How to have a function pointer to a generic lambda?

Question

As the title says, how can I have the following intent expressed in code ? The requirements being the function pointer takes any type of arguments. Variadic doesn't work because of std::string.

https://godbolt.org/z/1E1szT

Note that I cannot directly use auto fp = <the lambda> because fp is a class member variable.

#include <iostream>

template<typename T1, typename T2>
void(*fp)(T1 t1, T2 t2) = [](auto a, auto b){
                              std::cout << a << "--"
                              << b << std::endl;
                          };

int main(){
    fp(1, 2);
    fp('a', 'b');
}

Answer 1

A variable template is perfectly fine.
Even the way you initialize them is fine.

Just be aware it is a template for variables, not a variable storing a template (which cannot exist).

Thus when finally using it, things fall apart:

How should the compiler know which of the myriad potential instances you mean?
Simple, you have to actually tell it:

int main(){
    fp<int, int>(1, 2);
    fp<char, char>('a', 'b');
}

Of course, manually desugaring the lambda and getting an instance of it would be more practical:

struct {
    template <class T1, class T2>
    void operator()(T1 a, T2 b) const {
        std::cout << a << "--" << b << std::endl;
    };
} fp;

A shame we cannot simply give a lambda a name and let the compiler figure it out.
Brainstorming candidates for appropriate syntax:

struct A = []...;
struct B : []... {
};
using C = []...;

Answer 2

You cannot have such a template function pointer, but remember that a lambda is merely syntactical sugar, you can just write the class yourself.

class fp {
    template<class AT, class BT>
    void operator()(AT&& a, BT&& b) {
        std::cout << a << "--" << b << std::endl; 
    };
};
class class_with_functionoid_member {
    fp fn_;
};

And the more generic version would be that you can have the lambda as a member. You have to take the lambda type as a class parameter.

template<class fnT> 
class class_with_lambda_member {
    fnT fn_;
public:
    class_with_lambda_member(fnT fn) : fn_(std::move(fn)) {}
};

The gist is that a function pointer is a type of runtime type erasure, and template member functions require compile time lazy instantiation, and C++ has no way to mix these two concepts. All the workarounds that come to mind revolve around explicitly listing out every possible combination of T1 and T2` in the "interface", which doesn't mix with a function pointer, but can work with a function pointer looking object.

struct erasable_functions {
    virtual ~erasable_functions(){}
    virtual void operator()(int, int)=0;
    virtual void operator()(int, char)=0;
    virtual void operator()(char, int)=0;
    virtual void operator()(char, char)=0;
};

template<class lambdaT>
struct erased_functions : erasable_functions {
    lambdaT lambda_;
    erased_functions(lambdaT lambda) : lambda_(std::move(lambda)){}
    virtual void operator()(int a, int b) {lambda_(a, b);
    virtual void operator()(int a, char b) {lambda_(a, b);
    virtual void operator()(char a, int b) {lambda_(a, b);
    virtual void operator()(char a, char b) {lambda_(a, b);
};
template<class lambdaT>
erased_functions<lambdaT> erase_functions(lambdaT lambda)
{return {std::move(lambda)};}

struct class_with_functionoid_member {
    erasable_functions* functions_;
    class_with_functionoid_member(erasable_functions* functions) : functions_(functions){}
    void operator()(int a, int b) {(*functions_)(a, b);
    void operator()(int a, char b) {(*functions_)(a, b);
    void operator()(char a, int b) {(*functions_)(a, b);
    void operator()(char a, char b) {(*functions_)(a, b);
};

int main() {
    auto lambda = erase_functions([](auto a, auto b) {
            std::cout << a << "--" << b << std::endl;
        };
    class_with_functionoid_member c(&lambda);
}