This Haskell package provides three useful generalizations:

class Functor f => FunctorWithIndex i f | f -> i where
  imap :: (i -> a -> b) -> f a -> f b

class Foldable f => FoldableWithIndex i f | f -> i where
  ifoldMap :: Monoid m => (i -> a -> m) -> f a -> m

class (FunctorWithIndex i t, FoldableWithIndex i t, Traversable t)
       => TraversableWithIndex i t | t -> i where
  itraverse :: Applicative f => (i -> a -> f b) -> t a -> f (t b)

The ghc-keys package provides similar functionality, but uses associated TypeFamilies instead of FunctionalDependencies.