Composing functions into a higher-order function

In the previous recipe, we implemented two higher-order functions, map and fold, and saw various examples of using them. At the end of the recipe, we saw how they can be pipelined to produce a final value after several transformations of the original data. Pipelining is a form of composition, which means creating one new function from two or more given functions. In the mentioned example, we didn't actually compose functions; we only called a function with the result produced by another, but in this recipe, we will learn how to actually compose functions together into a new function. For simplicity, we will only consider unary functions (functions that take only one argument).

Getting ready

Before you go forward, it is recommended that you read the previous recipe, Implementing higher-order functions map and fold. It is not mandatory for understanding this recipe, but we will refer to the map and fold functions we...