All Monads are Functors
Lennart Augustsson
lennart at augustsson.net
Sun Aug 13 22:02:25 EDT 2006
If I remember right, Functor was a superclass of Monad in Haskell
early on, but it was taken away. I think this was the wrong
decision, but I seem to remember that the rationale was that it would
be too onerous to require programmers to write a Functor instance
every time they want a Monad instance. Bah!
-- Lennart
On Aug 13, 2006, at 21:39 , Donald Bruce Stewart wrote:
> jon.fairbairn:
>> I find myself dismayed that the mathematical relationship
>> between Monads and Functors isn't available in Haskell98; if
>> I use fmap in a Monad m=>... typed function, I get an extra
>> Functor m required in the context, but not only are all
>> mathematical monads functors, any instance of Monad has fmap
>> in the form (>>= return . f), so it's annoying.
>
> For interest. Here's the defn in the Gofer prelude from 1994:
>
> class Functor f where
> map :: (a -> b) -> (f a -> f b)
>
> class Functor m => Monad m where
> result :: a -> m a
> join :: m (m a) -> m a
> bind :: m a -> (a -> m b) -> m b
>
> join x = bind x id
> x `bind` f = join (map f x)
>
> class Monad m => Monad0 m where
> zero :: m a
>
> http://www.cse.unsw.edu.au/~dons/data/cc.prelude
>
> -- Don
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