`signature` for permutations has inconsistent signature compared to its behavior

[jhpalmieri]

Steps To Reproduce

sage: s = Permutations(4)[10]
sage: type(s.signature())
<class 'int'>

as compared to

def signature(self) -> Integer:

in combinat/permutation.py

Expected Behavior

I think that signature should return an Integer, not an int. There may be similar issues in this file; for example

    def size(self) -> Integer:
        return len(self)

and a few others that are supposed to return type Integer but actually return len(something).

Actual Behavior

The method returns an int, not an Integer.

Additional Information

See https://stackoverflow.com/questions/77052185/unexpected-error-with-sign-function-in-sagemath/77054009#77054009 for one person running into problems because of this.

Environment

- **OS**: OS X 13.5.1
- **Sage Version**: 10.2.beta1

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide

[dimpase]

Yes, one need mypy, most probably.
E.g.

$ pip install mypy --user
$ cat t.py
def f() -> float:
        return "hello"
$ mypy t.py
t.py:2: error: Incompatible return value type (got "str", expected "float")  [return-value]
Found 1 error in 1 file (checked 1 source file)

No idea how it plays with cython, though.

Should we run mypy on all the *.py files, at least, in our CI?

[jhpalmieri]

pyright was recommended, perhaps instead of mypy, on sage-devel. I don't have an opinion either way. Regardless, based on my understanding of the situation, I think it is appropriate that we are not currently recommending using type hints in the developer's guide. If we get good enough type-checking, we can change the documentation.

[jhpalmieri]

I tried sage --pip install mypy, followed by sage --sh and then mypy src/sage/combinat/permutation.py. Maybe I need to invoke this differently?

$ mypy src/sage/combinat/permutation.py
src/sage/combinat/permutation.py:247: error: Skipping analyzing "sage.arith.misc": module is installed, but missing library stubs or py.typed marker  [import]
src/sage/combinat/permutation.py:248: error: Skipping analyzing "sage.categories.finite_enumerated_sets": module is installed, but missing library stubs or py.typed marker  [import]
src/sage/combinat/permutation.py:249: error: Skipping analyzing "sage.categories.finite_permutation_groups": module is installed, but missing library stubs or py.typed marker  [import]
...
src/sage/combinat/permutation.py:9676: error: Skipping analyzing "sage.misc.persist": module is installed, but missing library stubs or py.typed marker  [import]
Found 48 errors in 1 file (checked 1 source file)

[fchapoton]

I am using the bash alias

alias mypy='python3 -m mypy --follow-imports=skip --ignore-missing-imports --python-version=3.10'