JavaScript: Functional Programming for JavaScript Developers

Implementing categories

It's about time we formally defined category theory as JavaScript objects. Categories are objects (types) and morphisms (functions that only work on those types). It's an extremely high-level, totally-declarative way to program, but it ensures that the code is extremely safe and reliable—perfect for APIs and libraries that are worried about concurrency and type safety.

First, we'll need a function that helps us create morphisms. We'll call it homoMorph() because they'll be homomorphisms. It will return a function that expects a function to be passed in and produces the composition of it, based on the inputs. The inputs are the types that the morphism accepts as input and gives as output. Just like our type signatures, that ...