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3 <title>Lazy Evaluation</title>
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6 <body>
7 <h1>Lazy Evaluation</h1>
8 <p>The 'lazy' vocabulary adds lazy lists to Factor. This provides the
9 ability to describe infinite structures, and to delay execution of
10 expressions until they are actually used.</p>
11 <p>Lazy lists, like normal lists, are composed of a head and tail. In
12 a lazy list the head and tail are something called a 'promise'.
13 To convert a
14 'promise' into its actual value a word called 'force' is used. To
15 convert a value into a 'promise' the word to use is 'delay'.</p>
16 <table border="1">
17 <tr><td><a href="#delay">delay</a></td></tr>
18 <tr><td><a href="#force">force</a></td></tr>
19 </table>
21 <p>Many of the lazy list words are named similar to the standard list
22 words but with an 'l' suffixed to it. Here are the commonly used
23 words and their equivalent list operation:</p>
24 <table border="1">
25 <tr><th>Lazy List</th><th>Normal List</th></tr>
26 <tr><td><a href="#lnil">lnil</a></td><td>[ ]</td></tr>
27 <tr><td><a href="#lnilp">lnil?</a></td><td>Test for nil value</td></tr>
28 <tr><td><a href="#lcons">lcons</a></td><td>cons</td></tr>
29 <tr><td><a href="#lunit">lunit</a></td><td>unit</td></tr>
30 <tr><td><a href="#lcar">lcar</a></td><td>car</td></tr>
31 <tr><td><a href="#lcdr">lcdr</a></td><td>cdr</td></tr>
32 <tr><td><a href="#lnth">lnth</a></td><td>nth</td></tr>
33 <tr><td><a href="#luncons">luncons</a></td><td>uncons</td></tr>
34 <tr><td><a href="#lmap">lmap</a></td><td>map</td></tr>
35 <tr><td><a href="#lsubset">lsubset</a></td><td>subset</td></tr>
36 <tr><td><a href="#leach">leach</a></td><td>each</td></tr>
37 <tr><td><a href="#lappend">lappend</a></td><td>append</td></tr>
38 </table>
39 <p>A few additional words specific to lazy lists are:</p>
40 <table border="1">
41 <tr><td><a href="#ltake">ltake</a></td><td>Returns a normal list containing a specified
42 number of items from the lazy list.</td></tr>
43 <tr><td><a href="#lappendstar">lappend*</a></td><td>Given a lazy list of lazy lists,
44 concatenate them together in a lazy manner, returning a single lazy
45 list.</td></tr>
46 <tr><td><a href="#list>llist">list>llist</a></td><td>Given a normal list, return a lazy list
47 that contains the same elements as the normal list.</td></tr>
48 </table>
49 <h2>Reference</h2>
50 <!-- delay description -->
51 <a name="delay">
52 <h3>delay ( quot -- &lt;promise&gt; )</h3>
53 <p>'delay' is used to convert a value or expression into a promise.
54 The word 'force' is used to convert that promise back to its
55 value, or to force evaluation of the expression to return a value.
56 </p>
57 <p>The value on the stack that 'delay' expects must be quoted. This is
58 a requirement to prevent it from being evaluated.
59 </p>
60 <pre class="code">
61 ( 1 ) [ 42 ] <a href="#delay">delay</a> dup .
62 => &lt;&lt; promise [ ] [ 42 ] [ ] [ ] &gt;&gt;
63 ( 2 ) <a href="#force">force</a> .
64 => 42
65 </pre>
67 <!-- force description -->
68 <a name="force">
69 <h3>force ( &lt;promise&gt; -- value )</h3>
70 <p>'force' will evaluate a promises original expression
71 and leave the value of that expression on the stack.
72 </p>
73 <p>A promise can be forced multiple times but the expression
74 is only evaluated once. Future calls of 'force' on the promise
75 will returned the cached value of the original force. If the
76 expression contains side effects, such as i/o, then that i/o
77 will only occur on the first 'force'. See below for an example
78 (steps 3-5).
79 </p>
80 <p>If a promise is itself delayed, a force will evaluate all promises
81 until a value is returned. Due to this behaviour it is generally not
82 possible to delay a promise. The example below shows what happens
83 in this case.
84 </p>
85 <pre class="code">
86 ( 1 ) [ 42 ] <a href="#delay">delay</a> dup .
