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Comment by gizmo686 | Hacker News Reader

Why can't you define a set monad? The first definition I can think of is making behave like Haskell's list monad?

That is to say that "xs ==> (\x -> f x)" Would take every element in the set "xs", pass each of them into f, and union the results into a single set.

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Set basically has an Ord constraint on the type of things you have a Set of since most of the functions on it have an Ord a constraint, and Monads can't be constrained in what types they wrap. This is also why it's not a Functor; you can define

  setMap :: (Ord a, Ord b) => (a -> b) -> Set a -> Set b

but that's still more restricted than fmap.

Because a monad is also a functor, but a set failed to be a functor.

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