-- Gabe Schoenbach

module TypeClasses where

  import Data.Foldable

  -- Exercise 5.1

  -- | A parsimonious instance of Ord for suitably type-constrained instances of Pair
  data Pair a b = Pair a b
    deriving (Eq, Show)

  instance (Ord a, Ord b) => Ord (Pair a b) where
    Pair a1 b1 <= Pair a2 b2 = a1 < a2 || (a1 == a2 && b1 <= b2)

  -- Exercise 5.3

  -- | The BinaryTree datatype
  data BinaryTree a
        = EmptyTree
        | Node a (BinaryTree a) (BinaryTree a) -- value leftChild rightChild
        deriving (Show)

  -- | Creates a BinaryTree that is a mirror image of the input BinaryTree.
  reverseTree :: BinaryTree a -> BinaryTree a
  reverseTree EmptyTree = EmptyTree
  reverseTree (Node v l r) = Node v (reverseTree r) (reverseTree l)

  tree :: BinaryTree Integer
  tree = Node 3
          (Node 1
              (Node 0 EmptyTree EmptyTree)
              (Node 2 EmptyTree EmptyTree))
          (Node 5
              (Node 4 EmptyTree EmptyTree)
              (Node 6 EmptyTree EmptyTree))