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
|
<?xml version="1.0" encoding="utf-8" ?>
<!DOCTYPE chapter SYSTEM "chapter.dtd">
<chapter>
<header>
<copyright>
<year>2003</year><year>2013</year>
<holder>Ericsson AB. All Rights Reserved.</holder>
</copyright>
<legalnotice>
The contents of this file are subject to the Erlang Public License,
Version 1.1, (the "License"); you may not use this file except in
compliance with the License. You should have received a copy of the
Erlang Public License along with this software. If not, it can be
retrieved online at http://www.erlang.org/.
Software distributed under the License is distributed on an "AS IS"
basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See
the License for the specific language governing rights and limitations
under the License.
</legalnotice>
<title>List Comprehensions</title>
<prepared></prepared>
<docno></docno>
<date></date>
<rev></rev>
<file>list_comprehensions.xml</file>
</header>
<section>
<title>Simple Examples</title>
<p>This section starts with a simple example, showing a generator and a filter:</p>
<pre>
> <input>[X || X <- [1,2,a,3,4,b,5,6], X > 3].</input>
[a,4,b,5,6]</pre>
<p>This is read as follows: The list of X such that X is taken from the list
<c>[1,2,a,...]</c> and X is greater than 3.</p>
<p>The notation <c><![CDATA[X <- [1,2,a,...]]]></c> is a generator and
the expression <c>X > 3</c> is a filter.</p>
<p>An additional filter, <c>integer(X)</c>, can be added to restrict
the result to integers:</p>
<pre>
> <input>[X || X <- [1,2,a,3,4,b,5,6], integer(X), X > 3].</input>
[4,5,6]</pre>
<p>Generators can be combined. For example, the Cartesian product
of two lists can be written as follows:</p>
<pre>
> <input>[{X, Y} || X <- [1,2,3], Y <- [a,b]].</input>
[{1,a},{1,b},{2,a},{2,b},{3,a},{3,b}]</pre>
</section>
<section>
<title>Quick Sort</title>
<p>The well-known quick sort routine can be written as follows:</p>
<code type="none"><![CDATA[
sort([Pivot|T]) ->
sort([ X || X <- T, X < Pivot]) ++
[Pivot] ++
sort([ X || X <- T, X >= Pivot]);
sort([]) -> [].]]></code>
<p>The expression <c><![CDATA[[X || X <- T, X < Pivot]]]></c> is the list of
all elements in <c>T</c> that are less than <c>Pivot</c>.</p>
<p><c><![CDATA[[X || X <- T, X >= Pivot]]]></c> is the list of all elements in
<c>T</c> that are greater than or equal to <c>Pivot</c>.</p>
<p>A list sorted as follows:</p>
<list type="bulleted">
<item>The first element in the list is isolated
and the list is split into two sublists.</item>
<item>The first sublist contains
all elements that are smaller than the first element in
the list.</item>
<item>The second sublist contains all elements that are greater
than, or equal to, the first element in the list.</item>
<item>Then the sublists are sorted and the results are combined.</item>
</list>
</section>
<section>
<title>Permutations</title>
<p>The following example generates all permutations of
the elements in a list:</p>
<code type="none"><![CDATA[
perms([]) -> [[]];
perms(L) -> [[H|T] || H <- L, T <- perms(L--[H])].]]></code>
<p>This takes <c>H</c> from <c>L</c> in all possible ways.
The result is the set of all lists <c>[H|T]</c>, where <c>T</c>
is the set of all possible permutations of <c>L</c>, with
<c>H</c> removed:</p>
<pre>
> <input>perms([b,u,g]).</input>
[[b,u,g],[b,g,u],[u,b,g],[u,g,b],[g,b,u],[g,u,b]]</pre>
</section>
<section>
<title>Pythagorean Triplets</title>
<p>Pythagorean triplets are sets of integers <c>{A,B,C}</c> such
that <c>A**2 + B**2 = C**2</c>.</p>
<p>The function <c>pyth(N)</c> generates a list of all integers
<c>{A,B,C}</c> such that <c>A**2 + B**2 = C**2</c> and where
the sum of the sides is equal to, or less than, <c>N</c>:</p>
<code type="none"><![CDATA[
pyth(N) ->
[ {A,B,C} ||
A <- lists:seq(1,N),
B <- lists:seq(1,N),
C <- lists:seq(1,N),
A+B+C =< N,
A*A+B*B == C*C
].]]></code>
<pre>
> <input>pyth(3).</input>
[].
