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<h1 style='display: inline' id='standard-ml-and-haskell'>Standard ML and Haskell</h1><br />
<br />
<span class='quote'>Published at 2010-04-09T22:57:36+01:00</span><br />
<br />
<span>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 knew a little Haskell, I could not help myself, and I also implemented the same exercises in Haskell.</span><br />
<br />
<span>As you will see, SML and Haskell are very similar (at least when it comes to the basics). However, the syntax of Haskell is a bit more "advanced". Haskell utilizes fewer keywords (e.g. no val, end, fun, fn ...). Haskell also allows to write down the function types explicitly. 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. </span><br />
<br />
<span>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:</span><br />
<br />
<h2 style='display: inline' id='table-of-contents'>Table of Contents</h2><br />
<br />
<ul>
<li><a href='#standard-ml-and-haskell'>Standard ML and Haskell</a></li>
<li>⇢ <a href='#defining-a-multi-data-type'>Defining a multi-data type</a></li>
<li>⇢ <a href='#processing-a-multi'>Processing a multi</a></li>
<li>⇢ <a href='#simplify-function'>Simplify function</a></li>
<li>⇢ <a href='#delete-all'>Delete all</a></li>
<li>⇢ <a href='#delete-one'>Delete one</a></li>
<li>⇢ <a href='#higher-order-functions'>Higher-order functions</a></li>
</ul><br />
<h2 style='display: inline' id='defining-a-multi-data-type'>Defining a multi-data type</h2><br />
<br />
<span>Standard ML:</span><br />
<br />
<!-- Generator: GNU source-highlight 3.1.9
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre><b><u><font color="#000000">datatype</font></u></b> ’a multi
= EMPTY
| ELEM <b><u><font color="#000000">of</font></u></b> ’a
| UNION <b><u><font color="#000000">of</font></u></b> ’a multi * ’a multi
</pre>
<br />
<span>Haskell:</span><br />
<br />
<!-- Generator: GNU source-highlight 3.1.9
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre><b><u><font color="#000000">data</font></u></b> (<b><font color="#000000">Eq</font></b> a) => <b><font color="#000000">Multi</font></b> a
= <b><font color="#000000">Empty</font></b>
| <b><font color="#000000">Elem</font></b> a
| <b><font color="#000000">Union</font></b> (<b><font color="#000000">Multi</font></b> a) (<b><font color="#000000">Multi</font></b> a)
<b><u><font color="#000000">deriving</font></u></b> <b><font color="#000000">Show</font></b>
</pre>
<br />
<h2 style='display: inline' id='processing-a-multi'>Processing a multi</h2><br />
<br />
<span>Standard ML:</span><br />
<br />
<!-- Generator: GNU source-highlight 3.1.9
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre><b><u><font color="#000000">fun</font></u></b> number (EMPTY) _ = <font color="#000000">0</font>
| number (ELEM x) w = <b><u><font color="#000000">if</font></u></b> x = w <b><u><font color="#000000">then</font></u></b> <font color="#000000">1</font> <b><u><font color="#000000">else</font></u></b> <font color="#000000">0</font>
| number (UNION (x,y)) w = (number x w) + (number y w)
<b><u><font color="#000000">fun</font></u></b> test_number w = number (UNION (EMPTY, \
UNION (ELEM <font color="#000000">4</font>, UNION (ELEM <font color="#000000">6</font>, \
UNION (UNION (ELEM <font color="#000000">4</font>, ELEM <font color="#000000">4</font>), EMPTY))))) w
</pre>
<br />
<span>Haskell:</span><br />
<br />
<!-- Generator: GNU source-highlight 3.1.9
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre>number <b><font color="#000000">Empty</font></b> <b><u><font color="#000000">_</font></u></b> = <font color="#000000">0</font>
