PurePath.__truediv__ and __rtruediv__ raise a TypeError when passed something which is not an instance of string or PurePath. This prevents creating any sort of compatible class that doesn't inherit from the previously mentioned types.

Thanks for the report and for the PR. Could you give us a little bit more information about your use case? Couldn't you make the class you want to use implement the __fspath__ protocol?

    import pathlib as p

    class Spam:
        def __fspath__(self):
            return 'pathlib.py'

And we can use it like:

    >>> p.Path('Lib') / Spam()
    PosixPath('Lib/pathlib.py')
    >>> (p.Path('Lib') / Spam()).exists()
    True

(3.4 and 3.5 are in security-fix-only mode, so I removed them from the versions field.)

Using your above example, my use case is returning an instance of Spam instead of PurePath from the division operation. The Spam class would have extra properties and methods for dealing with a substructure of our file system that can exist in different places, so being able to use a normal Path to locate it later with the division operation would be useful. (I know I could have a method that would do that, but I personally think reading the division left to right is clearer.)

The current implementation makes this impossible and I found raising a TypeError to be inconsistent with how Python handles operator overloading in the standard library.

New changeset 4c69be22df3852f17873a74d015528d9a8ae92d6 by Serhiy Storchaka (aiudirog) in branch 'master':
bpo-34775: Return NotImplemented in PurePath division. (GH-9509)
https://github.com/python/cpython/commit/4c69be22df3852f17873a74d015528d9a8ae92d6

New changeset 4adcaf81513e57a2a4e278073a89efb1375af8df by Ned Deily (Miss Islington (bot)) in branch '3.8':
bpo-34775: Return NotImplemented in PurePath division. (GH-9509) (GH-15172)
https://github.com/python/cpython/commit/4adcaf81513e57a2a4e278073a89efb1375af8df

The change was pushed for release in 3.8.0b4.  I don't think we should backport it to 3.7 at this stage in its lifecycle as the old behavior has been around for a long time. Thanks, everyone!