import SimplePrelude hiding (flip)

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

-- Derivation of a function on an argument:
derive :: (Float -> Float) -> (Float -> Float)
derive f = f'
 where f' :: Float -> Float
       f' x = (f (x +. dx) -. f x) /. dx

       dx :: Float
       dx = 0.0001

double :: Float -> Float
double = derive square

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

-- with lambda abstraction:
lderive :: (Float -> Float) -> (Float -> Float)
lderive f = \x -> (f (x +. dx) -. f x) /. dx
 where
  dx = 0.0001


-- Addition on floats:
add :: Float -> Float -> Float
add x y = x +. y

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

add2 :: (Float -> Float -> Float)
add2 = \x y -> x +. y

addp :: (Float,Float) -> Float
addp (x,y) = x +. y

sub :: Float -> Float -> Float
sub x y = x -. y

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