_relevant(l4); lits.push_back(l4); }
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if (l5 != null_literal && l5 != false_literal) { ctx.mark_as_relevant(l5); lits.push_back(l5); }
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if (l1 == true_literal || l2 == true_literal || l3 == true_literal ||
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l4 == true_literal || l5 == true_literal) return;
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if (l1 != null_literal && l1 != false_literal) lits.push_back(l1);
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if (l2 != null_literal && l2 != false_literal) lits.push_back(l2);
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if (l3 != null_literal && l3 != false_literal) lits.push_back(l3);
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if (l4 != null_literal && l4 != false_literal) lits.push_back(l4);
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if (l5 != null_literal && l5 != false_literal) lits.push_back(l5);
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add_axiom(lits);
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}
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void theory_seq::add_axiom(literal_vector & lits) {
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TRACE("seq", ctx.display_literals_verbose(tout << "assert:", lits) << "\n";);
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for (literal lit : lits)
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ctx.mark_as_relevant(lit);
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IF_VERBOSE(10, verbose_stream() << "ax ";
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for (literal l : lits) ctx.display_literal_smt2(verbose_stream() << " ", l);
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verbose_stream() << "\n");
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@ -617,6 +617,7 @@ namespace smt {
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void enque_axiom(expr* e);
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void deque_axiom(expr* e);
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void add_axiom(literal l1, literal l2 = null_literal, literal l3 = null_literal, literal l4 = null_literal, literal l5 = null_literal);
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void add_axiom(literal_vector& lits);
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bool has_length(expr *e) const { return m_has_length.contains(e); }
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void add_length(expr* e, expr* l);
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