/*++ Copyright (c) 2011 Microsoft Corporation Module Name: th_rewriter.h Abstract: Rewriter for applying all builtin (cheap) theory rewrite rules. Author: Leonardo (leonardo) 2011-04-07 Notes: --*/ #include"th_rewriter.h" #include"bool_rewriter.h" #include"arith_rewriter.h" #include"bv_rewriter.h" #include"datatype_rewriter.h" #include"array_rewriter.h" #include"float_rewriter.h" #include"dl_rewriter.h" #include"rewriter_def.h" #include"expr_substitution.h" #include"ast_smt2_pp.h" #include"cooperate.h" #include"var_subst.h" #include"ast_util.h" #include"well_sorted.h" struct th_rewriter_cfg : public default_rewriter_cfg { bool_rewriter m_b_rw; arith_rewriter m_a_rw; bv_rewriter m_bv_rw; array_rewriter m_ar_rw; datatype_rewriter m_dt_rw; float_rewriter m_f_rw; dl_rewriter m_dl_rw; arith_util m_a_util; bv_util m_bv_util; unsigned long long m_max_memory; // in bytes unsigned m_max_steps; bool m_pull_cheap_ite; bool m_flat; bool m_cache_all; bool m_push_ite_arith; bool m_push_ite_bv; // substitution support expr_dependency_ref m_used_dependencies; // set of dependencies of used substitutions expr_substitution * m_subst; ast_manager & m() const { return m_b_rw.m(); } void updt_local_params(params_ref const & p) { m_flat = p.get_bool(":flat", true); m_max_memory = megabytes_to_bytes(p.get_uint(":max-memory", UINT_MAX)); m_max_steps = p.get_uint(":max-steps", UINT_MAX); m_pull_cheap_ite = p.get_bool(":pull-cheap-ite", false); m_cache_all = p.get_bool(":cache-all", false); m_push_ite_arith = p.get_bool(":push-ite-arith", false); m_push_ite_bv = p.get_bool(":push-ite-bv", false); } void updt_params(params_ref const & p) { m_b_rw.updt_params(p); m_a_rw.updt_params(p); m_bv_rw.updt_params(p); m_ar_rw.updt_params(p); updt_local_params(p); } bool flat_assoc(func_decl * f) const { if (!m_flat) return false; family_id fid = f->get_family_id(); if (fid == null_family_id) return false; decl_kind k = f->get_decl_kind(); if (fid == m_b_rw.get_fid()) return k == OP_AND || k == OP_OR; if (fid == m_a_rw.get_fid()) return k == OP_ADD; if (fid == m_bv_rw.get_fid()) return k == OP_BADD || k == OP_BOR || k == OP_BAND || k == OP_BXOR; return false; } bool rewrite_patterns() const { return false; } bool cache_all_results() const { return m_cache_all; } bool max_steps_exceeded(unsigned num_steps) const { cooperate("simplifier"); if (memory::get_allocation_size() > m_max_memory) throw rewriter_exception(TACTIC_MAX_MEMORY_MSG); return num_steps > m_max_steps; } // Return true if t is of the form // (= t #b0) // (= t #b1) // (= #b0 t) // (= #b1 t) bool is_eq_bit(expr * t, expr * & x, unsigned & val) { if (!m().is_eq(t)) return false; expr * lhs = to_app(t)->get_arg(0); if (!m_bv_rw.is_bv(lhs)) return false; if (m_bv_rw.get_bv_size(lhs) != 1) return false; expr * rhs = to_app(t)->get_arg(1); rational v; unsigned sz; if (m_bv_rw.is_numeral(lhs, v, sz)) { x = rhs; val = v.get_unsigned(); SASSERT(val == 0 || val == 1); return true; } if (m_bv_rw.is_numeral(rhs, v, sz)) { x = lhs; val = v.get_unsigned(); SASSERT(val == 0 || val == 1); return true; } return false; } // (iff (= x bit1) A) // ---> // (= x (ite A bit1 bit0)) br_status apply_tamagotchi(expr * lhs, expr * rhs, expr_ref & result) { expr * x; unsigned val; if (is_eq_bit(lhs, x, val)) { result = m().mk_eq(x, m().mk_ite(rhs, m_bv_rw.mk_numeral(val, 1), m_bv_rw.mk_numeral(1-val, 1))); return BR_REWRITE2; } if (is_eq_bit(rhs, x, val)) { result = m().mk_eq(x, m().mk_ite(lhs, m_bv_rw.mk_numeral(val, 1), m_bv_rw.mk_numeral(1-val, 1))); return BR_REWRITE2; } return BR_FAILED; } br_status reduce_app_core(func_decl * f, unsigned num, expr * const * args, expr_ref & result) { family_id fid = f->get_family_id(); if (fid == null_family_id) return BR_FAILED; br_status st = BR_FAILED; if (fid == m_b_rw.get_fid()) { decl_kind k = f->get_decl_kind(); if (k == OP_EQ) { // theory dispatch for = SASSERT(num == 2); family_id s_fid = m().get_sort(args[0])->get_family_id(); if (s_fid == m_a_rw.get_fid()) st = m_a_rw.mk_eq_core(args[0], args[1], result); else if (s_fid == m_bv_rw.get_fid()) st = m_bv_rw.mk_eq_core(args[0], args[1], result); else if (s_fid == m_dt_rw.get_fid()) st = m_dt_rw.mk_eq_core(args[0], args[1], result); else if (s_fid == m_f_rw.get_fid()) st = m_f_rw.mk_eq_core(args[0], args[1], result); if (st != BR_FAILED) return st; } if (k == OP_EQ || k == OP_IFF) { SASSERT(num == 2); st = apply_tamagotchi(args[0], args[1], result); if (st != BR_FAILED) return st; } return m_b_rw.mk_app_core(f, num, args, result); } if (fid == m_a_rw.get_fid()) return m_a_rw.mk_app_core(f, num, args, result); if (fid == m_bv_rw.get_fid()) return m_bv_rw.mk_app_core(f, num, args, result); if (fid == m_ar_rw.get_fid()) return m_ar_rw.mk_app_core(f, num, args, result); if (fid == m_dt_rw.get_fid()) return m_dt_rw.mk_app_core(f, num, args, result); if (fid == m_f_rw.get_fid()) return m_f_rw.mk_app_core(f, num, args, result); if (fid == m_dl_rw.get_fid()) return m_dl_rw.mk_app_core(f, num, args, result); return BR_FAILED; } // auxiliary function for pull_ite_core expr * mk_eq_value(expr * lhs, expr * value) { SASSERT(m().is_value(value)); if (m().is_value(lhs)) { return lhs == value ? m().mk_true() : m().mk_false(); } return m().mk_eq(lhs, value); } template br_status pull_ite_core(func_decl * p, app * ite, app * value, expr_ref & result) { if (m().is_eq(p)) { result = m().mk_ite(ite->get_arg(0), mk_eq_value(ite->get_arg(1), value), mk_eq_value(ite->get_arg(2), value)); return BR_REWRITE2; } else { if (SWAP) { result = m().mk_ite(ite->get_arg(0), m().mk_app(p, value, ite->get_arg(1)), m().mk_app(p, value, ite->get_arg(2))); return BR_REWRITE2; } else { result = m().mk_ite(ite->get_arg(0), m().mk_app(p, ite->get_arg(1), value), m().mk_app(p, ite->get_arg(2), value)); return BR_REWRITE2; } } } // Return true if t is an ite-value-tree form defined as: // ite-value-tree := (ite c ) // subtree := value // | (ite c ) // bool is_ite_value_tree(expr * t) { if (!m().is_ite(t)) return false; ptr_buffer todo; todo.push_back(to_app(t)); while (!todo.empty()) { app * ite = todo.back(); todo.pop_back(); expr * arg1 = ite->get_arg(1); expr * arg2 = ite->get_arg(2); if (m().is_ite(arg1) && arg1->get_ref_count() == 1) // do not apply on shared terms, since it may blowup todo.push_back(to_app(arg1)); else if (!m().is_value(arg1)) return false; if (m().is_ite(arg2) && arg2->get_ref_count() == 1) // do not apply on shared terms, since it may blowup todo.push_back(to_app(arg2)); else if (!m().is_value(arg2)) return false; } return true; } br_status pull_ite(func_decl * f, unsigned