Arrows that are also Functors

Is it common to make a type an instance of both Arrow and Functor type class? If a type is both instance of Arrow and Functor, would you expect that fmap = (^<<) ? If yes, how about adding this as expected law to the Control.Arrow documentation? Same question for Applicative functors and liftA2 (,) = (&&&). (Btw. Control.Arrow haddock documentation does not mention any Arrow law so far.)