1 /*++
2 Copyright (c) 2010 Microsoft Corporation
3
4 Module Name:
5
6 quant_hoist.cpp
7
8 Abstract:
9
10 Quantifier hoisting utility.
11
12 Author:
13
14 Nikolaj Bjorner (nbjorner) 2010-02-19
15
16 Revision History:
17
18 Hoisted from quant_elim.
19
20 --*/
21
22 #include "ast/rewriter/quant_hoist.h"
23 #include "ast/expr_functors.h"
24 #include "ast/ast_smt_pp.h"
25 #include "ast/rewriter/bool_rewriter.h"
26 #include "ast/rewriter/var_subst.h"
27 #include "ast/ast_pp.h"
28 #include "ast/rewriter/ast_counter.h"
29 #include "ast/rewriter/expr_safe_replace.h"
30
31 //
32 // Bring quantifiers of common type into prenex form.
33 //
34 class quantifier_hoister::impl {
35 ast_manager& m;
36 bool_rewriter m_rewriter;
37
38 public:
impl(ast_manager & m)39 impl(ast_manager& m) :
40 m(m),
41 m_rewriter(m)
42 {}
43
operator ()(expr * fml,app_ref_vector & vars,bool & is_fa,expr_ref & result,bool use_fresh,bool rewrite_ok)44 void operator()(expr* fml, app_ref_vector& vars, bool& is_fa, expr_ref& result, bool use_fresh, bool rewrite_ok) {
45 quantifier_type qt = Q_none_pos;
46 pull_quantifier(fml, qt, vars, result, use_fresh, rewrite_ok);
47 TRACE("qe_verbose",
48 tout << mk_pp(fml, m) << "\n";
49 tout << mk_pp(result, m) << "\n";);
50 SASSERT(is_positive(qt));
51 is_fa = (Q_forall_pos == qt);
52 }
53
pull_exists(expr * fml,app_ref_vector & vars,expr_ref & result,bool use_fresh,bool rewrite_ok)54 void pull_exists(expr* fml, app_ref_vector& vars, expr_ref& result, bool use_fresh, bool rewrite_ok) {
55 quantifier_type qt = Q_exists_pos;
56 pull_quantifier(fml, qt, vars, result, use_fresh, rewrite_ok);
57 TRACE("qe_verbose",
58 tout << mk_pp(fml, m) << "\n";
59 tout << mk_pp(result, m) << "\n";);
60 }
61
pull_quantifier(bool is_forall,expr_ref & fml,app_ref_vector & vars,bool use_fresh,bool rewrite_ok)62 void pull_quantifier(bool is_forall, expr_ref& fml, app_ref_vector& vars, bool use_fresh, bool rewrite_ok) {
63 quantifier_type qt = is_forall?Q_forall_pos:Q_exists_pos;
64 expr_ref result(m);
65 pull_quantifier(fml, qt, vars, result, use_fresh, rewrite_ok);
66 TRACE("qe_verbose",
67 tout << mk_pp(fml, m) << "\n";
68 tout << mk_pp(result, m) << "\n";);
69 fml = std::move(result);
70 }
71
extract_quantifier(quantifier * q,app_ref_vector & vars,expr_ref & result,bool use_fresh)72 void extract_quantifier(quantifier* q, app_ref_vector& vars, expr_ref& result, bool use_fresh) {
73 unsigned nd = q->get_num_decls();
74 for (unsigned i = 0; i < nd; ++i) {
75 sort* s = q->get_decl_sort(i);
76 symbol const& sym = q->get_decl_name (i);
77 app* a = use_fresh ? m.mk_fresh_const(sym.str ().c_str (), s)
78 : m.mk_const (sym, s);
79 vars.push_back(a);
80 }
81 expr * const * exprs = (expr* const*) (vars.data() + vars.size()- nd);
82 result = instantiate(m, q, exprs);
83 }
84
pull_quantifier(bool _is_forall,expr_ref & fml,ptr_vector<sort> * sorts,svector<symbol> * names,bool use_fresh,bool rewrite_ok)85 unsigned pull_quantifier(bool _is_forall, expr_ref& fml, ptr_vector<sort>* sorts, svector<symbol>* names, bool use_fresh, bool rewrite_ok) {
86 unsigned index = var_counter().get_next_var(fml);
87 while (is_quantifier(fml) && _is_forall == is_forall(fml)) {
88 quantifier* q = to_quantifier(fml);
89 index += q->get_num_decls();
90 if (names) {
91 names->append(q->get_num_decls(), q->get_decl_names());
92 }
93 if (sorts) {
94 sorts->append(q->get_num_decls(), q->get_decl_sorts());
95 }
96 fml = q->get_expr();
97 }
98 if (!has_quantifiers(fml)) {
99 return index;
100 }
101 app_ref_vector vars(m);
102 pull_quantifier(_is_forall, fml, vars, use_fresh, rewrite_ok);
103 if (vars.empty()) {
104 return index;
105 }
106 // replace vars by de-bruijn indices
107 expr_safe_replace rep(m);
108 svector<symbol> bound_names;
