Lib/typing.py

import abc
from abc import abstractmethod, abstractproperty
import collections
import contextlib
import functools
import re as stdlib_re  # Avoid confusion with the re we export.
import sys
import types
try:
    import collections.abc as collections_abc
except ImportError:
    import collections as collections_abc  # Fallback for PY3.2.
try:
    from types import WrapperDescriptorType, MethodWrapperType, MethodDescriptorType
except ImportError:
    WrapperDescriptorType = type(object.__init__)
    MethodWrapperType = type(object().__str__)
    MethodDescriptorType = type(str.join)


# Please keep __all__ alphabetized within each category.
__all__ = [
    # Super-special typing primitives.
    'Any',
    'Callable',
    'ClassVar',
    'Generic',
    'Optional',
    'Tuple',
    'Type',
    'TypeVar',
    'Union',

    # ABCs (from collections.abc).
    'AbstractSet',  # collections.abc.Set.
    'GenericMeta',  # subclass of abc.ABCMeta and a metaclass
                    # for 'Generic' and ABCs below.
    'ByteString',
    'Container',
    'Hashable',
    'ItemsView',
    'Iterable',
    'Iterator',
    'KeysView',
    'Mapping',
    'MappingView',
    'MutableMapping',
    'MutableSequence',
    'MutableSet',
    'Sequence',
    'Sized',
    'ValuesView',
    # The following are added depending on presence
    # of their non-generic counterparts in stdlib:
    # Awaitable,
    # AsyncIterator,
    # AsyncIterable,
    # Coroutine,
    # Collection,
    # ContextManager,
    # AsyncGenerator,

    # Structural checks, a.k.a. protocols.
    'Reversible',
    'SupportsAbs',
    'SupportsBytes',
    'SupportsComplex',
    'SupportsFloat',
    'SupportsInt',
    'SupportsRound',

    # Concrete collection types.
    'Counter',
    'Deque',
    'Dict',
    'DefaultDict',
    'List',
    'Set',
    'FrozenSet',
    'NamedTuple',  # Not really a type.
    'Generator',

    # One-off things.
    'AnyStr',
    'cast',
    'get_type_hints',
    'NewType',
    'no_type_check',
    'no_type_check_decorator',
    'overload',
    'Text',
    'TYPE_CHECKING',
]

# The pseudo-submodules 're' and 'io' are part of the public
# namespace, but excluded from __all__ because they might stomp on
# legitimate imports of those modules.


def _qualname(x):
    if sys.version_info[:2] >= (3, 3):
        return x.__qualname__
    else:
        # Fall back to just name.
        return x.__name__


def _trim_name(nm):
    whitelist = ('_TypeAlias', '_ForwardRef', '_TypingBase', '_FinalTypingBase')
    if nm.startswith('_') and nm not in whitelist:
        nm = nm[1:]
    return nm


class TypingMeta(type):
    """Metaclass for most types defined in typing module
    (not a part of public API).

    This overrides __new__() to require an extra keyword parameter
    '_root', which serves as a guard against naive subclassing of the
    typing classes.  Any legitimate class defined using a metaclass
    derived from TypingMeta must pass _root=True.

    This also defines a dummy constructor (all the work for most typing
    constructs is done in __new__) and a nicer repr().
    """

    _is_protocol = False

    def __new__(cls, name, bases, namespace, *, _root=False):
        if not _root:
            raise TypeError("Cannot subclass %s" %
                            (', '.join(map(_type_repr, bases)) or '()'))
        return super().__new__(cls, name, bases, namespace)

    def __init__(self, *args, **kwds):
        pass

    def _eval_type(self, globalns, localns):
        """Override this in subclasses to interpret forward references.

        For example, List['C'] is internally stored as
        List[_ForwardRef('C')], which should evaluate to List[C],
        where C is an object found in globalns or localns (searching
        localns first, of course).
        """
        return self

    def _get_type_vars(self, tvars):
        pass

    def __repr__(self):
        qname = _trim_name(_qualname(self))
        return '%s.%s' % (self.__module__, qname)


class _TypingBase(metaclass=TypingMeta, _root=True):
    """Internal indicator of special typing constructs."""

    __slots__ = ('__weakref__',)

    def __init__(self, *args, **kwds):
        pass

    def __new__(cls, *args, **kwds):
        """Constructor.

        This only exists to give a better error message in case
        someone tries to subclass a special typing object (not a good idea).
        """
        if (len(args) == 3 and
                isinstance(args[0], str) and
                isinstance(args[1], tuple)):
            # Close enough.
            raise TypeError("Cannot subclass %r" % cls)
        return super().__new__(cls)

    # Things that are not classes also need these.
    def _eval_type(self, globalns, localns):
        return self

    def _get_type_vars(self, tvars):
        pass

    def __repr__(self):
        cls = type(self)
        qname = _trim_name(_qualname(cls))
        return '%s.%s' % (cls.__module__, qname)

    def __call__(self, *args, **kwds):
        raise TypeError("Cannot instantiate %r" % type(self))


class _FinalTypingBase(_TypingBase, _root=True):
    """Internal mix-in class to prevent instantiation.

    Prevents instantiation unless _root=True is given in class call.
    It is used to create pseudo-singleton instances Any, Union, Optional, etc.
    """

    __slots__ = ()

    def __new__(cls, *args, _root=False, **kwds):
        self = super().__new__(cls, *args, **kwds)
        if _root is True:
            return self
        raise TypeError("Cannot instantiate %r" % cls)

    def __reduce__(self):
        return _trim_name(type(self).__name__)


class _ForwardRef(_TypingBase, _root=True):
    """Internal wrapper to hold a forward reference."""

    __slots__ = ('__forward_arg__', '__forward_code__',
                 '__forward_evaluated__', '__forward_value__')

    def __init__(self, arg):
        super().__init__(arg)
        if not isinstance(arg, str):
            raise TypeError('Forward reference must be a string -- got %r' % (arg,))
        try:
            code = compile(arg, '<string>', 'eval')
        except SyntaxError:
            raise SyntaxError('Forward reference must be an expression -- got %r' %
                              (arg,))
        self.__forward_arg__ = arg
        self.__forward_code__ = code
        self.__forward_evaluated__ = False
        self.__forward_value__ = None

    def _eval_type(self, globalns, localns):
        if not self.__forward_evaluated__ or localns is not globalns:
            if globalns is None and localns is None:
                globalns = localns = {}
            elif globalns is None:
                globalns = localns
            elif localns is None:
                localns = globalns
            self.__forward_value__ = _type_check(
                eval(self.__forward_code__, globalns, localns),
                "Forward references must evaluate to types.")
            self.__forward_evaluated__ = True
        return self.__forward_value__

    def __eq__(self, other):
        if not isinstance(other, _ForwardRef):
            return NotImplemented
        return (self.__forward_arg__ == other.__forward_arg__ and
                self.__forward_value__ == other.__forward_value__)

    def __hash__(self):
        return hash((self.__forward_arg__, self.__forward_value__))

    def __instancecheck__(self, obj):
        raise TypeError("Forward references cannot be used with isinstance().")

    def __subclasscheck__(self, cls):
        raise TypeError("Forward references cannot be used with issubclass().")

    def __repr__(self):
        return '_ForwardRef(%r)' % (self.__forward_arg__,)


class _TypeAlias(_TypingBase, _root=True):
    """Internal helper class for defining generic variants of concrete types.

    Note that this is not a type; let's call it a pseudo-type.  It cannot
    be used in instance and subclass checks in parameterized form, i.e.
    ``isinstance(42, Match[str])`` raises ``TypeError`` instead of returning
    ``False``.
    """

    __slots__ = ('name', 'type_var', 'impl_type', 'type_checker')

    def __init__(self, name, type_var, impl_type, type_checker):
        """Initializer.

