app_c.c

#include <stdio.h>
#include "lib.h"

double f0(void) {
    return 123;
}

double f2(double a, double b) {
    return a + b;
}

int main() {
    cb_arity = 0;
    cb_func = f0;
    printf("%f\n", cb_call());

    cb_arity = 2;
    cb_func = f2;
    printf("%f\n", cb_call());
}

app_cpp.cpp

#include <stdio.h>
#include "lib.h"

int main() {
    cb_arity = 0;
    cb_func = []() { return 123.0; };
    printf("%f\n", cb_call());

    cb_arity = 2;
    cb_func = reinterpret_cast<double(*)()>(static_cast<double(*)(double, double)>(
        [](double a, double b) { return a + b; }
    ));
    printf("%f\n", cb_call());
}

build.sh

#!/bin/bash
set -xeuo pipefail
gcc lib.c -c
gcc app_c.c lib.o -o app_c
./app_c
g++ app_cpp.cpp lib.o -o app_cpp
./app_cpp

lib.c

#include "lib.h"
#include <stdlib.h>

int cb_arity;
double (*cb_func)();

double cb_call(void) {
    switch (cb_arity) {
        case 0:
            return cb_func();
        case 1:
            return cb_func(10.0);
        case 2:
            return cb_func(10.0, 20.0);
        case 3:
            return cb_func(10.0, 20.0, 30.0);
        default:
            abort();
    }
}

lib.h

#ifndef LIB_H_
#define LIB_H_

#ifdef __cplusplus
extern "C" {
#endif

extern int cb_arity;
extern double (*cb_func)();
double cb_call(void);

#ifdef __cplusplus
}
#endif

#endif  // LIB_H_