Exercise 12.11 [alt-measure-exercise]

An alternative scheme for representing measures involves applying the units function to an abstract length object. In such a scheme, one would write ${Inches}({Length}(L_1)) = {1.5}$. How does this scheme compare with the one in the chapter? Issues include conversion axioms, names for abstract quantities (such as “50 dollars”), and comparisons of abstract measures in different units (50 inches is more than 50 centimeters).