module Lecture01A where
import Test.QuickCheck
-- This is the file created during lecture 1 2009-10-27
-- David Sands, tr.im/tda451

euroRate = 10.21 

price :: Double
price = 5

euro,sek :: Double -> Double
sek e = e * euroRate
euro s = s / euroRate

prop_EuroSek :: Double -> Bool
prop_EuroSek e = euro (sek e) ~== e

(~==) :: Double -> Double -> Bool
x ~== y = abs (x - y) < epsilon 
        where epsilon = 0.000001


prop_ApproxEq :: Double -> Double -> Bool
prop_ApproxEq x y = if x ~== y then y ~== x else True

{-- Notes: Although this test was good enough to catch the bug in the
 original definition of ~==, there is a problem when using this for
 random testing: most of the time randomly generated x and y will
 not be "approximately equal" so the test will not be useful. Soon
 we will see ways that we can fix this problem using QuickCheck
 --}

absolute :: Integer -> Integer
absolute x | x >= 0  = x
absolute x | x < 0   = -x