> <input>pyth(11).</input>
[].
> <input>pyth(12).</input>
[{3,4,5},{4,3,5}]
> <input>pyth(50).</input>
[{3,4,5},
{4,3,5},
{5,12,13},
{6,8,10},
{8,6,10},
{8,15,17},
{9,12,15},
{12,5,13},
{12,9,15},
{12,16,20},
{15,8,17},
{16,12,20}]</pre>
<p>The following code reduces the search space and is more
efficient:</p>
<code type="none"><![CDATA[
pyth1(N) ->
[{A,B,C} ||
A <- lists:seq(1,N-2),
B <- lists:seq(A+1,N-1),
C <- lists:seq(B+1,N),
A+B+C =< N,
A*A+B*B == C*C ].]]></code>
</section>
<section>
<title>Simplifications With List Comprehensions</title>
<p>As an example, list comprehensions can be used to simplify some
of the functions in <c>lists.erl</c>:</p>
<code type="none"><![CDATA[
append(L) -> [X || L1 <- L, X <- L1].
map(Fun, L) -> [Fun(X) || X <- L].
filter(Pred, L) -> [X || X <- L, Pred(X)].]]></code>
</section>
<section>
<title>Variable Bindings in List Comprehensions</title>
<p>The scope rules for variables that occur in list
comprehensions are as follows:</p>
<list type="bulleted">
<item>All variables that occur in a generator pattern are
assumed to be "fresh" variables.</item>
<item>Any variables that are defined before the list
comprehension, and that are used in filters, have the values
they had before the list comprehension.</item>
<item>Variables cannot be exported from a list comprehension.</item>
</list>
<p>As an example of these rules, suppose you want to write
the function <c>select</c>, which selects certain elements from
a list of tuples. Suppose you write
<c><![CDATA[select(X, L) -> [Y || {X, Y} <- L].]]></c> with the intention
of extracting all tuples from <c>L</c>, where the first item is
<c>X</c>.</p>
<p>Compiling this gives the following diagnostic:</p>
<code type="none">
./FileName.erl:Line: Warning: variable 'X' shadowed in generate</code>
<p>This diagnostic warns that the variable <c>X</c> in
the pattern is not the same as the variable <c>X</c>
that occurs in the function head.</p>
<p>Evaluating <c>select</c> gives the following result:</p>
<pre>
> <input>select(b,[{a,1},{b,2},{c,3},{b,7}]).</input>
[1,2,3,7]</pre>
<p>This is not the wanted result. To achieve the desired
effect, <c>select</c> must be written as follows:</p>
<code type="none"><![CDATA[
select(X, L) -> [Y || {X1, Y} <- L, X == X1].]]></code>
<p>The generator now contains unbound variables and the test has
been moved into the filter.</p>
<p>This now works as expected:</p>
<pre>
> <input>select(b,[{a,1},{b,2},{c,3},{b,7}]).</input>
[2,7]</pre>
<p>A consequence of the rules for importing variables into a
list comprehensions is that certain pattern matching operations
must be moved into the filters and cannot be written directly
in the generators.</p>
<p>To illustrate this, do <em>not</em> write as follows:</p>
<code type="none"><![CDATA[
f(...) ->
Y = ...
[ Expression || PatternInvolving Y <- Expr, ...]
...]]></code>
<p>Instead, write as follows:</p>
<code type="none"><![CDATA[
f(...) ->
Y = ...
[ Expression || PatternInvolving Y1 <- Expr, Y == Y1, ...]
...]]></code>
</section>
</chapter>
|
