-- Code from Section 1.1; it won't work since join is left unimplemented!

module BinaryHeapTrees where

data Ord a => Tree a = Null | Fork a (Tree a) (Tree a)

isEmpty :: Ord a => Tree a -> Bool
isEmpty Null = True
isEmpty (Fork x a b) = False

minElem :: Ord a => Tree a -> a
minElem (Fork x a b) = x

deleteMin :: Ord a => Tree a -> Tree a
deleteMin (Fork x a b) = merge a b

insert :: Ord a => a -> Tree a -> Tree a
insert x a = merge (Fork x Null Null) a

merge :: Ord a => Tree a -> Tree a -> Tree a
merge a Null = a
merge Null b = b
merge a b
   | minElem a <= minElem b = join a b
   | otherwise = join b a

join (Fork x a b) c = Fork x undefined undefined