{-# Language FunctionalDependencies,MultiParamTypeClasses #-}

import Data.Functor.Apply
import Data.Maybe (fromJust)
class GetS_r r f | f -> r where
 getS_r :: f a -> (r a,Maybe (f a))

class SetS_r r f | f -> r  where
 setS_r :: (r a,Maybe (f a)) -> f a

--

type SafeState   s a = s -> (a, Maybe s)
type CoSafeState s a = (a, Maybe s) -> s

unfoldSafeState :: SafeState s a -> (CoSafeState b a) -> s ->  b
unfoldSafeState f c = go
 where
     go = c . fmap (fmap go) . f

traverse1Default :: (GetS_r r t, SetS_r r' t', Apply f) => (r a -> f (r' b)) -> t a -> f (t' b)
traverse1Default f = unfoldSafeState getS_r g
 where
  g (ra,Nothing) = (\ x     -> setS_r (x,Nothing))  <$> f ra
  g (ra,Just xs) = (\ x xs' -> setS_r (x,Just xs')) <$> f ra <.> xs