2.58.a¶

; New definitions of sum and product
; ============================================================
(define (sum? x) 
    (and (pair? x) (eq? (cadr x) '+)))
(define (make-sum a1 a2) 
    (cond ((=number? a1 0) a2) 
            ((=number? a2 0) a1)
            ((and (number? a1) (number? a2)) (+ a1 a2))
            (else (list a1 '+ a2)))) 
(define (addend s) (car s))
(define (augend s) (caddr s))

(define (product? x) 
    (and (pair? x) (eq? (cadr x) '*)))
(define (make-product m1 m2) 
    (cond ((or (=number? m1 0) (=number? m2 0)) 0)
            ((=number? m1 1) m2)
            ((=number? m2 1) m1)
            ((and (number? m1) (number? m2)) (* m1 m2))
            (else (list m1 '* m2))))
(define (multiplier p) (car p))
(define (multiplicand p) (caddr p))
; ============================================================

; Testing
(define (variable? x) (symbol? x))
(define (same-variable? v1 v2)
    (and (variable? v1) (variable? v2) (eq? v1 v2)))
(define (=number? exp num) 
    (and (number? exp) (= exp num)))

(define (deriv exp var)
    (cond ((number? exp) 0)
          ((variable? exp) (if (same-variable? exp var) 1 0))
          ((sum? exp) (make-sum (deriv (addend exp) var)
                                (deriv (augend exp) var)))
          ((product? exp)
            (make-sum
                (make-product 
                    (multiplier exp)
                    (deriv (multiplicand exp) var))
                (make-product
                    (deriv (multiplier exp) var)
                    (multiplicand exp))))
          (else
            (error "unknown expression type: DERIV" exp))))

(deriv '(x + 3) 'x)
; Value: 1

(deriv '(x * y) 'x)
; Value: y

(deriv '(x + (3 * (x + (y + 2)))) 'x)
; Value: 4