In hindsight, I strongly believe adding the ascending and descending properties was a mistake. These properties do not work like views do in the Standard Library, and their performance characteristics are very surprising.
Luckily, Heap isn't part of a public Collections release yet, so it's still time to correct this. I filed PR #119 to remove these from the Heap implementation.
(People who find these properties helpful are of course welcome to define them in ad-hoc extensions, outside of this package. After all, these properties are merely lightweight wrappers over the public popMin and popMax APIs -- they are built entirely out of public API.)
Note that the unordered property does work like a proper view -- it exposes the contents of the heap as a RandomAccessCollection with integer indices.
The idea is that having to explicitly add .unordered to use a heap as a sequence/collection will highlight the fact that this container does not define a specific ordering for its elements.