In that case the `a` is still not really "present", i.e. the only inhabitants of `Forall Predicate` would be `MkForall (Predicate \_ -> True)` and `MkForall (Predicate \_ -> False)`, unless, again, I'm totally missing something here.
It's true that here if you instead have Predicate Void you gain an additional value `Predicate \case`, but it still stands that you can't actually "use anything about the a", so I'm still curious regarding what the use case here is.

Wait, no, I forgot about values that aren't covariant. Forall $ Predicate $ const True is a valid value.

On Fri, Dec 12, 2025, 08:34 Georgi Lyubenov <godzbanebane@gmail.com> wrote:

Yeah, I think this is my intuition which I was trying to get at with my "isn't this Void" comment - it seems to me that in all cases where you have a `forall a. f a` that would be the same thing as having an `f Void`, i.e. the `a` is never relevant or alternatively the f a inside a Forall will never actually contain an a.

Is there still something else that I'm missing?

What's the concrete use case for Forall?

On 12/12/25 16:03, Zemyla wrote:

Wouldn't the only inhabited value of Forall [] be []?

On Fri, Dec 12, 2025, 02:18 Adam Gundry <adam@well-typed.com> wrote:

Hi Tom,

You may be interested in a ticket where a similar issue was discussed
before: https://gitlab.haskell.org/ghc/ghc/-/issues/20048

Given `forall a . Coercible (f a) (g a)` it seems intuitively obvious
that it should be sound to derive `Coercible f g`, but Core's typing
rules don't currently allow it. Since Core is proof irrelevant it is
probably safe just to add it, but actually proving soundness would take
a bit of work.

That said, you are asking about the subtly different

     Coercible (forall a . f a) (forall a . g a)

which is derivable from `Coercible f g`, but in fact I think is also
derivable from `forall a. Coercible (f a) (g a)` in today's Core type
system. The difficulty seems to be that GHC's constraint solver for
equality/Coercible constraints is incomplete in the presence of
quantified constraints. So unsafeCoerce seems defensible in this case.

Cheers,

Adam


On 11/12/2025 17:58, Tom Ellis wrote:
> Oh, I forgot to give the definition of Forall, so I may as well define
> it in its full glory, imports, extensions and all:
>
> {-# LANGUAGE QuantifiedConstraints #-}
>
> import Data.Coerce (Coercible)
> import Data.Type.Coercion (Coercion (Coercion))
> import GHC.Exts (Any)
> import Unsafe.Coerce (unsafeCoerce)
>
> newtype Forall f = MkForall (forall a. f a)
>
> forallCoercible ::
>    forall f g.
>    (forall a. Coercible (f a) (g a)) =>
>    Coercion (Forall f) (Forall g)
> forallCoercible =
>    unsafeCoerce (Coercion @(f Any) @(g Any))
>       
> On Thu, Dec 11, 2025 at 05:47:25PM +0000, Tom Ellis wrote:
>>      forallCoercible ::
>>        forall f g.
>>        (forall a. Coercible (f a) (g a)) =>
>>        Coercion (Forall f) (Forall g)
>>      forallCoercible =
>>        unsafeCoerce (Coercion @(f Any) @(g Any))

--
Adam Gundry, Haskell Consultant
Well-Typed LLP, https://www.well-typed.com/

Registered in England & Wales, OC335890
27 Old Gloucester Street, London WC1N 3AX, England
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