mirror of
https://github.com/Z3Prover/z3
synced 2026-03-17 18:43:45 +00:00
889 lines
33 KiB
C++
889 lines
33 KiB
C++
/*++
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Copyright (c) 2026 Microsoft Corporation
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Module Name:
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theory_nseq.cpp
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Abstract:
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ZIPT string solver theory for Z3.
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Implementation of theory_nseq.
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Author:
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Clemens Eisenhofer 2026-03-01
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Nikolaj Bjorner (nbjorner) 2026-03-01
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--*/
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#include "smt/theory_nseq.h"
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#include "smt/smt_context.h"
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#include "smt/smt_justification.h"
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#include "util/statistics.h"
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#include "util/trail.h"
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namespace smt {
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theory_nseq::theory_nseq(context& ctx) :
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theory(ctx, ctx.get_manager().mk_family_id("seq")),
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m_seq(m),
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m_autil(m),
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m_rewriter(m),
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m_arith_value(m),
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m_egraph(m),
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m_sgraph(m, m_egraph),
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m_context_solver(m),
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m_nielsen(m_sgraph, m_context_solver),
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m_state(),
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m_regex(m_sgraph),
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m_model(m, m_seq, m_rewriter, m_sgraph)
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{}
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// -----------------------------------------------------------------------
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// Initialization
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// -----------------------------------------------------------------------
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void theory_nseq::init() {
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m_arith_value.init(&get_context());
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}
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// -----------------------------------------------------------------------
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// Internalization
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// -----------------------------------------------------------------------
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bool theory_nseq::internalize_atom(app* atom, bool /*gate_ctx*/) {
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// str.in_re atoms are boolean predicates: register as bool_var
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// so that assign_eh fires when the SAT solver assigns them.
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// Following theory_seq: create a bool_var directly without an enode
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// for the str.in_re predicate (avoids needing to internalize the regex arg).
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if (m_seq.str.is_in_re(atom)) {
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expr* str_arg = atom->get_arg(0);
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mk_var(ensure_enode(str_arg));
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if (!ctx.b_internalized(atom)) {
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bool_var bv = ctx.mk_bool_var(atom);
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ctx.set_var_theory(bv, get_id());
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ctx.mark_as_relevant(bv);
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}
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get_snode(str_arg);
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return true;
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}
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return internalize_term(atom);
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}
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theory_var theory_nseq::mk_var(enode* n) {
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expr* o = n->get_expr();
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if (!m_seq.is_seq(o) && !m_seq.is_re(o) && !m_seq.str.is_nth_u(o))
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return null_theory_var;
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if (is_attached_to_var(n))
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return n->get_th_var(get_id());
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theory_var v = theory::mk_var(n);
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get_context().attach_th_var(n, this, v);
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get_context().mark_as_relevant(n);
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return v;
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}
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bool theory_nseq::internalize_term(app* term) {
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// ensure ALL children are internalized (following theory_seq pattern)
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for (auto arg : *term) {
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mk_var(ensure_enode(arg));
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}
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if (ctx.e_internalized(term)) {
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mk_var(ctx.get_enode(term));
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return true;
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}
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if (m.is_bool(term)) {
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bool_var bv = ctx.mk_bool_var(term);
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ctx.set_var_theory(bv, get_id());
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ctx.mark_as_relevant(bv);
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}
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enode* en;
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if (ctx.e_internalized(term))
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en = ctx.get_enode(term);
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else
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en = ctx.mk_enode(term, false, m.is_bool(term), true);
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mk_var(en);
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// register in our private sgraph
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get_snode(term);
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// track higher-order terms for lazy unfolding
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expr* ho_f = nullptr, *ho_s = nullptr, *ho_b = nullptr, *ho_i = nullptr;
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if (m_seq.str.is_map(term, ho_f, ho_s) ||
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m_seq.str.is_mapi(term, ho_f, ho_i, ho_s) ||
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m_seq.str.is_foldl(term, ho_f, ho_b, ho_s) ||
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m_seq.str.is_foldli(term, ho_f, ho_i, ho_b, ho_s)) {
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ctx.push_trail(restore_vector(m_ho_terms));
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m_ho_terms.push_back(term);
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ensure_length_var(ho_s);
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}
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return true;
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}
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// -----------------------------------------------------------------------
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// Equality / disequality notifications
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// -----------------------------------------------------------------------
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void theory_nseq::new_eq_eh(theory_var v1, theory_var v2) {
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expr* e1 = get_enode(v1)->get_expr();
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expr* e2 = get_enode(v2)->get_expr();
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if (m_seq.is_re(e1)) {
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push_unhandled_pred();
