data Interval = Interval Double Double deriving (Show)

upperBoundary :: Interval -> Double
upperBoundary (Interval a b) = max a b

lowerBoundary :: Interval -> Double
lowerBoundary (Interval a b) = min a b

instance Eq Interval where
	x == y = (lowerBoundary x == lowerBoundary y) && (upperBoundary x == upperBoundary y)

instance Num Interval where
	x + y = Interval (lowerBoundary x) + (lowerBoundary y) (upperBoundary x) + (upperBoundary y)
	x - y = Interval (lowerBoundary x) - (upperBoundary y) (upperBoundary x) - (lowerBoundary y)
	x * y = Interval (min (lowerBoundary x) * (lowerBoundary y) (lowerBoundary x) * (upperBoundary y) (upperBoundary x) * (lowerBoundary y) (upperBoundary x) * (upperBoundary y))
	                 (max (lowerBoundary x) * (lowerBoundary y) (lowerBoundary x) * (upperBoundary y) (upperBoundary x) * (lowerBoundary y) (upperBoundary x) * (upperBoundary y))

instance Fractional Interval where
	x / y = Interval (min (lowerBoundary x) * (1/(lowerBoundary y)) (lowerBoundary x) * (1/(upperBoundary y)) (upperBoundary x) * (1/(lowerBoundary y)) (upperBoundary x) * (1/(upperBoundary y)))
	                 (max (lowerBoundary x) * (1/(lowerBoundary y)) (lowerBoundary x) * (1/(upperBoundary y)) (upperBoundary x) * (1/(lowerBoundary y)) (upperBoundary x) * (1/(upperBoundary y)))