From Mathematics to Generic Programming

7. Deriving a Generic Algorithm

To generalize something means to think it.Hegel, Philosophy of Right

In this chapter we’ll take the Egyptian multiplication algorithm from Chapter 2 and, by using the mathematical abstractions introduced in the previous chapter, generalize it to apply to a wide variety of problems beyond simple arithmetic.

7.1 Untangling Algorithm Requirements

Two steps are required to write a good piece of code. The first step is to get the algorithm right. The second step is to figure out which sorts of things (types) it works for. Now, you might be thinking that you already know the type—it’s int or float or whatever you started with. But that may not always be the case; things change. Next year someone may want the code to ...