import QuickCheck

------------------------------------------------------------------------
-- Step

-- pulse returns 1 for arguments between 0 and 1, inclusive, and 0
-- otherwise.
pulse :: (Ord a, Num a, Num b) => a -> b
pulse x | 0 <= x && x <= 1 = 1
        | otherwise        = 0

pulse' :: Double -> Double
pulse' x | 0 <= x && x <= 1 = 1
         | x < 0            = 0
         | x > 1            = 0

prop_pulse_1 :: Double -> Property
prop_pulse_1 x = 0 <= x && x <= 1 ==> pulse x == 1

prop_pulse_0 :: Double -> Property
prop_pulse_0 x = x < 0 || x > 1 ==> pulse x == 0

------------------------------------------------------------------------
-- Square

-- Given two arguments, an x coordinate and a y coordinate, returns
-- True if the corresponding point lies in or on the unit square
-- centred around the origin.
unitSquare :: Double -> Double -> Bool
unitSquare x y | abs x <= 0.5 && abs y <= 0.5 = True
               | otherwise                    = False

unitSquare' :: Double -> Double -> Bool
unitSquare' x y = if abs x <= 0.5 && abs y <= 0.5 then
                    True
                   else
                    False

unitSquare'' :: Double -> Double -> Bool
unitSquare'' x y = abs x <= 0.5 && abs y <= 0.5

prop_unitSquare :: Bool
prop_unitSquare =
  unitSquare 0.5 (-0.5) == True &&
  unitSquare 0.5 0.5 == True &&
  unitSquare 1.0 0.0 == False &&
  unitSquare 0.0 0.0 == True

prop_unitSquareX :: Double -> Double -> Bool
prop_unitSquareX x y = unitSquare x y == unitSquare (-x) y

prop_unitSquareY :: Double -> Double -> Bool
prop_unitSquareY x y = unitSquare x y == unitSquare x (-y)

------------------------------------------------------------------------
-- Iff

-- Returns True iff both arguments are True.
iff :: Bool -> Bool -> Bool
iff True True = True
iff _    _    = False

prop_iffLeft :: Bool -> Bool -> Property
prop_iffLeft  x y = x `iff` y ==> x == True

prop_iffRight :: Bool -> Bool -> Property
prop_iffRight x y = x `iff` y ==> y == True

-- Returns True iff both arguments are True.
iff' :: Bool -> Bool -> Bool
iff' True True = True
iff' x    y    = False