mirror of
https://github.com/Z3Prover/z3
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1228 lines
37 KiB
C++
1228 lines
37 KiB
C++
/*++
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Copyright (c) 2015 Microsoft Corporation
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Module Name:
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theory_seq.h
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Abstract:
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Native theory solver for sequences.
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Author:
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Nikolaj Bjorner (nbjorner) 2015-6-12
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Revision History:
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--*/
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#include "value_factory.h"
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#include "smt_context.h"
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#include "smt_model_generator.h"
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#include "theory_seq.h"
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#include "seq_rewriter.h"
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#include "ast_trail.h"
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using namespace smt;
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void theory_seq::solution_map::update(expr* e, expr* r, enode_pair_dependency* d) {
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m_cache.reset();
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std::pair<expr*, enode_pair_dependency*> value;
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if (m_map.find(e, value)) {
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add_trail(DEL, e, value.first, value.second);
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}
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value.first = r;
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value.second = d;
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m_map.insert(e, value);
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add_trail(INS, e, r, d);
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}
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void theory_seq::solution_map::add_trail(map_update op, expr* l, expr* r, enode_pair_dependency* d) {
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m_updates.push_back(op);
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m_lhs.push_back(l);
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m_rhs.push_back(r);
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m_deps.push_back(d);
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}
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expr* theory_seq::solution_map::find(expr* e, enode_pair_dependency*& d) {
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std::pair<expr*, enode_pair_dependency*> value;
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d = 0;
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expr* result = e;
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while (m_map.find(result, value)) {
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d = m_dm.mk_join(d, value.second);
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result = value.first;
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}
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return result;
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}
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void theory_seq::solution_map::pop_scope(unsigned num_scopes) {
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if (num_scopes == 0) return;
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m_cache.reset();
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unsigned start = m_limit[m_limit.size() - num_scopes];
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for (unsigned i = m_updates.size(); i > start; ) {
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--i;
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if (m_updates[i] == INS) {
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m_map.remove(m_lhs[i].get());
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}
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else {
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m_map.insert(m_lhs[i].get(), std::make_pair(m_rhs[i].get(), m_deps[i]));
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}
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}
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m_updates.resize(start);
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m_lhs.resize(start);
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m_rhs.resize(start);
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m_deps.resize(start);
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m_limit.resize(m_limit.size() - num_scopes);
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}
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void theory_seq::solution_map::display(std::ostream& out) const {
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eqdep_map_t::iterator it = m_map.begin(), end = m_map.end();
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for (; it != end; ++it) {
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out << mk_pp(it->m_key, m) << " |-> " << mk_pp(it->m_value.first, m) << "\n";
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}
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}
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bool theory_seq::exclusion_table::contains(expr* e, expr* r) const {
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if (e->get_id() > r->get_id()) {
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std::swap(e, r);
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}
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return m_table.contains(std::make_pair(e, r));
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}
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void theory_seq::exclusion_table::update(expr* e, expr* r) {
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if (e->get_id() > r->get_id()) {
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std::swap(e, r);
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}
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if (e != r && !m_table.contains(std::make_pair(e, r))) {
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m_lhs.push_back(e);
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m_rhs.push_back(r);
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m_table.insert(std::make_pair(e, r));
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}
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}
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void theory_seq::exclusion_table::pop_scope(unsigned num_scopes) {
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if (num_scopes == 0) return;
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unsigned start = m_limit[m_limit.size() - num_scopes];
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for (unsigned i = start; i < m_lhs.size(); ++i) {
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m_table.erase(std::make_pair(m_lhs[i].get(), m_rhs[i].get()));
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}
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m_lhs.resize(start);
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m_rhs.resize(start);
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m_limit.resize(m_limit.size() - num_scopes);
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}
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void theory_seq::exclusion_table::display(std::ostream& out) const {
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table_t::iterator it = m_table.begin(), end = m_table.end();
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for (; it != end; ++it) {
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out << mk_pp(it->first, m) << " != " << mk_pp(it->second, m) << "\n";
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}
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}
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theory_seq::theory_seq(ast_manager& m):
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theory(m.mk_family_id("seq")),
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m(m),
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m_rep(m, m_dm),
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m_factory(0),
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m_ineqs(m),
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m_exclude(m),
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m_axioms(m),
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m_axioms_head(0),
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m_branch_variable_head(0),
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m_incomplete(false),
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m_has_length(false),
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m_model_completion(false),
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m_rewrite(m),
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m_util(m),
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m_autil(m),
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m_trail_stack(*this) {
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m_prefix_sym = "seq.prefix.suffix";
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m_suffix_sym = "seq.suffix.prefix";
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m_left_sym = "seq.left";
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m_right_sym = "seq.right";
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m_contains_left_sym = "seq.contains.left";
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m_contains_right_sym = "seq.contains.right";
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}
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theory_seq::~theory_seq() {
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}
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final_check_status theory_seq::final_check_eh() {
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context & ctx = get_context();
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TRACE("seq", display(tout););
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if (!check_ineqs()) {
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return FC_CONTINUE;
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}
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if (simplify_and_solve_eqs()) {
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return FC_CONTINUE;
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}
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if (ctx.inconsistent()) {
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return FC_CONTINUE;
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}
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if (branch_variable()) {
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TRACE("seq", tout << "branch\n";);
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return FC_CONTINUE;
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}
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if (split_variable()) {
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TRACE("seq", tout << "split_variable\n";);
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return FC_CONTINUE;
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}
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if (ctx.inconsistent()) {
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return FC_CONTINUE;
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}
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if (!check_length_coherence()) {
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TRACE("seq", tout << "check_length_coherence\n";);
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return FC_CONTINUE;
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}
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if (!check_length_coherence_tbd()) {
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TRACE("seq", tout << "check_length_coherence\n";);
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return FC_GIVEUP;
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}
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if (is_solved()) {
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TRACE("seq", tout << "is_solved\n";);
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return FC_DONE;
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}
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return FC_GIVEUP;
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}
