<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def autodoc_module(module):
 """Add a short summary of all implemented members to a modules docstring. """

    doc = getattr(module, '__doc__')
    if doc is None:
        doc = ''
    members = []
    for name, member in inspect.getmembers(module):
        if ((not name.startswith('_')) and
                (inspect.getmodule(member) is module)):
            members.append((name, member))
    members = sorted(members, key=_number_of_line)
    if members:
        lines = ['\n\nModule :mod:`~%s` implements the following members:\n'
                 % module.__name__]
        for (name, member) in members:
            if inspect.isfunction(member):
                type_ = 'func'
            elif inspect.isclass(member):
                type_ = 'class'
            else:
                type_ = 'obj'
            lines.append('      * :%s:`~%s` %s'
                         % (type_, name, objecttools.description(member)))
        doc = doc + '\n\n' + '\n'.join(lines) + '\n\n' + 80*'_'
        module.__doc__ = doc