collections.abc.Reversible doesn't work with types that are supported by reserved() but neither have the __reversed__ method nor are explicitly registered as collections.abc.Sequence. For example:

>>> issubclass(array.array, collections.abc.Reversible)
False 

The reversing protocol as well as the iterating protocol is supported not only by special method, but implicitly if the class has implemented __getitem__ and __len__ methods.

>>> class Counter(int):
...   def __getitem__(s, i): return i
...   def __len__(s): return s
... 
>>> list(reversed(Counter(10)))
[9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
>>> issubclass(Counter, collections.abc.Reversible)
False

typing.Reversible starves from the same bug. See https://github.com/python/typing/issues/170.

I don't think this is a bug.  The purpose collections.abc.Reversible is to recognize type where the behavior has been guaranteed, not to recognize all types where it happens to work.

Part of the original reason for introducing ABCs in the first place was that in general there is no reliable way to detect whether a class defining __getitem__ is a sequence or a mapping.

A creator of such a class either needs to subclass from Sequence or register as a Sequence.  The fact that reversed(Counter(10)) happens to work is no more interesting that the fact Counter(10)[5] happens to work eventhough isinstance(Counter, Sequence) returns False.

One other thought:  array.array() object should probably be registered so that it recognizable as a Sequence and as Reversible.

I'm with Raymond.

I propose to register array.array() in all the appropriate places and then close this bug as a won't fix.

The typing issue might eventually be resolved via PEP 544 (if accepted), or not -- the"fallback protocols" based on __getitem__ and __len__ seem to be a complicating special case that we may want to put off.

New changeset e51dd9dad6590bf3a940723fbbaaf4f64a3c9228 by Pablo Galindo in branch 'master':
bpo-29727: Register array.array as a MutableSequence (GH-21338)
https://github.com/python/cpython/commit/e51dd9dad6590bf3a940723fbbaaf4f64a3c9228