Further improve return types in the numbers module

stdlib/numbers.pyi

@@ -1,7 +1,7 @@
 # Note: these stubs are incomplete. The more complex type
 # signatures are currently omitted.
 #
-# Use SupportsComplex, SupportsFloat and SupportsIndex for return types in this module
+# Use _ComplexLike, _RealLike and _IntegralLike for return types in this module
 # rather than `numbers.Complex`, `numbers.Real` and `numbers.Integral`,
 # to avoid an excessive number of `type: ignore`s in subclasses of these ABCs
 # (since type checkers don't see `complex` as a subtype of `numbers.Complex`,
@@ -10,18 +10,56 @@
 import sys
 from _typeshed import Incomplete
 from abc import ABCMeta, abstractmethod
-from typing import Literal, SupportsFloat, SupportsIndex, overload
+from typing import Literal, Protocol, overload
 from typing_extensions import TypeAlias
 
+__all__ = ["Number", "Complex", "Real", "Rational", "Integral"]
+
+############################
+# Protocols for return types
+############################
+
+# `_ComplexLike` is a structural-typing approximation
+# of the `Complex` ABC, which is not (and cannot be) a protocol
+class _SupportsComplex(Protocol):
+    def __complex__(self) -> complex: ...
+    def __abs__(self) -> _RealLike: ...
+    def __neg__(self) -> _ComplexLike: ...
+    def __pos__(self) -> _ComplexLike: ...
+
 if sys.version_info >= (3, 11):
-    from typing import SupportsComplex as _SupportsComplex
+    _ComplexLike: TypeAlias = _SupportsComplex
 else:
     # builtins.complex didn't have a __complex__ method on older Pythons
-    import typing
+    _ComplexLike: TypeAlias = _SupportsComplex | complex
+
+# _RealLike is a structural-typing approximation
+# of the `Real` ABC, which is not (and cannot be) a protocol
+#
+# NOTE: _RealLike can't inherit from _SupportsComplex,
+# because not all builtin types that we want to be understood
+# as subtypes of _RealLike have a `__complex__` method
+# (e.g. `builtins.int.__complex__` does not exist)
+class _RealLike(Protocol):
+    def __neg__(self) -> _ComplexLike: ...  # TODO: ideally would be more precise
+    def __pos__(self) -> _ComplexLike: ...  # TODO: ideally would be more precise
+    def __abs__(self) -> _RealLike: ...
+    def __float__(self) -> float: ...
+    def __trunc__(self) -> _IntegralLike: ...
+    def __floor__(self) -> _IntegralLike: ...
+    def __ceil__(self) -> _IntegralLike: ...
 
-    _SupportsComplex: TypeAlias = typing.SupportsComplex | complex
+# _IntegralLike is a structural-typing approximation
+# of the `Integral` ABC, which is not (and cannot be) a protocol
+class _IntegralLike(_RealLike, Protocol):
+    def __int__(self) -> int: ...
+    def __index__(self) -> int: ...
+    def __invert__(self) -> _IntegralLike: ...
+    def __abs__(self) -> _IntegralLike: ...
 
-__all__ = ["Number", "Complex", "Real", "Rational", "Integral"]
+#################
+# Module "proper"
+#################
 
 class Number(metaclass=ABCMeta):
     @abstractmethod
@@ -35,86 +73,86 @@ class Complex(Number):
     def __bool__(self) -> bool: ...
     @property
     @abstractmethod
-    def real(self) -> SupportsFloat: ...
+    def real(self) -> _RealLike: ...
     @property
     @abstractmethod
-    def imag(self) -> SupportsFloat: ...
+    def imag(self) -> _RealLike: ...
     @abstractmethod
-    def __add__(self, other) -> _SupportsComplex: ...
+    def __add__(self, other) -> _ComplexLike: ...
     @abstractmethod
-    def __radd__(self, other) -> _SupportsComplex: ...
+    def __radd__(self, other) -> _ComplexLike: ...
     @abstractmethod
-    def __neg__(self) -> _SupportsComplex: ...
+    def __neg__(self) -> _ComplexLike: ...
     @abstractmethod
-    def __pos__(self) -> _SupportsComplex: ...
-    def __sub__(self, other) -> _SupportsComplex: ...
-    def __rsub__(self, other) -> _SupportsComplex: ...
+    def __pos__(self) -> _ComplexLike: ...
+    def __sub__(self, other) -> _ComplexLike: ...
+    def __rsub__(self, other) -> _ComplexLike: ...
     @abstractmethod
-    def __mul__(self, other) -> _SupportsComplex: ...
+    def __mul__(self, other) -> _ComplexLike: ...
     @abstractmethod
-    def __rmul__(self, other) -> _SupportsComplex: ...
+    def __rmul__(self, other) -> _ComplexLike: ...
     @abstractmethod
-    def __truediv__(self, other) -> _SupportsComplex: ...
+    def __truediv__(self, other) -> _ComplexLike: ...
     @abstractmethod
-    def __rtruediv__(self, other) -> _SupportsComplex: ...
+    def __rtruediv__(self, other) -> _ComplexLike: ...
     @abstractmethod
-    def __pow__(self, exponent) -> _SupportsComplex: ...
+    def __pow__(self, exponent) -> _ComplexLike: ...
     @abstractmethod
-    def __rpow__(self, base) -> _SupportsComplex: ...
+    def __rpow__(self, base) -> _ComplexLike: ...
     @abstractmethod
-    def __abs__(self) -> SupportsFloat: ...
+    def __abs__(self) -> _RealLike: ...
     @abstractmethod
-    def conjugate(self) -> _SupportsComplex: ...
+    def conjugate(self) -> _ComplexLike: ...
     @abstractmethod
     def __eq__(self, other: object) -> bool: ...
 
