import Data.Complex
import Test.QuickCheck


prop_linear :: Double -> Complex Double -> Complex Double -> Bool
prop_linear l x y =
 let g = fmap (*l) -- (*l) is a real linear function. fmap (*l) is a complex function
  in magnitude (g (x + y) - (g x + g y)) < 0.000001 -- equality on Double should be avoid

prop_linear_2 :: Double -> Double -> Complex Double -> Bool
prop_linear_2 l x y =
 let g = fmap (*l) 
  in magnitude (g (pure x * y) - (pure x * g y)) < 0.000001

main :: IO ()
main = do 
 putStrLn "Testing distribution of sum"
 quickCheckWith stdArgs{maxSuccess = 1000} prop_linear
 putStrLn "Testing multiplication by scalar"
 quickCheckWith stdArgs{maxSuccess = 1000} prop_linear_2