Are there rank N lenses?

Question

Suppose I have a simple GADT.

data Expr a where
  Int' :: Integer -> Expr Int
  Fun :: Text -> Expr a
  (:*) :: Expr (a -> b) -> Expr a -> Expr b

Now, I can define the following traversal over it:

transform :: Applicative f => (forall b. Expr b -> f (Expr b)) -> Expr a -> f (Expr a)
transform f (a :* b) = (:*) <$> transform f a <*> transform f b
transform f v = f v

The type looks curiously a lot like Traversal from lens. However, not exactly, it's higher ranked.

I can still define «conventional» set and over though. view is more complex, there are some obstacles to avoid (impredicative types), but doable.

Does this construction have a name? Is it supported in any way by the existing lens libraries or researched?

score 1 · Answer 1 · answered May 07 '23 at 15:08

Not really an answer but just additional relevant pointers:

Your transform function also appears to be a case of traverse from rank2classes.
I've found it to be more useful if the function would also get a witness for the child expression types, resulting in hypertypes' htraverse

Are there rank N lenses?

1 Answers1