from typing import Literal
from typing_extensions import Self

from sympy.assumptions import AppliedPredicate
from sympy.assumptions.predicates.common import CommutativePredicate as CommutativePredicate, IsTruePredicate as IsTruePredicate
from sympy.core import Basic, Symbol
from sympy.core.numbers import NaN, Number
from sympy.logic.boolalg import And, BooleanFalse, BooleanTrue, Equivalent, Implies, Not, Or

class AskHandler:
    def __new__(cls, *args, **kwargs) -> Self: ...

class CommonHandler(AskHandler):
    @staticmethod
    def AlwaysTrue(expr, assumptions) -> Literal[True]: ...
    @staticmethod
    def AlwaysFalse(expr, assumptions) -> Literal[False]: ...
    @staticmethod
    def AlwaysNone(expr, assumptions) -> None: ...

    NaN = ...

@CommutativePredicate.register(Symbol)
def _(expr, assumptions) -> bool: ...
@CommutativePredicate.register(Basic)
def _(expr, assumptions) -> bool: ...
@CommutativePredicate.register(Number)
def _(expr, assumptions) -> Literal[True]: ...
@CommutativePredicate.register(NaN)
def _(expr, assumptions) -> Literal[True]: ...
@IsTruePredicate.register(bool)
def _(expr, assumptions): ...
@IsTruePredicate.register(BooleanTrue)
def _(expr, assumptions) -> Literal[True]: ...
@IsTruePredicate.register(BooleanFalse)
def _(expr, assumptions) -> Literal[False]: ...
@IsTruePredicate.register(AppliedPredicate)
def _(expr, assumptions) -> bool | None: ...
@IsTruePredicate.register(Not)
def _(expr, assumptions) -> bool | None: ...
@IsTruePredicate.register(Or)
def _(expr, assumptions) -> bool | None: ...
@IsTruePredicate.register(And)
def _(expr, assumptions) -> bool | None: ...
@IsTruePredicate.register(Implies)
def _(expr, assumptions) -> bool | None: ...
@IsTruePredicate.register(Equivalent)
def _(expr, assumptions) -> bool | None: ...
def test_closed_group(expr, assumptions, key) -> bool | None: ...