Lib/inspect.py

"""Get useful information from live Python objects.

This module encapsulates the interface provided by the internal special
attributes (co_*, im_*, tb_*, etc.) in a friendlier fashion.
It also provides some help for examining source code and class layout.

Here are some of the useful functions provided by this module:

    ismodule(), isclass(), ismethod(), isfunction(), isgeneratorfunction(),
        isgenerator(), istraceback(), isframe(), iscode(), isbuiltin(),
        isroutine() - check object types
    getmembers() - get members of an object that satisfy a given condition

    getfile(), getsourcefile(), getsource() - find an object's source code
    getdoc(), getcomments() - get documentation on an object
    getmodule() - determine the module that an object came from
    getclasstree() - arrange classes so as to represent their hierarchy

    getargspec(), getargvalues(), getcallargs() - get info about function arguments
    getfullargspec() - same, with support for Python-3000 features
    formatargspec(), formatargvalues() - format an argument spec
    getouterframes(), getinnerframes() - get info about frames
    currentframe() - get the current stack frame
    stack(), trace() - get info about frames on the stack or in a traceback

    signature() - get a Signature object for the callable
"""

# This module is in the public domain.  No warranties.

__author__ = ('Ka-Ping Yee <ping@lfw.org>',
              'Yury Selivanov <yselivanov@sprymix.com>')

import importlib.machinery
import itertools
import linecache
import os
import re
import sys
import tokenize
import types
import warnings
import functools
import builtins
from operator import attrgetter
from collections import namedtuple, OrderedDict

# Create constants for the compiler flags in Include/code.h
# We try to get them from dis to avoid duplication, but fall
# back to hardcoding so the dependency is optional
try:
    from dis import COMPILER_FLAG_NAMES as _flag_names
except ImportError:
    CO_OPTIMIZED, CO_NEWLOCALS = 0x1, 0x2
    CO_VARARGS, CO_VARKEYWORDS = 0x4, 0x8
    CO_NESTED, CO_GENERATOR, CO_NOFREE = 0x10, 0x20, 0x40
else:
    mod_dict = globals()
    for k, v in _flag_names.items():
        mod_dict["CO_" + v] = k

# See Include/object.h
TPFLAGS_IS_ABSTRACT = 1 << 20

# ----------------------------------------------------------- type-checking
def ismodule(object):
    """Return true if the object is a module.

    Module objects provide these attributes:
        __cached__      pathname to byte compiled file
        __doc__         documentation string
        __file__        filename (missing for built-in modules)"""
    return isinstance(object, types.ModuleType)

def isclass(object):
    """Return true if the object is a class.

    Class objects provide these attributes:
        __doc__         documentation string
        __module__      name of module in which this class was defined"""
    return isinstance(object, type)

def ismethod(object):
    """Return true if the object is an instance method.

    Instance method objects provide these attributes:
        __doc__         documentation string
        __name__        name with which this method was defined
        __func__        function object containing implementation of method
        __self__        instance to which this method is bound"""
    return isinstance(object, types.MethodType)

def ismethoddescriptor(object):
    """Return true if the object is a method descriptor.

    But not if ismethod() or isclass() or isfunction() are true.

    This is new in Python 2.2, and, for example, is true of int.__add__.
    An object passing this test has a __get__ attribute but not a __set__
    attribute, but beyond that the set of attributes varies.  __name__ is
    usually sensible, and __doc__ often is.

    Methods implemented via descriptors that also pass one of the other
    tests return false from the ismethoddescriptor() test, simply because
    the other tests promise more -- you can, e.g., count on having the
    __func__ attribute (etc) when an object passes ismethod()."""
    if isclass(object) or ismethod(object) or isfunction(object):
        # mutual exclusion
        return False
    tp = type(object)
    return hasattr(tp, "__get__") and not hasattr(tp, "__set__")

def isdatadescriptor(object):
    """Return true if the object is a data descriptor.

    Data descriptors have both a __get__ and a __set__ attribute.  Examples are
    properties (defined in Python) and getsets and members (defined in C).
    Typically, data descriptors will also have __name__ and __doc__ attributes
    (properties, getsets, and members have both of these attributes), but this
    is not guaranteed."""
    if isclass(object) or ismethod(object) or isfunction(object):
        # mutual exclusion
        return False
    tp = type(object)
    return hasattr(tp, "__set__") and hasattr(tp, "__get__")

if hasattr(types, 'MemberDescriptorType'):
    # CPython and equivalent
    def ismemberdescriptor(object):
        """Return true if the object is a member descriptor.

        Member descriptors are specialized descriptors defined in extension
        modules."""
        return isinstance(object, types.MemberDescriptorType)
else:
    # Other implementations
    def ismemberdescriptor(object):
        """Return true if the object is a member descriptor.

        Member descriptors are specialized descriptors defined in extension
        modules."""
        return False

if hasattr(types, 'GetSetDescriptorType'):
    # CPython and equivalent
    def isgetsetdescriptor(object):
        """Return true if the object is a getset descriptor.

        getset descriptors are specialized descriptors defined in extension
        modules."""
        return isinstance(object, types.GetSetDescriptorType)
else:
    # Other implementations
    def isgetsetdescriptor(object):
        """Return true if the object is a getset descriptor.

        getset descriptors are specialized descriptors defined in extension
        modules."""
        return False

def isfunction(object):
    """Return true if the object is a user-defined function.

    Function objects provide these attributes:
        __doc__         documentation string
        __name__        name with which this function was defined
        __code__        code object containing compiled function bytecode
        __defaults__    tuple of any default values for arguments
        __globals__     global namespace in which this function was defined
        __annotations__ dict of parameter annotations
        __kwdefaults__  dict of keyword only parameters with defaults"""
    return isinstance(object, types.FunctionType)

def isgeneratorfunction(object):
    """Return true if the object is a user-defined generator function.

    Generator function objects provides same attributes as functions.

    See help(isfunction) for attributes listing."""
    return bool((isfunction(object) or ismethod(object)) and
                object.__code__.co_flags & CO_GENERATOR)

def isgenerator(object):
    """Return true if the object is a generator.

    Generator objects provide these attributes:
        __iter__        defined to support iteration over container
        close           raises a new GeneratorExit exception inside the
                        generator to terminate the iteration
        gi_code         code object
        gi_frame        frame object or possibly None once the generator has
                        been exhausted
        gi_running      set to 1 when generator is executing, 0 otherwise
        next            return the next item from the container
        send            resumes the generator and "sends" a value that becomes
                        the result of the current yield-expression
        throw           used to raise an exception inside the generator"""
    return isinstance(object, types.GeneratorType)

def istraceback(object):
    """Return true if the object is a traceback.

    Traceback objects provide these attributes:
        tb_frame        frame object at this level
        tb_lasti        index of last attempted instruction in bytecode
        tb_lineno       current line number in Python source code
        tb_next         next inner traceback object (called by this level)"""
    return isinstance(object, types.TracebackType)

def isframe(object):
    """Return true if the object is a frame object.

    Frame objects provide these attributes:
        f_back          next outer frame object (this frame's caller)
        f_builtins      built-in namespace seen by this frame
        f_code          code object being executed in this frame
        f_globals       global namespace seen by this frame
        f_lasti         index of last attempted instruction in bytecode
        f_lineno        current line number in Python source code
        f_locals        local namespace seen by this frame
        f_trace         tracing function for this frame, or None"""
    return isinstance(object, types.FrameType)

def iscode(object):
    """Return true if the object is a code object.

    Code objects provide these attributes:
        co_argcount     number of arguments (not including * or ** args)
        co_code         string of raw compiled bytecode
        co_consts       tuple of constants used in the bytecode
        co_filename     name of file in which this code object was created
        co_firstlineno  number of first line in Python source code
        co_flags        bitmap: 1=optimized | 2=newlocals | 4=*arg | 8=**arg
        co_lnotab       encoded mapping of line numbers to bytecode indices
        co_name         name with which this code object was defined
        co_names        tuple of names of local variables
        co_nlocals      number of local variables
        co_stacksize    virtual machine stack space required
        co_varnames     tuple of names of arguments and local variables"""
    return isinstance(object, types.CodeType)

def isbuiltin(object):
    """Return true if the object is a built-in function or method.

