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In order to implement pickling of instance methods, a means of separating
the object and the unbound method is necessary.
This is easily done for Python methods (f.__self__ and f.__func__),
but not all of builtins support __func__. Moreover, there currently
appears to be no good way to distinguish functions from bound methods.
As a first step in solving this issue, I have attached a patch which:
1) adds __func__ for all function types
2) adds a few new definitions in the types module (AllFunctionTypes etc.)
3) adds isanyfunction(), isanyboundfunction(), isanyunboundfunction() in
 inspect (admittedly these are bad names)
4) functools.unbind
In case applying this patch is being considered, serious review is necessary,
as I'm not knowledgeable of cpython internals.

Can you push patch in form available for review via Rietveld?

Yes, the patch is at http://codereview.appspot.com/6425052/
The code there also contains some tests I've written for functools.unbind.

Looks like PyCFunction_NewEx is part of Stable API.
If I'm right you have to make stub for this one as simple trampoline to new PyCFunction_NewExEx implementation.
Martin, please confirm.

Andrew is right: PyCFunction_NewEx must stay, and must continue to get the same parameters as it currently does. This not only applies to extensions already built, but also to extensions that are built against the new header files: they still need to run under old Python releases (if they only use the stable ABI).

Doesn't the definition I've added at the end of methodobject.c suffice? (http://codereview.appspot.com/6425052/patch/1/10) Or should the macro be removed altogether?

Stefan, you right.
A bit hairy idiom from my perspective, but it works.
Looks like this way used only for PyCFunction_New, all other code follows standard schema with trampoline.

Can't you unbind without any changes to the C code by doing
 def unbind(f):
 if hasattr(f, '__func__'):
 return f.__func__
 self = getattr(f, '__self__', None)
 if self is not None and not isinstance(self, types.ModuleType):
 return getattr(type(f.__self__), f.__name__)
 raise TypeError('not a bound method')
Also, I am not convinced that it is a good idea to return f if f is already "unbound". In practice I think you will always need to treat the bound and the unbound cases differently.

Stefan, I've fixed refleak found by you in #15404. Thanks.

Richard, yes, I think that would work, I didn't think of using f.__self__'s type.
You might want to replace
 if self is not None and not isinstance(self, types.ModuleType):
with
 if self is not None and not isinstance(self, types.ModuleType) \
 and not isinstance(self, type):
to correctly raise an exception when called on a classmethod too.

Andrew, thanks for creating a separate issue (the refleak was very rare and I thought I'd put it in the same place, but now I realize it was a bad idea).
Richard, actually, the isinstance(self, type) check I mentioned earlier would have to be before the hastattr(f, '__func__') check, because Python classmethods provide a __func__ too:
 def unbind(f):
 self = getattr(f, '__self__', None)
 if self is not None and not isinstance(self, types.ModuleType) \
 and not isinstance(self, type):
 if hasattr(f, '__func__'):
 return f.__func__
 return getattr(type(f.__self__), f.__name__)
 raise TypeError('not a bound method')
Anyway, I'm not convinced this is worth adding anymore. As Antoine Pitrou suggested on the ml, it would probably be a better idea if I implemented __reduce__ for builtin methods as well as Python methods rather than having a separate opcode for pickling methods.