How to parse a tree-like structure using PArrows?

Question

I'm trying to learn arrows, as well as how PArrows can replace Parsec, but there is an almost nonexistent number of tutorials. I believe we could benefit a lot from simple examples, so, given the binary tree:

data Tree = Node Tree Tree | A | B deriving Show

How can PArrow be used to parse a string similar to:

"((A B) (A (B A)))" 

So that it becomes:

Node (Node A B) (Node A (Node B A))

Answer 1

This is probably not the cleanest answer, but I managed to do it with:

import Text.ParserCombinators.PArrow
import Control.Arrow

data Tree = Node Tree Tree | A | B deriving Show

text = "((B A) (A B))"

fromToken :: Char -> Tree
fromToken 'A' = A
fromToken 'B' = B

token = anyOf "AB" >>> arr fromToken
node = arr (uncurry Node) 
    <<< ((char '(' >>> token <+> node)   -- left side
    >>! white                            -- whitespace
    &&& ((token <+> node) >>! char ')')) -- right side

main = print $ runParser node text

Mind I'm still working on my arrow familiarity.