Learning road map for functional programming from the viewpoint of category theory

Question

I am now considering about studying functional programming from the viewpoint of category theory. There are a lot of books about functional programming and category theory, I want some suggestions regarding some comprehensive books and reference materials (like online notes, courses etc)that would contain category theory viewpoint rather than plain functional programming. I have a solid background in Abstract Algebra,commutative algebra, functional programming and bit of category theory too.

Answer 1

There's no agreed upon "bible" for CT for computer science in the same way as for mathematicians (Mac Lane), probably because the field is younger and a bit broader. It really depends on whether you want to understand . Here are a few computer science concepts with category theory counterparts:

• Simple types (which correspond to Cartesian Closed Categories)

• dependent types (Locally Cartesian Closed Categories)

• Abstract data types (categorical algebras, coalgebras, as described in e.g. Uustalu & Vene)

• Programing with effects (Monads, monoidal categories, building on the foundational observations of Moggi)

• Ressource aware programing (Closed Monoidal Categories (?))

• CPS translations can be interpreted through the lens of the Yoneda lemma (see here for a brief explanation)

I'm missing a few, there are applications of category theory from everything to domain theory to database management.