That doesn't strike me as true, `A with B` represents the set intersection. `A | B` represents set union. You claim idempotency is why you can't have negation, but both intersection and union are idempotent!
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I concur, it's kinda how you can have `Int & String` it's also equivalent to `Nothing`, but the compiler can't necessarily check that
Int & String is not equivalent to Nothing at all! They happen to have the same members, but they're very different types. Types are defined by their properties, and Int & String represents the union of the sets of properties of Int and String...
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Whereas Nothing is the union of all properties of all types, which is the equivalent to the intersection of all types. It's a subtype of everything, which makes it the most constrained, most specific type.
Thanks. Twitter will use this to make your timeline better. UndoUndo
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Right, maybe we're talking about different equivalence relations. `Int & String` may not be `=:=` to Nothing, but sure as hell is isomorphic to it
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yeah i would probably use leibniz equality to talk about this personally (so all uninhabited types would be equivalent to nothing in that case)
End of conversation
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