Well we want to construct something sort of like a natural transformation, I am pretty sure we need closure, but even with it exactly what we want to do is vague to me.

Well we can do it with monotonic functions, just using forall. So maybe for cost it would be sum or maximum of the distance from F(x) to G(x) is the cost from F to G?

Well we can do it with monotonic functions, just using forall. So maybe for cost it would be sum or maximum of the distance from F(x) to G(x) is the cost from F to G?