109 ptr_vector<sort> bound_sorts;
110 for (unsigned i = 0; i < vars.size(); ++i) {
111 app* v = vars[i].get();
112 if (names) {
113 bound_names.push_back(v->get_decl()->get_name());
114 }
115 if (sorts) {
116 bound_sorts.push_back(v->get_sort());
117 }
118 rep.insert(v, m.mk_var(index++, v->get_sort()));
119 }
120 if (names && !bound_names.empty()) {
121 bound_names.reverse();
122 bound_names.append(*names);
123 names->reset();
124 names->append(bound_names);
125 }
126 if (sorts && !bound_sorts.empty()) {
127 bound_sorts.reverse();
128 bound_sorts.append(*sorts);
129 sorts->reset();
130 sorts->append(bound_sorts);
131 }
132 rep(fml);
133 return index;
134 }
135
136 private:
137
138 enum quantifier_type {
139 Q_forall_pos = 0x10,
140 Q_exists_pos = 0x20,
141 Q_none_pos = 0x40,
142 Q_forall_neg = 0x11,
143 Q_exists_neg = 0x21,
144 Q_none_neg = 0x41
145 };
146
display(quantifier_type qt,std::ostream & out)147 void display(quantifier_type qt, std::ostream& out) {
148 switch(qt) {
149 case Q_forall_pos: out << "Forall+"; break;
150 case Q_exists_pos: out << "Exists+"; break;
151 case Q_none_pos: out << "None+"; break;
152 case Q_forall_neg: out << "Forall-"; break;
153 case Q_exists_neg: out << "Exists-"; break;
154 case Q_none_neg: out << "None-"; break;
155 }
156 }
157
negate(quantifier_type & qt)158 quantifier_type& negate(quantifier_type& qt) {
159 qt = static_cast<quantifier_type>(qt ^0x1);
160 return qt;
161 }
162
is_negative(quantifier_type qt)163 static bool is_negative(quantifier_type qt) {
164 return 0 != (qt & 0x1);
165 }
166
is_positive(quantifier_type qt)167 static bool is_positive(quantifier_type qt) {
168 return 0 == (qt & 0x1);
169 }
170
set_quantifier_type(quantifier_type & qt,bool is_forall)171 static void set_quantifier_type(quantifier_type& qt, bool is_forall) {
172 switch(qt) {
173 case Q_forall_pos: SASSERT(is_forall); break;
174 case Q_forall_neg: SASSERT(!is_forall); break;
175 case Q_exists_pos: SASSERT(!is_forall); break;
176 case Q_exists_neg: SASSERT(is_forall); break;
177 case Q_none_pos: qt = is_forall?Q_forall_pos:Q_exists_pos; break;
178 case Q_none_neg: qt = is_forall?Q_exists_neg:Q_forall_neg; break;
179 }
180 }
181
is_compatible(quantifier_type qt,bool is_forall)182 bool is_compatible(quantifier_type qt, bool is_forall) {
183 switch(qt) {
184 case Q_forall_pos: return is_forall;
185 case Q_forall_neg: return !is_forall;
186 case Q_exists_pos: return !is_forall;
187 case Q_exists_neg: return is_forall;
188 case Q_none_pos: return true;
189 case Q_none_neg: return true;
190 default:
191 UNREACHABLE();
192 }
193 return false;
194 }
195
196
pull_quantifier(expr * fml,quantifier_type & qt,app_ref_vector & vars,expr_ref & result,bool use_fresh,bool rewrite_ok)197 void pull_quantifier(expr* fml, quantifier_type& qt, app_ref_vector& vars, expr_ref& result, bool use_fresh, bool rewrite_ok) {
198
199 if (!has_quantifiers(fml)) {
200 result = fml;
201 return;
202 }
203
204 switch(fml->get_kind()) {
205 case AST_APP: {
206 expr_ref_vector args(m);
207 expr_ref tmp(m);
208 expr* t1, *t2, *t3;
209 unsigned num_args = 0;
210 app* a = to_app(fml);
211 if (m.is_and(fml)) {
212 num_args = a->get_num_args();
213 for (unsigned i = 0; i < num_args; ++i) {
214 pull_quantifier(a->get_arg(i), qt, vars, tmp, use_fresh, rewrite_ok);
215 args.push_back(tmp);
216 }
217 if (rewrite_ok)
218 m_rewriter.mk_and(args.size(), args.data(), result);
219 else
220 result = m.mk_and (args.size (), args.data ());
221 }
222 else if (m.is_or(fml)) {
223 num_args = to_app(fml)->get_num_args();
224 for (unsigned i = 0; i < num_args; ++i) {
225 pull_quantifier(to_app(fml)->get_arg(i), qt, vars, tmp, use_fresh, rewrite_ok);
226 args.push_back(tmp);
227 }
228 if (rewrite_ok)