num, expr * const * args, expr_ref & result) { if (num == 2 && m().is_bool(f->get_range()) && !m().is_bool(args[0])) { if (m().is_ite(args[0])) { if (m().is_value(args[1])) return pull_ite_core(f, to_app(args[0]), to_app(args[1]), result); if (m().is_ite(args[1]) && to_app(args[0])->get_arg(0) == to_app(args[1])->get_arg(0)) { // (p (ite C A1 B1) (ite C A2 B2)) --> (ite (p A1 A2) (p B1 B2)) result = m().mk_ite(to_app(args[0])->get_arg(0), m().mk_app(f, to_app(args[0])->get_arg(1), to_app(args[1])->get_arg(1)), m().mk_app(f, to_app(args[0])->get_arg(2), to_app(args[1])->get_arg(2))); return BR_REWRITE2; } } if (m().is_ite(args[1]) && m().is_value(args[0])) return pull_ite_core(f, to_app(args[1]), to_app(args[0]), result); } family_id fid = f->get_family_id(); if (num == 2 && (fid == m().get_basic_family_id() || fid == m_a_rw.get_fid() || fid == m_bv_rw.get_fid())) { // (f v3 (ite c v1 v2)) --> (ite v (f v3 v1) (f v3 v2)) if (m().is_value(args[0]) && is_ite_value_tree(args[1])) return pull_ite_core(f, to_app(args[1]), to_app(args[0]), result); // (f (ite c v1 v2) v3) --> (ite v (f v1 v3) (f v2 v3)) if (m().is_value(args[1]) && is_ite_value_tree(args[0])) return pull_ite_core(f, to_app(args[0]), to_app(args[1]), result); } return BR_FAILED; } br_status pull_ite(expr_ref & result) { expr * t = result.get(); if (is_app(t)) { br_status st = pull_ite(to_app(t)->get_decl(), to_app(t)->get_num_args(), to_app(t)->get_args(), result); if (st != BR_FAILED) return st; } return BR_DONE; } bool is_arith_bv_app(expr * t) const { if (!is_app(t)) return false; family_id fid = to_app(t)->get_family_id(); return ((fid == m_a_rw.get_fid() && m_push_ite_arith) || (fid == m_bv_rw.get_fid() && m_push_ite_bv)); } bool get_neutral_elem(app * t, expr_ref & n) { family_id fid = t->get_family_id(); if (fid == m_a_rw.get_fid()) { switch (t->get_decl_kind()) { case OP_ADD: n = m_a_util.mk_numeral(rational(0), m().get_sort(t)); return true; case OP_MUL: n = m_a_util.mk_numeral(rational(1), m().get_sort(t)); return true; default: return false; } } if (fid == m_bv_rw.get_fid()) { switch (t->get_decl_kind()) { case OP_BADD: n = m_bv_util.mk_numeral(rational(0), m().get_sort(t)); return true; case OP_BMUL: n = m_bv_util.mk_numeral(rational(1), m().get_sort(t)); return true; default: return false; } } return false; } /** \brief Try to "unify" t1 and t2 Examples (+ 2 a) (+ 3 a) --> 2, 3, a (+ 2 a) a --> 2, 0, a ... */ bool unify_core(app * t1, expr * t2, expr_ref & new_t1, expr_ref & new_t2, expr_ref & c, bool & first) { if (t1->get_num_args() != 2) return false; expr * a1 = t1->get_arg(0); expr * b1 = t1->get_arg(1); if (t2 == b1) { if (get_neutral_elem(t1, new_t2)) { new_t1 = a1; c = b1; first = false; return true; } } else if (t2 == a1) { if (get_neutral_elem(t1, new_t2)) { new_t1 = b1; c = a1; first = true; return true; } } else if (is_app_of(t2, t1->get_decl()) && to_app(t2)->get_num_args() == 2) { expr * a2 = to_app(t2)->get_arg(0); expr * b2 = to_app(t2)->get_arg(1); if (b1 == b2) { new_t1 = a1; new_t2 = a2; c = b2; first = false; return true; } if (a1 == a2) { new_t1 = b1; new_t2 = b2; c = a1; first = true; return true; } if (t1->get_decl()->is_commutative()) { if (a1 == b2) { new_t1 = b1; new_t2 = a2; c = a1; first = true; // doesn't really matter for