        Args:
            name: The name, e.g. 'Pattern'.
            type_var: The type parameter, e.g. AnyStr, or the
                specific type, e.g. str.
            impl_type: The implementation type.
            type_checker: Function that takes an impl_type instance.
                and returns a value that should be a type_var instance.
        """
        assert isinstance(name, str), repr(name)
        assert isinstance(impl_type, type), repr(impl_type)
        assert not isinstance(impl_type, TypingMeta), repr(impl_type)
        assert isinstance(type_var, (type, _TypingBase)), repr(type_var)
        self.name = name
        self.type_var = type_var
        self.impl_type = impl_type
        self.type_checker = type_checker

    def __repr__(self):
        return "%s[%s]" % (self.name, _type_repr(self.type_var))

    def __getitem__(self, parameter):
        if not isinstance(self.type_var, TypeVar):
            raise TypeError("%s cannot be further parameterized." % self)
        if self.type_var.__constraints__ and isinstance(parameter, type):
            if not issubclass(parameter, self.type_var.__constraints__):
                raise TypeError("%s is not a valid substitution for %s." %
                                (parameter, self.type_var))
        if isinstance(parameter, TypeVar) and parameter is not self.type_var:
            raise TypeError("%s cannot be re-parameterized." % self)
        return self.__class__(self.name, parameter,
                              self.impl_type, self.type_checker)

    def __eq__(self, other):
        if not isinstance(other, _TypeAlias):
            return NotImplemented
        return self.name == other.name and self.type_var == other.type_var

    def __hash__(self):
        return hash((self.name, self.type_var))

    def __instancecheck__(self, obj):
        if not isinstance(self.type_var, TypeVar):
            raise TypeError("Parameterized type aliases cannot be used "
                            "with isinstance().")
        return isinstance(obj, self.impl_type)

    def __subclasscheck__(self, cls):
        if not isinstance(self.type_var, TypeVar):
            raise TypeError("Parameterized type aliases cannot be used "
                            "with issubclass().")
        return issubclass(cls, self.impl_type)


def _get_type_vars(types, tvars):
    for t in types:
        if isinstance(t, TypingMeta) or isinstance(t, _TypingBase):
            t._get_type_vars(tvars)


def _type_vars(types):
    tvars = []
    _get_type_vars(types, tvars)
    return tuple(tvars)


def _eval_type(t, globalns, localns):
    if isinstance(t, TypingMeta) or isinstance(t, _TypingBase):
        return t._eval_type(globalns, localns)
    return t


def _type_check(arg, msg):
    """Check that the argument is a type, and return it (internal helper).

    As a special case, accept None and return type(None) instead.
    Also, _TypeAlias instances (e.g. Match, Pattern) are acceptable.

    The msg argument is a human-readable error message, e.g.

        "Union[arg, ...]: arg should be a type."

    We append the repr() of the actual value (truncated to 100 chars).
    """
    if arg is None:
        return type(None)
    if isinstance(arg, str):
        arg = _ForwardRef(arg)
    if (
        isinstance(arg, _TypingBase) and type(arg).__name__ == '_ClassVar' or
        not isinstance(arg, (type, _TypingBase)) and not callable(arg)
    ):
        raise TypeError(msg + " Got %.100r." % (arg,))
    # Bare Union etc. are not valid as type arguments
    if (
        type(arg).__name__ in ('_Union', '_Optional') and
        not getattr(arg, '__origin__', None) or
        isinstance(arg, TypingMeta) and _gorg(arg) in (Generic, _Protocol)
    ):
        raise TypeError("Plain %s is not valid as type argument" % arg)
    return arg


def _type_repr(obj):
    """Return the repr() of an object, special-casing types (internal helper).

    If obj is a type, we return a shorter version than the default
    type.__repr__, based on the module and qualified name, which is
    typically enough to uniquely identify a type.  For everything
    else, we fall back on repr(obj).
    """
    if isinstance(obj, type) and not isinstance(obj, TypingMeta):
        if obj.__module__ == 'builtins':
            return _qualname(obj)
        return '%s.%s' % (obj.__module__, _qualname(obj))
    if obj is ...:
        return('...')
    if isinstance(obj, types.FunctionType):
        return obj.__name__
    return repr(obj)


class _Any(_FinalTypingBase, _root=True):
    """Special type indicating an unconstrained type.

    - Any is compatible with every type.
    - Any assumed to have all methods.
    - All values assumed to be instances of Any.

    Note that all the above statements are true from the point of view of
    static type checkers. At runtime, Any should not be used with instance
    or class checks.
    """

    __slots__ = ()

    def __instancecheck__(self, obj):
        raise TypeError("Any cannot be used with isinstance().")

    def __subclasscheck__(self, cls):
        raise TypeError("Any cannot be used with issubclass().")


Any = _Any(_root=True)


class _NoReturn(_FinalTypingBase, _root=True):
    """Special type indicating functions that never return.
    Example::

      from typing import NoReturn

      def stop() -> NoReturn:
          raise Exception('no way')

    This type is invalid in other positions, e.g., ``List[NoReturn]``
    will fail in static type checkers.
    """

    __slots__ = ()

    def __instancecheck__(self, obj):
        raise TypeError("NoReturn cannot be used with isinstance().")

    def __subclasscheck__(self, cls):
        raise TypeError("NoReturn cannot be used with issubclass().")


NoReturn = _NoReturn(_root=True)


class TypeVar(_TypingBase, _root=True):
    """Type variable.

    Usage::

      T = TypeVar('T')  # Can be anything
      A = TypeVar('A', str, bytes)  # Must be str or bytes

    Type variables exist primarily for the benefit of static type
    checkers.  They serve as the parameters for generic types as well
    as for generic function definitions.  See class Generic for more
    information on generic types.  Generic functions work as follows:

      def repeat(x: T, n: int) -> List[T]:
          '''Return a list containing n references to x.'''
          return [x]*n

      def longest(x: A, y: A) -> A:
          '''Return the longest of two strings.'''
          return x if len(x) >= len(y) else y

    The latter example's signature is essentially the overloading
    of (str, str) -> str and (bytes, bytes) -> bytes.  Also note
    that if the arguments are instances of some subclass of str,
    the return type is still plain str.

    At runtime, isinstance(x, T) and issubclass(C, T) will raise TypeError.

    Type variables defined with covariant=True or contravariant=True
    can be used do declare covariant or contravariant generic types.
    See PEP 484 for more details. By default generic types are invariant
    in all type variables.

    Type variables can be introspected. e.g.:

      T.__name__ == 'T'
      T.__constraints__ == ()
      T.__covariant__ == False
      T.__contravariant__ = False
      A.__constraints__ == (str, bytes)
    """

    __slots__ = ('__name__', '__bound__', '__constraints__',
                 '__covariant__', '__contravariant__')

    def __init__(self, name, *constraints, bound=None,
                 covariant=False, contravariant=False):
        super().__init__(name, *constraints, bound=bound,
                         covariant=covariant, contravariant=contravariant)
        self.__name__ = name
        if covariant and contravariant:
            raise ValueError("Bivariant types are not supported.")
        self.__covariant__ = bool(covariant)
        self.__contravariant__ = bool(contravariant)
        if constraints and bound is not None:
            raise TypeError("Constraints cannot be combined with bound=...")
        if constraints and len(constraints) == 1:
            raise TypeError("A single constraint is not allowed")
        msg = "TypeVar(name, constraint, ...): constraints must be types."
        self.__constraints__ = tuple(_type_check(t, msg) for t in constraints)
        if bound:
            self.__bound__ = _type_check(bound, "Bound must be a type.")
        else:
            self.__bound__ = None

    def _get_type_vars(self, tvars):
        if self not in tvars:
            tvars.append(self)

    def __repr__(self):
        if self.__covariant__:
            prefix = '+'
        elif self.__contravariant__:
            prefix = '-'
        else:
            prefix = '~'
        return prefix + self.__name__

    def __instancecheck__(self, instance):
        raise TypeError("Type variables cannot be used with isinstance().")

    def __subclasscheck__(self, cls):
        raise TypeError("Type variables cannot be used with issubclass().")


# Some unconstrained type variables.  These are used by the container types.
# (These are not for export.)
T = TypeVar('T')  # Any type.
KT = TypeVar('KT')  # Key type.
VT = TypeVar('VT')  # Value type.
T_co = TypeVar('T_co', covariant=True)  # Any type covariant containers.
V_co = TypeVar('V_co', covariant=True)  # Any type covariant containers.
VT_co = TypeVar('VT_co', covariant=True)  # Value type covariant containers.
T_contra = TypeVar('T_contra', contravariant=True)  # Ditto contravariant.

# A useful type variable with constraints.  This represents string types.
# (This one *is* for export!)
AnyStr = TypeVar('AnyStr', bytes, str)


def _replace_arg(arg, tvars, args):
    """An internal helper function: replace arg if it is a type variable
    found in tvars with corresponding substitution from args or
    with corresponding substitution sub-tree if arg is a generic type.
    """

    if tvars is None:
        tvars = []
    if hasattr(arg, '_subs_tree') and isinstance(arg, (GenericMeta, _TypingBase)):
        return arg._subs_tree(tvars, args)
    if isinstance(arg, TypeVar):
        for i, tvar in enumerate(tvars):
            if arg == tvar:
                return args[i]
    return arg


# Special typing constructs Union, Optional, Generic, Callable and Tuple
# use three special attributes for internal bookkeeping of generic types:
# * __parameters__ is a tuple of unique free type parameters of a generic
#   type, for example, Dict[T, T].__parameters__ == (T,);
# * __origin__ keeps a reference to a type that was subscripted,
#   e.g., Union[T, int].__origin__ == Union;
# * __args__ is a tuple of all arguments used in subscripting,
#   e.g., Dict[T, int].__args__ == (T, int).


def _subs_tree(cls, tvars=None, args=None):
    """An internal helper function: calculate substitution tree
    for generic cls after replacing its type parameters with
    substitutions in tvars -> args (if any).
    Repeat the same following __origin__'s.

