Higher-kinds and type-classes are distinct concepts.

functor.hs

{-# LANGUAGE RankNTypes #-}

module Functor where

import Prelude(
    foldr
  , (.)
  , Maybe(Nothing, Just)
  , maybe
  )

data Functor f =
  Functor {
    fmap :: forall a b. (a -> b) -> f a -> f b
  }

instanceList ::
  Functor []
instanceList =
  Functor (\f -> foldr ((:) . f) [])

instanceMaybe ::
  Functor Maybe
instanceMaybe =
  Functor (\f -> maybe Nothing (Just . f))

instanceReader ::
  Functor ((->) t)
instanceReader =
  Functor (.)