On 26 May 2008, at 23:02, Andrew Coppin wrote:
Haskell 98 provides a simple and clean type system, which I feel I understand very well.
GHC provides a vast zoo of strange and perplexing type system extensions, which I don't understand at all. (Well, some of it is simple enough - e.g., multiparameter type classes. But GADTs? FDs? ATs? Hmm...)
Anyway, it seems there is a large set of such type system extensions that involve writing "forall" all over the place. I have by now more or less managed to comprehend the fact that
data Thing = forall x. Thing x
allows a type variable to appear on the RHS that is *not* present on the LHS, thus "hiding" the type of something inside the structure. And for some reason, they call this "existential quantification" [which I can't spell never mind pronounce].
Today I was reading a potentially interesting paper, and I stumbled across something referred to as a "rank-2 type". Specifically,
class Typable x => Term x where gmapT :: (forall y. Term y => y -> y) -> x -> x
At this point, I am at a complete loss as to how this is any different from
gmapT :: Term y => (y -> y) -> x -> x
Can anybody enlighten me?
This is probably the first real use I've ever seen of so-called rank-2 types, and I'm curios to know why people think they need to exist. [Obviously when somebody vastly more intelligent than me says something is necessary, they probably know something I don't...]
At this point, I don't think I even wanna *know* what the hell a rank-N type is... o_O
This is perhaps best explained with an example of something that can be typed with rank-2 types, but can't be typed otherwise: main = f id 4 f g n = (g g) n We note that the same instance of id must be made to have both the type (Int -> Int) and ((Int -> Int) -> (Int -> Int)) at the same time. Rank 2 types allows us to do this. Bob