feat: Add partitionWith, partitionWithA, partitionEithers

[414owen]

Provides a generic partitionWith, witherable seems to be the logical place for such a thing, as it can be implemented in terms of the existing Filterable class.

I added it to the Filterable class because more efficient versions may be available.

Existing names I've found for this operation: Vector's partitionWith, base's partitionEithers, containers' mapEither.

I chose partitionWith, and partitionEithers, but I don't have a strong opinion on the name (although I'd prefer not to add a new name to the haskell ecosystem).

I saw #45 after I'd written this, I'm afraid. Does anyone have any concerns about this implementation?

[phadej]

I think I'd rather make relax laws of unalign :: f (These a b) -> (f a, f b) from semialign to allow sequence like instances, and provide partition there. It was asked there not so long time ago and I think it makes sense.

EDIT: I prefer that as unalign already exists.

[414owen]

Thanks @phadej,

The lack of [] and Vector instances of Unalign is a little unfortunate, as those are the concrete types that I want to use unalignWith/partitionWith for. I see that there's an issue for it here, but it requires dropping a law.

I'll add a law-breaking orphan instance to our codebase for now. Do you think the instances will end up making it into semialign?

If not, having the methods on Filterable might still be a good option?

[phadej]

Do you think the instances will end up making it into semialign?

Yes.

[echatav]

partitionEithers should definitely be included in witherable! It identifies Filterable as an oplax monoidal functor between coproduct and product.

const () :: f Void -> ()
partitionEithers :: Filterable f => f (Either a b) -> (f a, f b)

When f is also Alternative, we can say there is a strong monoidal functor between coproduct and product if the below are inverse to the above:

const empty :: Alternative f => () -> f Void
plusA :: Alternative f => (f a, f b) -> f (Either a b)
plusA (a,b) = Left <$> a <|> Right <$> b