229 m_rewriter.mk_or(args.size(), args.data(), result);
230 else
231 result = m.mk_or (args.size (), args.data ());
232 }
233 else if (m.is_not(fml)) {
234 pull_quantifier(to_app(fml)->get_arg(0), negate(qt), vars, tmp, use_fresh, rewrite_ok);
235 negate(qt);
236 result = m.mk_not(tmp);
237 }
238 else if (m.is_implies(fml, t1, t2)) {
239 pull_quantifier(t1, negate(qt), vars, tmp, use_fresh, rewrite_ok);
240 negate(qt);
241 pull_quantifier(t2, qt, vars, result, use_fresh, rewrite_ok);
242 result = m.mk_implies(tmp, result);
243 }
244 else if (m.is_ite(fml, t1, t2, t3)) {
245 expr_ref tt1(m), tt2(m), tt3(m), ntt1(m), nt1(m);
246 pull_quantifier(t2, qt, vars, tt2, use_fresh, rewrite_ok);
247 pull_quantifier(t3, qt, vars, tt3, use_fresh, rewrite_ok);
248 if (has_quantifiers(t1)) {
249 pull_quantifier(t1, qt, vars, tt1, use_fresh, rewrite_ok);
250 nt1 = m.mk_not(t1);
251 pull_quantifier(nt1, qt, vars, ntt1, use_fresh, rewrite_ok);
252 result = m.mk_and(m.mk_or(ntt1, tt2), m.mk_or(tt1, tt3));
253 }
254 else {
255 result = m.mk_ite(t1, tt2, tt3);
256 }
257 }
258 else if (m.is_eq(fml, t1, t2) && m.is_bool(t1)) {
259 expr_ref tt1(m), tt2(m), ntt1(m), ntt2(m), nt1(m), nt2(m);
260 pull_quantifier(t1, qt, vars, tt1, use_fresh, rewrite_ok);
261 pull_quantifier(t2, qt, vars, tt2, use_fresh, rewrite_ok);
262 nt1 = m.mk_not(t1);
263 nt2 = m.mk_not(t2);
264 pull_quantifier(nt1, qt, vars, ntt1, use_fresh, rewrite_ok);
265 pull_quantifier(nt2, qt, vars, ntt2, use_fresh, rewrite_ok);
266 result = m.mk_and(m.mk_or(ntt1, tt2), m.mk_or(ntt2, tt1));
267 }
268 else {
269 // the formula contains a quantifier, but it is "inaccessible"
270 result = fml;
271 }
272 break;
273 }
274 case AST_QUANTIFIER: {
275 quantifier* q = to_quantifier(fml);
276 if (is_lambda(q)) {
277 result = fml;
278 break;
279 }
280 expr_ref tmp(m);
281 if (!is_compatible(qt, is_forall(q))) {
282 result = fml;
283 break;
284 }
285 set_quantifier_type(qt, is_forall(q));
286 extract_quantifier(q, vars, tmp, use_fresh);
287 pull_quantifier(tmp, qt, vars, result, use_fresh, rewrite_ok);
288 break;
289 }
290 case AST_VAR:
291 result = fml;
292 break;
293 default:
294 UNREACHABLE();
295 result = fml;
296 break;
297 }
298 }
299
300 };
301
quantifier_hoister(ast_manager & m)302 quantifier_hoister::quantifier_hoister(ast_manager& m) {
303 m_impl = alloc(impl, m);
304 }
305
~quantifier_hoister()306 quantifier_hoister::~quantifier_hoister() {
307 dealloc(m_impl);
308 }
309
operator ()(expr * fml,app_ref_vector & vars,bool & is_fa,expr_ref & result,bool use_fresh,bool rewrite_ok)310 void quantifier_hoister::operator()(expr* fml, app_ref_vector& vars, bool& is_fa, expr_ref& result, bool use_fresh, bool rewrite_ok) {
311 (*m_impl)(fml, vars, is_fa, result, use_fresh, rewrite_ok);
312 }
313
pull_exists(expr * fml,app_ref_vector & vars,expr_ref & result,bool use_fresh,bool rewrite_ok)314 void quantifier_hoister::pull_exists(expr* fml, app_ref_vector& vars, expr_ref& result, bool use_fresh, bool rewrite_ok) {
315 m_impl->pull_exists(fml, vars, result, use_fresh, rewrite_ok);
316 }
317
pull_quantifier(bool is_forall,expr_ref & fml,app_ref_vector & vars,bool use_fresh,bool rewrite_ok)318 void quantifier_hoister::pull_quantifier(bool is_forall, expr_ref& fml, app_ref_vector& vars, bool use_fresh, bool rewrite_ok) {
319 m_impl->pull_quantifier(is_forall, fml, vars, use_fresh, rewrite_ok);
320 }
321
pull_quantifier(bool is_forall,expr_ref & fml,ptr_vector<sort> * sorts,svector<symbol> * names,bool use_fresh,bool rewrite_ok)322 unsigned quantifier_hoister::pull_quantifier(bool is_forall, expr_ref& fml, ptr_vector<sort>* sorts, svector<symbol>* names, bool use_fresh, bool rewrite_ok) {
323 return m_impl->pull_quantifier(is_forall, fml, sorts, names, use_fresh, rewrite_ok);
324 }
325