Category theory for beginners

category-theoryfunctional-programmingtype-theorymathematics

Abstraction: Category theory concepts mapped to functional programming abstractions

Key points:

Category theory (invented 1940s by Eilenberg and Mac Lane) provides composability primitives directly applicable to programming
A category consists of objects, arrows (morphisms), composition, and identity; examples include class hierarchies, posets, and the category of types and functions
Functors map between categories preserving structure; monads were discovered by Godement in 1958 and applied to programming by Moggi and Wadler in 1990
Monoids, algebraic data types, and functors are the core abstractions enabling composable software design in functional languages
Applicative functors introduced in 2006 "Applicative Programming with Effects" (McBride & Paterson)
Mathematical laws (associativity, identity) enforce correctness of compositions; Haskell's type system enforces many of these laws

Connections: Haskell · Category Theory · Functional Programming · Type Theory