    Return a list of arguments with all possible substitutions
    performed. Arguments that are generic classes themselves are represented
    as tuples (so that no new classes are created by this function).
    For example: _subs_tree(List[Tuple[int, T]][str]) == [(Tuple, int, str)]
    """

    if cls.__origin__ is None:
        return cls
    # Make of chain of origins (i.e. cls -> cls.__origin__)
    current = cls.__origin__
    orig_chain = []
    while current.__origin__ is not None:
        orig_chain.append(current)
        current = current.__origin__
    # Replace type variables in __args__ if asked ...
    tree_args = []
    for arg in cls.__args__:
        tree_args.append(_replace_arg(arg, tvars, args))
    # ... then continue replacing down the origin chain.
    for ocls in orig_chain:
        new_tree_args = []
        for arg in ocls.__args__:
            new_tree_args.append(_replace_arg(arg, ocls.__parameters__, tree_args))
        tree_args = new_tree_args
    return tree_args


def _remove_dups_flatten(parameters):
    """An internal helper for Union creation and substitution: flatten Union's
    among parameters, then remove duplicates and strict subclasses.
    """

    # Flatten out Union[Union[...], ...].
    params = []
    for p in parameters:
        if isinstance(p, _Union) and p.__origin__ is Union:
            params.extend(p.__args__)
        elif isinstance(p, tuple) and len(p) > 0 and p[0] is Union:
            params.extend(p[1:])
        else:
            params.append(p)
    # Weed out strict duplicates, preserving the first of each occurrence.
    all_params = set(params)
    if len(all_params) < len(params):
        new_params = []
        for t in params:
            if t in all_params:
                new_params.append(t)
                all_params.remove(t)
        params = new_params
        assert not all_params, all_params
    # Weed out subclasses.
    # E.g. Union[int, Employee, Manager] == Union[int, Employee].
    # If object is present it will be sole survivor among proper classes.
    # Never discard type variables.
    # (In particular, Union[str, AnyStr] != AnyStr.)
    all_params = set(params)
    for t1 in params:
        if not isinstance(t1, type):
            continue
        if any(isinstance(t2, type) and issubclass(t1, t2)
               for t2 in all_params - {t1}
               if not (isinstance(t2, GenericMeta) and
                       t2.__origin__ is not None)):
            all_params.remove(t1)
    return tuple(t for t in params if t in all_params)


def _check_generic(cls, parameters):
    # Check correct count for parameters of a generic cls (internal helper).
    if not cls.__parameters__:
        raise TypeError("%s is not a generic class" % repr(cls))
    alen = len(parameters)
    elen = len(cls.__parameters__)
    if alen != elen:
        raise TypeError("Too %s parameters for %s; actual %s, expected %s" %
                        ("many" if alen > elen else "few", repr(cls), alen, elen))


_cleanups = []


def _tp_cache(func):
    """Internal wrapper caching __getitem__ of generic types with a fallback to
    original function for non-hashable arguments.
    """

    cached = functools.lru_cache()(func)
    _cleanups.append(cached.cache_clear)

    @functools.wraps(func)
    def inner(*args, **kwds):
        try:
            return cached(*args, **kwds)
        except TypeError:
            pass  # All real errors (not unhashable args) are raised below.
        return func(*args, **kwds)
    return inner


class _Union(_FinalTypingBase, _root=True):
    """Union type; Union[X, Y] means either X or Y.

    To define a union, use e.g. Union[int, str].  Details:

    - The arguments must be types and there must be at least one.

    - None as an argument is a special case and is replaced by
      type(None).

    - Unions of unions are flattened, e.g.::

        Union[Union[int, str], float] == Union[int, str, float]

    - Unions of a single argument vanish, e.g.::

        Union[int] == int  # The constructor actually returns int

    - Redundant arguments are skipped, e.g.::

        Union[int, str, int] == Union[int, str]

    - When comparing unions, the argument order is ignored, e.g.::

        Union[int, str] == Union[str, int]

    - When two arguments have a subclass relationship, the least
      derived argument is kept, e.g.::

        class Employee: pass
        class Manager(Employee): pass
        Union[int, Employee, Manager] == Union[int, Employee]
        Union[Manager, int, Employee] == Union[int, Employee]
        Union[Employee, Manager] == Employee

    - Similar for object::

        Union[int, object] == object

    - You cannot subclass or instantiate a union.

    - You can use Optional[X] as a shorthand for Union[X, None].
    """

    __slots__ = ('__parameters__', '__args__', '__origin__', '__tree_hash__')

    def __new__(cls, parameters=None, origin=None, *args, _root=False):
        self = super().__new__(cls, parameters, origin, *args, _root=_root)
        if origin is None:
            self.__parameters__ = None
            self.__args__ = None
            self.__origin__ = None
            self.__tree_hash__ = hash(frozenset(('Union',)))
            return self
        if not isinstance(parameters, tuple):
            raise TypeError("Expected parameters=<tuple>")
        if origin is Union:
            parameters = _remove_dups_flatten(parameters)
            # It's not a union if there's only one type left.
            if len(parameters) == 1:
                return parameters[0]
        self.__parameters__ = _type_vars(parameters)
        self.__args__ = parameters
        self.__origin__ = origin
        # Pre-calculate the __hash__ on instantiation.
        # This improves speed for complex substitutions.
        subs_tree = self._subs_tree()
        if isinstance(subs_tree, tuple):
            self.__tree_hash__ = hash(frozenset(subs_tree))
        else:
            self.__tree_hash__ = hash(subs_tree)
        return self

    def _eval_type(self, globalns, localns):
        if self.__args__ is None:
            return self
        ev_args = tuple(_eval_type(t, globalns, localns) for t in self.__args__)
        ev_origin = _eval_type(self.__origin__, globalns, localns)
        if ev_args == self.__args__ and ev_origin == self.__origin__:
            # Everything is already evaluated.
            return self
        return self.__class__(ev_args, ev_origin, _root=True)

    def _get_type_vars(self, tvars):
        if self.__origin__ and self.__parameters__:
            _get_type_vars(self.__parameters__, tvars)

    def __repr__(self):
        if self.__origin__ is None:
            return super().__repr__()
        tree = self._subs_tree()
        if not isinstance(tree, tuple):
            return repr(tree)
        return tree[0]._tree_repr(tree)

    def _tree_repr(self, tree):
        arg_list = []
        for arg in tree[1:]:
            if not isinstance(arg, tuple):
                arg_list.append(_type_repr(arg))
            else:
                arg_list.append(arg[0]._tree_repr(arg))
        return super().__repr__() + '[%s]' % ', '.join(arg_list)

    @_tp_cache
    def __getitem__(self, parameters):
        if parameters == ():
            raise TypeError("Cannot take a Union of no types.")
        if not isinstance(parameters, tuple):
            parameters = (parameters,)
        if self.__origin__ is None:
            msg = "Union[arg, ...]: each arg must be a type."
        else:
            msg = "Parameters to generic types must be types."
        parameters = tuple(_type_check(p, msg) for p in parameters)
        if self is not Union:
            _check_generic(self, parameters)
        return self.__class__(parameters, origin=self, _root=True)

    def _subs_tree(self, tvars=None, args=None):
        if self is Union:
            return Union  # Nothing to substitute
        tree_args = _subs_tree(self, tvars, args)
        tree_args = _remove_dups_flatten(tree_args)
        if len(tree_args) == 1:
            return tree_args[0]  # Union of a single type is that type
        return (Union,) + tree_args

    def __eq__(self, other):
        if isinstance(other, _Union):
            return self.__tree_hash__ == other.__tree_hash__
        elif self is not Union:
            return self._subs_tree() == other
        else:
            return self is other

    def __hash__(self):
        return self.__tree_hash__

    def __instancecheck__(self, obj):
        raise TypeError("Unions cannot be used with isinstance().")

    def __subclasscheck__(self, cls):
        raise TypeError("Unions cannot be used with issubclass().")


Union = _Union(_root=True)


class _Optional(_FinalTypingBase, _root=True):
    """Optional type.

    Optional[X] is equivalent to Union[X, None].
    """

    __slots__ = ()

    @_tp_cache
    def __getitem__(self, arg):
        arg = _type_check(arg, "Optional[t] requires a single type.")
        return Union[arg, type(None)]


Optional = _Optional(_root=True)


def _gorg(a):
    """Return the farthest origin of a generic class (internal helper)."""
    assert isinstance(a, GenericMeta)
    while a.__origin__ is not None:
        a = a.__origin__
    return a


def _geqv(a, b):
    """Return whether two generic classes are equivalent (internal helper).

    The intention is to consider generic class X and any of its
    parameterized forms (X[T], X[int], etc.) as equivalent.

    However, X is not equivalent to a subclass of X.

    The relation is reflexive, symmetric and transitive.
    """
    assert isinstance(a, GenericMeta) and isinstance(b, GenericMeta)
    # Reduce each to its origin.
    return _gorg(a) is _gorg(b)


def _next_in_mro(cls):
    """Helper for Generic.__new__.

