Representing Quantities

The types listed above are still pure metadata; to typecheck real computations we'll need to somehow bind them to our runtime data. A simple numeric value wrapper, parameterized on the number type T and on its dimensions, fits the bill:

template <class T, class Dimensions>
struct quantity
{
    explicit quantity(T x)
       : m_value(x)
    {}

    T value() const { return m_value; }
 private:
    T m_value;
};

Now we have a way to represent numbers associated with dimensions. For instance, we can say:

quantity<float,length> l( 1.0f );
quantity<float,mass> m( 2.0f );

Note that Dimensions doesn't appear anywhere in the definition of quantity outside the template parameter list; its only role is to ensure that l and m have different types. Because they do, we cannot make the mistake of assigning a length to a mass:

m = l;    // compile-time type error