Primitive RPN calculator

-- A primitive command line reverse polish notation calculator. Valid
-- operations are adding, subtraction, multiplication, division.

main :: IO ()
main = do
  putStrLn
    "Enter a valid RPN expression with '+', '-', '*', '/' operators or 'quit'; hit ENTER"
  interaction

interaction :: IO ()
interaction = do
  input <- getLine
  if input == "quit"
    then return ()
    else if not $ all (`elem` "0123456789+-*/. ") input
           then do
             putStrLn "Invalid characters detected; try again"
             interaction
           else do
             putStrLn $ head $ fold input
             interaction

fold :: String -> [String]
fold s = foldl stackOrCalculate [] $ words s

stackOrCalculate :: [String] -> String -> [String]
stackOrCalculate a v =
  if v `notElem` ["+", "-", "*", "/"]
    then v : a
    else calculate a v

calculate :: [String] -> String -> [String]
calculate (a1:a2:as) v =
  let aux r = show r : as
      x = read a2
      y = read a1
   in case v of
        "+" -> aux $ x + y
        "-" -> aux $ x - y
        "*" -> aux $ x * y
        "/" -> aux $ x / y