meldable-heap-2.0.3: Asymptotically optimal, Coq-verified meldable heaps, AKA priority queues



A heap is a container supporting the insertion of elements and the extraction of the minimum element. This library models the implementation of asymptotically optimal purely functional heaps given by Brodal and Okasaki in their paper "Optimal Purely Functional Priority Queues". The Coq proof assistant has been used to prove this implementation correct. The proofs are available in the Cabal package or at

This implementation is strict. A lazy implementation is available in this package as Data.MeldableHeap.Lazy.



type PQ = BootWrap IntegerSource

empty :: Ord a => PQ aSource

empty is the heap with no elements

toList :: Ord a => PQ a -> [a]Source

toList (O(n)) returns a list of the elements in the heap in some arbitrary order.

 [] == toList empty

insert :: Ord a => a -> PQ a -> PQ aSource

insert (O(1)) adds an element to a heap.

 [1,2,1,0] == toList $ insert 1 $ insert 0 $ insert 2 $ insert 1 $ empty

findMin :: Ord a => PQ a -> Maybe aSource

findMin (O(1)) returns the minimum element of a nonempty heap.

 Just 0 == findMin $ insert 0 $ insert 2 $ insert 1 $ empty

extractMin :: Ord a => PQ a -> Maybe (a, PQ a)Source

extractMin (O(lg n)) returns (if the heap is nonempty) a pair containing the minimum element and a heap that contains all of the other elements. It does not remove copies of the minimum element if some exist in the heap.

 (0,[2,1]) == let x = insert 0 $ insert 2 $ insert 1 $ empty in let Just (p,q) = extractMin x in (p,toList q)

meld :: Ord a => PQ a -> PQ a -> PQ aSource

meld (O(1)) joins two heaps P and Q into a heap containing exactly the elements in P and Q. It does not remove duplicates.

 [2,1,0,2,1,0] == let x = insert 0 $ insert 2 $ insert 1 $ empty in toList (meld x x)