Exercise 3.45: Louis Reasoner thinks our
bank-account system is unnecessarily complex and error-prone now that deposits
and withdrawals aren’t automatically serialized.  He suggests that
make-account-and-serializer should have exported the serializer (for use
by such procedures as serialized-exchange) in addition to (rather than
instead of) using it to serialize accounts and deposits as make-account
did.  He proposes to redefine accounts as follows:


(define 
  (make-account-and-serializer balance)
  (define (withdraw amount)
    (if (>= balance amount)
        (begin (set! balance 
                     (- balance amount))
               balance)
        "Insufficient funds"))
  (define (deposit amount)
    (set! balance (+ balance amount))
    balance)
  (let ((balance-serializer 
         (make-serializer)))
    (define (dispatch m)
      (cond ((eq? m 'withdraw) 
             (balance-serializer withdraw))
            ((eq? m 'deposit) 
             (balance-serializer deposit))
            ((eq? m 'balance) 
             balance)
            ((eq? m 'serializer) 
             balance-serializer)
            (else (error "Unknown request: 
                          MAKE-ACCOUNT"
                         m))))
    dispatch))

Then deposits are handled as with the original make-account:


(define (deposit account amount)
  ((account 'deposit) amount))

Explain what is wrong with Louis’s reasoning.  In particular, consider what
happens when serialized-exchange is called.