Implementing `read` for a left-associative tree in Haskell

Question

I\'m having a hard time implementing Read for a tree structure. I want to take a left-associative string (with parens) like ABC(DE)F and convert it into a tree.

Answer 1

This very-much looks like a stack structure. When you encounter your input string "ABC(DE)F", you Leaf any atom you find (non-parenthesis) and put it in an accumulator list. When you have 2 items in the list, you Branch them together. This could be done with something like (note, untested, just including to give an idea):

read' [r,l] str  = read' [Branch l r] str
read' acc (c:cs) 
   -- read the inner parenthesis
   | c == '('  = let (result, rest) = read' [] cs 
                 in read' (result : acc) rest
   -- close parenthesis, return result, should be singleton
   | c == ')'  = (acc, cs) 
   -- otherwise, add a leaf
   | otherwise = read' (Leaf c : acc) cs
read' [result] [] = (result, [])
read' _ _  = error "invalid input"

This may require some modification, but I think its enough to get you on the right track.