`pow(complex(…), <value>, <value>)` and `pow(float(…), <value>, <value>)` should produce type errors

[posita]

complex's versions of __pow__ and __rpow__ invite the third modulo argument. That means that the following validates, when it shouldn't:

This applies to floats as well.

pow(complex(1), 2, 2)  # no type error?
pow(float(1), 2, 2)  # still no type error?

These are guaranteed to fail at runtime, even if the first arguments are losslessly convertible to ints:

>>> pow(complex(1), 2, 2)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: complex modulo
>>> pow(float(1), 2, 2)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: pow() 3rd argument not allowed unless all arguments are integers

I can't find an issue tracking this, and I don't think this is fixed by #6287.

---

As an aside, this "works" (in the sense it properly generates some error, but not what I would expect):

from numbers import Complex
my_complex: Complex = complex(1)  # type: ignore [assignment]  # see 3186
pow(my_complex, 2, 2)  # No overload variant of "pow" matches argument types "Complex", "int", "int"

That second error might just be some variation on python/mypy#3186, however?

[AlexWaygood]

I don't think the fix can be as simple as simply removing the third argument of float.__pow__/complex.__pow__, given that the following all succeed at runtime without error:

>>> pow(1.0, 2, None)
1.0
>>> 1.0.__pow__(2, None)
1.0
>>> pow(complex(1), 2, None)
(1+0j)
>>> complex(1).__pow__(3, None)
(1+0j)

[AlexWaygood]

Perhaps if we changed builtins._M (line 1283) from

from typing import TypeVar
_M = TypeVar("_M", contravariant=True)

to

from typing import TypeVar, SupportsIndex
_M = TypeVar("_M", contravariant=True, bound=SuppprtsIndex)

?

[posita]

And, to be fair, this works just fine at runtime:

>>> pow(complex(1), 2, None)
(1+0j)

In the bound proposal, is the intention to use SupportsIndex as a proxy for numbers.Integral-like things? (Kind of like how math.trunc accepts SupportsFloat?)

[AlexWaygood]

In the bound proposal, is the intention to use SupportsIndex as a proxy for numbers.Integral-like things? (Kind of like how math.trunc accepts SupportsFloat?)

Yeah, sort of. I think Mypy currently thinks pow(2.5, 3.9, 6) is okay because of the final overload of pow in line 1309, where we've told it that pow can be used with three arguments as long as the type passed in for argument 1 is annotated as having a __pow__ method that accepts three arguments. __float__ and __complex__ both are, and that's correct, because of course the None argument can be passed in explicitly at runtime! But the _M TypeVar used to parameterize the _SupportsPow3 protocol isn't restrictive enough.

[AlexWaygood]

Gotta go but some WIP experiments here https://mypy-play.net/?mypy=latest&python=3.10&flags=show-error-codes%2Cstrict&gist=b079cabb8620757ef16301a2dc12a352

[AlexWaygood]

Hmm, it's not the best error message, but this does seem to work: https://mypy-play.net/?mypy=latest&python=3.10&flags=show-error-codes%2Cstrict&gist=4e463e07a3a48610e140a4c98c18b0ca

It involves changing the 5th overload from

def pow(base: float, exp: float, mod: None = ...) -> Any: ...

to

def pow(base: complex, exp: complex, mod: None = ...) -> Any: ...

as well as the change to the _M TypeVar.

But, I haven't yet tested it with classes outside builtins.

[posita]

That's some expert level deep typing voodoo.

I just thought of another wrinkle. Mypy treats floats as equivalent to ints for many (all?) purposes. That may make guarding against that particular case problematic.

I also just noticed that Decimal is weird (but nobody cares about Decimal, so oh well, I guess):

>>> pow(Decimal("1.0"), Decimal("1.0"), Decimal("1.0"))  # works
Decimal('0')

[AlexWaygood]

Weird false-positive error in this implementation if you try to do pow(Fraction, complex) (though honestly, why would you??)

https://mypy-play.net/?mypy=latest&python=3.10&flags=show-error-codes%2Cstrict&gist=5b89b8868672e4cac1b4f6e2ead4422e

[AlexWaygood]

This is a better solution, I think -- introduce a third protocol to deal with classes that accept "three-argument pow but only if the third argument is None", rather than mucking around with binding the _M TypeVar. It even means that we can deal with the Decimal weirdness!

from typing import TypeVar, Protocol, Any, Literal, NoReturn, overload

_E = TypeVar("_E", contravariant=True)
_M = TypeVar("_M", contravariant=True)
_T_co = TypeVar("_T_co", covariant=True)

class _SupportsPow2(Protocol[_E, _T_co]):
    def __pow__(self, other: _E) -> _T_co: ...
    
class _SupportsPow3NoneOnly(Protocol[_E, _T_co]):
    def __pow__(self, other: _E, modulo: None = ...) -> _T_co: ...

class _SupportsPow3(Protocol[_E, _M, _T_co]):
    def __pow__(self, other: _E, modulo: _M = ...) -> _T_co: ...


@overload
def pow(base: int, exp: int, mod: Literal[0]) -> NoReturn: ...
# int base & positive-int exp -> int; int base & negative-int exp -> float
# return type must be Any as `int | float` causes too many false-positive errors
@overload
def pow(base: int, exp: int, mod: None = ...) -> Any: ...
@overload
def pow(base: int, exp: int, mod: int) -> int: ...
@overload
def pow(base: float, exp: int, mod: None = ...) -> float: ...
# float base & float exp could return float or complex
# return type must be Any as `float | complex` causes too many false-positive errors
@overload
def pow(base: complex, exp: complex, mod: None = ...) -> Any: ...
@overload
def pow(base: _SupportsPow2[_E, _T_co], exp: _E, mod: None = ...) -> _T_co: ...
@overload
def pow(base: _SupportsPow3NoneOnly[_E, _T_co], exp: _E, mod: None = ...) -> _T_co: ...
@overload
def pow(base: _SupportsPow3[_E, _M, _T_co], exp: _E, mod: _M = ...) -> _T_co: ...

There's still a false positive with Fraction ** complex though, and I can't work out why.

https://mypy-play.net/?mypy=latest&python=3.10&flags=show-error-codes%2Cstrict&gist=36736ab9a3edb91e8e890e5e373ec639

[posita]

I definitely need to up my TypeVar game. The thing that set me on this path was trying to type a helpful pow wrapper that would work with numerary (which has much less sophisticated SupportsComplexPow and SupportsIntegralPow protocols more akin to numbers.Complex and numbers.Integral).

[AlexWaygood]

I don't think this actually solves your original problem, but, er, here's a PR fixing some other problems with pow! #6325

[AlexWaygood]

@posita, I think this should maybe be refiled as a mypy issue now, since we now get error messages in the right places, it's just not the right kind of error messages. That feels like more of a mypy issue rather than a typeshed issue -- WDYT? 🙂

[AlexWaygood]

@posita, I think this should maybe be refiled as a mypy issue now, since we now get error messages in the right places, it's just not the right kind of error messages. That feels like more of a mypy issue rather than a typeshed issue -- WDYT? 🙂

Closing as per my comments here