Hi, I'm working with some classes that handle probabilities in terms of their log or log-odds. Such classes only handle non-negative real numbers. For example, from Numeric.Log: newtype Log a = Exp { ln :: a } Since the log of a positive number can be negative, we don't want to use the same type to hold the number and its logarithm. Standard functions exp, log, and (**) are awkward because they all assume that numbers and their powers have the same type: log,exp :: a -> a (**) :: a -> a -> a In comparison the ln function from Numeric.Log has a different signature that allows a number and its logarithm to have different types: ln :: Log a -> a Exp :: a -> Log a In order to address this, I have tried defining a type class Pow: class Fractional a => Pow a where pow :: a -> Double -> a ln :: a -> Double expTo :: Double -> a Probably I should replace "Double" here by a type variable b, but I have not done so yet. I'm mostly interested in abstracting over the type of non-negative number, because I have another type Prob that is designed to handle numbers like 1e - 100000, and 1.0 - 1e-100000. data Prob = Zero | Odds Double | One | IOdds Double | Infinity -- store probability in terms of log odds = log (p/(1-p)) Q1. Does anybody know of an existing Haskell module that implements something like the Pow class above? Also, it would be nice (notationally) if I could use log, exp, and (**) instead of ln, expTo, and pow. In theory we could factor out log, exp, (**), sqrt, and logBase from Floating into a new superclass of Floating, so that Floating only contains trig and hyper-trig functions. But I suspect this will not work because the methods in class Pow are more ambiguous. For example, if (x :: Double) then you can do (expTo x :: Prob) and (expTo x :: Log Double) and they will yield different types. Q2. Does anybody have a suggestion for a nicer design? Thanks! -BenRI