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
|
/********************* */
/*! \file alpha_equivalence.h
** \verbatim
** Top contributors (to current version):
** Andrew Reynolds, Paul Meng
** This file is part of the CVC4 project.
** Copyright (c) 2009-2019 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.\endverbatim
**
** \brief Alpha equivalence checking
**/
#include "cvc4_private.h"
#ifndef __CVC4__ALPHA_EQUIVALENCE_H
#define __CVC4__ALPHA_EQUIVALENCE_H
#include "theory/quantifiers_engine.h"
namespace CVC4 {
namespace theory {
namespace quantifiers {
/**
* This is a discrimination tree index for terms. It handles variadic
* operators by indexing based on operator arity, and flattens multiple
* occurrences of subterms.
*
* For example, the term
* +( f( x ), +( a, f(x), b ) )
* is stored at:
* d_children[+][2].d_children[f][1].
* d_children[x][0].d_children[+][3].
* d_children[a][0].d_children[f(x)][0].
* d_children[b][0]
* Notice that the second occurrence of f(x) is flattened.
*/
class AlphaEquivalenceNode {
public:
/** children of this node */
std::map<Node, std::map<int, AlphaEquivalenceNode> > d_children;
/** the data at this node */
Node d_quant;
/** Registers term q to this trie. The term t is the canonical form of q. */
Node registerNode(Node q, Node t);
};
/**
* This trie stores a trie of the above form for each multi-set of types. For
* each term t registered to this node, we store t in the appropriate
* AlphaEquivalenceNode trie. For example, if t contains 2 free variables
* of type T1 and 3 free variables of type T2, then it is stored at
* d_children[T1][2].d_children[T2][3].
*/
class AlphaEquivalenceTypeNode {
public:
/** children of this node */
std::map<TypeNode, std::map<int, AlphaEquivalenceTypeNode> > d_children;
/** the database of terms at this node */
AlphaEquivalenceNode d_data;
/** register node
*
* This registers term q to this trie. The term t is the canonical form of
* q, typs/typ_count represent a multi-set of types of free variables in t.
*/
Node registerNode(Node q,
Node t,
std::vector<TypeNode>& typs,
std::map<TypeNode, int>& typ_count);
};
/**
* Stores a database of quantified formulas, which computes alpha-equivalence.
*/
class AlphaEquivalenceDb
{
public:
AlphaEquivalenceDb(TermCanonize* tc) : d_tc(tc) {}
/** adds quantified formula q to this database
*
* This function returns a quantified formula q' that is alpha-equivalent to
* q. If q' != q, then q' was previously added to this database via a call
* to addTerm.
*/
Node addTerm(Node q);
private:
/** a trie per # of variables per type */
AlphaEquivalenceTypeNode d_ae_typ_trie;
/** pointer to the term canonize utility */
TermCanonize* d_tc;
};
/**
* A quantifiers module that computes reductions based on alpha-equivalence,
* using the above utilities.
*/
class AlphaEquivalence
{
public:
AlphaEquivalence(QuantifiersEngine* qe);
~AlphaEquivalence(){}
/** reduce quantifier
*
* If non-null, its return value is lemma justifying why q is reducible.
* This is of the form ( q = q' ) where q' is a quantified formula that
* was previously registered to this class via a call to reduceQuantifier,
* and q and q' are alpha-equivalent.
*/
Node reduceQuantifier( Node q );
private:
/** the database of quantified formulas registered to this class */
AlphaEquivalenceDb d_aedb;
};
}
}
}
#endif
|
