Effective Haskell: Calculator throws errors in parse'

@RebeccaSkinner,

Allright, so I have put all of the example code for Calculator in chapter 4 on page ~140 in a file and when loading it into GHCI it throws this:

    λ: :reload
    [1 of 1] Compiling Calculator       ( Calculator.hs, interpreted )

    Calculator.hs:40:9: error:
        • Couldn't match expected type ‘String -> Either String a1’
                      with actual type ‘Either String b0’
        • In the pattern: Left err
          In a case alternative: Left err -> Left err
          In the expression:
            case readEither of
              Left err -> Left err
              Right lit' -> Right (Lit lit', rest)
       |
    40 |         Left err -> Left err
       |         ^^^^^^^^

    Calculator.hs:41:9: error:
        • Couldn't match expected type ‘String -> Either String a1’
                      with actual type ‘Either a0 Int’
        • In the pattern: Right lit'
          In a case alternative: Right lit' -> Right (Lit lit', rest)
          In the expression:
            case readEither of
              Left err -> Left err
              Right lit' -> Right (Lit lit', rest)
       |
    41 |         Right lit' -> Right (Lit lit', rest)
       |         ^^^^^^^^^^
    Failed, no modules loaded.

I am not sure if maybe there is something that you forgot to add or that should be added.

Below I post my full calculator module:

module Calculator where

import Text.Read (readEither)

data Expr = Lit Int
  | Add Expr Expr
  | Sub Expr Expr
  | Mul Expr Expr
  | Div Expr Expr

eval :: Expr -> Int
eval expr =
  case expr of
    Lit num -> num
    Add arg1 arg2 -> eval' ( + ) arg1 arg2
    Sub arg1 arg2 -> eval' ( - ) arg1 arg2
    Mul arg1 arg2 -> eval' ( * ) arg1 arg2
    Div arg1 arg2 -> eval' div arg1 arg2
    where
      eval' :: (Int -> Int -> Int) -> Expr -> Expr -> Int
      eval' operator arg1 arg2 = operator (eval arg1) (eval arg2)

parse :: String -> Either String Expr
parse str =
  case parse' (words str) of
    Left err          -> Left err
    Right (e, [])     -> Right e
    Right (_, rest)   -> Left $ "Found extra tokens: " <> (unwords rest)

parse' :: [String] -> Either String (Expr, [String])
parse' [] = Left "unexpected end of expression"
parse' (token:rest) =
  case token of
    "+" -> parseBinary Add rest
    "*" -> parseBinary Mul rest
    "-" -> parseBinary Sub rest
    "/" -> parseBinary Div rest
    lit ->
      case readEither of
        Left err -> Left err
        Right lit' -> Right (Lit lit', rest)

parseBinary :: (Expr -> Expr -> Expr) -> [String] -> Either String (Expr, [String])
parseBinary exprConstructor args =
  case parse' args of
    Left err -> Left err
    Right (firstArg, rest') ->
      case parse' rest' of
        Left err -> Left err
        Right (secondArg, rest'') ->
          Right $ (exprConstructor firstArg secondArg, rest'')

run :: String -> String
run expr =
  case parse expr of
    Left err -> "Error: " <> err
    Right expr' ->
      let answer = show $ eval expr'
      in "The answer is: " <> answer