import Control.Monad
import Control.Applicative

calcRPN fs s = do
  [result] <- foldM f [] $ words s
  return result
  where
    f = foldr (\f g xs s -> f xs s <|> g xs s) push fs
    push xs s = (:xs) <$> case reads s of {[(x, "")] -> Just x; _ -> Nothing}


infixMaybe op a (y:x:xs) b | a == b = Just $ x `op` y : xs
                           | otherwise = Nothing
infixMaybe _ _ _ _ = Nothing

add = infixMaybe (+) "+"
sub = infixMaybe (-) "-"
mul = infixMaybe (*) "*"
fdiv = infixMaybe (/) "/"

extension (x:xs) "sum" = Just $ [sum (x:xs)]
extension (x:xs) "exp" = Just $ exp x : xs
extension _ _ = Nothing

main = do
  print $ calcRPN [add, sub, mul, fdiv] "3 19 + -2 /"
  print $ calcRPN [add, sub, mul, fdiv] "1 2 3"
  print $ calcRPN [add, sub, mul, fdiv, extension] "5 4 - exp 3 -2 1 sum"