module Exercise_9 where

{- Library DO NOT CHANGE -}

infixl 6 :+:
infixl 7 :*:

data Arith = Literal Integer
           | Var String
           | Arith :+: Arith
           | Arith :*: Arith
  deriving (Show, Eq)

{- End Library -}


{-H9.1-}

-- Beweis: abzugeben als map_tree.cprf


{-H9.2-}

eval :: (String -> Integer) -> Arith -> Integer
eval = undefined

equivalent :: (String -> Integer) -> Arith -> Arith -> Bool
equivalent = undefined

isSimple :: Arith -> Bool
isSimple = undefined

prop_isSimplification :: (Arith -> Arith) -> (String -> Integer) -> Arith -> Bool
prop_isSimplification simplify valuation a = undefined


{-H9.3-}

simplify :: Arith -> Arith
simplify = undefined


{-H9.4-}

g :: (a -> a') -> (b -> b') -> Either a b -> Either a' b'
g = undefined

h :: (a -> Either a b) -> a -> b
h = undefined