Difference between f(a,b) and f(a)(b) in Scala - scala

Question

I am very very new to Scala. I am reading a book called functional programming in scala by Paul Chiusano and Rúnar Bjarnason. So far I am finding it interesting. I see a solution for curry and uncurry
def curry[A,B,C](f: (A, B) => C): A => (B => C)= {
a => b => f(a,b)
}
def uncurry[A,B,C](f: A => B => C): (A, B) => C = {
(a,b) => f(a)(b)
}
In Curry I understand f(a,b) which results in value of type C but in uncurry I do not understand f(a)(b). Can anyone please tell me how to read f(a)(b) or how is this resulting to a type of C or please refer me some online material that can explain this to me?
Thanks for your help.

Answer 1

Basically the return type of f(a) is a function of type B => C lets call this result g.
If you then call g(b) you obtain a value of type C.
f(a)(b) can be expanded to f.apply(a).apply(b)

Answer 2

In the uncurry method you take a so-called "curried" function, meaning that instead of having a function that evaluates n arguments, you have n functions evaluating one argument, each returning a new function until you evaluate the final one.
Currying without a specific support from the language mean you have to do something like this:
// curriedSum is a function that takes an integer,
// which returns a function that takes an integer
// and returns the sum of the two
def curriedSum(a: Int): Int => Int =
b => a + b
Scala however provides further support for currying, allowing you to write this:
def curriedSum(a: Int)(b: Int): Int = a + b
In both cases, you can partially apply curriedSum, getting a function that takes an integer and sums it to the number you passed in originally, like this:
val sumTwo: Int => Int = curriedSum(2)
val four = sumTwo(2) // four equals 4
Let's go back to your case: as we mentioned, uncurry takes a curried function and turns it into a regular function, meaning that
f(a)(b)
can read as: "apply parameter a to the function f, then take the resulting function and apply the parameter b to it".

Answer 3

In case if somebody is looking for an explanation. This link explains it better
def add(x:Int, y:Int) = x + y
add(1, 2) // 3
add(7, 3) // 10
After currying
def add(x:Int) = (y:Int) => x + y
add(1)(2) // 3
add(7)(3) // 10
In the first sample, the add method takes two parameters and returns the result of adding the two. The second sample redefines the add method so that it takes only a single Int as a parameter and returns a functional (closure) as a result. Our driver code then calls this functional, passing the second “parameter”. This functional computes the value and returns the final result.