Will Fancher recently wrote a blog post (see also the Reddit thread) about sorting arbitrary Traversable containers without any of the ugly incomplete pattern matches that accompany the well-known technique of dumping all the entries into a list and then sucking them back out in State. Fancher used a custom applicative based on the usual free applicative. Unfortunately, this type is rather hard to work with, and Fancher was not immediately able to find a way to use anything better than insertion sort. This repository demonstrates an asymptotically optimal heap sort using a heap-merging applicative.

The three modules:

• BasicNat: unary natural numbers, singletons, and properties
• IndexedPairingHeap: size-indexed pairing heaps
• HSTrav: the big payoff: heap-sorting anything