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 explicitelly added to __all__.
* Internal helper functions: these should never be used in code outside this module.
* _SpecialForm and its instances (special forms): Any, NoReturn, ClassVar, Union, Optional
* Two classes whose instances can be type arguments in addition to types: ForwardRef and TypeVar
* 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
  (the latter is currently private, but will be made public after PEP 544 acceptance).
* 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 (may be added soon).
* Wrapper submodules for re and io related types.
"""

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

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

    # ABCs (from collections.abc).
    'AbstractSet',  # collections.abc.Set.
    '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',
    'SupportsInt',
    'SupportsRound',

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

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

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


def _type_check(arg, msg, is_argument=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 is_argument:
        invalid_generic_forms = invalid_generic_forms + (ClassVar, )

    if arg is None:
        return type(None)
    if isinstance(arg, str):
        return ForwardRef(arg)
    if (isinstance(arg, _GenericAlias) and
            arg.__origin__ in invalid_generic_forms):
        raise TypeError(f"{arg} is not valid as type argument")
    if (isinstance(arg, _SpecialForm) and arg is not Any or
            arg in (Generic, _Protocol)):
        raise TypeError(f"Plain {arg} is not valid as type argument")
    if isinstance(arg, (type, TypeVar, ForwardRef)):
        return arg
    if not callable(arg):
        raise TypeError(f"{msg} Got {arg!r:.100}.")
    return arg


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

    If obj is a type, we return a shorter version than the default
    type.__repr__, based on the module and qualified name, which is
    typically enough to uniquely identify a type.  For everything
    else, we fall back on repr(obj).
    """
    if isinstance(obj, type):
        if obj.__module__ == 'builtins':
            return obj.__qualname__
        return f'{obj.__module__}.{obj.__qualname__}'
    if obj is ...:
        return('...')
    if isinstance(obj, types.FunctionType):
        return obj.__name__
    return repr(obj)


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

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


def _subs_tvars(tp, tvars, subs):
    """Substitute type variables 'tvars' with substitutions 'subs'.
    These two must have the same length.
    """
    if not isinstance(tp, _GenericAlias):
        return tp
    new_args = list(tp.__args__)
    for a, arg in enumerate(tp.__args__):
        if isinstance(arg, TypeVar):
            for i, tvar in enumerate(tvars):
                if arg == tvar:
                    new_args[a] = subs[i]
        else:
            new_args[a] = _subs_tvars(arg, tvars, subs)
    if tp.__origin__ is Union:
        return Union[tuple(new_args)]
    return tp.copy_with(tuple(new_args))


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


def _remove_dups_flatten(parameters):
    """An internal helper for Union creation and substitution: flatten Union's
    among parameters, then remove duplicates and strict subclasses.
    """
    # Flatten out Union[Union[...], ...].
    params = []
    for p in parameters:
        if isinstance(p, _GenericAlias) and p.__origin__ is Union:
            params.extend(p.__args__)
        elif isinstance(p, tuple) and len(p) > 0 and p[0] is Union:
            params.extend(p[1:])
        else:
            params.append(p)
    # Weed out strict duplicates, preserving the first of each occurrence.
    all_params = set(params)
    if len(all_params) < len(params):
        new_params = []
        for t in params:
            if t in all_params:
                new_params.append(t)
                all_params.remove(t)
        params = new_params
        assert not all_params, all_params
    # Weed out subclasses.
    # E.g. Union[int, Employee, Manager] == Union[int, Employee].
    # If object is present it will be sole survivor among proper classes.
    # Never discard type variables.
    # (In particular, Union[str, AnyStr] != AnyStr.)
    all_params = set(params)
    for t1 in params:
        if not isinstance(t1, type):
            continue
        if any((isinstance(t2, type) or
                isinstance(t2, _GenericAlias) and t2._special) and issubclass(t1, t2)
               for t2 in all_params - {t1}):
            all_params.remove(t1)
    return tuple(t for t in params if t in all_params)


_cleanups = []


def _tp_cache(func):
    """Internal wrapper caching __getitem__ of generic types with a fallback to
    original function for non-hashable arguments.
    """
    cached = functools.lru_cache()(func)
    _cleanups.append(cached.cache_clear)

