inspect.getmembers currently uses `dir` to obtain a
list of an object's "members", which omits certain
things such as methods of the metaclass, e.g:

  >>> 'mro' in dict(inspect.getmembers(int))
  0

Since I can't find a description of what exactly
constitutes a "member", it is not strictly possible to
tell whether this is the intended behavior, but then
the documentation should be updated in this case to
clarify the semantics more.

It currently seems quite hard to answer seemingly
innocuous questions such as "What are the methods of
class/type X?" with introspection. 

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This is unclear indeed -- inspect is definitely underspecified.

It *is* clearly defined that dir() doesn't return metaclass
attributes when the argument is a class.

To find out the metaclass arguments, simply use
dir(int.__class__).

I'll leave this open, but I expect that at best some
documentation clarification will come out of this.

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A documentation clarification seems like a perfectly fine
solution to me. 

I know that I could use ``dir(type(int)`` but the problem I
have is not so much that I can't at all find out what I want
by introspection, but rather that I often can't do so in a
clean and reliable manner that is likely to work in future
releases (and dir's doc explicitly states that its behavior
can't be relied to stay stable across releases). Currently
trying to do metaprogramming in python can sometimes be
frustrating, because in the absence of clearly defined
semantics for important things it is often a noninutitive
(e.g. inspect.ismethod(str.find)) trial-and-error procedure
("oops, that didn't work because it was a ... (new-style
class/old-style class/builtin type/class with
__slots__/<dict-proxy> etc.)") that's unlikely to yield
particularly robust solutions.
Obviously vagueness allows more leeway for future
improvements, but I still think it would be nice if there at
least were a uniform and relatively well-defined way to get
at an object's attributes and a clarified getmembers could
fit the bill.

Added a doc clarification in r59775.