How would I introduce number classes that are extended with plus and minus infinity? I'd like to have polymorphism over these new classes, something like a signature f :: (Real a, Extended a b) => b -> b which clearly is not part of the current syntax, but I hope you get the picture. What are the elegant ways of doing this? Somewhat related (I think), I have a class of dyadic numbers, it is clearly in Num and Real, but not in Fractional. Now, I would like to have intervals, both dyadic and rational, providing operations like lower and upper end point, centre, diameter, the partial order of interval inclusion, and membership for a dyadic/rational number. All these operations can be computed on dyadic numbers (only division by 2 is needed). Could I make the rational numbers belong to a class of "averageable numbers" or something like that so that I can get actual dyadic numbers returned when they happen to be dyadic? Jens