Lib/typing.py

"""
The typing module: Support for gradual typing as defined by PEP 484.

At large scale, the structure of the module is following:
* Imports and exports, all public names should be explicitly added to __all__.
* Internal helper functions: these should never be used in code outside this module.
* _SpecialForm and its instances (special forms):
  Any, NoReturn, ClassVar, Union, Optional, Concatenate
* Classes whose instances can be type arguments in addition to types:
  ForwardRef, TypeVar and ParamSpec
* The core of internal generics API: _GenericAlias and _VariadicGenericAlias, the latter is
  currently only used by Tuple and Callable. All subscripted types like X[int], Union[int, str],
  etc., are instances of either of these classes.
* The public counterpart of the generics API consists of two classes: Generic and Protocol.
* Public helper functions: get_type_hints, overload, cast, no_type_check,
  no_type_check_decorator.
* Generic aliases for collections.abc ABCs and few additional protocols.
* Special types: NewType, NamedTuple, TypedDict.
* Wrapper submodules for re and io related types.
"""

from abc import abstractmethod, ABCMeta
import collections
import collections.abc
import contextlib
import functools
import operator
import re as stdlib_re  # Avoid confusion with the re we export.
import sys
import types
from types import WrapperDescriptorType, MethodWrapperType, MethodDescriptorType, GenericAlias

# Please keep __all__ alphabetized within each category.
__all__ = [
    # Super-special typing primitives.
    'Annotated',
    'Any',
    'Callable',
    'ClassVar',
    'Concatenate',
    'Final',
    'ForwardRef',
    'Generic',
    'Literal',
    'Optional',
    'ParamSpec',
    'Protocol',
    'Tuple',
    'Type',
    'TypeVar',
    'Union',

    # ABCs (from collections.abc).
    'AbstractSet',  # collections.abc.Set.
    'ByteString',
    'Container',
    'ContextManager',
    'Hashable',
    'ItemsView',
    'Iterable',
    'Iterator',
    'KeysView',
    'Mapping',
    'MappingView',
    'MutableMapping',
    'MutableSequence',
    'MutableSet',
    'Sequence',
    'Sized',
    'ValuesView',
    'Awaitable',
    'AsyncIterator',
    'AsyncIterable',
    'Coroutine',
    'Collection',
    'AsyncGenerator',
    'AsyncContextManager',

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

    # Concrete collection types.
    'ChainMap',
    'Counter',
    'Deque',
    'Dict',
    'DefaultDict',
    'List',
    'OrderedDict',
    'Set',
    'FrozenSet',
    'NamedTuple',  # Not really a type.
    'TypedDict',  # Not really a type.
    'Generator',
 
    # Other concrete types.
    'BinaryIO',
    'IO',
    'Match',
    'Pattern',
    'TextIO',

    # One-off things.
    'AnyStr',
    'cast',
    'final',
    'get_args',
    'get_origin',
    'get_type_hints',
    'is_typeddict',
    'NewType',
    'no_type_check',
    'no_type_check_decorator',
    'NoReturn',
    'overload',
    'ParamSpecArgs',
    'ParamSpecKwargs',
    'runtime_checkable',
    'Text',
    'TYPE_CHECKING',
    'TypeAlias',
    'TypeGuard',
]

# 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 _type_convert(arg):
    """For converting None to type(None), and strings to ForwardRef."""
    if arg is None:
        return type(None)
    if isinstance(arg, str):
        return ForwardRef(arg)
    return arg


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

    As a special case, accept None and return type(None) instead. Also wrap strings
    into ForwardRef instances. Consider several corner cases, for example plain
    special forms like Union are not valid, while Union[int, str] is OK, etc.
    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).
    """
    invalid_generic_forms = (Generic, Protocol)
    if is_argument:
        invalid_generic_forms = invalid_generic_forms + (ClassVar, Final)

    arg = _type_convert(arg)
    if (isinstance(arg, _GenericAlias) and
            arg.__origin__ in invalid_generic_forms):
        raise TypeError(f"{arg} is not valid as type argument")
    if arg in (Any, NoReturn):
        return arg
    if isinstance(arg, _SpecialForm) or arg in (Generic, Protocol):
        raise TypeError(f"Plain {arg} is not valid as type argument")
    if isinstance(arg, (type, TypeVar, ForwardRef, types.Union, ParamSpec)):
        return arg
    if not callable(arg):
        raise TypeError(f"{msg} Got {arg!r:.100}.")
    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, types.GenericAlias):
        return repr(obj)
    if isinstance(obj, type):
        if obj.__module__ == 'builtins':
            return obj.__qualname__
        return f'{obj.__module__}.{obj.__qualname__}'
    if obj is ...:
        return('...')
    if isinstance(obj, types.FunctionType):
        return obj.__name__
    return repr(obj)


def _collect_type_vars(types):
    """Collect all type variable-like variables contained
    in types in order of first appearance (lexicographic order). For example::

        _collect_type_vars((T, List[S, T])) == (T, S)
    """
    tvars = []
    for t in types:
        if isinstance(t, _TypeVarLike) and t not in tvars:
            tvars.append(t)
        if isinstance(t, (_GenericAlias, GenericAlias)):
            tvars.extend([t for t in t.__parameters__ if t not in tvars])
    return tuple(tvars)


def _check_generic(cls, parameters, elen):
    """Check correct count for parameters of a generic cls (internal helper).
    This gives a nice error message in case of count mismatch.
    """
    if not elen:
        raise TypeError(f"{cls} is not a generic class")
    alen = len(parameters)
    if alen != elen:
        raise TypeError(f"Too {'many' if alen > elen else 'few'} parameters for {cls};"
                        f" actual {alen}, expected {elen}")

def _prepare_paramspec_params(cls, params):
    """Prepares the parameters for a Generic containing ParamSpec
    variables (internal helper).
    """
    # Special case where Z[[int, str, bool]] == Z[int, str, bool] in PEP 612.
    if len(cls.__parameters__) == 1 and len(params) > 1:
        return (params,)
    else:
        _params = []
        # Convert lists to tuples to help other libraries cache the results.
        for p, tvar in zip(params, cls.__parameters__):
            if isinstance(tvar, ParamSpec) and isinstance(p, list):
                p = tuple(p)
            _params.append(p)
        return tuple(_params)

def _deduplicate(params):
    # 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
    return params


def _remove_dups_flatten(parameters):
    """An internal helper for Union creation and substitution: flatten Unions
    among parameters, then remove duplicates.
    """
    # Flatten out Union[Union[...], ...].
    params = []
    for p in parameters:
        if isinstance(p, (_UnionGenericAlias, types.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)

    return tuple(_deduplicate(params))


def _flatten_literal_params(parameters):
    """An internal helper for Literal creation: flatten Literals among parameters"""
    params = []
    for p in parameters:
        if isinstance(p, _LiteralGenericAlias):
            params.extend(p.__args__)
        else:
            params.append(p)
    return tuple(params)


