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
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"
"http://www.w3.org/TR/REC-html40/loose.dtd">
<HTML>
<HEAD>
<META http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<META name="GENERATOR" content="hevea 1.08">
<LINK rel="stylesheet" type="text/css" href="gprolog.css">
<TITLE>
Symbolic constraints
</TITLE>
</HEAD>
<BODY TEXT=black BGCOLOR=white>
<A HREF="gprolog061.html"><IMG SRC ="previous_motif.gif" ALT="Previous"></A>
<A HREF="gprolog054.html"><IMG SRC ="contents_motif.gif" ALT="Up"></A>
<A HREF="gprolog063.html"><IMG SRC ="next_motif.gif" ALT="Next"></A>
<HR>
<H3 CLASS="subsection"><A NAME="htoc330">8.8</A> Symbolic constraints</H3><UL>
<LI><A HREF="gprolog062.html#toc270"><TT>fd_all_different/1</TT></A>
<LI><A HREF="gprolog062.html#toc271"><TT>fd_element/3</TT></A>
<LI><A HREF="gprolog062.html#toc272"><TT>fd_element_var/3</TT></A>
<LI><A HREF="gprolog062.html#toc273"><TT>fd_atmost/3</TT>,
<TT>fd_atleast/3</TT>,
<TT>fd_exactly/3</TT></A>
<LI><A HREF="gprolog062.html#toc274"><TT>fd_relation/2</TT>,
<TT>fd_relationc/2</TT></A>
</UL>
<A NAME="toc270"></A>
<H4 CLASS="subsubsection"><A NAME="htoc331">8.8.1</A> <TT>fd_all_different/1</TT></H4>
<B>Templates</B>
<DL CLASS="list" COMPACT="compact"><DT CLASS="dt-list"><DD CLASS="dd-list"><TT>
fd_all_different(+fd_variable_list)</TT></DL>
<B>Description</B><BR>
<BR>
<TT>fd_all_different(List)</TT> constrains all variables in <TT>List</TT>
to take distinct values. This is equivalent to posting an inequality
constraint for each pair of variables. This constraint is triggered when a
variable becomes ground, removing its value from the domain of the other
variables.<BR>
<BR>
<B>Errors</B><BR>
<TABLE CELLSPACING=2 CELLPADDING=0>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>List</TT> is a partial list</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>instantiation_error</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>List</TT> is neither a partial list nor a list</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(list, List)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left>an element <TT>E</TT> of the <TT>List</TT> list is neither a
variable nor an integer nor an FD variable</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(fd_variable, E)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR></TABLE><BR>
<B>Portability</B><BR>
<BR>
GNU Prolog predicate.<BR>
<BR>
<A NAME="toc271"></A>
<H4 CLASS="subsubsection"><A NAME="htoc332">8.8.2</A> <TT>fd_element/3</TT></H4>
<A NAME="fd-element/3"></A>
<B>Templates</B>
<DL CLASS="list" COMPACT="compact"><DT CLASS="dt-list"><DD CLASS="dd-list"><TT>
fd_element(?fd_variable, +integer_list, ?fd_variable)</TT></DL>
<B>Description</B><BR>
<BR>
<TT>fd_element(I, List, X)</TT> constraints <TT>X</TT> to be equal to the
<TT>I</TT><EM>th</EM> integer (from 1) of <TT>List</TT>.<BR>
<BR>
<B>Errors</B><BR>
<TABLE CELLSPACING=2 CELLPADDING=0>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>I</TT> is neither a variable nor an FD variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(fd_variable, I)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>X</TT> is neither a variable nor an FD variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(fd_variable, X)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>List</TT> is a partial list or a list with an element
<TT>E</TT> which is a variable</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>instantiation_error</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>List</TT> is neither a partial list nor a list</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(list, List)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left>an element <TT>E</TT> of the <TT>List</TT> list is neither a
variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(integer, E)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR></TABLE><BR>
<B>Portability</B><BR>
<BR>
GNU Prolog predicate.<BR>
<BR>
<A NAME="toc272"></A>
<H4 CLASS="subsubsection"><A NAME="htoc333">8.8.3</A> <TT>fd_element_var/3</TT></H4>
<B>Templates</B>
<DL CLASS="list" COMPACT="compact"><DT CLASS="dt-list"><DD CLASS="dd-list"><TT>
fd_element_var(?fd_variable, +fd_variable_list, ?fd_variable)</TT></DL>
<B>Description</B><BR>
<BR>
<TT>fd_element_var(I, List, X)</TT> constraints <TT>X</TT> to be equal to
the <TT>I</TT><EM>th</EM> variable (from 1) of <TT>List</TT>. This
constraint is similar to <TT>fd_element/3</TT> (section <A HREF="#fd-element/3">8.8.2</A>) but
<TT>List</TT> can also contain FD variables (rather than just integers).<BR>
<BR>
<B>Errors</B><BR>
<TABLE CELLSPACING=2 CELLPADDING=0>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>I</TT> is neither a variable nor an FD variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(fd_variable, I)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>X</TT> is neither a variable nor an FD variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(fd_variable, X)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>List</TT> is a partial list</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>instantiation_error</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>List</TT> is neither a partial list nor a list</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(list, List)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left>an element <TT>E</TT> of the <TT>List</TT> list is neither a
variable nor an integer nor an FD variable</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(fd_variable, E)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR></TABLE><BR>
<B>Portability</B><BR>
