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
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
<meta name="robots" content="index,nofollow">
<title>ForLoops - MLton Standard ML Compiler (SML Compiler)</title>
<link rel="stylesheet" type="text/css" charset="iso-8859-1" media="all" href="common.css">
<link rel="stylesheet" type="text/css" charset="iso-8859-1" media="screen" href="screen.css">
<link rel="stylesheet" type="text/css" charset="iso-8859-1" media="print" href="print.css">
<link rel="Start" href="Home">
</head>
<body lang="en" dir="ltr">
<script src="http://www.google-analytics.com/urchin.js" type="text/javascript">
</script>
<script type="text/javascript">
_uacct = "UA-833377-1";
urchinTracker();
</script>
<table bgcolor = lightblue cellspacing = 0 style = "border: 0px;" width = 100%>
<tr>
<td style = "
border: 0px;
color: darkblue;
font-size: 150%;
text-align: left;">
<a class = mltona href="Home">MLton 20061025</a>
<td style = "
border: 0px;
font-size: 150%;
text-align: center;
width: 50%;">
ForLoops
<td style = "
border: 0px;
text-align: right;">
<table cellspacing = 0 style = "border: 0px">
<tr style = "vertical-align: middle;">
</table>
<tr style = "background-color: white;">
<td colspan = 3
style = "
border: 0px;
font-size:70%;
text-align: right;">
<a href = "Home">Home</a>
<a href = "Index">Index</a>
</table>
<div id="content" lang="en" dir="ltr">
A <tt>for</tt>-loop is typically used to iterate over a range of consecutive integers that denote indices of some sort. For example, in <a href="OCaml">OCaml</a> a <tt>for</tt>-loop takes either the form
<pre>for <name> = <lower> to <upper> do <body> done
</pre>or the form
<pre>for <name> = <upper> downto <lower> do <body> done
</pre>Some languages provide considerably more flexible <tt>for</tt>-loop or <tt>foreach</tt>-constructs. <p>
A bit surprisingly, <a href="StandardML">Standard ML</a> provides special syntax for <tt>while</tt>-loops, but not for <tt>for</tt>-loops. Indeed, in SML, many uses of <tt>for</tt>-loops are better expressed using <tt>app</tt>, <tt>foldl/foldr</tt>, <tt>map</tt> and many other higher-order functions provided by the <a href="BasisLibrary">Basis Library</a> for manipulating lists, vectors and arrays. However, the Basis Library does not provide a function for iterating over a range of integer values. Fortunately, it is very easy to write one.
</p>
<h2 id="head-256b31fc11b749803c8295d4ec8da28712f04f19">A fairly simple design</h2>
<p>
The following implementation imitates both the syntax and semantics of the OCaml <tt>for</tt>-loop.
</p>
<pre class=code>
<B><FONT COLOR="#A020F0">datatype</FONT></B> for <B><FONT COLOR="#5F9EA0">=</FONT></B> to <B><FONT COLOR="#A020F0">of</FONT></B> <B><FONT COLOR="#228B22">int</FONT></B> <B><FONT COLOR="#5F9EA0">*</FONT></B> <B><FONT COLOR="#228B22">int</FONT></B>
<B><FONT COLOR="#5F9EA0">|</FONT></B> downto <B><FONT COLOR="#A020F0">of</FONT></B> <B><FONT COLOR="#228B22">int</FONT></B> <B><FONT COLOR="#5F9EA0">*</FONT></B> <B><FONT COLOR="#228B22">int</FONT></B>
<B><FONT COLOR="#A020F0">infix</FONT></B> to downto
<B><FONT COLOR="#A020F0">val</FONT></B> for <B><FONT COLOR="#5F9EA0">=</FONT></B>
<B><FONT COLOR="#A020F0">fn</FONT></B> lo to up <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B>
(<B><FONT COLOR="#A020F0">fn</FONT></B> f <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> <B><FONT COLOR="#A020F0">let</FONT></B><B><FONT COLOR="#A020F0"> fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">loop</FONT></I></B></FONT></B> lo <B><FONT COLOR="#5F9EA0">=</FONT></B> <B><FONT COLOR="#A020F0">if</FONT></B> lo <B><FONT COLOR="#5F9EA0">></FONT></B> up <B><FONT COLOR="#A020F0">then</FONT></B> ()
<B><FONT COLOR="#A020F0">else</FONT></B> (f lo; loop (lo<B><FONT COLOR="#5F9EA0">+</FONT></B>1))
<B><FONT COLOR="#A020F0">in</FONT></B> loop lo <B><FONT COLOR="#A020F0">end</FONT></B>)
<B><FONT COLOR="#5F9EA0">|</FONT></B> up downto lo <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B>
(<B><FONT COLOR="#A020F0">fn</FONT></B> f <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> <B><FONT COLOR="#A020F0">let</FONT></B><B><FONT COLOR="#A020F0"> fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">loop</FONT></I></B></FONT></B> up <B><FONT COLOR="#5F9EA0">=</FONT></B> <B><FONT COLOR="#A020F0">if</FONT></B> up < lo <B><FONT COLOR="#A020F0">then</FONT></B> ()
<B><FONT COLOR="#A020F0">else</FONT></B> (f up; loop (up<B><FONT COLOR="#5F9EA0">-</FONT></B>1))
<B><FONT COLOR="#A020F0">in</FONT></B> loop up <B><FONT COLOR="#A020F0">end</FONT></B>)
</PRE>
<p>
</p>
<p>
For example,
<pre class=code>
for (1 to 9)
(<B><FONT COLOR="#A020F0">fn</FONT></B> i <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> <B><FONT COLOR="#A020F0">print</FONT></B> (Int.toString i))
</PRE>
would print <tt>123456789</tt> and
<pre class=code>
for (9 downto 1)
(<B><FONT COLOR="#A020F0">fn</FONT></B> i <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> <B><FONT COLOR="#A020F0">print</FONT></B> (Int.toString i))
</PRE>
would print <tt>987654321</tt>.
</p>
<p>
Straightforward formatting of nested loops
<pre class=code>
for (a to b)
(<B><FONT COLOR="#A020F0">fn</FONT></B> i <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B>
for (c to d)
(<B><FONT COLOR="#A020F0">fn</FONT></B> j <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B>
...))
</PRE>
is fairly readable, but tends to cause the body of the loop to be indented quite deeply.
</p>
<h2 id="head-db5cb13e652c830a05ed522c82b38855adf3f29d">Off-by-one</h2>
<p>
The above design has an annoying feature. In practice, the upper bound of the iterated range is almost always excluded and most loops would subtract one from the upper bound:
<pre class=code>
for (0 to n<B><FONT COLOR="#5F9EA0">-</FONT></B>1) ...
for (n<B><FONT COLOR="#5F9EA0">-</FONT></B>1 downto 0) ...
</PRE>
It is probably better to break convention and exclude the upper bound by default, because it leads to more concise code and becomes idiomatic with very little practise. The iterator combinators described below exclude the upper bound by default.
</p>
<h2 id="head-a43056e62b4e6692169c07351860dd6bb04042d0">Iterator combinators</h2>
<p>
While the simple <tt>for</tt>-function described in the previous section is probably good enough for many uses, it is a bit cumbersome when one needs to iterate over a cartesian product. One might also want to iterate over more than just consecutive integers. It turns out that one can provide a library of iterator combinators that allow one to implement iterators more flexibly.