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bool theory_seq::check_ineqs() {
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context & ctx = get_context();
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for (unsigned i = 0; i < m_ineqs.size(); ++i) {
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expr* a = m_ineqs[i].get();
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enode_pair_dependency* eqs = 0;
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expr_ref b = canonize(a, eqs);
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if (m.is_true(b)) {
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TRACE("seq", tout << "Evaluates to false: " << mk_pp(a,m) << "\n";);
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ctx.internalize(a, false);
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propagate_lit(eqs, ctx.get_literal(a));
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return false;
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}
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else if (!m.is_false(b)) {
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TRACE("seq", tout << "Disequality is undetermined: " << mk_pp(a, m) << " " << b << "\n";);
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}
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}
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return true;
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}
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bool theory_seq::branch_variable() {
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context& ctx = get_context();
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unsigned sz = m_eqs.size();
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ptr_vector<expr> ls, rs;
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for (unsigned i = 0; i < sz; ++i) {
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unsigned k = (i + m_branch_variable_head) % sz;
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eq e = m_eqs[k];
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TRACE("seq", tout << e.m_lhs << " = " << e.m_rhs << "\n";);
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ls.reset(); rs.reset();
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m_util.str.get_concat(e.m_lhs, ls);
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m_util.str.get_concat(e.m_rhs, rs);
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if (!ls.empty() && find_branch_candidate(ls[0], rs)) {
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m_branch_variable_head = k;
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return true;
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}
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if (!rs.empty() && find_branch_candidate(rs[0], ls)) {
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m_branch_variable_head = k;
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return true;
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}
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}
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return false;
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}
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bool theory_seq::find_branch_candidate(expr* l, ptr_vector<expr> const& rs) {
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TRACE("seq", tout << mk_pp(l, m) << " "
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<< (is_var(l)?"var":"not var") << "\n";);
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if (!is_var(l)) {
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return false;
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}
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expr_ref v0(m), v(m);
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v0 = m_util.str.mk_empty(m.get_sort(l));
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if (assume_equality(l, v0)) {
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return true;
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}
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for (unsigned j = 0; j < rs.size(); ++j) {
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if (occurs(l, rs[j])) {
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return false;
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}
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zstring s;
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if (m_util.str.is_string(rs[j], s)) {
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for (size_t k = 1; k < s.length(); ++k) {
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v = m_util.str.mk_string(s.extract(0, k));
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if (v0) v = m_util.str.mk_concat(v0, v);
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if (assume_equality(l, v)) {
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return true;
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}
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}
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}
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v0 = (j == 0)? rs[0] : m_util.str.mk_concat(v0, rs[j]);
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if (assume_equality(l, v0)) {
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return true;
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}
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}
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return false;
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}
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bool theory_seq::assume_equality(expr* l, expr* r) {
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context& ctx = get_context();
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if (m_exclude.contains(l, r)) {
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return false;
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}
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else {
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TRACE("seq", tout << mk_pp(l, m) << " = " << mk_pp(r, m) << "\n";);
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enode* n1 = ensure_enode(l);
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enode* n2 = ensure_enode(r);
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ctx.mark_as_relevant(n1);
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ctx.mark_as_relevant(n2);
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ctx.assume_eq(n1, n2);
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return true;
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}
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}
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bool theory_seq::split_variable() {
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return false;
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}
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bool theory_seq::check_length_coherence() {
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if (!m_has_length) return true;
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context& ctx = get_context();
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bool coherent = true;
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for (unsigned i = 0; i < m_eqs.size(); ++i) {
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m_eqs[i].m_dep;
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expr_ref v1(m), v2(m), l(m_eqs[i].m_lhs), r(m_eqs[i].m_rhs);
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expr_ref len1(m_util.str.mk_length(l), m);
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expr_ref len2(m_util.str.mk_length(r), m);
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enode* n1 = ensure_enode(len1);
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enode* n2 = ensure_enode(len2);
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if (n1->get_root() != n2->get_root()) {
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TRACE("seq", tout << len1 << " = " << len2 << "\n";);
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propagate_eq(m_eqs[i].m_dep, n1, n2);
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coherent = false;
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}
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}
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return coherent;
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}
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bool theory_seq::check_length_coherence_tbd() {
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if (!m_has_length) return true;
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context& ctx = get_context();
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bool coherent = true;
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// each variable that canonizes to itself can have length 0.
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unsigned sz = get_num_vars();
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for (unsigned i = 0; i < sz; ++i) {
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enode* n = get_enode(i);
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expr* e = n->get_owner();
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if (m_util.is_re(e)) {
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continue;
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}
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SASSERT(m_util.is_seq(e));
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// extend length of variables.
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enode_pair_dependency* dep = 0;
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expr* f = m_rep.find(e, dep);
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if (is_var(f) && f == e) {
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expr_ref emp(m_util.str.mk_empty(m.get_sort(e)), m);
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TRACE("seq", tout << "Unsolved " << mk_pp(e, m) << "\n";);
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#if 0
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if (!assume_equality(e, emp)) {
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// e = emp \/ e = head*tail & head = unit(v)
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sort* char_sort = 0;
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VERIFY(m_util.is_seq(m.get_sort(e), char_sort));
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expr_ref tail(mk_skolem(symbol("seq.tail"), e), m);
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expr_ref v(mk_skolem(symbol("seq.head.elem"), e, 0, 0, char_sort), m);
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expr_ref head(m_util.str.mk_unit(v), m);
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expr_ref conc(m_util.str.mk_concat(head, tail), m);
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literal e_eq_emp(mk_eq(e, emp, false));
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add_axiom(e_eq_emp, mk_eq(e, conc, false));
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}
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#endif
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coherent = false;
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}
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}
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return coherent;
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}
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bool theory_seq::check_ineq_coherence() {
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bool all_false = true;
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for (unsigned i = 0; all_false && i < m_ineqs.size(); ++i) {
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expr* a = m_ineqs[i].get();
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enode_pair_dependency* eqs = 0;
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expr_ref b = canonize(a, eqs);
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all_false = m.is_false(b);
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if (all_false) {
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TRACE("seq", tout << "equality is undetermined: " << mk_pp(a, m) << " " << b << "\n";);
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}
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}
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return all_false;
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}
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/*
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- Eqs = 0
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- Diseqs evaluate to false
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- lengths are coherent.
