Discussion: traversals for Data.Set

[David Feuer]

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
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