    Returns the class after the last occurrence of Generic or
    Generic[...] in cls.__mro__.
    """
    next_in_mro = object
    # Look for the last occurrence of Generic or Generic[...].
    for i, c in enumerate(cls.__mro__[:-1]):
        if isinstance(c, GenericMeta) and _gorg(c) is Generic:
            next_in_mro = cls.__mro__[i + 1]
    return next_in_mro


def _make_subclasshook(cls):
    """Construct a __subclasshook__ callable that incorporates
    the associated __extra__ class in subclass checks performed
    against cls.
    """
    if isinstance(cls.__extra__, abc.ABCMeta):
        # The logic mirrors that of ABCMeta.__subclasscheck__.
        # Registered classes need not be checked here because
        # cls and its extra share the same _abc_registry.
        def __extrahook__(subclass):
            res = cls.__extra__.__subclasshook__(subclass)
            if res is not NotImplemented:
                return res
            if cls.__extra__ in subclass.__mro__:
                return True
            for scls in cls.__extra__.__subclasses__():
                if isinstance(scls, GenericMeta):
                    continue
                if issubclass(subclass, scls):
                    return True
            return NotImplemented
    else:
        # For non-ABC extras we'll just call issubclass().
        def __extrahook__(subclass):
            if cls.__extra__ and issubclass(subclass, cls.__extra__):
                return True
            return NotImplemented
    return __extrahook__


def _no_slots_copy(dct):
    """Internal helper: copy class __dict__ and clean slots class variables.
    (They will be re-created if necessary by normal class machinery.)
    """
    dict_copy = dict(dct)
    if '__slots__' in dict_copy:
        for slot in dict_copy['__slots__']:
            dict_copy.pop(slot, None)
    return dict_copy


class GenericMeta(TypingMeta, abc.ABCMeta):
    """Metaclass for generic types.

    This is a metaclass for typing.Generic and generic ABCs defined in
    typing module. User defined subclasses of GenericMeta can override
    __new__ and invoke super().__new__. Note that GenericMeta.__new__
    has strict rules on what is allowed in its bases argument:
    * plain Generic is disallowed in bases;
    * Generic[...] should appear in bases at most once;
    * if Generic[...] is present, then it should list all type variables
      that appear in other bases.
    In addition, type of all generic bases is erased, e.g., C[int] is
    stripped to plain C.
    """

    def __new__(cls, name, bases, namespace,
                tvars=None, args=None, origin=None, extra=None, orig_bases=None):
        """Create a new generic class. GenericMeta.__new__ accepts
        keyword arguments that are used for internal bookkeeping, therefore
        an override should pass unused keyword arguments to super().
        """
        if tvars is not None:
            # Called from __getitem__() below.
            assert origin is not None
            assert all(isinstance(t, TypeVar) for t in tvars), tvars
        else:
            # Called from class statement.
            assert tvars is None, tvars
            assert args is None, args
            assert origin is None, origin

            # Get the full set of tvars from the bases.
            tvars = _type_vars(bases)
            # Look for Generic[T1, ..., Tn].
            # If found, tvars must be a subset of it.
            # If not found, tvars is it.
            # Also check for and reject plain Generic,
            # and reject multiple Generic[...].
            gvars = None
            for base in bases:
                if base is Generic:
                    raise TypeError("Cannot inherit from plain Generic")
                if (isinstance(base, GenericMeta) and
                        base.__origin__ is Generic):
                    if gvars is not None:
                        raise TypeError(
                            "Cannot inherit from Generic[...] multiple types.")
                    gvars = base.__parameters__
            if gvars is None:
                gvars = tvars
            else:
                tvarset = set(tvars)
                gvarset = set(gvars)
                if not tvarset <= gvarset:
                    raise TypeError(
                        "Some type variables (%s) "
                        "are not listed in Generic[%s]" %
                        (", ".join(str(t) for t in tvars if t not in gvarset),
                         ", ".join(str(g) for g in gvars)))
                tvars = gvars

        initial_bases = bases
        if extra is not None and type(extra) is abc.ABCMeta and extra not in bases:
            bases = (extra,) + bases
        bases = tuple(_gorg(b) if isinstance(b, GenericMeta) else b for b in bases)

        # remove bare Generic from bases if there are other generic bases
        if any(isinstance(b, GenericMeta) and b is not Generic for b in bases):
            bases = tuple(b for b in bases if b is not Generic)
        namespace.update({'__origin__': origin, '__extra__': extra})
        self = super().__new__(cls, name, bases, namespace, _root=True)

        self.__parameters__ = tvars
        # Be prepared that GenericMeta will be subclassed by TupleMeta
        # and CallableMeta, those two allow ..., (), or [] in __args___.
        self.__args__ = tuple(... if a is _TypingEllipsis else
                              () if a is _TypingEmpty else
                              a for a in args) if args else None
        # Speed hack (https://github.com/python/typing/issues/196).
        self.__next_in_mro__ = _next_in_mro(self)
        # Preserve base classes on subclassing (__bases__ are type erased now).
        if orig_bases is None:
            self.__orig_bases__ = initial_bases

        # This allows unparameterized generic collections to be used
        # with issubclass() and isinstance() in the same way as their
        # collections.abc counterparts (e.g., isinstance([], Iterable)).
        if (
            '__subclasshook__' not in namespace and extra or
            # allow overriding
            getattr(self.__subclasshook__, '__name__', '') == '__extrahook__'
        ):
            self.__subclasshook__ = _make_subclasshook(self)
        if isinstance(extra, abc.ABCMeta):
            self._abc_registry = extra._abc_registry
            self._abc_cache = extra._abc_cache
        elif origin is not None:
            self._abc_registry = origin._abc_registry
            self._abc_cache = origin._abc_cache

        if origin and hasattr(origin, '__qualname__'):  # Fix for Python 3.2.
            self.__qualname__ = origin.__qualname__
        self.__tree_hash__ = (hash(self._subs_tree()) if origin else
                              super(GenericMeta, self).__hash__())
        return self

    # _abc_negative_cache and _abc_negative_cache_version
    # realised as descriptors, since GenClass[t1, t2, ...] always
    # share subclass info with GenClass.
    # This is an important memory optimization.
    @property
    def _abc_negative_cache(self):
        if isinstance(self.__extra__, abc.ABCMeta):
            return self.__extra__._abc_negative_cache
        return _gorg(self)._abc_generic_negative_cache

    @_abc_negative_cache.setter
    def _abc_negative_cache(self, value):
        if self.__origin__ is None:
            if isinstance(self.__extra__, abc.ABCMeta):
                self.__extra__._abc_negative_cache = value
            else:
                self._abc_generic_negative_cache = value

    @property
    def _abc_negative_cache_version(self):
        if isinstance(self.__extra__, abc.ABCMeta):
            return self.__extra__._abc_negative_cache_version
        return _gorg(self)._abc_generic_negative_cache_version

    @_abc_negative_cache_version.setter
    def _abc_negative_cache_version(self, value):
        if self.__origin__ is None:
            if isinstance(self.__extra__, abc.ABCMeta):
                self.__extra__._abc_negative_cache_version = value
            else:
                self._abc_generic_negative_cache_version = value

    def _get_type_vars(self, tvars):
        if self.__origin__ and self.__parameters__:
            _get_type_vars(self.__parameters__, tvars)

    def _eval_type(self, globalns, localns):
        ev_origin = (self.__origin__._eval_type(globalns, localns)
                     if self.__origin__ else None)
        ev_args = tuple(_eval_type(a, globalns, localns) for a
                        in self.__args__) if self.__args__ else None
        if ev_origin == self.__origin__ and ev_args == self.__args__:
            return self
        return self.__class__(self.__name__,
                              self.__bases__,
                              _no_slots_copy(self.__dict__),
                              tvars=_type_vars(ev_args) if ev_args else None,
                              args=ev_args,
                              origin=ev_origin,
                              extra=self.__extra__,
                              orig_bases=self.__orig_bases__)

    def __repr__(self):
        if self.__origin__ is None:
            return super().__repr__()
        return self._tree_repr(self._subs_tree())

    def _tree_repr(self, tree):
        arg_list = []
        for arg in tree[1:]:
            if arg == ():
                arg_list.append('()')
            elif not isinstance(arg, tuple):
                arg_list.append(_type_repr(arg))
            else:
                arg_list.append(arg[0]._tree_repr(arg))
        return super().__repr__() + '[%s]' % ', '.join(arg_list)

    def _subs_tree(self, tvars=None, args=None):
        if self.__origin__ is None:
            return self
        tree_args = _subs_tree(self, tvars, args)
        return (_gorg(self),) + tuple(tree_args)

    def __eq__(self, other):
        if not isinstance(other, GenericMeta):
            return NotImplemented
        if self.__origin__ is None or other.__origin__ is None:
            return self is other
        return self.__tree_hash__ == other.__tree_hash__

