[muaddirac]

I studied monads in a Categorical context in college (Domain Theory, if interested).

Monads can be understood very simply in Category Theory if you don't care so much about the details: pick a couple of your favorite categories (which is just a bunch of objects with morphisms) and find a functor between them. Then find a functor back the other way. Composing those two functors gives a Monad - a functor from a category back into itself (an endofunctor). Not just any endofunctor will be a Monad though, so if you start with an endofunctor (instead of two functors) you need to also have two other "natural transformations". (That endofunctor + the two natural transformations is why monads are sometimes called triples).

The application of monads to programming was not obvious to me, even having dealt with them a bit mathematically. I started looking at Haskell earlier this year and it turns out that a Monad in haskell is defined on the Hask category, where objects are types and morphisms are functions between them. Even that wasn't enough for me to get why they're useful, and that seems to be because as far as I can tell they're only used for "threading" state through a series of functions...but perhaps I'm still missing something?

[mindslight]

> as far as I can tell they're only used for "threading" state through a series of functions

That is why people bump up against them when learning Haskell, but monads run much deeper in functional programming.. Even "pure" functions in Haskell are monadic with respect to the non-terminating "bottom".

I said it elsewhere in this topic, but check out Moggi's "Notions of computation and monads".