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return;
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}
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if (!m_seq.is_seq(e1) || !m_seq.is_seq(e2))
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return;
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euf::snode* s1 = get_snode(e1);
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euf::snode* s2 = get_snode(e2);
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if (s1 && s2) {
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unsigned idx = m_state.str_eqs().size();
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m_state.add_str_eq(s1, s2, get_enode(v1), get_enode(v2));
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ctx.push_trail(restore_vector(m_prop_queue));
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m_prop_queue.push_back({prop_item::eq_prop, idx});
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}
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}
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void theory_nseq::new_diseq_eh(theory_var v1, theory_var v2) {
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expr* e1 = get_enode(v1)->get_expr();
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expr* e2 = get_enode(v2)->get_expr();
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if (m_seq.is_re(e1)) {
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// regex disequality: nseq cannot verify language non-equivalence
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push_unhandled_pred();
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return;
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}
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if (!m_seq.is_seq(e1) || !m_seq.is_seq(e2))
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return;
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unsigned idx = m_state.diseqs().size();
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m_state.add_diseq(get_enode(v1), get_enode(v2));
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ctx.push_trail(restore_vector(m_prop_queue));
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m_prop_queue.push_back({prop_item::diseq_prop, idx});
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}
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// -----------------------------------------------------------------------
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// Boolean assignment notification
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// -----------------------------------------------------------------------
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void theory_nseq::assign_eh(bool_var v, bool is_true) {
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expr* e = ctx.bool_var2expr(v);
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expr* s = nullptr;
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expr* re = nullptr;
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if (!m_seq.str.is_in_re(e, s, re)) {
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// Track unhandled boolean string predicates (prefixof, contains, etc.)
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if (is_app(e) && to_app(e)->get_family_id() == m_seq.get_family_id())
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push_unhandled_pred();
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return;
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}
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euf::snode* sn_str = get_snode(s);
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euf::snode* sn_re = get_snode(re);
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if (!sn_str || !sn_re)
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return;
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unsigned idx = m_state.str_mems().size();
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literal lit(v, !is_true);
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if (is_true) {
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m_state.add_str_mem(sn_str, sn_re, lit);
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}
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else {
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// ¬(str ∈ R) ≡ str ∈ complement(R): store as a positive membership
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// so the Nielsen graph sees it uniformly; the original negative literal
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// is kept in mem_source for conflict reporting.
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expr_ref re_compl(m_seq.re.mk_complement(re), m);
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euf::snode* sn_re_compl = get_snode(re_compl.get());
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m_state.add_str_mem(sn_str, sn_re_compl, lit);
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}
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ctx.push_trail(restore_vector(m_prop_queue));
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m_prop_queue.push_back({prop_item::pos_mem_prop, idx});
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TRACE(seq, tout << "nseq assign_eh: " << (is_true ? "" : "¬")
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<< "str.in_re "
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<< mk_bounded_pp(s, m, 3) << " in "
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<< mk_bounded_pp(re, m, 3) << "\n";);
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}
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// -----------------------------------------------------------------------
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// Scope management
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// -----------------------------------------------------------------------
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void theory_nseq::push_scope_eh() {
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theory::push_scope_eh();
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m_state.push();
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m_sgraph.push();
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}
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void theory_nseq::pop_scope_eh(unsigned num_scopes) {
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theory::pop_scope_eh(num_scopes);
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m_state.pop(num_scopes);
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m_sgraph.pop(num_scopes);
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}
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void theory_nseq::push_unhandled_pred() {
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ctx.push_trail(value_trail<unsigned>(m_num_unhandled_bool));
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++m_num_unhandled_bool;
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}
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// -----------------------------------------------------------------------
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// Propagation: eager eq/diseq/literal dispatch
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// -----------------------------------------------------------------------
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bool theory_nseq::can_propagate() {
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return m_prop_qhead < m_prop_queue.size();
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}
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void theory_nseq::propagate() {
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if (m_prop_qhead == m_prop_queue.size())
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return;
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ctx.push_trail(value_trail(m_prop_qhead));
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while (m_prop_qhead < m_prop_queue.size() && !ctx.inconsistent()) {
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auto [k, idx] = m_prop_queue[m_prop_qhead++];
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switch (k) {
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case prop_item::eq_prop:
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propagate_eq(idx);
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break;
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case prop_item::diseq_prop:
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propagate_diseq(idx);
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break;
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case prop_item::pos_mem_prop:
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propagate_pos_mem(idx);
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break;
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}
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}
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}
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void theory_nseq::propagate_eq(unsigned idx) {
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// When s1 = s2 is learned, ensure len(s1) and len(s2) are
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// internalized so congruence closure propagates len(s1) = len(s2).
