{-# LANGUAGE TypeSynonymInstances #-}

module RealFunction
where


type RealFunction a = (a -> Double)

instance Show (RealFunction a) where
    show _ = "Real Function"

instance Eq (RealFunction a) where
    _ == _ = False

instance Num (RealFunction a) where
    (f1 + f2)  x = (f1 x) + (f2 x)
    (f1 - f2)  x = (f1 x) - (f2 x)
    (f1 * f2)  x = (f1 x) * (f2 x)
    (negate f) x = -1 * (f x)
    (abs    f) x = abs (f x)
    (signum f) x = signum (f x)
    fromInteger i _ = fromInteger i


-- Takes a constant, and a function as arguments. Returns a new
-- function representing the original function times the constant.
cmult :: Double -> (RealFunction a) -> (RealFunction a)
cmult coeff f = (*coeff) . f

-- Takes a function f and an exponent n. Returns a new function, f^n.
fexp :: (RealFunction a) -> Int -> (RealFunction a)
fexp f n
     | n == 0 = (\_ -> 1)
     | otherwise = \x -> (f x)^n