[Haskell-cafe] The container problem
Dan Weston
westondan at imageworks.com
Fri Sep 26 18:50:51 EDT 2008
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.
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