4 Steps to Defining Recursive Functions

A good set of steps to follow when defining recursive functions is:

1. Define the function type

   Thinking about function types is very helpful when defining functions, and explicitly

   defining the function type is good practice.

2. Enumerate different cases

   Considering the general cases we expect allows us to create the function structure that we can then fill out gradually. For example, two standard cases for lists are empty and non-empty lists.

3. Take care of the simple cases first (usually base cases)

   The simple cases are usually straightforward so it's easier to define them. For example, our

   sumN 0 = 0 is a simple case and also the base case.

4. Define the other cases

   Here, we have to think about how to calculate the wanted result using both the recursive call

   on the function itself and any other functions we might need. For example, in sumN x = x sumN (x - 1) we used both the (+) and (-) functions.