Is there anything useful about the class of functors which foralls can move across? In other words, functors f, for which for any function g there is this isomorphism f (forall a. g a) <=> forall a. f (g a) In this Haskell snippet I've called the class Hoistable and the isomorphism is (hoist,unhoist): newtype All g = MkAll (forall a. g a); class (Functor f) => Hoistable f where {     hoist :: forall g. (f (All g) -> (forall a. f (g a)));     hoist = fmap (\(MkAll ga) -> ga);     unhoist :: forall g. ((forall a. f (g a)) -> f (All g)); }; Functors that can be made instances of Hoistable: data Singleton a = MkSingleton newtype Identity a = MkIdentity a (->) p -- forall p. data Pair a = MkPair a a data Extra p a = MkExtra p a -- forall p. data Compose p q a = MkCompose (p (q a)) -- forall p q. (Hoistable p,Hoistable q) => On the other hand, Maybe and Either cannot. The key seems to be in only having one "form", i.e. no "|"s in the definition. Does this class actually have a use, or is it merely a curiosity? -- Ashley Yakeley Seattle WA