The Set=List functor

Set.hs

import Data.List

newtype Set a =
  Set [a]

size ::
  Eq a =>
  Set a
  -> Int
size (Set a) =
  length (nub a)

insert ::
  Eq a =>
  a
  -> Set a
  -> Set a
insert a (Set as) =
  let p = if a `elem` as
            then id
            else (a:)
  in Set (p as)

empty ::
  Set a
empty =
  Set []

instance (Eq a, Show a) => Show (Set a) where
  show (Set a) =
    show (nub a)

instance Eq a => Eq (Set a) where
  Set [] == Set [] =
    True
  Set [] == Set (_:_) =
    False
  Set (_:_) == Set [] =
    False
  Set (a:as) == Set x =
    let (q, r) = break (==a) x
    in case r of [] -> False
                 (_:t) -> Set as == Set t

instance Functor Set where
  fmap f (Set a) =
    Set (fmap f a)