How does the template parameter of std::function work? (implementation)

Question

In Bjarne Stroustrup's home page (C++11 FAQ):

struct X { int foo(int); };

std::function<int(X*, int)> f;
f = &X::foo; //pointer to member

X x;
int v = f(&x, 5); //call X::foo() for x with 5

How does it work? How does std::function call a foo member function?

The template parameter is int(X*, int), is &X::foo converted from the member function pointer to a non-member function pointer?!

(int(*)(X*, int))&X::foo //casting (int(X::*)(int) to (int(*)(X*, int))

---

To clarify: I know that we don't need to cast any pointer to use std::function, but I don't know how the internals of std::function handle this incompatibility between a member function pointer and a non-member function pointer. I don't know how the standard allows us to implement something like std::function!

Answer 1

After getting help from other answers and comments, and reading GCC source code and C++11 standard, I found that it is possible to parse a function type (its return type and its argument types) by using partial template specialization and function overloading.

The following is a simple (and incomplete) example to implement something like std::function:

template<class T> class Function { };

// Parse the function type
template<class Res, class Obj, class... ArgTypes>
class Function<Res (Obj*, ArgTypes...)> {
    union Pointers {
        Res (*func)(Obj*, ArgTypes...);
        Res (Obj::*mem_func)(ArgTypes...);
    };

    typedef Res Callback(Pointers&, Obj&, ArgTypes...);

    Pointers ptrs;
    Callback* callback;

    static Res call_func(Pointers& ptrs, Obj& obj, ArgTypes... args) {
        return (*ptrs.func)(&obj, args...);
    }

    static Res call_mem_func(Pointers& ptrs, Obj& obj, ArgTypes... args) {
        return (obj.*(ptrs.mem_func))(args...);
    }

  public:

    Function() : callback(0) { }

    // Parse the function type
    Function(Res (*func)(Obj*, ArgTypes...)) {
        ptrs.func = func;
        callback = &call_func;
    }

    // Parse the function type
    Function(Res (Obj::*mem_func)(ArgTypes...)) {
        ptrs.mem_func = mem_func;
        callback = &call_mem_func;
    }

    Function(const Function& function) {
        ptrs = function.ptrs;
        callback = function.callback;
    }

    Function& operator=(const Function& function) {
        ptrs = function.ptrs;
        callback = function.callback;
        return *this;
    }

    Res operator()(Obj& obj, ArgTypes... args) {
        if(callback == 0) throw 0; // throw an exception
        return (*callback)(ptrs, obj, args...);
    }
};

Usage:

#include <iostream>

struct Funny {
    void print(int i) {
        std::cout << "void (Funny::*)(int): " << i << std::endl;
    }
};

void print(Funny* funny, int i) {
    std::cout << "void (*)(Funny*, int): " << i << std::endl;
}

int main(int argc, char** argv) {
    Funny funny;
    Function<void(Funny*, int)> wmw;

    wmw = &Funny::print; // void (Funny::*)(int)
    wmw(funny, 10); // void (Funny::*)(int)

    wmw = &print; // void (*)(Funny*, int)
    wmw(funny, 8); // void (*)(Funny*, int)

    return 0;
}