I'd like to be able to define

{-# language PolyKinds, KindSignatures, GADTs, TypeFamilies #-}
data family Fix :: (k -> *) -> k
newtype instance Fix f = In { out :: f (Fix f) }

But currently this is disallowed:

Fix.hs:2:1: error:
    • Kind signature on data type declaration has non-* return kind
        (k -> *) -> k
    • In the data family declaration for ‘Fix’

Ultimately I think the issue here is that data instances should be required to end in kind *, not the families, but this generalization didn't mean anything until we had PolyKinds.

As an example of a usecase, with the above, I could define a bifunctor fixed point such as

newtype instance Fix f a = In2 { out2 :: f (Fix f a) a }