<BR>
GNU Prolog predicate.<BR>
<BR>
<A NAME="toc273"></A>
<H4 CLASS="subsubsection"><A NAME="htoc334">8.8.4</A> <TT>fd_atmost/3</TT>,
<TT>fd_atleast/3</TT>,
<TT>fd_exactly/3</TT></H4>
<B>Templates</B>
<DL CLASS="list" COMPACT="compact"><DT CLASS="dt-list"><DD CLASS="dd-list"><TT>
fd_atmost(+integer, +fd_variable_list, +integer)<BR>
fd_atleast(+integer, +fd_variable_list, +integer)<BR>
fd_exactly(+integer, +fd_variable_list, +integer)</TT></DL>
<B>Description</B><BR>
<BR>
<TT>fd_atmost(N, List, V)</TT> posts the constraint that at most <TT>N</TT>
variables of <TT>List</TT> are equal to the value <TT>V</TT>.<BR>
<BR>
<TT>fd_atleast(N, List, V)</TT> posts the constraint that at least
<TT>N</TT> variables of <TT>List</TT> are equal to the value <TT>V</TT>.<BR>
<BR>
<TT>fd_exactly(N, List, V)</TT> posts the constraint that at exactly
<TT>N</TT> variables of <TT>List</TT> are equal to the value <TT>V</TT>.<BR>
<BR>
These constraints are special cases of <TT>fd_cardinality/2</TT>
(section <A HREF="gprolog061.html#fd-cardinality/2">8.7.3</A>) but their implementation is more efficient.<BR>
<BR>
<B>Errors</B><BR>
<TABLE CELLSPACING=2 CELLPADDING=0>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>N</TT> is a variable</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>instantiation_error</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>N</TT> is neither a variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(integer, N)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>V</TT> is a variable</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>instantiation_error</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>V</TT> is neither a variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(integer, V)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>List</TT> is a partial list</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>instantiation_error</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>List</TT> is neither a partial list nor a list</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(list, List)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left>an element <TT>E</TT> of the <TT>List</TT> list is neither a
variable nor an FD variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(fd_variable, E)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR></TABLE><BR>
<B>Portability</B><BR>
<BR>
GNU Prolog predicates.<BR>
<BR>
<A NAME="toc274"></A>
<H4 CLASS="subsubsection"><A NAME="htoc335">8.8.5</A> <TT>fd_relation/2</TT>,
<TT>fd_relationc/2</TT></H4>
<B>Templates</B>
<DL CLASS="list" COMPACT="compact"><DT CLASS="dt-list"><DD CLASS="dd-list"><TT>
fd_relation(+integer_list_list, ?fd_variable_list)<BR>
fd_relationc(+integer_list_list, ?fd_variable_list)</TT></DL>
<B>Description</B><BR>
<BR>
<TT>fd_relation(Relation, Vars)</TT> constraints the tuple of variables
<TT>Vars</TT> to be equal to one tuple of the list <TT>Relation</TT>. A
tuple is represented by a list.<BR>
<BR>
Example: definition of the boolean AND relation so that X AND Y
⇔ Z:
<DL CLASS="list" COMPACT="compact"><DT CLASS="dt-list"><DD CLASS="dd-list">
<PRE CLASS="verbatim">
and(X,Y,Z):-
fd_relation([[0,0,0],[0,1,0],[1,0,0],[1,1,1]], [X,Y,Z]).
</PRE></DL>
<TT>fd_relationc(Columns, Vars)</TT> is similar to <TT>fd_relation/2</TT>
except that the relation is not given as the list of tuples but as the list
of the columns of the relation. A column is represented by a list.<BR>
<BR>
Example:
<DL CLASS="list" COMPACT="compact"><DT CLASS="dt-list"><DD CLASS="dd-list">
<PRE CLASS="verbatim">
and(X,Y,Z):-
fd_relationc([[0,0,1,1],[0,1,0,1],[0,0,0,1]], [X,Y,Z]).
</PRE></DL>
<B>Errors</B><BR>
<TABLE CELLSPACING=2 CELLPADDING=0>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>Relation</TT> is a partial list or a list with a sub-term
<TT>E</TT> which is a variable</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>instantiation_error</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>Relation</TT> is neither a partial list nor a list</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(list, Relation)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left>an element <TT>E</TT> of the <TT>Relation</TT> list is neither a
variable nor an integer</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(integer, E)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>Vars</TT> is a partial list</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>instantiation_error</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left><TT>Vars</TT> is neither a partial list nor a list</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(list, Vars)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR>
<TR><TD VALIGN=top ALIGN=left>an element <TT>E</TT> of the <TT>Vars</TT> list is neither a
variable nor an integer nor an FD variable</TD>
<TD VALIGN=top ALIGN=center NOWRAP> </TD>
<TD VALIGN=top ALIGN=left><TT>type_error(fd_variable, E)</TT></TD>
</TR>
<TR><TD BGCOLOR=black COLSPAN=3><TABLE BORDER=0 WIDTH="100%" CELLSPACING=0 CELLPADDING=1><TR><TD></TD></TR></TABLE></TD>
</TR></TABLE><BR>
<B>Portability</B><BR>
<BR>
GNU Prolog predicates.<BR>
<BR>
<HR SIZE=2>
Copyright (C) 1999-2007 Daniel Diaz
<BR>
<BR>
Verbatim copying and distribution of this entire article is permitted in any
medium, provided this notice is preserved. <BR>
<BR>
<A HREF="index.html#copyright">More about the copyright</A>
<HR>
<A HREF="gprolog061.html"><IMG SRC ="previous_motif.gif" ALT="Previous"></A>
<A HREF="gprolog054.html"><IMG SRC ="contents_motif.gif" ALT="Up"></A>
<A HREF="gprolog063.html"><IMG SRC ="next_motif.gif" ALT="Next"></A>
</BODY>
</HTML>
|
