Representable (Kleisli r a) given a phantom 'l' argument

[Icelandjack]

Does this instance exist anywhere? F l r a b is Kleisli r a b with a phantom l argument. It was inspired by the "In terms of representable functors" section.

type    F :: (Type -> Type) -> (Type -> Type) -> Type -> (Type -> Type)
newtype F l r a b = F (a -> r b)
  deriving Functor
  via Kleisli r a

instance Adjunction l r => Distributive (F l r a) where
  distribute :: Functor f => f (F l r a b) -> F l r a (f b)
  distribute = distributeRep

instance Adjunction l r => Representable (F l r a) where
 type Rep (F l r a) = l a

 index :: F l r a b -> (l a -> b)
 index (F f) = rightAdjunct f

 tabulate :: (l a -> b) -> F l r a b
 tabulate f = F (leftAdjunct f)