Find the top of the tree(the root) in haskell
haskell
Solution
You have no sensible value of `a` in case of the `Empty` constructor. The type `Maybe` encodes exactly what you need in this case: a sensible value or no value. Therefore the following would be an idiomatic way of implementing your function:
root :: Tree a -> Maybe a
root (Leaf a) = Just a
root (Node a _ _ _) = Just a
root _ = Nothing
You can easily compose this function with other functions of your library using functors, applicative functors and monads. E.g.:
functionOnPlainA :: a -> a
functionOnPlainA = error "implement me"
-- So simply we can lift our plain function to work on values of type `Maybe`.
-- This is a Functor example.
functionOnMaybeA :: Maybe a -> Maybe a
functionOnMaybeA = fmap functionOnPlainA
-- Because the above is so simple, it's conventional to inline it,
-- as in the following:
applyFunctionOnPlainAToResultOfRoot :: Tree a -> Maybe a
applyFunctionOnPlainAToResultOfRoot tree = fmap functionOnPlainA $ root tree
-- And here is an example of how Monads can serve us:
applyRootToMaybeTree :: Maybe (Tree a) -> Maybe a
applyRootToMaybeTree maybeTree = maybeTree >>= root
Problem
I have a tree like this: ``` data Tree a = Empty | Leaf a | Node a (Tree a) (Tree a) String deriving (Show) ``` and I need a function which finds the top of the tree. I have written this: ``` root :: Tree a -> a root (Leaf a) = a root (Node a _ _ _) = a ``` which perfectly works, but when I have an Empty tree, I have an error message. If I add ``` root Empty = Empty ``` I have an error again because it does not return a value of type `a`. What can I do ?