Issue with type families

[Daniel Fischer]

Am Donnerstag 04 März 2010 00:17:09 schrieb Tyson Whitehead:
> The following code
>
>   {-# LANGUAGE FlexibleInstances, TypeFamilies #-}
>
>   import Control.Applicative
>
>   class Z t where
>       type W t
>       z :: t -> W t
>
>   instance Z (a -> b) where
>       type W (a -> b) = a -> b
>       z = id
>
>   instance Z (IO (a -> b)) where
>       type W (IO (a -> b)) = IO a -> IO b
>       z = (<*>)
>
> works fine, but if I try and generalize to from IO to the Applicative
> classes
>
>   instance (Applicative m) => Z (m (a -> b)) where
>       type W (m (a -> b)) = m a -> m b
>       z = (<*>)
>
> I get the following error
>
>   Temp.hs:10:9:
>       Conflicting family instance declarations:
>         type instance W (a -> b) -- Defined at Temp.hs:10:9
>         type instance W (m (a -> b)) -- Defined at Temp.hs:14:9
>   Failed, modules loaded: none.
>
> unless I remove one of the instances, and then it is happy.
>
> Is this correct?  I don't claim to really understand the rules regarding
> type classes, but I can't see why these are overlapping.
>
> Thanks!  -Tyson

Because:

instance Applicative ((->) a) -- Defined in Control.Applicative

so, from the instance Z (a -> b), with b == c -> d, we have an 

instance Z (a -> (b -> c))

and from instance Z (m (u -> v)), we have, with m == ((->) x), an

instance Z (x -> (u -> v))