More specifically, although a set is a perfectly good (lowercase) functor, Set is not a (Haskell) Functor. Set's map has an Ord constraint, but the Functor type constructor is parametric over *all* types, not just that proper subset of them that have a total ordering. But see attempts to fix this: http://okmij.org/ftp/Haskell/types.html#restricted-datatypes http://www.randomhacks.net/articles/2007/03/15/data-set-monad-haskell-macros Dan Jonathan Cast wrote:
On Fri, 2008-09-26 at 15:25 -0700, Jason Dusek wrote:
Can someone explain, why is it that Set can not be a Monad?
It can't even be a functor (which all monads are). You can't implement
fmap (+) $ Set.fromList [1, 2, 3]
with Data.Set, because you can't order functions of type Integer -> Integer in a non-arbitrary way. So you can't have a balanced binary tree of them in a non-arbitrary way, either. Something like
fmap putStrLn $ Set.fromList ["Hello", "world"]
is similar.
Since Data.Set is implemented in Haskell, it can only use facilities available to Haskell libraries. So it can't work for arbitrary elements; but a Functor instance requires that it does work.