Re: [Haskell-cafe] Automatically Deriving Numeric Type Class Instances

Hi Jake. I wrote applicative-numbers. The key observation is that every applicative functor gives rise to instances of Num & friends in a standard way, as you've noticed. Since your examples are isomorphic to functions from a suitably chosen domain, and function-from-t is an applicative functor for all types t, your examples are also applicative functors, with instances you can derive (as in http://conal.net/papers/type-class-morphisms/). It might make for a simple and useful project to convert applicative-numbers to use Template Haskell. - Conal On Fri, Apr 22, 2016 at 12:39 PM, Jake wrote:

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 wrote:

...

Hi Jake

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

Regards Adam On Apr 22, 2016 10:23 AM, "Jake" 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

_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe

---

Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe