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https://github.com/Z3Prover/z3
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add equality propagation based on partial length information to sequence theory. Fix issue #429
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
9b979b6e1e
commit
9c7e5c37d1
8 changed files with 200 additions and 44 deletions
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@ -1484,6 +1484,7 @@ bool seq_rewriter::length_constrained(unsigned szl, expr* const* l, unsigned szr
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if (is_sat) {
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lhs.push_back(concat_non_empty(szl, l));
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rhs.push_back(concat_non_empty(szr, r));
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//split_units(lhs, rhs);
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}
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return true;
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}
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@ -1492,13 +1493,39 @@ bool seq_rewriter::length_constrained(unsigned szl, expr* const* l, unsigned szr
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if (is_sat) {
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lhs.push_back(concat_non_empty(szl, l));
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rhs.push_back(concat_non_empty(szr, r));
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//split_units(lhs, rhs);
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}
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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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void seq_rewriter::split_units(expr_ref_vector& lhs, expr_ref_vector& rhs) {
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expr* a, *b, *a1, *b1, *a2, *b2;
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while (true) {
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if (m_util.str.is_unit(lhs.back(), a) &&
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m_util.str.is_unit(rhs.back(), b)) {
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lhs[lhs.size()-1] = a;
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rhs[rhs.size()-1] = b;
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break;
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}
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if (m_util.str.is_concat(lhs.back(), a, a2) &&
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m_util.str.is_unit(a, a1) &&
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m_util.str.is_concat(rhs.back(), b, b2) &&
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m_util.str.is_unit(b, b1)) {
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expr_ref _pin_a(lhs.back(), m()), _pin_b(rhs.back(), m());
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lhs[lhs.size()-1] = a1;
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rhs[rhs.size()-1] = b1;
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lhs.push_back(a2);
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rhs.push_back(b2);
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}
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else {
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break;
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}
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}
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}
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bool seq_rewriter::is_epsilon(expr* e) const {
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expr* e1;
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return m_util.re.is_to_re(e, e1) && m_util.str.is_empty(e1);
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@ -113,6 +113,7 @@ class seq_rewriter {
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bool is_sequence(expr* e, expr_ref_vector& seq);
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bool is_sequence(eautomaton& aut, expr_ref_vector& seq);
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bool is_epsilon(expr* e) const;
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void split_units(expr_ref_vector& lhs, expr_ref_vector& rhs);
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public:
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seq_rewriter(ast_manager & m, params_ref const & p = params_ref()):
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@ -81,14 +81,6 @@ namespace smt {
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}
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};
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arith_simplifier_plugin * arith_eq_adapter::get_simplifier() {
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if (!m_as) {
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simplifier & s = get_context().get_simplifier();
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m_as = static_cast<arith_simplifier_plugin*>(s.get_plugin(m_owner.get_family_id()));
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}
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return m_as;
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}
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void arith_eq_adapter::mk_axioms(enode * n1, enode * n2) {
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SASSERT(n1 != n2);
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ast_manager & m = get_manager();
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@ -103,6 +95,9 @@ namespace smt {
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// We don't need to create axioms for 2 = 3
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return;
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}
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if (t1 == t2) {
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return;
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}
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context & ctx = get_context();
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CTRACE("arith_eq_adapter_relevancy", !(ctx.is_relevant(n1) && ctx.is_relevant(n2)),
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@ -192,6 +187,7 @@ namespace smt {
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// Old version that used to be buggy.
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// I fixed the theory arithmetic internalizer to accept non simplified terms of the form t1 - t2
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// if t1 and t2 already have slacks (theory variables) associated with them.
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// It also accepts terms with repeated variables (Issue #429).
