Functors, Applicatives, and Monads in Plain English

5/6/2016

This website provides an introduction to the concepts of monoids, monads, and functors in functional programming. It explains that monoids are mathematical structures with an associative binary operation and an identity element. Monads, on the other hand, are a way to encapsulate computations and manage side effects in a pure functional programming language. Functors, as described on the website, are objects that can be mapped over, allowing for transformations of their contents. The author presents examples and explanations of each concept, along with their practical applications in programming. This resource serves as a helpful guide for understanding these fundamental concepts in functional programming.

category theory ꞏ mathematics ꞏ computer science ꞏ functional programming ꞏ abstract algebra ꞏ monoid ꞏ monad ꞏ functor ꞏ programming languages ꞏ type theory ꞏ programming concepts ꞏ algebraic structures ꞏ mathematical structures ꞏ software development ꞏ software engineering ꞏ functional programming languages ꞏ programming paradigms ꞏ functional programming concepts ꞏ category theory concepts ꞏ type systems ꞏ computational theory ꞏ higher-order functions ꞏ mathematics in computer science ꞏ programming principles ꞏ programming abstractions ꞏ software design ꞏ formal methods ꞏ theory of computation ꞏ mathematical reasoning ꞏ programming logic ꞏ programming theory ꞏ software architecture ꞏ software modeling ꞏ software verification ꞏ abstraction ꞏ software specification ꞏ software correctness ꞏ composability ꞏ code reuse ꞏ programming patterns ꞏ programming language theory ꞏ software engineering concepts ꞏ pure functions ꞏ immutability ꞏ referential transparency ꞏ data transformation ꞏ functional composition ꞏ mathematical foundations ꞏ functional programming paradigms ꞏ type inference ꞏ software optimization ꞏ software performance ꞏ mathematical abstraction ꞏ functional programming principles ꞏ functional programming techniques ꞏ functional programming patterns ꞏ lambda calculus