</p>
<p>
Since the types of the combinators may be a bit difficult to infer from their implementations, let's first take a look at a signature of the iterator combinator library:
<pre class=code>
<B><FONT COLOR="#5F9EA0">signature</FONT></B> ITER <B><FONT COLOR="#5F9EA0">=</FONT></B>
<B><FONT COLOR="#5F9EA0">sig</FONT></B>
<B><FONT COLOR="#A020F0">type</FONT></B> 'a t <B><FONT COLOR="#5F9EA0">=</FONT></B> ('a <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> <B><FONT COLOR="#228B22">unit</FONT></B>) <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> <B><FONT COLOR="#228B22">unit</FONT></B>
<B><FONT COLOR="#A020F0">val</FONT></B> return : 'a <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> 'a t
<B><FONT COLOR="#A020F0">val</FONT></B> <B><FONT COLOR="#5F9EA0">></FONT></B><B><FONT COLOR="#5F9EA0">>=</FONT></B> : 'a t <B><FONT COLOR="#5F9EA0">*</FONT></B> ('a <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> 'b t) <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> 'b t
<B><FONT COLOR="#A020F0">val</FONT></B> none : 'a t
<B><FONT COLOR="#A020F0">val</FONT></B> to : <B><FONT COLOR="#228B22">int</FONT></B> <B><FONT COLOR="#5F9EA0">*</FONT></B> <B><FONT COLOR="#228B22">int</FONT></B> <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> <B><FONT COLOR="#228B22">int</FONT></B> t
<B><FONT COLOR="#A020F0">val</FONT></B> downto : <B><FONT COLOR="#228B22">int</FONT></B> <B><FONT COLOR="#5F9EA0">*</FONT></B> <B><FONT COLOR="#228B22">int</FONT></B> <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> <B><FONT COLOR="#228B22">int</FONT></B> t
<B><FONT COLOR="#A020F0">val</FONT></B> inList : 'a <B><FONT COLOR="#228B22">list</FONT></B> <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> 'a t
<B><FONT COLOR="#A020F0">val</FONT></B> inVector : 'a <B><FONT COLOR="#228B22">vector</FONT></B> <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> 'a t
<B><FONT COLOR="#A020F0">val</FONT></B> inArray : 'a <B><FONT COLOR="#228B22">array</FONT></B> <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> 'a t
<B><FONT COLOR="#A020F0">val</FONT></B> using : ('a, 'b) StringCvt.reader <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> 'b <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> 'a t
<B><FONT COLOR="#A020F0">val</FONT></B> when : 'a t <B><FONT COLOR="#5F9EA0">*</FONT></B> ('a <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> <B><FONT COLOR="#228B22">bool</FONT></B>) <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> 'a t
<B><FONT COLOR="#A020F0">val</FONT></B> by : 'a t <B><FONT COLOR="#5F9EA0">*</FONT></B> ('a <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> 'b) <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> 'b t
<B><FONT COLOR="#A020F0">val</FONT></B> <B><FONT COLOR="#5F9EA0">@</FONT></B><B><FONT COLOR="#5F9EA0">@</FONT></B> : 'a t <B><FONT COLOR="#5F9EA0">*</FONT></B> 'a t <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> 'a t
<B><FONT COLOR="#A020F0">val</FONT></B> <B><FONT COLOR="#5F9EA0">*</FONT></B><B><FONT COLOR="#5F9EA0">*</FONT></B> : 'a t <B><FONT COLOR="#5F9EA0">*</FONT></B> 'b t <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> ('a, 'b) product t
<B><FONT COLOR="#A020F0">val</FONT></B> for : 'a <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> 'a
<B><FONT COLOR="#A020F0">end</FONT></B>
</PRE>
</p>
<p>
Several of the above combinators are meant to be used as infix operators. Here is a set of suitable infix declarations:
<pre class=code>
<B><FONT COLOR="#A020F0">infix</FONT></B> 2 to downto
<B><FONT COLOR="#A020F0">infix</FONT></B> 1 <B><FONT COLOR="#5F9EA0">@</FONT></B><B><FONT COLOR="#5F9EA0">@</FONT></B> when by
<B><FONT COLOR="#A020F0">infix</FONT></B> 0 <B><FONT COLOR="#5F9EA0">></FONT></B><B><FONT COLOR="#5F9EA0">>=</FONT></B> <B><FONT COLOR="#5F9EA0">*</FONT></B><B><FONT COLOR="#5F9EA0">*</FONT></B>
</PRE>
</p>
<p>
A few notes are in order:
</p>
<ul>
<li>
<p>
The <tt>'a t</tt> type constructor with the <tt>return</tt> and <tt>>>=</tt> operators forms a monad.
