The Monoid class with various general-purpose instances.

Inspired by the paper Functional Programming with Overloading and Higher-Order Polymorphism, Mark P Jones (http://www.cse.ogi.edu/~mpj/) Advanced School of Functional Programming, 1995.

To implement find or findLast on any Foldable:

 findLast :: Foldable t => (a -> Bool) -> t a -> Maybe a
 findLast pred = getLast . foldMap (x -> if pred x
                                            then Last (Just x)
                                            else Last Nothing)
 

Much of Data.Map's interface can be implemented with alter. Some of the rest can be implemented with a new alterA function and either First or Last:

 alterA :: (Applicative f, Ord k) =>
           (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a)

 instance Monoid a => Applicative ((,) a)  -- from Control.Applicative

 insertLookupWithKey :: Ord k => (k -> v -> v -> v) -> k -> v
                     -> Map k v -> (Maybe v, Map k v)
 insertLookupWithKey combine key value =
   Arrow.first getFirst . alterA doChange key
   where
   doChange Nothing = (First Nothing, Just value)
   doChange (Just oldValue) =
     (First (Just oldValue),
      Just (combine key value oldValue))