CC: Functional dependencies question

[oleg@pobox.com]

>         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.