Thanks Adam! My only concern is that this package appears to use the CPP to generate the instances which at least to me feels more hacky than the mechanism by which instances are usually derived, like for Show or Eq or other classes.

I'd also be interested if someone could explain how those instances are derived if I could do something similar myself in this case.

On Fri, Apr 22, 2016, 15:14 adam vogt <vogt.adam@gmail.com> wrote:

Hi Jake

https://hackage.haskell.org/package/applicative-numbers can generate those instances.

Regards
Adam

On Apr 22, 2016 10:23 AM, "Jake" <jake.waksbaum@gmail.com> wrote:

Is it possible to automatically derive instances of Numeric type classes like Num, Fractional, Real, Floating, etc?

I currently have two datatypes, Pair and Triple, that are defined like this:

data Pair a = Pair a a

data Triple a = Triple a a a

I wrote these pretty trivial instances for Num and Floating:

instance Num a => Num (Pair a) where

  (+) = liftA2 (+)

  (*) = liftA2 (*)

  abs = liftA abs

  negate = liftA negate

  signum = liftA signum

  fromInteger = pure . fromInteger

instance Fractional a => Fractional (Pair a) where

  (/) = liftA2 (/)

  recip = liftA recip

  fromRational = pure . fromRational

and practically identical instances for Triple as well.

Is there anyway to have GHC derive these instances and the other numeric type classes?

Thanks,

Jake

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