Cannot initialize a lambda member variable a default argument

I would like to compile the code below with c++17, so that I can pass any function (lambda) that has a specific signature, int(int), while also allowing the default argument:

template <class F = int(int)> // for deduction
struct A{
        A(F f = [] (int x){return x;}) : f_{f} {}

        F f_;
};

int main() {
        A work([](int x){return x + 1;});
        A not_work; // compile error.
}

However, clang emits an error:

a.cpp:6:4: error: data member instantiated with function type 'int (int)'
        F f_;
          ^
a.cpp:11:4: note: in instantiation of template class 'A<int (int)>' requested here
        A not_work;
          ^

I don’t understand why the member f_ can be initialized when I pass the lambda and the default lambda argument cannot be?

Meanwhile, is there any better way to do this?

>Solution :

As the error message said, can’t declare a data member with a function type like int(int).

You might use a function pointer type (lambdas without capture could convert to function pointer implicitly) or std::function<int(int)>. E.g.

template <class F = int(*)(int)> // for deduction
struct A{
        A(F f = [] (int x){return x;}) : f_{f} {}

        F f_;
};

Or

template <class F = std::function<int(int)>> // for deduction
struct A{
        A(F f = [] (int x){return x;}) : f_{f} {}

        F f_;
};