commutative ops. return true; } if (b1 == a2) { new_t1 = a1; new_t2 = b2; c = b1; first = false; // doesn't really matter for commutative ops. return true; } } } return false; } // Return true if t1 and t2 are of the form: // t + a1*x1 + ... + an*xn // t' + a1*x1 + ... + an*xn // Store t in new_t1, t' in new_t2 and (a1*x1 + ... + an*xn) in c. bool unify_add(app * t1, expr * t2, expr_ref & new_t1, expr_ref & new_t2, expr_ref & c) { unsigned num1 = t1->get_num_args(); expr * const * ms1 = t1->get_args(); if (num1 < 2) return false; unsigned num2; expr * const * ms2; if (m_a_util.is_add(t2)) { num2 = to_app(t2)->get_num_args(); ms2 = to_app(t2)->get_args(); } else { num2 = 1; ms2 = &t2; } if (num1 != num2 && num1 != num2 + 1 && num1 != num2 - 1) return false; new_t1 = 0; new_t2 = 0; expr_fast_mark1 visited1; expr_fast_mark2 visited2; for (unsigned i = 0; i < num1; i++) { expr * arg = ms1[i]; visited1.mark(arg); } for (unsigned i = 0; i < num2; i++) { expr * arg = ms2[i]; visited2.mark(arg); if (visited1.is_marked(arg)) continue; if (new_t2) return false; // more than one missing term new_t2 = arg; } for (unsigned i = 0; i < num1; i++) { expr * arg = ms1[i]; if (visited2.is_marked(arg)) continue; if (new_t1) return false; // more than one missing term new_t1 = arg; } // terms matched... bool is_int = m_a_util.is_int(t1); if (!new_t1) new_t1 = m_a_util.mk_numeral(rational(0), is_int); if (!new_t2) new_t2 = m_a_util.mk_numeral(rational(0), is_int); // mk common part ptr_buffer args; for (unsigned i = 0; i < num1; i++) { expr * arg = ms1[i]; if (arg == new_t1.get()) continue; args.push_back(arg); } SASSERT(!args.empty()); if (args.size() == 1) c = args[0]; else c = m_a_util.mk_add(args.size(), args.c_ptr()); return true; } bool unify(expr * t1, expr * t2, func_decl * & f, expr_ref & new_t1, expr_ref & new_t2, expr_ref & c, bool & first) { #if 0 // Did not work for ring benchmarks // Hack for handling more complex cases of + apps // such as (+ 2 t1 t2 t3) and (+ 3 t3 t2 t1) if (m_a_util.is_add(t1)) { first = true; // doesn't matter for AC ops f = to_app(t1)->get_decl(); if (unify_add(to_app(t1), t2, new_t1, new_t2, c)) return true; } if (m_a_util.is_add(t2)) { first = true; // doesn't matter for AC ops f = to_app(t2)->get_decl(); if (unify_add(to_app(t2), t1, new_t2, new_t1, c)) return true; } #endif if (is_arith_bv_app(t1)) { f = to_app(t1)->get_decl(); return unify_core(to_app(t1), t2, new_t1, new_t2, c, first); } else { f = to_app(t2)->get_decl(); return unify_core(to_app(t2), t1, new_t2, new_t1, c, first); } } // Apply transformations of the form // // (ite c (+ k1 a) (+ k2 a)) --> (+ (ite c k1 k2) a) // (ite c (* k1 a) (* k2 a)) --> (* (ite c k1 k2) a) // // These transformations are useful for bit-vector problems, since // they will minimize the number of adders/multipliers/etc br_status push_ite(func_decl * f, unsigned num, expr * const * args, expr_ref & result) { if (!m().is_ite(f)) return BR_FAILED; expr * c = args[0]; expr * t = args[1]; expr * e = args[2]; func_decl * f_prime = 0; expr_ref new_t(m()), new_e(m()), common(m()); bool first; TRACE("push_ite", tout << "unifying:\n" << mk_ismt2_pp(t, m()) << "\n" << mk_ismt2_pp(e, m()) << "\n";); if (unify(t, e, f_prime, new_t, new_e, common, first)) { if (first) result = m().mk_app(f_prime, common, m().mk_ite(c, new_t, new_e)); else result = m().mk_app(f_prime, m().mk_ite(c, new_t, new_e), common); return BR_DONE; } TRACE("push_ite", tout << "failed\n";); return BR_FAILED; } br_status push_ite(expr_ref & result) { expr * t = result.get(); if (m().is_ite(t)) { br_status st = push_ite(to_app(t)->get_decl(), to_app(t)->get_num_args(), to_app(t)->get_args(), result); if (st != BR_FAILED) return st; } return BR_DONE; } br_status reduce_app(func_decl * f, unsigned num, expr * const * args, expr_ref & result, proof_ref & result_pr) { result_pr = 0; br_status st = reduce_app_core(f, num, args, result); if (st != BR_DONE && st != BR_FAILED) { CTRACE("th_rewriter_step", st != BR_FAILED, tout << f->get_name() << "\n"; for (unsigned i = 0; i < num; i++) tout << mk_ismt2_pp(args[i], m()) << "\n"; tout << "---------->\n" << mk_ismt2_pp(result, m()) << "\n";); return st; } if (m_push_ite_bv || m_push_ite_arith) { if (st == BR_FAILED) st = push_ite(f, num, args, result); else st = push_ite(result); } if (m_pull_cheap_ite) { if (st == BR_FAILED) st = pull_ite(f, num, args, result); else st = pull_ite(result); } CTRACE("th_rewriter_step", st != BR_FAILED, tout << f->get_name() << "\n"; for (unsigned i = 0; i < num; i++) tout << mk_ismt2_pp(args[i], m()) << "\n"; tout << "---------->\n" << mk_ismt2_pp(result, m()) << "\n";); return st; } bool reduce_quantifier(quantifier * old_q, expr * new_body, expr * const * new_patterns, expr * const * new_no_patterns, expr_ref & result, proof_ref & result_pr) { quantifier_ref q1(m()); proof * p1 = 0; if (is_quantifier(new_body) && to_quantifier(new_body)->is_forall() == old_q->is_forall() && !old_q->has_patterns() && !to_quantifier(new_body)->has_patterns()) { quantifier * nested_q = to_quantifier(new_body); ptr_buffer sorts; buffer names; sorts.append(old_q->get_num_decls(), old_q->get_decl_sorts()); names.append(old_q->get_num_decls(), old_q->get_decl_names()); sorts.append(nested_q->get_num_decls(), nested_q->get_decl_sorts()); names.append(nested_q->get_num_decls(), nested_q->get_decl_names()); q1 = m().mk_quantifier(old_q->is_forall(), sorts.size(), sorts.c_ptr(), names.c_ptr(), nested_q->get_expr(), std::min(old_q->get_weight(), nested_q->get_weight()), old_q->get_qid(), old_q->get_skid(), 0, 0, 0, 0); SASSERT(is_well_sorted(m(), q1)); if (m().proofs_enabled()) { SASSERT(old_q->get_expr() == new_body); p1 = m().mk_pull_quant(old_q, q1); } } else { ptr_buffer new_patterns_buf; ptr_buffer new_no_patterns_buf; new_patterns_buf.append(old_q->get_num_patterns(), new_patterns); new_no_patterns_buf.append(old_q->get_num_no_patterns(), new_no_patterns); remove_duplicates(new_patterns_buf); remove_duplicates(new_no_patterns_buf); q1 = m().update_quantifier(old_q, new_patterns_buf.size(), new_patterns_buf.c_ptr(), new_no_patterns_buf.size(), new_no_patterns_buf.c_ptr(), new_body); TRACE("reduce_quantifier", tout << mk_ismt2_pp(old_q, m()) << "\n----->\n" << mk_ismt2_pp(q1, m()) << "\n";); SASSERT(is_well_sorted(m(), q1)); } elim_unused_vars(m(), q1, result); TRACE("reduce_quantifier", tout << "after elim_unused_vars:\n" << mk_ismt2_pp(result, m()) << "\n";); result_pr = 0; if (m().proofs_enabled()) { proof * p2 = 0; if (q1.get() != result.get()) p2 = m().mk_elim_unused_vars(q1, result); result_pr = m().mk_transitivity(p1, p2); } return true; } th_rewriter_cfg(ast_manager & m, params_ref const & p): m_b_rw(m, p), m_a_rw(m, p), m_bv_rw(m, p), m_ar_rw(m, p), m_dt_rw(m), m_f_rw(m, p), m_dl_rw(m), m_a_util(m), m_bv_util(m), m_used_dependencies(m), m_subst(0) { updt_local_params(p); } void set_substitution(expr_substitution * s) { reset(); m_subst = s; } void reset() { m_subst = 0; } bool get_subst(expr * s, expr * & t, proof * & pr) { if (m_subst == 0) return false; expr_dependency * d = 0; if (m_subst->find(s, t, pr, d)) { m_used_dependencies = m().mk_join(m_used_dependencies, d); return true; } return false; } void set_cancel(bool f) { m_a_rw.set_cancel(f); } }; template class rewriter_tpl; struct th_rewriter::imp : public rewriter_tpl { th_rewriter_cfg m_cfg; imp(ast_manager & m, params_ref const & p): rewriter_tpl(m, m.proofs_enabled(), m_cfg), m_cfg(m, p) { } }; th_rewriter::th_rewriter(ast_manager & m, params_ref const & p): m_params(p) { m_imp = alloc(imp, m, p); } ast_manager & th_rewriter::m() const { return m_imp->m(); } void th_rewriter::updt_params(params_ref const & p) { m_params = p; m_imp->cfg().updt_params(p); } void th_rewriter::get_param_descrs(param_descrs & r) { bool_rewriter::get_param_descrs(r); arith_rewriter::get_param_descrs(r); bv_rewriter::get_param_descrs(r); array_rewriter::get_param_descrs(r); insert_max_memory(r); insert_max_steps(r); r.insert(":push-ite-arith", CPK_BOOL, "(default: false) push if-then-else over arithmetic terms."); r.insert(":push-ite-bv", CPK_BOOL, "(default: false) push if-then-else over bit-vector terms."); r.insert(":pull-cheap-ite", CPK_BOOL, "(default: false) pull if-then-else terms when cheap."); r.insert(":cache-all", CPK_BOOL, "(default: false) cache all intermediate results."); } th_rewriter::~th_rewriter() { dealloc(m_imp); } unsigned th_rewriter::get_cache_size() const { return m_imp->get_cache_size(); } unsigned th_rewriter::get_num_steps() const { return m_imp->get_num_steps(); } void th_rewriter::set_cancel(bool f) { #pragma omp critical (th_rewriter) { m_imp->set_cancel(f); m_imp->cfg().set_cancel(f); } } void th_rewriter::cleanup() { ast_manager & m = m_imp->m(); #pragma omp critical (th_rewriter) { dealloc(m_imp); m_imp = alloc(imp, m, m_params); } } void th_rewriter::reset() { m_imp->reset(); m_imp->cfg().reset(); } void th_rewriter::operator()(expr_ref & term) { expr_ref result(term.get_manager()); m_imp->operator()(term, result); term = result; } void th_rewriter::operator()(expr * t, expr_ref & result) { m_imp->operator()(t, result); } void th_rewriter::operator()(expr * t, expr_ref & result, proof_ref & result_pr) { m_imp->operator()(t, result, result_pr); } void th_rewriter::operator()(expr * n, unsigned num_bindings, expr * const * bindings, expr_ref & result) { m_imp->operator()(n, num_bindings, bindings, result); } void th_rewriter::set_substitution(expr_substitution * s) { m_imp->reset(); // reset the cache m_imp->cfg().set_substitution(s); } expr_dependency * th_rewriter::get_used_dependencies() { return m_imp->cfg().m_used_dependencies; } void th_rewriter::reset_used_dependencies() { if (get_used_dependencies() != 0) { set_substitution(m_imp->cfg().m_subst); // reset cache preserving subst m_imp->cfg().m_used_dependencies = 0; } }