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This experimental patch proposes to defer generator cleanup to the frame itself. In this scheme, the generator frame's tp_clear throws the GeneratorExit if necessary, so as to call cleanup code. The generator doesn't have any tp_del anymore, as it is now impossible to resurrect a generator (the frame, though, can be resurrected; I have to add a test for that).
The net effect is that generators caught in a reference cycle can always be reclaimed, and their cleanup code is run in a valid frame.

Patch with added tests.

Just a couple of minor comments on review. Everything else I looked for (including the path where a generator failing to stop during frame deallocation leads to reporting an unraisable exception) seemed fine.
One aspect I find interesting is that we've had other patches which proposed reducing the level of poking around generators needed to do inside frame objects by moving (some of) that state to the generators. This patch goes the other way, by moving the related cleanup functionality into the frame objects.
I think that's actually a reasonable option - the frame is always going to be involved at some point in order to actually execute the cleanup code, so our only real chance to break the cycle is to eliminate the generator's involvement.

Updated patch keeping PyGen_NeedsFinalizing() for backwards compatibility (always returning 0).

New changeset c89febab4648 by Antoine Pitrou in branch 'default':
Issue #17807: Generators can now be finalized even when they are part of a reference cycle.
http://hg.python.org/cpython/rev/c89febab4648 

Committing for now, we'll see what people say.

New changeset edefd3450834 by Antoine Pitrou in branch 'default':
Backout c89febab4648 following private feedback by Guido.
http://hg.python.org/cpython/rev/edefd3450834 

After getting some private feedback from Guido, I'm convinced this patch isn't ready for consumption. Objects visible from the frame when it is finalized can be in a weird, incomplete state (Guido reports failing to get the __class__ of an object, for instance).
I'm keeping the issue open for now and will try to find further ways to solve the underlying problem.

Obsoleted by PEP 442.