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


def _eval_type(t, globalns, localns):
    """Evaluate all forward reverences in the given type t.
    For use of globalns and localns see the docstring for get_type_hints().
    """
    if isinstance(t, ForwardRef):
        return t._evaluate(globalns, localns)
    if isinstance(t, _GenericAlias):
        ev_args = tuple(_eval_type(a, globalns, localns) for a in t.__args__)
        if ev_args == t.__args__:
            return t
        res = t.copy_with(ev_args)
        res._special = t._special
        return res
    return t


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

    __slots__ = ('__weakref__',)

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

class _Immutable:
    """Mixin to indicate that object should not be copied."""

    def __copy__(self):
        return self

    def __deepcopy__(self, memo):
        return self


class _SpecialForm(_Final, _Immutable, _root=True):
    """Internal indicator of special typing constructs.
    See _doc instance attribute for specific docs.
    """

    __slots__ = ('_name', '_doc')

    def __getstate__(self):
        return {'name': self._name, 'doc': self._doc}

    def __setstate__(self, state):
        self._name = state['name']
        self._doc = state['doc']

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

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

    def __init__(self, name, doc):
        self._name = name
        self._doc = doc

    def __eq__(self, other):
        if not isinstance(other, _SpecialForm):
            return NotImplemented
        return self._name == other._name

    def __hash__(self):
        return hash((self._name,))

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

    def __reduce__(self):
        return self._name

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

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

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

    @_tp_cache
    def __getitem__(self, parameters):
        if self._name == 'ClassVar':
            item = _type_check(parameters, 'ClassVar accepts only single type.')
            return _GenericAlias(self, (item,))
        if self._name == 'Union':
            if parameters == ():
                raise TypeError("Cannot take a Union of no types.")
            if not isinstance(parameters, tuple):
                parameters = (parameters,)
            msg = "Union[arg, ...]: each arg must be a type."
            parameters = tuple(_type_check(p, msg) for p in parameters)
            parameters = _remove_dups_flatten(parameters)
            if len(parameters) == 1:
                return parameters[0]
            return _GenericAlias(self, parameters)
        if self._name == 'Optional':
            arg = _type_check(parameters, "Optional[t] requires a single type.")
            return Union[arg, type(None)]
        raise TypeError(f"{self} is not subscriptable")


Any = _SpecialForm('Any', doc=
    """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.
    """)

NoReturn = _SpecialForm('NoReturn', doc=
    """Special type indicating functions that never return.
    Example::

      from typing import NoReturn

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

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

ClassVar = _SpecialForm('ClassVar', doc=
    """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().
    """)

Union = _SpecialForm('Union', doc=
    """Union type; Union[X, Y] means either X or Y.

    To define a union, use e.g. Union[int, str].  Details:
    - The arguments must be types and there must be at least one.
    - None as an argument is a special case and is replaced by
      type(None).
    - Unions of unions are flattened, e.g.::

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

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

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

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

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

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

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

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

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

    - Similar for object::

        Union[int, object] == object

    - You cannot subclass or instantiate a union.
    - You can use Optional[X] as a shorthand for Union[X, None].
    """)

Optional = _SpecialForm('Optional', doc=
    """Optional type.

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


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

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

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

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

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

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

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


def _find_name(mod, name):
    return getattr(sys.modules[mod], name)


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

    Usage::

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

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

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

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

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

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

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

    Type variables can be introspected. e.g.:

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

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

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

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

    def __getstate__(self):
        return {'name': self.__name__,
                'bound': self.__bound__,
                'constraints': self.__constraints__,
                'co': self.__covariant__,
                'contra': self.__contravariant__}

    def __setstate__(self, state):
        self.__name__ = state['name']
        self.__bound__ = state['bound']
        self.__constraints__ = state['constraints']
        self.__covariant__ = state['co']
        self.__contravariant__ = state['contra']

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

    def __reduce__(self):
        return (_find_name, (self._def_mod, self.__name__))


# 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).


# Mapping from non-generic type names that have a generic alias in typing
# but with a different name.
_normalize_alias = {'list': 'List',
                    'tuple': 'Tuple',
                    'dict': 'Dict',
                    'set': 'Set',
                    'frozenset': 'FrozenSet',
                    'deque': 'Deque',
                    'defaultdict': 'DefaultDict',
                    'type': 'Type',
                    'Set': 'AbstractSet'}

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


class _GenericAlias(_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, params, *, inst=True, special=False, name=None):
        self._inst = inst
        self._special = special
        if special and name is None:
            orig_name = origin.__name__
            name = _normalize_alias.get(orig_name, orig_name)
        self._name = name
        if not isinstance(params, tuple):
            params = (params,)
        self.__origin__ = origin
        self.__args__ = tuple(... if a is _TypingEllipsis else
                              () if a is _TypingEmpty else
                              a for a in params)
        self.__parameters__ = _collect_type_vars(params)
        self.__slots__ = None  # This is not documented.
        if not name:
            self.__module__ = origin.__module__

    @_tp_cache
    def __getitem__(self, params):
        if self.__origin__ in (Generic, _Protocol):
            # Can't subscript Generic[...] or _Protocol[...].
            raise TypeError(f"Cannot subscript already-subscripted {self}")
        if not isinstance(params, tuple):
            params = (params,)
        msg = "Parameters to generic types must be types."
        params = tuple(_type_check(p, msg) for p in params)
        _check_generic(self, params)
        return _subs_tvars(self, self.__parameters__, params)

    def copy_with(self, params):
        # We don't copy self._special.
        return _GenericAlias(self.__origin__, params, name=self._name, inst=self._inst)

    def __repr__(self):
        if (self._name != 'Callable' or
                len(self.__args__) == 2 and self.__args__[0] is Ellipsis):
            if self._name:
                name = 'typing.' + self._name
            else:
                name = _type_repr(self.__origin__)
            if not self._special:
                args = f'[{", ".join([_type_repr(a) for a in self.__args__])}]'
            else:
                args = ''
            return (f'{name}{args}')
        if self._special:
            return 'typing.Callable'
        return (f'typing.Callable'
                f'[[{", ".join([_type_repr(a) for a in self.__args__[:-1]])}], '
                f'{_type_repr(self.__args__[-1])}]')

    def __eq__(self, other):
        if not isinstance(other, _GenericAlias):
            return NotImplemented
        if self.__origin__ != other.__origin__:
            return False
        if self.__origin__ is Union and other.__origin__ is Union:
            return frozenset(self.__args__) == frozenset(other.__args__)
        return self.__args__ == other.__args__

    def __hash__(self):
        if self.__origin__ is Union:
            return hash((Union, frozenset(self.__args__)))
        return hash((self.__origin__, self.__args__))

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

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

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

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

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

    def __subclasscheck__(self, cls):
        if self._special:
            if not isinstance(cls, _GenericAlias):
                return issubclass(cls, self.__origin__)
            if cls._special:
                return issubclass(cls.__origin__, self.__origin__)
        raise TypeError("Subscripted generics cannot be used with"
                        " class and instance checks")

    def __reduce__(self):
        if self._special:
            return self._name
        return super().__reduce__()


class _VariadicGenericAlias(_GenericAlias, _root=True):
    """Same as _GenericAlias above but for variadic aliases. Currently,
    this is used only by special internal aliases: Tuple and Callable.
    """
    def __getitem__(self, params):
        if self._name != 'Callable' or not self._special:
            return self.__getitem_inner__(params)
        if not isinstance(params, tuple) or len(params) != 2:
            raise TypeError("Callable must be used as "
                            "Callable[[arg, ...], result].")
        args, result = params
        if args is Ellipsis:
            params = (Ellipsis, result)
        else:
            if not isinstance(args, list):
                raise TypeError(f"Callable[args, result]: args must be a list."
                                f" Got {args}")
            params = (tuple(args), result)
        return self.__getitem_inner__(params)

