(define reduce!
  (lambda (expr-stack)
    (cond ((equal? (top-minus expr-stack 0) 'rparen)
           (let ((value (top-minus expr-stack 1)))
             (pop! expr-stack)  ; remove rparen
             (pop! expr-stack)  ; remove the value
             (pop! expr-stack)  ; remove lparen
             (push! expr-stack value)))
          (else                 ; a simple arithmetic operation
           (let ((left-operand  (top-minus expr-stack 2))
                 (operator      (top-minus expr-stack 1))
                 (right-operand (top-minus expr-stack 0)))
             (pop! expr-stack)  ; remove right operand
             (pop! expr-stack)  ; remove operator
             (pop! expr-stack)  ; remove left operand
             (push! expr-stack ((look-up-value operator)
                                left-operand
                                right-operand)))))))