Currying syntax in scala - scala

Question

The syntax of currying in scala is for example
def f(x: Int, b: Int) = x + y
is
def f(x: Int)(b: Int) = x + y
And currying for sum to sum for given range a and b is
def sum(f: Int => Int, a: Int, b: Int) = {
...
}
sum(x=>x, 3, 6) // outcome is 18 (3+4+5+6)
is
def sum(f: Int => Int): (Int, Int) => Int = {
def sumF(a: Int, b: Int): Int =
if (a > b) 0
else f(a) + sumF(a + 1, b)
sumF
}
sum(x=>x)(3, 6) // outcome is 18 (3+4+5+6)
But I don't understand why colon(:)
exists between (f: Int => Int) and (Int, Int)
in def sum(f: Int => Int): (Int, Int) => Int = {
instead of
def sum(f: Int => Int)(Int, Int) => Int = {

Answer 1

Your sum example is not curried. If you wanted it curried you'd do something like:
def sum(f: Int => Int)(a: Int, b: Int): Int =
if (a > b) 0
else f(a) + sum(f)(a + 1, b)
sum(x=>x)(3, 6) // res0: Int = 18
Your code defines a method that takes a single argument, def sum(f: Int => Int). That argument is a function that takes and Int and returns an Int. So no currying involved.
This sum method returns a function, : (Int, Int) => Int. This returned function takes 2 Ints and returns and Int. Invoking this sum method looks like currying, but it's not.
sum(x=>x)(3, 6)
Instead you are invoking sum() with a single argument (x=>x) and then invoking the returned function with two arguments (3,6).

Answer 2

(Int, Int) => Int between : and = specify the function's return type, i.e, it says sum will return another method of signature (Int, Int) => Int which takes two Int and returns another Int, and this is the signature of your inner sumF function:
You can rewrite this to the currying syntax as follows:
def sum(f: Int => Int)(a: Int, b: Int): Int = {
def sumF(a: Int, b: Int): Int =
if (a > b) 0
else f(a) + sumF(a + 1, b)
sumF(a, b)
}
This will more or less do the same thing as the method defined in OP:
sum(x => x)(3, 6)
// res11: Int = 18
But these two definitions are not exactly the same, for instance, for the currying syntax defined here, if you want to generate a new method from it, you have to specify the variable type, like:
val mysum: (Int, Int)=> Int = sum(x => x)
But for the one in OP, it can be simply val mysum = sum(x => x) as the return type of sum as already been specified.