import Prelude hiding (flip)

-- Compute the derivation of a (continuous) function.
derive :: (Float -> Float) -> (Float -> Float)
derive f = f'
 where f' x = (f (x + dx) - f x) / dx

dx :: Float
dx = 0.001

square :: Float -> Float
square x = x * x

cubic :: Float -> Float
cubic x = x * x * x

-- with lambda abstraction
deriveL :: (Float -> Float) -> (Float -> Float)
deriveL f = \x -> (f (x + dx) - f x) / dx

-- Addition of two floats:
add :: Float -> Float -> Float
add x y = x + y

add0 :: Float -> Float -> Float
add0 = \x y -> x + y

add1 :: Float -> (Float -> Float)
add1 x = \y -> x + y

takeFive :: [a] -> [a]
takeFive = take 5

inc :: Int -> Int
--inc = (+) 1
--inc = (1 +)
inc = (+ 1)

takeABC :: Int -> String
takeABC = (flip take) "abcdefghijkl"

-- Flips the order of the two arguments
flip :: (a -> b -> c) -> (b -> a -> c)
flip f = \y x -> f x y