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Maybe it has "brutal practical cost", I don't know, but even most high-level languages don't have set-theoretic type systems. Perhaps because the approach is relatively new and most popular languages are old.

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the set theoretic type system variant has one issue I think the algebraic one avoids: An overlap between types is ambiguous, i.e. "int | int" doesn't make any sense to write. In a function parse_postal_code, where you either get the postal code, or an error code you wouldn't be able to differentiate. You could write your own types for that, but now you've essentially recreated what the algebraic versions do by forcing a selection through the type constructor on the inner type instead of the wrapping union type.

That being said, in cases where there is no overlap I don't see why "the old way" shouldn't behave like typescript through implicit conversion as there is only one applicable constructor. Forcing explicit selection if there is overlap, but do it automatically when there is none seems like reasonable behavior that is a strict superset of what you wrote before.

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