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

The parsec answer by dbaupp is very easy to understand. As an example of a "low-level" approach, here is a hand written parser which uses a success continuation to handle the left-associative tree building:

instance Read Tree where readsPrec _prec s = maybeToList (readTree s)

type TreeCont = (Tree,String) -> Maybe (Tree,String)

readTree :: String -> Maybe (Tree,String)
readTree = read'top Just where
  valid ')' = False
  valid '(' = False
  valid _ = True

  read'top :: TreeCont -> String -> Maybe (Tree,String)
  read'top acc s@(x:ys) | valid x =
    case ys of
      [] -> acc (Leaf x,[])
      (y:zs) -> read'branch acc s
  read'top _ _ = Nothing

  -- The next three are mutually recursive

  read'branch :: TreeCont -> String -> Maybe (Tree,String)
  read'branch acc (x:y:zs) | valid x = read'right (combine (Leaf x) >=> acc) y zs
  read'branch _ _ = Nothing

  read'right :: TreeCont -> Char -> String -> Maybe (Tree,String)
  read'right acc y ys | valid y = acc (Leaf y,ys)
  read'right acc '(' ys = read'branch (drop'close >=> acc) ys
     where drop'close (b,')':zs) = Just (b,zs)
           drop'close _ = Nothing
  read'right _ _ _ = Nothing  -- assert y==')' here

  combine :: Tree -> TreeCont
  combine build (t, []) = Just (Branch build t,"")
  combine build (t, ys@(')':_)) = Just (Branch build t,ys)  -- stop when lookahead shows ')'
  combine build (t, y:zs) = read'right (combine (Branch build t)) y zs