Dan Doel wrote:
On Sunday 19 April 2009 4:56:29 pm wren ng thornton wrote:
Bulat Ziganshin wrote:
Hello R.A.,
Sunday, April 19, 2009, 11:46:53 PM, you wrote:
Does anybody know if there are any plans to incorporate some of these extensions into GHC - specifically the existential typing ?
it is already here, but you should use "forall" keyword instead odf "exists"
More particularly, enable Rank2Types and then for any type lambda F and for any type Y which does not capture @a@:
(x :: exists a. F a) ==> (x :: forall a. F a)
(f :: exists a. (F a -> Y)) ==> (f :: (forall a. F a) -> Y)
Eh? I don't think this is right, at least not precisely. The first is certainly not correct, because
exists a. F a
is F A for some hidden A, whereas
forall a. F a
can be instantiated to any concrete F A.
Yes, however, because consumers (e.g. @f@) demand that their arguments remain polymorphic, anything which reduces the polymorphism of @a@ in @x@ will make it ineligible for being passed to consumers. Maybe not precise, but it works. Another take is to use (x :: forall a. () -> F a) and then once you pass () in then the return value is "for some @a@". It's easy to see that this is the same as the version above.
A higher rank encoding of this existential would be:
forall r. (forall a. F a -> r) -> r
encoding the existential as its universal eliminator, similar to encoding an inductive type by its corresponding fold.
Exactly. Whether you pass a polymorphic function to an eliminator (as I had), or pass the universal eliminator to an applicator (as you're suggesting) isn't really important, it's just type lifting: (x :: forall a. F a) ==> (x :: forall r. (forall a. F a -> r) -> r) (f :: (forall a. F a) -> Y) ==> (f :: ((forall a. F a -> Y) -> Y) -> Y)) The type lifted version is more precise in the sense that it distinguishes polymorphic values from existential values (rather than overloading the sense of polymorphism), but I don't think it's more correct in any deep way.
What you can do in GHC is create existentially quantified data types, like so:
data E f = forall a. E (f a)
Then E F is roughly equivalent to (exists a. F a).
But only roughly. E F has extra bottoms which distinguish it from (exists a. F a), which can be of real interest. -- Live well, ~wren