import sys
from typing import Any, Callable, Generic, Dict, Hashable, Iterable, Mapping, Optional, Sequence, Tuple, Type, TypeVar, NamedTuple, Union, overload

_AnyCallable = Callable[..., Any]

_T = TypeVar("_T")
_S = TypeVar("_S")

@overload
def reduce(function: Callable[[_T, _S], _T],
           sequence: Iterable[_S], initial: _T) -> _T: ...
@overload
def reduce(function: Callable[[_T, _T], _T],
           sequence: Iterable[_T]) -> _T: ...

class _CacheInfo(NamedTuple):
    hits: int
    misses: int
    maxsize: int
    currsize: int

class _lru_cache_wrapper(Generic[_T]):
    __wrapped__: Callable[..., _T]
    def __call__(self, *args: Hashable, **kwargs: Hashable) -> _T: ...
    def cache_info(self) -> _CacheInfo: ...
    def cache_clear(self) -> None: ...

if sys.version_info >= (3, 8):
    @overload
    def lru_cache(maxsize: Optional[int] = ..., typed: bool = ...) -> Callable[[Callable[..., _T]], _lru_cache_wrapper[_T]]: ...
    @overload
    def lru_cache(maxsize: Callable[..., _T], typed: bool = ...) -> _lru_cache_wrapper[_T]: ...
else:
    def lru_cache(maxsize: Optional[int] = ..., typed: bool = ...) -> Callable[[Callable[..., _T]], _lru_cache_wrapper[_T]]: ...

WRAPPER_ASSIGNMENTS: Sequence[str]
WRAPPER_UPDATES: Sequence[str]

def update_wrapper(wrapper: _AnyCallable, wrapped: _AnyCallable, assigned: Sequence[str] = ...,
                   updated: Sequence[str] = ...) -> _AnyCallable: ...
def wraps(wrapped: _AnyCallable, assigned: Sequence[str] = ..., updated: Sequence[str] = ...) -> Callable[[_AnyCallable], _AnyCallable]: ...
def total_ordering(cls: Type[_T]) -> Type[_T]: ...
def cmp_to_key(mycmp: Callable[[_T, _T], int]) -> Callable[[_T], Any]: ...

class partial(Generic[_T]):
    func: Callable[..., _T]
    args: Tuple[Any, ...]
    keywords: Dict[str, Any]
    def __init__(self, func: Callable[..., _T], *args: Any, **kwargs: Any) -> None: ...
    def __call__(self, *args: Any, **kwargs: Any) -> _T: ...

# With protocols, this could change into a generic protocol that defines __get__ and returns _T
_Descriptor = Any

class partialmethod(Generic[_T]):
    func: Union[Callable[..., _T], _Descriptor]
    args: Tuple[Any, ...]
    keywords: Dict[str, Any]

    @overload
    def __init__(self, func: Callable[..., _T], *args: Any, **keywords: Any) -> None: ...
    @overload
    def __init__(self, func: _Descriptor, *args: Any, **keywords: Any) -> None: ...
    def __get__(self, obj: Any, cls: Type[Any]) -> Callable[..., _T]: ...
    @property
    def __isabstractmethod__(self) -> bool: ...

class _SingleDispatchCallable(Generic[_T]):
    registry: Mapping[Any, Callable[..., _T]]
    def dispatch(self, cls: Any) -> Callable[..., _T]: ...
    @overload
    def register(self, cls: Any) -> Callable[[Callable[..., _T]], Callable[..., _T]]: ...
    @overload
    def register(self, cls: Any, func: Callable[..., _T]) -> Callable[..., _T]: ...
    def _clear_cache(self) -> None: ...
    def __call__(self, *args: Any, **kwargs: Any) -> _T: ...

def singledispatch(func: Callable[..., _T]) -> _SingleDispatchCallable[_T]: ...

if sys.version_info >= (3, 8):
    class singledispatchmethod(Generic[_T]):
        dispatcher: _SingleDispatchCallable[_T]
        func: Callable[..., _T]
        def __init__(self, func: Callable[..., _T]) -> None: ...
        @overload
        def register(self, cls: Any, method: None = ...) -> Callable[[Callable[..., _T]], Callable[..., _T]]: ...
        @overload
        def register(self, cls: Any, method: Callable[..., _T]) -> Callable[..., _T]: ...
        def __call__(self, *args: Any, **kwargs: Any) -> _T: ...

    class cached_property(Generic[_T]):
        func: Callable[[Any], _T]
        attrname: Optional[str]
        def __init__(self, func: Callable[[Any], _T]) -> None: ...
        @overload
        def __get__(self, instance: None, owner: Optional[Type[Any]] = ...) -> cached_property[_T]: ...
        @overload
        def __get__(self, instance: _S, owner: Optional[Type[Any]] = ...) -> _T: ...
        def __set_name__(self, owner: Type[Any], name: str) -> None: ...

if sys.version_info >= (3, 9):
    class TopologicalSorter(Generic[_T]):
        def __init__(self, graph: Optional[Dict[_T, Iterable[_T]]] = ...) -> None: ...
        def add(self, node: _T, *predecessors: _T) -> None: ...
        def prepare(self) -> None: ...
        def is_active(self) -> bool: ...
        def done(self, *nodes: _T) -> None: ...
        def get_ready(self) -> Tuple[_T, ...]: ...
        def static_order(self) -> Iterable[_T]: ...

    class CycleError(ValueError): ...

    def cache(__user_function: Callable[..., _T]) -> _lru_cache_wrapper[_T]: ...