ok wrote:
It is considerably more than a little revisionist to identify Haskell monads with Category Theory monads.
So a category theory monad is a functor from some category to itself. How is IO a a functor? Which category does it operate on? What does it do to the points of that category? What does it do to the arrows?
IO is a fully paid up Monad in the categorical sense. The category is the category whose objects are types and whose arrows are functions between those types. IO is a functor. The object a maps to IO a. An arrow f::a->b maps to (>>= return . f)::IO a -> IO b and that can be used to make IO an instance of Functor. The natural transforms eta and mu are called return and join. I make no claim that beginners need to know this stuff, but it's useful to understand when you start having to compose monads and create new monads. -- Dan