_cleanups = []


def _tp_cache(func=None, /, *, typed=False):
    """Internal wrapper caching __getitem__ of generic types with a fallback to
    original function for non-hashable arguments.
    """
    def decorator(func):
        cached = functools.lru_cache(typed=typed)(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

    if func is not None:
        return decorator(func)

    return decorator

def _eval_type(t, globalns, localns, recursive_guard=frozenset()):
    """Evaluate all forward references in the given type t.
    For use of globalns and localns see the docstring for get_type_hints().
    recursive_guard is used to prevent prevent infinite recursion
    with recursive ForwardRef.
    """
    if isinstance(t, ForwardRef):
        return t._evaluate(globalns, localns, recursive_guard)
    if isinstance(t, (_GenericAlias, GenericAlias)):
        ev_args = tuple(_eval_type(a, globalns, localns, recursive_guard) for a in t.__args__)
        if ev_args == t.__args__:
            return t
        if isinstance(t, GenericAlias):
            return GenericAlias(t.__origin__, ev_args)
        else:
            return t.copy_with(ev_args)
    return t


class _Final:
    """Mixin to prohibit subclassing"""

    __slots__ = ('__weakref__',)

    def __init_subclass__(self, /, *args, **kwds):
        if '_root' not in kwds:
            raise TypeError("Cannot subclass special typing classes")

class _Immutable:
    """Mixin to indicate that object should not be copied."""
    __slots__ = ()

    def __copy__(self):
        return self

    def __deepcopy__(self, memo):
        return self


# Internal indicator of special typing constructs.
# See __doc__ instance attribute for specific docs.
class _SpecialForm(_Final, _root=True):
    __slots__ = ('_name', '__doc__', '_getitem')

    def __init__(self, getitem):
        self._getitem = getitem
        self._name = getitem.__name__
        self.__doc__ = getitem.__doc__

    def __mro_entries__(self, bases):
        raise TypeError(f"Cannot subclass {self!r}")

    def __repr__(self):
        return 'typing.' + self._name

    def __reduce__(self):
        return self._name

    def __call__(self, *args, **kwds):
        raise TypeError(f"Cannot instantiate {self!r}")

    def __instancecheck__(self, obj):
        raise TypeError(f"{self} cannot be used with isinstance()")

    def __subclasscheck__(self, cls):
        raise TypeError(f"{self} cannot be used with issubclass()")

    @_tp_cache
    def __getitem__(self, parameters):
        return self._getitem(self, parameters)


class _LiteralSpecialForm(_SpecialForm, _root=True):
    @_tp_cache(typed=True)
    def __getitem__(self, parameters):
        return self._getitem(self, parameters)


@_SpecialForm
def Any(self, parameters):
    """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.
    """
    raise TypeError(f"{self} is not subscriptable")

@_SpecialForm
def NoReturn(self, parameters):
    """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.
    """
    raise TypeError(f"{self} is not subscriptable")

@_SpecialForm
def ClassVar(self, parameters):
    """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().
    """
    item = _type_check(parameters, f'{self} accepts only single type.')
    return _GenericAlias(self, (item,))

@_SpecialForm
def Final(self, parameters):
    """Special typing construct to indicate final names to type checkers.

    A final name cannot be re-assigned or overridden in a subclass.
    For example:

      MAX_SIZE: Final = 9000
      MAX_SIZE += 1  # Error reported by type checker

      class Connection:
          TIMEOUT: Final[int] = 10

      class FastConnector(Connection):
          TIMEOUT = 1  # Error reported by type checker

    There is no runtime checking of these properties.
    """
    item = _type_check(parameters, f'{self} accepts only single type.')
    return _GenericAlias(self, (item,))

@_SpecialForm
def Union(self, parameters):
    """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]

    - You cannot subclass or instantiate a union.
    - You can use Optional[X] as a shorthand for Union[X, None].
    """
    if parameters == ():
        raise TypeError("Cannot take a Union of no types.")
    if not isinstance(parameters, tuple):
        parameters = (parameters,)
    msg = "Union[arg, ...]: each arg must be a type."
    parameters = tuple(_type_check(p, msg) for p in parameters)
    parameters = _remove_dups_flatten(parameters)
    if len(parameters) == 1:
        return parameters[0]
    return _UnionGenericAlias(self, parameters)

@_SpecialForm
def Optional(self, parameters):
    """Optional type.

    Optional[X] is equivalent to Union[X, None].
    """
    arg = _type_check(parameters, f"{self} requires a single type.")
    return Union[arg, type(None)]

@_LiteralSpecialForm
def Literal(self, parameters):
    """Special typing form to define literal types (a.k.a. value types).

    This form can be used to indicate to type checkers that the corresponding
    variable or function parameter has a value equivalent to the provided
    literal (or one of several literals):

      def validate_simple(data: Any) -> Literal[True]:  # always returns True
          ...

      MODE = Literal['r', 'rb', 'w', 'wb']
      def open_helper(file: str, mode: MODE) -> str:
          ...

      open_helper('/some/path', 'r')  # Passes type check
      open_helper('/other/path', 'typo')  # Error in type checker

    Literal[...] cannot be subclassed. At runtime, an arbitrary value
    is allowed as type argument to Literal[...], but type checkers may
    impose restrictions.
    """
    # There is no '_type_check' call because arguments to Literal[...] are
    # values, not types.
    if not isinstance(parameters, tuple):
        parameters = (parameters,)

    parameters = _flatten_literal_params(parameters)

    try:
        parameters = tuple(p for p, _ in _deduplicate(list(_value_and_type_iter(parameters))))
    except TypeError:  # unhashable parameters
        pass

    return _LiteralGenericAlias(self, parameters)


@_SpecialForm
def TypeAlias(self, parameters):
    """Special marker indicating that an assignment should
    be recognized as a proper type alias definition by type
    checkers.

    For example::

        Predicate: TypeAlias = Callable[..., bool]

    It's invalid when used anywhere except as in the example above.
    """
    raise TypeError(f"{self} is not subscriptable")


@_SpecialForm
def Concatenate(self, parameters):
    """Used in conjunction with ``ParamSpec`` and ``Callable`` to represent a
    higher order function which adds, removes or transforms parameters of a
    callable.

    For example::

       Callable[Concatenate[int, P], int]

    See PEP 612 for detailed information.
    """
    if parameters == ():
        raise TypeError("Cannot take a Concatenate of no types.")
    if not isinstance(parameters, tuple):
        parameters = (parameters,)
    if not isinstance(parameters[-1], ParamSpec):
        raise TypeError("The last parameter to Concatenate should be a "
                        "ParamSpec variable.")
    msg = "Concatenate[arg, ...]: each arg must be a type."
    parameters = tuple(_type_check(p, msg) for p in parameters)
    return _ConcatenateGenericAlias(self, parameters)


@_SpecialForm
def TypeGuard(self, parameters):
    """Special typing form used to annotate the return type of a user-defined
    type guard function.  ``TypeGuard`` only accepts a single type argument.
    At runtime, functions marked this way should return a boolean.

    ``TypeGuard`` aims to benefit *type narrowing* -- a technique used by static
    type checkers to determine a more precise type of an expression within a
    program's code flow.  Usually type narrowing is done by analyzing
    conditional code flow and applying the narrowing to a block of code.  The
    conditional expression here is sometimes referred to as a "type guard".

    Sometimes it would be convenient to use a user-defined boolean function
    as a type guard.  Such a function should use ``TypeGuard[...]`` as its
    return type to alert static type checkers to this intention.

    Using  ``-> TypeGuard`` tells the static type checker that for a given
    function:

    1. The return value is a boolean.
    2. If the return value is ``True``, the type of its argument
       is the type inside ``TypeGuard``.

       For example::

          def is_str(val: Union[str, float]):
              # "isinstance" type guard
              if isinstance(val, str):
                  # Type of ``val`` is narrowed to ``str``
                  ...
              else:
                  # Else, type of ``val`` is narrowed to ``float``.
                  ...

    Strict type narrowing is not enforced -- ``TypeB`` need not be a narrower
    form of ``TypeA`` (it can even be a wider form) and this may lead to
    type-unsafe results.  The main reason is to allow for things like
    narrowing ``List[object]`` to ``List[str]`` even though the latter is not
    a subtype of the former, since ``List`` is invariant.  The responsibility of
    writing type-safe type guards is left to the user.

    ``TypeGuard`` also works with type variables.  For more information, see
    PEP 647 (User-Defined Type Guards).
    """
    item = _type_check(parameters, f'{self} accepts only single type.')
    return _GenericAlias(self, (item,))


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

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

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

    def _evaluate(self, globalns, localns, recursive_guard):
        if self.__forward_arg__ in recursive_guard:
            return self
        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
            type_ =_type_check(
                eval(self.__forward_code__, globalns, localns),
                "Forward references must evaluate to types.",
                is_argument=self.__forward_is_argument__,
            )
            self.__forward_value__ = _eval_type(
                type_, globalns, localns, recursive_guard | {self.__forward_arg__}
            )
            self.__forward_evaluated__ = True
        return self.__forward_value__

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

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

    def __repr__(self):
        return f'ForwardRef({self.__forward_arg__!r})'

class _TypeVarLike:
    """Mixin for TypeVar-like types (TypeVar and ParamSpec)."""
    def __init__(self, bound, covariant, contravariant):
        """Used to setup TypeVars and ParamSpec's bound, covariant and
        contravariant attributes.
        """
        if covariant and contravariant:
            raise ValueError("Bivariant types are not supported.")
        self.__covariant__ = bool(covariant)
        self.__contravariant__ = bool(contravariant)
        if bound:
            self.__bound__ = _type_check(bound, "Bound must be a type.")
        else:
            self.__bound__ = None

    def __or__(self, right):
        return Union[self, right]

    def __ror__(self, left):
        return Union[left, self]

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

    def __reduce__(self):
        return self.__name__


class TypeVar( _Final, _Immutable, _TypeVarLike, _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 to 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)

    Note that only type variables defined in global scope can be pickled.
    """

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

    def __init__(self, name, *constraints, bound=None,
                 covariant=False, contravariant=False):
        self.__name__ = name
        super().__init__(bound, covariant, 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)
        try:
            def_mod = sys._getframe(1).f_globals.get('__name__', '__main__')  # for pickling
        except (AttributeError, ValueError):
            def_mod = None
        if def_mod != 'typing':
            self.__module__ = def_mod


class ParamSpecArgs(_Final, _Immutable, _root=True):
    """The args for a ParamSpec object.

    Given a ParamSpec object P, P.args is an instance of ParamSpecArgs.

    ParamSpecArgs objects have a reference back to their ParamSpec:

       P.args.__origin__ is P

    This type is meant for runtime introspection and has no special meaning to
    static type checkers.
    """
    def __init__(self, origin):
        self.__origin__ = origin

    def __repr__(self):
        return f"{self.__origin__.__name__}.args"


class ParamSpecKwargs(_Final, _Immutable, _root=True):
    """The kwargs for a ParamSpec object.

    Given a ParamSpec object P, P.kwargs is an instance of ParamSpecKwargs.

    ParamSpecKwargs objects have a reference back to their ParamSpec:

       P.kwargs.__origin__ is P

    This type is meant for runtime introspection and has no special meaning to
    static type checkers.
    """
    def __init__(self, origin):
        self.__origin__ = origin

    def __repr__(self):
        return f"{self.__origin__.__name__}.kwargs"


class ParamSpec(_Final, _Immutable, _TypeVarLike, _root=True):
    """Parameter specification variable.

    Usage::

       P = ParamSpec('P')

    Parameter specification variables exist primarily for the benefit of static
    type checkers.  They are used to forward the parameter types of one
    callable to another callable, a pattern commonly found in higher order
    functions and decorators.  They are only valid when used in ``Concatenate``,
    or s the first argument to ``Callable``, or as parameters for user-defined
    Generics.  See class Generic for more information on generic types.  An
    example for annotating a decorator::

       T = TypeVar('T')
       P = ParamSpec('P')

       def add_logging(f: Callable[P, T]) -> Callable[P, T]:
           '''A type-safe decorator to add logging to a function.'''
           def inner(*args: P.args, **kwargs: P.kwargs) -> T:
               logging.info(f'{f.__name__} was called')
               return f(*args, **kwargs)
           return inner

       @add_logging
       def add_two(x: float, y: float) -> float:
           '''Add two numbers together.'''
           return x + y

    Parameter specification variables defined with covariant=True or
    contravariant=True can be used to declare covariant or contravariant
    generic types.  These keyword arguments are valid, but their actual semantics
    are yet to be decided.  See PEP 612 for details.

    Parameter specification variables can be introspected. e.g.:

       P.__name__ == 'T'
       P.__bound__ == None
       P.__covariant__ == False
       P.__contravariant__ == False

    Note that only parameter specification variables defined in global scope can
    be pickled.
    """

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

    @property
    def args(self):
        return ParamSpecArgs(self)

    @property
    def kwargs(self):
        return ParamSpecKwargs(self)

    def __init__(self, name, *, bound=None, covariant=False, contravariant=False):
        self.__name__ = name
        super().__init__(bound, covariant, contravariant)
        try:
            def_mod = sys._getframe(1).f_globals.get('__name__', '__main__')
        except (AttributeError, ValueError):
            def_mod = None
        if def_mod != 'typing':
            self.__module__ = def_mod


def _is_dunder(attr):
    return attr.startswith('__') and attr.endswith('__')

class _BaseGenericAlias(_Final, _root=True):
    """The central part of internal API.

    This represents a generic version of type 'origin' with type arguments 'params'.
    There are two kind of these aliases: user defined and special. The special ones
    are wrappers around builtin collections and ABCs in collections.abc. These must
    have 'name' always set. If 'inst' is False, then the alias can't be instantiated,
    this is used by e.g. typing.List and typing.Dict.
    """
    def __init__(self, origin, *, inst=True, name=None):
        self._inst = inst
        self._name = name
        self.__origin__ = origin
        self.__slots__ = None  # This is not documented.

    def __call__(self, *args, **kwargs):
        if not self._inst:
            raise TypeError(f"Type {self._name} cannot be instantiated; "
                            f"use {self.__origin__.__name__}() instead")
        result = self.__origin__(*args, **kwargs)
        try:
            result.__orig_class__ = self
        except AttributeError:
            pass
        return result

    def __mro_entries__(self, bases):
        res = []
        if self.__origin__ not in bases:
            res.append(self.__origin__)
        i = bases.index(self)
        for b in bases[i+1:]:
            if isinstance(b, _BaseGenericAlias) or issubclass(b, Generic):
                break
        else:
            res.append(Generic)
        return tuple(res)

    def __getattr__(self, attr):
        # We are careful for copy and pickle.
        # Also for simplicity we just don't relay all dunder names
        if '__origin__' in self.__dict__ and not _is_dunder(attr):
            return getattr(self.__origin__, attr)
        raise AttributeError(attr)

    def __setattr__(self, attr, val):
        if _is_dunder(attr) or attr in ('_name', '_inst', '_nparams'):
            super().__setattr__(attr, val)
        else:
            setattr(self.__origin__, attr, val)

    def __instancecheck__(self, obj):
        return self.__subclasscheck__(type(obj))

    def __subclasscheck__(self, cls):
        raise TypeError("Subscripted generics cannot be used with"
                        " class and instance checks")


# 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, or the non-generic version of
#   the type.
# * __args__ is a tuple of all arguments used in subscripting,
#   e.g., Dict[T, int].__args__ == (T, int).


class _GenericAlias(_BaseGenericAlias, _root=True):
    def __init__(self, origin, params, *, inst=True, name=None):
        super().__init__(origin, inst=inst, name=name)
        if not isinstance(params, tuple):
            params = (params,)
        self.__args__ = tuple(... if a is _TypingEllipsis else
                              () if a is _TypingEmpty else
                              a for a in params)
        self.__parameters__ = _collect_type_vars(params)
        if not name:
            self.__module__ = origin.__module__

    def __eq__(self, other):
        if not isinstance(other, _GenericAlias):
            return NotImplemented
        return (self.__origin__ == other.__origin__
                and self.__args__ == other.__args__)

    def __hash__(self):
        return hash((self.__origin__, self.__args__))

    def __or__(self, right):
        return Union[self, right]

    def __ror__(self, right):
        return Union[self, right]

    @_tp_cache
    def __getitem__(self, params):
        if self.__origin__ in (Generic, Protocol):
            # Can't subscript Generic[...] or Protocol[...].
            raise TypeError(f"Cannot subscript already-subscripted {self}")
        if not isinstance(params, tuple):
            params = (params,)
        params = tuple(_type_convert(p) for p in params)
        if any(isinstance(t, ParamSpec) for t in self.__parameters__):
            params = _prepare_paramspec_params(self, params)
        _check_generic(self, params, len(self.__parameters__))

        subst = dict(zip(self.__parameters__, params))
        new_args = []
        for arg in self.__args__:
            if isinstance(arg, _TypeVarLike):
                arg = subst[arg]
            elif isinstance(arg, (_GenericAlias, GenericAlias)):
                subparams = arg.__parameters__
                if subparams:
                    subargs = tuple(subst[x] for x in subparams)
                    arg = arg[subargs]
            # Required to flatten out the args for CallableGenericAlias
            if self.__origin__ == collections.abc.Callable and isinstance(arg, tuple):
                new_args.extend(arg)
            else:
                new_args.append(arg)
        return self.copy_with(tuple(new_args))

    def copy_with(self, params):
        return self.__class__(self.__origin__, params, name=self._name, inst=self._inst)

    def __repr__(self):
        if self._name:
            name = 'typing.' + self._name
        else:
            name = _type_repr(self.__origin__)
        args = ", ".join([_type_repr(a) for a in self.__args__])
        return f'{name}[{args}]'

    def __reduce__(self):
        if self._name:
            origin = globals()[self._name]
        else:
            origin = self.__origin__
        args = tuple(self.__args__)
        if len(args) == 1 and not isinstance(args[0], tuple):
            args, = args
        return operator.getitem, (origin, args)

    def __mro_entries__(self, bases):
        if self._name:  # generic version of an ABC or built-in class
            return super().__mro_entries__(bases)
        if self.__origin__ is Generic:
            if Protocol in bases:
                return ()
            i = bases.index(self)
            for b in bases[i+1:]:
                if isinstance(b, _BaseGenericAlias) and b is not self:
                    return ()
        return (self.__origin__,)


# _nparams is the number of accepted parameters, e.g. 0 for Hashable,
# 1 for List and 2 for Dict.  It may be -1 if variable number of
# parameters are accepted (needs custom __getitem__).

class _SpecialGenericAlias(_BaseGenericAlias, _root=True):
    def __init__(self, origin, nparams, *, inst=True, name=None):
        if name is None:
            name = origin.__name__
        super().__init__(origin, inst=inst, name=name)
        self._nparams = nparams
        if origin.__module__ == 'builtins':
            self.__doc__ = f'A generic version of {origin.__qualname__}.'
        else:
            self.__doc__ = f'A generic version of {origin.__module__}.{origin.__qualname__}.'

    @_tp_cache
    def __getitem__(self, params):
        if not isinstance(params, tuple):
            params = (params,)
        msg = "Parameters to generic types must be types."
        params = tuple(_type_check(p, msg) for p in params)
        _check_generic(self, params, self._nparams)
        return self.copy_with(params)

    def copy_with(self, params):
        return _GenericAlias(self.__origin__, params,
                             name=self._name, inst=self._inst)

    def __repr__(self):
        return 'typing.' + self._name

    def __subclasscheck__(self, cls):
        if isinstance(cls, _SpecialGenericAlias):
            return issubclass(cls.__origin__, self.__origin__)
        if not isinstance(cls, _GenericAlias):
            return issubclass(cls, self.__origin__)
        return super().__subclasscheck__(cls)

    def __reduce__(self):
        return self._name

    def __or__(self, right):
        return Union[self, right]

    def __ror__(self, right):
        return Union[self, right]

class _CallableGenericAlias(_GenericAlias, _root=True):
    def __repr__(self):
        assert self._name == 'Callable'
        args = self.__args__
        if len(args) == 2 and (args[0] is Ellipsis
                               or isinstance(args[0], (ParamSpec, _ConcatenateGenericAlias))):
            return super().__repr__()
        return (f'typing.Callable'
                f'[[{", ".join([_type_repr(a) for a in args[:-1]])}], '
                f'{_type_repr(args[-1])}]')

    def __reduce__(self):
        args = self.__args__
        if not (len(args) == 2 and (args[0] is Ellipsis
                                    or isinstance(args[0], (ParamSpec, _ConcatenateGenericAlias)))):
            args = list(args[:-1]), args[-1]
        return operator.getitem, (Callable, args)


class _CallableType(_SpecialGenericAlias, _root=True):
    def copy_with(self, params):
        return _CallableGenericAlias(self.__origin__, params,
                                     name=self._name, inst=self._inst)

    def __getitem__(self, params):
        if not isinstance(params, tuple) or len(params) != 2:
            raise TypeError("Callable must be used as "
                            "Callable[[arg, ...], result].")
        args, result = params
        # This relaxes what args can be on purpose to allow things like
        # PEP 612 ParamSpec.  Responsibility for whether a user is using
        # Callable[...] properly is deferred to static type checkers.
        if isinstance(args, list):
            params = (tuple(args), result)
        else:
            params = (args, result)
        return self.__getitem_inner__(params)

    @_tp_cache
    def __getitem_inner__(self, params):
        args, result = params
        msg = "Callable[args, result]: result must be a type."
        result = _type_check(result, msg)
        if args is Ellipsis:
            return self.copy_with((_TypingEllipsis, result))
        if not isinstance(args, tuple):
            args = (args,)
        args = tuple(_type_convert(arg) for arg in args)
        params = args + (result,)
        return self.copy_with(params)


class _TupleType(_SpecialGenericAlias, _root=True):
    @_tp_cache
    def __getitem__(self, params):
        if params == ():
            return self.copy_with((_TypingEmpty,))
        if not isinstance(params, tuple):
            params = (params,)
        if len(params) == 2 and params[1] is ...:
            msg = "Tuple[t, ...]: t must be a type."
            p = _type_check(params[0], msg)
            return self.copy_with((p, _TypingEllipsis))
        msg = "Tuple[t0, t1, ...]: each t must be a type."
        params = tuple(_type_check(p, msg) for p in params)
        return self.copy_with(params)


class _UnionGenericAlias(_GenericAlias, _root=True):
    def copy_with(self, params):
        return Union[params]

    def __eq__(self, other):
        if not isinstance(other, _UnionGenericAlias):
            return NotImplemented
        return set(self.__args__) == set(other.__args__)

    def __hash__(self):
        return hash(frozenset(self.__args__))

    def __repr__(self):
        args = self.__args__
        if len(args) == 2:
            if args[0] is type(None):
                return f'typing.Optional[{_type_repr(args[1])}]'
            elif args[1] is type(None):
                return f'typing.Optional[{_type_repr(args[0])}]'
        return super().__repr__()

    def __instancecheck__(self, obj):
        return self.__subclasscheck__(type(obj))

    def __subclasscheck__(self, cls):
        for arg in self.__args__:
            if issubclass(cls, arg):
                return True


def _value_and_type_iter(parameters):
    return ((p, type(p)) for p in parameters)


class _LiteralGenericAlias(_GenericAlias, _root=True):

    def __eq__(self, other):
        if not isinstance(other, _LiteralGenericAlias):
            return NotImplemented

        return set(_value_and_type_iter(self.__args__)) == set(_value_and_type_iter(other.__args__))

    def __hash__(self):
        return hash(frozenset(_value_and_type_iter(self.__args__)))


class _ConcatenateGenericAlias(_GenericAlias, _root=True):
    pass


class Generic:
    """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__ = ()
    _is_protocol = False

    @_tp_cache
    def __class_getitem__(cls, params):
        if not isinstance(params, tuple):
            params = (params,)
        if not params and cls is not Tuple:
            raise TypeError(
                f"Parameter list to {cls.__qualname__}[...] cannot be empty")
        params = tuple(_type_convert(p) for p in params)
        if cls in (Generic, Protocol):
            # Generic and Protocol can only be subscripted with unique type variables.
            if not all(isinstance(p, _TypeVarLike) for p in params):
                raise TypeError(
                    f"Parameters to {cls.__name__}[...] must all be type variables "
                    f"or parameter specification variables.")
            if len(set(params)) != len(params):
                raise TypeError(
                    f"Parameters to {cls.__name__}[...] must all be unique")
        else:
            # Subscripting a regular Generic subclass.
            if any(isinstance(t, ParamSpec) for t in cls.__parameters__):
                params = _prepare_paramspec_params(cls, params)
            _check_generic(cls, params, len(cls.__parameters__))
        return _GenericAlias(cls, params)

    def __init_subclass__(cls, *args, **kwargs):
        super().__init_subclass__(*args, **kwargs)
        tvars = []
        if '__orig_bases__' in cls.__dict__:
            error = Generic in cls.__orig_bases__
        else:
            error = Generic in cls.__bases__ and cls.__name__ != 'Protocol'
        if error:
            raise TypeError("Cannot inherit from plain Generic")
        if '__orig_bases__' in cls.__dict__:
            tvars = _collect_type_vars(cls.__orig_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 cls.__orig_bases__:
                if (isinstance(base, _GenericAlias) and
                        base.__origin__ is Generic):
                    if gvars is not None:
                        raise TypeError(
                            "Cannot inherit from Generic[...] multiple types.")
                    gvars = base.__parameters__
            if gvars is not None:
                tvarset = set(tvars)
                gvarset = set(gvars)
                if not tvarset <= gvarset:
                    s_vars = ', '.join(str(t) for t in tvars if t not in gvarset)
                    s_args = ', '.join(str(g) for g in gvars)
                    raise TypeError(f"Some type variables ({s_vars}) are"
                                    f" not listed in Generic[{s_args}]")
                tvars = gvars
        cls.__parameters__ = tuple(tvars)


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)."""


_TYPING_INTERNALS = ['__parameters__', '__orig_bases__',  '__orig_class__',
                     '_is_protocol', '_is_runtime_protocol']

_SPECIAL_NAMES = ['__abstractmethods__', '__annotations__', '__dict__', '__doc__',
                  '__init__', '__module__', '__new__', '__slots__',
                  '__subclasshook__', '__weakref__', '__class_getitem__']

# These special attributes will be not collected as protocol members.
EXCLUDED_ATTRIBUTES = _TYPING_INTERNALS + _SPECIAL_NAMES + ['_MutableMapping__marker']


def _get_protocol_attrs(cls):
    """Collect protocol members from a protocol class objects.

    This includes names actually defined in the class dictionary, as well
    as names that appear in annotations. Special names (above) are skipped.
    """
    attrs = set()
    for base in cls.__mro__[:-1]:  # without object
        if base.__name__ in ('Protocol', 'Generic'):
            continue
        annotations = getattr(base, '__annotations__', {})
        for attr in list(base.__dict__.keys()) + list(annotations.keys()):
            if not attr.startswith('_abc_') and attr not in EXCLUDED_ATTRIBUTES:
                attrs.add(attr)
    return attrs


def _is_callable_members_only(cls):
    # PEP 544 prohibits using issubclass() with protocols that have non-method members.
    return all(callable(getattr(cls, attr, None)) for attr in _get_protocol_attrs(cls))


def _no_init(self, *args, **kwargs):
    if type(self)._is_protocol:
        raise TypeError('Protocols cannot be instantiated')


def _allow_reckless_class_checks(depth=3):
    """Allow instance and class checks for special stdlib modules.

    The abc and functools modules indiscriminately call isinstance() and
    issubclass() on the whole MRO of a user class, which may contain protocols.
    """
    try:
        return sys._getframe(depth).f_globals['__name__'] in ['abc', 'functools']
    except (AttributeError, ValueError):  # For platforms without _getframe().
        return True


_PROTO_ALLOWLIST = {
    'collections.abc': [
        'Callable', 'Awaitable', 'Iterable', 'Iterator', 'AsyncIterable',
        'Hashable', 'Sized', 'Container', 'Collection', 'Reversible',
    ],
    'contextlib': ['AbstractContextManager', 'AbstractAsyncContextManager'],
}


class _ProtocolMeta(ABCMeta):
    # This metaclass is really unfortunate and exists only because of
    # the lack of __instancehook__.
    def __instancecheck__(cls, instance):
        # We need this method for situations where attributes are
        # assigned in __init__.
        if (
            getattr(cls, '_is_protocol', False) and
            not getattr(cls, '_is_runtime_protocol', False) and
            not _allow_reckless_class_checks(depth=2)
        ):
            raise TypeError("Instance and class checks can only be used with"
                            " @runtime_checkable protocols")

        if ((not getattr(cls, '_is_protocol', False) or
                _is_callable_members_only(cls)) and
                issubclass(instance.__class__, cls)):
            return True
        if cls._is_protocol:
            if all(hasattr(instance, attr) and
                    # All *methods* can be blocked by setting them to None.
                    (not callable(getattr(cls, attr, None)) or
                     getattr(instance, attr) is not None)
                    for attr in _get_protocol_attrs(cls)):
                return True
        return super().__instancecheck__(instance)


class Protocol(Generic, metaclass=_ProtocolMeta):
    """Base class for protocol classes.

    Protocol classes are defined as::

        class Proto(Protocol):
            def meth(self) -> int:
                ...

    Such classes are primarily used with static type checkers that recognize
    structural subtyping (static duck-typing), for example::

        class C:
            def meth(self) -> int:
                return 0

        def func(x: Proto) -> int:
            return x.meth()

        func(C())  # Passes static type check

    See PEP 544 for details. Protocol classes decorated with
    @typing.runtime_checkable act as simple-minded runtime protocols that check
    only the presence of given attributes, ignoring their type signatures.
    Protocol classes can be generic, they are defined as::

        class GenProto(Protocol[T]):
            def meth(self) -> T:
                ...
    """
    __slots__ = ()
    _is_protocol = True
    _is_runtime_protocol = False

    def __init_subclass__(cls, *args, **kwargs):
        super().__init_subclass__(*args, **kwargs)

        # Determine if this is a protocol or a concrete subclass.
        if not cls.__dict__.get('_is_protocol', False):
            cls._is_protocol = any(b is Protocol for b in cls.__bases__)

        # Set (or override) the protocol subclass hook.
        def _proto_hook(other):
            if not cls.__dict__.get('_is_protocol', False):
                return NotImplemented

            # First, perform various sanity checks.
            if not getattr(cls, '_is_runtime_protocol', False):
                if _allow_reckless_class_checks():
                    return NotImplemented
                raise TypeError("Instance and class checks can only be used with"
                                " @runtime_checkable protocols")
            if not _is_callable_members_only(cls):
                if _allow_reckless_class_checks():
                    return NotImplemented
                raise TypeError("Protocols with non-method members"
                                " don't support issubclass()")
            if not isinstance(other, type):
                # Same error message as for issubclass(1, int).
                raise TypeError('issubclass() arg 1 must be a class')

            # Second, perform the actual structural compatibility check.
            for attr in _get_protocol_attrs(cls):
                for base in other.__mro__:
                    # Check if the members appears in the class dictionary...
                    if attr in base.__dict__:
                        if base.__dict__[attr] is None:
                            return NotImplemented
                        break

                    # ...or in annotations, if it is a sub-protocol.
                    annotations = getattr(base, '__annotations__', {})
                    if (isinstance(annotations, collections.abc.Mapping) and
                            attr in annotations and
                            issubclass(other, Generic) and other._is_protocol):
                        break
                else:
                    return NotImplemented
            return True

        if '__subclasshook__' not in cls.__dict__:
            cls.__subclasshook__ = _proto_hook

        # We have nothing more to do for non-protocols...
        if not cls._is_protocol:
            return

        # ... otherwise check consistency of bases, and prohibit instantiation.
        for base in cls.__bases__:
            if not (base in (object, Generic) or
                    base.__module__ in _PROTO_ALLOWLIST and
                    base.__name__ in _PROTO_ALLOWLIST[base.__module__] or
                    issubclass(base, Generic) and base._is_protocol):
                raise TypeError('Protocols can only inherit from other'
                                ' protocols, got %r' % base)
        cls.__init__ = _no_init


class _AnnotatedAlias(_GenericAlias, _root=True):
    """Runtime representation of an annotated type.

    At its core 'Annotated[t, dec1, dec2, ...]' is an alias for the type 't'
    with extra annotations. The alias behaves like a normal typing alias,
    instantiating is the same as instantiating the underlying type, binding
    it to types is also the same.
    """
    def __init__(self, origin, metadata):
        if isinstance(origin, _AnnotatedAlias):
            metadata = origin.__metadata__ + metadata
            origin = origin.__origin__
        super().__init__(origin, origin)
        self.__metadata__ = metadata

    def copy_with(self, params):
        assert len(params) == 1
        new_type = params[0]
        return _AnnotatedAlias(new_type, self.__metadata__)

    def __repr__(self):
        return "typing.Annotated[{}, {}]".format(
            _type_repr(self.__origin__),
            ", ".join(repr(a) for a in self.__metadata__)
        )

    def __reduce__(self):
        return operator.getitem, (
            Annotated, (self.__origin__,) + self.__metadata__
        )

    def __eq__(self, other):
        if not isinstance(other, _AnnotatedAlias):
            return NotImplemented
        return (self.__origin__ == other.__origin__
                and self.__metadata__ == other.__metadata__)

    def __hash__(self):
        return hash((self.__origin__, self.__metadata__))


class Annotated:
    """Add context specific metadata to a type.

    Example: Annotated[int, runtime_check.Unsigned] indicates to the
    hypothetical runtime_check module that this type is an unsigned int.
    Every other consumer of this type can ignore this metadata and treat
    this type as int.

    The first argument to Annotated must be a valid type.

    Details:

    - It's an error to call `Annotated` with less than two arguments.
    - Nested Annotated are flattened::

        Annotated[Annotated[T, Ann1, Ann2], Ann3] == Annotated[T, Ann1, Ann2, Ann3]

    - Instantiating an annotated type is equivalent to instantiating the
    underlying type::

        Annotated[C, Ann1](5) == C(5)

    - Annotated can be used as a generic type alias::

        Optimized = Annotated[T, runtime.Optimize()]
        Optimized[int] == Annotated[int, runtime.Optimize()]

        OptimizedList = Annotated[List[T], runtime.Optimize()]
        OptimizedList[int] == Annotated[List[int], runtime.Optimize()]
    """

    __slots__ = ()

    def __new__(cls, *args, **kwargs):
        raise TypeError("Type Annotated cannot be instantiated.")

    @_tp_cache
    def __class_getitem__(cls, params):
        if not isinstance(params, tuple) or len(params) < 2:
            raise TypeError("Annotated[...] should be used "
                            "with at least two arguments (a type and an "
                            "annotation).")
        msg = "Annotated[t, ...]: t must be a type."
        origin = _type_check(params[0], msg)
        metadata = tuple(params[1:])
        return _AnnotatedAlias(origin, metadata)

    def __init_subclass__(cls, *args, **kwargs):
        raise TypeError(
            "Cannot subclass {}.Annotated".format(cls.__module__)
        )


def runtime_checkable(cls):
    """Mark a protocol class as a runtime protocol.

    Such protocol can be used with isinstance() and issubclass().
    Raise TypeError if applied to a non-protocol class.
    This allows a simple-minded structural check very similar to
    one trick ponies in collections.abc such as Iterable.
    For example::

        @runtime_checkable
        class Closable(Protocol):
            def close(self): ...

        assert isinstance(open('/some/file'), Closable)

    Warning: this will check only the presence of the required methods,
    not their type signatures!
    """
    if not issubclass(cls, Generic) or not cls._is_protocol:
        raise TypeError('@runtime_checkable can be only applied to protocol classes,'
                        ' got %r' % cls)
    cls._is_runtime_protocol = True
    return cls


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, include_extras=False):
    """Return type hints for an object.

    This is often the same as obj.__annotations__, but it handles
    forward references encoded as string literals, adds Optional[t] if a
    default value equal to None is set and recursively replaces all
    'Annotated[T, ...]' with 'T' (unless 'include_extras=True').

    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 (or the respective module's globals for classes),
      and these are also used as the locals.  If the object does not appear
      to have globals, an empty dictionary is used.  For classes, the search
      order is globals first then locals.

    - 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 {}
    # Classes require a special treatment.
    if isinstance(obj, type):
        hints = {}
        for base in reversed(obj.__mro__):
            if globalns is None:
                try:
                    base_globals = sys.modules[base.__module__].__dict__
                except KeyError:
                    continue
            else:
                base_globals = globalns
            ann = base.__dict__.get('__annotations__', {})
            if isinstance(ann, types.GetSetDescriptorType):
                ann = {}
            base_locals = dict(vars(base)) if localns is None else localns
            if localns is None and globalns is None:
                # This is surprising, but required.  Before Python 3.10,
                # get_type_hints only evaluated the globalns of
                # a class.  To maintain backwards compatibility, we reverse
                # the globalns and localns order so that eval() looks into
                # *base_globals* first rather than *base_locals*.
                # This only affects ForwardRefs.
                base_globals, base_locals = base_locals, base_globals
            for name, value in ann.items():
                if value is None:
                    value = type(None)
                if isinstance(value, str):
                    value = ForwardRef(value, is_argument=False)
                value = _eval_type(value, base_globals, base_locals)
                hints[name] = value
        return hints if include_extras else {k: _strip_annotations(t) for k, t in hints.items()}

    if globalns is None:
        if isinstance(obj, types.ModuleType):
            globalns = obj.__dict__
        else:
            nsobj = obj
            # Find globalns for the unwrapped object.
            while hasattr(nsobj, '__wrapped__'):
                nsobj = nsobj.__wrapped__
            globalns = getattr(nsobj, '__globals__', {})
        if localns is None:
            localns = globalns
    elif localns is None:
        localns = globalns
    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 if include_extras else {k: _strip_annotations(t) for k, t in hints.items()}


def _strip_annotations(t):
    """Strips the annotations from a given type.
    """
    if isinstance(t, _AnnotatedAlias):
        return _strip_annotations(t.__origin__)
    if isinstance(t, _GenericAlias):
        stripped_args = tuple(_strip_annotations(a) for a in t.__args__)
        if stripped_args == t.__args__:
            return t
        return t.copy_with(stripped_args)
    if isinstance(t, GenericAlias):
        stripped_args = tuple(_strip_annotations(a) for a in t.__args__)
        if stripped_args == t.__args__:
            return t
        return GenericAlias(t.__origin__, stripped_args)
    return t


def get_origin(tp):
    """Get the unsubscripted version of a type.

    This supports generic types, Callable, Tuple, Union, Literal, Final, ClassVar
    and Annotated. Return None for unsupported types. Examples::

        get_origin(Literal[42]) is Literal
        get_origin(int) is None
        get_origin(ClassVar[int]) is ClassVar
        get_origin(Generic) is Generic
        get_origin(Generic[T]) is Generic
        get_origin(Union[T, int]) is Union
        get_origin(List[Tuple[T, T]][int]) == list
        get_origin(P.args) is P
    """
    if isinstance(tp, _AnnotatedAlias):
        return Annotated
    if isinstance(tp, (_BaseGenericAlias, GenericAlias,
                       ParamSpecArgs, ParamSpecKwargs)):
        return tp.__origin__
    if tp is Generic:
        return Generic
    if isinstance(tp, types.Union):
        return types.Union
    return None


def get_args(tp):
    """Get type arguments with all substitutions performed.

    For unions, basic simplifications used by Union constructor are performed.
    Examples::
        get_args(Dict[str, int]) == (str, int)
        get_args(int) == ()
        get_args(Union[int, Union[T, int], str][int]) == (int, str)
        get_args(Union[int, Tuple[T, int]][str]) == (int, Tuple[str, int])
        get_args(Callable[[], T][int]) == ([], int)
    """
    if isinstance(tp, _AnnotatedAlias):
        return (tp.__origin__,) + tp.__metadata__
    if isinstance(tp, (_GenericAlias, GenericAlias)):
        res = tp.__args__
        if (tp.__origin__ is collections.abc.Callable
                and not (res[0] is Ellipsis
                         or isinstance(res[0], (ParamSpec, _ConcatenateGenericAlias)))):
            res = (list(res[:-1]), res[-1])
        return res
    if isinstance(tp, types.Union):
        return tp.__args__
    return ()


def is_typeddict(tp):
    """Check if an annotation is a TypedDict class

    For example::
        class Film(TypedDict):
            title: str
            year: int

        is_typeddict(Film)  # => True
        is_typeddict(Union[list, str])  # => False
    """
    return isinstance(tp, _TypedDictMeta)


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,):
                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


def final(f):
    """A decorator to indicate final methods and final classes.

    Use this decorator to indicate to type checkers that the decorated
    method cannot be overridden, and decorated class cannot be subclassed.
    For example:

      class Base:
          @final
          def done(self) -> None:
              ...
      class Sub(Base):
          def done(self) -> None:  # Error reported by type checker
                ...

      @final
      class Leaf:
          ...
      class Other(Leaf):  # Error reported by type checker
          ...

    There is no runtime checking of these properties.
    """
    return f


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

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


# Various ABCs mimicking those in collections.abc.
_alias = _SpecialGenericAlias

Hashable = _alias(collections.abc.Hashable, 0)  # Not generic.
Awaitable = _alias(collections.abc.Awaitable, 1)
Coroutine = _alias(collections.abc.Coroutine, 3)
AsyncIterable = _alias(collections.abc.AsyncIterable, 1)
AsyncIterator = _alias(collections.abc.AsyncIterator, 1)
Iterable = _alias(collections.abc.Iterable, 1)
Iterator = _alias(collections.abc.Iterator, 1)
Reversible = _alias(collections.abc.Reversible, 1)
Sized = _alias(collections.abc.Sized, 0)  # Not generic.
Container = _alias(collections.abc.Container, 1)
Collection = _alias(collections.abc.Collection, 1)
Callable = _CallableType(collections.abc.Callable, 2)
Callable.__doc__ = \
    """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.
    """
AbstractSet = _alias(collections.abc.Set, 1, name='AbstractSet')
MutableSet = _alias(collections.abc.MutableSet, 1)
# NOTE: Mapping is only covariant in the value type.
Mapping = _alias(collections.abc.Mapping, 2)
MutableMapping = _alias(collections.abc.MutableMapping, 2)
Sequence = _alias(collections.abc.Sequence, 1)
MutableSequence = _alias(collections.abc.MutableSequence, 1)
ByteString = _alias(collections.abc.ByteString, 0)  # Not generic
# Tuple accepts variable number of parameters.
Tuple = _TupleType(tuple, -1, inst=False, name='Tuple')
Tuple.__doc__ = \
    """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, ...].
    """
List = _alias(list, 1, inst=False, name='List')
Deque = _alias(collections.deque, 1, name='Deque')
Set = _alias(set, 1, inst=False, name='Set')
FrozenSet = _alias(frozenset, 1, inst=False, name='FrozenSet')
MappingView = _alias(collections.abc.MappingView, 1)
KeysView = _alias(collections.abc.KeysView, 1)
ItemsView = _alias(collections.abc.ItemsView, 2)
ValuesView = _alias(collections.abc.ValuesView, 1)
ContextManager = _alias(contextlib.AbstractContextManager, 1, name='ContextManager')
AsyncContextManager = _alias(contextlib.AbstractAsyncContextManager, 1, name='AsyncContextManager')
Dict = _alias(dict, 2, inst=False, name='Dict')
DefaultDict = _alias(collections.defaultdict, 2, name='DefaultDict')
OrderedDict = _alias(collections.OrderedDict, 2)
Counter = _alias(collections.Counter, 1)
ChainMap = _alias(collections.ChainMap, 2)
Generator = _alias(collections.abc.Generator, 3)
AsyncGenerator = _alias(collections.abc.AsyncGenerator, 2)
Type = _alias(type, 1, inst=False, name='Type')
Type.__doc__ = \
    """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.
    """


@runtime_checkable
class SupportsInt(Protocol):
    """An ABC with one abstract method __int__."""
    __slots__ = ()

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


@runtime_checkable
class SupportsFloat(Protocol):
    """An ABC with one abstract method __float__."""
    __slots__ = ()