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eq_source const& src = m_state.get_eq_source(idx);
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ensure_length_var(src.m_n1->get_expr());
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ensure_length_var(src.m_n2->get_expr());
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}
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void theory_nseq::propagate_diseq(unsigned idx) {
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// Disequalities are recorded for use during final_check.
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// No eager propagation beyond recording.
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TRACE(seq,
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auto const& d = m_state.get_diseq(idx);
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tout << "nseq diseq: "
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<< mk_bounded_pp(d.m_n1->get_expr(), m, 3)
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<< " != "
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<< mk_bounded_pp(d.m_n2->get_expr(), m, 3) << "\n";);
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}
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void theory_nseq::propagate_pos_mem(unsigned idx) {
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auto const& mem = m_state.str_mems()[idx];
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auto const& src = m_state.get_mem_source(idx);
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if (!mem.m_str || !mem.m_regex)
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return;
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// regex is ∅ → conflict
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if (m_regex.is_empty_regex(mem.m_regex)) {
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enode_pair_vector eqs;
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literal_vector lits;
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lits.push_back(src.m_lit);
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set_conflict(eqs, lits);
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return;
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}
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// empty string in non-nullable regex → conflict
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if (mem.m_str->is_empty() && !mem.m_regex->is_nullable()) {
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enode_pair_vector eqs;
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literal_vector lits;
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lits.push_back(src.m_lit);
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set_conflict(eqs, lits);
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return;
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}
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// ensure length term exists for the string argument
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expr* s_expr = mem.m_str->get_expr();
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if (s_expr)
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ensure_length_var(s_expr);
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}
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void theory_nseq::ensure_length_var(expr* e) {
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if (!e || !m_seq.is_seq(e))
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return;
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expr_ref len(m_seq.str.mk_length(e), m);
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if (!ctx.e_internalized(len))
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ctx.internalize(len, false);
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}
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// -----------------------------------------------------------------------
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// Final check: build Nielsen graph and search
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// -----------------------------------------------------------------------
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void theory_nseq::populate_nielsen_graph() {
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m_nielsen.reset();
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m_nielsen_to_state_mem.reset();
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// transfer string equalities from state to nielsen graph root
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for (auto const& eq : m_state.str_eqs()) {
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m_nielsen.add_str_eq(eq.m_lhs, eq.m_rhs);
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}
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// transfer regex memberships, pre-processing through seq_regex
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// to consume ground prefixes via Brzozowski derivatives
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for (unsigned state_idx = 0; state_idx < m_state.str_mems().size(); ++state_idx) {
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auto const& mem = m_state.str_mems()[state_idx];
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int triv = m_regex.check_trivial(mem);
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if (triv > 0)
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continue; // trivially satisfied, skip
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if (triv < 0) {
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// trivially unsat: add anyway so solve() detects conflict
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m_nielsen.add_str_mem(mem.m_str, mem.m_regex);
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m_nielsen_to_state_mem.push_back(state_idx);
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continue;
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}
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// pre-process: consume ground prefix characters
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vector<seq::str_mem> processed;
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if (!m_regex.process_str_mem(mem, processed)) {
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// conflict during ground prefix consumption
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m_nielsen.add_str_mem(mem.m_str, mem.m_regex);
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m_nielsen_to_state_mem.push_back(state_idx);
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continue;
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}
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for (auto const& pm : processed) {
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m_nielsen.add_str_mem(pm.m_str, pm.m_regex);
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m_nielsen_to_state_mem.push_back(state_idx);
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}
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}
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TRACE(seq, tout << "nseq populate: " << m_state.str_eqs().size() << " eqs, "
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<< m_state.str_mems().size() << " mems -> nielsen root with "
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<< m_nielsen.num_input_eqs() << " eqs, "
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<< m_nielsen.num_input_mems() << " mems\n";);
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}
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final_check_status theory_nseq::final_check_eh(unsigned /*final_check_round*/) {
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// Always assert non-negativity for all string theory vars,
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// even when there are no string equations/memberships.