87 => &lt;&lt; promise [ ] [ 42 ] [ ] [ ] &gt;&gt;
88 ( 2 ) <a href="#force">force</a> .
89 => 42
91 #! Multiple forces on a promise returns cached value
92 ( 3 ) [ "hello" print 42 ] <a href="#delay">delay</a> dup .
93 => << promise [ ] [ "hello" print 42 ] [ ] [ ] >>
94 ( 4 ) dup <a href="#force">force</a> .
95 => hello
97 ( 5 ) <a href="#force">force</a> .
98 => 42
100 #! Forcing a delayed promise cascades up to return
101 #! original value, rather than the promise.
102 ( 6 ) [ [ 42 ] <a href="#delay">delay</a> ] <a href="#delay">delay</a> dup .
103 => << promise [ ] [ [ 42 ] delay ] [ ] [ ] >>
104 ( 7 ) <a href="#force">force</a> .
105 => 42
106 </pre>
108 <!-- lnil description -->
109 <a name="lnil">
110 <h3>lnil ( -- lcons )</h3>
111 <p>Returns a value representing the empty lazy list.</p>
112 <pre class="code">
113 ( 1 ) <a href="#lnil">lnil</a> .
114 => << promise [ ] [ [ ] ] t [ ] >>
115 </pre>
117 <!-- lnil description -->
118 <a name="lnilp">
119 <h3>lnil? ( lcons -- bool )</h3>
120 <p>Returns true if the given lazy cons is the value representing
121 the empty lazy list.</p>
122 <pre class="code">
123 ( 1 ) <a href="#lnil">lnil</a> <a href="#lnilp">lnil?</a> .
124 => t
125 ( 2 ) [ 1 ] <a href="#list2llist">list&gt;llist</a> dup <a href="#lnilp">lnil?</a> .
126 => [ ]
127 ( 3 ) <a href="#lcdr">lcdr</a> <a href="#lnilp">lnil?</a> .
128 => t
129 </pre>
131 <!-- lcons description -->
132 <a name="lcons">
133 <h3>lcons ( car-promise cdr-promise -- lcons )</h3>
134 <p>Provides the same effect as 'cons' does for normal lists.
135 Both values provided must be promises (ie. expressions that have
136 had <a href="#delay">delay</a> called on them).
137 </p>
138 <p>As the car and cdr passed on the stack are promises, they are not
139 evaluated until <a href="#lcar">lcar</a> or <a href="#lcdr">lcdr</a>
140 are called on the lazy cons.</p>
141 <pre class="code">
142 ( 1 ) [ "car" ] <a href="#delay">delay</a> [ "cdr" ] <a href="#delay">delay</a> <a href="#lcons">lcons</a> dup .
143 => &lt;&lt; promise ... &gt;&gt;
144 ( 2 ) dup <a href="#lcar">lcar</a> .
145 => "car"
146 ( 3 ) dup <a href="#lcdr">lcdr</a> .
147 => "cdr"
148 </pre>
150 <!-- lunit description -->
151 <a name="lunit">
152 <h3>lunit ( value-promise -- llist )</h3>
153 <p>Provides the same effect as 'unit' does for normal lists. It
154 creates a lazy list where the first element is the value given.</p>
155 <p>Like <a href="#lcons">lcons</a>, the value on the stack must be
156 a promise and is not evaluated until the <a href="#lcar">lcar</a>
157 of the list is requested.</a>
158 <pre class="code">
159 ( 1 ) [ 42 ] <a href="#delay">delay</a> <a href="#lunit">lunit</a> dup .
160 => &lt;&lt; promise ... &gt;&gt;
161 ( 2 ) dup <a href="#lcar">lcar</a> .
162 => 42
163 ( 3 ) dup <a href="#lcdr">lcdr</a> <a href="#lnilp">lnil?</a> .
164 => t
165 ( 4 ) [ . ] <a href="#leach">leach</a>
166 => 42
167 </pre>
169 <!-- lcar description -->
170 <a name="lcar">
171 <h3>lcar ( lcons -- value )</h3>
172 <p>Provides the same effect as 'car' does for normal lists. It
173 returns the first element in a lazy cons cell. This will force
174 the evaluation of that element.</p>
175 <pre class="code">
176 ( 1 ) [ 42 ] <a href="#delay">delay</a> <a href="#lunit">lunit</a> dup .