</p>
</li>
<li>
<p>
The <tt>to</tt> and <tt>downto</tt> combinators will omit the upper bound of the range.
</p>
</li>
<li>
<p>
<tt>for</tt> is the identity function. It is purely for syntactic sugar and is not strictly required.
</p>
</li>
<li>
<p>
The <tt>@@</tt> combinator produces an iterator for the concatenation of the given iterators.
</p>
</li>
<li>
<p>
The <tt>**</tt> combinator produces an iterator for the cartesian product of the given iterators.
</p>
</li>
<ul>
<li>
<p>
See <a href="ProductType">ProductType</a> for the type constructor <tt>('a, 'b) product</tt> used in the type of the iterator produced by <tt>**</tt>.
</p>
</li>
</ul>
<li>
<p>
The <tt>using</tt> combinator allows one to iterate over slices, streams and many other kinds of sequences.
</p>
</li>
<li>
<p>
<tt>when</tt> is the filtering combinator. The name <tt>when</tt> is inspired by <a href="OCaml">OCaml</a>'s guard clauses.
</p>
</li>
<li>
<p>
<tt>by</tt> is the mapping combinator.
</p>
</li>
</ul>
<p>
The below implementation of the <tt>ITER</tt>-signature makes use of the following basic combinators:
<pre class=code>
<B><FONT COLOR="#A020F0">fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">const</FONT></I></B></FONT></B> x _ <B><FONT COLOR="#5F9EA0">=</FONT></B> x
<B><FONT COLOR="#A020F0">fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">flip</FONT></I></B></FONT></B> f x y <B><FONT COLOR="#5F9EA0">=</FONT></B> f y x
<B><FONT COLOR="#A020F0">fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">id</FONT></I></B></FONT></B> x <B><FONT COLOR="#5F9EA0">=</FONT></B> x
<B><FONT COLOR="#A020F0">fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">opt</FONT></I></B></FONT></B> fno fso <B><FONT COLOR="#5F9EA0">=</FONT></B> <B><FONT COLOR="#A020F0">fn</FONT></B> <B><FONT COLOR="#5F9EA0">NONE</FONT></B> <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> fno () <B><FONT COLOR="#5F9EA0">|</FONT></B> <B><FONT COLOR="#5F9EA0">SOME</FONT></B> ? <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> fso ?
<B><FONT COLOR="#A020F0">fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">pass</FONT></I></B></FONT></B> x f <B><FONT COLOR="#5F9EA0">=</FONT></B> f x
</PRE>
</p>
<p>
Here is an implementation the <tt>ITER</tt>-signature:
<pre class=code>
<B><FONT COLOR="#5F9EA0">structure</FONT></B> Iter :<B><FONT COLOR="#5F9EA0">></FONT></B> ITER <B><FONT COLOR="#5F9EA0">=</FONT></B>
<B><FONT COLOR="#5F9EA0">struct</FONT></B>
<B><FONT COLOR="#A020F0">type</FONT></B> 'a t <B><FONT COLOR="#5F9EA0">=</FONT></B> ('a <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> <B><FONT COLOR="#228B22">unit</FONT></B>) <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> <B><FONT COLOR="#228B22">unit</FONT></B>
<B><FONT COLOR="#A020F0">val</FONT></B> return <B><FONT COLOR="#5F9EA0">=</FONT></B> pass
<B><FONT COLOR="#A020F0">fun</FONT></B> (iA <B><FONT COLOR="#5F9EA0">></FONT></B><B><FONT COLOR="#5F9EA0">>=</FONT></B> a2iB) f <B><FONT COLOR="#5F9EA0">=</FONT></B> iA (flip a2iB f)
<B><FONT COLOR="#A020F0">val</FONT></B> none <B><FONT COLOR="#5F9EA0">=</FONT></B> ignore
