Ok, but what should (A ∩ B) \ B give if A = C ∩ B? A might be abstract. Here's a concrete example with types. What is, (Some[Int] with Product) \ Product ?
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I don't think so, unfortunately... it would be useful as the lower bound of an existential parameter to an invariant type which should accept String and Int as the parameter, but not much else. It will be inferred from, say, List(Ordering[Int], Ordering[String]).
Can you name me one use case where `Int & String` would be a useful type and `Nothing` wouldn't do?Now, you *could* use Nothing as the lower bound, but you would be losing type information when you don't need to, and it would allow you to have Orderings of any type in your List.
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In general, when the compiler can't find a universal solution to a least upper-bound, it will infer an existential, bounded above by the LUB of the types, and bounded below by the GLB, which is the intersection type.
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