Empty heap.

Singleton heap.

Insertion.

>>> insert 7 (fromList [5,3]) == fromList [3,5,7]
True
>>> insert 5 empty            == singleton 5
True

Creating a heap from a list.

>>> empty == fromList []
True
>>> singleton 'a' == fromList ['a']
True
>>> fromList [5,3] == fromList [5,3]
True

Creating a list from a heap. O(N)

>>> let xs = [5,3,5]
>>> length (toList (fromList xs)) == length xs
True
>>> toList empty
[]

Deleting the minimum element.

>>> deleteMin (fromList [5,3,7]) == fromList [5,7]
True
>>> deleteMin empty == empty
True

See if the heap is empty.

>>> Data.Heap.Leftist.null empty
True
>>> Data.Heap.Leftist.null (singleton 1)
False

Merging two heaps

>>> merge (fromList [5,3]) (fromList [5,7]) == fromList [3,5,5,7]
True

Finding the minimum element.

>>> minimum (fromList [3,5,1])
Just 1
>>> minimum empty
Nothing

Checking validity of a heap.