<B><FONT COLOR="#A020F0">fun</FONT></B> (l to u) f <B><FONT COLOR="#5F9EA0">=</FONT></B> <B><FONT COLOR="#A020F0">let</FONT></B> <B><FONT COLOR="#A020F0">fun</FONT></B> `l <B><FONT COLOR="#5F9EA0">=</FONT></B> <B><FONT COLOR="#A020F0">if</FONT></B> l<u <B><FONT COLOR="#A020F0">then</FONT></B> (f l; `(l<B><FONT COLOR="#5F9EA0">+</FONT></B>1)) <B><FONT COLOR="#A020F0">else</FONT></B> () <B><FONT COLOR="#A020F0">in</FONT></B> `l <B><FONT COLOR="#A020F0">end</FONT></B>
<B><FONT COLOR="#A020F0">fun</FONT></B> (u downto l) f <B><FONT COLOR="#5F9EA0">=</FONT></B> <B><FONT COLOR="#A020F0">let</FONT></B> <B><FONT COLOR="#A020F0">fun</FONT></B> `u <B><FONT COLOR="#5F9EA0">=</FONT></B> <B><FONT COLOR="#A020F0">if</FONT></B> u<B><FONT COLOR="#5F9EA0">></FONT></B>l <B><FONT COLOR="#A020F0">then</FONT></B> (f (u<B><FONT COLOR="#5F9EA0">-</FONT></B>1); `(u<B><FONT COLOR="#5F9EA0">-</FONT></B>1)) <B><FONT COLOR="#A020F0">else</FONT></B> () <B><FONT COLOR="#A020F0">in</FONT></B> `u <B><FONT COLOR="#A020F0">end</FONT></B>
<B><FONT COLOR="#A020F0"> fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">inList</FONT></I></B></FONT></B> ? <B><FONT COLOR="#5F9EA0">=</FONT></B> flip List.app ?
<B><FONT COLOR="#A020F0"> fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">inVector</FONT></I></B></FONT></B> ? <B><FONT COLOR="#5F9EA0">=</FONT></B> flip Vector.app ?
<B><FONT COLOR="#A020F0"> fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">inArray</FONT></I></B></FONT></B> ? <B><FONT COLOR="#5F9EA0">=</FONT></B> flip Array.app ?
<B><FONT COLOR="#A020F0"> fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">using</FONT></I></B></FONT></B> get s f <B><FONT COLOR="#5F9EA0">=</FONT></B> <B><FONT COLOR="#A020F0">let</FONT></B> <B><FONT COLOR="#A020F0">fun</FONT></B> `s <B><FONT COLOR="#5F9EA0">=</FONT></B> opt (const ()) (<B><FONT COLOR="#A020F0">fn</FONT></B> (x, s) <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> (f x; `s)) (get s) <B><FONT COLOR="#A020F0">in</FONT></B> `s <B><FONT COLOR="#A020F0">end</FONT></B>
<B><FONT COLOR="#A020F0">fun</FONT></B> (iA when p) f <B><FONT COLOR="#5F9EA0">=</FONT></B> iA (<B><FONT COLOR="#A020F0">fn</FONT></B> a <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> <B><FONT COLOR="#A020F0">if</FONT></B> p a <B><FONT COLOR="#A020F0">then</FONT></B> f a <B><FONT COLOR="#A020F0">else</FONT></B> ())
<B><FONT COLOR="#A020F0">fun</FONT></B> (iA by g) f <B><FONT COLOR="#5F9EA0">=</FONT></B> iA (f <B><FONT COLOR="#A020F0">o</FONT></B> g)
<B><FONT COLOR="#A020F0">fun</FONT></B> (iA <B><FONT COLOR="#5F9EA0">@</FONT></B><B><FONT COLOR="#5F9EA0">@</FONT></B> iB) f <B><FONT COLOR="#5F9EA0">=</FONT></B> (iA f : <B><FONT COLOR="#228B22">unit</FONT></B>; iB f)
<B><FONT COLOR="#A020F0">fun</FONT></B> (iA <B><FONT COLOR="#5F9EA0">*</FONT></B><B><FONT COLOR="#5F9EA0">*</FONT></B> iB) f <B><FONT COLOR="#5F9EA0">=</FONT></B> iA (<B><FONT COLOR="#A020F0">fn</FONT></B> a <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> iB (<B><FONT COLOR="#A020F0">fn</FONT></B> b <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> f (a & b)))
<B><FONT COLOR="#A020F0">val</FONT></B> for <B><FONT COLOR="#5F9EA0">=</FONT></B> id
<B><FONT COLOR="#A020F0">end</FONT></B>
</PRE>
</p>
<p>
Note that some of the above combinators (e.g. <tt>**</tt>) could be expressed in terms of the other combinators, most notably <tt>return</tt> and <tt>>>=</tt>. Another implementation issue worth mentioning is that <tt>downto</tt> is written specifically to avoid computing <tt>l-1</tt>, which could cause an <tt>Overflow</tt>.
