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/****************************************************************************** |
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* Top contributors (to current version): |
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* Tim King, Dejan Jovanovic, Haniel Barbosa |
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* |
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* This file is part of the cvc5 project. |
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* |
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* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS |
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* in the top-level source directory and their institutional affiliations. |
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* All rights reserved. See the file COPYING in the top-level source |
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* directory for licensing information. |
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* **************************************************************************** |
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* |
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* [[ Add one-line brief description here ]] |
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* |
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* [[ Add lengthier description here ]] |
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* \todo document this file |
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*/ |
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#include "theory/booleans/theory_bool_rewriter.h" |
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#include <algorithm> |
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#include <unordered_set> |
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#include "expr/node_value.h" |
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#include "util/cardinality.h" |
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namespace cvc5 { |
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namespace theory { |
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namespace booleans { |
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|
31 |
12130253 |
RewriteResponse TheoryBoolRewriter::postRewrite(TNode node) { |
32 |
12130253 |
return preRewrite(node); |
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} |
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|
35 |
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/** |
36 |
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* flattenNode looks for children of same kind, and if found merges |
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* them into the parent. |
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* |
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* It simultaneously handles a couple of other optimizations: |
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* - trivialNode - if found during exploration, return that node itself |
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* (like in case of OR, if "true" is found, makes sense to replace |
42 |
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* whole formula with "true") |
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* - skipNode - as name suggests, skip them |
44 |
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* (like in case of OR, you may want to skip any "false" nodes found) |
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* |
46 |
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* Use a null node if you want to ignore any of the optimizations. |
47 |
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*/ |
48 |
716971 |
RewriteResponse flattenNode(TNode n, TNode trivialNode, TNode skipNode) |
49 |
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{ |
50 |
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typedef std::unordered_set<TNode> node_set; |
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|
52 |
1433942 |
node_set visited; |
53 |
716971 |
visited.insert(skipNode); |
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|
55 |
1433942 |
std::vector<TNode> toProcess; |
56 |
716971 |
toProcess.push_back(n); |
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|
58 |
716971 |
