RE [Haskell-cafe] Monad Description For Imperative
dpiponi at gmail.com
Thu Aug 2 19:50:09 EDT 2007
> 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.
More information about the Haskell-Cafe