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
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Having fun with computers!</title>
<link rel="shortcut icon" type="image/gif" href="/favicon.ico" />
<style type="text/css">
body {
margin: auto;
max-width: 900px;
background-color: #FFFFEF;
border: 1px dashed #880000;
border-radius: 8px;
padding: 5px;
}
img {
display:block;
max-width: 80%;
}
p.quote:before {
content: " | ";
padding-left: 2px;
}
a.textlink:before {
content: " ⇒ ";
padding-left: 2px;
}
a.textlink {
text-decoration: none;
color: #FF0000;
}
a.textlink:hover {
text-decoration: underline;
}
pre {
background-color: #F1F8E9;
border: 1px dashed #BB0000;
border-radius: 8px;
padding: 5px;
font-family: "Lucida Console", "Courier New", monospace;
}
h1 {
text-align: center;
color: #880000;
}
h2, h3 {
color: #BB0000;
}
</style>
</head>
<body>
<h1>Standard ML and Haskell</h1>
<p class="quote"><i>Written by Paul Buetow 2010-04-09</i></p>
<p>I am currently looking into the functional programming language Standard ML (aka SML). The purpose is to refresh my functional programming skills and to learn something new too. Since I already know a little Haskell, could I do not help myself and I implemented the same exercises in Haskell too.</p>
<p>As you will see, SML and Haskell are very similar (at least when it comes to the basics). However, the syntax of Haskell is little bit more "advanced". Haskell utilises fewer keywords (e.g. no val, end, fun, fn ...). Haskell also allows to explicitly write down the function types. What I have been missing in SML so far is the so-called pattern guards. Although this is a very superficial comparison for now, so far I like Haskell more than SML. Nevertheless, I thought it would be fun to demonstrate a few simple functions of both languages to show off the similarities. </p>
<p>Haskell is also a "pure functional" programming language, whereas SML also makes explicit use of imperative concepts. I am by far not a specialist in either of these languages but here are a few functions implemented in both, SML and Haskell:</p>
<h2>Defining a multi data type</h2>
<p>Standard ML:</p>
<pre>
datatype ’a multi
= EMPTY
| ELEM of ’a
| UNION of ’a multi * ’a multi
</pre>
<p>Haskell:</p>
<pre>
data (Eq a) => Multi a
= Empty
| Elem a
| Union (Multi a) (Multi a)
deriving Show
</pre>
<h2>Processing a multi</h2>
<p>Standard ML:</p>
<pre>
fun number (EMPTY) _ = 0
| number (ELEM x) w = if x = w then 1 else 0
| number (UNION (x,y)) w = (number x w) + (number y w)
fun test_number w = number (UNION (EMPTY, \
UNION (ELEM 4, UNION (ELEM 6, \
UNION (UNION (ELEM 4, ELEM 4), EMPTY))))) w
</pre>
<p>Haskell:</p>
<pre>
number Empty _ = 0
number (Elem x) w = if x == w then 1 else 0
test_number w = number (Union Empty \
(Union (Elem 4) (Union (Elem 6) \
(Union (Union (Elem 4) (Elem 4)) Empty)))) w
</pre>
<h2>Simplify function</h2>
<p>Standard ML:</p>
<pre>
fun simplify (UNION (x,y)) =
let fun is_empty (EMPTY) = true | is_empty _ = false
val x’ = simplify x
val y’ = simplify y
in if (is_empty x’) andalso (is_empty y’)
then EMPTY
else if (is_empty x’)
then y’
else if (is_empty y’)
then x’
else UNION (x’, y’)
end
| simplify x = x
</pre>
<p>Haskell:</p>
<pre>
simplify (Union x y)
| (isEmpty x’) && (isEmpty y’) = Empty
| isEmpty x’ = y’
| isEmpty y’ = x’
| otherwise = Union x’ y’
where
isEmpty Empty = True
isEmpty _ = False
x’ = simplify x
y’ = simplify y
simplify x = x
</pre>
<h2>Delete all</h2>
<p>Standard ML:</p>
<pre>
fun delete_all m w =
let fun delete_all’ (ELEM x) = if x = w then EMPTY else ELEM x
| delete_all’ (UNION (x,y)) = UNION (delete_all’ x, delete_all’ y)
| delete_all’ x = x
in simplify (delete_all’ m)
end
</pre>
<p>Haskell:</p>
<pre>
delete_all m w = simplify (delete_all’ m)
where
delete_all’ (Elem x) = if x == w then Empty else Elem x
delete_all’ (Union x y) = Union (delete_all’ x) (delete_all’ y)
delete_all’ x = x
</pre>
<h2>Delete one</h2>
<p>Standard ML:</p>
<pre>
fun delete_one m w =
let fun delete_one’ (UNION (x,y)) =
let val (x’, deleted) = delete_one’ x
in if deleted
then (UNION (x’, y), deleted)
else let val (y’, deleted) = delete_one’ y
in (UNION (x, y’), deleted)
end
end
| delete_one’ (ELEM x) =
if x = w then (EMPTY, true) else (ELEM x, false)
| delete_one’ x = (x, false)
val (m’, _) = delete_one’ m
in simplify m’
end
</pre>
<p>Haskell:</p>
<pre>
delete_one m w = do
let (m’, _) = delete_one’ m
simplify m’
where
delete_one’ (Union x y) =
let (x’, deleted) = delete_one’ x
in if deleted
then (Union x’ y, deleted)
else let (y’, deleted) = delete_one’ y
in (Union x y’, deleted)
delete_one’ (Elem x) =
if x == w then (Empty, True) else (Elem x, False)
delete_one’ x = (x, False)
</pre>
<h2>Higher order functions</h2>
<p>The first line is always the SML code, the second line always the Haskell variant:</p>
<pre>
fun make_map_fn f1 = fn (x,y) => f1 x :: y
make_map_fn f1 = \x y -> f1 x : y
fun make_filter_fn f1 = fn (x,y) => if f1 x then x :: y else y
make_filter_fn f1 = \x y -> if f1 then x : y else y
fun my_map f l = foldr (make_map_fn f) [] l
my_map f l = foldr (make_map_fn f) [] l
fun my_filter f l = foldr (make_filter_fn f) [] l
my_filter f l = foldr (make_filter_fn f) [] l
</pre>
<p>E-Mail me your thoughts at comments@mx.buetow.org!</p>
<a class="textlink" href="../">Go back to the main site</a><br />
</body>
</html>
|
