solve.hs

data List a = Node a (List a) | Empty -- Recursive
data Maze = Maze {grid::Grid, visited::Path, stack::Stack}
type Path = List Cell
--type Stack = [Cell]
type Stack = List Cell
type Grid = [[Char]]

-- Linked List --
push :: List a -> List a -> List a
push Empty ys = ys
push (Node x xs) ys = Node x (push xs ys)

peek :: List a -> a
peek Empty = error "Can't peek"
peek (Node x xs) = x

pop :: List a -> List a
pop Empty = error "Can't pop"
pop (Node x xs) = xs

elem' :: (Eq a) => a -> List a -> Bool
elem' _ Empty = False
elem' y (Node x xs) = y == x || (elem' y xs)

 
instance Functor List where
    -- fmap :: (a -> b) -> List a -> List b
    fmap _ Empty = Empty
    fmap f (Node x xs) = Node (f x) (fmap f xs)
 
instance Applicative List where
    -- pure :: a -> List a
    pure x = Node x Empty
    -- (<*>) :: List (a -> b) -> List a -> List b
    Empty <*> _ = Empty
    (Node g gs) <*> xs = fmap g xs `push` (gs <*> xs)
 
instance Monad List where
    -- (>>=) :: List a -> (a -> List b) -> List b
    Empty >>= _ = Empty
    (Node x xs) >>= f = (f x) `push` (xs >>= f)

instance Monoid (List a) where
    mappend = push
    mempty = Empty