177 => &lt;&lt; promise ... &gt;&gt;
178 ( 2 ) <a href="#lcar">lcar</a> .
179 => 42
180 </pre>
182 <!-- lcdr description -->
183 <a name="lcdr">
184 <h3>lcdr ( lcons -- value )</h3>
185 <p>Provides the same effect as 'cdr' does for normal lists. It
186 returns the second element in a lazy cons cell and forces it. This
187 causes that element to be evaluated immediately.</p>
188 <pre class="code">
189 ( 1 ) [ 1 ] <a href="#delay">delay</a> [ 5 6 + ] <a href="#delay">delay</a> <a href="#lcons">lcons</a> dup .
190 => &lt;&lt; promise ... &gt;&gt;
191 ( 2 ) <a href="#lcdr">lcdr</a> .
192 => 11
193 </pre>
195 <pre class="code">
196 ( 1 ) 5 <a href="#lfrom">lfrom</a> dup .
197 => &lt;&lt; promise ... &gt;&gt;
198 ( 2 ) <a href="#lcdr">lcdr</a> dup <a href="#lcar">lcar</a> .
199 => 6
200 ( 3 ) <a href="#lcdr">lcdr</a> dup <a href="#lcar">lcar</a> .
201 => 7
202 ( 4 ) <a href="#lcdr">lcdr</a> dup <a href="#lcar">lcar</a> .
203 => 8
204 </pre>
206 <!-- lnth description -->
207 <a name="lnth">
208 <h3>lnth ( n llist -- value )</h3>
209 <p>Provides the same effect as 'nth' does for normal lists. It
210 returns the nth value in the lazy list. It causes all the values up to
211 'n' to be evaluated.</p>
212 <pre class="code">
213 ( 1 ) 1 <a href="#lfrom">lfrom</a> dup .
214 => &lt;&lt; promise ... &gt;&gt;
215 ( 2 ) 5 swap <a href="#lnth">lnth</a> .
216 => 6
217 </pre>
219 <!-- luncons description -->
220 <a name="luncons">
221 <h3>luncons ( lcons -- car cdr )</h3>
222 <p>Provides the same effect as 'uncons' does for normal lists. It
223 returns the car and cdr of the lazy list.</p>
224 <pre class="code">
225 ( 1 ) [ 5 ] <a href="#delay">delay</a> [ 6 ] <a href="#delay">delay</a> <a href="#lcons">lcons</a> dup .
226 => &lt;&lt; promise ... &gt;&gt;
227 ( 2 ) <a href="#luncons">luncons</a> . .
228 => 6
230 </pre>
232 <!-- lmap description -->
233 <a name="lmap">
234 <h3>lmap ( llist quot -- llist )</h3>
235 <p>Lazily maps over a lazy list applying the quotation to each element.
236 A new lazy list is returned which contains the results of the
237 quotation.</p>
238 <p>When intially called nothing in the original lazy list is
239 evaluated. Only when <a href="#lcar">lcar</a> is called will the item
240 in the list be evaluated and applied to the quotation. Ditto with <a
241 href="#lcdr">lcdr</a>, thus allowing infinite lists to be mapped over.</p>
242 <pre class="code">
243 ( 1 ) 1 <a href="#lfrom">lfrom</a>
244 => < infinite list of incrementing numbers >
245 ( 2 ) [ 2 * ] <a href="#lmap">lmap</a>
246 => < infinite list of numbers incrementing by 2 >
247 ( 3 ) 5 swap <a href="#ltake">ltake</a> <a href="#llist2list">llist&gt;list</a> .
248 => [ 2 4 6 8 10 ]
249 </pre>
251 <!-- lsubset description -->
252 <a name="lsubset">
253 <h3>lsubset ( llist pred -- llist )</h3>
254 <p>Provides the same effect as 'subset' does for normal lists. It
255 lazily iterates over a lazy list applying the predicate quotation to each
256 element. If that quotation returns true, the element will be included
257 in the resulting lazy list. If it is false, the element will be skipped.
