1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
|
/******************************************************************************
* Top contributors (to current version):
* Mudathir Mohamed, Gereon Kremer
*
* This file is part of the cvc5 project.
*
* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS
* in the top-level source directory and their institutional affiliations.
* All rights reserved. See the file COPYING in the top-level source
* directory for licensing information.
* ****************************************************************************
*
* Bags theory rewriter.
*/
#include "cvc5_private.h"
#ifndef CVC5__THEORY__BAGS__THEORY_BAGS_REWRITER_H
#define CVC5__THEORY__BAGS__THEORY_BAGS_REWRITER_H
#include "theory/bags/rewrites.h"
#include "theory/theory_rewriter.h"
#include "util/statistics_stats.h"
namespace cvc5 {
namespace theory {
namespace bags {
/** a class represents the result of rewriting bag nodes */
struct BagsRewriteResponse
{
BagsRewriteResponse();
BagsRewriteResponse(Node n, Rewrite rewrite);
BagsRewriteResponse(const BagsRewriteResponse& r);
/** the rewritten node */
Node d_node;
/** type of rewrite used by bags */
Rewrite d_rewrite;
}; /* struct BagsRewriteResponse */
class BagsRewriter : public TheoryRewriter
{
public:
BagsRewriter(HistogramStat<Rewrite>* statistics = nullptr);
/**
* postRewrite nodes with kinds: MK_BAG, BAG_COUNT, UNION_MAX, UNION_DISJOINT,
* INTERSECTION_MIN, DIFFERENCE_SUBTRACT, DIFFERENCE_REMOVE, BAG_CHOOSE,
* BAG_CARD, BAG_IS_SINGLETON.
* See the rewrite rules for these kinds below.
*/
RewriteResponse postRewrite(TNode n) override;
/**
* preRewrite nodes with kinds: EQUAL, SUBBAG.
* See the rewrite rules for these kinds below.
*/
RewriteResponse preRewrite(TNode n) override;
private:
/**
* rewrites for n include:
* - (= A A) = true where A is a bag
*/
BagsRewriteResponse preRewriteEqual(const TNode& n) const;
/**
* rewrites for n include:
* - (bag.is_included A B) = ((difference_subtract A B) == emptybag)
*/
BagsRewriteResponse rewriteSubBag(const TNode& n) const;
/**
* rewrites for n include:
* - (bag x 0) = (emptybag T) where T is the type of x
* - (bag x (-c)) = (emptybag T) where T is the type of x, and c > 0 is a
* constant
* - otherwise = n
*/
BagsRewriteResponse rewriteMakeBag(const TNode& n) const;
/**
* rewrites for n include:
* - (bag.count x emptybag) = 0
* - (bag.count x (bag x c) = c
* - otherwise = n
*/
BagsRewriteResponse rewriteBagCount(const TNode& n) const;
/**
* rewrites for n include:
* - (duplicate_removal (bag x n)) = (bag x 1)
* where n is a positive constant
*/
BagsRewriteResponse rewriteDuplicateRemoval(const TNode& n) const;
/**
* rewrites for n include:
* - (union_max A emptybag) = A
* - (union_max emptybag A) = A
* - (union_max A A) = A
* - (union_max A (union_max A B)) = (union_max A B)
* - (union_max A (union_max B A)) = (union_max B A)
* - (union_max (union_max A B) A) = (union_max A B)
* - (union_max (union_max B A) A) = (union_max B A)
* - (union_max A (union_disjoint A B)) = (union_disjoint A B)
* - (union_max A (union_disjoint B A)) = (union_disjoint B A)
* - (union_max (union_disjoint A B) A) = (union_disjoint A B)
* - (union_max (union_disjoint B A) A) = (union_disjoint B A)
* - otherwise = n
*/
BagsRewriteResponse rewriteUnionMax(const TNode& n) const;
/**
* rewrites for n include:
* - (union_disjoint A emptybag) = A
* - (union_disjoint emptybag A) = A
* - (union_disjoint (union_max A B) (intersection_min A B)) =
* (union_disjoint A B) // sum(a,b) = max(a,b) + min(a,b)
* - other permutations of the above like swapping A and B, or swapping
* intersection_min and union_max
* - otherwise = n
*/
BagsRewriteResponse rewriteUnionDisjoint(const TNode& n) const;
/**
* rewrites for n include:
* - (intersection_min A emptybag) = emptybag
* - (intersection_min emptybag A) = emptybag
* - (intersection_min A A) = A
* - (intersection_min A (union_disjoint A B)) = A
* - (intersection_min A (union_disjoint B A)) = A
* - (intersection_min (union_disjoint A B) A) = A
* - (intersection_min (union_disjoint B A) A) = A
* - (intersection_min A (union_max A B)) = A
* - (intersection_min A (union_max B A)) = A
* - (intersection_min (union_max A B) A) = A
* - (intersection_min (union_max B A) A) = A
* - otherwise = n
*/
BagsRewriteResponse rewriteIntersectionMin(const TNode& n) const;
/**
* rewrites for n include:
* - (difference_subtract A emptybag) = A
* - (difference_subtract emptybag A) = emptybag
* - (difference_subtract A A) = emptybag
* - (difference_subtract (union_disjoint A B) A) = B
* - (difference_subtract (union_disjoint B A) A) = B
* - (difference_subtract A (union_disjoint A B)) = emptybag
* - (difference_subtract A (union_disjoint B A)) = emptybag
* - (difference_subtract A (union_max A B)) = emptybag
* - (difference_subtract A (union_max B A)) = emptybag
* - (difference_subtract (intersection_min A B) A) = emptybag
* - (difference_subtract (intersection_min B A) A) = emptybag
* - otherwise = n
*/
BagsRewriteResponse rewriteDifferenceSubtract(const TNode& n) const;
/**
* rewrites for n include:
* - (difference_remove A emptybag) = A
* - (difference_remove emptybag A) = emptybag
* - (difference_remove A A) = emptybag
* - (difference_remove A (union_disjoint A B)) = emptybag
* - (difference_remove A (union_disjoint B A)) = emptybag
* - (difference_remove A (union_max A B)) = emptybag
* - (difference_remove A (union_max B A)) = emptybag
* - (difference_remove (intersection_min A B) A) = emptybag
* - (difference_remove (intersection_min B A) A) = emptybag
* - otherwise = n
*/
BagsRewriteResponse rewriteDifferenceRemove(const TNode& n) const;
/**
* rewrites for n include:
* - (bag.choose (bag x c)) = x where c is a constant > 0
* - otherwise = n
*/
BagsRewriteResponse rewriteChoose(const TNode& n) const;
/**
* rewrites for n include:
* - (bag.card (bag x c)) = c where c is a constant > 0
* - (bag.card (union-disjoint A B)) = (+ (bag.card A) (bag.card B))
* - otherwise = n
*/
BagsRewriteResponse rewriteCard(const TNode& n) const;
/**
* rewrites for n include:
* - (bag.is_singleton (bag x c)) = (c == 1)
*/
BagsRewriteResponse rewriteIsSingleton(const TNode& n) const;
/**
* rewrites for n include:
* - (bag.from_set (singleton (singleton_op Int) x)) = (bag x 1)
*/
BagsRewriteResponse rewriteFromSet(const TNode& n) const;
/**
* rewrites for n include:
* - (bag.to_set (bag x n)) = (singleton (singleton_op T) x)
* where n is a positive constant and T is the type of the bag's elements
*/
BagsRewriteResponse rewriteToSet(const TNode& n) const;
/**
* rewrites for n include:
* - (= A A) = true
* - (= A B) = false if A and B are different bag constants
* - (= B A) = (= A B) if A < B and at least one of A or B is not a constant
*/
BagsRewriteResponse postRewriteEqual(const TNode& n) const;
private:
/** Reference to the rewriter statistics. */
NodeManager* d_nm;
Node d_zero;
Node d_one;
/** Reference to the rewriter statistics. */
HistogramStat<Rewrite>* d_statistics;
}; /* class TheoryBagsRewriter */
} // namespace bags
} // namespace theory
} // namespace cvc5
#endif /* CVC5__THEORY__BAGS__THEORY_BAGS_REWRITER_H */
|