    Built-in functions and methods provide these attributes:
        __doc__         documentation string
        __name__        original name of this function or method
        __self__        instance to which a method is bound, or None"""
    return isinstance(object, types.BuiltinFunctionType)

def isroutine(object):
    """Return true if the object is any kind of function or method."""
    return (isbuiltin(object)
            or isfunction(object)
            or ismethod(object)
            or ismethoddescriptor(object))

def isabstract(object):
    """Return true if the object is an abstract base class (ABC)."""
    return bool(isinstance(object, type) and object.__flags__ & TPFLAGS_IS_ABSTRACT)

def getmembers(object, predicate=None):
    """Return all members of an object as (name, value) pairs sorted by name.
    Optionally, only return members that satisfy a given predicate."""
    if isclass(object):
        mro = (object,) + getmro(object)
    else:
        mro = ()
    results = []
    for key in dir(object):
        # First try to get the value via __dict__. Some descriptors don't
        # like calling their __get__ (see bug #1785).
        for base in mro:
            if key in base.__dict__:
                value = base.__dict__[key]
                break
        else:
            try:
                value = getattr(object, key)
            except AttributeError:
                continue
        if not predicate or predicate(value):
            results.append((key, value))
    results.sort()
    return results

Attribute = namedtuple('Attribute', 'name kind defining_class object')

def classify_class_attrs(cls):
    """Return list of attribute-descriptor tuples.

    For each name in dir(cls), the return list contains a 4-tuple
    with these elements:

        0. The name (a string).

        1. The kind of attribute this is, one of these strings:
               'class method'    created via classmethod()
               'static method'   created via staticmethod()
               'property'        created via property()
               'method'          any other flavor of method
               'data'            not a method

        2. The class which defined this attribute (a class).

        3. The object as obtained directly from the defining class's
           __dict__, not via getattr.  This is especially important for
           data attributes:  C.data is just a data object, but
           C.__dict__['data'] may be a data descriptor with additional
           info, like a __doc__ string.
    """

    mro = getmro(cls)
    names = dir(cls)
    result = []
    for name in names:
        # Get the object associated with the name, and where it was defined.
        # Getting an obj from the __dict__ sometimes reveals more than
        # using getattr.  Static and class methods are dramatic examples.
        # Furthermore, some objects may raise an Exception when fetched with
        # getattr(). This is the case with some descriptors (bug #1785).
        # Thus, we only use getattr() as a last resort.
        homecls = None
        for base in (cls,) + mro:
            if name in base.__dict__:
                obj = base.__dict__[name]
                homecls = base
                break
        else:
            obj = getattr(cls, name)
            homecls = getattr(obj, "__objclass__", homecls)

        # Classify the object.
        if isinstance(obj, staticmethod):
            kind = "static method"
        elif isinstance(obj, classmethod):
            kind = "class method"
        elif isinstance(obj, property):
            kind = "property"
        elif ismethoddescriptor(obj):
            kind = "method"
        elif isdatadescriptor(obj):
            kind = "data"
        else:
            obj_via_getattr = getattr(cls, name)
            if (isfunction(obj_via_getattr) or
                ismethoddescriptor(obj_via_getattr)):
                kind = "method"
            else:
                kind = "data"
            obj = obj_via_getattr

        result.append(Attribute(name, kind, homecls, obj))

    return result

# ----------------------------------------------------------- class helpers

def getmro(cls):
    "Return tuple of base classes (including cls) in method resolution order."
    return cls.__mro__

# -------------------------------------------------------- function helpers

def unwrap(func, *, stop=None):
    """Get the object wrapped by *func*.

   Follows the chain of :attr:`__wrapped__` attributes returning the last
   object in the chain.

   *stop* is an optional callback accepting an object in the wrapper chain
   as its sole argument that allows the unwrapping to be terminated early if
   the callback returns a true value. If the callback never returns a true
   value, the last object in the chain is returned as usual. For example,
   :func:`signature` uses this to stop unwrapping if any object in the
   chain has a ``__signature__`` attribute defined.

   :exc:`ValueError` is raised if a cycle is encountered.

    """
    if stop is None:
        def _is_wrapper(f):
            return hasattr(f, '__wrapped__')
    else:
        def _is_wrapper(f):
            return hasattr(f, '__wrapped__') and not stop(f)
    f = func  # remember the original func for error reporting
    memo = {id(f)} # Memoise by id to tolerate non-hashable objects
    while _is_wrapper(func):
        func = func.__wrapped__
        id_func = id(func)
        if id_func in memo:
            raise ValueError('wrapper loop when unwrapping {!r}'.format(f))
        memo.add(id_func)
    return func

# -------------------------------------------------- source code extraction
def indentsize(line):
    """Return the indent size, in spaces, at the start of a line of text."""
    expline = line.expandtabs()
    return len(expline) - len(expline.lstrip())

def getdoc(object):
    """Get the documentation string for an object.

    All tabs are expanded to spaces.  To clean up docstrings that are
    indented to line up with blocks of code, any whitespace than can be
    uniformly removed from the second line onwards is removed."""
    try:
        doc = object.__doc__
    except AttributeError:
        return None
    if not isinstance(doc, str):
        return None
    return cleandoc(doc)

def cleandoc(doc):
    """Clean up indentation from docstrings.

    Any whitespace that can be uniformly removed from the second line
    onwards is removed."""
    try:
        lines = doc.expandtabs().split('\n')
    except UnicodeError:
        return None
    else:
        # Find minimum indentation of any non-blank lines after first line.
        margin = sys.maxsize
        for line in lines[1:]:
            content = len(line.lstrip())
            if content:
                indent = len(line) - content
                margin = min(margin, indent)
        # Remove indentation.
        if lines:
            lines[0] = lines[0].lstrip()
        if margin < sys.maxsize:
            for i in range(1, len(lines)): lines[i] = lines[i][margin:]
        # Remove any trailing or leading blank lines.
        while lines and not lines[-1]:
            lines.pop()
        while lines and not lines[0]:
            lines.pop(0)
        return '\n'.join(lines)

def getfile(object):
    """Work out which source or compiled file an object was defined in."""
    if ismodule(object):
        if hasattr(object, '__file__'):
            return object.__file__
        raise TypeError('{!r} is a built-in module'.format(object))
    if isclass(object):
        object = sys.modules.get(object.__module__)
        if hasattr(object, '__file__'):
            return object.__file__
        raise TypeError('{!r} is a built-in class'.format(object))
    if ismethod(object):
        object = object.__func__
    if isfunction(object):
        object = object.__code__
    if istraceback(object):
        object = object.tb_frame
    if isframe(object):
        object = object.f_code
    if iscode(object):
        return object.co_filename
    raise TypeError('{!r} is not a module, class, method, '
                    'function, traceback, frame, or code object'.format(object))

ModuleInfo = namedtuple('ModuleInfo', 'name suffix mode module_type')

def getmoduleinfo(path):
    """Get the module name, suffix, mode, and module type for a given file."""
    warnings.warn('inspect.getmoduleinfo() is deprecated', DeprecationWarning,
                  2)
    with warnings.catch_warnings():
        warnings.simplefilter('ignore', PendingDeprecationWarning)
        import imp
    filename = os.path.basename(path)
    suffixes = [(-len(suffix), suffix, mode, mtype)
                    for suffix, mode, mtype in imp.get_suffixes()]
    suffixes.sort() # try longest suffixes first, in case they overlap
    for neglen, suffix, mode, mtype in suffixes:
        if filename[neglen:] == suffix:
            return ModuleInfo(filename[:neglen], suffix, mode, mtype)

def getmodulename(path):
    """Return the module name for a given file, or None."""
    fname = os.path.basename(path)
    # Check for paths that look like an actual module file
    suffixes = [(-len(suffix), suffix)
                    for suffix in importlib.machinery.all_suffixes()]
    suffixes.sort() # try longest suffixes first, in case they overlap
    for neglen, suffix in suffixes:
        if fname.endswith(suffix):
            return fname[:neglen]
    return None

def getsourcefile(object):
    """Return the filename that can be used to locate an object's source.
    Return None if no way can be identified to get the source.
    """
    filename = getfile(object)
    all_bytecode_suffixes = importlib.machinery.DEBUG_BYTECODE_SUFFIXES[:]
    all_bytecode_suffixes += importlib.machinery.OPTIMIZED_BYTECODE_SUFFIXES[:]
    if any(filename.endswith(s) for s in all_bytecode_suffixes):
        filename = (os.path.splitext(filename)[0] +
                    importlib.machinery.SOURCE_SUFFIXES[0])
    elif any(filename.endswith(s) for s in
                 importlib.machinery.EXTENSION_SUFFIXES):
        return None
    if os.path.exists(filename):
        return filename
    # only return a non-existent filename if the module has a PEP 302 loader
    if getattr(getmodule(object, filename), '__loader__', None) is not None:
        return filename
    # or it is in the linecache
    if filename in linecache.cache:
        return filename

def getabsfile(object, _filename=None):
    """Return an absolute path to the source or compiled file for an object.

