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
|
<!doctype html public "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!--
Generated from r6rs-lib.tex by tex2page, v 20070803
(running on MzScheme 371, unix),
(c) Dorai Sitaram,
http://www.ccs.neu.edu/~dorai/tex2page/tex2page-doc.html
-->
<head>
<title>
r6rs-lib
</title>
<link rel="stylesheet" type="text/css" href="r6rs-lib-Z-S.css" title=default>
<meta name=robots content="index,follow">
</head>
<body>
<div id=slidecontent>
<div align=right class=navigation>[Go to <span><a href="r6rs-lib.html">first</a>, <a href="r6rs-lib-Z-H-14.html">previous</a></span><span>, <a href="r6rs-lib-Z-H-16.html">next</a></span> page<span>; </span><span><a href="r6rs-lib-Z-H-1.html#node_toc_start">contents</a></span><span><span>; </span><a href="r6rs-lib-Z-H-21.html#node_index_start">index</a></span>]</div>
<p></p>
<a name="node_chap_14"></a>
<h1 class=chapter>
<div class=chapterheading><a href="r6rs-lib-Z-H-1.html#node_toc_node_chap_14">Chapter 14</a></div><br>
<a href="r6rs-lib-Z-H-1.html#node_toc_node_chap_14">Enumerations</a></h1>
<p></p>
<p>
This chapter describes the <tt>(rnrs enums (6))</tt><a name="node_idx_1226"></a>library for dealing with enumerated values
<a name="node_idx_1228"></a>and sets of enumerated values. Enumerated
values are represented by ordinary symbols, while finite sets of
enumerated values form a separate type, known as the
<a name="node_idx_1230"></a><em>enumeration sets</em>.
The enumeration sets are further partitioned into sets that
share the same <a name="node_idx_1232"></a><em>universe</em> and <a name="node_idx_1234"></a><em>enumeration type</em>.
These universes and enumeration types are created by the
<tt>make-enumeration</tt> procedure. Each call to that procedure
creates a new enumeration type.</p>
<p>
This library interprets each enumeration set with respect to
its specific universe of symbols and enumeration type.
This facilitates efficient implementation of enumeration sets
and enables the complement operation.</p>
<p>
In the descriptions of the following procedures, <i>enum-set</i>
ranges over the enumeration sets, which are defined as the subsets
of the universes that can be defined using <tt>make-enumeration</tt>.</p>
<p>
</p>
<p></p>
<div align=left><tt>(<a name="node_idx_1236"></a>make-enumeration<i> symbol-list</i>)</tt> procedure </div>
<p>
<i>Symbol-list</i> must be a list of symbols.
The <tt>make-enumeration</tt> procedure
creates a new enumeration type whose universe consists of
those symbols (in canonical order of their first appearance
in the list) and returns that universe as an enumeration
set whose universe is itself and whose enumeration type is
the newly created enumeration type.
</p>
<p></p>
<p>
</p>
<p></p>
<div align=left><tt>(<a name="node_idx_1238"></a>enum-set-universe<i> enum-set</i>)</tt> procedure </div>
<p>
Returns the set of all symbols that comprise
the universe of its argument, as an enumeration set.
</p>
<p></p>
<p>
</p>
<p></p>
<div align=left><tt>(<a name="node_idx_1240"></a>enum-set-indexer<i> enum-set</i>)</tt> procedure </div>
<p>
Returns a unary procedure that, given a symbol
that is in the universe of <i>enum-set</i>, returns its 0-origin index
within the canonical ordering of the symbols in the universe; given a
value not in the universe, the unary procedure returns <tt>#f</tt>.</p>
<p>
</p>
<tt>(let* ((e (make-enumeration ’(red green blue)))<br>
(i (enum-set-indexer e)))<br>
(list (i ’red) (i ’green) (i ’blue) (i ’yellow))) <br> ⇒ (0 1 2 <tt>#f</tt>)<p></tt></p>
<p>
The <tt>enum-set-indexer</tt> procedure could be defined as follows using the
<tt>memq</tt> procedure from the <tt>(rnrs lists (6))</tt> library:</p>
<p>
</p>
<tt>(define (enum-set-indexer set)<br>
(let* ((symbols (enum-set->list<br>
(enum-set-universe set)))<br>
(cardinality (length symbols)))<br>
(lambda (x)<br>
(cond<br>
((memq x symbols)<br>
=> (lambda (probe)<br>
(- cardinality (length probe))))<br>
(else <tt>#f</tt>)))))<p></tt>
</p>
<p></p>
<p>
</p>
<p></p>
<div align=left><tt>(<a name="node_idx_1242"></a>enum-set-constructor<i> enum-set</i>)</tt> procedure </div>
<p>
Returns a unary procedure that, given a
list of symbols that belong to the universe of <i>enum-set</i>, returns
a subset of that universe that contains exactly the symbols in the
list. The values in the list must all belong to the universe.