    def __hash__(self):
        return self.__tree_hash__

    @_tp_cache
    def __getitem__(self, params):
        if not isinstance(params, tuple):
            params = (params,)
        if not params and not _gorg(self) is Tuple:
            raise TypeError(
                "Parameter list to %s[...] cannot be empty" % _qualname(self))
        msg = "Parameters to generic types must be types."
        params = tuple(_type_check(p, msg) for p in params)
        if self is Generic:
            # Generic can only be subscripted with unique type variables.
            if not all(isinstance(p, TypeVar) for p in params):
                raise TypeError(
                    "Parameters to Generic[...] must all be type variables")
            if len(set(params)) != len(params):
                raise TypeError(
                    "Parameters to Generic[...] must all be unique")
            tvars = params
            args = params
        elif self in (Tuple, Callable):
            tvars = _type_vars(params)
            args = params
        elif self is _Protocol:
            # _Protocol is internal, don't check anything.
            tvars = params
            args = params
        elif self.__origin__ in (Generic, _Protocol):
            # Can't subscript Generic[...] or _Protocol[...].
            raise TypeError("Cannot subscript already-subscripted %s" %
                            repr(self))
        else:
            # Subscripting a regular Generic subclass.
            _check_generic(self, params)
            tvars = _type_vars(params)
            args = params

        prepend = (self,) if self.__origin__ is None else ()
        return self.__class__(self.__name__,
                              prepend + self.__bases__,
                              _no_slots_copy(self.__dict__),
                              tvars=tvars,
                              args=args,
                              origin=self,
                              extra=self.__extra__,
                              orig_bases=self.__orig_bases__)

    def __subclasscheck__(self, cls):
        if self.__origin__ is not None:
            if sys._getframe(1).f_globals['__name__'] not in ['abc', 'functools']:
                raise TypeError("Parameterized generics cannot be used with class "
                                "or instance checks")
            return False
        if self is Generic:
            raise TypeError("Class %r cannot be used with class "
                            "or instance checks" % self)
        return super().__subclasscheck__(cls)

    def __instancecheck__(self, instance):
        # Since we extend ABC.__subclasscheck__ and
        # ABC.__instancecheck__ inlines the cache checking done by the
        # latter, we must extend __instancecheck__ too. For simplicity
        # we just skip the cache check -- instance checks for generic
        # classes are supposed to be rare anyways.
        return issubclass(instance.__class__, self)

    def __copy__(self):
        return self.__class__(self.__name__, self.__bases__,
                              _no_slots_copy(self.__dict__),
                              self.__parameters__, self.__args__, self.__origin__,
                              self.__extra__, self.__orig_bases__)

    def __setattr__(self, attr, value):
        # We consider all the subscripted genrics as proxies for original class
        if (
            attr.startswith('__') and attr.endswith('__') or
            attr.startswith('_abc_')
        ):
            super(GenericMeta, self).__setattr__(attr, value)
        else:
            super(GenericMeta, _gorg(self)).__setattr__(attr, value)


# Prevent checks for Generic to crash when defining Generic.
Generic = None


def _generic_new(base_cls, cls, *args, **kwds):
    # Assure type is erased on instantiation,
    # but attempt to store it in __orig_class__
    if cls.__origin__ is None:
        return base_cls.__new__(cls)
    else:
        origin = _gorg(cls)
        obj = base_cls.__new__(origin)
        try:
            obj.__orig_class__ = cls
        except AttributeError:
            pass
        obj.__init__(*args, **kwds)
        return obj


class Generic(metaclass=GenericMeta):
    """Abstract base class for generic types.

    A generic type is typically declared by inheriting from
    this class parameterized with one or more type variables.
    For example, a generic mapping type might be defined as::

      class Mapping(Generic[KT, VT]):
          def __getitem__(self, key: KT) -> VT:
              ...
          # Etc.

    This class can then be used as follows::

      def lookup_name(mapping: Mapping[KT, VT], key: KT, default: VT) -> VT:
          try:
              return mapping[key]
          except KeyError:
              return default
    """

    __slots__ = ()

    def __new__(cls, *args, **kwds):
        if _geqv(cls, Generic):
            raise TypeError("Type Generic cannot be instantiated; "
                            "it can be used only as a base class")
        return _generic_new(cls.__next_in_mro__, cls, *args, **kwds)


class _TypingEmpty:
    """Internal placeholder for () or []. Used by TupleMeta and CallableMeta
    to allow empty list/tuple in specific places, without allowing them
    to sneak in where prohibited.
    """


class _TypingEllipsis:
    """Internal placeholder for ... (ellipsis)."""


class TupleMeta(GenericMeta):
    """Metaclass for Tuple (internal)."""

    @_tp_cache
    def __getitem__(self, parameters):
        if self.__origin__ is not None or not _geqv(self, Tuple):
            # Normal generic rules apply if this is not the first subscription
            # or a subscription of a subclass.
            return super().__getitem__(parameters)
        if parameters == ():
            return super().__getitem__((_TypingEmpty,))
        if not isinstance(parameters, tuple):
            parameters = (parameters,)
        if len(parameters) == 2 and parameters[1] is ...:
            msg = "Tuple[t, ...]: t must be a type."
            p = _type_check(parameters[0], msg)
            return super().__getitem__((p, _TypingEllipsis))
        msg = "Tuple[t0, t1, ...]: each t must be a type."
        parameters = tuple(_type_check(p, msg) for p in parameters)
        return super().__getitem__(parameters)

    def __instancecheck__(self, obj):
        if self.__args__ is None:
            return isinstance(obj, tuple)
        raise TypeError("Parameterized Tuple cannot be used "
                        "with isinstance().")

    def __subclasscheck__(self, cls):
        if self.__args__ is None:
            return issubclass(cls, tuple)
        raise TypeError("Parameterized Tuple cannot be used "
                        "with issubclass().")


class Tuple(tuple, extra=tuple, metaclass=TupleMeta):
    """Tuple type; Tuple[X, Y] is the cross-product type of X and Y.

    Example: Tuple[T1, T2] is a tuple of two elements corresponding
    to type variables T1 and T2.  Tuple[int, float, str] is a tuple
    of an int, a float and a string.

    To specify a variable-length tuple of homogeneous type, use Tuple[T, ...].
    """

    __slots__ = ()

    def __new__(cls, *args, **kwds):
        if _geqv(cls, Tuple):
            raise TypeError("Type Tuple cannot be instantiated; "
                            "use tuple() instead")
        return _generic_new(tuple, cls, *args, **kwds)


class CallableMeta(GenericMeta):
    """Metaclass for Callable (internal)."""

    def __repr__(self):
        if self.__origin__ is None:
            return super().__repr__()
        return self._tree_repr(self._subs_tree())

    def _tree_repr(self, tree):
        if _gorg(self) is not Callable:
            return super()._tree_repr(tree)
        # For actual Callable (not its subclass) we override
        # super()._tree_repr() for nice formatting.
        arg_list = []
        for arg in tree[1:]:
            if not isinstance(arg, tuple):
                arg_list.append(_type_repr(arg))
            else:
                arg_list.append(arg[0]._tree_repr(arg))
        if arg_list[0] == '...':
            return repr(tree[0]) + '[..., %s]' % arg_list[1]
        return (repr(tree[0]) +
                '[[%s], %s]' % (', '.join(arg_list[:-1]), arg_list[-1]))

    def __getitem__(self, parameters):
        """A thin wrapper around __getitem_inner__ to provide the latter
        with hashable arguments to improve speed.
        """

        if self.__origin__ is not None or not _geqv(self, Callable):
            return super().__getitem__(parameters)
        if not isinstance(parameters, tuple) or len(parameters) != 2:
            raise TypeError("Callable must be used as "
                            "Callable[[arg, ...], result].")
        args, result = parameters
        if args is Ellipsis:
            parameters = (Ellipsis, result)
        else:
            if not isinstance(args, list):
                raise TypeError("Callable[args, result]: args must be a list."
                                " Got %.100r." % (args,))
            parameters = (tuple(args), result)
        return self.__getitem_inner__(parameters)

    @_tp_cache
    def __getitem_inner__(self, parameters):
        args, result = parameters
        msg = "Callable[args, result]: result must be a type."
        result = _type_check(result, msg)
        if args is Ellipsis:
            return super().__getitem__((_TypingEllipsis, result))
        msg = "Callable[[arg, ...], result]: each arg must be a type."
        args = tuple(_type_check(arg, msg) for arg in args)
        parameters = args + (result,)
        return super().__getitem__(parameters)


class Callable(extra=collections_abc.Callable, metaclass=CallableMeta):
    """Callable type; Callable[[int], str] is a function of (int) -> str.

    The subscription syntax must always be used with exactly two
    values: the argument list and the return type.  The argument list
    must be a list of types or ellipsis; the return type must be a single type.

