Exponentiation in Haskell

Question

Can someone tell me why the Haskell Prelude defines two separate functions for exponentiation (i.e. ^ and **)? I thought the type system was suppo

Answer 1

Haskell's type system isn't powerful enough to express the three exponentiation operators as one. What you'd really want is something like this:

class Exp a b where (^) :: a -> b -> a
instance (Num a,        Integral b) => Exp a b where ... -- current ^
instance (Fractional a, Integral b) => Exp a b where ... -- current ^^
instance (Floating a,   Floating b) => Exp a b where ... -- current **

This doesn't really work even if you turn on the multi-parameter type class extension, because the instance selection needs to be more clever than Haskell currently allows.