Template specialization example

To my understanding, template specialization works as follows

template< typename T > 
void dummy(T a)
std::cout<<a<<std::endl;

template<>
void dummy<int>(int a)
  std::cout<<"special"<<std::endl;
};

I was looking at the following code which checks if something is a pointer or not:

template< typename T > 
struct is_ptr{ 
  constexpr static bool value = false;
};

template<typename T>
struct is_ptr<T*>{ 
  constexpr static bool value = true; 
};

Is this still a template specialization? Why is the line template <typename T> there again in the specialization, and not <>. Is it because multiple specializations are generated by the compiler whenever we have T* rather than T?

Would this code expand to

template<>
struct is_ptr<int*>
{
  constexpr static bool value = true;
 }

?