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
|
/********************* */
/*! \file fun_def_process.cpp
** \verbatim
** Original author: Andrew Reynolds
** Major contributors: Morgan Deters
** Minor contributors (to current version): Kshitij Bansal
** This file is part of the CVC4 project.
** Copyright (c) 2009-2014 New York University and The University of Iowa
** See the file COPYING in the top-level source directory for licensing
** information.\endverbatim
**
** \brief Sort inference module
**
** This class implements pre-process steps for well-defined functions
**/
#include <vector>
#include "theory/quantifiers/fun_def_process.h"
#include "theory/rewriter.h"
#include "theory/quantifiers/term_database.h"
#include "theory/quantifiers/quant_util.h"
using namespace CVC4;
using namespace std;
using namespace CVC4::theory;
using namespace CVC4::theory::quantifiers;
using namespace CVC4::kind;
void FunDefFmf::simplify( std::vector< Node >& assertions, bool doRewrite ) {
std::vector< int > fd_assertions;
//first pass : find defined functions, transform quantifiers
for( unsigned i=0; i<assertions.size(); i++ ){
if( assertions[i].getKind()==FORALL ){
if( quantifiers::TermDb::isFunDef( assertions[i] ) ){
Assert( assertions[i][1].getKind()==EQUAL || assertions[i][1].getKind()==IFF );
Node n = assertions[i][1][0];
Assert( n.getKind()==APPLY_UF );
Node f = n.getOperator();
//check if already defined, if so, throw error
if( d_sorts.find( f )!=d_sorts.end() ){
Message() << "Cannot define function " << f << " more than once." << std::endl;
exit( 0 );
}
//create a sort S that represents the inputs of the function
std::stringstream ss;
ss << "I_" << f;
TypeNode iType = NodeManager::currentNM()->mkSort( ss.str() );
d_sorts[f] = iType;
//create functions f1...fn mapping from this sort to concrete elements
for( unsigned j=0; j<n.getNumChildren(); j++ ){
TypeNode typ = NodeManager::currentNM()->mkFunctionType( iType, n[j].getType() );
std::stringstream ss;
ss << f << "_arg_" << j;
d_input_arg_inj[f].push_back( NodeManager::currentNM()->mkSkolem( ss.str(), typ, "op created during fun def fmf" ) );
}
//construct new quantifier forall S. F[f1(S)/x1....fn(S)/xn]
std::vector< Node > children;
Node bv = NodeManager::currentNM()->mkBoundVar("?i", iType );
Node bvl = NodeManager::currentNM()->mkNode( kind::BOUND_VAR_LIST, bv );
std::vector< Node > subs;
std::vector< Node > vars;
for( unsigned j=0; j<n.getNumChildren(); j++ ){
vars.push_back( n[j] );
subs.push_back( NodeManager::currentNM()->mkNode( APPLY_UF, d_input_arg_inj[f][j], bv ) );
}
Node bd = assertions[i][1].substitute( vars.begin(), vars.end(), subs.begin(), subs.end() );
Trace("fmf-fun-def") << "FMF fun def: rewrite " << assertions[i] << " to ";
assertions[i] = NodeManager::currentNM()->mkNode( FORALL, bvl, bd );
Trace("fmf-fun-def") << assertions[i] << std::endl;
fd_assertions.push_back( i );
}
}
}
//second pass : rewrite assertions
for( unsigned i=0; i<assertions.size(); i++ ){
bool is_fd = std::find( fd_assertions.begin(), fd_assertions.end(), i )!=fd_assertions.end();
std::vector< Node > constraints;
Node n = simplify( assertions[i], true, true, constraints, is_fd );
Assert( constraints.empty() );
if( n!=assertions[i] ){
n = Rewriter::rewrite( n );
Trace("fmf-fun-def-rewrite") << "FMF fun def : rewrite " << assertions[i] << " to " << n << std::endl;
assertions[i] = n;
}
}
}
