(define derivative-rules
  (rule-simplifier
   '( ((d/d ?u ?x)
       (constant? ?u ?x)
       0)

      ((d/d ?x ?x)
       none
       1)

      ((d/d (+ ?u ?v) ?x)
       none
       (+ (d/d ?u ?x)
	  (d/d ?v ?x)))

      ((d/d (* ?u ?v) ?x)
       none
       (+ (* (d/d ?u ?x) ?v)
	  (* ?u (d/d ?v ?x))))

      ((d/d (expt ?u ?n) ?x)
       (constant ?n ?x)
       (* ?n
	  (expt ?u (- ?n 1))
	  (d/d ?u ?x)))

      ;; ... more rules ...
      ) ))

(define (constant? expr var)
  (not (occurs-in? var expr)))

(define (occurs-in? x u)
  (cond ((equal? x u) #t)
	((pair? u)
	 (or (occurs-in? x (car u))
	     (occurs-in? x (cdr u))))
	(else #f)))

#|
(derivative-rules
 '(+ (d/d (* a (* x x)) x) 1))
;Value:
(+ (+ (* 0
	 (* x x))
      (* a
	 (+ (* 1 x)
	    (* x 1))))
   1)
|#


(define algebra-rules
  (rule-simplifier
   '( ((+ 0 ?x) none ?x)
      ((+ ?x 0) none ?x)

      ((* 0 ?x) none 0)
      ((* ?x 0) none 0)
      ((* 1 ?x) none ?x)
      ((* ?x 1) none ?x)
      ) ))

#|
(algebra-rules
 (derivative-rules
  '(+ (d/d (* a (* x x)) x) 1)))
;Value: (+ (* a (+ x x)) 1)
|#