number (<b><font color="#000000">Elem</font></b> x) w = <b><u><font color="#000000">if</font></u></b> x == w <b><u><font color="#000000">then</font></u></b> <font color="#000000">1</font> <b><u><font color="#000000">else</font></u></b> <font color="#000000">0</font>
test_number w = number (<b><font color="#000000">Union</font></b> <b><font color="#000000">Empty</font></b> \
(<b><font color="#000000">Union</font></b> (<b><font color="#000000">Elem</font></b> <font color="#000000">4</font>) (<b><font color="#000000">Union</font></b> (<b><font color="#000000">Elem</font></b> <font color="#000000">6</font>) \
(<b><font color="#000000">Union</font></b> (<b><font color="#000000">Union</font></b> (<b><font color="#000000">Elem</font></b> <font color="#000000">4</font>) (<b><font color="#000000">Elem</font></b> <font color="#000000">4</font>)) <b><font color="#000000">Empty</font></b>)))) w
</pre>
<br />
<h2 style='display: inline' id='simplify-function'>Simplify function</h2><br />
<br />
<span>Standard ML:</span><br />
<br />
<!-- Generator: GNU source-highlight 3.1.9
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre><b><u><font color="#000000">fun</font></u></b> simplify (UNION (x,y)) =
<b><u><font color="#000000">let</font></u></b> <b><u><font color="#000000">fun</font></u></b> is_empty (EMPTY) = true | is_empty _ = false
<b><u><font color="#000000">val</font></u></b> x’ = simplify x
<b><u><font color="#000000">val</font></u></b> y’ = simplify y
<b><u><font color="#000000">in</font></u></b> <b><u><font color="#000000">if</font></u></b> (is_empty x’) <b><u><font color="#000000">andalso</font></u></b> (is_empty y’)
<b><u><font color="#000000">then</font></u></b> EMPTY
<b><u><font color="#000000">else</font></u></b> <b><u><font color="#000000">if</font></u></b> (is_empty x’)
<b><u><font color="#000000">then</font></u></b> y’
<b><u><font color="#000000">else</font></u></b> <b><u><font color="#000000">if</font></u></b> (is_empty y’)
<b><u><font color="#000000">then</font></u></b> x’
<b><u><font color="#000000">else</font></u></b> UNION (x’, y’)
<b><u><font color="#000000">end</font></u></b>
| simplify x = x
</pre>
<br />
<span>Haskell:</span><br />
<br />
<!-- Generator: GNU source-highlight 3.1.9
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre>simplify (<b><font color="#000000">Union</font></b> x y)
| (isEmpty x’) && (isEmpty y’) = <b><font color="#000000">Empty</font></b>
| isEmpty x’ = y’
| isEmpty y’ = x’
| otherwise = <b><font color="#000000">Union</font></b> x’ y’
<b><u><font color="#000000">where</font></u></b>
isEmpty <b><font color="#000000">Empty</font></b> = <b><font color="#000000">True</font></b>
isEmpty <b><u><font color="#000000">_</font></u></b> = <b><font color="#000000">False</font></b>
x’ = simplify x
y’ = simplify y
simplify x = x
</pre>
<br />
<h2 style='display: inline' id='delete-all'>Delete all</h2><br />
<br />
<span>Standard ML:</span><br />
<br />
<!-- Generator: GNU source-highlight 3.1.9
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre><b><u><font color="#000000">fun</font></u></b> delete_all m w =
<b><u><font color="#000000">let</font></u></b> <b><u><font color="#000000">fun</font></u></b> delete_all’ (ELEM x) = <b><u><font color="#000000">if</font></u></b> x = w <b><u><font color="#000000">then</font></u></b> EMPTY <b><u><font color="#000000">else</font></u></b> ELEM x
| delete_all’ (UNION (x,y)) = UNION (delete_all’ x, delete_all’ y)
| delete_all’ x = x
<b><u><font color="#000000">in</font></u></b> simplify (delete_all’ m)
<b><u><font color="#000000">end</font></u></b>
</pre>
<br />
<span>Haskell:</span><br />
<br />
<!-- Generator: GNU source-highlight 3.1.9
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre>delete_all m w = simplify (delete_all’ m)
<b><u><font color="#000000">where</font></u></b>