    The idea is for each object to have a unique origin, so this routine
    normalizes the result as much as possible."""
    if _filename is None:
        _filename = getsourcefile(object) or getfile(object)
    return os.path.normcase(os.path.abspath(_filename))

modulesbyfile = {}
_filesbymodname = {}

def getmodule(object, _filename=None):
    """Return the module an object was defined in, or None if not found."""
    if ismodule(object):
        return object
    if hasattr(object, '__module__'):
        return sys.modules.get(object.__module__)
    # Try the filename to modulename cache
    if _filename is not None and _filename in modulesbyfile:
        return sys.modules.get(modulesbyfile[_filename])
    # Try the cache again with the absolute file name
    try:
        file = getabsfile(object, _filename)
    except TypeError:
        return None
    if file in modulesbyfile:
        return sys.modules.get(modulesbyfile[file])
    # Update the filename to module name cache and check yet again
    # Copy sys.modules in order to cope with changes while iterating
    for modname, module in list(sys.modules.items()):
        if ismodule(module) and hasattr(module, '__file__'):
            f = module.__file__
            if f == _filesbymodname.get(modname, None):
                # Have already mapped this module, so skip it
                continue
            _filesbymodname[modname] = f
            f = getabsfile(module)
            # Always map to the name the module knows itself by
            modulesbyfile[f] = modulesbyfile[
                os.path.realpath(f)] = module.__name__
    if file in modulesbyfile:
        return sys.modules.get(modulesbyfile[file])
    # Check the main module
    main = sys.modules['__main__']
    if not hasattr(object, '__name__'):
        return None
    if hasattr(main, object.__name__):
        mainobject = getattr(main, object.__name__)
        if mainobject is object:
            return main
    # Check builtins
    builtin = sys.modules['builtins']
    if hasattr(builtin, object.__name__):
        builtinobject = getattr(builtin, object.__name__)
        if builtinobject is object:
            return builtin

def findsource(object):
    """Return the entire source file and starting line number for an object.

    The argument may be a module, class, method, function, traceback, frame,
    or code object.  The source code is returned as a list of all the lines
    in the file and the line number indexes a line in that list.  An OSError
    is raised if the source code cannot be retrieved."""

    file = getfile(object)
    sourcefile = getsourcefile(object)
    if not sourcefile and file[:1] + file[-1:] != '<>':
        raise OSError('source code not available')
    file = sourcefile if sourcefile else file

    module = getmodule(object, file)
    if module:
        lines = linecache.getlines(file, module.__dict__)
    else:
        lines = linecache.getlines(file)
    if not lines:
        raise OSError('could not get source code')

    if ismodule(object):
        return lines, 0

    if isclass(object):
        name = object.__name__
        pat = re.compile(r'^(\s*)class\s*' + name + r'\b')
        # make some effort to find the best matching class definition:
        # use the one with the least indentation, which is the one
        # that's most probably not inside a function definition.
        candidates = []
        for i in range(len(lines)):
            match = pat.match(lines[i])
            if match:
                # if it's at toplevel, it's already the best one
                if lines[i][0] == 'c':
                    return lines, i
                # else add whitespace to candidate list
                candidates.append((match.group(1), i))
        if candidates:
            # this will sort by whitespace, and by line number,
            # less whitespace first
            candidates.sort()
            return lines, candidates[0][1]
        else:
            raise OSError('could not find class definition')

    if ismethod(object):
        object = object.__func__
    if isfunction(object):
        object = object.__code__
    if istraceback(object):
        object = object.tb_frame
    if isframe(object):
        object = object.f_code
    if iscode(object):
        if not hasattr(object, 'co_firstlineno'):
            raise OSError('could not find function definition')
        lnum = object.co_firstlineno - 1
        pat = re.compile(r'^(\s*def\s)|(.*(?<!\w)lambda(:|\s))|^(\s*@)')
        while lnum > 0:
            if pat.match(lines[lnum]): break
            lnum = lnum - 1
        return lines, lnum
    raise OSError('could not find code object')

def getcomments(object):
    """Get lines of comments immediately preceding an object's source code.

    Returns None when source can't be found.
    """
    try:
        lines, lnum = findsource(object)
    except (OSError, TypeError):
        return None

    if ismodule(object):
        # Look for a comment block at the top of the file.
        start = 0
        if lines and lines[0][:2] == '#!': start = 1
        while start < len(lines) and lines[start].strip() in ('', '#'):
            start = start + 1
        if start < len(lines) and lines[start][:1] == '#':
            comments = []
            end = start
            while end < len(lines) and lines[end][:1] == '#':
                comments.append(lines[end].expandtabs())
                end = end + 1
            return ''.join(comments)

    # Look for a preceding block of comments at the same indentation.
    elif lnum > 0:
        indent = indentsize(lines[lnum])
        end = lnum - 1
        if end >= 0 and lines[end].lstrip()[:1] == '#' and \
            indentsize(lines[end]) == indent:
            comments = [lines[end].expandtabs().lstrip()]
            if end > 0:
                end = end - 1
                comment = lines[end].expandtabs().lstrip()
                while comment[:1] == '#' and indentsize(lines[end]) == indent:
                    comments[:0] = [comment]
                    end = end - 1
                    if end < 0: break
                    comment = lines[end].expandtabs().lstrip()
            while comments and comments[0].strip() == '#':
                comments[:1] = []
            while comments and comments[-1].strip() == '#':
                comments[-1:] = []
            return ''.join(comments)

class EndOfBlock(Exception): pass

class BlockFinder:
    """Provide a tokeneater() method to detect the end of a code block."""
    def __init__(self):
        self.indent = 0
        self.islambda = False
        self.started = False
        self.passline = False
        self.last = 1

    def tokeneater(self, type, token, srowcol, erowcol, line):
        if not self.started:
            # look for the first "def", "class" or "lambda"
            if token in ("def", "class", "lambda"):
                if token == "lambda":
                    self.islambda = True
                self.started = True
            self.passline = True    # skip to the end of the line
        elif type == tokenize.NEWLINE:
            self.passline = False   # stop skipping when a NEWLINE is seen
            self.last = srowcol[0]
            if self.islambda:       # lambdas always end at the first NEWLINE
                raise EndOfBlock
        elif self.passline:
            pass
        elif type == tokenize.INDENT:
            self.indent = self.indent + 1
            self.passline = True
        elif type == tokenize.DEDENT:
            self.indent = self.indent - 1
            # the end of matching indent/dedent pairs end a block
            # (note that this only works for "def"/"class" blocks,
            #  not e.g. for "if: else:" or "try: finally:" blocks)
            if self.indent <= 0:
                raise EndOfBlock
        elif self.indent == 0 and type not in (tokenize.COMMENT, tokenize.NL):
            # any other token on the same indentation level end the previous
            # block as well, except the pseudo-tokens COMMENT and NL.
            raise EndOfBlock

def getblock(lines):
    """Extract the block of code at the top of the given list of lines."""
    blockfinder = BlockFinder()
    try:
        tokens = tokenize.generate_tokens(iter(lines).__next__)
        for _token in tokens:
            blockfinder.tokeneater(*_token)
    except (EndOfBlock, IndentationError):
        pass
    return lines[:blockfinder.last]

def getsourcelines(object):
    """Return a list of source lines and starting line number for an object.

    The argument may be a module, class, method, function, traceback, frame,
    or code object.  The source code is returned as a list of the lines
    corresponding to the object and the line number indicates where in the
    original source file the first line of code was found.  An OSError is
    raised if the source code cannot be retrieved."""
    lines, lnum = findsource(object)

    if ismodule(object): return lines, 0
    else: return getblock(lines[lnum:]), lnum + 1

def getsource(object):
    """Return the text of the source code for an object.

    The argument may be a module, class, method, function, traceback, frame,
    or code object.  The source code is returned as a single string.  An
    OSError is raised if the source code cannot be retrieved."""
    lines, lnum = getsourcelines(object)
    return ''.join(lines)

# --------------------------------------------------- class tree extraction
def walktree(classes, children, parent):
    """Recursive helper function for getclasstree()."""
    results = []
    classes.sort(key=attrgetter('__module__', '__name__'))
    for c in classes:
        results.append((c, c.__bases__))
        if c in children:
            results.append(walktree(children[c], children, c))
    return results

def getclasstree(classes, unique=False):
    """Arrange the given list of classes into a hierarchy of nested lists.

