import Prelude hiding ((.), curry, uncurry, const)

-- Function composition: (f . g) means: apply g, then f to its result
-- (.) :: (b -> c) -> (a -> b) -> (a -> c)
-- f . g = \x -> f (g x)

(.) :: (b -> c) -> (a -> b) -> a -> c
(f . g) x = f (g x)

-- Transforms a "pair" function into a "Curry-fied" function
curry :: ((a,b) -> c) -> a -> b -> c
-- curry f = \x y -> f (x,y)
curry f x y = f (x,y)

-- The opposite direction:
uncurry :: (a -> b -> c) -> (a,b) -> c
-- uncurry f = \ (x,y) -> f x y
uncurry f (x,y) = f x y

-- multiplies all sums of a list of pairs:
prodMult :: [(Int,Int)] -> Int
-- prodMult xs = prod (map (uncurry (+)) xs)
prodMult = prod . map (uncurry (+))
 where
   prod = foldr (*) 1

-- Constant function:
const :: a -> b -> a
const x _ = x