Set.hs

{-# LANGUAGE TypeFamilies #-}
module Set where

class Set a where
  type E a
  empty  :: a
  insert :: E a -> a -> a
  member :: E a -> a -> Bool

data Tree a = Empty | MkTree (Tree a) a (Tree a)

treeEmpty :: Tree a
treeEmpty = Empty

treeInsert :: Ord a => a -> Tree a -> Tree a
treeInsert = undefined

treeMember :: Ord a => a -> Tree a -> Bool
treeMember = undefined

instance Ord a => Set (Tree a) where
  type E (Tree a) = a
  empty  = treeEmpty
  insert = treeInsert
  member = treeMember