Why do we need monads? We want to program only using functions. (“functional programming (FP)” after all). Then, we have a first big problem. This is a program: f(x) = 2 * x g(x,y) = x / y How can we say what is to be executed first? How can we form an ordered sequence … Read more
Here’s an even simpler answer: A Monad is something that “computes” when monadic context is collapsed by join :: m (m a) -> m a (recalling that >>= can be defined as x >>= y = join (fmap y x)). This is how Monads carry context through a sequential chain of computations: because at each … Read more
In the usual encoding an enumerator is essentially a StepT[E, F, ?] ~> F[StepT[E, F, ?]]. If you try to write a generic method converting this type into a Step[E, G, ?] ~> G[Step[E, G, ?]] given an F ~> G, you’ll quickly run into an issue: you need to “lower” a Step[E, G, A] … Read more
I talk a bit about this in Engineering Large Projects in Haskell and in the Design and Implementation of XMonad. Engineering in the large is about managing complexity. The primary code structuring mechanisms in Haskell for managing complexity are: The type system Use the type system to enforce abstractions, simplifying interactions. Enforce key invariants via … Read more
UPDATE: This question was the subject of an immensely long blog series, which you can read at Monads — thanks for the great question! In terms that an OOP programmer would understand (without any functional programming background), what is a monad? A monad is an “amplifier” of types that obeys certain rules and which has … Read more
That particular phrasing is by James Iry, from his highly entertaining Brief, Incomplete and Mostly Wrong History of Programming Languages, in which he fictionally attributes it to Philip Wadler. The original quote is from Saunders Mac Lane in Categories for the Working Mathematician, one of the foundational texts of Category Theory. Here it is in … Read more
First: The term monad is a bit vacuous if you are not a mathematician. An alternative term is computation builder which is a bit more descriptive of what they are actually useful for. They are a pattern for chaining operations. It looks a bit like method chaining in object-oriented languages, but the mechanism is slightly … Read more