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*/
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bool theory_seq::is_solved() {
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if (!m_eqs.empty()) {
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return false;
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}
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if (!check_ineq_coherence()) {
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return false;
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}
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SASSERT(check_length_coherence());
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return true;
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}
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void theory_seq::propagate_lit(enode_pair_dependency* dep, literal lit) {
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context& ctx = get_context();
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ctx.mark_as_relevant(lit);
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vector<enode_pair, false> _eqs;
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m_dm.linearize(dep, _eqs);
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TRACE("seq", ctx.display_detailed_literal(tout, lit);
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tout << " <- "; display_deps(tout, dep););
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justification* js =
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ctx.mk_justification(
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ext_theory_propagation_justification(
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get_id(), ctx.get_region(), 0, 0, _eqs.size(), _eqs.c_ptr(), lit));
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ctx.assign(lit, js);
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}
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void theory_seq::set_conflict(enode_pair_dependency* dep) {
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context& ctx = get_context();
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vector<enode_pair, false> _eqs;
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m_dm.linearize(dep, _eqs);
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TRACE("seq", display_deps(tout, dep););
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ctx.set_conflict(
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ctx.mk_justification(
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ext_theory_conflict_justification(
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get_id(), ctx.get_region(), 0, 0, _eqs.size(), _eqs.c_ptr(), 0, 0)));
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}
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void theory_seq::propagate_eq(enode_pair_dependency* dep, enode* n1, enode* n2) {
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context& ctx = get_context();
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vector<enode_pair, false> _eqs;
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m_dm.linearize(dep, _eqs);
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TRACE("seq",
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tout << mk_pp(n1->get_owner(), m) << " = " << mk_pp(n2->get_owner(), m) << " <- ";
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display_deps(tout, dep);
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);
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justification* js = ctx.mk_justification(
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ext_theory_eq_propagation_justification(
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get_id(), ctx.get_region(), 0, 0, _eqs.size(), _eqs.c_ptr(), n1, n2));
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ctx.assign_eq(n1, n2, eq_justification(js));
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}
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bool theory_seq::simplify_eq(expr* l, expr* r, enode_pair_dependency* deps) {
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context& ctx = get_context();
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seq_rewriter rw(m);
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expr_ref_vector lhs(m), rhs(m);
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expr_ref lh = canonize(l, deps);
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expr_ref rh = canonize(r, deps);
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if (!rw.reduce_eq(lh, rh, lhs, rhs)) {
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// equality is inconsistent.
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TRACE("seq", tout << lh << " != " << rh << "\n";);
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set_conflict(deps);
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return true;
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}
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if (lhs.size() == 1 && l == lhs[0].get() &&
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rhs.size() == 1 && r == rhs[0].get()) {
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return false;
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}
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SASSERT(lhs.size() == rhs.size());
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for (unsigned i = 0; i < lhs.size(); ++i) {
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expr_ref l(lhs[i].get(), m);
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expr_ref r(rhs[i].get(), m);
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if (m_util.is_seq(l) || m_util.is_re(l)) {
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m_eqs.push_back(eq(l, r, deps));
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}
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else {
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propagate_eq(deps, ensure_enode(l), ensure_enode(r));
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}
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}
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TRACE("seq",
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tout << mk_pp(l, m) << " = " << mk_pp(r, m) << " => ";
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for (unsigned i = 0; i < m_eqs.size(); ++i) {
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tout << m_eqs[i].m_lhs << " = " << m_eqs[i].m_rhs << "; ";
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}
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tout << "\n";
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);
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return true;
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}
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bool theory_seq::solve_unit_eq(expr* l, expr* r, enode_pair_dependency* deps) {
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expr_ref lh = canonize(l, deps);
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expr_ref rh = canonize(r, deps);
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if (lh == rh) {
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return true;
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}
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if (is_var(lh) && !occurs(lh, rh)) {
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add_solution(lh, rh, deps);
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return true;
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}
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if (is_var(rh) && !occurs(rh, lh)) {
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add_solution(rh, lh, deps);
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return true;
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}
|
|
// Use instead reference counts for dependencies to GC?
|
|
|
|
// TBD: Solutions to units are not necessarily variables, but
|
|
// they may induce new equations.
|
|
|
|
return false;
|
|
}
|
|
|
|
bool theory_seq::occurs(expr* a, expr* b) {
|
|
// true if a occurs under an interpreted function or under left/right selector.
|
|
SASSERT(is_var(a));
|
|
expr* e1, *e2;
|
|
while (is_left_select(a, e1) || is_right_select(a, e1)) {
|
|
a = e1;
|
|
}
|
|
if (m_util.str.is_concat(b, e1, e2)) {
|
|
return occurs(a, e1) || occurs(a, e2);
|
|
}
|
|
while (is_left_select(b, e1) || is_right_select(b, e1)) {
|
|
b = e1;
|
|
}
|
|
if (a == b) {
|
|
return true;
|
|
}
|
|
return false;
|
|
}
|
|
|
|
bool theory_seq::is_var(expr* a) {
|
|
return
|
|
m_util.is_seq(a) &&
|
|
!m_util.str.is_concat(a) &&
|
|
!m_util.str.is_empty(a) &&
|
|
!m_util.str.is_string(a) &&
|
|
!m_util.str.is_unit(a);
|
|
}
|
|
|
|
bool theory_seq::is_left_select(expr* a, expr*& b) {
|
|
return m_util.is_skolem(a) &&
|
|
to_app(a)->get_decl()->get_parameter(0).get_symbol() == m_left_sym && (b = to_app(a)->get_arg(0), true);
|
|
}
|
|
|
|
bool theory_seq::is_right_select(expr* a, expr*& b) {
|
|
return m_util.is_skolem(a) &&
|
|
to_app(a)->get_decl()->get_parameter(0).get_symbol() == m_right_sym && (b = to_app(a)->get_arg(0), true);
|
|
}
|
|
|
|
void theory_seq::add_solution(expr* l, expr* r, enode_pair_dependency* deps) {
|
|
context& ctx = get_context();
|
|
m_rep.update(l, r, deps);
|
|
// TBD: skip new equalities for non-internalized terms.
|
|
if (ctx.e_internalized(l) && ctx.e_internalized(r)) {
|
|
propagate_eq(deps, ctx.get_enode(l), ctx.get_enode(r));
|
|
}
|
|
}
|
|
|
|
bool theory_seq::simplify_eqs() {
|
|
return pre_process_eqs(true);
|
|
}
|
|
|
|
bool theory_seq::solve_basic_eqs() {
|
|
return pre_process_eqs(false);
|
|
}
|
|
|
|
bool theory_seq::pre_process_eqs(bool simplify_or_solve) {
|
|
context& ctx = get_context();
|
|
bool change = false;
|
|
for (unsigned i = 0; !ctx.inconsistent() && i < m_eqs.size(); ++i) {
|
|
eq e = m_eqs[i];
|
|
|
|
if (simplify_or_solve?
