2.56-make-exponentiation.rkt

(require racket/trace)

(trace-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)
			(make-product
				(make-product (exponent exp)
							  (make-exponentiation (base exp) (- (exponent exp) 1)))
				(deriv (base exp) var)))
		  (else
			(error "unknown expression type: DERIV"))))

(define (variable? x) (symbol? x))

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

(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))))

(trace-define (make-exponentiation base exponent)
	(cond ((=number? exponent 0) 1)
		  ((=number? exponent 1) base)
		  ((and (number? base) (number? exponent)) (expt base exponent))
		  (else (list '** base exponent))))

(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 (exponentiation? x)
	(and (pair? x) (eq? (car x) '**)))

(define (base e) (cadr e))

(define (exponent e) (caddr e))