데이타를 여러방식으로 구현할 때 Multiple Representations 데이터 구현방식마다 꼬리표를 붙이고. 데이터 속내용 감추기 원리를 유지하면서. 예를 들어 complex number data 구현방안들을 생각해 보자 – complex number 만들기 make-from-real-imag: real * real -> complex make-from-mag-angle: real * real -> complex – complex number 사용하기 is-complex?:  -> bool real: complex -> real imag: complex -> real mag: complex -> real angle: complex -> real

add-complex mul-complex make-from-real-imag make-from-mag-angle real img mag angle is-complex? rectangular representation

(define (make-from-real-imag x y) (cons x y)) (define (make-from-mag-angle m a) (cons (* m (cos a)) (* m (sin a)))) (define (is-complex? c) (and (pair? c) (real? (car c)) (real? (cdr c))) (define (real c) (cond ((not (is-complex? c)) (error)) (else (car c)))) (define (imag c) (cond ((not (is-complex? c) (error)) (else (cdr c)))) (define (mag c) (cond ((not (is-complex? c) (error)) (else (sqrt (+ (square (real c)) (square (imag c))))) )) (define (angle c) (cond ((not (is-complex? c) (error)) (else (atan (imag c) (real c)))))

외부에서는, (define (add-complex c1 c2) (make-from-real-imag (+ (real c1) (real c2)) (+ (imag c1) (imag c2)) )) (define (mul-complex c1 c2) (make-from-mag-angle (* (mag c1) (mag c2)) (+ (angle c1) (angle c2)) ))

rectangular representation polar representation make … make-from-real-imag make-from-mag-angle real imag mag angle is-complex? add-complex mul-complex

rectagular complex 속내용 감추기data abstraction – make-from-real-imag-rectangular: real * real -> complex – make-from-mag-angle-rectangular: real * real -> complex – is-rectangular?: complex -> bool – real-rectangular: complex -> real – imag-rectangular: complex -> real – mag-rectangular: complex -> real – angle-rectangular: complex -> real (define rectangular-tag ‘ rectangular) (define (make-from-real-imag-rectangular x y) (cons rectangular-tag (cons x y))) (define (make-from-mag-angle-rectangular m a) (cons rectangular-tag (cons (* m (cos a)) (* m (sin a))))) (define (is-rectangular? c) (equal? (car c) rectangular-tag)) (define (real-rectangular c) (car (cdr c))) (define (imag-rectangular c) (cdr (cdr c))) (define (mag-rectangular c) (sqrt (+ (square (real-rectangular c))) (+ (square (imag-rectangular c))))) (define (angle-rectangular c) (atan (imag-rectangular c) (real-rectangular c)))

polar complex 속내용 감추기data abstraction – make-from-real-imag-polar: real * real -> complex – make-from-mag-angle-polar: real * real -> complex – is-polar?: complex -> bool – real-polar: complex -> real – imag-polar: complex -> real – mag-polar: complex -> real – angle-polar: complex -> real (define polar-tag ‘ polar) (define (make-from-real-imag-polar x y) (cons polar-tag (cons … ))) (define (make-from-mag-angle-polar m a) (cons polar-tag (cons m a))) (define (is-polar? c) (equal? (car c) polar-tag)) (define (mag-polar c) (car (cdr c))) (define (angle-polar c) (cdr (cdr c))) (define (real-polar c) (* (mag-polar c) (cos (angle-polar c)))) (define (imag-polarr c) (* (mag-polar c) (sin (angle-polar c))))

(define (make-from-real-imag x y) (make-from-real-imag-rectangular x y)) (define (make-from-mag-angle m a) (make-from-mag-angle-polar m a)) (define (is-complex? c) (and (pair? c) (cond ((is-rectangular? c) (and (real? (real-rectangular c)) (real? (imag-rectangular c)))) ((is-polar? c) (and (real? (mag-polar c)) (real? (angle-polar c)))) (else #f)) ))

(define (real c) (cond ((not (is-complex? c)) (error)) ((is-rectangular? c) (real-rectangular c)) ((is-polar? c) (real-polar c)))) (define (imag c) (cond ((not (is-complex? c)) (error)) ((is-rectangular? c) (imag-rectangular c)) ((is-polar? c) (imag-polar c)))) (define (mag c) (cond ((not (is-complex? c)) (error)) ((is-rectangllar? c) (mag-rectangular c)) ((is-polar? c) (mag-polar c)))) (define (angle c) (cond ((not (is-complex? c)) (error)) ((is-rectangular? c) (angle-rectangular c)) ((is-polar? c) (angle-polar c))))

외부에서는, 변함없이 (define (add-complex c1 c2) (make-from-real-imag (+ (real c1) (real c2)) (+ (imag c1) (imag c2)) )) (define (mul-complex c1 c2) (make-from-mag-angle (* (mag c1) (mag c2)) (+ (angle c1) (angle c2)) ))

데이타를 여러방식으로 구현할 때 Multiple Representations 데이터 구현방식마다 꼬리표를 붙이고. 데이터 속내용 감추기 원리를 유지하면서. rectangular representation polar representation make … make-from-real-imag make-from-mag-angle real imag mag angle is-complex? add-complex mul-complex

또다른 complex number 구현방식을 품고 있게 하려면? rectangular representation polar representation make … make-from-real-imag make-from-mag-angle real imag mag angle is-complex? add-complex mul-complex make … xyz representation 어디를 어떻게 바꾸어야 할까? 적어도 real, imag, mag, angle, is-complex?를 확 장해야.

(define (real c) (cond ((not (is-complex? c)) (error)) ((is-rectangular? c) (real-rectangular c)) ((is-polar? c) (real-polar c)) ((is-xyz? c) (real-xyz c)) )) (define (imag c) (cond ((not (is-complex? c)) (error)) ((is-rectangular? c) (imag-rectangular c)) ((is-polar? c) (imag-polar c)) ((is-xyz? c) (imag-xyz c)) )) (define (mag c) (cond ((not (is-complex? c)) (error)) ((is-rectangllar? c) (mag-rectangular c)) ((is-polar? c) (mag-polar c)) ((is-xyz? c) (mag-xyz c)) )) (define (angle c) (cond ((not (is-complex? c)) (error)) ((is-rectangular? c) (angle-rectangular c)) ((is-polar? c) (angle-polar c)) ((is-xyz? c) (angle-xyz c)) ))