In Chapter 10, we introduced a simple algebraic structure, the monoid. This was our first instance of a completely abstract, purely algebraic interface, and it led us to think about interfaces in a new way. A useful interface may be defined only by a collection of operations related by laws.

In Chapter 11, we’ll continue this mode of thinking and apply it to the problem of factoring out code duplication across some of the libraries we wrote in parts 1 and 2. We’ll discover two new abstract interfaces, Functor and Monad, and get more general experience with spotting these sorts of abstract structures in our code.

In Chapter 12 we’ll learn about a related abstraction, applicative functors, which are less powerful than monads, but more general (and hence more common). The process of arriving at applicative functors will also provide some insight into how to discover such abstractions, and we’ll use some of these ideas to uncover another useful abstraction, traversable functors. It may take some time for the full significance and usefulness of these abstractions to sink in, but you’ll see them popping up again and again in your daily work with FP if you pay attention.

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