SICP問題2.83

(複素数を除く)各型について、その型のオブジェクトを塔の中で一レベル高める汎用手続きraise 演算の設計。
強制型変換(coercion)用の塔
complex
↑
real
↑
rational
↑
integer

; 汎用演算パッケージ
(define (add x y) (apply-generic 'add x y))
(define (sub x y) (apply-generic 'sub x y))
(define (mul x y) (apply-generic 'mul x y))
(define (div x y) (apply-generic 'div x y))
(define (equ? x y) (apply-generic 'equ? x y))
(define (=zero? x) (apply-generic '=zero? x))
(define (raise x) (apply-generic 'raise x))

(define (install-integer-package)
  (define (tag x)
    (attach-tag 'integer x))
  (define (integer->rational n)
    (make-rational n 1))
  (put 'add '(integer integer)
       (lambda (x y) (tag (+ x y))))
  (put 'sub '(integer integer)
       (lambda (x y) (tag (- x y))))
  (put 'mul '(integer integer)
       (lambda (x y) (tag (* x y))))
  (put 'div '(integer integer)
       (lambda (x y) (tag (/ x y))))
  (put 'equ? '(integer integer)
       (lambda (x y) (= x y)))
  (put '=zero? '(integer)
       (lambda (x) (= x 0)))
  (put 'make 'integer
       (lambda (x) (tag x)))
  (put 'exp '(integer integer)
       (lambda (x y) (tag (expt x y))))
  ; 追加
  (put 'raise '(integer)
       (lambda (x) (integer->rational x)))
  'done)
(install-integer-package)
(define (make-integer n)
  ((get 'make 'integer) n))

; 有理数算術演算
(define (install-rational-package)
  ;; 内部手続き
  (define (numer x) (car x))
  (define (denom x) (cdr x))
  (define (make-rat n d)
    (let ((g (gcd n d)))
      (cons (/ n g) (/ d g))))
  (define (add-rat x y)
    (make-rat (+ (* (numer x) (denom y))
		 (* (numer y) (denom x)))
	      (* (denom x) (denom y))))
  (define (sub-rat x y)
    (make-rat (- (* (numer x) (denom y))
		 (* (numer y) (denom x)))
	      (* (denom x) (denom y))))
  (define (mul-rat x y)
    (make-rat (* (numer x) (numer y))
	      (* (denom x) (denom y))))
  (define (div-rat x y)
    (make-rat (* (numer x) (denom y))
	      (* (denom x) (numer y))))
  (define (equ-rat x y)
    (= (* (numer x) (denom y))
       (* (numer y) (denom x))))
  (define (=zero-rat x)
    (and (= (numer x) 0)
	 (not (= (denom x) 0))))
  ;; システムの他の部分へのインタフェース
  (define (tag x) (attach-tag 'rational x))
  (define (rational->real x)
    (make-real (/ (numer x) (denom x))))
  (put 'add '(rational rational)
       (lambda (x y) (tag (add-rat x y))))
  (put 'sub '(rational rational)
       (lambda (x y) (tag (sub-rat x y))))
  (put 'mul '(rational rational)
       (lambda (x y) (tag (mul-rat x y))))
  (put 'div '(rational rational)
       (lambda (x y) (tag (div-rat x y))))
  (put 'equ? '(rational rational)
       (lambda (x y) (equ-rat x y)))
  (put '=zero? '(rational)
       (lambda (x) (=zero-rat x)))
  (put 'make 'rational
       (lambda (n d) (tag (make-rat n d))))
  ; 追加
  (put 'raise '(rational)
       (lambda (x) (rational->real x)))
  'done)
(define (make-rational n d)
  ((get 'make 'rational) n d))

;; 実数パッケージ
(define (install-real-package)
  (define (tag x)
    (attach-tag 'real x))
  (define (real->complex x)
    (make-complex-from-real-imag x 0))
  (put 'add '(real real)
       (lambda (x y) (tag (+ x y))))
  (put 'sub '(real real)
       (lambda (x y) (tag (- x y))))
  (put 'mul '(real real)
       (lambda (x y) (tag (* x y))))
  (put 'div '(real real)
       (lambda (x y) (tag (/ x y))))
  (put 'equ? '(real real)
       (lambda (x y) (= x y)))
  (put '=zero? '(real)
       (lambda (x) (= x 0)))
  (put 'make 'real
       (lambda (x) (tag (* x 1.0)))) ;; rational->real で 1/3 とかになってしまうのでごまかし
  (put 'exp '(real real)
       (lambda (x y) (tag (expt x y))))
  ; 追加
  (put 'raise '(real)
       (lambda (x) (real->complex x)))
  'done)
(install-real-package)
(define (make-real x)
  ((get 'make 'real) x))

; 複素数
; 直行座標の場合
(define (install-rectangular-package)
  ;;内部手続き
  (define (real-part z) (car z))
  (define (imag-part z) (cdr z))
  (define (make-from-real-imag x y) (cons x y))
  (define (magnitude z)
    (sqrt (+ (square (real-part z))
	     (square (imag-part z)))))
  (define (angle z)
    (atan (imag-part z) (real-part z)))
  (define (make-from-mag-ang r a)
    (cons (* r (cos a)) (* r (sin a))))
  ;; システムの他の部分とのインタフェース
  (define (tag x) (attach-tag 'rectangular x))
  (put 'real-part '(rectangular) real-part)
  (put 'imag-part '(rectangular) imag-part)
  (put 'magnitude '(rectangular) magnitude)
  (put 'angle '(rectangular) angle)
  (put 'make-from-real-imag 'rectangular
       (lambda (x y) (tag (make-from-real-imag x y))))
  (put 'make-from-mag-ang 'rectangular
       (lambda (r a) (tag (make-from-mag-ang r a))))
  'done)

