newFactorial.scala

// Here is how I would curry a product function. I really like the word curry, btw.
def product(f: Int => Int)(a: Int, b: Int): Int =
  if (a > b) 1 else f(a) * product(f)(a + 1, b)

// Factorial can now be written as follows
// Because factorial is by definition the product of all numbers 1 to n
def factorial(n: Int) = product(identity)(1, n)

// True!
factorial(5) == 120