[QUESTION] disambiguating lambda arguments in function overloads

I have a question about writing overloaded function bindings and I could not find the answer anywhere in the docs or FAQ.

In my C++ code I have two overloaded variants of a function (call it "func"), each of which takes a single argument that is a std::function instance (lambda function). When I run my code in pure C++, disambiguation of the two argument types works just fine. However, when I try to write a pybind11 python module using the py::overload_cast tool, the disambiguation fails and I get a TypeError. Here is a simplified demonstration of the issue I'm running into. I am using C++14.

C++ source:

#include <pybind11/pybind11.h>
#include <pybind11/functional.h>

namespace py = pybind11;

int func(const std::function<int(int)> &f) { return f(10); }

int func(const std::function<int(int,int)> &f) { return f(10,4); }

PYBIND11_MODULE(mymodule, m) {
    m.def("func", py::overload_cast<const std::function<int(int)> &>(&func));
    m.def("func", py::overload_cast<const std::function<int(int,int)> &>(&func));
}

Python source:

import mymodule

def f1(a):
    return 2*a

def f2(a, b):
    return 2*a + b

print(mymodule.func(f1))
print(mymodule.func(f2))

Python output:

20
Traceback (most recent call last):
  File "test.py", line 10, in <module>
    print(mymodule.func(f2))
TypeError: f2() missing 1 required positional argument: 'b'

Is there a way to get the desired overloading behavior with pybind11? I've tried adding type hints to the f1 and f2 python functions, thinking perhaps this would help pybind11 disambiguate the different lambda arguments. No luck.

Start with the PYBIND11_MODULE binding definitions using py::overload_cast and the included pybind11/functional.h support, then reproduce the f1 and f2 calls from the Python example. Compare how the two std::function overloads are selected and determine whether the desired behavior is supported; done means documenting or validating the appropriate approach.