-- uvedené typy neupravujte, kromě případného přidávání instancí typových tříd

data OpType = Add | Mul deriving Show

data Expr a = Con a
            | Var String
            | Op OpType [Expr a]
            | Let String (Expr a) (Expr a)  -- let a = x in y
            deriving Show

freeVars :: Expr a -> [String]
freeVars = undefined

simplifyArity01 :: Num a => Expr a -> Expr a
simplifyArity01 = undefined

eval :: Num a => Expr a -> [(String, a)] -> Maybe a
eval = undefined

flatten :: Expr a -> Expr a
flatten = undefined

simplifyIdentity :: (Eq a, Num a) => Expr a -> Expr a
simplifyIdentity = undefined

simplifyAnnihilating :: (Eq a, Num a) => Expr a -> Expr a
simplifyAnnihilating = undefined

simplifyConstants :: Num a => Expr a -> Expr a
simplifyConstants = undefined