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if (assert_nonneg_for_all_vars()) {
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IF_VERBOSE(1, verbose_stream() << "nseq final_check: nonneg assertions added, FC_CONTINUE\n";);
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return FC_CONTINUE;
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}
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if (m_state.empty() && m_ho_terms.empty() && !has_unhandled_preds()) {
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IF_VERBOSE(1, verbose_stream() << "nseq final_check: empty state+ho, FC_DONE (no solve)\n";);
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return FC_DONE;
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}
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// unfold higher-order terms when sequence structure is known
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if (unfold_ho_terms()) {
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IF_VERBOSE(1, verbose_stream() << "nseq final_check: unfolded ho_terms, FC_CONTINUE\n";);
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return FC_CONTINUE;
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}
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if (m_state.empty() && !has_unhandled_preds()) {
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IF_VERBOSE(1, verbose_stream() << "nseq final_check: empty state (after ho), FC_DONE (no solve)\n";);
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return FC_DONE;
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}
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IF_VERBOSE(1, verbose_stream() << "nseq final_check: populating graph with "
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<< m_state.str_eqs().size() << " eqs, " << m_state.str_mems().size() << " mems\n";);
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populate_nielsen_graph();
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// assert length constraints derived from string equalities
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if (assert_length_constraints()) {
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IF_VERBOSE(1, verbose_stream() << "nseq final_check: length constraints asserted, FC_CONTINUE\n";);
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return FC_CONTINUE;
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}
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++m_num_final_checks;
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m_nielsen.set_max_search_depth(get_fparams().m_nseq_max_depth);
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m_nielsen.set_max_nodes(get_fparams().m_nseq_max_nodes);
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m_nielsen.set_parikh_enabled(get_fparams().m_nseq_parikh);
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// Regex membership pre-check: before running DFS, check intersection
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// emptiness for each variable's regex constraints. This handles
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// regex-only problems that the DFS cannot efficiently solve.
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if (get_fparams().m_nseq_regex_precheck) {
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lbool precheck = check_regex_memberships_precheck();
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switch (precheck) {
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case l_true:
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// conflict was asserted inside check_regex_memberships_precheck
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IF_VERBOSE(1, verbose_stream() << "nseq final_check: regex precheck UNSAT\n";);
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return FC_CONTINUE;
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case l_false:
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// all regex constraints satisfiable, no word eqs/diseqs → SAT
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IF_VERBOSE(1, verbose_stream() << "nseq final_check: regex precheck SAT\n";);
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return FC_DONE;
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default:
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break;
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}
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}
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IF_VERBOSE(1, verbose_stream() << "nseq final_check: calling solve()\n";);
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// here the actual Nielsen solving happens
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auto result = m_nielsen.solve();
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#ifdef Z3DEBUG
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// Examining the Nielsen graph is probably the best way of debugging
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std::string dot = m_nielsen.to_dot();
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IF_VERBOSE(1, verbose_stream() << dot << "\n";);
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#endif
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if (result == seq::nielsen_graph::search_result::unsat) {
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IF_VERBOSE(1, verbose_stream() << "nseq final_check: solve UNSAT\n";);
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explain_nielsen_conflict();
