Scala Curry

"All functions are curried in Haskell by default" that is, all functions in Haskell take only one argument. How does it do this? By currying.

Scala has currying built-in. To demonstrate, take this method that takes tow Ints and returns an Int:

  def aMethodWith2Args(x: Int, y: Int): Int = x + y

Let's lift it:

  val lifted: (Int, Int) => Int = aMethodWith2Args(_, _)

and curry it:

  val curried: Int => Int => Int = lifted.curried
 
So, we too now have a function that only takes one argument. It just returns another function that also takes only one argument. That's currying.

Now we can partially apply it

  val partial: Int => Int = curried(1)
  println(partial(2)) // prints out '3'

Just like Haskell.

The math behind it can be found here. Using Haskell notation:

($) :: (a -> b) -> (a -> b)
// $ takes function, returns function, this is the same as ((a -> b), a) -> b, instead of passing all
// arguments at once, we can pass first argument to function, receive partially applied function, 
// and pass second argument to it.