Num instances for Sum and Product

[Dan Burton]

Data.Monoid in the base package specifies newtypes Sum and Product. It
would be convenient if these newtypes had appropriate Num instances, which
are trivial to write in plain Haskell:

import Data.Monoid
liftTy2 wrap unwrap op x y = wrap $ unwrap x `op` unwrap yliftTy wrap
unwrap f = wrap . f . unwrap
liftSum = liftTy Sum getSumliftSum2 = liftTy2 Sum getSum
instance (Num a) => Num (Sum a) where
  (+) = liftSum2 (+)
  (-) = liftSum2 (-)
  (*) = liftSum2 (*)
  abs = liftSum abs
  negate = liftSum negate
  signum = liftSum signum
  fromInteger = Sum . fromInteger
liftProd = liftTy Product getProductliftProd2 = liftTy2 Product getProduct
instance (Num a) => Num (Product a) where
  (+) = liftProd2 (+)
  (-) = liftProd2 (-)
  (*) = liftProd2 (*)
  abs = liftProd abs
  negate = liftProd negate
  signum = liftProd signum
  fromInteger = Product . fromInteger


Or with a few extensions (as noted by Daniel Wagner):

{-# LANGUAGE StandaloneDeriving, GeneralizedNewtypeDeriving #-}
import Data.Monoid
deriving instance Num a => Num (Sum a)deriving instance Num a => Num (Product a)


--
Dan Burton
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