</p>
<p></p>
<p>
</p>
<p></p>
<div align=left><tt>(<a name="node_idx_1244"></a>enum-set->list<i> enum-set</i>)</tt> procedure </div>
<p>
Returns a list of the symbols that belong to its
argument, in the canonical order of the universe of <i>enum-set</i>.</p>
<p>
</p>
<tt>(let* ((e (make-enumeration ’(red green blue)))<br>
(c (enum-set-constructor e)))<br>
(enum-set->list (c ’(blue red)))) <br> ⇒ (red blue)<br>
<p></tt>
</p>
<p></p>
<p>
</p>
<p></p>
<div align=left><tt>(<a name="node_idx_1246"></a>enum-set-member?<i> symbol enum-set</i>)</tt> procedure </div>
<div align=left><tt>(<a name="node_idx_1248"></a>enum-set-subset?<i> <i>enum-set<sub>1</sub></i> <i>enum-set<sub>2</sub></i></i>)</tt> procedure </div>
<div align=left><tt>(<a name="node_idx_1250"></a>enum-set=?<i> <i>enum-set<sub>1</sub></i> <i>enum-set<sub>2</sub></i></i>)</tt> procedure </div>
<p>
The <tt>enum-set-member?</tt> procedure returns <tt>#t</tt> if its first argument is an
element of its second argument, <tt>#f</tt> otherwise.</p>
<p>
The <tt>enum-set-subset?</tt> procedure returns <tt>#t</tt> if the universe of
<i>enum-set<sub>1</sub></i> is a subset of the universe of <i>enum-set<sub>2</sub></i>
(considered as sets of symbols) and every element of <i>enum-set<sub>1</sub></i>
is a member of <i>enum-set<sub>2</sub></i>. It returns <tt>#f</tt> otherwise.</p>
<p>
The <tt>enum-set=?</tt> procedure returns <tt>#t</tt> if <i>enum-set<sub>1</sub></i> is a
subset of <i>enum-set<sub>2</sub></i> and vice versa, as determined by the
<tt>enum-set-subset?</tt> procedure. This implies that the universes of
the two sets are equal as sets of symbols, but does not imply
that they are equal as enumeration types. Otherwise, <tt>#f</tt> is
returned.</p>
<p>
</p>
<tt>(let* ((e (make-enumeration ’(red green blue)))<br>
(c (enum-set-constructor e)))<br>
(list<br>
(enum-set-member? ’blue (c ’(red blue)))<br>
(enum-set-member? ’green (c ’(red blue)))<br>
(enum-set-subset? (c ’(red blue)) e)<br>
(enum-set-subset? (c ’(red blue)) (c ’(blue red)))<br>
(enum-set-subset? (c ’(red blue)) (c ’(red)))<br>
(enum-set=? (c ’(red blue)) (c ’(blue red)))))<br>
⇒ (<tt>#t</tt> <tt>#f</tt> <tt>#t</tt> <tt>#t</tt> <tt>#f</tt> <tt>#t</tt>)<p></tt>
</p>
<p></p>
<p>
</p>
<p></p>
<div align=left><tt>(<a name="node_idx_1252"></a>enum-set-union<i> <i>enum-set<sub>1</sub></i> <i>enum-set<sub>2</sub></i></i>)</tt> procedure </div>
<div align=left><tt>(<a name="node_idx_1254"></a>enum-set-intersection<i> <i>enum-set<sub>1</sub></i> <i>enum-set<sub>2</sub></i></i>)</tt> procedure </div>
<div align=left><tt>(<a name="node_idx_1256"></a>enum-set-difference<i> <i>enum-set<sub>1</sub></i> <i>enum-set<sub>2</sub></i></i>)</tt> procedure </div>
<p>
<i>Enum-set<sub>1</sub></i> and <i>enum-set<sub>2</sub></i> must be enumeration sets
that have the same enumeration type.</p>
<p>
The <tt>enum-set-union</tt> procedure returns the union of <i>enum-set<sub>1</sub></i> and <i>enum-set<sub>2</sub></i>.
The <tt>enum-set-intersection</tt> procedure returns the intersection of <i>enum-set<sub>1</sub></i> and <i>enum-set<sub>2</sub></i>.