258 A new lazy list is returned which contains all elements where the
259 predicate returned true.</p>
260 <p>Like <a href="#lmap">lmap</a>, when initially called no evaluation
261 will occur. A lazy list is returned that when values are retrieved
262 from in then items are evaluated and checked against the predicate.</p>
263 <pre class="code">
264 ( 1 ) 1 <a href="#lfrom">lfrom</a>
265 => < infinite list of incrementing numbers >
266 ( 2 ) [ <a href="#primep">prime?</a> ] <a href="#lsubset">lsubset</a>
267 => < infinite list of prime numbers >
268 ( 3 ) 5 swap <a href="#ltake">ltake</a> <a href="#llist2list">llist&gt;list</a> .
269 => [ 2 3 5 7 11 ]
270 </pre>
272 <!-- leach description -->
273 <a name="leach">
274 <h3>leach ( llist quot -- )</h3>
275 <p>Provides the same effect as 'each' does for normal lists. It
276 lazily iterates over a lazy list applying the quotation to each
277 element. If this operation is applied to an infinite list it will
278 never return unless the quotation escapes out by calling a continuation.</p>
279 <pre class="code">
280 ( 1 ) 1 <a href="#lfrom">lfrom</a>
281 => < infinite list of incrementing numbers >
282 ( 2 ) [ 2 mod 1 = ] <a href="#lsubset">lsubset</a>
283 => < infinite list of odd numbers >
284 ( 3 ) [ . ] <a href="#leach">leach</a>
285 => 1
289 ... for ever ...
290 </pre>
292 <!-- ltake description -->
293 <a name="ltake">
294 <h3>ltake ( n llist -- llist )</h3>
295 <p>Iterates over the lazy list 'n' times, appending each element to a
296 lazy list. This provides a convenient way of getting elements out of
297 an infinite lazy list.</p>
298 <pre class="code">
299 ( 1 ) : ones [ 1 ] delay [ ones ] delay <a href="#lcons">lcons</a> ;
300 ( 2 ) 5 ones <a href="#ltake">ltake</a> <a href="#llist2list">llist&gt;list</a> .
301 => [ 1 1 1 1 1 ]
302 </pre>
304 <!-- lappend description -->
305 <a name="lappend">
306 <h3>lappend ( llist1 llist2 -- llist )</h3>
307 <p>Lazily appends two lists together. The actual appending is done
308 lazily on iteration rather than immediately so it works very fast no
309 matter how large the list.</p>
310 <pre class="code">
311 ( 1 ) [ 1 2 3 ] <a href="#list2llist">list&gt;llist</a> [ 4 5 6 ] <a href="#list2llist">list&gt;llist</a> <a href="#lappend">lappend</a>
312 ( 2 ) [ . ] <a href="#leach">leach</a>
313 => 1
319 </pre>
321 <!-- lappend* description -->
322 <a name="lappendstar">
323 <h3>lappend* ( llists -- llist )</h3>
324 <p>Given a lazy list of lazy lists, concatenate them together in a
325 lazy fashion. The actual appending is done lazily on iteration rather
326 than immediately so it works very fast no matter how large the lists.</p>
327 <pre class="code">
328 ( 1 ) [ 1 2 3 ] <a href="#list2>llist">list&gt;llist</a>
329 ( 2 ) [ 4 5 6 ] <a href="#list2llist">list&gt;llist</a>
330 ( 3 ) [ 7 8 9 ] <a href="#list2llist">list&gt;llist</a>
331 ( 4 ) 3list <a href="#list2llist">list&gt;llist</a> <a href="#lappendstar">lappend*</a>
332 ( 5 ) [ . ] <a href="#leach">leach</a>
333 => 1
342 </pre>
344 <!-- list>llist description -->
345 <a name="list2llist">
346 <h3>list&gt;llist ( list -- llist )</h3>
347 <p>Converts a normal list into a lazy list. This is done lazily so the
348 initial list is not iterated through immediately.</p>
349 <pre class="code">
350 ( 1 ) [ 1 2 3 ] <a href="#list2llist">list&gt;llist</a>
351 ( 2 ) [ . ] <a href="#leach">leach</a>
352 => 1
355 </pre>
357 <p class="footer">
358 News and updates to this software can be obtained from the authors
359 weblog: <a href="http://radio.weblogs.com/0102385">Chris Double</a>.</p>
360 <p id="copyright">Copyright (c) 2004, Chris Double. All Rights Reserved.</p>
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