[Haskell-beginners] Re: Thinking about monads

[Brent Yorgey]

On Mon, Apr 13, 2009 at 03:11:42PM -0700, Michael Mossey wrote:
>
> I know Maybe is both a functor and a monad, and I was thinking: what's the 
> difference? They are both wrappers on types. Then I realized, the 
> difference is: they have different class definitions.

In fact, every monad should be a functor, but not every functor is a
monad.  Being a monad is a much stronger condition than being a functor.

>
> class Functor f where
>   fmap :: (a->b) -> f a -> f b
>
> (Note how fussy this definition would be in C++. It would be a kind of 
> template, but would probably look a lot more complex and would require 
> lengthy declarations.)
>
> class Monad m where
>    a >>= b :: m a -> (a -> m b) -> m b

Don't forget  return :: a -> m a  !  That's the other key method in the Monad
class.  (There are also >> and 'fail' but those are unimportant---the
first is just a specialization of >>=, and fail is a hack).

-Brent