    There is no syntax to indicate optional or keyword arguments,
    such function types are rarely used as callback types.
    """

    __slots__ = ()

    def __new__(cls, *args, **kwds):
        if _geqv(cls, Callable):
            raise TypeError("Type Callable cannot be instantiated; "
                            "use a non-abstract subclass instead")
        return _generic_new(cls.__next_in_mro__, cls, *args, **kwds)


class _ClassVar(_FinalTypingBase, _root=True):
    """Special type construct to mark class variables.

    An annotation wrapped in ClassVar indicates that a given
    attribute is intended to be used as a class variable and
    should not be set on instances of that class. Usage::

      class Starship:
          stats: ClassVar[Dict[str, int]] = {} # class variable
          damage: int = 10                     # instance variable

    ClassVar accepts only types and cannot be further subscribed.

    Note that ClassVar is not a class itself, and should not
    be used with isinstance() or issubclass().
    """

    __slots__ = ('__type__',)

    def __init__(self, tp=None, **kwds):
        self.__type__ = tp

    def __getitem__(self, item):
        cls = type(self)
        if self.__type__ is None:
            return cls(_type_check(item,
                       '{} accepts only single type.'.format(cls.__name__[1:])),
                       _root=True)
        raise TypeError('{} cannot be further subscripted'
                        .format(cls.__name__[1:]))

    def _eval_type(self, globalns, localns):
        new_tp = _eval_type(self.__type__, globalns, localns)
        if new_tp == self.__type__:
            return self
        return type(self)(new_tp, _root=True)

    def __repr__(self):
        r = super().__repr__()
        if self.__type__ is not None:
            r += '[{}]'.format(_type_repr(self.__type__))
        return r

    def __hash__(self):
        return hash((type(self).__name__, self.__type__))

    def __eq__(self, other):
        if not isinstance(other, _ClassVar):
            return NotImplemented
        if self.__type__ is not None:
            return self.__type__ == other.__type__
        return self is other


ClassVar = _ClassVar(_root=True)


def cast(typ, val):
    """Cast a value to a type.

    This returns the value unchanged.  To the type checker this
    signals that the return value has the designated type, but at
    runtime we intentionally don't check anything (we want this
    to be as fast as possible).
    """
    return val


def _get_defaults(func):
    """Internal helper to extract the default arguments, by name."""
    try:
        code = func.__code__
    except AttributeError:
        # Some built-in functions don't have __code__, __defaults__, etc.
        return {}
    pos_count = code.co_argcount
    arg_names = code.co_varnames
    arg_names = arg_names[:pos_count]
    defaults = func.__defaults__ or ()
    kwdefaults = func.__kwdefaults__
    res = dict(kwdefaults) if kwdefaults else {}
    pos_offset = pos_count - len(defaults)
    for name, value in zip(arg_names[pos_offset:], defaults):
        assert name not in res
        res[name] = value
    return res


_allowed_types = (types.FunctionType, types.BuiltinFunctionType,
                  types.MethodType, types.ModuleType,
                  WrapperDescriptorType, MethodWrapperType, MethodDescriptorType)


def get_type_hints(obj, globalns=None, localns=None):
    """Return type hints for an object.

    This is often the same as obj.__annotations__, but it handles
    forward references encoded as string literals, and if necessary
    adds Optional[t] if a default value equal to None is set.

    The argument may be a module, class, method, or function. The annotations
    are returned as a dictionary. For classes, annotations include also
    inherited members.

    TypeError is raised if the argument is not of a type that can contain
    annotations, and an empty dictionary is returned if no annotations are
    present.

    BEWARE -- the behavior of globalns and localns is counterintuitive
    (unless you are familiar with how eval() and exec() work).  The
    search order is locals first, then globals.

    - If no dict arguments are passed, an attempt is made to use the
      globals from obj, and these are also used as the locals.  If the
      object does not appear to have globals, an exception is raised.

    - If one dict argument is passed, it is used for both globals and
      locals.

    - If two dict arguments are passed, they specify globals and
      locals, respectively.
    """

    if getattr(obj, '__no_type_check__', None):
        return {}
    if globalns is None:
        globalns = getattr(obj, '__globals__', {})
        if localns is None:
            localns = globalns
    elif localns is None:
        localns = globalns
    # Classes require a special treatment.
    if isinstance(obj, type):
        hints = {}
        for base in reversed(obj.__mro__):
            ann = base.__dict__.get('__annotations__', {})
            for name, value in ann.items():
                if value is None:
                    value = type(None)
                if isinstance(value, str):
                    value = _ForwardRef(value)
                value = _eval_type(value, globalns, localns)
                hints[name] = value
        return hints
    hints = getattr(obj, '__annotations__', None)
    if hints is None:
        # Return empty annotations for something that _could_ have them.
        if isinstance(obj, _allowed_types):
            return {}
        else:
            raise TypeError('{!r} is not a module, class, method, '
                            'or function.'.format(obj))
    defaults = _get_defaults(obj)
    hints = dict(hints)
    for name, value in hints.items():
        if value is None:
            value = type(None)
        if isinstance(value, str):
            value = _ForwardRef(value)
        value = _eval_type(value, globalns, localns)
        if name in defaults and defaults[name] is None:
            value = Optional[value]
        hints[name] = value
    return hints


def no_type_check(arg):
    """Decorator to indicate that annotations are not type hints.

    The argument must be a class or function; if it is a class, it
    applies recursively to all methods and classes defined in that class
    (but not to methods defined in its superclasses or subclasses).

    This mutates the function(s) or class(es) in place.
    """
    if isinstance(arg, type):
        arg_attrs = arg.__dict__.copy()
        for attr, val in arg.__dict__.items():
            if val in arg.__bases__:
                arg_attrs.pop(attr)
        for obj in arg_attrs.values():
            if isinstance(obj, types.FunctionType):
                obj.__no_type_check__ = True
            if isinstance(obj, type):
                no_type_check(obj)
    try:
        arg.__no_type_check__ = True
    except TypeError:  # built-in classes
        pass
    return arg


def no_type_check_decorator(decorator):
    """Decorator to give another decorator the @no_type_check effect.

    This wraps the decorator with something that wraps the decorated
    function in @no_type_check.
    """

    @functools.wraps(decorator)
    def wrapped_decorator(*args, **kwds):
        func = decorator(*args, **kwds)
        func = no_type_check(func)
        return func

    return wrapped_decorator


def _overload_dummy(*args, **kwds):
    """Helper for @overload to raise when called."""
    raise NotImplementedError(
        "You should not call an overloaded function. "
        "A series of @overload-decorated functions "
        "outside a stub module should always be followed "
        "by an implementation that is not @overload-ed.")


def overload(func):
    """Decorator for overloaded functions/methods.

    In a stub file, place two or more stub definitions for the same
    function in a row, each decorated with @overload.  For example:

      @overload
      def utf8(value: None) -> None: ...
      @overload
      def utf8(value: bytes) -> bytes: ...
      @overload
      def utf8(value: str) -> bytes: ...

    In a non-stub file (i.e. a regular .py file), do the same but
    follow it with an implementation.  The implementation should *not*
    be decorated with @overload.  For example:

      @overload
      def utf8(value: None) -> None: ...
      @overload
      def utf8(value: bytes) -> bytes: ...
      @overload
      def utf8(value: str) -> bytes: ...
      def utf8(value):
          # implementation goes here
    """
    return _overload_dummy


class _ProtocolMeta(GenericMeta):
    """Internal metaclass for _Protocol.

    This exists so _Protocol classes can be generic without deriving
    from Generic.
    """

    def __instancecheck__(self, obj):
        if _Protocol not in self.__bases__:
            return super().__instancecheck__(obj)
        raise TypeError("Protocols cannot be used with isinstance().")

    def __subclasscheck__(self, cls):
        if not self._is_protocol:
            # No structural checks since this isn't a protocol.
            return NotImplemented

        if self is _Protocol:
            # Every class is a subclass of the empty protocol.
            return True

        # Find all attributes defined in the protocol.
        attrs = self._get_protocol_attrs()

        for attr in attrs:
            if not any(attr in d.__dict__ for d in cls.__mro__):
                return False
        return True

    def _get_protocol_attrs(self):
        # Get all Protocol base classes.
        protocol_bases = []
        for c in self.__mro__:
            if getattr(c, '_is_protocol', False) and c.__name__ != '_Protocol':
                protocol_bases.append(c)

        # Get attributes included in protocol.
        attrs = set()
        for base in protocol_bases:
            for attr in base.__dict__.keys():
                # Include attributes not defined in any non-protocol bases.
                for c in self.__mro__:
                    if (c is not base and attr in c.__dict__ and
                            not getattr(c, '_is_protocol', False)):
                        break
                else:
                    if (not attr.startswith('_abc_') and
                            attr != '__abstractmethods__' and
                            attr != '__annotations__' and
                            attr != '__weakref__' and
                            attr != '_is_protocol' and
                            attr != '__dict__' and
                            attr != '__args__' and
                            attr != '__slots__' and
                            attr != '_get_protocol_attrs' and
                            attr != '__next_in_mro__' and
                            attr != '__parameters__' and
                            attr != '__origin__' and
                            attr != '__orig_bases__' and
                            attr != '__extra__' and
                            attr != '__tree_hash__' and
                            attr != '__module__'):
                        attrs.add(attr)

        return attrs


class _Protocol(metaclass=_ProtocolMeta):
    """Internal base class for protocol classes.

