4.7. Currying

We’ve already seen that an OCaml function that takes two arguments of types t1 and t2 and returns a value of type t3 has the type t1 -> t2 -> t3. We use two variables after the function name in the let expression:

let add x y = x + y
val add : int -> int -> int = <fun>

Another way to define a function that takes two arguments is to write a function that takes a tuple:

let add' t = fst t + snd t
val add' : int * int -> int = <fun>

Instead of using fst and snd, we could use a tuple pattern in the definition of the function, leading to a third implementation:

let add'' (x, y) = x + y
val add'' : int * int -> int = <fun>

Functions written using the first style (with type t1 -> t2 -> t3) are called curried functions, and functions using the second style (with type t1 * t2 -> t3) are called uncurried. Metaphorically, curried functions are “spicier” because you can partially apply them (something you can’t do with uncurried functions: you can’t pass in half of a pair). Actually, the term curry does not refer to spices, but to a logician named Haskell Curry (one of a very small set of people with programming languages named after both their first and last names).

Sometimes you will come across libraries that offer an uncurried version of a function, but you want a curried version of it to use in your own code; or vice versa. So it is useful to know how to convert between the two kinds of functions, as we did with add above.

You could even write a couple of higher-order functions to do the conversion for you:

let curry f x y = f (x, y)
let uncurry f (x, y) = f x y
val curry : ('a * 'b -> 'c) -> 'a -> 'b -> 'c = <fun>
val uncurry : ('a -> 'b -> 'c) -> 'a * 'b -> 'c = <fun>
let uncurried_add = uncurry add
let curried_add = curry add''
val uncurried_add : int * int -> int = <fun>
val curried_add : int -> int -> int = <fun>