Kind k = n.getKind(); |
59 |
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typedef std::vector<TNode> ChildList; |
60 |
1433942 |
ChildList childList; //TNode should be fine, since 'n' is still there |
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|
62 |
2082837 |
for (unsigned i = 0; i < toProcess.size(); ++ i) { |
63 |
2746776 |
TNode current = toProcess[i]; |
64 |
8338165 |
for(unsigned j = 0, j_end = current.getNumChildren(); j < j_end; ++ j) { |
65 |
12754193 |
TNode child = current[j]; |
66 |
6972299 |
if(visited.find(child) != visited.end()) { |
67 |
1175361 |
continue; |
68 |
5796938 |
} else if(child == trivialNode) { |
69 |
15044 |
return RewriteResponse(REWRITE_DONE, trivialNode); |
70 |
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} else { |
71 |
5781894 |
visited.insert(child); |
72 |
5781894 |
if(child.getKind() == k) |
73 |
664773 |
toProcess.push_back(child); |
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else |
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5117121 |
childList.push_back(child); |
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} |
77 |
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} |
78 |
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} |
79 |
701927 |
if (childList.size() == 0) return RewriteResponse(REWRITE_DONE, skipNode); |
80 |
610941 |
if (childList.size() == 1) return RewriteResponse(REWRITE_AGAIN, childList[0]); |
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|
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/* Trickery to stay under number of children possible in a node */ |
83 |
465515 |
NodeManager* nodeManager = NodeManager::currentNM(); |
84 |
465515 |
if (childList.size() < expr::NodeValue::MAX_CHILDREN) |
85 |
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{ |
86 |
931030 |
Node retNode = nodeManager->mkNode(k, childList); |
87 |
465515 |
return RewriteResponse(REWRITE_DONE, retNode); |
88 |
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} |
89 |
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else |
90 |
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{ |
91 |
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Assert(childList.size() |
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< static_cast<size_t>(expr::NodeValue::MAX_CHILDREN) |
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* static_cast<size_t>(expr::NodeValue::MAX_CHILDREN)); |
94 |
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NodeBuilder nb(k); |
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ChildList::iterator cur = childList.begin(), next, en = childList.end(); |
96 |
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while (cur != en) |
97 |
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{ |
98 |
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next = min(cur + expr::NodeValue::MAX_CHILDREN, en); |
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nb << (nodeManager->mkNode(k, ChildList(cur, next))); |
100 |
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cur = next; |
101 |
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} |
102 |
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return RewriteResponse(REWRITE_DONE, nb.constructNode()); |
103 |
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} |
104 |
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} |
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|
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// Equality parity returns |
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// * 0 if no relation between a and b is found |
108 |
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// * 1 if a == b |
109 |
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// * 2 if a == not(b) |
110 |
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// * 3 or b == not(a) |
111 |
5023128 |
inline int equalityParity(TNode a, TNode b){ |
112 |
5023128 |
if(a == b){ |
113 |
15417 |
return 1; |
114 |
5007711 |
}else if(a.getKind() == kind::NOT && a[0] == b){ |
115 |
136 |
return 2; |
116 |
5007575 |
}else if(b.getKind() == kind::NOT && b[0] == a){ |
117 |
3455 |
return 3; |
118 |
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}else{ |
119 |
5004120 |
return 0; |
120 |
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} |
121 |
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} |
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|
123 |
144626 |
inline Node makeNegation(TNode n){ |
124 |
144626 |
bool even = false; |
125 |
158952 |
while(n.getKind() == kind::NOT){ |
126 |
7163 |
n = n[0]; |
127 |
7163 |
even = !even; |
128 |
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} |
129 |
144626 |
if(even){ |
130 |
7015 |
return n; |
131 |
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} else { |
132 |
137611 |
if(n.isConst()){ |
133 |
7121 |
return NodeManager::currentNM()->mkConst(!n.getConst<bool>()); |
134 |
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}else{ |
135 |
130490 |
return n.notNode(); |
136 |
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} |
137 |
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} |
138 |
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} |
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|
140 |
19075620 |
RewriteResponse TheoryBoolRewriter::preRewrite(TNode n) { |
141 |
19075620 |
NodeManager* nodeManager = NodeManager::currentNM(); |
142 |
38151240 |
Node tt = nodeManager->mkConst(true); |
143 |
38151240 |
Node ff = nodeManager->mkConst(false); |
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|
145 |
19075620 |
switch(n.getKind()) { |
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3908775 |
case kind::NOT: { |
147 |
3908775 |
if (n[0] == tt) return RewriteResponse(REWRITE_DONE, ff); |
148 |
3827809 |
if (n[0] == ff) return RewriteResponse(REWRITE_DONE, tt); |
149 |
3740863 |
if (n[0].getKind() == kind::NOT) return RewriteResponse(REWRITE_AGAIN, n[0][0]); |
150 |
3566167 |
break; |
151 |
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} |
152 |
4665824 |
case kind::OR: { |
153 |
4665824 |
bool done = true; |
154 |
4665824 |
TNode::iterator i = n.begin(), iend = n.end(); |
155 |
32528954 |
for(; i != iend; ++i) { |
156 |
13992566 |
if (*i == tt) return RewriteResponse(REWRITE_DONE, tt); |
157 |
13931565 |
if (*i == ff) done = false; |
158 |
13931565 |
if ((*i).getKind() == kind::OR) done = false; |
159 |
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} |
160 |
4604823 |
if (!done) { |
161 |
291254 |
return flattenNode(n, /* trivialNode = */ tt, /* skipNode = */ ff); |
162 |
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} |
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// x v ... v x --> x |
164 |
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unsigned ind, size; |
165 |
4321628 |
for (ind = 0, size = n.getNumChildren(); ind < size - 1; ++ind) |
166 |
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{ |
167 |
4318264 |
if (n[ind] != n[ind+1]) |
168 |
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{ |
169 |
4310205 |
break; |
170 |
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} |
171 |
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} |
172 |
4313569 |
if (ind == size - 1) |
173 |
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{ |
174 |
3364 |
return RewriteResponse(REWRITE_AGAIN, n[0]); |
175 |
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} |
176 |
4310205 |
break; |
177 |
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} |
178 |
4617652 |
case kind::AND: { |
179 |
4617652 |
bool done = true; |
180 |
4617652 |
TNode::iterator i = n.begin(), iend = n.end(); |
181 |
57438298 |
for(; i != iend; ++i) { |
182 |
26621559 |
if (*i == ff) return RewriteResponse(REWRITE_DONE, ff); |
183 |
26410323 |
if (*i == tt) done = false; |
184 |
26410323 |
if ((*i).getKind() == kind::AND) done = false; |
185 |
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} |
186 |
4406416 |
if (!done) { |
187 |
851434 |
RewriteResponse ret = flattenNode(n, /* trivialNode = */ ff, /* skipNode = */ tt); |
188 |
425717 |
Debug("bool-flatten") << n << ": " << ret.d_node << std::endl; |
189 |
425717 |
return ret; |
190 |
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} |
191 |
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// x ^ ... ^ x --> x |
192 |
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unsigned ind, size; |
193 |
4004526 |
for (ind = 0, size = n.getNumChildren(); ind < size - 1; ++ind) |
194 |
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{ |
195 |
3999739 |
if (n[ind] != n[ind+1]) |
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{ |
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3975912 |
break; |
198 |
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} |
199 |
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} |
200 |
3980699 |
if (ind == size - 1) |
201 |
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{ |
202 |
4787 |
return RewriteResponse(REWRITE_AGAIN, n[0]); |
203 |
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} |
204 |
3975912 |
break; |
205 |
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} |
206 |
528082 |
case kind::IMPLIES: { |
207 |
528082 |
if (n[0] == ff || n[1] == tt) return RewriteResponse(REWRITE_DONE, tt); |
208 |
525457 |
if (n[0] == tt && n[1] == ff) return RewriteResponse(REWRITE_DONE, ff); |
209 |
525353 |
if (n[0] == tt) return RewriteResponse(REWRITE_AGAIN, n[1]); |
210 |
513972 |
if (n[1] == ff) return RewriteResponse(REWRITE_AGAIN, makeNegation(n[0])); |
211 |
504208 |
break; |
212 |
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} |
213 |
1586828 |
case kind::EQUAL: { |
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// rewrite simple cases of IFF |
215 |
1586828 |
if(n[0] == tt) { |
216 |
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// IFF true x |
217 |
13596 |
return RewriteResponse(REWRITE_AGAIN, n[1]); |
218 |
1573232 |
} else if(n[1] == tt) { |
219 |
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// IFF x true |
220 |
29408 |
return RewriteResponse(REWRITE_AGAIN, n[0]); |
221 |
1543824 |
} else if(n[0] == ff) { |
222 |
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// IFF false x |
223 |
43046 |
return RewriteResponse(REWRITE_AGAIN, makeNegation(n[1])); |
224 |
1500778 |
} else if(n[1] == ff) { |
225 |
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// IFF x false |
226 |
66271 |
return RewriteResponse(REWRITE_AGAIN, makeNegation(n[0])); |
227 |
1434507 |
} else if(n[0] == n[1]) { |
228 |
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// IFF x x |
229 |
12921 |
return RewriteResponse(REWRITE_DONE, tt); |
230 |
1421586 |
} else if(n[0].getKind() == kind::NOT && n[0][0] == n[1]) { |
231 |
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// IFF (NOT x) x |
232 |
311 |
return RewriteResponse(REWRITE_DONE, ff); |
233 |
1421275 |
} else if(n[1].getKind() == kind::NOT && n[1][0] == n[0]) { |
234 |
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// IFF x (NOT x) |
235 |
601 |
return RewriteResponse(REWRITE_DONE, ff); |
236 |
1420674 |
} else if(n[0].getKind() == kind::EQUAL && n[1].getKind() == kind::EQUAL) { |
237 |
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// a : (= i x) |
238 |
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// i : (= j k) |
239 |
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// x : (= y z) |
240 |
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|
241 |
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// assume wlog k, z are constants and j is the same symbol as y |
242 |
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// (iff (= j k) (= j z)) |
243 |
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// if k = z |
244 |
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// then (iff (= j k) (= j k)) => true |
245 |
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// else |
246 |
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// (iff (= j k) (= j z)) <=> b |
247 |
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// b : (and (not (= j k)) (not (= j z))) |
248 |
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// (= j k) (= j z) | a b |
249 |
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// f f | t t |
250 |
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// f t | f f |
251 |
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// t f | f f |
252 |
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// t t | * f |
253 |
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// * j cannot equal both k and z in a theory model |
254 |
41356 |
TNode t,c; |
255 |
20686 |
if (n[0][0].isConst()) { |
256 |
956 |
c = n[0][0]; |
257 |
956 |
t = n[0][1]; |
258 |
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} |
259 |
19730 |
else if (n[0][1].isConst()) { |
260 |
1796 |
c = n[0][1]; |
261 |
1796 |
t = n[0][0]; |
262 |
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} |
263 |
20686 |
bool matchesForm = false; |
264 |
20686 |
bool constantsEqual = false; |
265 |
20686 |
if (!c.isNull()) { |
266 |
2752 |
if (n[1][0] == t && n[1][1].isConst()) { |
267 |
8 |
matchesForm = true; |
268 |
8 |
constantsEqual = (n[1][1] == c); |
269 |
|
} |
270 |
2744 |
else if (n[1][1] == t && n[1][0].isConst()) { |
271 |
8 |
matchesForm = true; |
272 |
8 |
constantsEqual = (n[1][0] == c); |
273 |
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} |
274 |
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} |
275 |
20686 |
if(matchesForm){ |
276 |
16 |
if(constantsEqual){ |
277 |
1 |
return RewriteResponse(REWRITE_DONE, tt); |
278 |
|
}else{ |
279 |
30 |
Cardinality kappa = t.getType().getCardinality(); |
280 |
30 |
Cardinality two(2l); |
281 |
15 |
if(kappa.knownLessThanOrEqual(two)){ |
282 |
2 |
return RewriteResponse(REWRITE_DONE, ff); |
283 |
|
}else{ |
284 |
26 |
Node neitherEquality = (makeNegation(n[0])).andNode(makeNegation(n[1])); |
285 |
13 |
return RewriteResponse(REWRITE_AGAIN, neitherEquality); |
286 |
|
} |
287 |
|
} |
288 |
|
} |
289 |
|
} |
290 |
|
// sort |
291 |
1420658 |
if (n[0].getId() > n[1].getId()) |
292 |
|
{ |
293 |
|
return RewriteResponse(REWRITE_AGAIN, |
294 |
187264 |
nodeManager->mkNode(kind::EQUAL, n[1], n[0])); |
295 |
|
} |
296 |
1233394 |
return RewriteResponse(REWRITE_DONE, n); |
297 |
|
} |
298 |
1210295 |
case kind::XOR: { |
299 |
|
// rewrite simple cases of XOR |
300 |
1210295 |
if(n[0] == tt) { |
301 |
|
// XOR true x |
302 |
6412 |
return RewriteResponse(REWRITE_AGAIN, makeNegation(n[1])); |
303 |
1203883 |
} else if(n[1] == tt) { |
304 |
|
// XOR x true |
305 |
15454 |
return RewriteResponse(REWRITE_AGAIN, makeNegation(n[0])); |
306 |
1188429 |
} else if(n[0] == ff) { |
307 |
|
// XOR false x |
308 |
37999 |
return RewriteResponse(REWRITE_AGAIN, n[1]); |
309 |
1150430 |
} else if(n[1] == ff) { |
310 |
|
// XOR x false |
311 |
114634 |
return RewriteResponse(REWRITE_AGAIN, n[0]); |
312 |
1035796 |
} else if(n[0] == n[1]) { |
313 |
|
// XOR x x |
314 |
937 |
return RewriteResponse(REWRITE_DONE, ff); |
315 |
1034859 |
} else if(n[0].getKind() == kind::NOT && n[0][0] == n[1]) { |
316 |
|
// XOR (NOT x) x |
317 |
29 |
return RewriteResponse(REWRITE_DONE, tt); |
318 |
1034830 |
} else if(n[1].getKind() == kind::NOT && n[1][0] == n[0]) { |
319 |
|
// XOR x (NOT x) |
320 |
196 |
return RewriteResponse(REWRITE_DONE, tt); |
321 |
|
} |
322 |
1034634 |
break; |
323 |
|
} |
324 |
1868563 |
case kind::ITE: { |
325 |
|
// non-Boolean-valued ITEs should have been removed in place of |
326 |
|
// a variable |
327 |
|
// rewrite simple cases of ITE |
328 |
1868563 |
if (n[0].isConst()) { |
329 |
244168 |
if (n[0] == tt) { |
330 |
|
// ITE true x y |
331 |
32406 |
Debug("bool-ite") << "TheoryBoolRewriter::preRewrite_ITE: n[0] ==tt " |
332 |
16203 |
<< n << ": " << n[1] << std::endl; |
333 |
16203 |
return RewriteResponse(REWRITE_AGAIN, n[1]); |
334 |
|
} else { |
335 |
227965 |
Assert(n[0] == ff); |
336 |
|
// ITE false x y |
337 |
455930 |
Debug("bool-ite") << "TheoryBoolRewriter::preRewrite_ITE: n[0] ==ff " |
338 |
227965 |
<< n << ": " << n[1] << std::endl; |
339 |
227965 |
return RewriteResponse(REWRITE_AGAIN, n[2]); |
340 |
|
} |
341 |
1624395 |
} else if (n[1].isConst()) { |
342 |
364096 |
if (n[1] == tt && n[2] == ff) { |
343 |
9336 |
Debug("bool-ite") |
344 |
4668 |
<< "TheoryBoolRewriter::preRewrite_ITE: n[1] ==tt && n[2] == ff " |
345 |
4668 |
<< n << ": " << n[0] << std::endl; |
346 |
4668 |
return RewriteResponse(REWRITE_AGAIN, n[0]); |
347 |
|
} |
348 |
359428 |
else if (n[1] == ff && n[2] == tt) { |
349 |
7306 |
Debug("bool-ite") |
350 |
3653 |
<< "TheoryBoolRewriter::preRewrite_ITE: n[1] ==ff && n[2] == tt " |
351 |
3653 |
<< n << ": " << n[0].notNode() << std::endl; |
352 |
3653 |
return RewriteResponse(REWRITE_AGAIN, makeNegation(n[0])); |
353 |
|
} |
354 |
|
} |
355 |
|
|
356 |
1616074 |
if (n[0].getKind() == kind::NOT) |
357 |
|
{ |
358 |
|
// ite(not(c), x, y) ---> ite(c, y, x) |
359 |
|
return RewriteResponse( |
360 |
117537 |
REWRITE_AGAIN, nodeManager->mkNode(kind::ITE, n[0][0], n[2], n[1])); |
361 |
|
} |
362 |
|
|
363 |
|
int parityTmp; |
364 |
1498537 |
if ((parityTmp = equalityParity(n[1], n[2])) != 0) { |
365 |
23890 |
Node resp = (parityTmp == 1) ? (Node)n[1] : n[0].eqNode(n[1]); |
366 |
23890 |
Debug("bool-ite") |
367 |
11945 |
<< "TheoryBoolRewriter::preRewrite_ITE: equalityParity n[1], n[2] " |
368 |
11945 |
<< parityTmp << " " << n << ": " << resp << std::endl; |
369 |
11945 |
return RewriteResponse(REWRITE_AGAIN, resp); |
370 |
|
// Curiously, this rewrite affects several benchmarks dramatically, including copy_array and some simple_startup - disable for now |
371 |
|
// } else if (n[0].getKind() == kind::NOT) { |
372 |
|
// return RewriteResponse(REWRITE_AGAIN, n[0][0].iteNode(n[2], n[1])); |
373 |
1486592 |
} else if(!n[1].isConst() && (parityTmp = equalityParity(n[0], n[1])) != 0){ |
374 |
|
// (parityTmp == 1) if n[0] == n[1] |
375 |
|
// otherwise, n[0] == not(n[1]) or not(n[0]) == n[1] |
376 |
|
|
377 |
|
// if n[1] is constant this can loop, this is possible in prewrite |
378 |
5814 |
Node resp = n[0].iteNode( (parityTmp == 1) ? tt : ff, n[2]); |
379 |
5814 |
Debug("bool-ite") |
380 |
2907 |
<< "TheoryBoolRewriter::preRewrite_ITE: equalityParity n[0], n[1] " |
381 |
2907 |
<< parityTmp << " " << n << ": " << resp << std::endl; |
382 |
2907 |
return RewriteResponse(REWRITE_AGAIN, resp); |
383 |
1483685 |
} else if(!n[2].isConst() && (parityTmp = equalityParity(n[0], n[2])) != 0){ |
384 |
|
// (parityTmp == 1) if n[0] == n[2] |
385 |
|
// otherwise, n[0] == not(n[2]) or not(n[0]) == n[2] |
386 |
756 |
Node resp = n[0].iteNode(n[1], (parityTmp == 1) ? ff : tt); |
387 |
756 |
Debug("bool-ite") |
388 |
378 |
<< "TheoryBoolRewriter::preRewrite_ITE: equalityParity n[0], n[2] " |
389 |
378 |
<< parityTmp << " " << n << ": " << resp << std::endl; |
390 |
378 |
return RewriteResponse(REWRITE_AGAIN, resp); |
391 |
4352167 |
} else if(n[1].getKind() == kind::ITE && |
392 |
2868860 |
(parityTmp = equalityParity(n[0], n[1][0])) != 0){ |
393 |
|
// (parityTmp == 1) then n : (ite c (ite c x y) z) |
394 |
|
// (parityTmp > 1) then n : (ite c (ite (not c) x y) z) or |
395 |
|
// n: (ite (not c) (ite c x y) z) |
396 |
3624 |
Node resp = n[0].iteNode((parityTmp == 1) ? n[1][1] : n[1][2], n[2]); |
397 |
3624 |
Debug("bool-ite") |
398 |
1812 |
<< "TheoryBoolRewriter::preRewrite: equalityParity n[0], n[1][0] " |
399 |
1812 |
<< parityTmp << " " << n << ": " << resp << std::endl; |
400 |
1812 |
return RewriteResponse(REWRITE_AGAIN, resp); |
401 |
4780006 |
} else if(n[2].getKind() == kind::ITE && |
402 |
3298511 |
(parityTmp = equalityParity(n[0], n[2][0])) != 0){ |
403 |
|
// (parityTmp == 1) then n : (ite c x (ite c y z)) |
404 |
|
// (parityTmp > 1) then n : (ite c x (ite (not c) y z)) or |
405 |
|
// n: (ite (not c) x (ite c y z)) |
406 |
3932 |
Node resp = n[0].iteNode(n[1], (parityTmp == 1) ? n[2][2] : n[2][1]); |
407 |
3932 |
Debug("bool-ite") |
408 |
1966 |
<< "TheoryBoolRewriter::preRewrite: equalityParity n[0], n[2][0] " |
409 |
1966 |
<< parityTmp << " " << n << ": " << resp << std::endl; |
410 |
1966 |
return RewriteResponse(REWRITE_AGAIN, resp); |
411 |
|
} |
412 |
|
|
413 |
|
// Rewrites for ITEs with a constant branch. These rewrites are applied |
414 |
|
// after the parity rewrites above because they may simplify ITEs such as |
415 |
|
// `(ite c c true)` to `(ite c true true)`. As a result, we avoid |
416 |
|
// introducing an unnecessary conjunction/disjunction here. |
417 |
1479529 |
if (n[1].isConst() && (n[1] == tt || n[1] == ff)) |
418 |
|
{ |
419 |
|
// ITE C true y --> C v y |
420 |
|
// ITE C false y --> ~C ^ y |
421 |
|
Node resp = |
422 |
93484 |
n[1] == tt ? n[0].orNode(n[2]) : (n[0].negate()).andNode(n[2]); |
423 |
93484 |
Debug("bool-ite") << "TheoryBoolRewriter::preRewrite_ITE: n[1] const " |
424 |
46742 |
<< n << ": " << resp << std::endl; |
425 |
46742 |
return RewriteResponse(REWRITE_AGAIN, resp); |
426 |
|
} |
427 |
1432787 |
else if (n[2].isConst() && (n[2] == tt || n[2] == ff)) |
428 |
|
{ |
429 |
|
// ITE C x true --> ~C v x |
430 |
|
// ITE C x false --> C ^ x |
431 |
|
Node resp = |
432 |
109792 |
n[2] == tt ? (n[0].negate()).orNode(n[1]) : n[0].andNode(n[1]); |
433 |
109792 |
Debug("bool-ite") << "TheoryBoolRewriter::preRewrite_ITE: n[2] const " |
434 |
54896 |
<< n << ": " << resp << std::endl; |
435 |
54896 |
return RewriteResponse(REWRITE_AGAIN, resp); |
436 |
|
} |
437 |
|
|
438 |
1377891 |
break; |
439 |
|
} |
440 |
689601 |
default: |
441 |
689601 |
return RewriteResponse(REWRITE_DONE, n); |
442 |
|
} |
443 |
14769017 |
return RewriteResponse(REWRITE_DONE, n); |
444 |
|
} |
445 |
|
|
446 |
|
} // namespace booleans |
447 |
|
} // namespace theory |
448 |
29502 |
} // namespace cvc5 |