Data.List is already a LinkedList

linkedlist.hs

import Data.Semigroup

data Node a             -- a Node containing type a is
    = Val a (Node a)    -- either a Value of type a and another Node
    | End               -- or the end of the list

-- Makes it possible for REPL to display a linked list
-- Val 5 (Val 3 (Val 9 End)) becomes 5->3->9->()
instance (Show a) => Show (Node a) where
    show (Val a next) = (show a) <> "->" <> (show next)
    show End = "()"

-- Allows fmap for linked lists
instance Functor Node where
    fmap f End          = End
    fmap f (Val v next) = Val (f v) (fmap f next)

-- Allows <>, sconcat, and stimes
-- <> is "associative combine"
-- which is basically concatenation
-- (0->2->5->()) <> (3->3->4->()) = (0->2->5->3->3->4->())
-- stimes 3 (0->3->2->()) = (0->3->2->0->3->2->0->3->2->())
instance Semigroup (Node a) where
    (<>) End          End = End
    (<>) End          ls  = ls
    (<>) (Val v next) ls  = Val v (next <> ls)

-- gets nth node of list
-- index (0->3->4->()) 1 = 3->4->()
index :: Node a -> Int -> Maybe (Node a)

index n            0 = Just n
index End          _ = Nothing
index (Val _ next) i = index next (i - 1)

-- linkedlist from native Haskell list
-- fromList [2, 3, 1] = 2->3->1->()
fromList :: [a] -> Node a

fromList []     = End
fromList (x:xs) = Val x (fromList xs)

ls = fromList [0..10] -- 0->1->2->3->4->5->6->7->8->9->10->()
ls2 = fmap (*2) ls -- 0->2->4->6->8->10->12->14->16->18->20->()
circularLS = (fromList [0..3]) <> circularLS -- 0->1->2->3->0->1->2->3->0->...

fibs = 1 : 1 : zipWith (+) fibs (tail fibs)
fibsLL = fromList fibs -- 1->1->2->3->5->8->13...

linkedlist2.hs

import Data.Semigroup hiding (Last)

data List a             -- a List is either
    = Node a (List a)   -- a Node followed by another list
    | Last a            -- or the last node of the list

-- Makes it possible for REPL to display a linked list
-- Val 5 (Val 3 (Val 9 End)) becomes 5->3->9->()
instance (Show a) => Show (List a) where
    show (Node a next) = (show a) <> "->" <> (show next)
    show (Last a)      = show a

-- Allows fmap for linked lists
instance Functor List where
    fmap f (Last a)      = Last (f a)
    fmap f (Node v next) = Node (f v) (fmap f next)

-- Allows <>, sconcat, and stimes
-- <> is "associative combine"
-- which is basically concatenation
-- (0->2->5->()) <> (3->3->4->()) = (0->2->5->3->3->4->())
-- stimes 3 (0->3->2->()) = (0->3->2->0->3->2->0->3->2->())
instance Semigroup (List a) where
    (<>) (Last a)      ls       = Node a ls
    (<>) (Node v next) ls       = Node v (next <> ls)

-- gets nth node of list
-- index (0->3->4->()) 1 = 3->4->()
index :: List a -> Int -> Maybe (List a)

index n             0 = Just n
index (Node _ next) i = index next (i - 1)

-- linkedlist from native Haskell list
-- fromList [2, 3, 1] = 2->3->1->()
fromList :: [a] -> List a

fromList [x]    = Last x
fromList (x:xs) = Node x (fromList xs)

ls = fromList [0..10] -- 0->1->2->3->4->5->6->7->8->9->10->()
ls2 = fmap (*2) ls -- 0->2->4->6->8->10->12->14->16->18->20->()
circularLS = (fromList [0..3]) <> circularLS -- 0->1->2->3->0->1->2->3->0->...

fibs = 1 : 1 : zipWith (+) fibs (tail fibs)
fibsLL = fromList fibs -- 1->1->2->3->5->8->13...