Further improve pow

[AlexWaygood]

With the current stubs, mypy produces this output with the following code snippet:

from fractions import Fraction

reveal_type(pow(2, 4))                            # Revealed type is "Any"
reveal_type(pow(5, -7))                           # Revealed type is "Any"
reveal_type(pow(Fraction(), 4, None))             # error: No overload variant of "pow" matches argument types "Fraction", "int", "None"
reveal_type(pow(Fraction(3, 7), complex(1, 8)))   # error: Cannot infer type argument 1 of "pow"
reveal_type(pow(complex(4, -8), Fraction(2, 3)))  # error: Cannot infer type argument 1 of "pow"
reveal_type(4 .__pow__(7, 4))                     # Revealed type is "Any"
reveal_type(4 .__pow__(6, None))                  # Revealed type is "Any"

With the patch that this PR proposes, the output changes to the following:

from fractions import Fraction

reveal_type(pow(2, 4))                            # Revealed type is "builtins.int"
reveal_type(pow(5, -7))                           # Revealed type is "builtins.float"
reveal_type(pow(Fraction(), 4, None))             # Revealed type is "fractions.Fraction*"
reveal_type(pow(Fraction(3, 7), complex(1, 8)))   # Revealed type is "builtins.complex"
reveal_type(pow(complex(4, -8), Fraction(2, 3)))  # Revealed type is "builtins.complex"
reveal_type(4 .__pow__(7, 4))                     # Revealed type is "builtins.int"
reveal_type(4 .__pow__(6, None))                  # Revealed type is "builtins.int"

All other cases that I tested remain unchanged. A more exhaustive test script is attached, as are results of the test script with the current stubs, and with this PR applied:

• test_pow.txt (Uploaded here as a .txt file because GitHub won't let me upload a .py file, but this is really a Python file. Save it with a .py extension and run mypy on it to test pow.)
• pow_results_prior_to_changes.txt
• pow_results_with_changes.txt

The exact command I ran to test this patch was:

mypy --python-version 3.10 --no-site-packages --show-traceback --no-implicit-optional --disallow-any-generics --warn-incomplete-stub --no-error-summary --custom-typeshed-dir . --warn-unused-ignores test_pow.py

[github-actions]

According to mypy_primer, this change has no effect on the checked open source code. 🤖🎉

[AlexWaygood]

I have no idea how this could be implemented, but it would be great if typeshed could have some kind of regression tests for really thorny cases like pow. Something like

assert_revealed_type_equality(pow(Fraction(), 4, None), Fraction)

stubtest and mypy_primer are amazing tools, but the corner cases of pow aren't common enough for these tools to reveal any change in behaviour here.

[JelleZijlstra]

Yes, that's #1339. We never got around to actually implementing this, and stubtest and mypy-primer have removed some of the need for it, but it would still be useful.

[posita]

I love this:

… _SupportsSomeKindOfPow …

🤣

[Molkree]

@AlexWaygood, could you answer a couple of my questions?

1. As far I understand the reason to have _PositiveInteger/_NegativeInteger is because we can't create "all positive/negative ints" types, right? So by defining a Literal we have at least some type inference for small exponents.
2. Why did you choose to stop at 25/-20? My only guess now is that it fits in one line according to the formatting rules in typeshed 😅
3. Why wasn't 0 exponent included in _PositiveInteger? I know it wouldn't be strictly "positive" integer then but 2**0 produces int in Python and currently it is Any according to typeshed.

Thank you!

[AlexWaygood]

1. Yup, you're quite correct! There's no way (not yet, anyway) of expressing "positive integer" in a general way, but if you're calling it with literal types, they're likely to be quite small -- and this hack is better than nothing :)
2. Yup, once again spot on! I can't remember whether this is exactly the maximum line length black will allow under the settings typeshed has in pyproject.toml -- but it's close to it, and they're nice round numbers ;)
3. Um... good catch! No reason at all! Feel free to submit a PR correcting my oversight! 🙂

[srittau]

I love this:

… _SupportsSomeKindOfPow …

rofl

Too bad emoijs don't work as names, otherwise we could have named this _SupportsSomeKindOf💥.