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diff --git a/gemfeed/2010-04-09-standard-ml-and-haskell.gmi b/gemfeed/2010-04-09-standard-ml-and-haskell.gmi new file mode 100644 index 00000000..a4a1dc57 --- /dev/null +++ b/gemfeed/2010-04-09-standard-ml-and-haskell.gmi @@ -0,0 +1,174 @@ +# 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 +``` + +E-Mail me your thoughts at comments@mx.buetow.org! + +=> ../ Go back to the main site |