Why isn't this Typeable?

[Richard Eisenberg]

I suppose this is conceivable, but it would complicate the representation and solver for TypeReps considerably. Do you have a real use case?

Richard

> On Sep 25, 2017, at 2:28 PM, David Feuer <david at well-typed.com> wrote:
> 
> My example wasn't quite the one I intended (although I think it should
> work as well, and it's simpler). Here's the sort of example I really intended:
> 
>    data Bar :: forall (j :: forall k. k -> Maybe k) (a :: Type). Proxy (j a) ->  Type
> 
> I would expect
> 
>    Bar :: Proxy ('Just Int) -> Type
> 
> or, to abuse notation a bit,
> 
>    Bar @'Just @Int
> 
> to be Typeable. What I'm really suggesting is that we should distinguish between things that are typeable and
> things that can be decomposed into typeable components. We already make a limited distinction
> here. For example, we have
> 
>  'Just :: forall a. a -> Maybe a
> 
> 'Just itself cannot be Typeable, but once it's applied to a kind variable, it is Typeable.
> 'Just @Int is Typeable even though that (kind) application cannot be broken with App. Similarly, I'd expect
> Foo 'Just to be Typeable even though that (type) application cannot be broken with App (or Fun).
> 
> Putting things in terms of fingerprints, we can offer type-indexed fingerprints
> 
> newtype Finger a = Finger Fingerprint
> 
> for anything we can fingerprint. Is there any difficulty fingerprinting types like Foo 'Just and
> Bar @'Just @Int? Fingerprints are useful for lots of applications where decomposition isn't
> necessary.
> 
> On Sunday, September 24, 2017 1:16:37 PM EDT Richard Eisenberg wrote:
>> The problem is that to get Typeable (Foo 'Just), we need Typeable 'Just. However, the kind parameter for Typeable 'Just would be (forall a. a -> Maybe a), making the full constraint Typable (forall a. a -> Maybe a) 'Just. And saying that would be impredicative. In other contexts, 'Just *can* be Typeable, but it's 'Just invisibly instantiated at some monotype for `a`.
>> 
>> So I think that this boils down to impredicativity and that the implementation is doing the right thing here.
>> 
>> Richard
>> 
>>> On Sep 24, 2017, at 5:45 AM, David Feuer <david at well-typed.com> wrote:
>>> 
>>> data Foo :: (forall a. a -> Maybe a) -> Type
>>> 
>>> Neither Foo nor Foo 'Just is Typeable. There seems to be a certain sense to excluding Foo proper, because it can't be decomposed with Fun. But why not Foo 'Just? Is there a fundamental reason, or is that largely an implementation artifact?
>>> 
>>> David Feuer
>>> Well-Typed, LLP
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>> 
> 
>