-- A datatype for lists
data List a
    = Empty
    | Add a (List a)
  deriving (Eq, Show)

-- type Hand = List Card

-- tom l checks whether l is empty
tom :: List a -> Bool
tom Empty = True
tom _     = False

-- forst list returns the first element of the list
forst :: List a -> a
forst (Add apa _) = apa
forst Empty       = error "forst Empty"

forst' :: List a -> Maybe a
forst' (Add a _) = Just a
forst' Empty     = Nothing

-- sist l returns the last element of l
sist :: List a -> a
sist (Add a Empty) = a
sist (Add _ list)  = sist list
sist Empty         = error "sist Empty"

rev :: List a -> List a
rev Empty        = Empty
rev (Add a list) = rev list +++ Add a Empty

(+++) :: List a -> List a -> List a
Empty    +++ l2 = l2
Add a l1 +++ l2 = Add a (l1 +++ l2)

append :: List a -> List a -> List a
append Empty      l2 = l2
append (Add a l1) l2 = Add a (append l1 l2)

list1 = Add 1 (Add 2 Empty)
list2 = Add 3 (Add 4 Empty)

-- alternative
sist' :: List a -> a
sist' list = forst (rev list)

-- Introduce standard lists

forstL :: [a] -> a
forstL (a:_) = a
forstL []    = error "forstL []"

-- l1 ++++ l2 (a.k.a. ++) appends l2 after l1
[]     ++++ bs = bs
(a:as) ++++ bs = a : (as ++++ bs)

-- size l (a.k.a length) returns the number of elements in l
size :: [a] -> Int
size []     = 0
size (_:as) = 1 + size as

-- summan xs (a.k.a sum) calculates the sum of all elements in xs
summan :: Num a => [a] -> a
summan []     = 0
summan (a:as) = a + summan as

list3 = [1,2,3] :: [Int]
list4 = [1,2,3] :: [Double]

-- mest l (a.k.a. maximum) returns the largest element in l
mest :: Ord a => [a] -> a
mest []     = error "mest []"
mest [a]    = a
mest (a:as) = max a (mest as)