|
|
simplify_eq(e.m_lhs, e.m_rhs, e.m_dep):
|
|
solve_unit_eq(e.m_lhs, e.m_rhs, e.m_dep)) {
|
|
if (i + 1 != m_eqs.size()) {
|
|
eq e1 = m_eqs[m_eqs.size()-1];
|
|
m_eqs.set(i, e1);
|
|
--i;
|
|
++m_stats.m_num_reductions;
|
|
}
|
|
m_eqs.pop_back();
|
|
change = true;
|
|
}
|
|
}
|
|
return change;
|
|
}
|
|
|
|
bool theory_seq::simplify_and_solve_eqs() {
|
|
context & ctx = get_context();
|
|
bool change = simplify_eqs();
|
|
while (!ctx.inconsistent() && solve_basic_eqs()) {
|
|
simplify_eqs();
|
|
change = true;
|
|
}
|
|
return change;
|
|
}
|
|
|
|
void theory_seq::internalize_eq_eh(app * atom, bool_var v) {
|
|
}
|
|
|
|
bool theory_seq::internalize_atom(app* a, bool) {
|
|
return internalize_term(a);
|
|
}
|
|
|
|
bool theory_seq::internalize_term(app* term) {
|
|
TRACE("seq", tout << mk_pp(term, m) << "\n";);
|
|
context & ctx = get_context();
|
|
unsigned num_args = term->get_num_args();
|
|
for (unsigned i = 0; i < num_args; i++) {
|
|
expr* arg = term->get_arg(i);
|
|
mk_var(ensure_enode(arg));
|
|
}
|
|
if (m.is_bool(term)) {
|
|
bool_var bv = ctx.mk_bool_var(term);
|
|
ctx.set_var_theory(bv, get_id());
|
|
}
|
|
else {
|
|
enode* e = 0;
|
|
if (ctx.e_internalized(term)) {
|
|
e = ctx.get_enode(term);
|
|
}
|
|
else {
|
|
e = ctx.mk_enode(term, false, m.is_bool(term), true);
|
|
}
|
|
mk_var(e);
|
|
}
|
|
if (m_util.str.is_length(term) && !m_has_length) {
|
|
m_trail_stack.push(value_trail<theory_seq, bool>(m_has_length));
|
|
m_has_length = true;
|
|
}
|
|
if (!m_util.str.is_concat(term) &&
|
|
!m_util.str.is_string(term) &&
|
|
!m_util.str.is_empty(term) &&
|
|
!m_util.str.is_unit(term) &&
|
|
!m_util.str.is_suffix(term) &&
|
|
!m_util.str.is_prefix(term) &&
|
|
!m_util.str.is_contains(term) &&
|
|
!m_util.is_skolem(term)) {
|
|
set_incomplete(term);
|
|
}
|
|
return true;
|
|
}
|
|
|
|
void theory_seq::apply_sort_cnstr(enode* n, sort* s) {
|
|
mk_var(n);
|
|
}
|
|
|
|
void theory_seq::display(std::ostream & out) const {
|
|
if (m_eqs.size() == 0 &&
|
|
m_ineqs.empty() &&
|
|
m_rep.empty() &&
|
|
m_exclude.empty()) {
|
|
return;
|
|
}
|
|
out << "Theory seq\n";
|
|
if (m_eqs.size() > 0) {
|
|
out << "Equations:\n";
|
|
display_equations(out);
|
|
}
|
|
if (!m_ineqs.empty()) {
|
|
out << "Negative constraints:\n";
|
|
for (unsigned i = 0; i < m_ineqs.size(); ++i) {
|
|
out << mk_pp(m_ineqs[i], m) << "\n";
|
|
}
|
|
}
|
|
if (!m_rep.empty()) {
|
|
out << "Solved equations:\n";
|
|
m_rep.display(out);
|
|
}
|
|
if (!m_exclude.empty()) {
|
|
out << "Exclusions:\n";
|
|
m_exclude.display(out);
|
|
}
|
|
}
|
|
|
|
void theory_seq::display_equations(std::ostream& out) const {
|
|
for (unsigned i = 0; i < m_eqs.size(); ++i) {
|
|
eq const& e = m_eqs[i];
|
|
out << e.m_lhs << " = " << e.m_rhs << " <- ";
|
|
display_deps(out, e.m_dep);
|
|
}
|
|
}
|
|
|
|
void theory_seq::display_deps(std::ostream& out, enode_pair_dependency* dep) const {
|
|
vector<enode_pair, false> _eqs;
|
|
const_cast<enode_pair_dependency_manager&>(m_dm).linearize(dep, _eqs);
|
|
for (unsigned i = 0; i < _eqs.size(); ++i) {
|
|
out << " " << mk_pp(_eqs[i].first->get_owner(), m) << " = " << mk_pp(_eqs[i].second->get_owner(), m);
|
|
}
|
|
out << "\n";
|
|
}
|
|
|
|
void theory_seq::collect_statistics(::statistics & st) const {
|
|
st.update("seq num splits", m_stats.m_num_splits);
|
|
st.update("seq num reductions", m_stats.m_num_reductions);
|
|
}
|
|
|
|
void theory_seq::init_model(model_generator & mg) {
|
|
m_factory = alloc(seq_factory, get_manager(), get_family_id(), mg.get_model());
|
|
mg.register_factory(m_factory);
|
|
}
|
|
|
|
model_value_proc * theory_seq::mk_value(enode * n, model_generator & mg) {
|
|
enode_pair_dependency* deps = 0;
|
|
expr_ref e(n->get_owner(), m);
|
|
flet<bool> _model_completion(m_model_completion, true);
|
|
e = canonize(e, deps);
|
|
SASSERT(is_app(e));
|
|
m_factory->add_trail(e);
|
|
return alloc(expr_wrapper_proc, to_app(e));
|
|
}
|
|
|
|
|
|
|
|
void theory_seq::set_incomplete(app* term) {
|
|
if (!m_incomplete) {
|
|
TRACE("seq", tout << "Incomplete operator: " << mk_pp(term, m) << "\n";);
|
|
m_trail_stack.push(value_trail<theory_seq, bool>(m_incomplete));
|
|
m_incomplete = true;
|
|
}
|
|
}
|
|
|
|
theory_var theory_seq::mk_var(enode* n) {
|
|
if (!m_util.is_seq(n->get_owner()) &&
|
|
