Template functors which must provide themself as a template arguments

Question

I would very much like to be able to provide a functor as a template argument. The functors must be able to provide "themself" as that argument.

I imagine something like this:

template<typename T, template<typename> class SumFunctor> class foo;

template<typename T>
struct sum_default
{
    foo<T, sum_default> operator()(foo<T, sum_default> a, foo<T, sum_default> b) const 
    {
            T a_data = a.data();
            T b_data = b.data();
            return foo<T, sum_default>(a_data + b_data);
    }
};

template<typename T>
struct sum_awesome
{
    foo<T, sum_awesome> operator()(foo<T, sum_awesome> a, foo<T, sum_awesome> b) const 
    {
            T a_data = a.data();
            T b_data = b.data();
            return foo<T, sum_awesome>(a_data - b_data);
    }
};

template<typename T=int, template<typename> class SumFunctor=sum_default>
class foo
{
private:
    T _data;
    SumFunctor<T> _functor;
public:
    foo<T, SumFunctor>(T data) : _data(data) {}

    T data() { return _data; }

    friend const foo operator +(const foo& lhs, const foo& rhs)
    {
            return lhs._functor(lhs,rhs);
    }
};

int main(){
    foo<> a(42); 
    foo<double> b(1.0);
    foo<double,sum_default> c(4.0);
    foo<double,sum_awesome> d(4.0);

    a+a;
    d+d;
}

Is this possible, and if so, how?

An alternative solution is to provide the functor to the constructor, but this is very ugly i think, as the user must dynamically allocate the functor himself (As we cannot determine the type of the functor in the constructor. Using RTTI to do so also seems a bit ugly):

foo<double> a(42, new sum_default<double>() );

This also forces all functors to be derived from some pre-defined base functor.

UPDATE

Attempting to add template arguments to the sum_default template argument does not appear to solve the problem:

template<typename T>
struct sum_default
{
// Error    1   error C3200: 'sum_default<T>' : invalid template argument for template parameter 'SumFunctor', expected a class template
foo<T, sum_default<T> > operator()(foo<T, sum_default<T> > a, foo<T, sum_default<T> > b) const 
{
    T a_data = a.data();
    T b_data = b.data();
    return foo<T, sum_default<T> >(a_data + b_data);
}
};

Answer 1

What's biting you here is known as "class name injection" – inside of a class template, e.g. Foo<T>, unqualified use of Foo is actually treated as Foo<T>. Citing C++11 §14.6.1/1:

Like normal (non-template) classes, class templates have an injected-class-name. The injected-class-name can be used as a template-name or a type-name. When it is used with a template-argument-list, as a template-argument for a template template-parameter, or as the final identifier in the elaborated-type-specifier of a friend class template declaration, it refers to the class template itself. Otherwise, it is equivalent to the template-name followed by the template-parameters of the class template enclosed in <>.

Consequently, inside of sum_default<T>, when you have foo<T, sum_default>, it's treated as though you typed foo<T, sum_default<T> > (which obviously won't work as foo wants a template template parameter).

In order to avoid this behavior, you need to qualify uses of the class template names inside of those class templates. Because your class templates are in the global scope, :: is sufficient:

template<typename T>
struct sum_default;

template<typename T = int, template<typename> class SumFunctor = sum_default>
class foo
{
    T _data;
    SumFunctor<T> _functor;

public:
    foo<T, SumFunctor>(T data) : _data(data) { }

    T data() { return _data; } const

    friend foo operator +(foo const& lhs, foo const& rhs)
    {
        return lhs._functor(lhs, rhs);
    }
};

template<typename T>
struct sum_default
{
    foo<T, ::sum_default> operator ()(foo<T, ::sum_default> a,
                                      foo<T, ::sum_default> b) const
    {
        return foo<T, ::sum_default>(a.data() + b.data());
    }
};

template<typename T>
struct sum_awesome
{
    foo<T, ::sum_awesome> operator()(foo<T, ::sum_awesome> a,
                                     foo<T, ::sum_awesome> b) const
    {
        return foo<T, ::sum_awesome>(a.data() - b.data());
    }
};

int main()
{
    foo<> a(42);
    foo<double> b(1.0);
    foo<double, sum_default> c(4.0);
    foo<double, sum_awesome> d(4.0);

    a + a;
    d + d;
}

Note that this also allows you to define foo's constructor thusly, reducing a bit of noise:

foo(T data) : _data(data) { }