Key-value apply

I just wrote this function:

apply :: (Ord k) => k -> v -> (v -> v) -> [(k,v)] -> [(k,v)]
apply k v f ds =
  let (p1,px) = span ( (k >) . fst) ds
      (p2,p3) = case px of
        []     -> ((k,v),[])
        (x:xs) -> if fst x == k
           then ((k, f $ snd x), xs)
           else ((k, v),       x:xs)
  in  p1 ++ (p2 : p3)

As you can see (?!), this takes a list of key/value pairs and processes it as follows:

• The function is given a key to look for.
• If the key is found, a function is applied to the associated value.
• If the key is not found, it is inserted (at the correct place) with a specified 'default value'.

Notice that if you start with a completely empty list, you can call apply several times and you will end up with a sorted list. (Note that apply uses the fact that the list is sorted to cut the search short in the 'I can't find it' case - hence the Ord context.)

Does a function like this already exist somewhere? (Hoogle seems to indicate not.) Is this a special case of something more general? Is there a better implementation? (The code isn't very readable at it is.) Can you think of a better name than just 'apply'? Have you ever had call to use such a function yourself?