A name for a product of `Const` and a functor?

Question

Is SF already defined anywhere, or does it at least have a name?

data SF a f x = SF a (f x)

instance Functor f => Functor (SF a f) where
  fmap g (SF a fx) = SF a (fmap g fx)

Answer 1

Your functor looks like

type SF a f = (,) a :. f

using functor-combo notation.

(I somehow prefer to look at it using composition, rather than using product and Const.)

Answer 2

You could just define functor products

data (f :* g) a = P (f a) (g a) deriving Functor

and then write it directly

type SF a f = Const a :* f