C++ "unsigned" classes

Question

I'm writing some object code for processing fractional data (as opposed to floating-point data), and so far have the following:

 class frac {
    public:
       int numerator;
       unsigned int denominator;
 };

My question is:
How can I configure my class definition such that writing unsigned frac foo; makes an object identical to frac foo;, except int numerator; would become unsigned int numerator;?

Edit: While ordinarily I'd just use a template (frac <unsigned>), this code is going into a larger math API, and I'd prefer the final product to use the unsigned frac syntax

Extension: Many answers have stated that it is not possible to implement the unsigned frac syntax, but does anyone know why not? Does the C++ compiler have some special processing rule that accommodates for the existing unsigned types, or is there something else I'm missing?

Answer 1

You can achieve such things with Templates. For example

template <class Integral>
class frac {
  public:
    Integral numerator;
    std::make_unsigned_t<Integral> denominator;
};

http://en.cppreference.com/w/cpp/types/make_unsigned

You can use this class like this:

frac<int> signed;
frac<unsigned> nonnegative;

Answer 2

I don't think that it is possible. You can achieve something similar using templates:

template<typename T>
class frac_template
{
public:
    T numerator;
    unsigned int denominator;
};

class frac : public frac_template<int> {};
class ufrac : public frac_template<unsigned int> {};