What should a “higher order Traversable” class look like?

Question

In this answer I made up on the spot something which looks a bit like a \"higher order Traversable\": like Traversable but for functors from the ca

Answer 1

In first order, we have sequence = traverse id.

Here the first argument of htraverse has type forall x. f x -> a (g x), we can't have id, but we can try with an isomorphism instead. For f x to be isomorphic to a (g x), we can pick f ~ Compose a g.

htraverse = hsequence . hmap (Compose . eta)

hsequence :: Applicative a => t (Compose a g) -> a (t g)
hsequence = htraverse getCompose