delete_all’ (<b><font color="#000000">Elem</font></b> x) = <b><u><font color="#000000">if</font></u></b> x == w <b><u><font color="#000000">then</font></u></b> <b><font color="#000000">Empty</font></b> <b><u><font color="#000000">else</font></u></b> <b><font color="#000000">Elem</font></b> x
delete_all’ (<b><font color="#000000">Union</font></b> x y) = <b><font color="#000000">Union</font></b> (delete_all’ x) (delete_all’ y)
delete_all’ x = x
</pre>
<br />
<h2 style='display: inline' id='delete-one'>Delete one</h2><br />
<br />
<span>Standard ML:</span><br />
<br />
<!-- Generator: GNU source-highlight 3.1.9
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre><b><u><font color="#000000">fun</font></u></b> delete_one m w =
<b><u><font color="#000000">let</font></u></b> <b><u><font color="#000000">fun</font></u></b> delete_one’ (UNION (x,y)) =
<b><u><font color="#000000">let</font></u></b> <b><u><font color="#000000">val</font></u></b> (x’, deleted) = delete_one’ x
<b><u><font color="#000000">in</font></u></b> <b><u><font color="#000000">if</font></u></b> deleted
<b><u><font color="#000000">then</font></u></b> (UNION (x’, y), deleted)
<b><u><font color="#000000">else</font></u></b> <b><u><font color="#000000">let</font></u></b> <b><u><font color="#000000">val</font></u></b> (y’, deleted) = delete_one’ y
<b><u><font color="#000000">in</font></u></b> (UNION (x, y’), deleted)
<b><u><font color="#000000">end</font></u></b>
<b><u><font color="#000000">end</font></u></b>
| delete_one’ (ELEM x) =
<b><u><font color="#000000">if</font></u></b> x = w <b><u><font color="#000000">then</font></u></b> (EMPTY, true) <b><u><font color="#000000">else</font></u></b> (ELEM x, false)
| delete_one’ x = (x, false)
<b><u><font color="#000000">val</font></u></b> (m’, _) = delete_one’ m
<b><u><font color="#000000">in</font></u></b> simplify m’
<b><u><font color="#000000">end</font></u></b>
</pre>
<br />
<span>Haskell:</span><br />
<br />
<!-- Generator: GNU source-highlight 3.1.9
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre>delete_one m w = <b><u><font color="#000000">do</font></u></b>
<b><u><font color="#000000">let</font></u></b> (m’, <b><u><font color="#000000">_</font></u></b>) = delete_one’ m
simplify m’
<b><u><font color="#000000">where</font></u></b>
delete_one’ (<b><font color="#000000">Union</font></b> x y) =
<b><u><font color="#000000">let</font></u></b> (x’, deleted) = delete_one’ x
<b><u><font color="#000000">in</font></u></b> <b><u><font color="#000000">if</font></u></b> deleted
<b><u><font color="#000000">then</font></u></b> (<b><font color="#000000">Union</font></b> x’ y, deleted)
<b><u><font color="#000000">else</font></u></b> <b><u><font color="#000000">let</font></u></b> (y’, deleted) = delete_one’ y
<b><u><font color="#000000">in</font></u></b> (<b><font color="#000000">Union</font></b> x y’, deleted)
delete_one’ (<b><font color="#000000">Elem</font></b> x) =
<b><u><font color="#000000">if</font></u></b> x == w <b><u><font color="#000000">then</font></u></b> (<b><font color="#000000">Empty</font></b>, <b><font color="#000000">True</font></b>) <b><u><font color="#000000">else</font></u></b> (<b><font color="#000000">Elem</font></b> x, <b><font color="#000000">False</font></b>)
delete_one’ x = (x, <b><font color="#000000">False</font></b>)
</pre>
<br />
<h2 style='display: inline' id='higher-order-functions'>Higher-order functions</h2><br />
<br />
<span>The first line is always the SML code, the second line the Haskell variant:</span><br />
<br />
<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>
<br />
<span>E-Mail your comments to <span class='inlinecode'>paul@nospam.buetow.org</span> :-)</span><br />
<br />
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