The <tt>enum-set-difference</tt> procedure returns the difference of <i>enum-set<sub>1</sub></i>
and <i>enum-set<sub>2</sub></i>.</p>
<p>
</p>
<tt>(let* ((e (make-enumeration ’(red green blue)))<br>
(c (enum-set-constructor e)))<br>
(list (enum-set->list<br>
(enum-set-union (c ’(blue)) (c ’(red))))<br>
(enum-set->list<br>
(enum-set-intersection (c ’(red green))<br>
(c ’(red blue))))<br>
(enum-set->list<br>
(enum-set-difference (c ’(red green))<br>
(c ’(red blue))))))<br>
<br> ⇒ ((red blue) (red) (green))<br>
<p></tt>
</p>
<p></p>
<p>
</p>
<p></p>
<div align=left><tt>(<a name="node_idx_1258"></a>enum-set-complement<i> enum-set</i>)</tt> procedure </div>
<p>
Returns <i>enum-set</i>’s
complement with respect to its universe.</p>
<p>
</p>
<tt>(let* ((e (make-enumeration ’(red green blue)))<br>
(c (enum-set-constructor e)))<br>
(enum-set->list<br>
(enum-set-complement (c ’(red)))))<br>
⇒ (green blue)<br>
<p></tt>
</p>
<p></p>
<p>
</p>
<p></p>
<div align=left><tt>(<a name="node_idx_1260"></a>enum-set-projection<i> <i>enum-set<sub>1</sub></i> <i>enum-set<sub>2</sub></i></i>)</tt> procedure </div>
<p>
Projects <i>enum-set<sub>1</sub></i> into the universe
of <i>enum-set<sub>2</sub></i>, dropping any elements of <i>enum-set<sub>1</sub></i> that do
not belong to the universe of <i>enum-set<sub>2</sub></i>. (If <i>enum-set<sub>1</sub></i>
is a subset of the universe of its second, no elements are
dropped, and the injection is returned.)</p>
<p>
</p>
<tt>(let ((e1 (make-enumeration<br>
’(red green blue black)))<br>
(e2 (make-enumeration<br>
’(red black white))))<br>
(enum-set->list<br>
(enum-set-projection e1 e2))))<br>
⇒ (red black)<br>
<p></tt>
</p>
<p></p>
<p>
</p>
<p>
</p>
<div align=left><tt>(define-enumeration <type-name></tt> syntax </div>
<a name="node_idx_1262"></a><tt>(<symbol> <tt>...</tt>)<br>
<constructor-syntax>)</tt><p>
The <tt>define-enumeration</tt> form defines an enumeration type and
provides two macros for constructing its members and sets of its
members.</p>
<p>
A <tt>define-enumeration</tt> form is a definition and can appear
anywhere any other <definition> can appear.</p>
<p>
<Type-name> is an identifier that is bound as a syntactic keyword;
<symbol> <tt>...</tt> are the symbols that comprise the
universe of the enumeration (in order).</p>
<p>
<tt>(<type-name> <symbol>)</tt> checks at macro-expansion
time whether the name of <symbol> is in the universe associated with
<type-name>. If it is, <tt>(<type-name>
<symbol>)</tt> is equivalent to <tt><symbol></tt>.
It is a syntax violation if it is not.</p>
<p>
<Constructor-syntax> is an identifier that is bound to a
macro that, given any finite sequence of the symbols in the universe,
possibly with duplicates, expands into an expression that evaluates
to the enumeration set of those symbols.</p>
<p>
<tt>(<constructor-syntax> <symbol> <tt>...</tt>)</tt> checks at
macro-expansion time whether every <symbol> <tt>...</tt> is in the
universe associated with <type-name>. It is a syntax violation
if one or more is not.
Otherwise
</p>
<tt>(<constructor-syntax> <symbol> <tt>...</tt>)<br>
<p></tt>
is equivalent to
</p>
<tt>((enum-set-constructor (<constructor-syntax>))<br>
’(<symbol> <tt>...</tt>)).<br>
<p></tt></p>
<p>
Example:</p>
<p>
</p>
<tt>(define-enumeration color<br>
(black white purple maroon)<br>
color-set)<br>
<br>
(color black) ⇒ black<br>
(color purpel) ⇒ <tt> &syntax</tt> <i>exception</i><br>
(enum-set->list (color-set)) ⇒ ()<br>
(enum-set->list<br>
(color-set maroon white)) ⇒ (white maroon)<br>
<p></tt></p>
<p>
</p>
<blockquote><em>Note: </em>
In <tt>(<type-name> <symbol>)</tt> and <tt>(<constructor-syntax> <symbol> <tt>...</tt>)</tt> forms,
only the names of the <symbol>s are significant.
</blockquote>
<p></p>
<p>
</p>
<p>
</p>
<p></p>
<div class=smallskip></div>
<p style="margin-top: 0pt; margin-bottom: 0pt">
<div align=right class=navigation>[Go to <span><a href="r6rs-lib.html">first</a>, <a href="r6rs-lib-Z-H-14.html">previous</a></span><span>, <a href="r6rs-lib-Z-H-16.html">next</a></span> page<span>; </span><span><a href="r6rs-lib-Z-H-1.html#node_toc_start">contents</a></span><span><span>; </span><a href="r6rs-lib-Z-H-21.html#node_index_start">index</a></span>]</div>
</p>
<p></p>
</div>
</body>
</html>
|
