How to forward declare a C++ template class?

This is how you would do it:

template<typename Type, typename IDType=typename Type::IDType>
class Mappings;

template<typename Type, typename IDType>
class Mappings
{
public:
    ...
    Type valueFor(const IDType& id) { // return value }
    ...
};

Note that the default is in the forward declaration and not in the actual definition.