 # See comment at the top of the file
 # for why some of these return types are purposefully vague
-class Real(Complex, SupportsFloat):
+class Real(Complex):
     @abstractmethod
     def __float__(self) -> float: ...
     @abstractmethod
-    def __trunc__(self) -> SupportsIndex: ...
+    def __trunc__(self) -> _IntegralLike: ...
     @abstractmethod
-    def __floor__(self) -> SupportsIndex: ...
+    def __floor__(self) -> _IntegralLike: ...
     @abstractmethod
-    def __ceil__(self) -> SupportsIndex: ...
+    def __ceil__(self) -> _IntegralLike: ...
     @abstractmethod
     @overload
-    def __round__(self, ndigits: None = None) -> SupportsIndex: ...
+    def __round__(self, ndigits: None = None) -> _IntegralLike: ...
     @abstractmethod
     @overload
-    def __round__(self, ndigits: int) -> SupportsFloat: ...
-    def __divmod__(self, other) -> tuple[SupportsFloat, SupportsFloat]: ...
-    def __rdivmod__(self, other) -> tuple[SupportsFloat, SupportsFloat]: ...
+    def __round__(self, ndigits: int) -> _RealLike: ...
+    def __divmod__(self, other) -> tuple[_RealLike, _RealLike]: ...
+    def __rdivmod__(self, other) -> tuple[_RealLike, _RealLike]: ...
     @abstractmethod
-    def __floordiv__(self, other) -> SupportsFloat: ...
+    def __floordiv__(self, other) -> _RealLike: ...
     @abstractmethod
-    def __rfloordiv__(self, other) -> SupportsFloat: ...
+    def __rfloordiv__(self, other) -> _RealLike: ...
     @abstractmethod
-    def __mod__(self, other) -> SupportsFloat: ...
+    def __mod__(self, other) -> _RealLike: ...
     @abstractmethod
-    def __rmod__(self, other) -> SupportsFloat: ...
+    def __rmod__(self, other) -> _RealLike: ...
     @abstractmethod
     def __lt__(self, other) -> bool: ...
     @abstractmethod
     def __le__(self, other) -> bool: ...
     def __complex__(self) -> complex: ...
     @property
-    def real(self) -> SupportsFloat: ...
+    def real(self) -> _RealLike: ...
     @property
     def imag(self) -> Literal[0]: ...
-    def conjugate(self) -> SupportsFloat: ...  # type: ignore[override]
+    def conjugate(self) -> _RealLike: ...  # type: ignore[override]
 
 # See comment at the top of the file
 # for why some of these return types are purposefully vague
 class Rational(Real):
     @property
     @abstractmethod
-    def numerator(self) -> SupportsIndex: ...
+    def numerator(self) -> _IntegralLike: ...
     @property
     @abstractmethod
-    def denominator(self) -> SupportsIndex: ...
+    def denominator(self) -> _IntegralLike: ...
     def __float__(self) -> float: ...
 
 # See comment at the top of the file
@@ -124,31 +162,35 @@ class Integral(Rational):
     def __int__(self) -> int: ...
     def __index__(self) -> int: ...
     @abstractmethod
-    def __pow__(self, exponent, modulus: Incomplete | None = None) -> SupportsIndex: ...  # type: ignore[override]
+    def __pow__(self, exponent, modulus: Incomplete | None = None) -> _IntegralLike: ...  # type: ignore[override]
     @abstractmethod
-    def __lshift__(self, other) -> SupportsIndex: ...
+    def __lshift__(self, other) -> _IntegralLike: ...
     @abstractmethod
-    def __rlshift__(self, other) -> SupportsIndex: ...
+    def __rlshift__(self, other) -> _IntegralLike: ...
     @abstractmethod
-    def __rshift__(self, other) -> SupportsIndex: ...
+    def __rshift__(self, other) -> _IntegralLike: ...
     @abstractmethod
-    def __rrshift__(self, other) -> SupportsIndex: ...
+    def __rrshift__(self, other) -> _IntegralLike: ...
     @abstractmethod
-    def __and__(self, other) -> SupportsIndex: ...
+    def __and__(self, other) -> _IntegralLike: ...
     @abstractmethod
-    def __rand__(self, other) -> SupportsIndex: ...
+    def __rand__(self, other) -> _IntegralLike: ...
     @abstractmethod
-    def __xor__(self, other) -> SupportsIndex: ...
+    def __xor__(self, other) -> _IntegralLike: ...
     @abstractmethod
-    def __rxor__(self, other) -> SupportsIndex: ...
+    def __rxor__(self, other) -> _IntegralLike: ...
     @abstractmethod
-    def __or__(self, other) -> SupportsIndex: ...
+    def __or__(self, other) -> _IntegralLike: ...
     @abstractmethod
-    def __ror__(self, other) -> SupportsIndex: ...
+    def __ror__(self, other) -> _IntegralLike: ...
     @abstractmethod
-    def __invert__(self) -> SupportsIndex: ...
+    def __invert__(self) -> _IntegralLike: ...
     def __float__(self) -> float: ...
     @property
-    def numerator(self) -> SupportsIndex: ...
+    def numerator(self) -> _IntegralLike: ...
     @property
     def denominator(self) -> Literal[1]: ...
+    # Not actually overridden at runtime,
+    # but we override it in the stub to give it a more precise return type:
+    @abstractmethod
+    def __abs__(self) -> _IntegralLike: ...