Currying is when you break down a function that takes multiple arguments into a series of functions that each take only one argument.

Example

Ex1: Write a function that takes the product of all the integers on a given interval

def product(a: Int)(b: Int): Int = {
  if (a > b) 1
  else a * product(a + 1)(b)
}

product(2)(3)

Ex2: Write a function that takes the product of the factorials of all the integers  on a given interval

def fact(x: Int): Int = if (x == 0) 1 else x * fact(x - 1)

def productFacts(a: Int)(b: Int): Int = {

  if(a > b) 1

  else fact(a) * productFacts(a + 1)(b)

}

productFacts(2)(3)

Ex3: Write a general function which generalizes both sum and product? 

def fact(x: Int): Int = if (x == 0) 1 else x * fact(x - 1)

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

def product(x: Int, y: Int): Int = x * y

def mapReduce(f: Int => Int, compose: (Int, Int) => Int, zero: Int)(a: Int, b: Int): Int = {

  if(a > b) zero

  else compose(f(a), mapReduce(f, compose, zero)(a + 1, b))

}

def productFacts: (Int, Int) => Int = mapReduce(fact, product, 1)(_, _)

def sumFacts: (Int, Int) => Int = mapReduce(fact, sum, 0)(_, _)

productFacts(2, 3)

sumFacts(2, 3)