Parse error when using case expression inside guards haskell

Question

I am new to Haskell and I am having issues with syntax. What I want to do is given data and a tree of this datatype, find the path to the corresponding node in the tree. I believe my logic for the function is correct but I am not sure how to make it valid Haskell. I have tried changing tabs to spaces.

-- | 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]
pathTo :: Eq a => a -> Tree a -> Maybe Path
pathTo a End = Nothing
pathTo a (Node b l r)
    | a == b = Just []
    | case (pathTo a l) of
                Just p  -> Just [L:p]
                Nothing -> case (pathTo a r) of
                                    Just p  -> Just [R:p]
                                    Nothing -> Nothing

This is the error:

  parse error (possibly incorrect indentation or mismatched brackets)

Answer 1

The underlying problem here is that this does not look like a guard: a guard is an expression with type Bool, this determines if the guard "fires" or not. Here this is likely `otherwise:

pathTo :: Eq a => a -> Tree a -> Maybe Path
pathTo a End = Nothing
pathTo a (Node b l r)
    | a == b = Just []
    | otherwise = case (pathTo a l) of
                Just p  -> Just (L:p)
                Nothing -> case (pathTo a r) of
                                    Just p  -> Just (R:p)
                                    Nothing -> Nothing

This also revealed some extra mistakes: Just [L:p] is a Maybe [[Step]], you likely wanted to use Just (L:p), the same applies for Just [R:p].

You furthermore do not need to use nested cases, you can work with the Alternative typeclass:

import Control.Applicative((<|>))

pathTo :: Eq a => a -> Tree a -> Maybe Path
pathTo a End = Nothing
pathTo a (Node b l r)
    | a == b = Just []
    | otherwise = ((L:) <$> pathTo a l) <|> ((R:) <$> pathTo a r)

Here x <|> y will take x if it is a Just …, and y otherwise. We use (L:) <$> … to prepend the list wrapped in the Just data constructor, or return Nothing in case … is Nothing.