But that's not really a solution, since it doesn't make a Functor
instance for Set; it makes a Functor' instance for Set.
If you are willing to not be upwards compatible then, yes, there are solutions.
I think the best bet for an upwards compatible solutions is the
associated constraints,
www.cs.kuleuven.be/~toms/Research/papers/constraint_families.pdf
On Tue, Jul 27, 2010 at 10:17 AM,
Lennart Augustsson wrote:
Try to make Set an instance of Functor and you'll see why it isn't. It's very annoying.
And yet the very simple, and old solution works.
http://okmij.org/ftp/Haskell/types.html#restricted-datatypes
We just properly generalize Functor, so that all old functors are new functors. In addition, many more functors become possible, including Set. In general, we can have functors fmap' :: (C1 a, C2 b) => (a -> b) -> f a -> f b Incidentally, even an Integer may be considered a functor: we can define the fmap' operation fitting the above signature, where the constraint C1 a is a ~ Integer.
Although the use of OverlappingInstances is not required, the extension leads to the nicest code; all old functors just work.
{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances #-} {-# LANGUAGE OverlappingInstances #-}
module FunctorEx where
import Control.Monad import Data.Set as S
class Functor' f a b where fmap' :: (a -> b) -> f a -> f b
-- The default instance: -- All ordinary Functors are also extended functors
instance Functor f => Functor' f a b where fmap' = fmap
-- Now define a functor for a set instance (Ord a, Ord b) => Functor' S.Set a b where fmap' = S.map
-- Define a degenerate functor, for an integer newtype I a = I Integer deriving Show
instance Functor' I Integer Integer where fmap' f (I x) = I $ f x
-- tests
-- Lists as functors test_l = fmap' (+10) [1,2,3,4] -- [11,12,13,14]
-- Sets as functors test_s = fmap' (\x -> x `mod` 3) $ S.fromList [1,2,3,4] -- fromList [0,1,2]
-- Integer as functor test_i = fmap' (* (6::Integer)) $ I 7 -- I 42
_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe