cpython/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, Never, ClassVar, Union, Optional, Concatenate, Unpack
* 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
import warnings
from types import WrapperDescriptorType, MethodWrapperType, MethodDescriptorType, GenericAlias


try:
    from _typing import _idfunc
except ImportError:
    def _idfunc(_, x):
        return x

# 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',
    'TypeVarTuple',
    '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',
    'assert_type',
    'assert_never',
    'cast',
    'final',
    'get_args',
    'get_origin',
    'get_type_hints',
    'is_typeddict',
    'Never',
    'NewType',
    'no_type_check',
    'no_type_check_decorator',
    'NoReturn',
    'overload',
    'ParamSpecArgs',
    'ParamSpecKwargs',
    'reveal_type',
    'runtime_checkable',
    'Self',
    'Text',
    'TYPE_CHECKING',
    'TypeAlias',
    'TypeGuard',
    'Unpack',
]

# 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, module=None, *, allow_special_forms=False):
    """For converting None to type(None), and strings to ForwardRef."""
    if arg is None:
        return type(None)
    if isinstance(arg, str):
        return ForwardRef(arg, module=module, is_class=allow_special_forms)
    return arg


def _type_check(arg, msg, is_argument=True, module=None, *, allow_special_forms=False):
    """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 not allow_special_forms:
        invalid_generic_forms += (ClassVar,)
        if is_argument:
            invalid_generic_forms += (Final,)

    arg = _type_convert(arg, module=module, allow_special_forms=allow_special_forms)
    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, Never, Self, TypeAlias):
        return arg
    if allow_special_forms and arg in (ClassVar, Final):
        return arg
    if isinstance(arg, _SpecialForm) or arg in (Generic, Protocol):
        raise TypeError(f"Plain {arg} is not valid as type argument")
    if type(arg) is tuple:
        raise TypeError(f"{msg} Got {arg!r:.100}.")
    return arg


def _is_param_expr(arg):
    return arg is ... or isinstance(arg,
            (tuple, list, ParamSpec, _ConcatenateGenericAlias))


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_parameters(args):
    """Collect all type variables and parameter specifications in args
    in order of first appearance (lexicographic order). For example::

        _collect_parameters((T, Callable[P, T])) == (T, P)
    """
    parameters = []
    for t in args:
        if hasattr(t, '__typing_subst__'):
            if t not in parameters:
                parameters.append(t)
        else:
            for x in getattr(t, '__parameters__', ()):
                if x not in parameters:
                    parameters.append(x)
    return tuple(parameters)


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'} arguments 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 params and not _is_param_expr(params[0])):
        assert isinstance(cls.__parameters__[0], ParamSpec)
        return (params,)
    else:
        _check_generic(cls, params, len(cls.__parameters__))
        _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.UnionType)):
            params.extend(p.__args__)
        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 infinite recursion with a recursive
    ForwardRef.
    """
    if isinstance(t, ForwardRef):
        return t._evaluate(globalns, localns, recursive_guard)
    if isinstance(t, (_GenericAlias, GenericAlias, types.UnionType)):
        if isinstance(t, GenericAlias):
            args = tuple(
                ForwardRef(arg) if isinstance(arg, str) else arg
                for arg in t.__args__
            )
            t = t.__origin__[args]
        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)
        if isinstance(t, types.UnionType):
            return functools.reduce(operator.or_, ev_args)
        else:
            return t.copy_with(ev_args)
    return t


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

    __slots__ = ('__weakref__',)

    def __init_subclass__(cls, /, *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 __getattr__(self, item):
        if item in {'__name__', '__qualname__'}:
            return self._name

        raise AttributeError(item)

    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 __or__(self, other):
        return Union[self, other]

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

    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):
    def __getitem__(self, parameters):
        if not isinstance(parameters, tuple):
            parameters = (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')

    NoReturn can also be used as a bottom type, a type that
    has no values. Starting in Python 3.11, the Never type should
    be used for this concept instead. Type checkers should treat the two
    equivalently.

    """
    raise TypeError(f"{self} is not subscriptable")

# This is semantically identical to NoReturn, but it is implemented
# separately so that type checkers can distinguish between the two
# if they want.
@_SpecialForm
def Never(self, parameters):
    """The bottom type, a type that has no members.

    This can be used to define a function that should never be
    called, or a function that never returns::

        from typing import Never

        def never_call_me(arg: Never) -> None:
            pass

        def int_or_str(arg: int | str) -> None:
            never_call_me(arg)  # type checker error
            match arg:
                case int():
                    print("It's an int")
                case str():
                    print("It's a str")
                case _:
                    never_call_me(arg)  # ok, arg is of type Never

    """
    raise TypeError(f"{self} is not subscriptable")


@_SpecialForm
def Self(self, parameters):
    """Used to spell the type of "self" in classes.

    Example::

      from typing import Self

      class Foo:
          def returns_self(self) -> Self:
              ...
              return self

    This is especially useful for:
        - classmethods that are used as alternative constructors
        - annotating an `__enter__` method which returns self
    """
    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]
    if len(parameters) == 2 and type(None) in parameters:
        return _UnionGenericAlias(self, parameters, name="Optional")
    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
@_tp_cache(typed=True)
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.
    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 = (*(_type_check(p, msg) for p in parameters[:-1]), parameters[-1])
    return _ConcatenateGenericAlias(self, parameters,
                                    _paramspec_tvars=True)


@_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__', '__forward_is_class__',
                 '__forward_module__')

    def __init__(self, arg, is_argument=True, module=None, *, is_class=False):
        if not isinstance(arg, str):
            raise TypeError(f"Forward reference must be a string -- got {arg!r}")

        # If we do `def f(*args: *Ts)`, then we'll have `arg = '*Ts'`.
        # Unfortunately, this isn't a valid expression on its own, so we
        # do the unpacking manually.
        if arg[0] == '*':
            arg_to_compile = f'({arg},)[0]'  # E.g. (*Ts,)[0]
        else:
            arg_to_compile = arg
        try:
            code = compile(arg_to_compile, '<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
        self.__forward_is_class__ = is_class
        self.__forward_module__ = module

    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
            if self.__forward_module__ is not None:
                globalns = getattr(
                    sys.modules.get(self.__forward_module__, None), '__dict__', globalns
                )
            type_ = _type_check(
                eval(self.__forward_code__, globalns, localns),
                "Forward references must evaluate to types.",
                is_argument=self.__forward_is_argument__,
                allow_special_forms=self.__forward_is_class__,
            )
            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__ and
                self.__forward_module__ == other.__forward_module__)

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

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

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

    def __repr__(self):
        if self.__forward_module__ is None:
            module_repr = ''
        else:
            module_repr = f', module={self.__forward_module__!r}'
        return f'ForwardRef({self.__forward_arg__!r}{module_repr})'


def _is_unpacked_typevartuple(x: Any) -> bool:
    return (
            isinstance(x, _UnpackGenericAlias)
            # If x is Unpack[tuple[...]], __parameters__ will be empty.
            and x.__parameters__
            and isinstance(x.__parameters__[0], TypeVarTuple)
    )


def _is_typevar_like(x: Any) -> bool:
    return isinstance(x, (TypeVar, ParamSpec)) or _is_unpacked_typevartuple(x)


class _BoundVarianceMixin:
    """Mixin giving __init__ bound and variance arguments.

    This is used by TypeVar and ParamSpec, which both employ the notions of
    a type 'bound' (restricting type arguments to be a subtype of some
    specified type) and type 'variance' (determining subtype relations between
    generic types).
    """
    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, _BoundVarianceMixin, _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.
    """

    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)
        def_mod = _caller()
        if def_mod != 'typing':
            self.__module__ = def_mod

    def __typing_subst__(self, arg):
        msg = "Parameters to generic types must be types."
        arg = _type_check(arg, msg, is_argument=True)
        return arg


class TypeVarTuple(_Final, _Immutable, _root=True):
    """Type variable tuple.

    Usage:

      Ts = TypeVarTuple('Ts')  # Can be given any name

    Just as a TypeVar (type variable) is a placeholder for a single type,
    a TypeVarTuple is a placeholder for an *arbitrary* number of types. For
    example, if we define a generic class using a TypeVarTuple:

      class C(Generic[*Ts]): ...

    Then we can parameterize that class with an arbitrary number of type
    arguments:

      C[int]       # Fine
      C[int, str]  # Also fine
      C[()]        # Even this is fine

    For more details, see PEP 646.
    """

    def __init__(self, name):
        self.__name__ = name

    def __iter__(self):
        yield Unpack[self]

    def __repr__(self):
        return self.__name__

    def __typing_subst__(self, arg):
        raise AssertionError


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"

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


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"

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


class ParamSpec(_Final, _Immutable, _BoundVarianceMixin, _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 as 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.
    """

    @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)
        def_mod = _caller()
        if def_mod != 'typing':
            self.__module__ = def_mod

    def __typing_subst__(self, arg):
        if isinstance(arg, (list, tuple)):
            arg = tuple(_type_check(a, "Expected a type.") for a in arg)
        elif not _is_param_expr(arg):
            raise TypeError(f"Expected a list of types, an ellipsis, "
                            f"ParamSpec, or Concatenate. Got {arg}")
        return arg


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):
        if attr in {'__name__', '__qualname__'}:
            return self._name or self.__origin__.__name__

        # We are careful for copy and pickle.
        # Also for simplicity we don't relay any 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',
                                        '_paramspec_tvars'}:
            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")

    def __dir__(self):
        return list(set(super().__dir__()
                + [attr for attr in dir(self.__origin__) if not _is_dunder(attr)]))


def _is_unpacked_tuple(x: Any) -> bool:
    # Is `x` something like `*tuple[int]` or `*tuple[int, ...]`?
    if not isinstance(x, _UnpackGenericAlias):
        return False
    # Alright, `x` is `Unpack[something]`.

    # `x` will always have `__args__`, because Unpack[] and Unpack[()]
    # aren't legal.
    unpacked_type = x.__args__[0]

    return getattr(unpacked_type, '__origin__', None) is tuple


def _is_unpacked_arbitrary_length_tuple(x: Any) -> bool:
    if not _is_unpacked_tuple(x):
        return False
    unpacked_tuple = x.__args__[0]

    if not hasattr(unpacked_tuple, '__args__'):
        # It's `Unpack[tuple]`. We can't make any assumptions about the length
        # of the tuple, so it's effectively an arbitrary-length tuple.
        return True

    tuple_args = unpacked_tuple.__args__
    if not tuple_args:
        # It's `Unpack[tuple[()]]`.
        return False

    last_arg = tuple_args[-1]
    if last_arg is Ellipsis:
        # It's `Unpack[tuple[something, ...]]`, which is arbitrary-length.
        return True

    # If the arguments didn't end with an ellipsis, then it's not an
    # arbitrary-length tuple.
    return False


# 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):
    # The type of parameterized generics.
    #
    # That is, for example, `type(List[int])` is `_GenericAlias`.
    #
    # Objects which are instances of this class include:
    # * Parameterized container types, e.g. `Tuple[int]`, `List[int]`.
    #  * Note that native container types, e.g. `tuple`, `list`, use
    #    `types.GenericAlias` instead.
    # * Parameterized classes:
    #     T = TypeVar('T')
    #     class C(Generic[T]): pass
    #     # C[int] is a _GenericAlias
    # * `Callable` aliases, generic `Callable` aliases, and
    #   parameterized `Callable` aliases:
    #     T = TypeVar('T')
    #     # _CallableGenericAlias inherits from _GenericAlias.
    #     A = Callable[[], None]  # _CallableGenericAlias
    #     B = Callable[[T], None]  # _CallableGenericAlias
    #     C = B[int]  # _CallableGenericAlias
    # * Parameterized `Final`, `ClassVar` and `TypeGuard`:
    #     # All _GenericAlias
    #     Final[int]
    #     ClassVar[float]
    #     TypeVar[bool]

    def __init__(self, origin, args, *, inst=True, name=None,
                 _paramspec_tvars=False):
        super().__init__(origin, inst=inst, name=name)
        if not isinstance(args, tuple):
            args = (args,)
        self.__args__ = tuple(... if a is _TypingEllipsis else
                              a for a in args)
        self.__parameters__ = _collect_parameters(args)
        self._paramspec_tvars = _paramspec_tvars
        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, left):
        return Union[left, self]

    @_tp_cache
    def __getitem__(self, args):
        # Parameterizes an already-parameterized object.
        #
        # For example, we arrive here doing something like:
        #   T1 = TypeVar('T1')
        #   T2 = TypeVar('T2')
        #   T3 = TypeVar('T3')
        #   class A(Generic[T1]): pass
        #   B = A[T2]  # B is a _GenericAlias
        #   C = B[T3]  # Invokes _GenericAlias.__getitem__
        #
        # We also arrive here when parameterizing a generic `Callable` alias:
        #   T = TypeVar('T')
        #   C = Callable[[T], None]
        #   C[int]  # Invokes _GenericAlias.__getitem__

        if self.__origin__ in (Generic, Protocol):
            # Can't subscript Generic[...] or Protocol[...].
            raise TypeError(f"Cannot subscript already-subscripted {self}")

        # Preprocess `args`.
        if not isinstance(args, tuple):
            args = (args,)
        args = tuple(_type_convert(p) for p in args)
        if (self._paramspec_tvars
                and any(isinstance(t, ParamSpec) for t in self.__parameters__)):
            args = _prepare_paramspec_params(self, args)
        elif not any(isinstance(p, TypeVarTuple) for p in self.__parameters__):
            # We only run this if there are no TypeVarTuples, because we
            # don't check variadic generic arity at runtime (to reduce
            # complexity of typing.py).
            _check_generic(self, args, len(self.__parameters__))

        new_args = self._determine_new_args(args)
        r = self.copy_with(new_args)
        return r

    def _determine_new_args(self, args):
        # Determines new __args__ for __getitem__.
        #
        # For example, suppose we had:
        #   T1 = TypeVar('T1')
        #   T2 = TypeVar('T2')
        #   class A(Generic[T1, T2]): pass
        #   T3 = TypeVar('T3')
        #   B = A[int, T3]
        #   C = B[str]
        # `B.__args__` is `(int, T3)`, so `C.__args__` should be `(int, str)`.
        # Unfortunately, this is harder than it looks, because if `T3` is
        # anything more exotic than a plain `TypeVar`, we need to consider
        # edge cases.

        params = self.__parameters__
        # In the example above, this would be {T3: str}
        new_arg_by_param = {}
        for i, param in enumerate(params):
            if isinstance(param, TypeVarTuple):
                j = len(args) - (len(params) - i - 1)
                if j < i:
                    raise TypeError(f"Too few arguments for {self}")
                new_arg_by_param.update(zip(params[:i], args[:i]))
                new_arg_by_param[param] = args[i: j]
                new_arg_by_param.update(zip(params[i + 1:], args[j:]))
                break
        else:
            new_arg_by_param.update(zip(params, args))

        new_args = []
        for old_arg in self.__args__:

            substfunc = getattr(old_arg, '__typing_subst__', None)
            if substfunc:
                new_arg = substfunc(new_arg_by_param[old_arg])
            else:
                subparams = getattr(old_arg, '__parameters__', ())
                if not subparams:
                    new_arg = old_arg
                else:
                    subargs = []
                    for x in subparams:
                        if isinstance(x, TypeVarTuple):
                            subargs.extend(new_arg_by_param[x])
                        else:
                            subargs.append(new_arg_by_param[x])
                    new_arg = old_arg[tuple(subargs)]

            if self.__origin__ == collections.abc.Callable and isinstance(new_arg, tuple):
                # Consider the following `Callable`.
                #   C = Callable[[int], str]
                # Here, `C.__args__` should be (int, str) - NOT ([int], str).
                # That means that if we had something like...
                #   P = ParamSpec('P')
                #   T = TypeVar('T')
                #   C = Callable[P, T]
                #   D = C[[int, str], float]
                # ...we need to be careful; `new_args` should end up as
                # `(int, str, float)` rather than `([int, str], float)`.
                new_args.extend(new_arg)
            elif _is_unpacked_typevartuple(old_arg):
                # Consider the following `_GenericAlias`, `B`:
                #   class A(Generic[*Ts]): ...
                #   B = A[T, *Ts]
                # If we then do:
                #   B[float, int, str]
                # The `new_arg` corresponding to `T` will be `float`, and the
                # `new_arg` corresponding to `*Ts` will be `(int, str)`. We
                # should join all these types together in a flat list
                # `(float, int, str)` - so again, we should `extend`.
                new_args.extend(new_arg)
            else:
                new_args.append(new_arg)

        return tuple(new_args)

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

    def __repr__(self):
        if self._name:
            name = 'typing.' + self._name
        else:
            name = _type_repr(self.__origin__)
        if self.__args__:
            args = ", ".join([_type_repr(a) for a in self.__args__])
        else:
            # To ensure the repr is eval-able.
            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 isinstance(self.__origin__, _SpecialForm):
            raise TypeError(f"Cannot subclass {self!r}")

        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__,)

    def __iter__(self):
        yield Unpack[self]


# _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, left):
        return Union[left, self]

class _CallableGenericAlias(_GenericAlias, _root=True):
    def __repr__(self):
        assert self._name == 'Callable'
        args = self.__args__
        if len(args) == 2 and _is_param_expr(args[0]):
            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 _is_param_expr(args[0])):
            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,
                                     _paramspec_tvars=True)

    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 not isinstance(params, tuple):
            params = (params,)
        if len(params) >= 2 and params[-1] is ...:
            msg = "Tuple[t, ...]: t must be a type."
            params = tuple(_type_check(p, msg) for p in params[:-1])
            return self.copy_with((*params, _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, types.UnionType)):
            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 __reduce__(self):
        func, (origin, args) = super().__reduce__()
        return func, (Union, args)


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):
    def copy_with(self, params):
        if isinstance(params[-1], (list, tuple)):
            return (*params[:-1], *params[-1])
        if isinstance(params[-1], _ConcatenateGenericAlias):
            params = (*params[:-1], *params[-1].__args__)
        elif not isinstance(params[-1], ParamSpec):
            raise TypeError("The last parameter to Concatenate should be a "
                            "ParamSpec variable.")
        return super().copy_with(params)


@_SpecialForm
def Unpack(self, parameters):
    """Type unpack operator.

    The type unpack operator takes the child types from some container type,
    such as `tuple[int, str]` or a `TypeVarTuple`, and 'pulls them out'. For
    example:

      # For some generic class `Foo`:
      Foo[Unpack[tuple[int, str]]]  # Equivalent to Foo[int, str]

      Ts = TypeVarTuple('Ts')
      # Specifies that `Bar` is generic in an arbitrary number of types.
      # (Think of `Ts` as a tuple of an arbitrary number of individual
      #  `TypeVar`s, which the `Unpack` is 'pulling out' directly into the
      #  `Generic[]`.)
      class Bar(Generic[Unpack[Ts]]): ...
      Bar[int]  # Valid
      Bar[int, str]  # Also valid

    From Python 3.11, this can also be done using the `*` operator:

        Foo[*tuple[int, str]]
        class Bar(Generic[*Ts]): ...

    Note that there is only some runtime checking of this operator. Not
    everything the runtime allows may be accepted by static type checkers.

    For more information, see PEP 646.
    """
    item = _type_check(parameters, f'{self} accepts only single type.')
    return _UnpackGenericAlias(origin=self, args=(item,))


class _UnpackGenericAlias(_GenericAlias, _root=True):

    def __repr__(self):
        # `Unpack` only takes one argument, so __args__ should contain only
        # a single item.
        return '*' + repr(self.__args__[0])

    def __getitem__(self, args):
        if (len(self.__parameters__) == 1 and
                isinstance(self.__parameters__[0], TypeVarTuple)):
            return args
        return super().__getitem__(args)


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):
        """Parameterizes a generic class.

        At least, parameterizing a generic class is the *main* thing this method
        does. For example, for some generic class `Foo`, this is called when we
        do `Foo[int]` - there, with `cls=Foo` and `params=int`.

        However, note that this method is also called when defining generic
        classes in the first place with `class Foo(Generic[T]): ...`.
        """
        if not isinstance(params, tuple):
            params = (params,)

        if not params:
            # We're only ok with `params` being empty if the class's only type
            # parameter is a `TypeVarTuple` (which can contain zero types).
            class_params = getattr(cls, "__parameters__", None)
            only_class_parameter_is_typevartuple = (
                    class_params is not None
                    and len(class_params) == 1
                    and isinstance(class_params[0], TypeVarTuple)
            )
            if not only_class_parameter_is_typevartuple:
                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(_is_typevar_like(p) 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)
            elif not any(isinstance(p, TypeVarTuple) for p in cls.__parameters__):
                # We only run this if there are no TypeVarTuples, because we
                # don't check variadic generic arity at runtime (to reduce
                # complexity of typing.py).
                _check_generic(cls, params, len(cls.__parameters__))
        return _GenericAlias(cls, params,
                             _paramspec_tvars=True)

    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_parameters(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 _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_or_replace_init(self, *args, **kwargs):
    cls = type(self)

    if cls._is_protocol:
        raise TypeError('Protocols cannot be instantiated')

    # Already using a custom `__init__`. No need to calculate correct
    # `__init__` to call. This can lead to RecursionError. See bpo-45121.
    if cls.__init__ is not _no_init_or_replace_init:
        return

    # Initially, `__init__` of a protocol subclass is set to `_no_init_or_replace_init`.
    # The first instantiation of the subclass will call `_no_init_or_replace_init` which
    # searches for a proper new `__init__` in the MRO. The new `__init__`
    # replaces the subclass' old `__init__` (ie `_no_init_or_replace_init`). Subsequent
    # instantiation of the protocol subclass will thus use the new
    # `__init__` and no longer call `_no_init_or_replace_init`.
    for base in cls.__mro__:
        init = base.__dict__.get('__init__', _no_init_or_replace_init)
        if init is not _no_init_or_replace_init:
            cls.__init__ = init
            break
    else:
        # should not happen
        cls.__init__ = object.__init__

    cls.__init__(self, *args, **kwargs)


def _caller(depth=1, default='__main__'):
    try:
        return sys._getframe(depth + 1).f_globals.get('__name__', default)
    except (AttributeError, ValueError):  # For platforms without _getframe()
        return None


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.
    """
    return _caller(depth) in {'abc', 'functools', None}


_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_or_replace_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__))

    def __getattr__(self, attr):
        if attr in {'__name__', '__qualname__'}:
            return 'Annotated'
        return super().__getattr__(attr)


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, allow_special_forms=True)
        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 assert_type(val, typ, /):
    """Ask a static type checker to confirm that the value is of the given type.

    When the type checker encounters a call to assert_type(), it
    emits an error if the value is not of the specified type::

        def greet(name: str) -> None:
            assert_type(name, str)  # ok
            assert_type(name, int)  # type checker error

    At runtime this returns the first argument unchanged and otherwise
    does nothing.
    """
    return val


_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 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:
                base_globals = getattr(sys.modules.get(base.__module__, None), '__dict__', {})
            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, is_class=True)
                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))
    hints = dict(hints)
    for name, value in hints.items():
        if value is None:
            value = type(None)
        if isinstance(value, str):
            # class-level forward refs were handled above, this must be either
            # a module-level annotation or a function argument annotation
            value = ForwardRef(
                value,
                is_argument=not isinstance(obj, types.ModuleType),
                is_class=False,
            )
        hints[name] = _eval_type(value, globalns, localns)
    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)
    if isinstance(t, types.UnionType):
        stripped_args = tuple(_strip_annotations(a) for a in t.__args__)
        if stripped_args == t.__args__:
            return t
        return functools.reduce(operator.or_, 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.UnionType):
        return types.UnionType
    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 (len(res) == 2 and _is_param_expr(res[0]))):
            res = (list(res[:-1]), res[-1])
        return res
    if isinstance(tp, types.UnionType):
        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 assert_never(arg: Never, /) -> Never:
    """Statically assert that a line of code is unreachable.

    Example::

        def int_or_str(arg: int | str) -> None:
            match arg:
                case int():
                    print("It's an int")
                case str():
                    print("It's a str")
                case _:
                    assert_never(arg)

    If a type checker finds that a call to assert_never() is
    reachable, it will emit an error.

    At runtime, this throws an exception when called.

    """
    raise AssertionError("Expected code to be unreachable")


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):
        for key in dir(arg):
            obj = getattr(arg, key)
            if (
                not hasattr(obj, '__qualname__')
                or obj.__qualname__ != f'{arg.__qualname__}.{obj.__name__}'
                or getattr(obj, '__module__', None) != arg.__module__
            ):
                # We only modify objects that are defined in this type directly.
                # If classes / methods are nested in multiple layers,
                # we will modify them when processing their direct holders.
                continue
            # Instance, class, and static methods:
            if isinstance(obj, types.FunctionType):
                obj.__no_type_check__ = True
            if isinstance(obj, types.MethodType):
                obj.__func__.__no_type_check__ = True
            # Nested types:
            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. The decorator
    sets the ``__final__`` attribute to ``True`` on the decorated object
    to allow runtime introspection.
    """
    try:
        f.__final__ = True
    except (AttributeError, TypeError):
        # Skip the attribute silently if it is not writable.
        # AttributeError happens if the object has __slots__ or a
        # read-only property, TypeError if it's a builtin class.
        pass
    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")
    return _make_nmtuple(typename, fields, module=_caller())

_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, module=tp_dict.__module__)
            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 an additional equivalent form::

        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 the other
    syntax form works 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")
    if kwargs:
        warnings.warn(
            "The kwargs-based syntax for TypedDict definitions is deprecated "
            "in Python 3.11, will be removed in Python 3.13, and may not be "
            "understood by third-party type checkers.",
            DeprecationWarning,
            stacklevel=2,
        )

    ns = {'__annotations__': dict(fields)}
    module = _caller()
    if module is not None:
        # Setting correct module is necessary to make typed dict classes pickleable.
        ns['__module__'] = module

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

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


class NewType:
    """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 callable 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
    """

    __call__ = _idfunc

    def __init__(self, name, tp):
        self.__qualname__ = name
        if '.' in name:
            name = name.rpartition('.')[-1]
        self.__name__ = name
        self.__supertype__ = tp
        def_mod = _caller()
        if def_mod != 'typing':
            self.__module__ = def_mod

    def __mro_entries__(self, bases):
        # We defined __mro_entries__ to get a better error message
        # if a user attempts to subclass a NewType instance. bpo-46170
        superclass_name = self.__name__

        class Dummy:
            def __init_subclass__(cls):
                subclass_name = cls.__name__
                raise TypeError(
                    f"Cannot subclass an instance of NewType. Perhaps you were looking for: "
                    f"`{subclass_name} = NewType({subclass_name!r}, {superclass_name})`"
                )

        return (Dummy,)

    def __repr__(self):
        return f'{self.__module__}.{self.__qualname__}'

    def __reduce__(self):
        return self.__qualname__

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

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


# 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 _DeprecatedType(type):
    def __getattribute__(cls, name):
        if name not in ("__dict__", "__module__") and name in cls.__dict__:
            warnings.warn(
                f"{cls.__name__} is deprecated, import directly "
                f"from typing instead. {cls.__name__} will be removed "
                "in Python 3.12.",
                DeprecationWarning,
                stacklevel=2,
            )
        return super().__getattribute__(name)


class io(metaclass=_DeprecatedType):
    """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(metaclass=_DeprecatedType):
    """Wrapper namespace for re type aliases."""

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


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


def reveal_type(obj: T, /) -> T:
    """Reveal the inferred type of a variable.

    When a static type checker encounters a call to ``reveal_type()``,
    it will emit the inferred type of the argument::

        x: int = 1
        reveal_type(x)

    Running a static type checker (e.g., ``mypy``) on this example
    will produce output similar to 'Revealed type is "builtins.int"'.

    At runtime, the function prints the runtime type of the
    argument and returns it unchanged.

    """
    print(f"Runtime type is {type(obj).__name__!r}", file=sys.stderr)
    return obj