Assign C++ type to `std::function` with pybind11 without going through python

binding.cpp

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

#include <functional>

namespace py = pybind11;

struct Outer {
  std::function<double(int, int)> func{nullptr};
};

struct Callable {
  double operator()(int a, int b) { return a + b; }
};

PYBIND11_MODULE(demo, m) {
  py::class_<Outer>(m, "Outer")
      .def(py::init<>())
      .def_readwrite("func", &Outer::func);

  auto c = py::class_<Callable>(m, "Callable")
      .def(py::init<>());

  // adding this line fixes the python error, but the call now goes through python
  // c.def("__call__", &Callable::operator());
}

CMakeLists.txt

project(pybind_repro)
cmake_minimum_required(VERSION 3.14)

find_package(pybind11 CONFIG REQUIRED)

pybind11_add_module(demo binding.cpp) 

test.cpp

int main() {
  Outer outer;
  Callable callable;
  outer.func = callable; // no problem
}

test.py

#!/usr/bin/env python3

import demo

outer = demo.Outer()
callable = demo.Callable()
outer.func = callable
# ^ this gives the following error
"""
Traceback (most recent call last):
  File "test.py", line 7, in <module>
    outer.func = callable
TypeError: (): incompatible function arguments. The following argument types are supported:
    1. (self: demo.Outer, arg0: Callable[[int, int], float]) -> None

Invoked with: <demo.Outer object at 0x7fc275a716f0>, <demo.Callable object at 0x7fc275a71770>
"""