[Haskell-cafe] Type arithmetic with ATs/TFs

[Andrew Coppin]

Ryan Ingram wrote:
> Actually, at least in GHC, associated types are just syntax sugar for
> type families.
>
> That is, this code:
>
> class Container c where
>    type Element c :: *
>    view :: c -> Maybe (Element c,c)
>
> instance Container [a] where
>    type Element [a] = a
>    view [] = Nothing
>    view (x:xs) = Just (x,xs)
>
> is the same as this code:
>
> type family Element c :: *
> class Container c where
>    view :: c -> Maybe (Element c, c)
> type instance Container [a] = a
> instance Container [a] where
>    view [] = Nothing
>    view (x:xs) = Just (x,xs)
>   

OK, well in that case, I'm utterly puzzled as to why both forms exist in 
the first place. If TFs don't allow you to do anything that can't be 
done with ATs, why have them?

My head hurts...