Find Element in Tree Given a List of Directions

Question

Looking at Learn You a Haskell, I implemented a function that, given a binary tree, i.e. left and right branches, give a list of Directions and give the element at that location.

Here's the Tree:

data Tree a = Empty | Node a (Tree a) (Tree a) deriving (Show)

And then the functions:

elemAt :: Directions -> Tree a -> a 
elemAt [] (Node x _ _) = x
elemAt (R:ds) (Node _ _ r) = elemAt ds r
elemAt (L:ds) (Node _ l _) = elemAt ds l

But, I re-wrote it to be safe (maybe not)

maybeElemAt :: Directions -> Tree a -> Maybe a 
maybeElemAt [] (Node x _ _) = Just x
maybeElemAt (R:ds) (Node _ _ Empty) = Nothing
maybeElemAt (R:ds) (Node _ _ r) = maybeElemAt ds r
maybeElemAt (L:ds) (Node _ Empty _) = Nothing
maybeElemAt (L:ds) (Node _ l _) = maybeElemAt ds l

Testing

anotherTree :: Tree Char
anotherTree = Node 'A' (Node 'B' Empty Empty) Empty
ghci> maybeElemAt [R,R,R] anotherTree
Nothing
ghci> maybeElemAt [R] anotherTree
Nothing
ghci> maybeElemAt [L] anotherTree
Just 'B'

Please critique my implementations of either function.

Answer 1

It's not that safe.

*Main> maybeElemAt [] Empty
*** Exception: tree.hs:(7,1)-(11,54): Non-exhaustive patterns in function maybeElemAt

So let's add a pattern

maybeElemAt :: Directions -> Tree a -> Maybe a 
maybeElemAt [] (Node x _ _) = Just x
maybeElemAt (R:ds) (Node _ _ Empty) = Nothing
maybeElemAt (R:ds) (Node _ _ r) = maybeElemAt ds r
maybeElemAt (L:ds) (Node _ Empty _) = Nothing
maybeElemAt (L:ds) (Node _ l _) = maybeElemAt ds l
maybeElemAt _ Empty = Nothing

And now we can see that two of the patterns can be removed:

maybeElemAt [] (Node x _ _) = Just x
maybeElemAt (R:ds) (Node _ _ r) = maybeElemAt ds r
maybeElemAt (L:ds) (Node _ l _) = maybeElemAt ds l
maybeElemAt _ Empty = Nothing

GHC has an option -fwarn-incomplete-patterns, or you can use -W to get that plus other warnings. See Warnings and sanity-checking in the GHC User's Guide.