    Where a nested list appears, it contains classes derived from the class
    whose entry immediately precedes the list.  Each entry is a 2-tuple
    containing a class and a tuple of its base classes.  If the 'unique'
    argument is true, exactly one entry appears in the returned structure
    for each class in the given list.  Otherwise, classes using multiple
    inheritance and their descendants will appear multiple times."""
    children = {}
    roots = []
    for c in classes:
        if c.__bases__:
            for parent in c.__bases__:
                if not parent in children:
                    children[parent] = []
                if c not in children[parent]:
                    children[parent].append(c)
                if unique and parent in classes: break
        elif c not in roots:
            roots.append(c)
    for parent in children:
        if parent not in classes:
            roots.append(parent)
    return walktree(roots, children, None)

# ------------------------------------------------ argument list extraction
Arguments = namedtuple('Arguments', 'args, varargs, varkw')

def getargs(co):
    """Get information about the arguments accepted by a code object.

    Three things are returned: (args, varargs, varkw), where
    'args' is the list of argument names. Keyword-only arguments are
    appended. 'varargs' and 'varkw' are the names of the * and **
    arguments or None."""
    args, varargs, kwonlyargs, varkw = _getfullargs(co)
    return Arguments(args + kwonlyargs, varargs, varkw)

def _getfullargs(co):
    """Get information about the arguments accepted by a code object.

    Four things are returned: (args, varargs, kwonlyargs, varkw), where
    'args' and 'kwonlyargs' are lists of argument names, and 'varargs'
    and 'varkw' are the names of the * and ** arguments or None."""

    if not iscode(co):
        raise TypeError('{!r} is not a code object'.format(co))

    nargs = co.co_argcount
    names = co.co_varnames
    nkwargs = co.co_kwonlyargcount
    args = list(names[:nargs])
    kwonlyargs = list(names[nargs:nargs+nkwargs])
    step = 0

    nargs += nkwargs
    varargs = None
    if co.co_flags & CO_VARARGS:
        varargs = co.co_varnames[nargs]
        nargs = nargs + 1
    varkw = None
    if co.co_flags & CO_VARKEYWORDS:
        varkw = co.co_varnames[nargs]
    return args, varargs, kwonlyargs, varkw


ArgSpec = namedtuple('ArgSpec', 'args varargs keywords defaults')

def getargspec(func):
    """Get the names and default values of a function's arguments.

    A tuple of four things is returned: (args, varargs, varkw, defaults).
    'args' is a list of the argument names.
    'args' will include keyword-only argument names.
    'varargs' and 'varkw' are the names of the * and ** arguments or None.
    'defaults' is an n-tuple of the default values of the last n arguments.

    Use the getfullargspec() API for Python-3000 code, as annotations
    and keyword arguments are supported. getargspec() will raise ValueError
    if the func has either annotations or keyword arguments.
    """

    args, varargs, varkw, defaults, kwonlyargs, kwonlydefaults, ann = \
        getfullargspec(func)
    if kwonlyargs or ann:
        raise ValueError("Function has keyword-only arguments or annotations"
                         ", use getfullargspec() API which can support them")
    return ArgSpec(args, varargs, varkw, defaults)

FullArgSpec = namedtuple('FullArgSpec',
    'args, varargs, varkw, defaults, kwonlyargs, kwonlydefaults, annotations')

def getfullargspec(func):
    """Get the names and default values of a function's arguments.

    A tuple of seven things is returned:
    (args, varargs, varkw, defaults, kwonlyargs, kwonlydefaults annotations).
    'args' is a list of the argument names.
    'varargs' and 'varkw' are the names of the * and ** arguments or None.
    'defaults' is an n-tuple of the default values of the last n arguments.
    'kwonlyargs' is a list of keyword-only argument names.
    'kwonlydefaults' is a dictionary mapping names from kwonlyargs to defaults.
    'annotations' is a dictionary mapping argument names to annotations.

    The first four items in the tuple correspond to getargspec().
    """

    if ismethod(func):
        func = func.__func__
    if not isfunction(func):
        raise TypeError('{!r} is not a Python function'.format(func))
    args, varargs, kwonlyargs, varkw = _getfullargs(func.__code__)
    return FullArgSpec(args, varargs, varkw, func.__defaults__,
            kwonlyargs, func.__kwdefaults__, func.__annotations__)

ArgInfo = namedtuple('ArgInfo', 'args varargs keywords locals')

def getargvalues(frame):
    """Get information about arguments passed into a particular frame.

    A tuple of four things is returned: (args, varargs, varkw, locals).
    'args' is a list of the argument names.
    'varargs' and 'varkw' are the names of the * and ** arguments or None.
    'locals' is the locals dictionary of the given frame."""
    args, varargs, varkw = getargs(frame.f_code)
    return ArgInfo(args, varargs, varkw, frame.f_locals)

def formatannotation(annotation, base_module=None):
    if isinstance(annotation, type):
        if annotation.__module__ in ('builtins', base_module):
            return annotation.__name__
        return annotation.__module__+'.'+annotation.__name__
    return repr(annotation)

def formatannotationrelativeto(object):
    module = getattr(object, '__module__', None)
    def _formatannotation(annotation):
        return formatannotation(annotation, module)
    return _formatannotation

def formatargspec(args, varargs=None, varkw=None, defaults=None,
                  kwonlyargs=(), kwonlydefaults={}, annotations={},
                  formatarg=str,
                  formatvarargs=lambda name: '*' + name,
                  formatvarkw=lambda name: '**' + name,
                  formatvalue=lambda value: '=' + repr(value),
                  formatreturns=lambda text: ' -> ' + text,
                  formatannotation=formatannotation):
    """Format an argument spec from the values returned by getargspec
    or getfullargspec.

    The first seven arguments are (args, varargs, varkw, defaults,
    kwonlyargs, kwonlydefaults, annotations).  The other five arguments
    are the corresponding optional formatting functions that are called to
    turn names and values into strings.  The last argument is an optional
    function to format the sequence of arguments."""
    def formatargandannotation(arg):
        result = formatarg(arg)
        if arg in annotations:
            result += ': ' + formatannotation(annotations[arg])
        return result
    specs = []
    if defaults:
        firstdefault = len(args) - len(defaults)
    for i, arg in enumerate(args):
        spec = formatargandannotation(arg)
        if defaults and i >= firstdefault:
            spec = spec + formatvalue(defaults[i - firstdefault])
        specs.append(spec)
    if varargs is not None:
        specs.append(formatvarargs(formatargandannotation(varargs)))
    else:
        if kwonlyargs:
            specs.append('*')
    if kwonlyargs:
        for kwonlyarg in kwonlyargs:
            spec = formatargandannotation(kwonlyarg)
            if kwonlydefaults and kwonlyarg in kwonlydefaults:
                spec += formatvalue(kwonlydefaults[kwonlyarg])
            specs.append(spec)
    if varkw is not None:
        specs.append(formatvarkw(formatargandannotation(varkw)))
    result = '(' + ', '.join(specs) + ')'
    if 'return' in annotations:
        result += formatreturns(formatannotation(annotations['return']))
    return result

def formatargvalues(args, varargs, varkw, locals,
                    formatarg=str,
                    formatvarargs=lambda name: '*' + name,
                    formatvarkw=lambda name: '**' + name,
                    formatvalue=lambda value: '=' + repr(value)):
    """Format an argument spec from the 4 values returned by getargvalues.

