On Sun, 10 Sep 2006, Aaron Denney wrote:
Of course, there's always a typeclass, where we could add all sorts of other encodings of the Peano axioms, such as binary trees,, but I don't see that that buys us much if we don't also get access to operations beyond them, such as (an _efficient_) `div` for fastexp.
I don't see why Natural can't have an instance of whatever class ends up owning âdivâ. It's perfectly well behaved on Naturals.
True. It seems odd to have a multiplicative (pseudo) inverse, but not an additive, though. Breaking up the numeric hierarchy too finely seems like it would be a pain -- take it to the limit of a separate class per function. What else would you drag in with "div"? "mod", (*), ...?
from http://darcs.haskell.org/numericprelude/src/Algebra/Core.lhs :
class (Num a) => Integral a where div, mod :: a -> a -> a divMod :: a -> a -> (a,a)
-- Minimal definition: divMod or (div and mod) div a b = fst (divMod a b) mod a b = snd (divMod a b) divMod a b = (div a b, mod a b)