    This implements a simple-minded structural issubclass check
    (similar but more general than the one-offs in collections.abc
    such as Hashable).
    """

    __slots__ = ()

    _is_protocol = True


# Various ABCs mimicking those in collections.abc.
# A few are simply re-exported for completeness.

Hashable = collections_abc.Hashable  # Not generic.


if hasattr(collections_abc, 'Awaitable'):
    class Awaitable(Generic[T_co], extra=collections_abc.Awaitable):
        __slots__ = ()

    __all__.append('Awaitable')


if hasattr(collections_abc, 'Coroutine'):
    class Coroutine(Awaitable[V_co], Generic[T_co, T_contra, V_co],
                    extra=collections_abc.Coroutine):
        __slots__ = ()

    __all__.append('Coroutine')


if hasattr(collections_abc, 'AsyncIterable'):

    class AsyncIterable(Generic[T_co], extra=collections_abc.AsyncIterable):
        __slots__ = ()

    class AsyncIterator(AsyncIterable[T_co],
                        extra=collections_abc.AsyncIterator):
        __slots__ = ()

    __all__.append('AsyncIterable')
    __all__.append('AsyncIterator')


class Iterable(Generic[T_co], extra=collections_abc.Iterable):
    __slots__ = ()


class Iterator(Iterable[T_co], extra=collections_abc.Iterator):
    __slots__ = ()


class SupportsInt(_Protocol):
    __slots__ = ()

    @abstractmethod
    def __int__(self) -> int:
        pass


class SupportsFloat(_Protocol):
    __slots__ = ()

    @abstractmethod
    def __float__(self) -> float:
        pass


class SupportsComplex(_Protocol):
    __slots__ = ()

    @abstractmethod
    def __complex__(self) -> complex:
        pass


class SupportsBytes(_Protocol):
    __slots__ = ()

    @abstractmethod
    def __bytes__(self) -> bytes:
        pass


class SupportsAbs(_Protocol[T_co]):
    __slots__ = ()

    @abstractmethod
    def __abs__(self) -> T_co:
        pass


class SupportsRound(_Protocol[T_co]):
    __slots__ = ()

    @abstractmethod
    def __round__(self, ndigits: int = 0) -> T_co:
        pass


if hasattr(collections_abc, 'Reversible'):
    class Reversible(Iterable[T_co], extra=collections_abc.Reversible):
        __slots__ = ()
else:
    class Reversible(_Protocol[T_co]):
        __slots__ = ()

        @abstractmethod
        def __reversed__(self) -> 'Iterator[T_co]':
            pass


Sized = collections_abc.Sized  # Not generic.


class Container(Generic[T_co], extra=collections_abc.Container):
    __slots__ = ()


if hasattr(collections_abc, 'Collection'):
    class Collection(Sized, Iterable[T_co], Container[T_co],
                     extra=collections_abc.Collection):
        __slots__ = ()

    __all__.append('Collection')


# Callable was defined earlier.

if hasattr(collections_abc, 'Collection'):
    class AbstractSet(Collection[T_co],
                      extra=collections_abc.Set):
        __slots__ = ()
else:
    class AbstractSet(Sized, Iterable[T_co], Container[T_co],
                      extra=collections_abc.Set):
        __slots__ = ()


class MutableSet(AbstractSet[T], extra=collections_abc.MutableSet):
    __slots__ = ()


# NOTE: It is only covariant in the value type.
if hasattr(collections_abc, 'Collection'):
    class Mapping(Collection[KT], Generic[KT, VT_co],
                  extra=collections_abc.Mapping):
        __slots__ = ()
else:
    class Mapping(Sized, Iterable[KT], Container[KT], Generic[KT, VT_co],
                  extra=collections_abc.Mapping):
        __slots__ = ()


class MutableMapping(Mapping[KT, VT], extra=collections_abc.MutableMapping):
    __slots__ = ()


if hasattr(collections_abc, 'Reversible'):
    if hasattr(collections_abc, 'Collection'):
        class Sequence(Reversible[T_co], Collection[T_co],
                       extra=collections_abc.Sequence):
            __slots__ = ()
    else:
        class Sequence(Sized, Reversible[T_co], Container[T_co],
                       extra=collections_abc.Sequence):
            __slots__ = ()
else:
    class Sequence(Sized, Iterable[T_co], Container[T_co],
                   extra=collections_abc.Sequence):
        __slots__ = ()


class MutableSequence(Sequence[T], extra=collections_abc.MutableSequence):
    __slots__ = ()


class ByteString(Sequence[int], extra=collections_abc.ByteString):
    __slots__ = ()


class List(list, MutableSequence[T], extra=list):

    __slots__ = ()

    def __new__(cls, *args, **kwds):
        if _geqv(cls, List):
            raise TypeError("Type List cannot be instantiated; "
                            "use list() instead")
        return _generic_new(list, cls, *args, **kwds)


class Deque(collections.deque, MutableSequence[T], extra=collections.deque):

    __slots__ = ()

    def __new__(cls, *args, **kwds):
        if _geqv(cls, Deque):
            return collections.deque(*args, **kwds)
        return _generic_new(collections.deque, cls, *args, **kwds)


class Set(set, MutableSet[T], extra=set):

    __slots__ = ()

    def __new__(cls, *args, **kwds):
        if _geqv(cls, Set):
            raise TypeError("Type Set cannot be instantiated; "
                            "use set() instead")
        return _generic_new(set, cls, *args, **kwds)


class FrozenSet(frozenset, AbstractSet[T_co], extra=frozenset):
    __slots__ = ()

    def __new__(cls, *args, **kwds):
        if _geqv(cls, FrozenSet):
            raise TypeError("Type FrozenSet cannot be instantiated; "
                            "use frozenset() instead")
        return _generic_new(frozenset, cls, *args, **kwds)


class MappingView(Sized, Iterable[T_co], extra=collections_abc.MappingView):
    __slots__ = ()


class KeysView(MappingView[KT], AbstractSet[KT],
               extra=collections_abc.KeysView):
    __slots__ = ()


class ItemsView(MappingView[Tuple[KT, VT_co]],
                AbstractSet[Tuple[KT, VT_co]],
                Generic[KT, VT_co],
                extra=collections_abc.ItemsView):
    __slots__ = ()


class ValuesView(MappingView[VT_co], extra=collections_abc.ValuesView):
    __slots__ = ()


if hasattr(contextlib, 'AbstractContextManager'):
    class ContextManager(Generic[T_co], extra=contextlib.AbstractContextManager):
        __slots__ = ()
    __all__.append('ContextManager')


class Dict(dict, MutableMapping[KT, VT], extra=dict):

    __slots__ = ()

    def __new__(cls, *args, **kwds):
        if _geqv(cls, Dict):
            raise TypeError("Type Dict cannot be instantiated; "
                            "use dict() instead")
        return _generic_new(dict, cls, *args, **kwds)


class DefaultDict(collections.defaultdict, MutableMapping[KT, VT],
                  extra=collections.defaultdict):

    __slots__ = ()

    def __new__(cls, *args, **kwds):
        if _geqv(cls, DefaultDict):
            return collections.defaultdict(*args, **kwds)
        return _generic_new(collections.defaultdict, cls, *args, **kwds)


class Counter(collections.Counter, Dict[T, int], extra=collections.Counter):

    __slots__ = ()

    def __new__(cls, *args, **kwds):
        if _geqv(cls, Counter):
            return collections.Counter(*args, **kwds)
        return _generic_new(collections.Counter, cls, *args, **kwds)


if hasattr(collections, 'ChainMap'):
    # ChainMap only exists in 3.3+
    __all__.append('ChainMap')

    class ChainMap(collections.ChainMap, MutableMapping[KT, VT],
                   extra=collections.ChainMap):

        __slots__ = ()

        def __new__(cls, *args, **kwds):
            if _geqv(cls, ChainMap):
                return collections.ChainMap(*args, **kwds)
            return _generic_new(collections.ChainMap, cls, *args, **kwds)


# Determine what base class to use for Generator.
if hasattr(collections_abc, 'Generator'):
    # Sufficiently recent versions of 3.5 have a Generator ABC.
    _G_base = collections_abc.Generator
else:
    # Fall back on the exact type.
    _G_base = types.GeneratorType


class Generator(Iterator[T_co], Generic[T_co, T_contra, V_co],
                extra=_G_base):
    __slots__ = ()

    def __new__(cls, *args, **kwds):
        if _geqv(cls, Generator):
            raise TypeError("Type Generator cannot be instantiated; "
                            "create a subclass instead")
        return _generic_new(_G_base, cls, *args, **kwds)


if hasattr(collections_abc, 'AsyncGenerator'):
    class AsyncGenerator(AsyncIterator[T_co], Generic[T_co, T_contra],
                         extra=collections_abc.AsyncGenerator):
        __slots__ = ()

    __all__.append('AsyncGenerator')


# Internal type variable used for Type[].
CT_co = TypeVar('CT_co', covariant=True, bound=type)


# This is not a real generic class.  Don't use outside annotations.
class Type(Generic[CT_co], extra=type):
    """A special construct usable to annotate class objects.