    The first four arguments are (args, varargs, varkw, locals).  The
    next four arguments are the corresponding optional formatting functions
    that are called to turn names and values into strings.  The ninth
    argument is an optional function to format the sequence of arguments."""
    def convert(name, locals=locals,
                formatarg=formatarg, formatvalue=formatvalue):
        return formatarg(name) + formatvalue(locals[name])
    specs = []
    for i in range(len(args)):
        specs.append(convert(args[i]))
    if varargs:
        specs.append(formatvarargs(varargs) + formatvalue(locals[varargs]))
    if varkw:
        specs.append(formatvarkw(varkw) + formatvalue(locals[varkw]))
    return '(' + ', '.join(specs) + ')'

def _missing_arguments(f_name, argnames, pos, values):
    names = [repr(name) for name in argnames if name not in values]
    missing = len(names)
    if missing == 1:
        s = names[0]
    elif missing == 2:
        s = "{} and {}".format(*names)
    else:
        tail = ", {} and {}".format(names[-2:])
        del names[-2:]
        s = ", ".join(names) + tail
    raise TypeError("%s() missing %i required %s argument%s: %s" %
                    (f_name, missing,
                      "positional" if pos else "keyword-only",
                      "" if missing == 1 else "s", s))

def _too_many(f_name, args, kwonly, varargs, defcount, given, values):
    atleast = len(args) - defcount
    kwonly_given = len([arg for arg in kwonly if arg in values])
    if varargs:
        plural = atleast != 1
        sig = "at least %d" % (atleast,)
    elif defcount:
        plural = True
        sig = "from %d to %d" % (atleast, len(args))
    else:
        plural = len(args) != 1
        sig = str(len(args))
    kwonly_sig = ""
    if kwonly_given:
        msg = " positional argument%s (and %d keyword-only argument%s)"
        kwonly_sig = (msg % ("s" if given != 1 else "", kwonly_given,
                             "s" if kwonly_given != 1 else ""))
    raise TypeError("%s() takes %s positional argument%s but %d%s %s given" %
            (f_name, sig, "s" if plural else "", given, kwonly_sig,
             "was" if given == 1 and not kwonly_given else "were"))

def getcallargs(func, *positional, **named):
    """Get the mapping of arguments to values.

    A dict is returned, with keys the function argument names (including the
    names of the * and ** arguments, if any), and values the respective bound
    values from 'positional' and 'named'."""
    spec = getfullargspec(func)
    args, varargs, varkw, defaults, kwonlyargs, kwonlydefaults, ann = spec
    f_name = func.__name__
    arg2value = {}


    if ismethod(func) and func.__self__ is not None:
        # implicit 'self' (or 'cls' for classmethods) argument
        positional = (func.__self__,) + positional
    num_pos = len(positional)
    num_args = len(args)
    num_defaults = len(defaults) if defaults else 0

    n = min(num_pos, num_args)
    for i in range(n):
        arg2value[args[i]] = positional[i]
    if varargs:
        arg2value[varargs] = tuple(positional[n:])
    possible_kwargs = set(args + kwonlyargs)
    if varkw:
        arg2value[varkw] = {}
    for kw, value in named.items():
        if kw not in possible_kwargs:
            if not varkw:
                raise TypeError("%s() got an unexpected keyword argument %r" %
                                (f_name, kw))
            arg2value[varkw][kw] = value
            continue
        if kw in arg2value:
            raise TypeError("%s() got multiple values for argument %r" %
                            (f_name, kw))
        arg2value[kw] = value
    if num_pos > num_args and not varargs:
        _too_many(f_name, args, kwonlyargs, varargs, num_defaults,
                   num_pos, arg2value)
    if num_pos < num_args:
        req = args[:num_args - num_defaults]
        for arg in req:
            if arg not in arg2value:
                _missing_arguments(f_name, req, True, arg2value)
        for i, arg in enumerate(args[num_args - num_defaults:]):
            if arg not in arg2value:
                arg2value[arg] = defaults[i]
    missing = 0
    for kwarg in kwonlyargs:
        if kwarg not in arg2value:
            if kwarg in kwonlydefaults:
                arg2value[kwarg] = kwonlydefaults[kwarg]
            else:
                missing += 1
    if missing:
        _missing_arguments(f_name, kwonlyargs, False, arg2value)
    return arg2value

ClosureVars = namedtuple('ClosureVars', 'nonlocals globals builtins unbound')

def getclosurevars(func):
    """
    Get the mapping of free variables to their current values.

    Returns a named tuple of dicts mapping the current nonlocal, global
    and builtin references as seen by the body of the function. A final
    set of unbound names that could not be resolved is also provided.
    """

    if ismethod(func):
        func = func.__func__

    if not isfunction(func):
        raise TypeError("'{!r}' is not a Python function".format(func))

    code = func.__code__
    # Nonlocal references are named in co_freevars and resolved
    # by looking them up in __closure__ by positional index
    if func.__closure__ is None:
        nonlocal_vars = {}
    else:
        nonlocal_vars = {
            var : cell.cell_contents
            for var, cell in zip(code.co_freevars, func.__closure__)
       }

    # Global and builtin references are named in co_names and resolved
    # by looking them up in __globals__ or __builtins__
    global_ns = func.__globals__
    builtin_ns = global_ns.get("__builtins__", builtins.__dict__)
    if ismodule(builtin_ns):
        builtin_ns = builtin_ns.__dict__
    global_vars = {}
    builtin_vars = {}
    unbound_names = set()
    for name in code.co_names:
        if name in ("None", "True", "False"):
            # Because these used to be builtins instead of keywords, they
            # may still show up as name references. We ignore them.
            continue
        try:
            global_vars[name] = global_ns[name]
        except KeyError:
            try:
                builtin_vars[name] = builtin_ns[name]
            except KeyError:
                unbound_names.add(name)

    return ClosureVars(nonlocal_vars, global_vars,
                       builtin_vars, unbound_names)

# -------------------------------------------------- stack frame extraction

Traceback = namedtuple('Traceback', 'filename lineno function code_context index')

def getframeinfo(frame, context=1):
    """Get information about a frame or traceback object.

    A tuple of five things is returned: the filename, the line number of
    the current line, the function name, a list of lines of context from
    the source code, and the index of the current line within that list.
    The optional second argument specifies the number of lines of context
    to return, which are centered around the current line."""
    if istraceback(frame):
        lineno = frame.tb_lineno
        frame = frame.tb_frame
    else:
        lineno = frame.f_lineno
    if not isframe(frame):
        raise TypeError('{!r} is not a frame or traceback object'.format(frame))

    filename = getsourcefile(frame) or getfile(frame)
    if context > 0:
        start = lineno - 1 - context//2
        try:
            lines, lnum = findsource(frame)
        except OSError:
            lines = index = None
        else:
            start = max(start, 1)
            start = max(0, min(start, len(lines) - context))
            lines = lines[start:start+context]
            index = lineno - 1 - start
    else:
        lines = index = None

    return Traceback(filename, lineno, frame.f_code.co_name, lines, index)

def getlineno(frame):
    """Get the line number from a frame object, allowing for optimization."""
    # FrameType.f_lineno is now a descriptor that grovels co_lnotab
    return frame.f_lineno

def getouterframes(frame, context=1):
    """Get a list of records for a frame and all higher (calling) frames.

    Each record contains a frame object, filename, line number, function
    name, a list of lines of context, and index within the context."""
    framelist = []
    while frame:
        framelist.append((frame,) + getframeinfo(frame, context))
        frame = frame.f_back
    return framelist

def getinnerframes(tb, context=1):
    """Get a list of records for a traceback's frame and all lower frames.

    Each record contains a frame object, filename, line number, function
    name, a list of lines of context, and index within the context."""
    framelist = []
    while tb:
        framelist.append((tb.tb_frame,) + getframeinfo(tb, context))
        tb = tb.tb_next
    return framelist

def currentframe():
    """Return the frame of the caller or None if this is not possible."""
    return sys._getframe(1) if hasattr(sys, "_getframe") else None

def stack(context=1):
    """Return a list of records for the stack above the caller's frame."""
    return getouterframes(sys._getframe(1), context)

def trace(context=1):
    """Return a list of records for the stack below the current exception."""
    return getinnerframes(sys.exc_info()[2], context)


# ------------------------------------------------ static version of getattr

_sentinel = object()

def _static_getmro(klass):
    return type.__dict__['__mro__'].__get__(klass)

def _check_instance(obj, attr):
    instance_dict = {}
    try:
        instance_dict = object.__getattribute__(obj, "__dict__")
    except AttributeError:
        pass
    return dict.get(instance_dict, attr, _sentinel)


def _check_class(klass, attr):
    for entry in _static_getmro(klass):
        if _shadowed_dict(type(entry)) is _sentinel:
            try:
                return entry.__dict__[attr]
            except KeyError:
                pass
    return _sentinel

def _is_type(obj):
    try:
        _static_getmro(obj)
    except TypeError:
        return False
    return True

def _shadowed_dict(klass):
    dict_attr = type.__dict__["__dict__"]
    for entry in _static_getmro(klass):
        try:
            class_dict = dict_attr.__get__(entry)["__dict__"]
        except KeyError:
            pass
        else:
            if not (type(class_dict) is types.GetSetDescriptorType and
                    class_dict.__name__ == "__dict__" and
                    class_dict.__objclass__ is entry):
                return class_dict
    return _sentinel

def getattr_static(obj, attr, default=_sentinel):
    """Retrieve attributes without triggering dynamic lookup via the
       descriptor protocol,  __getattr__ or __getattribute__.