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return FC_CONTINUE;
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}
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if (result == seq::nielsen_graph::search_result::sat) {
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IF_VERBOSE(1, verbose_stream() << "nseq final_check: solve SAT, sat_node="
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<< (m_nielsen.sat_node() ? "set" : "null") << "\n";);
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// Nielsen found a consistent assignment for positive constraints.
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// If there are disequalities we haven't verified, we cannot soundly declare sat.
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if (!m_state.diseqs().empty())
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return FC_GIVEUP;
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if (!has_unhandled_preds())
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return FC_DONE;
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}
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IF_VERBOSE(1, verbose_stream() << "nseq final_check: solve UNKNOWN, FC_GIVEUP\n";);
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return FC_GIVEUP;
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}
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// -----------------------------------------------------------------------
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// Conflict explanation
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// -----------------------------------------------------------------------
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void theory_nseq::deps_to_lits(seq::dep_tracker const& deps, enode_pair_vector& eqs, literal_vector& lits) {
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vector<seq::dep_source, false> vs;
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m_nielsen.dep_mgr().linearize(deps, vs);
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for (seq::dep_source const& d : vs) {
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if (std::holds_alternative<seq::dep_eq>(d)) {
|
|
eq_source const& src = m_state.get_eq_source(std::get<seq::dep_eq>(d).index);
|
|
if (src.m_n1->get_root() == src.m_n2->get_root())
|
|
eqs.push_back({src.m_n1, src.m_n2});
|
|
}
|
|
else {
|
|
unsigned idx = std::get<seq::dep_mem>(d).index;
|
|
if (idx < m_nielsen_to_state_mem.size()) {
|
|
unsigned state_mem_idx = m_nielsen_to_state_mem[idx];
|
|
mem_source const& src = m_state.get_mem_source(state_mem_idx);
|
|
SASSERT(ctx.get_assignment(src.m_lit) == l_true);
|
|
lits.push_back(src.m_lit);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void theory_nseq::add_conflict_clause(seq::dep_tracker const& deps) {
|
|
enode_pair_vector eqs;
|
|
literal_vector lits;
|
|
deps_to_lits(deps, eqs, lits);
|
|
++m_num_conflicts;
|
|
set_conflict(eqs, lits);
|
|
}
|
|
|
|
void theory_nseq::explain_nielsen_conflict() {
|
|
seq::dep_tracker deps = m_nielsen.dep_mgr().mk_empty();
|
|
m_nielsen.collect_conflict_deps(deps);
|
|
add_conflict_clause(deps);
|
|
}
|
|
|
|
void theory_nseq::set_conflict(enode_pair_vector const& eqs, literal_vector const& lits) {
|
|
TRACE(seq, tout << "nseq conflict: " << eqs.size() << " eqs, " << lits.size() << " lits\n";);
|
|
ctx.set_conflict(
|
|
ctx.mk_justification(
|
|
ext_theory_conflict_justification(
|
|
get_id(), ctx, lits.size(), lits.data(), eqs.size(), eqs.data(), 0, nullptr)));
|
|
}
|
|
|
|
// -----------------------------------------------------------------------
|
|
// Model generation
|
|
// -----------------------------------------------------------------------
|
|
|
|
void theory_nseq::init_model(model_generator& mg) {
|
|
m_model.init(mg, m_nielsen, m_state);
|
|
}
|
|
|
|
model_value_proc* theory_nseq::mk_value(enode* n, model_generator& mg) {
|
|
return m_model.mk_value(n, mg);
|
|
}
|
|
|
|
void theory_nseq::finalize_model(model_generator& mg) {
|
|
m_model.finalize(mg);
|
|
}
|
|
|
|
void theory_nseq::validate_model(proto_model& mdl) {
|
|
m_model.validate_regex(m_state, mdl);
|
|
}
|
|
|
|
// -----------------------------------------------------------------------
|
|
// Statistics / display
|
|
// -----------------------------------------------------------------------
|
|
|
|
void theory_nseq::collect_statistics(::statistics& st) const {
|
|
st.update("nseq conflicts", m_num_conflicts);
|
|
st.update("nseq final checks", m_num_final_checks);
|
|
st.update("nseq length axioms", m_num_length_axioms);
|
|
st.update("nseq ho unfolds", m_num_ho_unfolds);
|
|
m_nielsen.collect_statistics(st);
|
|
}
|
|
|
|
void theory_nseq::display(std::ostream& out) const {
|
|
out << "theory_nseq\n";
|
|
out << " str_eqs: " << m_state.str_eqs().size() << "\n";
|
|
out << " str_mems: " << m_state.str_mems().size() << "\n";
|
|
out << " diseqs: " << m_state.diseqs().size() << "\n";
|
|
out << " prop_queue: " << m_prop_qhead << "/" << m_prop_queue.size() << "\n";
|
|
out << " ho_terms: " << m_ho_terms.size() << "\n";
|
|
}
|
|
|
|
// -----------------------------------------------------------------------
|
|
// Factory / clone
|
|
// -----------------------------------------------------------------------
|
|
|
|
theory* theory_nseq::mk_fresh(context* ctx) {
|
|
return alloc(theory_nseq, *ctx);
|
|
}
|
|
|
|
// -----------------------------------------------------------------------
|
|
// Higher-order term unfolding (seq.map, seq.foldl, etc.)
