-- IB016 Seminar on Functional Programming
-- Task from lecture 03

import Control.Applicative
import Data.List ( sort )

newtype Triple a = Triple { unTriple :: (a, a, a) }
    deriving (Eq, Ord, Show, Read)

instance Functor Triple where
  fmap f (Triple (x, y, z)) = Triple (f x, f y, f z)

instance Applicative Triple where
  pure x = Triple (x, x, x)
  Triple (f, g, h) <*> Triple (x, y, z) = Triple (f x, g y, h z)

expand :: Num a => a -> [a]
expand x = [x-1, x, x+1]

(~+~) :: Num a => a -> a -> [a]
x ~+~ y = expand $ x + y

(~*~) :: Num a => a -> a -> [a]
x ~*~ y = liftA2 (*) (expand x) (pure y)
       ++ liftA2 (*) (pure x) (expand y)

almostPlusTimes :: Num a => a -> a -> a -> [a]
almostPlusTimes x y z = do
  tmp <- x ~+~ y
  tmp2 <- tmp ~*~ z
  return tmp2

maxMinEval :: (Num a, Ord a) => [a] -> (a, a)
maxMinEval list = (head sorted, last sorted)
  where sorted = sort list