Function data type is unclear in SML

Question

Given the following function in SML:

fun i a b = let fun j()=a+1 in j end;

The data type of the function is:

val i = fn : int -> 'a -> unit -> int

I don't understand why int -> 'a -> unit -> int?

And why not (int * a') -> unit -> int, since the function i receives two inputs.

Perhaps [this](http://stackoverflow.com/questions/14550740/sml-why-functions-always-take-one-argument-make-language-flexible/14554122#14554122), [this](http://stackoverflow.com/questions/14432696/what-does-this-function-signature-mean-in-sml/14438864#14438864) and [this](http://stackoverflow.com/questions/8395564/what-are-curry-and-uncurry-in-high-order-functions-in-ml/8400194#8400194) will enlighten you a bit more on currying? — Jesper.Reenberg, Feb 16 '13 at 23:01

score 2 · Answer 1 · edited May 23 '17 at 12:18

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This function (as well, as any function in SML) is actually receive one input, because of currying.

Technically there is function that takes unit, that returns function that takes 'a that returns function that takes int.

So

fun foo a b = a + b;

is just an syntactic sugar to

fun foo a = fn b => a + b;

and so on.

edited May 23 '17 at 12:18

Community

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answered Feb 16 '13 at 22:39

om-nom-nom

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Currying, not carrying. ;) – Andreas Rossberg Feb 17 '13 at 16:11
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@AndreasRossberg I hope mr. Haskell will forgive me ;-) – om-nom-nom Feb 17 '13 at 20:00

score 2 · Accepted Answer · answered Feb 16 '13 at 22:40

If you defined the function as fun i (a,b) = ... then it would take a tuple as an argument and its type would indeed be (int * 'a) -> unit -> int. It would be called as i (23,42) () ((23,42) being a tuple and () being the unit value).

However you defined it as fun i a b = ..., which defines a function that takes an argument and then returns another function that takes the next argument. It is a shortcut for fun i a = fn b => .... It can be called as i a b ().

Function data type is unclear in SML

2 Answers2