foldr3'.hs

foldr3' _ z [] p k _ = k z
foldr3' f'cps z (x:xs) p k k'
    | p x = k' x
    | otherwise = f'cps x (foldr3' f'cps z xs p k k') $ \y -> k y

main = do print $ foldr3' (\x y k -> k $ x ++ y) []
                    [[1,2],[3,4],[5,6]] (== []) id id
          print $ foldr3' (\x y k -> k $ x ++ y) []
                    [[1,2],[3,4],[],[5,6]] (== []) id id

foldr3.hs

foldr3' _ z [] p k _ = k z
foldr3' f_cps z (x:xs) p k k'
    | p x = k' x
    | otherwise = f_cps x (foldr3' f_cps z xs p k k') $ \y -> k y

main = do print $ foldr3' (\x y k -> k $ x ++ y) []
                    [[1,2],[3,4],[5,6]] (== []) id id
          print $ foldr3' (\x y k -> k $ x ++ y) []
                    [[1,2],[3,4],[],[5,6]] (== []) id id