Work for CS-381, Programming Language Fundamentals
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module HW2 where
-- | Binary trees with nodes labeled by values of an arbitrary type.
data Tree a
= Node a (Tree a) (Tree a)
| End
deriving (Eq,Show)
-- | One step in a path, indicating whether to follow the left subtree (L)
-- or the right subtree (R).
data Step = L | R
deriving (Eq,Show)
-- | A path is a sequence of steps. Each node in a binary tree can be
-- identified by a path, indicating how to move down the tree starting
-- from the root.
type Path = [Step]
-- | Create a leaf node.
leaf :: a -> Tree a
leaf x = Node x End End
-- | An example tree.
ex :: Tree Int
ex = Node 4 (Node 3 (leaf 2) End)
(Node 7 (Node 5 End (leaf 6))
(leaf 8))
instance Functor Tree where
fmap f End = End
fmap f (Node v l r) = Node (f v) (fmap f l) (fmap f r)
-- | Map a function over a tree. Applies the given function to every label
-- in the tree, preserving the tree's structure.
--
-- >>> mapTree odd End
-- End
--
-- >>> mapTree even (Node 5 (leaf 2) End)
-- Node False (Node True End End) End
--
-- >>> (mapTree not . mapTree even) (Node 5 End (leaf 2))
-- Node True End (Node False End End)
--
-- >>> mapTree (+10) ex
-- Node 14 (Node 13 (Node 12 End End) End) (Node 17 (Node 15 End (Node 16 End End)) (Node 18 End End))
--
-- >>> ex == (mapTree (subtract 27) . mapTree (+27)) ex
-- True
--
mapTree :: (a -> b) -> Tree a -> Tree b
mapTree = fmap
-- | Get the value at the node specified by a path. Returns 'Nothing' if
-- the given path is invalid.
--
-- >>> valueAt [] ex
-- Just 4
--
-- >>> valueAt [L,L] ex
-- Just 2
--
-- >>> valueAt [L,R] ex
-- Nothing
--
-- >>> valueAt [R,L,R] ex
-- Just 6
--
-- >>> valueAt [L,L,L] ex
-- Nothing
--
valueAt :: Path -> Tree a -> Maybe a
valueAt _ End = Nothing
valueAt [] (Node a _ _) = Just a
valueAt (x:xs) (Node _ l r) = valueAt xs $ if x == L then l else r
-- | Find a path to a node that contains the given value.
--
-- >>> pathTo 3 (leaf 5)
-- Nothing
--
-- >>> pathTo 5 ex
-- Just [R,L]
--
-- >>> pathTo 6 ex
-- Just [R,L,R]
--
-- >>> pathTo 4 ex
-- Just []
--
-- >>> pathTo 10 ex
-- Nothing
--
pathTo :: Eq a => a -> Tree a -> Maybe Path
pathTo _ End = Nothing
pathTo v (Node a l r) = orElse currentNode $ orElse (pathHelper v l L) $ pathHelper v r R
where
currentNode = if a == v then Just [] else Nothing
pathHelper _ tree dir = fmap (dir:) (pathTo v tree)
orElse m1 m2 = if isJust m1 then m1 else m2
isJust mx = mx /= Nothing