    @_tp_cache
    def __getitem_inner__(self, params):
        if self.__origin__ is tuple and self._special:
            if params == ():
                return self.copy_with((_TypingEmpty,))
            if not isinstance(params, tuple):
                params = (params,)
            if len(params) == 2 and params[1] is ...:
                msg = "Tuple[t, ...]: t must be a type."
                p = _type_check(params[0], msg)
                return self.copy_with((p, _TypingEllipsis))
            msg = "Tuple[t0, t1, ...]: each t must be a type."
            params = tuple(_type_check(p, msg) for p in params)
            return self.copy_with(params)
        if self.__origin__ is collections.abc.Callable and self._special:
            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))
            msg = "Callable[[arg, ...], result]: each arg must be a type."
            args = tuple(_type_check(arg, msg) for arg in args)
            params = args + (result,)
            return self.copy_with(params)
        return super().__getitem__(params)


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__ = ()

    def __new__(cls, *args, **kwds):
        if cls is Generic:
            raise TypeError("Type Generic cannot be instantiated; "
                            "it can be used only as a base class")
        if super().__new__ is object.__new__ and cls.__init__ is not object.__init__:
            obj = super().__new__(cls)
        else:
            obj = super().__new__(cls, *args, **kwds)
        return obj

    @_tp_cache
    def __class_getitem__(cls, params):
        if not isinstance(params, tuple):
            params = (params,)
        if not params and cls is not Tuple:
            raise TypeError(
                f"Parameter list to {cls.__qualname__}[...] cannot be empty")
        msg = "Parameters to generic types must be types."
        params = tuple(_type_check(p, msg) for p in params)
        if cls is Generic:
            # Generic can only be subscripted with unique type variables.
            if not all(isinstance(p, TypeVar) for p in params):
                raise TypeError(
                    "Parameters to Generic[...] must all be type variables")
            if len(set(params)) != len(params):
                raise TypeError(
                    "Parameters to Generic[...] must all be unique")
        elif cls is _Protocol:
            # _Protocol is internal at the moment, just skip the check
            pass
        else:
            # Subscripting a regular Generic subclass.
            _check_generic(cls, params)
        return _GenericAlias(cls, params)

    def __init_subclass__(cls, *args, **kwargs):
        super().__init_subclass__(*args, **kwargs)
        tvars = []
        if '__orig_bases__' in cls.__dict__:
            error = Generic in cls.__orig_bases__
        else:
            error = Generic in cls.__bases__ and cls.__name__ != '_Protocol'
        if error:
            raise TypeError("Cannot inherit from plain Generic")
        if '__orig_bases__' in cls.__dict__:
            tvars = _collect_type_vars(cls.__orig_bases__)
            # Look for Generic[T1, ..., Tn].
            # If found, tvars must be a subset of it.
            # If not found, tvars is it.
            # Also check for and reject plain Generic,
            # and reject multiple Generic[...].
            gvars = None
            for base in cls.__orig_bases__:
                if (isinstance(base, _GenericAlias) and
                        base.__origin__ is Generic):
                    if gvars is not None:
                        raise TypeError(
                            "Cannot inherit from Generic[...] multiple types.")
                    gvars = base.__parameters__
            if gvars is None:
                gvars = tvars
            else:
                tvarset = set(tvars)
                gvarset = set(gvars)
                if not tvarset <= gvarset:
                    s_vars = ', '.join(str(t) for t in tvars if t not in gvarset)
                    s_args = ', '.join(str(g) for g in gvars)
                    raise TypeError(f"Some type variables ({s_vars}) are"
                                    f" not listed in Generic[{s_args}]")
                tvars = gvars
        cls.__parameters__ = tuple(tvars)


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


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


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

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


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


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


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

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

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

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

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

    - If no dict arguments are passed, an attempt is made to use the
      globals from obj (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.

