On 3/15/07, Steve Downey <sdowney@gmail.com> wrote:

EOk, i'm trying to write down, not another monad tutorial, because I
don't know that much yet, but an explication of my current
understanding of monads.

But before I write down something that is just flat worng, I thought
I'd get a cross check. (and I can't get to #haskell)

Monads are Functors. Functors are projections from one category to
another such that structure is preserved. One example I have in mind
is the embedding of the natural numbers into the real numbers. The
mapping is so good, that we don't flinch at saying 1 == 1.0.

Monads are endofunctors (functors from one category to itself). This is easy to see from the type of join:

join : m (m a) -> m a

For Haskell monads the category is the category of Haskell types and Haskell functions. In this category N and R are objects, so you'll get the wrong idea trying to see them as categories.

/ Ulf