(define reduce?
  (lambda (expr-stack next-token)
    (let ((stack-top (top-minus expr-stack 0)))
      (cond ((number? stack-top)
             (let ((stack-second (top-minus expr-stack 1)))
               (cond ((equal? next-token '$)
                      (operator? stack-second))
                     ((operator? next-token)
                      (and (operator? stack-second)
                           (not (lower-precedence?
                                 stack-second
                                 next-token))))
                     ((equal? next-token 'rparen)
                      (operator? stack-second))
                     (else #f))))
            ((equal? stack-top 'rparen)
             (or (equal? next-token '$)
                 (operator? next-token)
                 (equal? next-token 'rparen)))
            (else #f)))))