From 27ed46c9129db86669052d4e7211340da1081d89 Mon Sep 17 00:00:00 2001 From: Paul Buetow Date: Wed, 19 May 2021 12:39:49 +0100 Subject: html branch --- gemfeed/2010-04-09-standard-ml-and-haskell.html | 192 ++++++++++++++++++++++++ 1 file changed, 192 insertions(+) create mode 100644 gemfeed/2010-04-09-standard-ml-and-haskell.html (limited to 'gemfeed/2010-04-09-standard-ml-and-haskell.html') diff --git a/gemfeed/2010-04-09-standard-ml-and-haskell.html b/gemfeed/2010-04-09-standard-ml-and-haskell.html new file mode 100644 index 00000000..307c3593 --- /dev/null +++ b/gemfeed/2010-04-09-standard-ml-and-haskell.html @@ -0,0 +1,192 @@ + + + + +Standard ML and Haskell + + + + +

Standard ML and Haskell

Written by Paul Buetow 2010-04-09

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.

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 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.

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:

Defining a multi data type

Standard ML:

+datatype ’a multi
+	= EMPTY
+	| ELEM of ’a
+	| UNION of ’a multi * ’a multi
+

Haskell:

+data (Eq a) => Multi a
+    = Empty
+    | Elem a
+    | Union (Multi a) (Multi a)
+    deriving Show
+

Processing a multi

Standard ML:

+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 
+

Haskell:

+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
+

Simplify function

Standard ML:

+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
+

Haskell:

+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
+

Delete all

Standard ML:

+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
+

Haskell:

+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
+

Delete one

Standard ML:

+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
+

Haskell:

+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)
+

Higher order functions

The first line is always the SML code, the second line always the Haskell variant:

+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
+

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