       Note: this function may not be able to retrieve all attributes
       that getattr can fetch (like dynamically created attributes)
       and may find attributes that getattr can't (like descriptors
       that raise AttributeError). It can also return descriptor objects
       instead of instance members in some cases. See the
       documentation for details.
    """
    instance_result = _sentinel
    if not _is_type(obj):
        klass = type(obj)
        dict_attr = _shadowed_dict(klass)
        if (dict_attr is _sentinel or
            type(dict_attr) is types.MemberDescriptorType):
            instance_result = _check_instance(obj, attr)
    else:
        klass = obj

    klass_result = _check_class(klass, attr)

    if instance_result is not _sentinel and klass_result is not _sentinel:
        if (_check_class(type(klass_result), '__get__') is not _sentinel and
            _check_class(type(klass_result), '__set__') is not _sentinel):
            return klass_result

    if instance_result is not _sentinel:
        return instance_result
    if klass_result is not _sentinel:
        return klass_result

    if obj is klass:
        # for types we check the metaclass too
        for entry in _static_getmro(type(klass)):
            if _shadowed_dict(type(entry)) is _sentinel:
                try:
                    return entry.__dict__[attr]
                except KeyError:
                    pass
    if default is not _sentinel:
        return default
    raise AttributeError(attr)


# ------------------------------------------------ generator introspection

GEN_CREATED = 'GEN_CREATED'
GEN_RUNNING = 'GEN_RUNNING'
GEN_SUSPENDED = 'GEN_SUSPENDED'
GEN_CLOSED = 'GEN_CLOSED'

def getgeneratorstate(generator):
    """Get current state of a generator-iterator.

    Possible states are:
      GEN_CREATED: Waiting to start execution.
      GEN_RUNNING: Currently being executed by the interpreter.
      GEN_SUSPENDED: Currently suspended at a yield expression.
      GEN_CLOSED: Execution has completed.
    """
    if generator.gi_running:
        return GEN_RUNNING
    if generator.gi_frame is None:
        return GEN_CLOSED
    if generator.gi_frame.f_lasti == -1:
        return GEN_CREATED
    return GEN_SUSPENDED


def getgeneratorlocals(generator):
    """
    Get the mapping of generator local variables to their current values.

    A dict is returned, with the keys the local variable names and values the
    bound values."""

    if not isgenerator(generator):
        raise TypeError("'{!r}' is not a Python generator".format(generator))

    frame = getattr(generator, "gi_frame", None)
    if frame is not None:
        return generator.gi_frame.f_locals
    else:
        return {}

###############################################################################
### Function Signature Object (PEP 362)
###############################################################################


_WrapperDescriptor = type(type.__call__)
_MethodWrapper = type(all.__call__)

_NonUserDefinedCallables = (_WrapperDescriptor,
                            _MethodWrapper,
                            types.BuiltinFunctionType)


def _get_user_defined_method(cls, method_name):
    try:
        meth = getattr(cls, method_name)
    except AttributeError:
        return
    else:
        if not isinstance(meth, _NonUserDefinedCallables):
            # Once '__signature__' will be added to 'C'-level
            # callables, this check won't be necessary
            return meth


def signature(obj):
    '''Get a signature object for the passed callable.'''

    if not callable(obj):
        raise TypeError('{!r} is not a callable object'.format(obj))

    if isinstance(obj, types.MethodType):
        # In this case we skip the first parameter of the underlying
        # function (usually `self` or `cls`).
        sig = signature(obj.__func__)
        return sig.replace(parameters=tuple(sig.parameters.values())[1:])

    # Was this function wrapped by a decorator?
    obj = unwrap(obj, stop=(lambda f: hasattr(f, "__signature__")))

    try:
        sig = obj.__signature__
    except AttributeError:
        pass
    else:
        if sig is not None:
            return sig


    if isinstance(obj, types.FunctionType):
        return Signature.from_function(obj)

    if isinstance(obj, functools.partial):
        sig = signature(obj.func)

        new_params = OrderedDict(sig.parameters.items())

        partial_args = obj.args or ()
        partial_keywords = obj.keywords or {}
        try:
            ba = sig.bind_partial(*partial_args, **partial_keywords)
        except TypeError as ex:
            msg = 'partial object {!r} has incorrect arguments'.format(obj)
            raise ValueError(msg) from ex

        for arg_name, arg_value in ba.arguments.items():
            param = new_params[arg_name]
            if arg_name in partial_keywords:
                # We set a new default value, because the following code
                # is correct:
                #
                #   >>> def foo(a): print(a)
                #   >>> print(partial(partial(foo, a=10), a=20)())
                #   20
                #   >>> print(partial(partial(foo, a=10), a=20)(a=30))
                #   30
                #
                # So, with 'partial' objects, passing a keyword argument is
                # like setting a new default value for the corresponding
                # parameter
                #
                # We also mark this parameter with '_partial_kwarg'
                # flag.  Later, in '_bind', the 'default' value of this
                # parameter will be added to 'kwargs', to simulate
                # the 'functools.partial' real call.
                new_params[arg_name] = param.replace(default=arg_value,
                                                     _partial_kwarg=True)

            elif (param.kind not in (_VAR_KEYWORD, _VAR_POSITIONAL) and
                            not param._partial_kwarg):
                new_params.pop(arg_name)

        return sig.replace(parameters=new_params.values())

    sig = None
    if isinstance(obj, type):
        # obj is a class or a metaclass

        # First, let's see if it has an overloaded __call__ defined
        # in its metaclass
        call = _get_user_defined_method(type(obj), '__call__')
        if call is not None:
            sig = signature(call)
        else:
            # Now we check if the 'obj' class has a '__new__' method
            new = _get_user_defined_method(obj, '__new__')
            if new is not None:
                sig = signature(new)
            else:
                # Finally, we should have at least __init__ implemented
                init = _get_user_defined_method(obj, '__init__')
                if init is not None:
                    sig = signature(init)
    elif not isinstance(obj, _NonUserDefinedCallables):
        # An object with __call__
        # We also check that the 'obj' is not an instance of
        # _WrapperDescriptor or _MethodWrapper to avoid
        # infinite recursion (and even potential segfault)
        call = _get_user_defined_method(type(obj), '__call__')
        if call is not None:
            sig = signature(call)

    if sig is not None:
        # For classes and objects we skip the first parameter of their
        # __call__, __new__, or __init__ methods
        return sig.replace(parameters=tuple(sig.parameters.values())[1:])

    if isinstance(obj, types.BuiltinFunctionType):
        # Raise a nicer error message for builtins
        msg = 'no signature found for builtin function {!r}'.format(obj)
        raise ValueError(msg)

    raise ValueError('callable {!r} is not supported by signature'.format(obj))


class _void:
    '''A private marker - used in Parameter & Signature'''


class _empty:
    pass


class _ParameterKind(int):
    def __new__(self, *args, name):
        obj = int.__new__(self, *args)
        obj._name = name
        return obj

    def __str__(self):
        return self._name

    def __repr__(self):
        return '<_ParameterKind: {!r}>'.format(self._name)


_POSITIONAL_ONLY        = _ParameterKind(0, name='POSITIONAL_ONLY')
_POSITIONAL_OR_KEYWORD  = _ParameterKind(1, name='POSITIONAL_OR_KEYWORD')
_VAR_POSITIONAL         = _ParameterKind(2, name='VAR_POSITIONAL')
_KEYWORD_ONLY           = _ParameterKind(3, name='KEYWORD_ONLY')
_VAR_KEYWORD            = _ParameterKind(4, name='VAR_KEYWORD')


class Parameter:
    '''Represents a parameter in a function signature.

