{-# LANGUAGE FlexibleContexts, UndecidableInstances, FlexibleInstances #-}

-- Lifting Num over Applicative
module ApplicativeNum where

import Control.Applicative

-- The property that allows the lifting.  We can't lift all
-- Applicatives, so we need to bless the ones we can.
class Applicative a => NumericApp a  
class NumericApp a => NumericAppOpaque a

-- These don't work in general.
instance NumericAppOpaque a => Eq (a n) where (==) _ _ = False
instance NumericAppOpaque a => Show (a n) where show _ = "#<...>"


instance (NumericApp a, Num n, Show (a n), Eq (a n)) => Num (a n) where
  (+) = liftA2 (+)
  (*) = liftA2 (*)
  abs = fmap abs
  signum = fmap signum
  fromInteger = pure . fromInteger