Node FunDefFmf::simplify( Node n, bool pol, bool hasPol, std::vector< Node >& constraints, bool is_fun_def ) {
Trace("fmf-fun-def-debug") << "Simplify " << n << " " << pol << " " << hasPol << " " << is_fun_def << std::endl;
if( n.getKind()==FORALL ){
Node c = simplify( n[1], pol, hasPol, constraints, is_fun_def );
if( c!=n[1] ){
return NodeManager::currentNM()->mkNode( FORALL, n[0], c );
}else{
return n;
}
}else if( n.getType().isBoolean() && n.getKind()!=APPLY_UF ){
std::vector< Node > children;
bool childChanged = false;
for( unsigned i=0; i<n.getNumChildren(); i++ ){
Node c = n[i];
//do not process LHS of definition
if( !is_fun_def || i!=0 ){
bool newHasPol;
bool newPol;
QuantPhaseReq::getPolarity( n, i, hasPol, pol, newHasPol, newPol );
//get child constraints
std::vector< Node > cconstraints;
c = simplify( n[i], newPol, newHasPol, cconstraints );
constraints.insert( constraints.end(), cconstraints.begin(), cconstraints.end() );
}
children.push_back( c );
childChanged = c!=n[i] || childChanged;
}
if( !constraints.empty() || childChanged ){
std::vector< Node > c;
if( childChanged ){
c.push_back( NodeManager::currentNM()->mkNode( n.getKind(), children ) );
}else{
c.push_back( n );
}
if( hasPol ){
//conjoin with current
for( unsigned i=0; i<constraints.size(); i++ ){
if( pol ){
c.push_back( constraints[i] );
}else{
c.push_back( constraints[i].negate() );
}
}
constraints.clear();
}else{
//must add at higher level
}
return c.size()==1 ? c[0] : NodeManager::currentNM()->mkNode( AND, c );
}
}else{
//simplify term
simplifyTerm( n, constraints );
}
return n;
}
void FunDefFmf::simplifyTerm( Node n, std::vector< Node >& constraints ) {
Trace("fmf-fun-def-debug") << "Simplify term " << n << std::endl;
if( n.getKind()==ITE ){
simplifyTerm( n[0], constraints );
std::vector< Node > ccons1;
std::vector< Node > ccons2;
simplifyTerm( n[1], ccons1 );
simplifyTerm( n[2], ccons2 );
if( !ccons1.empty() || !ccons2.empty() ){
Node n1 = ccons1.empty() ? NodeManager::currentNM()->mkConst( true ) : ( ccons1.size()==1 ? ccons1[0] : NodeManager::currentNM()->mkNode( AND, ccons1 ) );
Node n2 = ccons2.empty() ? NodeManager::currentNM()->mkConst( true ) : ( ccons2.size()==1 ? ccons2[0] : NodeManager::currentNM()->mkNode( AND, ccons2 ) );
constraints.push_back( NodeManager::currentNM()->mkNode( ITE, n[0], n1, n2 ) );
}
}else{
if( n.getKind()==APPLY_UF ){
//check if f is defined, if so, we must enforce domain constraints for this f-application
Node f = n.getOperator();
std::map< Node, TypeNode >::iterator it = d_sorts.find( f );
if( it!=d_sorts.end() ){
//create existential
Node z = NodeManager::currentNM()->mkBoundVar("?z", it->second );
Node bvl = NodeManager::currentNM()->mkNode( BOUND_VAR_LIST, z );
std::vector< Node > children;
for( unsigned j=0; j<n.getNumChildren(); j++ ){
Node uz = NodeManager::currentNM()->mkNode( APPLY_UF, d_input_arg_inj[f][j], z );
if( !n[j].getType().isBoolean() ){
children.push_back( uz.eqNode( n[j] ) );
}else{
children.push_back( uz.iffNode( n[j] ) );
}
}
Node bd = children.size()==1 ? children[0] : NodeManager::currentNM()->mkNode( AND, children );
bd = bd.negate();
Node ex = NodeManager::currentNM()->mkNode( FORALL, bvl, bd );
ex = ex.negate();
constraints.push_back( ex );
Trace("fmf-fun-def-debug") << "---> add constraint " << ex << std::endl;
}
}
for( unsigned i=0; i<n.getNumChildren(); i++ ){
simplifyTerm( n[i], constraints );
}
}
}
|