You can do it in Scala just by forming the intersection type. Subtyping might get in the way (you "lose" types in the intersection which have a subtyping relationship with another) so you can wrap them in an invariant type constructor to work around that.
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This gives you a type like `Inv[A] with Inv[B] with Inv[C]`, and you get a subset test "for free", as it's equivalent to taking the supertype.
You probably want to throw another type into the mix as well (IDK, pick one - it doesn't matter as long as you're consistent and it's got no subtype relationship with `Inv`) so that you have a good representation the empty set.
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If you want, you could add a type member to an HList and have it form this intersection on the head and the tail (recursively) to get this type automatically.
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The supertype/subset relationship is the most useful thing you get out of this. Most obviously, you can't remove an element from an intersection type, but that's more to do with sets: If you add ten identical Bippys to a set and remove one, is there a Bippy in the set? Who knows?
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