|
|
// -----------------------------------------------------------------------
|
|
|
|
bool theory_nseq::unfold_ho_terms() {
|
|
if (m_ho_terms.empty())
|
|
return false;
|
|
|
|
bool progress = false;
|
|
|
|
for (app* term : m_ho_terms) {
|
|
expr* f = nullptr, *s = nullptr, *b = nullptr, *idx = nullptr;
|
|
|
|
if (!m_seq.str.is_map(term, f, s) &&
|
|
!m_seq.str.is_mapi(term, f, idx, s) &&
|
|
!m_seq.str.is_foldl(term, f, b, s) &&
|
|
!m_seq.str.is_foldli(term, f, idx, b, s))
|
|
continue;
|
|
|
|
if (!ctx.e_internalized(s))
|
|
continue;
|
|
|
|
// Find a structural representative in s's equivalence class
|
|
enode* s_root = ctx.get_enode(s)->get_root();
|
|
expr* repr = nullptr;
|
|
enode* curr = s_root;
|
|
do {
|
|
expr* e = curr->get_expr();
|
|
expr *a1, *a2;
|
|
if (m_seq.str.is_empty(e) ||
|
|
m_seq.str.is_unit(e, a1) ||
|
|
m_seq.str.is_concat(e, a1, a2)) {
|
|
repr = e;
|
|
break;
|
|
}
|
|
curr = curr->get_next();
|
|
} while (curr != s_root);
|
|
|
|
if (!repr)
|
|
continue;
|
|
|
|
// Build ho_term with structural seq arg, then rewrite
|
|
expr_ref ho_repr(m);
|
|
if (m_seq.str.is_map(term))
|
|
ho_repr = m_seq.str.mk_map(f, repr);
|
|
else if (m_seq.str.is_mapi(term))
|
|
ho_repr = m_seq.str.mk_mapi(f, idx, repr);
|
|
else if (m_seq.str.is_foldl(term))
|
|
ho_repr = m_seq.str.mk_foldl(f, b, repr);
|
|
else
|
|
ho_repr = m_seq.str.mk_foldli(f, idx, b, repr);
|
|
|
|
expr_ref rewritten(m);
|
|
br_status st = m_rewriter.mk_app_core(
|
|
to_app(ho_repr)->get_decl(),
|
|
to_app(ho_repr)->get_num_args(),
|
|
to_app(ho_repr)->get_args(),
|
|
rewritten);
|
|
|
|
if (st == BR_FAILED)
|
|
continue;
|
|
|
|
// Internalize both the structural ho_term and its rewrite
|
|
if (!ctx.e_internalized(ho_repr))
|
|
ctx.internalize(ho_repr, false);
|
|
if (!ctx.e_internalized(rewritten))
|
|
ctx.internalize(rewritten, false);
|
|
|
|
enode* ho_en = ctx.get_enode(ho_repr);
|
|
enode* res_en = ctx.get_enode(rewritten);
|
|
|
|
if (ho_en->get_root() == res_en->get_root())
|
|
continue;
|
|
|
|
// Assert tautological axiom: ho_repr = rewritten
|
|
// Congruence closure merges map(f,s) with map(f,repr)
|
|
// since s = repr in the E-graph.
|
|
expr_ref eq_expr(m.mk_eq(ho_repr, rewritten), m);
|
|
if (!ctx.b_internalized(eq_expr))
|
|
ctx.internalize(eq_expr, true);
|
|
literal eq_lit = ctx.get_literal(eq_expr);
|
|
if (ctx.get_assignment(eq_lit) != l_true) {
|
|
ctx.mk_th_axiom(get_id(), 1, &eq_lit);
|
|
TRACE(seq, tout << "nseq ho unfold: "
|
|
<< mk_bounded_pp(ho_repr, m, 3) << " = "
|
|
<< mk_bounded_pp(rewritten, m, 3) << "\n";);
|
|
++m_num_ho_unfolds;
|
|
progress = true;
|
|
}
|
|
}
|
|
|
|
// For map/mapi: propagate length preservation
|
|
for (app* term : m_ho_terms) {
|
|
expr* f = nullptr, *s = nullptr, *idx = nullptr;
|
|
bool is_map = m_seq.str.is_map(term, f, s);
|
|
bool is_mapi = !is_map && m_seq.str.is_mapi(term, f, idx, s);
|
|
if (!is_map && !is_mapi)
|
|
continue;
|
|
if (!m_seq.is_seq(term))
|
|
continue;
|
|
|
|
// len(map(f, s)) = len(s)
|
|
expr_ref len_map(m_seq.str.mk_length(term), m);
|
|
expr_ref len_s(m_seq.str.mk_length(s), m);
|
|
expr_ref len_eq(m.mk_eq(len_map, len_s), m);
|
|
if (!ctx.b_internalized(len_eq))
|
|
ctx.internalize(len_eq, true);
|
|
literal len_lit = ctx.get_literal(len_eq);
|
|
if (ctx.get_assignment(len_lit) != l_true) {
|
|
ctx.mk_th_axiom(get_id(), 1, &len_lit);
|
|
++m_num_length_axioms;
|
|
progress = true;
|
|
}
|
|
}
|
|
|
|
return progress;
|
|
}
|
|
|
|
// -----------------------------------------------------------------------
|
|
// Helpers
|
|
// -----------------------------------------------------------------------
|
|
|
|
euf::snode* theory_nseq::get_snode(expr* e) {
|
|
euf::snode* s = m_sgraph.find(e);
|
|
if (!s)
|
|
s = m_sgraph.mk(e);
|
|
return s;
|
|
}
|
|
|
|
// -----------------------------------------------------------------------
|
|
