sicp 2.56

sicp_2_56

(define (variable? x) (symbol? x))
(define (same-variable? v1 v2)
(and (variable? v1) (variable? v2) (eq? v1 v2)))
(define (sum? x)
(and (pair? x) (eq? (car x) '+)))
(define (exponentiation? x)
(and (pair? x) (eq? (car x) '**)))
(define (addend s) (cadr s))
(define (augend s) (caddr s))
(define (product? x)
(and (pair? x) (eq? (car x) '*)))
(define (multiplier p) (cadr p))
(define (multiplicand p) (caddr p))

(define (base p) (cadr p))
(define (exponent p) (caddr p))
(define (make-exponentiation a1 a2)
(cond ((=number? a2 0) 1)
((=number? a2 1) a1)
((and (number? a1) (number? a2)) (** a1 a2))
(else (list '** a1 a2))))

(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 (=number? exp num)
(and (number? exp) (= exp num)))

(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 (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)))
        ((exponentiation? exp)
         (make-exponentiation (make-product (exponent exp) (base exp)) (- (exponent exp) 1)))
        ((product? exp)
         (make-sum
          (make-product (multiplier exp)
                        (deriv (multiplicand exp) var))
          (make-product (deriv (multiplier exp) var)
                        (multiplicand exp))))
        (else
         (error "error -- DERIV" exp))))

(deriv '(* (* x y) (** x 3)) 'x)