!m_util.is_re(n->get_owner())) {
|
|
return null_theory_var;
|
|
}
|
|
if (is_attached_to_var(n)) {
|
|
return n->get_th_var(get_id());
|
|
}
|
|
else {
|
|
theory_var v = theory::mk_var(n);
|
|
get_context().attach_th_var(n, this, v);
|
|
get_context().mark_as_relevant(n);
|
|
return v;
|
|
}
|
|
}
|
|
|
|
bool theory_seq::can_propagate() {
|
|
return m_axioms_head < m_axioms.size();
|
|
}
|
|
|
|
expr_ref theory_seq::canonize(expr* e, enode_pair_dependency*& eqs) {
|
|
expr_ref result = expand(e, eqs);
|
|
m_rewrite(result);
|
|
return result;
|
|
}
|
|
|
|
expr_ref theory_seq::expand(expr* e, enode_pair_dependency*& eqs) {
|
|
enode_pair_dependency* deps = 0;
|
|
expr_dep ed;
|
|
if (m_rep.find_cache(e, ed)) {
|
|
eqs = m_dm.mk_join(eqs, ed.second);
|
|
return expr_ref(ed.first, m);
|
|
}
|
|
e = m_rep.find(e, deps);
|
|
expr_ref result(m);
|
|
expr* e1, *e2;
|
|
if (m_util.str.is_concat(e, e1, e2)) {
|
|
result = m_util.str.mk_concat(expand(e1, deps), expand(e2, deps));
|
|
}
|
|
else if (m_util.str.is_empty(e) || m_util.str.is_string(e)) {
|
|
result = e;
|
|
}
|
|
else if (m.is_eq(e, e1, e2)) {
|
|
result = m.mk_eq(expand(e1, deps), expand(e2, deps));
|
|
}
|
|
else if (m_util.str.is_prefix(e, e1, e2)) {
|
|
result = m_util.str.mk_prefix(expand(e1, deps), expand(e2, deps));
|
|
}
|
|
else if (m_util.str.is_suffix(e, e1, e2)) {
|
|
result = m_util.str.mk_suffix(expand(e1, deps), expand(e2, deps));
|
|
}
|
|
else if (m_util.str.is_contains(e, e1, e2)) {
|
|
result = m_util.str.mk_contains(expand(e1, deps), expand(e2, deps));
|
|
}
|
|
else if (m_model_completion && is_var(e)) {
|
|
SASSERT(m_factory);
|
|
expr_ref val(m);
|
|
val = m_factory->get_some_value(m.get_sort(e));
|
|
if (val) {
|
|
m_rep.update(e, val, 0);
|
|
result = val;
|
|
}
|
|
else {
|
|
result = e;
|
|
}
|
|
}
|
|
else {
|
|
result = e;
|
|
}
|
|
expr_dep edr(result, deps);
|
|
m_rep.add_cache(e, edr);
|
|
eqs = m_dm.mk_join(eqs, deps);
|
|
return result;
|
|
}
|
|
|
|
void theory_seq::add_dependency(enode_pair_dependency*& dep, enode* a, enode* b) {
|
|
if (a != b) {
|
|
dep = m_dm.mk_join(dep, m_dm.mk_leaf(std::make_pair(a, b)));
|
|
}
|
|
}
|
|
|
|
|
|
void theory_seq::propagate() {
|
|
context & ctx = get_context();
|
|
while (m_axioms_head < m_axioms.size() && !ctx.inconsistent()) {
|
|
expr_ref e(m);
|
|
e = m_axioms[m_axioms_head].get();
|
|
deque_axiom(e);
|
|
++m_axioms_head;
|
|
}
|
|
}
|
|
|
|
void theory_seq::enque_axiom(expr* e) {
|
|
TRACE("seq", tout << "add axioms for: " << mk_pp(e, m) << "\n";);
|
|
m_trail_stack.push(push_back_vector<theory_seq, expr_ref_vector>(m_axioms));
|
|
m_axioms.push_back(e);
|
|
}
|
|
|
|
void theory_seq::deque_axiom(expr* n) {
|
|
if (m_util.str.is_length(n)) {
|
|
add_length_axiom(n);
|
|
}
|
|
else if (m_util.str.is_index(n)) {
|
|
add_indexof_axiom(n);
|
|
}
|
|
else if (m_util.str.is_replace(n)) {
|
|
add_replace_axiom(n);
|
|
}
|
|
else if (m_util.str.is_extract(n)) {
|
|
add_extract_axiom(n);
|
|
}
|
|
else if (m_util.str.is_at(n)) {
|
|
add_at_axiom(n);
|
|
}
|
|
else if (m_util.str.is_unit(n)) {
|
|
add_length_unit_axiom(n);
|
|
}
|
|
else if (m_util.str.is_empty(n)) {
|
|
add_length_empty_axiom(n);
|
|
}
|
|
else if (m_util.str.is_concat(n)) {
|
|
add_length_concat_axiom(n);
|
|
}
|
|
else if (m_util.str.is_string(n)) {
|
|
add_elim_string_axiom(n);
|
|
// add_length_string_axiom(n);
|
|
}
|
|
}
|
|
|
|
|
|
/*
|
|
encode that s is not a proper prefix of xs1
|
|
where s1 is all of s, except the last element.
|
|
|
|
lit or s = "" or s = s1*c
|
|
lit or s = "" or len(c) = 1
|
|
lit or s = "" or !prefix(s, x*s1)
|
|
*/
|
|
void theory_seq::tightest_prefix(expr* s, expr* x, literal lit1, literal lit2) {
|
|
expr_ref s1 = mk_skolem(symbol("seq.first"), s);
|
|
expr_ref c = mk_skolem(symbol("seq.last"), s);
|
|
expr_ref s1c(m_util.str.mk_concat(s1, c), m);
|
|
expr_ref lc(m_util.str.mk_length(c), m);
|
|
expr_ref one(m_autil.mk_int(1), m);
|
|
expr_ref emp(m_util.str.mk_empty(m.get_sort(s)), m);
|
|
literal s_eq_emp = mk_eq(s, emp, false);
|
|
add_axiom(lit1, lit2, s_eq_emp, mk_eq(s, s1c, false));
|
|
add_axiom(lit1, lit2, s_eq_emp, mk_eq(lc, one, false));
|
|
add_axiom(lit1, lit2, s_eq_emp, ~mk_literal(m_util.str.mk_contains(s, m_util.str.mk_concat(x, s1))));
|
|
}
|
|
|
|
/*
|
|
// index of s in t starting at offset.