</p>
<p>
To use the above combinators the <tt>Iter</tt>-structure needs to be opened
<pre class=code>
<B><FONT COLOR="#A020F0">open</FONT></B> Iter
</PRE>
and one usually also wants to declare the infix status of the operators as shown earlier.
</p>
<p>
Here is an example that illustrates some of the features:
<pre class=code>
for (0 to 10 when (<B><FONT COLOR="#A020F0">fn</FONT></B> x <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> x <B><FONT COLOR="#5F9EA0">mod</FONT></B> 3 <B><FONT COLOR="#5F9EA0"><></FONT></B> 0) <B><FONT COLOR="#5F9EA0">*</FONT></B><B><FONT COLOR="#5F9EA0">*</FONT></B> inList [<B><FONT COLOR="#BC8F8F">"a"</FONT></B>, <B><FONT COLOR="#BC8F8F">"b"</FONT></B>] <B><FONT COLOR="#5F9EA0">*</FONT></B><B><FONT COLOR="#5F9EA0">*</FONT></B> 2 downto 1 by <B><FONT COLOR="#228B22">real</FONT></B>)
(<B><FONT COLOR="#A020F0">fn</FONT></B> x & y & z <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B>
<B><FONT COLOR="#A020F0">print</FONT></B> (<B><FONT COLOR="#BC8F8F">"("</FONT></B><B><FONT COLOR="#5F9EA0">^</FONT></B>Int.toString x<B><FONT COLOR="#5F9EA0">^</FONT></B><B><FONT COLOR="#BC8F8F">", \""</FONT></B><B><FONT COLOR="#5F9EA0">^</FONT></B>y<B><FONT COLOR="#5F9EA0">^</FONT></B><B><FONT COLOR="#BC8F8F">"\", "</FONT></B><B><FONT COLOR="#5F9EA0">^</FONT></B>Real.toString z<B><FONT COLOR="#5F9EA0">^</FONT></B><B><FONT COLOR="#BC8F8F">")\n"</FONT></B>))
</PRE>
</p>
<p>
Using the <tt>Iter</tt> combinators one can easily produce more complicated iterators. For example, here is an iterator over a "triangle":
<pre class=code>
<B><FONT COLOR="#A020F0">fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">triangle</FONT></I></B></FONT></B> (l, u) <B><FONT COLOR="#5F9EA0">=</FONT></B> l to u <B><FONT COLOR="#5F9EA0">></FONT></B><B><FONT COLOR="#5F9EA0">>=</FONT></B> (<B><FONT COLOR="#A020F0">fn</FONT></B> i <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> i to u <B><FONT COLOR="#5F9EA0">></FONT></B><B><FONT COLOR="#5F9EA0">>=</FONT></B> (<B><FONT COLOR="#A020F0">fn</FONT></B> j <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">></FONT></B> return (i, j)))
</PRE>
</p>
</div>
<p>
<hr>
Last edited on 2006-03-26 14:16:53 by <span title="cs180212.pp.htv.fi"><a href="VesaKarvonen">VesaKarvonen</a></span>.
</body></html>
|
