Hi I was always under the impression that the fact that Data.Set.Set can not be made an instance of Functor was a sort of unavoidable limitation. But if we look at the definition of Data.Set.map: map :: (Ord a, Ord b) => (a->b) -> Set a -> Set b map f = fromList . List.map f . toList we see that 1) "Ord a" is not really used and 2) "Ord b" is only needed for the final fromList. Since every interesting function in Data.Set requires an Ord dictionary anyway, one could implement fmap using only the "List.map f . toList" part and leave the "fromList" to the successive function calls. It appears to me, then, that if "Set a" were implemented as the sum of a list of a and a BST, it could be made an instance of Functor, Applicative and even Monad without affecting asymptotic complexity (proof of concept below). Am I right here? Would the overhead be significant? The one downside I can think of is that one would have to sacrifice the Foldable instance. Thanks, Daniel import qualified Data.Set as Internal import Data.Monoid import Control.Applicative data Set a = This (Internal.Set a) | List [a] toInternal :: Ord a => Set a -> Internal.Set a toInternal (This s) = s toInternal (List s) = Internal.fromList s toAscList :: Ord a => Set a -> [a] toAscList (This s) = Internal.toAscList s toAscList (List s) = Internal.toAscList $ Internal.fromAscList s toList :: Set a -> [a] toList (This s) = Internal.toList s toList (List s) = s -- Here we break the API by requiring (Ord a). -- We could require (Eq a) instead, but this would force us to use -- nub in certain cases, which is horribly inefficient. instance Ord a => Eq (Set a) where l == r = toInternal l == toInternal r instance Ord a => Ord (Set a) where compare l r = compare (toInternal l) (toInternal r) instance Functor Set where fmap f = List . map f . toList instance Applicative Set where pure = singleton f <*> x = List $ toList f <*> toList x instance Monad Set where return = pure s >>= f = List $ toList s >>= (toList . f) empty :: Set a empty = This Internal.empty singleton :: a -> Set a singleton = This . Internal.singleton insert :: Ord a => a -> Set a -> Set a insert a = This . Internal.insert a . toInternal delete :: Ord a => a -> Set a -> Set a delete a = This . Internal.delete a . toInternal instance Ord a => Monoid (Set a) where mempty = This mempty mappend (This l) (This r) = This (mappend l r) mappend l r = This . Internal.fromAscList $ mergeAsc (toAscList l) (toAscList r) where mergeAsc :: Ord a => [a] -> [a] -> [a] mergeAsc [] ys = ys mergeAsc xs [] = xs mergeAsc ls@(x:xs) rs@(y:ys) = case compare x y of EQ -> x : mergeAsc xs ys LT -> x : mergeAsc xs rs GT -> y : mergeAsc rs ys