<SICP> 2.3

deriv.rkt

#lang racket

(define variable? symbol?)

(define (same-variable? v1 v2)
  (and (variable? v1) (variable? v2) (eq? v1 v2)))

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

;; (define (make-sum a1 a2) (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 (make-product m1 m2) (list '* m1 m2))
(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 (sum? 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 (exponent x y)
  (if (= y 0)
      1
      (* x (exponent x (- y 1)))))

(define (exponentiation? x)
  (and (pair? x) (eq? (car x) 'exponent)))

(define (make-exponent x y)
  (cond [(=number? y 0) 1]
        [(=number? y 1) x]
        [(and (number? x) (number? y)) (exponent x y)]
        [else (list 'exponent x y)]))

;; (exponentiation? '(exponent 2 10))

(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)))]
        [(exponentiation? exp)
         (let ([pow (cadr (cdr exp))]
               [base (cadr exp)])
           (make-product (pow exp)
                         (make-exponent base (- pow 1))))
         ]
        [else
         (error "unknown expression type -- DERIV" exp)]))

(deriv '(+ x 3) 'x)

(deriv '(* x y) 'x)

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