|
|
|
|
let i = Index(t, s, 0):
|
|
|
|
len(t) = 0 => i = -1
|
|
len(t) != 0 & !contains(t, s) => i = -1
|
|
len(t) != 0 & contains(t, s) => t = xsy & i = len(x)
|
|
len(t) != 0 & contains(t, s) & s != emp => tightest_prefix(x, s)
|
|
|
|
let i = Index(t, s, offset)
|
|
|
|
|
|
0 <= offset < len(t) => xy = t & len(x) = offset & (-1 = indexof(t, s, 0) => -1 = i)
|
|
& (indexof(t, s, 0) >= 0 => indexof(t, s, 0) + offset = i)
|
|
|
|
|
|
offset = len(t) => i = -1
|
|
|
|
if offset < 0 or offset >= len(t)
|
|
under specified
|
|
|
|
optional lemmas:
|
|
(len(s) > len(t) -> i = -1)
|
|
(len(s) <= len(t) -> i <= len(t)-len(s))
|
|
*/
|
|
void theory_seq::add_indexof_axiom(expr* i) {
|
|
expr* s, *t, *offset;
|
|
rational r;
|
|
VERIFY(m_util.str.is_index(i, t, s, offset));
|
|
expr_ref emp(m), minus_one(m), zero(m), xsy(m);
|
|
minus_one = m_autil.mk_int(-1);
|
|
zero = m_autil.mk_int(0);
|
|
emp = m_util.str.mk_empty(m.get_sort(s));
|
|
literal offset_ne_zero = null_literal;
|
|
bool is_num = m_autil.is_numeral(offset, r);
|
|
if (is_num && r.is_zero()) {
|
|
offset_ne_zero = null_literal;
|
|
}
|
|
else {
|
|
offset_ne_zero = ~mk_eq(offset, zero, false);
|
|
}
|
|
if (!is_num || r.is_zero()) {
|
|
expr_ref x = mk_skolem(m_contains_left_sym, t, s);
|
|
expr_ref y = mk_skolem(m_contains_right_sym, t, s);
|
|
xsy = m_util.str.mk_concat(x,s,y);
|
|
literal cnt = mk_literal(m_util.str.mk_contains(t, s));
|
|
literal eq_empty = mk_eq(s, emp, false);
|
|
add_axiom(offset_ne_zero, cnt, mk_eq(i, minus_one, false));
|
|
add_axiom(offset_ne_zero, ~eq_empty, mk_eq(i, zero, false));
|
|
add_axiom(offset_ne_zero, ~cnt, eq_empty, mk_eq(t, xsy, false));
|
|
tightest_prefix(s, x, ~cnt, offset_ne_zero);
|
|
}
|
|
if (is_num && r.is_zero()) {
|
|
return;
|
|
}
|
|
// offset >= len(t) => indexof(s, t, offset) = -1
|
|
expr_ref len_t(m_util.str.mk_length(t), m);
|
|
literal offset_ge_len = mk_literal(m_autil.mk_ge(mk_sub(offset, len_t), zero));
|
|
add_axiom(offset_ge_len, mk_eq(i, minus_one, false));
|
|
|
|
// 0 <= offset & offset < len(t) => t = xy
|
|
// 0 <= offset & offset < len(t) => len(x) = offset
|
|
// 0 <= offset & offset < len(t) & ~contains(s, y) => indexof(t, s, offset) = -1
|
|
// 0 <= offset & offset < len(t) & contains(s, y) => index(t, s, offset) = indexof(y, s, 0) + len(t)
|
|
expr_ref x = mk_skolem(symbol("seq.indexof.left"), t, s, offset);
|
|
expr_ref y = mk_skolem(symbol("seq.indexof.right"), t, s, offset);
|
|
expr_ref indexof(m_util.str.mk_index(y, s, zero), m);
|
|
// TBD:
|
|
//literal offset_ge_0 = mk_literal(m_autil.mk_ge(offset, zero));
|
|
//add_axiom(~offset_ge_0, offset_ge_len, mk_eq(indexof, i, false));
|
|
//add_axiom(~offset_ge_0, offset_ge_len, mk_eq(m_util.str.mk_length(x), offset, false));
|
|
//add_axiom(~offset_ge_0, offset_ge_len, mk_eq(t, m_util.str.mk_concat(x, y), false));
|
|
}
|
|
|
|
/*
|
|
let r = replace(a, s, t)
|
|
|
|
(contains(a, s) -> tightest_prefix(s,xs))
|
|
(contains(a, s) -> r = xty & a = xsy) &
|
|
(!contains(a, s) -> r = a)
|
|
|
|
*/
|
|
void theory_seq::add_replace_axiom(expr* r) {
|
|
expr* a, *s, *t;
|
|
VERIFY(m_util.str.is_replace(r, a, s, t));
|
|
expr_ref x = mk_skolem(m_contains_left_sym, a, s);
|
|
expr_ref y = mk_skolem(m_contains_right_sym, a, s);
|
|
expr_ref xty(m_util.str.mk_concat(x, t, y), m);
|
|
expr_ref xsy(m_util.str.mk_concat(x, s, y), m);
|
|
literal cnt = mk_literal(m_util.str.mk_contains(a ,s));
|
|
add_axiom(cnt, mk_eq(r, a, false));
|
|
add_axiom(~cnt, mk_eq(a, xsy, false));
|
|
add_axiom(~cnt, mk_eq(r, xty, false));
|
|
tightest_prefix(s, x, ~cnt);
|
|
}
|
|
|
|
void theory_seq::add_length_unit_axiom(expr* n) {
|
|
if (!m_has_length) return;
|
|
SASSERT(m_util.str.is_unit(n));
|
|
expr_ref one(m_autil.mk_int(1), m), len(m_util.str.mk_length(n), m);
|
|
add_axiom(mk_eq(len, one, false));
|
|
}
|
|
|
|
void theory_seq::add_length_empty_axiom(expr* n) {
|
|
if (!m_has_length) return;
|
|
SASSERT(m_util.str.is_empty(n));
|
|
expr_ref zero(m_autil.mk_int(0), m), len(m_util.str.mk_length(n), m);
|
|
add_axiom(mk_eq(len, zero, false));
|
|
}
|
|
|
|
void theory_seq::add_elim_string_axiom(expr* n) {
|
|
zstring s;
|
|
VERIFY(m_util.str.is_string(n, s));
|
|
SASSERT(s.length() > 0);
|
|
expr_ref result(m_util.str.mk_unit(m_util.str.mk_char(s, 0)), m);
|
|
