Export Set intersections and Intersection

[meooow25]

#756 added these two definitions

containers/containers/src/Data/Set/Internal.hs

Lines 897 to 911 in 028e187

	-- | The intersection of a series of sets. Intersections are performed left-to-right.
	intersections :: Ord a => NonEmpty (Set a) -> Set a
	intersections (s0 :| ss) = List.foldr go id ss s0
	where
	go s r acc
	| null acc = empty
	| otherwise = r (intersection acc s)
	-- | Sets form a 'Semigroup' under 'intersection'.
	newtype Intersection a = Intersection { getIntersection :: Set a }
	deriving (Show, Eq, Ord)
	instance (Ord a) => Semigroup (Intersection a) where
	(Intersection a) <> (Intersection b) = Intersection $ intersection a b
	stimes = stimesIdempotent

but they were never exported from Data.Set.

We should export them, but there is an opportunity for improvement today. base-4.18 got Foldable1, so we could change intersections to be (Ord a, Foldable1 f) => f (Set a) -> Set a.

And whatever we do for Set we should also do for IntSet.

[meooow25]

Ah, there's something to be considered about IntSet. Unlike Set, we can have a monoid because mempty is well defined here (fromList [minBound..maxBound]). But this set cannot be constructed in practice because it is too large. So I think we should not have the instance, though technically it could be defined correctly.

If we end up implementing #999 it will be practical to construct this set and we can revise this decision.

[alexfmpe]

Unlike Set
But this set cannot be constructed in practice because it is too large.

I mean, isn't this the same issue with the Set monoid for intersections?
One could have instance (Finite a, Ord a) => Monoid (Set a) and the same "small enough" concern applies.

[meooow25]

Sure, you could say that. But there is no class Finite in base, which makes it less of a concern for containers.