// Arithmetic value queries
|
|
// -----------------------------------------------------------------------
|
|
|
|
bool theory_nseq::get_num_value(expr* e, rational& val) const {
|
|
return m_arith_value.get_value_equiv(e, val) && val.is_int();
|
|
}
|
|
|
|
bool theory_nseq::lower_bound(expr* e, rational& lo) const {
|
|
bool is_strict = true;
|
|
return m_arith_value.get_lo(e, lo, is_strict) && !is_strict && lo.is_int();
|
|
}
|
|
|
|
bool theory_nseq::upper_bound(expr* e, rational& hi) const {
|
|
bool is_strict = true;
|
|
return m_arith_value.get_up(e, hi, is_strict) && !is_strict && hi.is_int();
|
|
}
|
|
|
|
bool theory_nseq::get_length(expr* e, rational& val) {
|
|
rational val1;
|
|
expr* e1 = nullptr;
|
|
expr* e2 = nullptr;
|
|
ptr_vector<expr> todo;
|
|
todo.push_back(e);
|
|
val.reset();
|
|
zstring s;
|
|
while (!todo.empty()) {
|
|
expr* c = todo.back();
|
|
todo.pop_back();
|
|
if (m_seq.str.is_concat(c, e1, e2)) {
|
|
todo.push_back(e1);
|
|
todo.push_back(e2);
|
|
}
|
|
else if (m_seq.str.is_unit(c))
|
|
val += rational(1);
|
|
else if (m_seq.str.is_empty(c))
|
|
continue;
|
|
else if (m_seq.str.is_string(c, s))
|
|
val += rational(s.length());
|
|
else {
|
|
expr_ref len(m_seq.str.mk_length(c), m);
|
|
if (m_arith_value.get_value(len, val1) && !val1.is_neg())
|
|
val += val1;
|
|
else
|
|
return false;
|
|
}
|
|
}
|
|
return val.is_int();
|
|
}
|
|
|
|
void theory_nseq::add_length_axiom(literal lit) {
|
|
ctx.mark_as_relevant(lit);
|
|
ctx.mk_th_axiom(get_id(), 1, &lit);
|
|
++m_num_length_axioms;
|
|
}
|
|
|
|
bool theory_nseq::propagate_length_lemma(literal lit, seq::length_constraint const& lc) {
|
|
// unconditional constraints: assert as theory axiom
|
|
if (lc.m_kind == seq::length_kind::nonneg) {
|
|
add_length_axiom(lit);
|
|
return true;
|
|
}
|
|
|
|
// conditional constraints: propagate with justification from dep_tracker
|
|
enode_pair_vector eqs;
|
|
literal_vector lits;
|
|
deps_to_lits(lc.m_dep, eqs, lits);
|
|
|
|
ctx.mark_as_relevant(lit);
|
|
justification* js = ctx.mk_justification(
|
|
ext_theory_propagation_justification(
|
|
get_id(), ctx,
|
|
lits.size(), lits.data(),
|
|
eqs.size(), eqs.data(),
|
|
lit));
|
|
ctx.assign(lit, js);
|
|
|
|
TRACE(seq, tout << "nseq length propagation: " << mk_pp(lc.m_expr, m)
|
|
<< " (" << eqs.size() << " eqs, " << lits.size() << " lits)\n";);
|
|
++m_num_length_axioms;
|
|
return true;
|
|
}
|
|
|
|
bool theory_nseq::assert_nonneg_for_all_vars() {
|
|
arith_util arith(m);
|
|
bool new_axiom = false;
|
|
unsigned nv = get_num_vars();
|
|
for (unsigned v = 0; v < nv; ++v) {
|
|
expr* e = get_enode(v)->get_expr();
|
|
if (!m_seq.is_seq(e))
|
|
continue;
|
|
expr_ref len_var(m_seq.str.mk_length(e), m);
|
|
expr_ref ge_zero(arith.mk_ge(len_var, arith.mk_int(0)), m);
|
|
if (!ctx.b_internalized(ge_zero))
|
|
ctx.internalize(ge_zero, true);
|
|
literal lit = ctx.get_literal(ge_zero);
|
|
if (ctx.get_assignment(lit) != l_true) {
|
|
add_length_axiom(lit);
|
|
new_axiom = true;
|
|
}
|
|
}
|
|
return new_axiom;
|
|
}
|
|
|
|
bool theory_nseq::assert_length_constraints() {
|
|
vector<seq::length_constraint> constraints;
|
|
m_nielsen.generate_length_constraints(constraints);
|
|
|
|
bool new_axiom = false;
|
|
for (auto const& lc : constraints) {
|
|
expr* e = lc.m_expr;
|
|
if (!ctx.b_internalized(e))
|
|
ctx.internalize(e, true);
|
|
literal lit = ctx.get_literal(e);
|
|
if (ctx.get_assignment(lit) != l_true) {
|
|
TRACE(seq, tout << "nseq length lemma: " << mk_pp(e, m) << "\n";);
|
|
propagate_length_lemma(lit, lc);
|
|
new_axiom = true;
|
|
}
|
|
}
|
|
return new_axiom;
|
|
}
|
|
|
|
// -----------------------------------------------------------------------
|
|
// Regex membership pre-check
|
|
// For each variable with regex membership constraints, check intersection
|
|
// emptiness before DFS. Mirrors ZIPT's per-variable regex evaluation.