for (unsigned i = 1; i < s.length(); ++i) {
|
|
result = m_util.str.mk_concat(result, m_util.str.mk_unit(m_util.str.mk_char(s, i)));
|
|
}
|
|
add_axiom(mk_eq(n, result, false));
|
|
m_rep.update(n, result, 0);
|
|
}
|
|
|
|
void theory_seq::add_length_string_axiom(expr* n) {
|
|
if (!m_has_length) return;
|
|
zstring s;
|
|
VERIFY(m_util.str.is_string(n, s));
|
|
expr_ref len(m_util.str.mk_length(n), m);
|
|
expr_ref ls(m_autil.mk_numeral(rational(s.length(), rational::ui64()), true), m);
|
|
add_axiom(mk_eq(len, ls, false));
|
|
}
|
|
|
|
void theory_seq::add_length_concat_axiom(expr* n) {
|
|
if (!m_has_length) return;
|
|
expr* a, *b;
|
|
VERIFY(m_util.str.is_concat(n, a, b));
|
|
expr_ref len(m_util.str.mk_length(n), m);
|
|
expr_ref _a(m_util.str.mk_length(a), m);
|
|
expr_ref _b(m_util.str.mk_length(b), m);
|
|
expr_ref a_p_b(m_autil.mk_add(_a, _b), m);
|
|
add_axiom(mk_eq(len, a_p_b, false));
|
|
}
|
|
|
|
/*
|
|
let n = len(x)
|
|
|
|
len(x) >= 0
|
|
len(x) = 0 => x = ""
|
|
x = "" => len(x) = 0
|
|
*/
|
|
void theory_seq::add_length_axiom(expr* n) {
|
|
expr* x;
|
|
VERIFY(m_util.str.is_length(n, x));
|
|
if (!m_util.str.is_unit(x) &&
|
|
!m_util.str.is_empty(x) &&
|
|
!m_util.str.is_string(x) &&
|
|
!m_util.str.is_concat(x)) {
|
|
expr_ref zero(m_autil.mk_int(0), m);
|
|
expr_ref emp(m_util.str.mk_empty(m.get_sort(x)), m);
|
|
literal eq1(mk_eq(zero, n, false));
|
|
literal eq2(mk_eq(x, emp, false));
|
|
add_axiom(mk_literal(m_autil.mk_ge(n, zero)));
|
|
add_axiom(~eq1, eq2);
|
|
add_axiom(~eq2, eq1);
|
|
}
|
|
}
|
|
|
|
expr* theory_seq::mk_sub(expr* a, expr* b) {
|
|
return m_autil.mk_add(a, m_autil.mk_mul(m_autil.mk_int(-1), b));
|
|
}
|
|
|
|
enode* theory_seq::ensure_enode(expr* e) {
|
|
context& ctx = get_context();
|
|
if (!ctx.e_internalized(e)) {
|
|
ctx.internalize(e, false);
|
|
ctx.mark_as_relevant(ctx.get_enode(e));
|
|
}
|
|
return ctx.get_enode(e);
|
|
}
|
|
|
|
/*
|
|
TBD: check semantics of extract.
|
|
|
|
let e = extract(s, i, l)
|
|
|
|
0 <= i < len(s) -> prefix(xe,s) & len(x) = i
|
|
0 <= i < len(s) & l >= len(s) - i -> len(e) = len(s) - i
|
|
0 <= i < len(s) & 0 <= l < len(s) - i -> len(e) = l
|
|
0 <= i < len(s) & l < 0 -> len(e) = 0
|
|
* i < 0 -> e = s
|
|
* i >= len(s) -> e = empty
|
|
*/
|
|
|
|
void theory_seq::add_extract_axiom(expr* e) {
|
|
expr* s, *i, *l;
|
|
VERIFY(m_util.str.is_extract(e, s, i, l));
|
|
expr_ref x(mk_skolem(symbol("seq.extract.prefix"), s, e), m);
|
|
expr_ref ls(m_util.str.mk_length(s), m);
|
|
expr_ref lx(m_util.str.mk_length(x), m);
|
|
expr_ref le(m_util.str.mk_length(e), m);
|
|
expr_ref ls_minus_i(mk_sub(ls, i), m);
|
|
expr_ref xe(m_util.str.mk_concat(x, e), m);
|
|
expr_ref zero(m_autil.mk_int(0), m);
|
|
|
|
literal i_ge_0 = mk_literal(m_autil.mk_ge(i, zero));
|
|
literal i_ge_ls = mk_literal(m_autil.mk_ge(mk_sub(i, ls), zero));
|
|
literal l_ge_ls = mk_literal(m_autil.mk_ge(mk_sub(l, ls), zero));
|
|
literal l_ge_zero = mk_literal(m_autil.mk_ge(l, zero));
|
|
|
|
add_axiom(~i_ge_0, i_ge_ls, mk_literal(m_util.str.mk_prefix(xe, s)));
|
|
add_axiom(~i_ge_0, i_ge_ls, mk_eq(lx, i, false));
|
|
add_axiom(~i_ge_0, i_ge_ls, ~l_ge_ls, mk_eq(le, ls_minus_i, false));
|
|
add_axiom(~i_ge_0, i_ge_ls, l_ge_zero, mk_eq(le, zero, false));
|
|
}
|
|
|
|
/*
|
|
let e = at(s, i)
|
|
|
|
0 <= i < len(s) -> s = xey & len(x) = i & len(e) = 1
|
|
|
|
*/
|
|
void theory_seq::add_at_axiom(expr* e) {
|
|
expr* s, *i;
|
|
VERIFY(m_util.str.is_at(e, s, i));
|
|
expr_ref x(m), y(m), lx(m), le(m), xey(m), zero(m), one(m), len_e(m), len_x(m);
|
|
x = mk_skolem(symbol("seq.at.left"), s);
|
|
y = mk_skolem(symbol("seq.at.right"), s);
|
|
xey = m_util.str.mk_concat(x, e, y);
|
|
zero = m_autil.mk_int(0);
|
|
one = m_autil.mk_int(1);
|
|
len_e = m_util.str.mk_length(e);
|
|
len_x = m_util.str.mk_length(x);
|
|
|
|
literal i_ge_0 = mk_literal(m_autil.mk_ge(i, zero));
|
|
literal i_ge_len_s = mk_literal(m_autil.mk_ge(mk_sub(i, m_util.str.mk_length(s)), zero));
|
|
|
|
add_axiom(~i_ge_0, i_ge_len_s, mk_eq(s, xey, false));
|
|
add_axiom(~i_ge_0, i_ge_len_s, mk_eq(one, len_e, false));
|
|
add_axiom(~i_ge_0, i_ge_len_s, mk_eq(i, len_x, false));
|
|
}
|
|
|
|
|
|
literal theory_seq::mk_literal(expr* _e) {
|
|
expr_ref e(_e, m);
|
|
context& ctx = get_context();
|
|
ensure_enode(e);
|
|
return ctx.get_literal(e);
