Currying in Scala, what are the types that make these statements compile?

Question

So I have this function in Scala:

def f(a: Int)(b: Int)(c: Double)(d: Double): Double = a * c + b * d

The question is What are the three types that make the following statements compile.

def g: <Type1> = f(1)(2)(3.0) 
def h: <Type2> = f(1)(2) 
def k: <Type3> = f(1)

I'm still new to Scala and I am not really understanding the concept of currying. Maybe an answer to this question with some explanation will really help me. Thanks.

Answer 1

First, one main thing: function that takes two parameters a and b and returns a value c can be viewed as a function that takes an a and returns a function that takes b and returns c. This "change of point of view" is called currying.

Imagine a function that sums up two numbers. You give it 2 and 3, it returns 5. It can be viewed as a function that takes one number and returns a function from a number to a number. You give it a 2, it returns a function that takes some number and adds 2 to it.

Now, some types that you requested:

// pseudocode!

def g: Double => Double 
  = f(1)(2)(3.0) // we supply three params and are left with only one, "d"
  = (d: Double) => 1 * 3.0 + 2 * d // we comply with g's type

def h: Double => Double => Double // or (Double, Double) => Double 
  = f(1)(2) // we supply two params and are left with two more, "c" and "d"
  = (c: Double)(d: Double) => 1 * c + 2 * d // we comply with h's type

def k: Double => Double => Double => Double // or (Double, Double, Double) => Double
  = f(1) // we supply one param and are left with three more, "b", "c" and "d"
  = (b: Double)(c: Double)(d: Double) => 1 * c + b * d // we comply with k's type