    Has the following public attributes:

    * name : str
        The name of the parameter as a string.
    * default : object
        The default value for the parameter if specified.  If the
        parameter has no default value, this attribute is not set.
    * annotation
        The annotation for the parameter if specified.  If the
        parameter has no annotation, this attribute is not set.
    * kind : str
        Describes how argument values are bound to the parameter.
        Possible values: `Parameter.POSITIONAL_ONLY`,
        `Parameter.POSITIONAL_OR_KEYWORD`, `Parameter.VAR_POSITIONAL`,
        `Parameter.KEYWORD_ONLY`, `Parameter.VAR_KEYWORD`.
    '''

    __slots__ = ('_name', '_kind', '_default', '_annotation', '_partial_kwarg')

    POSITIONAL_ONLY         = _POSITIONAL_ONLY
    POSITIONAL_OR_KEYWORD   = _POSITIONAL_OR_KEYWORD
    VAR_POSITIONAL          = _VAR_POSITIONAL
    KEYWORD_ONLY            = _KEYWORD_ONLY
    VAR_KEYWORD             = _VAR_KEYWORD

    empty = _empty

    def __init__(self, name, kind, *, default=_empty, annotation=_empty,
                 _partial_kwarg=False):

        if kind not in (_POSITIONAL_ONLY, _POSITIONAL_OR_KEYWORD,
                        _VAR_POSITIONAL, _KEYWORD_ONLY, _VAR_KEYWORD):
            raise ValueError("invalid value for 'Parameter.kind' attribute")
        self._kind = kind

        if default is not _empty:
            if kind in (_VAR_POSITIONAL, _VAR_KEYWORD):
                msg = '{} parameters cannot have default values'.format(kind)
                raise ValueError(msg)
        self._default = default
        self._annotation = annotation

        if name is None:
            if kind != _POSITIONAL_ONLY:
                raise ValueError("None is not a valid name for a "
                                 "non-positional-only parameter")
            self._name = name
        else:
            name = str(name)
            if kind != _POSITIONAL_ONLY and not name.isidentifier():
                msg = '{!r} is not a valid parameter name'.format(name)
                raise ValueError(msg)
            self._name = name

        self._partial_kwarg = _partial_kwarg

    @property
    def name(self):
        return self._name

    @property
    def default(self):
        return self._default

    @property
    def annotation(self):
        return self._annotation

    @property
    def kind(self):
        return self._kind

    def replace(self, *, name=_void, kind=_void, annotation=_void,
                default=_void, _partial_kwarg=_void):
        '''Creates a customized copy of the Parameter.'''

        if name is _void:
            name = self._name

        if kind is _void:
            kind = self._kind

        if annotation is _void:
            annotation = self._annotation

        if default is _void:
            default = self._default

        if _partial_kwarg is _void:
            _partial_kwarg = self._partial_kwarg

        return type(self)(name, kind, default=default, annotation=annotation,
                          _partial_kwarg=_partial_kwarg)

    def __str__(self):
        kind = self.kind

        formatted = self._name
        if kind == _POSITIONAL_ONLY:
            if formatted is None:
                formatted = ''
            formatted = '<{}>'.format(formatted)

        # Add annotation and default value
        if self._annotation is not _empty:
            formatted = '{}:{}'.format(formatted,
                                       formatannotation(self._annotation))

        if self._default is not _empty:
            formatted = '{}={}'.format(formatted, repr(self._default))

        if kind == _VAR_POSITIONAL:
            formatted = '*' + formatted
        elif kind == _VAR_KEYWORD:
            formatted = '**' + formatted

        return formatted

    def __repr__(self):
        return '<{} at {:#x} {!r}>'.format(self.__class__.__name__,
                                           id(self), self.name)

    def __eq__(self, other):
        return (issubclass(other.__class__, Parameter) and
                self._name == other._name and
                self._kind == other._kind and
                self._default == other._default and
                self._annotation == other._annotation)

    def __ne__(self, other):
        return not self.__eq__(other)


class BoundArguments:
    '''Result of `Signature.bind` call.  Holds the mapping of arguments
    to the function's parameters.

    Has the following public attributes:

    * arguments : OrderedDict
        An ordered mutable mapping of parameters' names to arguments' values.
        Does not contain arguments' default values.
    * signature : Signature
        The Signature object that created this instance.
    * args : tuple
        Tuple of positional arguments values.
    * kwargs : dict
        Dict of keyword arguments values.
    '''

    def __init__(self, signature, arguments):
        self.arguments = arguments
        self._signature = signature

    @property
    def signature(self):
        return self._signature

    @property
    def args(self):
        args = []
        for param_name, param in self._signature.parameters.items():
            if (param.kind in (_VAR_KEYWORD, _KEYWORD_ONLY) or
                                                    param._partial_kwarg):
                # Keyword arguments mapped by 'functools.partial'
                # (Parameter._partial_kwarg is True) are mapped
                # in 'BoundArguments.kwargs', along with VAR_KEYWORD &
                # KEYWORD_ONLY
                break

            try:
                arg = self.arguments[param_name]
            except KeyError:
                # We're done here. Other arguments
                # will be mapped in 'BoundArguments.kwargs'
                break
            else:
                if param.kind == _VAR_POSITIONAL:
                    # *args
                    args.extend(arg)
                else:
                    # plain argument
                    args.append(arg)

        return tuple(args)

    @property
    def kwargs(self):
        kwargs = {}
        kwargs_started = False
        for param_name, param in self._signature.parameters.items():
            if not kwargs_started:
                if (param.kind in (_VAR_KEYWORD, _KEYWORD_ONLY) or
                                                param._partial_kwarg):
                    kwargs_started = True
                else:
                    if param_name not in self.arguments:
                        kwargs_started = True
                        continue

            if not kwargs_started:
                continue

            try:
                arg = self.arguments[param_name]
            except KeyError:
                pass
            else:
                if param.kind == _VAR_KEYWORD:
                    # **kwargs
                    kwargs.update(arg)
                else:
                    # plain keyword argument
                    kwargs[param_name] = arg

        return kwargs

    def __eq__(self, other):
        return (issubclass(other.__class__, BoundArguments) and
                self.signature == other.signature and
                self.arguments == other.arguments)

    def __ne__(self, other):
        return not self.__eq__(other)


class Signature:
    '''A Signature object represents the overall signature of a function.
    It stores a Parameter object for each parameter accepted by the
    function, as well as information specific to the function itself.

    A Signature object has the following public attributes and methods:

    * parameters : OrderedDict
        An ordered mapping of parameters' names to the corresponding
        Parameter objects (keyword-only arguments are in the same order
        as listed in `code.co_varnames`).
    * return_annotation : object
        The annotation for the return type of the function if specified.
        If the function has no annotation for its return type, this
        attribute is not set.
    * bind(*args, **kwargs) -> BoundArguments
        Creates a mapping from positional and keyword arguments to
        parameters.
    * bind_partial(*args, **kwargs) -> BoundArguments
        Creates a partial mapping from positional and keyword arguments
        to parameters (simulating 'functools.partial' behavior.)
    '''

    __slots__ = ('_return_annotation', '_parameters')

    _parameter_cls = Parameter
    _bound_arguments_cls = BoundArguments

    empty = _empty

    def __init__(self, parameters=None, *, return_annotation=_empty,
                 __validate_parameters__=True):
        '''Constructs Signature from the given list of Parameter
        objects and 'return_annotation'.  All arguments are optional.
        '''

        if parameters is None:
            params = OrderedDict()
        else:
            if __validate_parameters__:
                params = OrderedDict()
                top_kind = _POSITIONAL_ONLY

                for idx, param in enumerate(parameters):
                    kind = param.kind
                    if kind < top_kind:
                        msg = 'wrong parameter order: {} before {}'
                        msg = msg.format(top_kind, param.kind)
                        raise ValueError(msg)
                    else:
                        top_kind = kind

                    name = param.name
                    if name is None:
                        name = str(idx)
                        param = param.replace(name=name)

                    if name in params:
                        msg = 'duplicate parameter name: {!r}'.format(name)
                        raise ValueError(msg)
                    params[name] = param
            else:
                params = OrderedDict(((param.name, param)
                                                for param in parameters))

        self._parameters = types.MappingProxyType(params)
        self._return_annotation = return_annotation

    @classmethod
    def from_function(cls, func):
        '''Constructs Signature for the given python function'''

        if not isinstance(func, types.FunctionType):
            raise TypeError('{!r} is not a Python function'.format(func))

        Parameter = cls._parameter_cls

        # Parameter information.
        func_code = func.__code__
        pos_count = func_code.co_argcount
        arg_names = func_code.co_varnames
        positional = tuple(arg_names[:pos_count])
        keyword_only_count = func_code.co_kwonlyargcount
        keyword_only = arg_names[pos_count:(pos_count + keyword_only_count)]
        annotations = func.__annotations__
        defaults = func.__defaults__
        kwdefaults = func.__kwdefaults__

        if defaults:
            pos_default_count = len(defaults)
        else:
            pos_default_count = 0

        parameters = []