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app * le = 0;
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app * ge = 0;
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if (m_util.is_numeral(t1))
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@ -199,12 +195,13 @@ namespace smt {
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if (m_util.is_numeral(t2)) {
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le = m_util.mk_le(t1, t2);
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ge = m_util.mk_ge(t1, t2);
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}
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}
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else {
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sort * st = m.get_sort(t1);
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app * minus_one = m_util.mk_numeral(rational::minus_one(), st);
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app * zero = m_util.mk_numeral(rational::zero(), st);
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app_ref s(m_util.mk_add(t1, m_util.mk_mul(minus_one, t2)), m);
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app_ref minus_one(m_util.mk_numeral(rational::minus_one(), st), m);
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app_ref zero(m_util.mk_numeral(rational::zero(), st), m);
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app_ref t3(m_util.mk_mul(minus_one, t2), m);
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app_ref s(m_util.mk_add(t1, t3), m);
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le = m_util.mk_le(s, zero);
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ge = m_util.mk_ge(s, zero);
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}
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@ -75,8 +75,6 @@ namespace smt {
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ast_manager & get_manager() const { return m_owner.get_manager(); }
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enode * get_enode(theory_var v) const { return m_owner.get_enode(v); }
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arith_simplifier_plugin * get_simplifier();
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public:
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arith_eq_adapter(theory & owner, theory_arith_params & params, arith_util & u):m_owner(owner), m_params(params), m_util(u), m_as(0) {}
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void new_eq_eh(theory_var v1, theory_var v2);
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@ -450,6 +450,9 @@ namespace smt {
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svector<theory_var> m_nl_propagated; // non linear monomials that became linear
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v_dependency_manager m_dep_manager; // for tracking bounds during non-linear reasoning
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vector<uint_set> m_row_vars; // variables in a given row. Used during internalization to detect repeated variables.
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unsigned m_row_vars_top;
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var_heap m_to_patch; // heap containing all variables v s.t. m_value[v] does not satisfy bounds of v.
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nat_set m_left_basis; // temporary: set of variables that already left the basis in make_feasible
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bool m_blands_rule;
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@ -583,6 +586,9 @@ namespace smt {
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void mk_enode_if_reflect(app * n);
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template<bool invert>
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void add_row_entry(unsigned r_id, numeral const & coeff, theory_var v);
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uint_set& row_vars();
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class scoped_row_vars;
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void internalize_internal_monomial(app * m, unsigned r_id);
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theory_var internalize_add(app * n);
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theory_var internalize_mul_core(app * m);
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@ -197,6 +197,15 @@ namespace smt {
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}
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}
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/**
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\brief access the current set of variables associated with row.
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*/
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template<typename Ext>
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uint_set& theory_arith<Ext>::row_vars() {
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SASSERT(m_row_vars_top > 0);
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return m_row_vars[m_row_vars_top-1];
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}
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/**
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\brief Add coeff * v to the row r.
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The column is also updated.
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@ -206,6 +215,26 @@ namespace smt {
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void theory_arith<Ext>::add_row_entry(unsigned r_id, numeral const & coeff, theory_var v) {
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row & r = m_rows[r_id];
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column & c = m_columns[v];
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if (row_vars().contains(v)) {
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typename vector<row_entry>::iterator it = r.begin_entries();
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typename vector<row_entry>::iterator end = r.end_entries();
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bool found = false;
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for (; !found && it != end; ++it) {
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SASSERT(!it->is_dead());
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if (it->m_var == v) {
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if (invert) {
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it->m_coeff -= coeff;
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}
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else {
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it->m_coeff += coeff;
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}
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found = true;
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}
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}
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SASSERT(found);
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return;
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}
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row_vars().insert(v);
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int r_idx;
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row_entry & r_entry = r.add_row_entry(r_idx);
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int c_idx;
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@ -238,12 +267,13 @@ namespace smt {
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}
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}
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rational _val;
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if (m_util.is_mul(m) && m_util.is_numeral(m->get_arg(0), _val)) {
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expr* arg1, *arg2;
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if (m_util.is_mul(m, arg1, arg2) && m_util.is_numeral(arg1, _val)) {
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SASSERT(m->get_num_args() == 2);
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numeral val(_val);
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theory_var v = internalize_term_core(to_app(m->get_arg(1)));
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theory_var v = internalize_term_core(to_app(arg2));
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if (reflection_enabled()) {
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internalize_term_core(to_app(m->get_arg(0)));
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internalize_term_core(to_app(arg1));
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mk_enode(m);
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}
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add_row_entry<true>(r_id, val, v);
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@ -264,6 +294,7 @@ namespace smt {
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CTRACE("internalize_add_bug", n->get_num_args() == 2 && n->get_arg(0) == n->get_arg(1), tout << "n: " << mk_pp(n, get_manager()) << "\n";);
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SASSERT(m_util.is_add(n));
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unsigned r_id = mk_row();
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scoped_row_vars _sc(m_row_vars, m_row_vars_top);
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unsigned num_args = n->get_num_args();
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for (unsigned i = 0; i < num_args; i++) {
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internalize_internal_monomial(to_app(n->get_arg(i)), r_id);
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@ -324,6 +355,7 @@ namespace smt {
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numeral val(_val);
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SASSERT(!val.is_one());
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unsigned r_id = mk_row();
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scoped_row_vars _sc(m_row_vars, m_row_vars_top);
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if (reflection_enabled())
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internalize_term_core(to_app(m->get_arg(0)));
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theory_var v = internalize_mul_core(to_app(m->get_arg(1)));
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@ -617,6 +649,7 @@ namespace smt {
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enode * e = mk_enode(n);
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theory_var r = mk_var(e);
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unsigned r_id = mk_row();
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scoped_row_vars _sc(m_row_vars, m_row_vars_top);
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add_row_entry<true>(r_id, numeral(1), arg);
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add_row_entry<false>(r_id, numeral(1), r);
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init_row(r_id);
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@ -644,6 +677,25 @@ namespace smt {
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return v;
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}
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template<typename Ext>
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class theory_arith<Ext>::scoped_row_vars {
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unsigned& m_top;
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public:
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scoped_row_vars(vector<uint_set>& row_vars, unsigned& top):
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m_top(top)
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{
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SASSERT(row_vars.size() >= top);
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if (row_vars.size() == top) {
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row_vars.push_back(uint_set());
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}
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row_vars[top].reset();
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++m_top;
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}
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~scoped_row_vars() {
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--m_top;
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}
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};
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/**
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\brief Internalize the given term and return an alias for it.
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Return null_theory_var if the term was not implemented by the theory yet.
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@ -1579,6 +1631,7 @@ namespace smt {
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m_liberal_final_check(true),
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m_changed_assignment(false),
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m_assume_eq_head(0),
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m_row_vars_top(0),
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m_nl_rounds(0),
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m_nl_gb_exhausted(false),
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m_nl_new_exprs(m),
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@ -533,11 +533,14 @@ bool theory_seq::is_eq(expr* e, expr*& a, expr*& b) const {
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(a = to_app(e)->get_arg(0), b = to_app(e)->get_arg(1), true);
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}
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bool theory_seq::is_pre(expr* e, expr*& s, expr*& i) {
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return is_skolem(m_pre, e) && (s = to_app(e)->get_arg(0), i = to_app(e)->get_arg(1), true);
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}
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bool theory_seq::is_post(expr* e, expr*& s, expr*& i) {
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return is_skolem(m_post, e) && (s = to_app(e)->get_arg(0), i = to_app(e)->get_arg(1), true);
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}
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expr_ref theory_seq::mk_nth(expr* s, expr* idx) {
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@ -782,6 +785,9 @@ bool theory_seq::simplify_eq(expr_ref_vector& ls, expr_ref_vector& rs, dependenc
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if (lhs.empty()) {
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return true;
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}
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TRACE("seq",
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tout << ls << " = " << rs << "\n";
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tout << lhs << " = " << rhs << "\n";);
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for (unsigned i = 0; !ctx.inconsistent() && i < lhs.size(); ++i) {
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expr_ref li(lhs[i].get(), m);
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expr_ref ri(rhs[i].get(), m);
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@ -789,8 +795,7 @@ bool theory_seq::simplify_eq(expr_ref_vector& ls, expr_ref_vector& rs, dependenc
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// no-op
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}
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else if (m_util.is_seq(li) || m_util.is_re(li)) {
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reduce_length(li, ri);
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m_eqs.push_back(mk_eqdep(li, ri, deps));
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m_eqs.push_back(mk_eqdep(li, ri, deps));
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}
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else {
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propagate_eq(deps, ensure_enode(li), ensure_enode(ri));
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@ -817,16 +822,11 @@ bool theory_seq::solve_unit_eq(expr_ref_vector const& l, expr_ref_vector const&
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return false;
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}
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bool theory_seq::reduce_length(expr* l, expr* r) {
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expr* l2, *r2;
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bool theory_seq::reduce_length(expr* l, expr* r, literal_vector& lits) {
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expr_ref len1(m), len2(m);
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literal_vector lits;
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m_util.str.is_concat(l, l, l2);
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m_util.str.is_concat(r, r, r2);
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lits.reset();
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if (get_length(l, len1, lits) &&
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get_length(r, len2, lits) && len1 == len2) {
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TRACE("seq", tout << "Propagate equal lengths\n";);
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//propagate_eq(lits, l, r, true);
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return true;
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}
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else {
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@ -914,8 +914,8 @@ bool theory_seq::solve_eqs(unsigned i) {
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eq e1 = m_eqs[m_eqs.size()-1];
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m_eqs.set(i, e1);
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--i;
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++m_stats.m_num_reductions;
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}
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++m_stats.m_num_reductions;
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m_eqs.pop_back();
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change = true;
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}
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@ -945,6 +945,10 @@ bool theory_seq::solve_eq(expr_ref_vector const& l, expr_ref_vector const& r, de
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TRACE("seq", tout << "unit\n";);
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return true;
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}
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if (!ctx.inconsistent() && reduce_length_eq(ls, rs, deps)) {
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TRACE("seq", tout << "length\n";);
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return true;
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}
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if (!ctx.inconsistent() && solve_binary_eq(ls, rs, deps)) {
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TRACE("seq", tout << "binary\n";);
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return true;
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@ -990,6 +994,43 @@ bool theory_seq::is_binary_eq(expr_ref_vector const& ls, expr_ref_vector const&
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return false;
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}
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bool theory_seq::reduce_length_eq(expr_ref_vector const& ls, expr_ref_vector const& rs, dependency* deps) {
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if (ls.empty() || rs.empty()) {
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return false;
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}
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if (ls.size() <= 1 && rs.size() <= 1) {
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return false;
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}
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SASSERT(ls.size() > 1 || rs.size() > 1);
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literal_vector lits;
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expr_ref l(ls[0], m), r(rs[0], m);
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if (reduce_length(l, r, lits)) {
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expr_ref_vector lhs(m), rhs(m);
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lhs.append(ls.size()-1, ls.c_ptr() + 1);
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rhs.append(rs.size()-1, rs.c_ptr() + 1);
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SASSERT(!lhs.empty() || !rhs.empty());
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m_eqs.push_back(eq(m_eq_id++, lhs, rhs, deps));
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TRACE("seq", tout << "Propagate equal lengths " << l << " " << r << "\n";);
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propagate_eq(deps, lits, l, r, true);
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return true;
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}
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l = ls.back(); r = rs.back();
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if (reduce_length(l, r, lits)) {