|
|
}
|
|
|
|
void theory_seq::add_axiom(literal l1, literal l2, literal l3, literal l4) {
|
|
context& ctx = get_context();
|
|
literal_vector lits;
|
|
if (l1 != null_literal) { ctx.mark_as_relevant(l1); lits.push_back(l1); }
|
|
if (l2 != null_literal) { ctx.mark_as_relevant(l2); lits.push_back(l2); }
|
|
if (l3 != null_literal) { ctx.mark_as_relevant(l3); lits.push_back(l3); }
|
|
if (l4 != null_literal) { ctx.mark_as_relevant(l4); lits.push_back(l4); }
|
|
TRACE("seq", ctx.display_literals_verbose(tout, lits.size(), lits.c_ptr()); tout << "\n";);
|
|
ctx.mk_th_axiom(get_id(), lits.size(), lits.c_ptr());
|
|
}
|
|
|
|
|
|
expr_ref theory_seq::mk_skolem(symbol const& name, expr* e1,
|
|
expr* e2, expr* e3, sort* range) {
|
|
expr* es[3] = { e1, e2, e3 };
|
|
unsigned len = e3?3:(e2?2:1);
|
|
if (!range) {
|
|
range = m.get_sort(e1);
|
|
}
|
|
return expr_ref(m_util.mk_skolem(name, len, es, range), m);
|
|
}
|
|
|
|
void theory_seq::propagate_eq(bool_var v, expr* e1, expr* e2) {
|
|
context& ctx = get_context();
|
|
TRACE("seq",
|
|
tout << mk_pp(ctx.bool_var2enode(v)->get_owner(), m) << " => "
|
|
<< mk_pp(e1, m) << " = " << mk_pp(e2, m) << "\n";);
|
|
|
|
SASSERT(ctx.e_internalized(e2));
|
|
enode* n1 = ensure_enode(e1);
|
|
enode* n2 = ensure_enode(e2);
|
|
literal lit(v);
|
|
justification* js =
|
|
ctx.mk_justification(
|
|
ext_theory_eq_propagation_justification(
|
|
get_id(), ctx.get_region(), 1, &lit, 0, 0, n1, n2));
|
|
|
|
ctx.assign_eq(n1, n2, eq_justification(js));
|
|
}
|
|
|
|
void theory_seq::assign_eq(bool_var v, bool is_true) {
|
|
context & ctx = get_context();
|
|
enode* n = ctx.bool_var2enode(v);
|
|
app* e = n->get_owner();
|
|
if (is_true) {
|
|
expr* e1, *e2;
|
|
expr_ref f(m);
|
|
if (m_util.str.is_prefix(e, e1, e2)) {
|
|
f = mk_skolem(m_prefix_sym, e1, e2);
|
|
f = m_util.str.mk_concat(e1, f);
|
|
propagate_eq(v, f, e2);
|
|
}
|
|
else if (m_util.str.is_suffix(e, e1, e2)) {
|
|
f = mk_skolem(m_suffix_sym, e1, e2);
|
|
f = m_util.str.mk_concat(f, e1);
|
|
propagate_eq(v, f, e2);
|
|
}
|
|
else if (m_util.str.is_contains(e, e1, e2)) {
|
|
expr_ref f1 = mk_skolem(m_contains_left_sym, e1, e2);
|
|
expr_ref f2 = mk_skolem(m_contains_right_sym, e1, e2);
|
|
f = m_util.str.mk_concat(m_util.str.mk_concat(f1, e2), f2);
|
|
propagate_eq(v, f, e1);
|
|
}
|
|
else if (m_util.str.is_in_re(e, e1, e2)) {
|
|
// TBD
|
|
}
|
|
else {
|
|
UNREACHABLE();
|
|
}
|
|
}
|
|
else {
|
|
m_trail_stack.push(push_back_vector<theory_seq, expr_ref_vector>(m_ineqs));
|
|
m_ineqs.push_back(e);
|
|
}
|
|
}
|
|
|
|
void theory_seq::new_eq_eh(theory_var v1, theory_var v2) {
|
|
enode* n1 = get_enode(v1);
|
|
enode* n2 = get_enode(v2);
|
|
if (n1 != n2) {
|
|
expr_ref o1(n1->get_owner(), m);
|
|
expr_ref o2(n2->get_owner(), m);
|
|
TRACE("seq", tout << o1 << " = " << o2 << "\n";);
|
|
m_eqs.push_back(eq(o1, o2, m_dm.mk_leaf(enode_pair(n1, n2))));
|
|
}
|
|
}
|
|
|
|
void theory_seq::new_diseq_eh(theory_var v1, theory_var v2) {
|
|
expr* e1 = get_enode(v1)->get_owner();
|
|
expr* e2 = get_enode(v2)->get_owner();
|
|
m_trail_stack.push(push_back_vector<theory_seq, expr_ref_vector>(m_ineqs));
|
|
m_ineqs.push_back(mk_eq_atom(e1, e2));
|
|
m_exclude.update(e1, e2);
|
|
}
|
|
|
|
void theory_seq::push_scope_eh() {
|
|
TRACE("seq", tout << "push " << m_eqs.size() << "\n";);
|
|
theory::push_scope_eh();
|
|
m_rep.push_scope();
|
|
m_exclude.push_scope();
|
|
m_dm.push_scope();
|
|
m_trail_stack.push_scope();
|
|
m_trail_stack.push(value_trail<theory_seq, unsigned>(m_axioms_head));
|
|
m_eqs.push_scope();
|
|
}
|
|
|
|
void theory_seq::pop_scope_eh(unsigned num_scopes) {
|
|
TRACE("seq", tout << "pop " << m_eqs.size() << "\n";);
|
|
m_trail_stack.pop_scope(num_scopes);
|
|
theory::pop_scope_eh(num_scopes);
|
|
m_dm.pop_scope(num_scopes);
|
|
m_rep.pop_scope(num_scopes);
|
|
m_exclude.pop_scope(num_scopes);
|
|
m_eqs.pop_scopes(num_scopes);
|
|
}
|
|
|
|
void theory_seq::restart_eh() {
|
|
}
|
|
|
|
void theory_seq::relevant_eh(app* n) {
|
|
if (m_util.str.is_length(n) ||
|
|
m_util.str.is_index(n) ||
|
|
m_util.str.is_replace(n) ||
|
|
m_util.str.is_extract(n) ||
|
|
m_util.str.is_at(n) ||
|
|
m_util.str.is_concat(n) ||
|
|
m_util.str.is_empty(n) ||
|
|
m_util.str.is_unit(n) ||
|
|
m_util.str.is_string(n)) {
|
|
enque_axiom(n);
|
|
}
|
|
}
|