    For example, suppose we have the following classes::

      class User: ...  # Abstract base for User classes
      class BasicUser(User): ...
      class ProUser(User): ...
      class TeamUser(User): ...

    And a function that takes a class argument that's a subclass of
    User and returns an instance of the corresponding class::

      U = TypeVar('U', bound=User)
      def new_user(user_class: Type[U]) -> U:
          user = user_class()
          # (Here we could write the user object to a database)
          return user

      joe = new_user(BasicUser)

    At this point the type checker knows that joe has type BasicUser.
    """

    __slots__ = ()


def _make_nmtuple(name, types):
    msg = "NamedTuple('Name', [(f0, t0), (f1, t1), ...]); each t must be a type"
    types = [(n, _type_check(t, msg)) for n, t in types]
    nm_tpl = collections.namedtuple(name, [n for n, t in types])
    # Prior to PEP 526, only _field_types attribute was assigned.
    # Now, both __annotations__ and _field_types are used to maintain compatibility.
    nm_tpl.__annotations__ = nm_tpl._field_types = collections.OrderedDict(types)
    try:
        nm_tpl.__module__ = sys._getframe(2).f_globals.get('__name__', '__main__')
    except (AttributeError, ValueError):
        pass
    return nm_tpl


_PY36 = sys.version_info[:2] >= (3, 6)

# attributes prohibited to set in NamedTuple class syntax
_prohibited = ('__new__', '__init__', '__slots__', '__getnewargs__',
               '_fields', '_field_defaults', '_field_types',
               '_make', '_replace', '_asdict', '_source')

_special = ('__module__', '__name__', '__qualname__', '__annotations__')


class NamedTupleMeta(type):

    def __new__(cls, typename, bases, ns):
        if ns.get('_root', False):
            return super().__new__(cls, typename, bases, ns)
        if not _PY36:
            raise TypeError("Class syntax for NamedTuple is only supported"
                            " in Python 3.6+")
        types = ns.get('__annotations__', {})
        nm_tpl = _make_nmtuple(typename, types.items())
        defaults = []
        defaults_dict = {}
        for field_name in types:
            if field_name in ns:
                default_value = ns[field_name]
                defaults.append(default_value)
                defaults_dict[field_name] = default_value
            elif defaults:
                raise TypeError("Non-default namedtuple field {field_name} cannot "
                                "follow default field(s) {default_names}"
                                .format(field_name=field_name,
                                        default_names=', '.join(defaults_dict.keys())))
        nm_tpl.__new__.__defaults__ = tuple(defaults)
        nm_tpl._field_defaults = defaults_dict
        # update from user namespace without overriding special namedtuple attributes
        for key in ns:
            if key in _prohibited:
                raise AttributeError("Cannot overwrite NamedTuple attribute " + key)
            elif key not in _special and key not in nm_tpl._fields:
                setattr(nm_tpl, key, ns[key])
        return nm_tpl


class NamedTuple(metaclass=NamedTupleMeta):
    """Typed version of namedtuple.

    Usage in Python versions >= 3.6::

        class Employee(NamedTuple):
            name: str
            id: int

    This is equivalent to::

        Employee = collections.namedtuple('Employee', ['name', 'id'])

    The resulting class has extra __annotations__ and _field_types
    attributes, giving an ordered dict mapping field names to types.
    __annotations__ should be preferred, while _field_types
    is kept to maintain pre PEP 526 compatibility. (The field names
    are in the _fields attribute, which is part of the namedtuple
    API.) Alternative equivalent keyword syntax is also accepted::

        Employee = NamedTuple('Employee', name=str, id=int)

    In Python versions <= 3.5 use::

        Employee = NamedTuple('Employee', [('name', str), ('id', int)])
    """
    _root = True

    def __new__(self, typename, fields=None, **kwargs):
        if kwargs and not _PY36:
            raise TypeError("Keyword syntax for NamedTuple is only supported"
                            " in Python 3.6+")
        if fields is None:
            fields = kwargs.items()
        elif kwargs:
            raise TypeError("Either list of fields or keywords"
                            " can be provided to NamedTuple, not both")
        return _make_nmtuple(typename, fields)


def NewType(name, tp):
    """NewType creates simple unique types with almost zero
    runtime overhead. NewType(name, tp) is considered a subtype of tp
    by static type checkers. At runtime, NewType(name, tp) returns
    a dummy function that simply returns its argument. Usage::

        UserId = NewType('UserId', int)

        def name_by_id(user_id: UserId) -> str:
            ...

        UserId('user')          # Fails type check

        name_by_id(42)          # Fails type check
        name_by_id(UserId(42))  # OK

        num = UserId(5) + 1     # type: int
    """

    def new_type(x):
        return x

    new_type.__name__ = name
    new_type.__supertype__ = tp
    return new_type


# Python-version-specific alias (Python 2: unicode; Python 3: str)
Text = str


# Constant that's True when type checking, but False here.
TYPE_CHECKING = False


class IO(Generic[AnyStr]):
    """Generic base class for TextIO and BinaryIO.

    This is an abstract, generic version of the return of open().

    NOTE: This does not distinguish between the different possible
    classes (text vs. binary, read vs. write vs. read/write,
    append-only, unbuffered).  The TextIO and BinaryIO subclasses
    below capture the distinctions between text vs. binary, which is
    pervasive in the interface; however we currently do not offer a
    way to track the other distinctions in the type system.
    """

    __slots__ = ()

    @abstractproperty
    def mode(self) -> str:
        pass

    @abstractproperty
    def name(self) -> str:
        pass

    @abstractmethod
    def close(self) -> None:
        pass

    @abstractmethod
    def closed(self) -> bool:
        pass

    @abstractmethod
    def fileno(self) -> int:
        pass

    @abstractmethod
    def flush(self) -> None:
        pass

    @abstractmethod
    def isatty(self) -> bool:
        pass

    @abstractmethod
    def read(self, n: int = -1) -> AnyStr:
        pass

    @abstractmethod
    def readable(self) -> bool:
        pass

    @abstractmethod
    def readline(self, limit: int = -1) -> AnyStr:
        pass

    @abstractmethod
    def readlines(self, hint: int = -1) -> List[AnyStr]:
        pass

    @abstractmethod
    def seek(self, offset: int, whence: int = 0) -> int:
        pass

    @abstractmethod
    def seekable(self) -> bool:
        pass

    @abstractmethod
    def tell(self) -> int:
        pass

    @abstractmethod
    def truncate(self, size: int = None) -> int:
        pass

    @abstractmethod
    def writable(self) -> bool:
        pass

    @abstractmethod
    def write(self, s: AnyStr) -> int:
        pass

    @abstractmethod
    def writelines(self, lines: List[AnyStr]) -> None:
        pass

    @abstractmethod
    def __enter__(self) -> 'IO[AnyStr]':
        pass

    @abstractmethod
    def __exit__(self, type, value, traceback) -> None:
        pass


class BinaryIO(IO[bytes]):
    """Typed version of the return of open() in binary mode."""

    __slots__ = ()

    @abstractmethod
    def write(self, s: Union[bytes, bytearray]) -> int:
        pass

    @abstractmethod
    def __enter__(self) -> 'BinaryIO':
        pass


class TextIO(IO[str]):
    """Typed version of the return of open() in text mode."""

    __slots__ = ()

    @abstractproperty
    def buffer(self) -> BinaryIO:
        pass

    @abstractproperty
    def encoding(self) -> str:
        pass

    @abstractproperty
    def errors(self) -> Optional[str]:
        pass

    @abstractproperty
    def line_buffering(self) -> bool:
        pass

    @abstractproperty
    def newlines(self) -> Any:
        pass

    @abstractmethod
    def __enter__(self) -> 'TextIO':
        pass


class io:
    """Wrapper namespace for IO generic classes."""

    __all__ = ['IO', 'TextIO', 'BinaryIO']
    IO = IO
    TextIO = TextIO
    BinaryIO = BinaryIO


io.__name__ = __name__ + '.io'
sys.modules[io.__name__] = io


Pattern = _TypeAlias('Pattern', AnyStr, type(stdlib_re.compile('')),
                     lambda p: p.pattern)
Match = _TypeAlias('Match', AnyStr, type(stdlib_re.match('', '')),
                   lambda m: m.re.pattern)


class re:
    """Wrapper namespace for re type aliases."""

    __all__ = ['Pattern', 'Match']
    Pattern = Pattern
    Match = Match


re.__name__ = __name__ + '.re'
sys.modules[re.__name__] = re