hbar :: (Mult Energy Time t) => t hbar = PhysicalUnit 6.62606876e-34
But what if we add to our library joule::Energy = PhysicalUnit 1.0 cal::Energy = PhysicalUnit 4.8 second::Time = PhysicalUnit 1.0 nanosec::Time = PhysicalUnit 1.0e-9 and scalarm:: Double -> (PhysicalUnit a1 b1 c1) -> (PhysicalUnit a1 b1 c1) x `scalarm` (PhysicalUnit y) = PhysicalUnit $ x * y then the user can write hbar = 6.62606876e-34 `scalarm` (joule `mult` second) or hbar = 6.62606876e-25 `scalarm` (joule `mult` nanosec) or hbar = (6.62606876e-25/4.8) `scalarm` (cal `mult` nanosec) Can't we? Or I'm missing something? GHC seems happy. We can probably define in the library transf:: (PhysicalUnit a1 b1 c1) -> (PhysicalUnit a1 b1 c1) -> Double transf (PhysicalUnit x) (PhysicalUnit y) = x/y and write hbar = (6.62606876e-25/(cal `transf` joule)) `scalarm` (cal `mult` nanosec) P.S. Just for the record: yet another way to introduce negative numbers is through an explicit constructor Neg. For example: http://pobox.com/~oleg/ftp/Computation/type-arithmetics.html (sorry, the code uses C++ templates. The idea is just the same however: a mere Prolog in a more verbose notation). The above example demonstrates division of signed Peano numbers. The Neg constructor becomes quite handy then.