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


@runtime_checkable
class SupportsComplex(Protocol):
    """An ABC with one abstract method __complex__."""
    __slots__ = ()

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


@runtime_checkable
class SupportsBytes(Protocol):
    """An ABC with one abstract method __bytes__."""
    __slots__ = ()

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


@runtime_checkable
class SupportsIndex(Protocol):
    """An ABC with one abstract method __index__."""
    __slots__ = ()

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


@runtime_checkable
class SupportsAbs(Protocol[T_co]):
    """An ABC with one abstract method __abs__ that is covariant in its return type."""
    __slots__ = ()

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


@runtime_checkable
class SupportsRound(Protocol[T_co]):
    """An ABC with one abstract method __round__ that is covariant in its return type."""
    __slots__ = ()

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


def _make_nmtuple(name, types, module, defaults = ()):
    fields = [n for n, t in types]
    types = {n: _type_check(t, f"field {n} annotation must be a type")
             for n, t in types}
    nm_tpl = collections.namedtuple(name, fields,
                                    defaults=defaults, module=module)
    nm_tpl.__annotations__ = nm_tpl.__new__.__annotations__ = types
    return nm_tpl


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

_special = frozenset({'__module__', '__name__', '__annotations__'})


class NamedTupleMeta(type):

    def __new__(cls, typename, bases, ns):
        assert bases[0] is _NamedTuple
        types = ns.get('__annotations__', {})
        default_names = []
        for field_name in types:
            if field_name in ns:
                default_names.append(field_name)
            elif default_names:
                raise TypeError(f"Non-default namedtuple field {field_name} "
                                f"cannot follow default field"
                                f"{'s' if len(default_names) > 1 else ''} "
                                f"{', '.join(default_names)}")
        nm_tpl = _make_nmtuple(typename, types.items(),
                               defaults=[ns[n] for n in default_names],
                               module=ns['__module__'])
        # 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


def NamedTuple(typename, fields=None, /, **kwargs):
    """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 an extra __annotations__ attribute, giving a
    dict that maps field names to types.  (The field names are also 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)])
    """
    if fields is None:
        fields = kwargs.items()
    elif kwargs:
        raise TypeError("Either list of fields or keywords"
                        " can be provided to NamedTuple, not both")
    try:
        module = sys._getframe(1).f_globals.get('__name__', '__main__')
    except (AttributeError, ValueError):
        module = None
    return _make_nmtuple(typename, fields, module=module)

_NamedTuple = type.__new__(NamedTupleMeta, 'NamedTuple', (), {})

def _namedtuple_mro_entries(bases):
    if len(bases) > 1:
        raise TypeError("Multiple inheritance with NamedTuple is not supported")
    assert bases[0] is NamedTuple
    return (_NamedTuple,)

NamedTuple.__mro_entries__ = _namedtuple_mro_entries


class _TypedDictMeta(type):
    def __new__(cls, name, bases, ns, total=True):
        """Create new typed dict class object.

        This method is called when TypedDict is subclassed,
        or when TypedDict is instantiated. This way
        TypedDict supports all three syntax forms described in its docstring.
        Subclasses and instances of TypedDict return actual dictionaries.
        """
        for base in bases:
            if type(base) is not _TypedDictMeta:
                raise TypeError('cannot inherit from both a TypedDict type '
                                'and a non-TypedDict base class')
        tp_dict = type.__new__(_TypedDictMeta, name, (dict,), ns)

        annotations = {}
        own_annotations = ns.get('__annotations__', {})
        own_annotation_keys = set(own_annotations.keys())
        msg = "TypedDict('Name', {f0: t0, f1: t1, ...}); each t must be a type"
        own_annotations = {
            n: _type_check(tp, msg) for n, tp in own_annotations.items()
        }
        required_keys = set()
        optional_keys = set()

        for base in bases:
            annotations.update(base.__dict__.get('__annotations__', {}))
            required_keys.update(base.__dict__.get('__required_keys__', ()))
            optional_keys.update(base.__dict__.get('__optional_keys__', ()))

        annotations.update(own_annotations)
        if total:
            required_keys.update(own_annotation_keys)
        else:
            optional_keys.update(own_annotation_keys)

        tp_dict.__annotations__ = annotations
        tp_dict.__required_keys__ = frozenset(required_keys)
        tp_dict.__optional_keys__ = frozenset(optional_keys)
        if not hasattr(tp_dict, '__total__'):
            tp_dict.__total__ = total
        return tp_dict

    __call__ = dict  # static method

    def __subclasscheck__(cls, other):
        # Typed dicts are only for static structural subtyping.
        raise TypeError('TypedDict does not support instance and class checks')

    __instancecheck__ = __subclasscheck__


def TypedDict(typename, fields=None, /, *, total=True, **kwargs):
    """A simple typed namespace. At runtime it is equivalent to a plain dict.

    TypedDict creates a dictionary type that expects all of its
    instances to have a certain set of keys, where each key is
    associated with a value of a consistent type. This expectation
    is not checked at runtime but is only enforced by type checkers.
    Usage::

        class Point2D(TypedDict):
            x: int
            y: int
            label: str

        a: Point2D = {'x': 1, 'y': 2, 'label': 'good'}  # OK
        b: Point2D = {'z': 3, 'label': 'bad'}           # Fails type check

        assert Point2D(x=1, y=2, label='first') == dict(x=1, y=2, label='first')

    The type info can be accessed via the Point2D.__annotations__ dict, and
    the Point2D.__required_keys__ and Point2D.__optional_keys__ frozensets.
    TypedDict supports two additional equivalent forms::

        Point2D = TypedDict('Point2D', x=int, y=int, label=str)
        Point2D = TypedDict('Point2D', {'x': int, 'y': int, 'label': str})

    By default, all keys must be present in a TypedDict. It is possible
    to override this by specifying totality.
    Usage::

        class point2D(TypedDict, total=False):
            x: int
            y: int

    This means that a point2D TypedDict can have any of the keys omitted.A type
    checker is only expected to support a literal False or True as the value of
    the total argument. True is the default, and makes all items defined in the
    class body be required.

    The class syntax is only supported in Python 3.6+, while two other
    syntax forms work for Python 2.7 and 3.2+
    """
    if fields is None:
        fields = kwargs
    elif kwargs:
        raise TypeError("TypedDict takes either a dict or keyword arguments,"
                        " but not both")

    ns = {'__annotations__': dict(fields)}
    try:
        # Setting correct module is necessary to make typed dict classes pickleable.
        ns['__module__'] = sys._getframe(1).f_globals.get('__name__', '__main__')
    except (AttributeError, ValueError):
        pass

    return _TypedDictMeta(typename, (), ns, total=total)

_TypedDict = type.__new__(_TypedDictMeta, 'TypedDict', (), {})
TypedDict.__mro_entries__ = lambda bases: (_TypedDict,)


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__ = ()

    @property
    @abstractmethod
    def mode(self) -> str:
        pass

    @property
    @abstractmethod
    def name(self) -> str:
        pass

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

    @property
    @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__ = ()

    @property
    @abstractmethod
    def buffer(self) -> BinaryIO:
        pass

    @property
    @abstractmethod
    def encoding(self) -> str:
        pass

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

    @property
    @abstractmethod
    def line_buffering(self) -> bool:
        pass

    @property
    @abstractmethod
    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 = _alias(stdlib_re.Pattern, 1)
Match = _alias(stdlib_re.Match, 1)

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

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


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