[joe_the_user]

I have an MA in math and I was somewhat exposed to category theory and algebraic structures in my time at the university. I find knowing math generally is useful for programming but I haven't found it useful for understanding functional programming in particular.

I think functional programming uses category theory in a different fashion than even fairly advanced mathematics; Breaking Hungerford's Algebra text, in the chapter on Category Theory, he writes, "A significant part of the elementary theory of categories is the attempt to generalize as many concepts as possible from well-known categories (for example, sets or modules) to arbitrary categories". Which is a rather different approach than building programs.

Which is to say that for most mathematics, categories are tools for generalization or for providing a firmer foundation for existing mathematical structures. For understands monads as used by FP, the description as "little languages" seemed the best - it's way of not having side effects by using functions to incrementally construct output instead of doing output in the middle of computation.

[codebje]

Much of software design is about composition, which is where category theory shines, just at the most shallow levels.

If I dream up a way to tackle a problem, have I made a category? If I have two modules, can I compose them into one, is there an initial or final module, is composition associative? If there's some underlying structure, what's the free module based on it?

Those questions can help make more durable designs.