On Jun 22, 2:19 pm, "wren ng thornton"
In contrast, ordered pairs and disjoint unions are tidy, simple, and obvious.
Disjoint pairs are sufficient; they needn't be ordered. All we need is that they are "tagged" in the same way that disjoint unions are, so that we can distinguish the components of A*A.
So union types are a bad idea; disjoint unions are the far superior option for a variety of reasons. Is there any reason why we don't have either anonymous disjoint union types, or why some of the proposals here (e.g. type (:|:) a b = Either a b ) haven't been implemented, or put into the standard libraries (and publicised in beginner texts)? Also, I don't think that the formulation of (:|:) above is sufficient. Suppose: foo :: Foo -> Bar baz :: Baz -> Quux foobaz :: [Foo :|: Baz] -- map foo and baz over foobaz barquux :: [Bar :|: Quux] barquux = map f foobaz how would f be implemented? It seems to me that you'd need an additional function: either' :: (a -> c) -> (b -> d) -> Either a b -> Either c d However, it still seems to me that that isn't sufficient. Suppose instead: a :: A -> B :|: C d :: D -> E :|: F ad :: [A :|: D] if we want to map a and d over ad using either' to get bcef :: [B :|: C :|: E :|: F] it wouldn't work, we'd get bcef :: [(B :|: C) :|: (E :|: F)] i.e. bcef :: [Either (Either B C) (Either E F)] instead, which is presumably not what we wanted... Is there a better formulation or something that would allow you to do that?