Nice. This is interesting and definitely something worth implementing. I hope you don't mind but I have some discussion points.
If it were me, rather than monkey patching array I'd be tempted introduce a new dedicated Heap class that implements existing API (push, pop, <<, shift) so that it's closer to existing Array and Queue implementations instead of adding dedicated heap_push, heap_pop, etc..
As well as better duck typing this allows introspection via .is_a? and case statements.
Also I wonder if it would be useful to base the implementation on the Queue[1] rather than Array to maintain thread safety.
If it were me, rather than monkey patching array I'd be tempted introduce a new dedicated Heap class that implements existing API (push, pop, <<, shift) so that it's closer to existing Array and Queue implementations instead of adding dedicated heap_push, heap_pop, etc..
As well as better duck typing this allows introspection via .is_a? and case statements.
Also I wonder if it would be useful to base the implementation on the Queue[1] rather than Array to maintain thread safety.
1. https://ruby-doc.org/core-2.5.0/Queue.html