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.

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.

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
```

```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
```

```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
```

```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
```

```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
```

```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 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
```