Currying

In the sum function, there is repetition in the parameters a and b which just get passed from one function to another. We can get rid of these with currying. Then, we can rewrite sum as follows:

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
}

Now sum is a function that returns another function. This function applies the input function parameter and sums up the result. We can redefine the three sum functions as:

def sumInts = sum(x => x)
def sumCubes = sum(x => x * x * x)
def sumFacts = sum(factorial)

If we wanted to just use the function sumCubes without explicitly defining it, we could do it another way: sum(cube)(1, 10).  sum(cube) applies the cube function to the sum function and returns the sum of cubes function. This function is then applied to the parameters (1,10). We see that sum(cube) is equivalent to our definition of sumCubes. Function application associates to the left.