    - 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 = sys.modules[base.__module__].__dict__
            else:
                base_globals = globalns
            ann = base.__dict__.get('__annotations__', {})
            for name, value in ann.items():
                if value is None:
                    value = type(None)
                if isinstance(value, str):
                    value = ForwardRef(value, is_argument=True)
                value = _eval_type(value, base_globals, localns)
                hints[name] = value
        return hints

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


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

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

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


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

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

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

    return wrapped_decorator


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


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

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

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

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

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


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

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

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

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

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

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

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

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

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

        return attrs


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

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

    __slots__ = ()

    _is_protocol = True

    def __class_getitem__(cls, params):
        return super().__class_getitem__(params)


# 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.
def _alias(origin, params, inst=True):
    return _GenericAlias(origin, params, special=True, inst=inst)

Hashable = _alias(collections.abc.Hashable, ())  # Not generic.
Awaitable = _alias(collections.abc.Awaitable, T_co)
Coroutine = _alias(collections.abc.Coroutine, (T_co, T_contra, V_co))
AsyncIterable = _alias(collections.abc.AsyncIterable, T_co)
AsyncIterator = _alias(collections.abc.AsyncIterator, T_co)
Iterable = _alias(collections.abc.Iterable, T_co)
Iterator = _alias(collections.abc.Iterator, T_co)
Reversible = _alias(collections.abc.Reversible, T_co)
Sized = _alias(collections.abc.Sized, ())  # Not generic.
Container = _alias(collections.abc.Container, T_co)
Collection = _alias(collections.abc.Collection, T_co)
Callable = _VariadicGenericAlias(collections.abc.Callable, (), special=True)
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, T_co)
MutableSet = _alias(collections.abc.MutableSet, T)
# NOTE: Mapping is only covariant in the value type.
Mapping = _alias(collections.abc.Mapping, (KT, VT_co))
MutableMapping = _alias(collections.abc.MutableMapping, (KT, VT))
Sequence = _alias(collections.abc.Sequence, T_co)
MutableSequence = _alias(collections.abc.MutableSequence, T)
ByteString = _alias(collections.abc.ByteString, ())  # Not generic
Tuple = _VariadicGenericAlias(tuple, (), inst=False, special=True)
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, T, inst=False)
Deque = _alias(collections.deque, T)
Set = _alias(set, T, inst=False)
FrozenSet = _alias(frozenset, T_co, inst=False)
MappingView = _alias(collections.abc.MappingView, T_co)
KeysView = _alias(collections.abc.KeysView, KT)
ItemsView = _alias(collections.abc.ItemsView, (KT, VT_co))
ValuesView = _alias(collections.abc.ValuesView, VT_co)
ContextManager = _alias(contextlib.AbstractContextManager, T_co)
AsyncContextManager = _alias(contextlib.AbstractAsyncContextManager, T_co)
Dict = _alias(dict, (KT, VT), inst=False)
DefaultDict = _alias(collections.defaultdict, (KT, VT))
Counter = _alias(collections.Counter, T)
ChainMap = _alias(collections.ChainMap, (KT, VT))
Generator = _alias(collections.abc.Generator, (T_co, T_contra, V_co))
AsyncGenerator = _alias(collections.abc.AsyncGenerator, (T_co, T_contra))
Type = _alias(type, CT_co, inst=False)
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.
    """


class SupportsInt(_Protocol):
    __slots__ = ()

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


class SupportsFloat(_Protocol):
    __slots__ = ()

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


class SupportsComplex(_Protocol):
    __slots__ = ()

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


class SupportsBytes(_Protocol):
    __slots__ = ()

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


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

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


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

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


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


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

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


class NamedTupleMeta(type):

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


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

    Usage in Python versions >= 3.6::

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

    This is equivalent to::

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

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

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

    In Python versions <= 3.5 use::

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

    def __new__(self, typename, fields=None, **kwargs):
        if fields is None:
            fields = kwargs.items()
        elif kwargs:
            raise TypeError("Either list of fields or keywords"
                            " can be provided to NamedTuple, not both")
        return _make_nmtuple(typename, fields)


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

        UserId = NewType('UserId', int)

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

        UserId('user')          # Fails type check

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

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

    def new_type(x):
        return x

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


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


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


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

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

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

    __slots__ = ()

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

    __slots__ = ()

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

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


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

    __slots__ = ()

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

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

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

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

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

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


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

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


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

Pattern = _alias(stdlib_re.Pattern, AnyStr)
Match = _alias(stdlib_re.Match, AnyStr)

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

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


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