; 極座標の場合
(define (install-polar-package)
  ;;内部手続き
  (define (magnitude z) (car z))
  (define (angle z) (cdr z))
  (define (make-from-mag-ang r a) (cons r a))
  (define (real-part z) 
    (* (magnitude z) (cos (angle z))))
  (define (imag-part z) 
    (* (magnitude z) (sin (angle z))))
  (define (make-from-real-imag x y) 
    (cons (sqrt (+ (square x) (square y)))
	  (atan y x)))
  ;; システムの他の部分とのインタフェース
  (define (tag x) (attach-tag 'polar x))
  (put 'real-part '(polar) real-part)
  (put 'imag-part '(polar) imag-part)
  (put 'magnitude '(polar) magnitude)
  (put 'angle '(polar) angle)
  (put 'make-from-real-imag 'polar
       (lambda (x y) (tag (make-from-real-imag x y))))
  (put 'make-from-mag-ang 'polar
       (lambda (r a) (tag (make-from-mag-ang r a))))
  'done)

; apply-generic を使った汎用選択子の定義
(define (real-part z) (apply-generic 'real-part z))
(define (imag-part z) (apply-generic 'imag-part z))
(define (magnitude z) (apply-generic 'magnitude z))
(define (angle z) (apply-generic 'angle z))
; パッケージの外部のプログラムから、それぞれの構成子を使用する
(define (make-from-real-imag x y)
  ((get 'make-from-real-imag 'rectangular) x y))
(define (make-from-mag-ang r a)
  ((get 'make-from-mag-ang 'polar) r a))

; 複素数
(define (install-complex-package)
  ;; 直交座標と極座標パッケージから取り入れた手続き
  (define (make-from-real-imag x y)
    ((get 'make-from-real-imag 'rectangular) x y))
  (define (make-from-mag-ang r a)
    ((get 'make-from-mag-ang 'polar) r a))
  ;; 内部手続き
  (define (add-complex z1 z2)
    (make-from-real-imag (+ (real-part z1) (real-part z2))
			 (+ (imag-part z1) (imag-part z2))))
  (define (sub-complex z1 z2)
    (make-from-real-imag (- (real-part z1) (real-part z2))
			 (- (imag-part z1) (imag-part z2))))
  (define (mul-complex z1 z2)
    (make-from-real-imag (* (magnitude z1) (magnitude z2))
			 (* (angle z1) (angle z2))))
  (define (div-complex z1 z2)
    (make-from-real-imag (/ (magnitude z1) (magnitude z2))
			 (- (angle z1) (angle z2))))
  (define (equ-complex z1 z2)
    (and (= (real-part z1) (real-part z2))
	 (= (imag-part z1) (imag-part z2))))
  (define (=zero-complex z)
    (and (= (real-part z) 0)
	 (= (imag-part z) 0)))
  ;; システムの他の部分へのインタフェース
  (define (tag z) (attach-tag 'complex z))
  (put 'add '(complex complex)
       (lambda (z1 z2) (tag (add-complex z1 z2))))
  (put 'sub '(complex complex)
       (lambda (z1 z2) (tag (sub-complex z1 z2))))
  (put 'mul '(complex complex)
       (lambda (z1 z2) (tag (mul-complex z1 z2))))
  (put 'div '(complex complex)
       (lambda (z1 z2) (tag (div-complex z1 z2))))
  (put 'make-from-real-imag 'complex
       (lambda (x y) (tag (make-from-real-imag x y))))
  (put 'make-from-mag-ang 'complex
       (lambda (r a) (tag (make-from-mag-ang r a))))
  (put 'equ? '(complex complex)
       (lambda (z1 z2) (equ-complex z1 z2)))
  (put '=zero? '(complex)
       (lambda (x) (=zero-complex x)))
  (put 'real-part '(complex) real-part)
  (put 'imag-part '(complex) imag-part)
  (put 'magnitude '(complex) magnitude)
  (put 'ange '(complex) angle)
  'done)
(define (make-complex-from-real-imag x y)
  ((get 'make-from-real-imag 'complex) x y))
(define (make-complex-from-mag-ang r a)
  ((get 'make-from-mag-ang 'complex) r a))

(install-integer-package)
(install-rational-package)
(install-real-package)
(install-rectangular-package)
(install-polar-package)
(install-complex-package)

テスト

(make-integer 7)
; (integer . 7)
(raise (make-integer 7))
; (rational 7 . 1)
(raise (raise (make-integer 7)))
; (real . 7.0)
(raise (raise (raise (make-integer 7))))
; (complex rectangular 7.0 . 0)
(make-rational 1 3)
; (rational 1 . 3)
(raise (make-rational 1 3))
; (real . 0.3333333333333333)
(raise (raise (make-rational 1 3)))
; (complex rectangular 0.3333333333333333 . 0)