A Parsec parser which only recognizes balanced binary trees.

parse_nested.hs

import Text.Parsec

data Tree a = Tip a | Branch (Tree (a, a)) deriving (Show)

tree :: Parsec String u (Tree Int)
tree = tree' $ do
  ds <- many digit
  return $ read ds
  where
  tree' :: Parsec String u a -> Parsec String u (Tree a)
  tree' next = (between (char '(') (char ')') 
    $ fmap Branch 
    $ tree' 
    $ do
      x <- next
      char ','
      y <- next
      return $ (x, y)) <|> fmap Tip next
  
-- ghci> parse tree "(1,2)"
-- Right (Branch (Tip (1,2)))
-- ghci> parseTest tree "((1,2,3,4))"
-- Right (Branch (Branch (Tip ((1,2),(3,4)))))
-- ghci> parseTest tree "((1,2,3))"
-- parse error at (line 1, column 8):
-- unexpected ")"
-- expecting digit or ","