tried some polynoms 2: now with some `*` and foldr(-p), Haskell

tried some polynoms 2: now with some `*` and foldr(-p)

main :: IO ()
main = do
    print $ foldr (\x acc -> x * acc) 1 Null
    print $ foldr (\x acc -> x * acc) 1 (1:+:2:+:Null)
    print $ (1 :+: 2 :+: 3 :+: 4 :+: Null) * (1 :+: 1 :+: Null)
    
infixr 5 :+:
data Polynomial a = Null | a :+: Polynomial a
    deriving (Show, Eq)
    
deg :: Polynomial a -> Int
deg Null = -1
deg (c :+: cs) = deg cs + 1

terms :: (Num a) => Polynomial a -> [Polynomial a]
terms Null = []
terms (c :+: cs) = (c :+: foldr (\x acc -> 0 :+: acc) Null [0 .. deg cs]) : terms cs

times :: (Num a) => a -> Polynomial a -> Polynomial a
times k g = foldr (\x acc -> (k * x) :+: acc) Null g

infixl 4 << -- I can't define :^: and :<< somewhy
(<<) :: (Num a) => Polynomial a -> Int -> Polynomial a
(<<) Null _ = Null
(<<) g@(a :+: as) n
    | n > 0 = foldrp (\x acc -> x :+: acc) (foldr (\x acc -> 0 :+: acc) Null [1 .. n]) g
    | otherwise = g

foldrp :: (Num a) => (a -> b -> b) -> b -> Polynomial a -> b
foldrp f z Null = f 0 z
foldrp f z (c :+: Null) = f c z
foldrp f z (c :+: cs) = f c (foldr f z cs)

instance Foldable Polynomial where
    --foldr = foldrp isn't working; also idk what this means:
    foldMap f Null = mempty
    foldMap f (c :+: Null) = f c
    foldMap f (c :+: cs) = f c `mappend` foldMap f cs
    
instance (Num a, Eq a) => Num (Polynomial a) where
    (+) Null g = g
    (+) h Null = h
    (+) (0 :+: as) (0 :+: bs) = as + bs
    (+) h@(a :+: as) g@(b :+: bs)
        | deg h == deg g = a + b :+: as + bs
        | deg h > deg g = a :+: as + g
        | otherwise = b :+: h + bs
    
    (*) Null h = Null
    (*) g Null = Null
    (*) g@(0 :+: as) h@(b :+: bs) = as * h
    (*) g@(a :+: as) h@(0 :+: bs) = g * bs
    (*) g@(a :+: as) h = (a `times` h << deg g) + as * h
        
    negate Null = Null
    negate (c :+: cs) = negate c :+: negate cs
    
    abs Null = Null
    abs (0 :+: cs) = abs cs
    abs (c :+: cs) = abs c :+: abs cs
    
    signum Null = 0
    signum _ = undefined
    
    fromInteger 0 = Null
    fromInteger i = fromInteger i :+: Null
    
toInteger Null = 0
toInteger (c :+: Null) = c
toInteger g = undefined
    
----------

data GF2 = Zero | One
    deriving (Show)
    
instance Num (GF2) where
    (+) Zero Zero = Zero
    (+) Zero One = One
    (+) One Zero = One
    (+) One One = Zero
    
    (*) Zero Zero = Zero
    (*) Zero One = Zero
    (*) One Zero = Zero
    (*) One One = One
    
    (-) Zero Zero = Zero
    (-) Zero One = One
    (-) One Zero = One
    (-) One One = Zero
    
    abs = id
    signum = id
    
    fromInteger k
        | odd k = One
        | otherwise = Zero

--data GF n = 0,1..n
  --  deriving (Show, Num)


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