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expr_ref_vector lhs(m), rhs(m);
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lhs.append(ls.size()-1, ls.c_ptr());
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rhs.append(rs.size()-1, rs.c_ptr());
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SASSERT(!lhs.empty() || !rhs.empty());
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m_eqs.push_back(eq(m_eq_id++, lhs, rhs, deps));
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TRACE("seq", tout << "Propagate equal lengths " << l << " " << r << "\n";);
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propagate_eq(deps, lits, l, r, true);
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return true;
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}
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return false;
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}
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bool theory_seq::solve_binary_eq(expr_ref_vector const& ls, expr_ref_vector const& rs, dependency* dep) {
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context& ctx = get_context();
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ptr_vector<expr> xs, ys;
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@ -1064,51 +1105,78 @@ bool theory_seq::solve_binary_eq(expr_ref_vector const& ls, expr_ref_vector cons
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bool theory_seq::get_length(expr* e, expr_ref& len, literal_vector& lits) {
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context& ctx = get_context();
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expr* s, *i, *l;
|
||||
rational r;
|
||||
if (m_util.str.is_extract(e, s, i, l)) {
|
||||
// 0 <= i <= len(s), 0 <= l, i + l <= len(s)
|
||||
expr_ref zero(m_autil.mk_int(0), m);
|
||||
expr_ref ls(m_util.str.mk_length(s), m);
|
||||
expr_ref ls_minus_i_l(mk_sub(mk_sub(ls, i),l), m);
|
||||
literal i_ge_0 = mk_literal(m_autil.mk_ge(i, zero));
|
||||
bool i_is_zero = m_autil.is_numeral(i, r) && r.is_zero();
|
||||
literal i_ge_0 = i_is_zero?true_literal:mk_literal(m_autil.mk_ge(i, zero));
|
||||
literal i_lt_len_s = ~mk_literal(m_autil.mk_ge(mk_sub(i, ls), zero));
|
||||
literal li_ge_ls = mk_literal(m_autil.mk_ge(ls_minus_i_l, zero));
|
||||
literal l_ge_zero = mk_literal(m_autil.mk_ge(l, zero));
|
||||
literal _lits[4] = { i_ge_0, i_lt_len_s, li_ge_ls, l_ge_zero };
|
||||
if (ctx.get_assignment(i_ge_0) == l_true &&
|
||||
ctx.get_assignment(i_lt_len_s) == l_true &&
|
||||
ctx.get_assignment(li_ge_ls) == l_true &&
|
||||
ctx.get_assignment(l_ge_zero) == l_true) {
|
||||
len = l;
|
||||
lits.push_back(i_ge_0); lits.push_back(i_lt_len_s); lits.push_back(li_ge_ls); lits.push_back(l_ge_zero);
|
||||
lits.append(4, _lits);
|
||||
return true;
|
||||
}
|
||||
TRACE("seq", tout << mk_pp(e, m) << "\n"; ctx.display_literals_verbose(tout, 4, _lits); tout << "\n";
|
||||
for (unsigned i = 0; i < 4; ++i) tout << ctx.get_assignment(_lits[i]) << "\n";);
|
||||
}
|
||||
else if (m_util.str.is_at(e, s, i)) {
|
||||
// has length 1 if 0 <= i < len(s)
|
||||
expr_ref zero(m_autil.mk_int(0), m);
|
||||
literal i_ge_0 = mk_literal(m_autil.mk_ge(i, zero));
|
||||
bool i_is_zero = m_autil.is_numeral(i, r) && r.is_zero();
|
||||
literal i_ge_0 = i_is_zero?true_literal:mk_literal(m_autil.mk_ge(i, zero));
|
||||
literal i_lt_len_s = ~mk_literal(m_autil.mk_ge(mk_sub(i, m_util.str.mk_length(s)), zero));
|
||||
literal _lits[2] = { i_ge_0, i_lt_len_s};
|
||||
if (ctx.get_assignment(i_ge_0) == l_true &&
|
||||
ctx.get_assignment(i_lt_len_s) == l_true) {
|
||||
len = m_autil.mk_int(1);
|
||||
lits.push_back(i_ge_0); lits.push_back(i_lt_len_s);
|
||||
lits.append(2, _lits);
|
||||
return true;
|
||||
}
|
||||
TRACE("seq", ctx.display_literals_verbose(tout, 2, _lits); tout << "\n";);
|
||||
}
|
||||
else if (is_pre(e, s, i)) {
|
||||
expr_ref zero(m_autil.mk_int(0), m);
|
||||
literal i_ge_0 = mk_literal(m_autil.mk_ge(i, zero));
|
||||
bool i_is_zero = m_autil.is_numeral(i, r) && r.is_zero();
|
||||
literal i_ge_0 = i_is_zero?true_literal:mk_literal(m_autil.mk_ge(i, zero));
|
||||
literal i_lt_len_s = ~mk_literal(m_autil.mk_ge(mk_sub(i, m_util.str.mk_length(s)), zero));
|
||||
literal _lits[2] = { i_ge_0, i_lt_len_s };
|
||||
if (ctx.get_assignment(i_ge_0) == l_true &&
|
||||
ctx.get_assignment(i_lt_len_s) == l_true) {
|
||||
len = i;
|
||||
lits.push_back(i_ge_0); lits.push_back(i_lt_len_s);
|
||||
lits.append(2, _lits);
|
||||
return true;
|
||||
}
|
||||
TRACE("seq", ctx.display_literals_verbose(tout, 2, _lits); tout << "\n";);
|
||||
}
|
||||
else if (is_post(e, s, l)) {
|
||||
expr_ref zero(m_autil.mk_int(0), m);
|
||||
literal l_ge_0 = mk_literal(m_autil.mk_ge(l, zero));
|
||||
literal l_le_len_s = mk_literal(m_autil.mk_ge(mk_sub(m_util.str.mk_length(s), l), zero));
|
||||
literal _lits[2] = { l_ge_0, l_le_len_s };
|
||||
if (ctx.get_assignment(l_ge_0) == l_true &&
|
||||
ctx.get_assignment(l_le_len_s) == l_true) {
|
||||
len = l;
|
||||
lits.append(2, _lits);
|
||||
return true;
|
||||
}
|
||||
TRACE("seq", ctx.display_literals_verbose(tout, 2, _lits); tout << "\n";);
|
||||
}
|
||||
else if (m_util.str.is_unit(e)) {
|
||||
len = m_autil.mk_int(1);
|
||||
return true;
|
||||
}
|
||||
else {
|
||||
TRACE("seq", tout << "unhandled: " << mk_pp(e, m) << "\n";);
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
|
|
@ -2526,10 +2594,10 @@ bool theory_seq::is_skolem(symbol const& s, expr* e) const {
|
|||
void theory_seq::propagate_eq(literal lit, expr* e1, expr* e2, bool add_to_eqs) {
|
||||
literal_vector lits;
|
||||
lits.push_back(lit);
|
||||
propagate_eq(lits, e1, e2, add_to_eqs);
|
||||
propagate_eq(0, lits, e1, e2, add_to_eqs);
|
||||
}
|
||||
|
||||
void theory_seq::propagate_eq(literal_vector const& lits, expr* e1, expr* e2, bool add_to_eqs) {
|
||||
void theory_seq::propagate_eq(dependency* deps, literal_vector const& _lits, expr* e1, expr* e2, bool add_to_eqs) {
|
||||
context& ctx = get_context();
|
||||
|
||||
enode* n1 = ensure_enode(e1);
|
||||
|
|
@ -2539,10 +2607,14 @@ void theory_seq::propagate_eq(literal_vector const& lits, expr* e1, expr* e2, bo
|
|||
}
|
||||
ctx.mark_as_relevant(n1);
|
||||
ctx.mark_as_relevant(n2);
|
||||
|
||||
literal_vector lits(_lits);
|
||||
enode_pair_vector eqs;
|
||||
linearize(deps, eqs, lits);
|
||||
|
||||
if (add_to_eqs) {
|
||||
dependency* deps = 0;
|
||||
for (unsigned i = 0; i < lits.size(); ++i) {
|
||||
literal lit = lits[i];
|
||||
for (unsigned i = 0; i < _lits.size(); ++i) {
|
||||
literal lit = _lits[i];
|
||||
SASSERT(l_true == ctx.get_assignment(lit));
|
||||
deps = m_dm.mk_join(deps, m_dm.mk_leaf(assumption(lit)));
|
||||
}
|
||||
|
|
@ -2554,7 +2626,7 @@ void theory_seq::propagate_eq(literal_vector const& lits, expr* e1, expr* e2, bo
|
|||
justification* js =
|
||||
ctx.mk_justification(
|
||||
ext_theory_eq_propagation_justification(
|
||||
get_id(), ctx.get_region(), lits.size(), lits.c_ptr(), 0, 0, n1, n2));
|
||||
get_id(), ctx.get_region(), lits.size(), lits.c_ptr(), eqs.size(), eqs.c_ptr(), n1, n2));
|
||||
|
||||
m_new_propagation = true;
|
||||
ctx.assign_eq(n1, n2, eq_justification(js));
|
||||
|
|
|
|||
|
|
@ -335,7 +335,8 @@ namespace smt {
|
|||
bool propagate_max_length(expr* l, expr* r, dependency* dep);
|
||||
|
||||
bool get_length(expr* s, expr_ref& len, literal_vector& lits);
|
||||
bool reduce_length(expr* l, expr* r);
|
||||
bool reduce_length(expr* l, expr* r, literal_vector& lits);
|
||||
bool reduce_length_eq(expr_ref_vector const& ls, expr_ref_vector const& rs, dependency* deps);
|
||||
|
||||
expr_ref mk_empty(sort* s) { return expr_ref(m_util.str.mk_empty(s), m); }
|
||||
expr_ref mk_concat(unsigned n, expr*const* es) { return expr_ref(m_util.str.mk_concat(n, es), m); }
|
||||
|
|
@ -365,7 +366,7 @@ namespace smt {
|
|||
void propagate_lit(dependency* dep, unsigned n, literal const* lits, literal lit);
|
||||
void propagate_eq(dependency* dep, enode* n1, enode* n2);
|
||||
void propagate_eq(literal lit, expr* e1, expr* e2, bool add_to_eqs);
|
||||
void propagate_eq(literal_vector const& lits, expr* e1, expr* e2, bool add_to_eqs);
|
||||
void propagate_eq(dependency* dep, literal_vector const& lits, expr* e1, expr* e2, bool add_to_eqs);
|
||||
void set_conflict(dependency* dep, literal_vector const& lits = literal_vector());
|
||||
|
||||
u_map<unsigned> m_branch_start;
|
||||
|
|
@ -384,6 +385,7 @@ namespace smt {
|
|||
bool is_tail(expr* a, expr*& s, unsigned& idx) const;
|
||||
bool is_eq(expr* e, expr*& a, expr*& b) const;
|
||||
bool is_pre(expr* e, expr*& s, expr*& i);
|
||||
bool is_post(expr* e, expr*& s, expr*& i);
|
||||
expr_ref mk_nth(expr* s, expr* idx);
|
||||
expr_ref mk_last(expr* e);
|
||||
expr_ref mk_first(expr* e);
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue