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
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
|
/************************************************************************
************************************************************************
FAUST compiler
Copyright (C) 2003-2018 GRAME, Centre National de Creation Musicale
---------------------------------------------------------------------
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
************************************************************************
************************************************************************/
#include <iostream>
#include <vector>
#include "dcond.hh"
#include "global.hh"
#include "ppsig.hh"
/*
* Dcond are conditions, boolean expressions in disjunctive normal form implemented
* as set of set of Tree
*
* disjoint: two boolean expressions a and b are disjoint if : a != a|b != b
* less specific : a is less specific than b if : a == a|b. True is the less specific condition.
*
* {{a,b,c},{d,e,..},...} = (a & b & c) | (d & e &...) | ...
* where {a,b,c}, {d,e,...} etc. are all disjoint two by two
* {{}} = True
*
* if A={a1,a2,a3...} denotes a1&a2&a3, and B={b1,b2,b3,..} denotes b1&b2&b3&...
* A and B are disjoint if A inter B != A and != B
* if B superset of A then A|B = A
* if A n B = A
*/
// create a dnfCond from a simple expression
Tree dnfCond(Tree c)
{
return singleton(singleton(c));
}
// create a cnfCond from a simple expression
Tree cnfCond(Tree c)
{
return singleton(singleton(c));
}
// OR operation between two boolean expressions in CNF
// x&y v z = (x v z) & (y v z)
// x&y v a&b = (x v a&b) & (y v a&b)
// = (x v a) & (x v b) & (y v a) & (y v b)
// (a & b & c) v (e & f & g) =
// A*b + c*d
// a v c&d)
#if 0
Tree cnfOr(Tree c1, Tree c2)
{
if (isNil(c1)) { return c1; }
else if (isNil(c2)) { return c2; }
else {
std::vector<Tree> A;
while (isList(c1)) {
Tree h1 = hd(c1); c1 = tl(c1);
Tree t2 = c2;
while (isList(t2)) {
Tree h2 = hd(t2); t2 = tl(t2);
A.push_back(setUnion(h1,h2));
}
}
for(auto t1 : A) {
for (auto t2 : A) {
Tree ii = setUnion(t1,t2);
if (t1 == ii) {
t2 = ii;
} else if (t2 == ii) {
t1 = ii;
}
}
}
Tree c3 = gGlobal->nil;
for (auto t1 : A) { c3 = addElement(t1,c3); }
return c3;
}
}
#else
Tree cnfOr(Tree c1, Tree c2)
{
if (isNil(c1)) {
return c1;
} else if (isNil(c2)) {
return c2;
} else {
std::vector<Tree> A;
while (isList(c1)) {
Tree h1 = hd(c1);
c1 = tl(c1);
Tree t2 = c2;
while (isList(t2)) {
Tree h2 = hd(t2);
t2 = tl(t2);
A.push_back(setUnion(h1, h2));
}
}
// simplify conditions that can be simplied
size_t n = A.size();
for (size_t i = 0; i < n; i++) { // for each A[i]
for (size_t j = i + 1; j < n; j++) { // for each A[i]
Tree ii = setUnion(A[i], A[j]);
if (A[j] == ii) {
A[i] = A[j]; // A[j] is more general and replace A[i]
} else if (A[i] == ii) {
A[j] = A[i]; // A[i] is more general and replace A[j]
}
}
}
Tree c3 = gGlobal->nil;
for (auto t1 : A) {
c3 = addElement(t1, c3);
}
return c3;
}
}
#endif
// AND operation between two boolean expressions in CNF
Tree cnfAnd(Tree c1, Tree c2)
{
if (isNil(c1)) {
return c2;
} else if (isNil(c2)) {
return c1;
} else {
// convert sets to vectors for convenient manipulations
int n = 0;
std::vector<Tree> A;
while (isList(c1)) {
A.push_back(hd(c1));
c1 = tl(c1);
n++;
}
int m = 0;
std::vector<Tree> B;
while (isList(c2)) {
B.push_back(hd(c2));
c2 = tl(c2);
m++;
}
// simplify conditions that can be simplied
for (int i = 0; i < n; i++) { // for each A[i]
for (int j = 0; j < m; j++) { // for each B[i]
Tree ii = setUnion(A[i], B[j]);
if (B[j] == ii) {
A[i] = B[j]; // B[j] is more general and replace A[i]
} else if (A[i] == ii) {
B[j] = A[i]; // A[i] is more general and replace B[j]
}
}
}
// compute the resulting expression
Tree c3 = gGlobal->nil;
for (int i = 0; i < n; i++) {
c3 = addElement(A[i], c3);
}
for (int j = 0; j < m; j++) {
c3 = addElement(B[j], c3);
}
return c3;
}
}
// True c1 is less specific (i.e. more general) than c2
bool cnfLess(Tree c1, Tree c2)
{
return c1 == cnfOr(c1, c2);
}
// And operation between two boolean expressions in DNF : A REVOIR !!!
Tree TRACE_dnfAnd(Tree c1, Tree c2)
{
if (isNil(c1)) {
return c2;
} else if (isNil(c2)) {
return c1;
} else {
int n = 0;
std::vector<Tree> A;
while (isList(c1)) {
Tree h1 = hd(c1);
c1 = tl(c1);
Tree t2 = c2;
while (isList(t2)) {
Tree h2 = hd(t2);
t2 = tl(t2);
A.push_back(setUnion(h1, h2));
n++;
}
}
// simplify conditions that can be simplied
for (int i = 0; i < n; i++) { // for each A[i]
for (int j = i + 1; j < n; j++) { // for each B[i]
Tree ii = setIntersection(A[i], A[j]);
if (A[j] == ii) {
A[i] = A[j]; // B[j] is more general and replace A[i]
} else if (A[i] == ii) {
A[j] = A[i]; // A[i] is more general and replace B[j]
}
}
}
// compute the resulting expression
Tree c3 = gGlobal->nil;
for (int i = 0; i < n; i++) {
c3 = addElement(A[i], c3);
}
return c3;
}
}
Tree dnfAnd(Tree c1, Tree c2)
{
// std::cout << ppsig(c1) << " .AND. " << ppsig(c2) << " = ";
Tree r = TRACE_dnfAnd(c1, c2);
// std::cout << ppsig(r) << std::endl;
return r;
}
// Or operation between two boolean expressions in DNF
Tree TRACE_dnfOr(Tree c1, Tree c2)
{
if (isNil(c1)) {
return c1;
} else if (isNil(c2)) {
return c2;
} else {
// convert sets to vectors for convenient manipulations
int n = 0;
std::vector<Tree> A;
while (isList(c1)) {
A.push_back(hd(c1));
c1 = tl(c1);
n++;
}
int m = 0;
std::vector<Tree> B;
while (isList(c2)) {
B.push_back(hd(c2));
c2 = tl(c2);
m++;
}
// simplify conditions that can be simplied
for (int i = 0; i < n; i++) { // for each A[i]
for (int j = 0; j < m; j++) { // for each B[i]
Tree ii = setIntersection(A[i], B[j]);
if (B[j] == ii) {
A[i] = B[j]; // B[j] is more general and replace A[i]
} else if (A[i] == ii) {
B[j] = A[i]; // A[i] is more general and replace B[j]
}
}
}
// compute the resulting expression
Tree c3 = gGlobal->nil;
for (int i = 0; i < n; i++) {
c3 = addElement(A[i], c3);
}
for (int j = 0; j < m; j++) {
c3 = addElement(B[j], c3);
}
return c3;
}
}
Tree dnfOr(Tree c1, Tree c2)
{
// std::cout << ppsig(c1) << " .OR. " << ppsig(c2) << " = ";
Tree r = TRACE_dnfOr(c1, c2);
// std::cout << ppsig(r) << std::endl;
return r;
}
// True c1 is less specific (i.e. more general) than c2
bool dnfLess(Tree c1, Tree c2)
{
return c1 == dnfOr(c1, c2);
}
|
