[Haskell-cafe] Aren't type system extensions fun?
tom.davie at gmail.com
Mon May 26 17:26:40 EDT 2008
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.
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