[Haskell-cafe] log, exp, (**), and non-negative real numbers

[Benjamin Redelings]

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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.haskell.org/pipermail/haskell-cafe/attachments/20230404/cbdd2f05/attachment.html>