|
|
//
|
|
// Returns:
|
|
// l_true — conflict asserted (empty intersection for some variable)
|
|
// l_false — all variables satisfiable and no word eqs/diseqs → SAT
|
|
// l_undef — inconclusive, proceed to DFS
|
|
// -----------------------------------------------------------------------
|
|
|
|
lbool theory_nseq::check_regex_memberships_precheck() {
|
|
auto const& mems = m_state.str_mems();
|
|
if (mems.empty())
|
|
return l_undef;
|
|
|
|
// Group membership indices by variable snode id.
|
|
// Only consider memberships whose string snode is a plain variable (s_var).
|
|
u_map<unsigned_vector> var_to_mems;
|
|
bool all_var_str = true;
|
|
|
|
for (unsigned i = 0; i < mems.size(); ++i) {
|
|
auto const& mem = mems[i];
|
|
if (!mem.m_str || !mem.m_regex)
|
|
continue;
|
|
if (mem.m_str->is_var()) {
|
|
auto& vec = var_to_mems.insert_if_not_there(mem.m_str->id(), unsigned_vector());
|
|
vec.push_back(i);
|
|
}
|
|
else
|
|
all_var_str = false;
|
|
}
|
|
|
|
if (var_to_mems.empty())
|
|
return l_undef;
|
|
|
|
bool any_undef = false;
|
|
|
|
// Check intersection emptiness for each variable.
|
|
for (auto& kv : var_to_mems) {
|
|
unsigned var_id = kv.m_key;
|
|
unsigned_vector const& mem_indices = kv.m_value;
|
|
ptr_vector<euf::snode> regexes;
|
|
for (unsigned i : mem_indices) {
|
|
euf::snode* re = mems[i].m_regex;
|
|
if (re)
|
|
regexes.push_back(re);
|
|
}
|
|
if (regexes.empty())
|
|
continue;
|
|
|
|
// Use a bounded BFS (50 states) for the pre-check to keep it fast.
|
|
// If the BFS times out (l_undef), we fall through to DFS.
|
|
lbool result = m_regex.check_intersection_emptiness(regexes, 50);
|
|
|
|
if (result == l_true) {
|
|
// Intersection is empty → the memberships on this variable are
|
|
// jointly unsatisfiable. Assert a conflict from all their literals.
|
|
enode_pair_vector eqs;
|
|
literal_vector lits;
|
|
for (unsigned i : mem_indices) {
|
|
mem_source const& src = m_state.get_mem_source(i);
|
|
SASSERT(ctx.get_assignment(src.m_lit) == l_true); // we already stored the polarity of the literal
|
|
lits.push_back(src.m_lit);
|
|
}
|
|
TRACE(seq, tout << "nseq regex precheck: empty intersection for var "
|
|
<< var_id << ", conflict with " << lits.size() << " lits\n";);
|
|
set_conflict(eqs, lits);
|
|
return l_true; // conflict asserted
|
|
}
|
|
if (result == l_undef)
|
|
any_undef = true;
|
|
// l_false = non-empty intersection, this variable's constraints are satisfiable
|
|
}
|
|
|
|
if (any_undef)
|
|
return l_undef; // cannot fully determine; let DFS decide
|
|
|
|
// All variables' regex intersections are non-empty.
|
|
// If there are no word equations and no disequalities, variables are
|
|
// independent and each can be assigned a witness string → SAT.
|
|
if (all_var_str && m_state.str_eqs().empty() && m_state.diseqs().empty() && !has_unhandled_preds()) {
|
|
TRACE(seq, tout << "nseq regex precheck: all intersections non-empty, "
|
|
<< "no word eqs/diseqs → SAT\n";);
|
|
return l_false; // signals SAT (non-empty / satisfiable)
|
|
}
|
|
|
|
return l_undef; // mixed constraints; let DFS decide
|
|
}
|
|
|
|
}
|