You shouldn't need rational exponents to take square roots as long as no *ground* type requires them. If polymorphism over units were primitive, then we'd have something like sqrt :: Real (u.u) -> Real u for a fixed numeric type Real that's parameterized over its units. (BTW, it's not possible to define such a function in the language using, say, only standard arithmetic operators and comparison; you have to build it in instead). In your encoding, is the following a valid type? sqrt :: (Num rep, Add kg kg kg', Add m m m', Add s s s') => Dimensioned kg' m' s' rep -> Dimensioned kg m s rep Or have I misunderstood multi-parameter classes with functional dependencies? - Andrew.
-----Original Message----- From: anatoli [mailto:anatoli@yahoo.com] Sent: Monday, April 09, 2001 5:37 PM To: haskell@haskell.org Subject: Dimensional analysis with fundeps
There is a couple of things :) left to make this usable:
...
2) Make it work with rational (not just integer) exponents, so one can take square roots and the like. (Can one do GCD in this style, without resorting to undecidable and/or overlapping instances?);