Issue with type families

[Daniel Fischer]

Am Donnerstag 04 März 2010 02:39:30 schrieb Tyson Whitehead:
> On March 3, 2010 18:35:26 Daniel Fischer wrote:
> > 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))
>
> Thanks Daniel,
>
> That makes sense.  Strangely enough though, I had actually originally
> tried it with my own Applicative class just in case I was being tripped
> up by something like the (->) instance you pointed out, and it still
> didn't work.

Well, GHC takes only the class head into account for instance selection, 
and

u -> (v -> w)

matches both,

a -> b   --  (a == u, b == v -> w)

and

m (c -> d)    -- (m == ((->) u), c == v, d == w),

so there's the overlap without any other type classes involved.
And since u -> (v -> w) matches both instance heads,

type W (u -> (v -> w)) = u -> (v -> w)

and

type W (((->) u) (v -> w)) = (u -> v) -> (u -> w)

are indeed conflicting, so you can't even use OverlappingInstances etc. to 
make it work.

> That is
>
>   {-# LANGUAGE FlexibleInstances, TypeFamilies #-}
>
>   newtype I a = I a
>
>   class A t where
>       ap :: t (a -> b) -> t a -> t b
>
>   class Z t where
>       type W t
>       z :: t -> W t
>
>   instance A I where
>       ap (I f) (I x) = I $ f x
>
>   instance Z (a -> b) where
>       type W (a -> b) = a -> b
>       z = id
>
>   instance A t => Z (t (a -> b)) where
>       type W (t (a -> b)) = t a -> t b
>       z = ap
>
> also gives me
>
>   Temp.hs:17:9:
>       Conflicting family instance declarations:
>         type instance W (a -> b) -- Defined at Temp.hs:17:9
>         type instance W (t (a -> b)) -- Defined at Temp.hs:21:9
>   Failed, modules loaded: none.
>
> Is the compiler somehow anticipating that I could add an instance for
> (->) to A and thus be back to the Applicative class situation?

The compiler works on an open-world assumption, if the kinds match, there 
could be an instance defined somewhere.

>
> Thanks!  -Tyson
>
> PS:  I asked this here because type classes is a GHC issue, would the
> haskell- cafe list been a more appropriate place?

Either is fine.

Cheers,
Daniel