Set difference and union in one

[noughtmare]

Set difference and union sometimes have to be computed together, such as in semi-naive fixed point computation:

seminaive :: Ord a => Set a -> (Set a -> Set a) -> Set a
seminaive x f = go Set.empty x where
  go !done !todo
    | Set.null todo' = done
    | otherwise = go (done `Set.union` todo') (f todo')
    where todo' = todo Set.\\ done

If there was a combined operation:

differenceAndUnion :: Ord a => Set a -> Set a -> (Set a, Set a)

Then I can write it more efficiently:

seminaive :: Ord a => Set a -> (Set a -> Set a) -> Set a
seminaive x f = go Set.empty x where
  go !done !todo
    | Set.null dif = uni
    | otherwise = go uni (f dif)
    where (dif, uni) = Set.differenceAndUnion todo done

[konsumlamm]

This feels way too specialized. Most combinations of operations can probably be implemented more efficiently by having a combined operation, but that doesn't mean we should do it. This isn't something I'd expect any library to implement, on the contrary, I'd feel like this would be bloat.

[treeowl]

I've been wanting to make an equivalent of the Data.Map mergeA interface for sets for a long time, but I've never gotten around to it. That would include this operation.

[noughtmare]

@treeowl that sounds much better than what I proposed here!

Which applicative would you use? I believe the straightforward Writer (Set a) wouldn't have the right time complexity, or would it?

[treeowl]

I'd think

data Pair a = Pair a a

We'd have to make sure it generated good code in typical cases.