Arithmetic expression operator precedence parsing

parse.hs

{-# LANGUAGE OverloadedStrings #-}

import Control.Applicative
import Data.Char (isAlpha)

import Data.Attoparsec.ByteString.Char8

data Expr = Mul Expr Expr | Add Expr Expr | Lit Char | Var Char deriving Show

expr = (add <|> mul <|> (Var <$> satisfy isAlpha) <|> (Lit <$> satisfy isDigit)) <* endOfInput
  where
  add = Add <$> ((takeTill (=='+') <* char8 '+') >>= either fail pure . parseOnly expr) <*> expr
  mul = Mul <$> ((takeTill (=='*') <* char8 '*') >>= either fail pure . parseOnly expr) <*> expr

main = do
  print $ parseOnly expr "1+2+3*4+5+6*7+8"
  print $ parseOnly expr "1*3+4+5+6*7*8"
  print $ parseOnly expr "1+?+3*4+5+6*7+8"