On Jun 7, 2011, at 12:43 PM, MigMit wrote:
One particularly trivial example that comes to mind is:
newtype Mu f = Mu (f (Mu f))
instance Show (f (Mu f)) => Show (Mu f) where show (Mu x) = "Mu (" ++ show x ++ ")" -- Or however you'd like to show it
Ehm, that does look like poor design.
Sure you don't mean "Mu f can be printed if and only if f (Mu f) can be printed". What you probably mean is "if f transforms printable things to printable things, then Mu f is a printable thing". And you CAN express just that:
Actually, I would argue that the former _is_ what is meant. It's a weaker condition than the latter and it is the necessary and sufficient condition to define the instance - one of the steps involved in formatting a value of type "Mu f" is to format a value of type "f (Mu f)". It doesn't actually matter whether "forall x. Show x => Show (f x)" holds in general.
type ShowD a = forall p. (forall x. Show x => p x) -> p a
showD :: Show a => ShowD a showD px = px
class ShowF f where showF :: Show a => ShowD (f a)
instance Show a => Show (F a) where... -- here goes your "f"
instance ShowF F where showF = showD -- and that is the only line of boilerplate
instance ShowF f => Show (Mu f) where show (Mu fm) = "Mu (" ++ runShowHelper (showF (ShowHelper show)) fm ++ ")"
newtype ShowHelper x = ShowHelper {runShowHelper :: x -> String}
Sorry for possible bugs — I don't have ghc anywhere near me at the moment, but the idea is clear, I guess.
I don't really see how this is preferable when the compiler can solve the equation automatically. All that is needed is to tell it to try. If portability is a concern then I could see going through the gymnastics (and also eliminating the use of higher-rank types), but that's the only case in which I would consider it the preferred option. -- James