Is there a way to test whether a C++ class has a default constructor (other than compiler-provided type traits)?

Question

Traits classes can be defined to check if a C++ class has a member variable, function or a type (see here).

Curiously, the ConceptTraits do not include traits to che

Answer 1

A modification of Potatoswatter's answer

Works on gcc-4.6

#include 

template< class T >
struct identity {
typedef T type;
};

template
struct if_c : identity {};

template< typename T, typename F>
struct if_c : identity {};

template
struct if_ : if_c< Bool::value, T, F> {};

template< class T >
struct is_default_constructible_;

template< class T >
struct is_default_constructible :
  if_< std::is_arithmetic,
    std::true_type,
    is_default_constructible_ >::type { };


template< class T >
struct is_default_constructible_ {

    template class Acessible : public D
    {
      friend class is_default_constructible_;
      public:
      //using D::D; may be needed once N2540 is implemented 
    };

    template
    class receive_size{};

    template< class U >
    static int sfinae( receive_size< sizeof Acessible() > * );

    template< class U >
    static char sfinae( ... );

public:
    enum { value = sizeof( sfinae(0) ) == sizeof(int) };

};

struct p { p(); };
class q { q(); };
class r { r(int); };

#include 
using namespace std;

int main() {
    cerr << is_default_constructible::value << endl // outputs 1
        << is_default_constructible
::value << endl
        << is_default_constructible::value << endl
        << is_default_constructible::value << endl; // outputs 0
}

# g++-mp-4.6 --std=c++0x -Wall test.cpp && ./a.out
1
1
0
0