Julian Ospald has opened a pull request[*] for containers to add a traversal operation to Data.Set. Julian specifically requested forM :: (Ord b, Monad m) => Set a -> (a -> m b) -> m (Set b) Personally, I think it would be better to offer the unflipped versions: -- The most general version traverse :: (Ord b, Applicative f) => (a -> f b) -> Set a -> f (Set b) traverse f = fmap fromList . traverse f . toList -- A more efficient, strictly accumulating version for "strict" -- monads like IO, strict State, etc. mapM :: (Ord b, Monad m) => (a -> m b) -> Set a -> m (Set b) mapM f s0 = foldr go return s0 empty where go x r s = f x >>= \y -> r $! insert y s The latter can also be written, perhaps less efficiently, as mapM :: (Ord b, Monad m) => (a -> m b) -> Set a -> m (Set b) mapM f = foldM go empty where go s x = f x >>= \y -> pure $! insert y s As usual, the main question is what names are appropriate. Typically, containers assumes that users import its modules qualified, and therefore we should just use `traverse` and `mapM`. But clashing with well-known and widely-used names often causes breakage anyway, so I figured I should bring the matter to the libraries list. Thanks, David Feuer [*] https://github.com/haskell/containers/pull/592