        # Non-keyword-only parameters w/o defaults.
        non_default_count = pos_count - pos_default_count
        for name in positional[:non_default_count]:
            annotation = annotations.get(name, _empty)
            parameters.append(Parameter(name, annotation=annotation,
                                        kind=_POSITIONAL_OR_KEYWORD))

        # ... w/ defaults.
        for offset, name in enumerate(positional[non_default_count:]):
            annotation = annotations.get(name, _empty)
            parameters.append(Parameter(name, annotation=annotation,
                                        kind=_POSITIONAL_OR_KEYWORD,
                                        default=defaults[offset]))

        # *args
        if func_code.co_flags & 0x04:
            name = arg_names[pos_count + keyword_only_count]
            annotation = annotations.get(name, _empty)
            parameters.append(Parameter(name, annotation=annotation,
                                        kind=_VAR_POSITIONAL))

        # Keyword-only parameters.
        for name in keyword_only:
            default = _empty
            if kwdefaults is not None:
                default = kwdefaults.get(name, _empty)

            annotation = annotations.get(name, _empty)
            parameters.append(Parameter(name, annotation=annotation,
                                        kind=_KEYWORD_ONLY,
                                        default=default))
        # **kwargs
        if func_code.co_flags & 0x08:
            index = pos_count + keyword_only_count
            if func_code.co_flags & 0x04:
                index += 1

            name = arg_names[index]
            annotation = annotations.get(name, _empty)
            parameters.append(Parameter(name, annotation=annotation,
                                        kind=_VAR_KEYWORD))

        return cls(parameters,
                   return_annotation=annotations.get('return', _empty),
                   __validate_parameters__=False)

    @property
    def parameters(self):
        return self._parameters

    @property
    def return_annotation(self):
        return self._return_annotation

    def replace(self, *, parameters=_void, return_annotation=_void):
        '''Creates a customized copy of the Signature.
        Pass 'parameters' and/or 'return_annotation' arguments
        to override them in the new copy.
        '''

        if parameters is _void:
            parameters = self.parameters.values()

        if return_annotation is _void:
            return_annotation = self._return_annotation

        return type(self)(parameters,
                          return_annotation=return_annotation)

    def __eq__(self, other):
        if (not issubclass(type(other), Signature) or
                    self.return_annotation != other.return_annotation or
                    len(self.parameters) != len(other.parameters)):
            return False

        other_positions = {param: idx
                           for idx, param in enumerate(other.parameters.keys())}

        for idx, (param_name, param) in enumerate(self.parameters.items()):
            if param.kind == _KEYWORD_ONLY:
                try:
                    other_param = other.parameters[param_name]
                except KeyError:
                    return False
                else:
                    if param != other_param:
                        return False
            else:
                try:
                    other_idx = other_positions[param_name]
                except KeyError:
                    return False
                else:
                    if (idx != other_idx or
                                    param != other.parameters[param_name]):
                        return False

        return True

    def __ne__(self, other):
        return not self.__eq__(other)

    def _bind(self, args, kwargs, *, partial=False):
        '''Private method.  Don't use directly.'''

        arguments = OrderedDict()

        parameters = iter(self.parameters.values())
        parameters_ex = ()
        arg_vals = iter(args)

        if partial:
            # Support for binding arguments to 'functools.partial' objects.
            # See 'functools.partial' case in 'signature()' implementation
            # for details.
            for param_name, param in self.parameters.items():
                if (param._partial_kwarg and param_name not in kwargs):
                    # Simulating 'functools.partial' behavior
                    kwargs[param_name] = param.default

        while True:
            # Let's iterate through the positional arguments and corresponding
            # parameters
            try:
                arg_val = next(arg_vals)
            except StopIteration:
                # No more positional arguments
                try:
                    param = next(parameters)
                except StopIteration:
                    # No more parameters. That's it. Just need to check that
                    # we have no `kwargs` after this while loop
                    break
                else:
                    if param.kind == _VAR_POSITIONAL:
                        # That's OK, just empty *args.  Let's start parsing
                        # kwargs
                        break
                    elif param.name in kwargs:
                        if param.kind == _POSITIONAL_ONLY:
                            msg = '{arg!r} parameter is positional only, ' \
                                  'but was passed as a keyword'
                            msg = msg.format(arg=param.name)
                            raise TypeError(msg) from None
                        parameters_ex = (param,)
                        break
                    elif (param.kind == _VAR_KEYWORD or
                                                param.default is not _empty):
                        # That's fine too - we have a default value for this
                        # parameter.  So, lets start parsing `kwargs`, starting
                        # with the current parameter
                        parameters_ex = (param,)
                        break
                    else:
                        if partial:
                            parameters_ex = (param,)
                            break
                        else:
                            msg = '{arg!r} parameter lacking default value'
                            msg = msg.format(arg=param.name)
                            raise TypeError(msg) from None
            else:
                # We have a positional argument to process
                try:
                    param = next(parameters)
                except StopIteration:
                    raise TypeError('too many positional arguments') from None
                else:
                    if param.kind in (_VAR_KEYWORD, _KEYWORD_ONLY):
                        # Looks like we have no parameter for this positional
                        # argument
                        raise TypeError('too many positional arguments')

                    if param.kind == _VAR_POSITIONAL:
                        # We have an '*args'-like argument, let's fill it with
                        # all positional arguments we have left and move on to
                        # the next phase
                        values = [arg_val]
                        values.extend(arg_vals)
                        arguments[param.name] = tuple(values)
                        break

                    if param.name in kwargs:
                        raise TypeError('multiple values for argument '
                                        '{arg!r}'.format(arg=param.name))

                    arguments[param.name] = arg_val

        # Now, we iterate through the remaining parameters to process
        # keyword arguments
        kwargs_param = None
        for param in itertools.chain(parameters_ex, parameters):
            if param.kind == _POSITIONAL_ONLY:
                # This should never happen in case of a properly built
                # Signature object (but let's have this check here
                # to ensure correct behaviour just in case)
                raise TypeError('{arg!r} parameter is positional only, '
                                'but was passed as a keyword'. \
                                format(arg=param.name))

            if param.kind == _VAR_KEYWORD:
                # Memorize that we have a '**kwargs'-like parameter
                kwargs_param = param
                continue

            param_name = param.name
            try:
                arg_val = kwargs.pop(param_name)
            except KeyError:
                # We have no value for this parameter.  It's fine though,
                # if it has a default value, or it is an '*args'-like
                # parameter, left alone by the processing of positional
                # arguments.
                if (not partial and param.kind != _VAR_POSITIONAL and
                                                    param.default is _empty):
                    raise TypeError('{arg!r} parameter lacking default value'. \
                                    format(arg=param_name)) from None

            else:
                arguments[param_name] = arg_val

        if kwargs:
            if kwargs_param is not None:
                # Process our '**kwargs'-like parameter
                arguments[kwargs_param.name] = kwargs
            else:
                raise TypeError('too many keyword arguments')

        return self._bound_arguments_cls(self, arguments)

    def bind(__bind_self, *args, **kwargs):
        '''Get a BoundArguments object, that maps the passed `args`
        and `kwargs` to the function's signature.  Raises `TypeError`
        if the passed arguments can not be bound.
        '''
        return __bind_self._bind(args, kwargs)

    def bind_partial(__bind_self, *args, **kwargs):
        '''Get a BoundArguments object, that partially maps the
        passed `args` and `kwargs` to the function's signature.
        Raises `TypeError` if the passed arguments can not be bound.
        '''
        return __bind_self._bind(args, kwargs, partial=True)

    def __str__(self):
        result = []
        render_kw_only_separator = True
        for idx, param in enumerate(self.parameters.values()):
            formatted = str(param)

            kind = param.kind
            if kind == _VAR_POSITIONAL:
                # OK, we have an '*args'-like parameter, so we won't need
                # a '*' to separate keyword-only arguments
                render_kw_only_separator = False
            elif kind == _KEYWORD_ONLY and render_kw_only_separator:
                # We have a keyword-only parameter to render and we haven't
                # rendered an '*args'-like parameter before, so add a '*'
                # separator to the parameters list ("foo(arg1, *, arg2)" case)
                result.append('*')
                # This condition should be only triggered once, so
                # reset the flag
                render_kw_only_separator = False

            result.append(formatted)

        rendered = '({})'.format(', '.join(result))

        if self.return_annotation is not _empty:
            anno = formatannotation(self.return_annotation)
            rendered += ' -> {}'.format(anno)

        return rendered