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Recursive partial objects are legitimate. Here is a patch that makes partial's repr to support recursive partial objects. Also added a test for pickling.
Cases for Element and file-like objects are questionable. Recursive Element.tag and TextIOWrapper.name don't make a sense, and I don't think we should special support (and encourage) these cases. To avoid stack overflow we can add a restriction for tag to be str or None, but file's name attribute can be dynamic. We can omit name from repr if it is not None, str, bytes or int.