SICP 問題 2.80(ゼロ確認述語手続きを追加。)
解答
これも汎用演算を定義するのと、各パッケージに専用の演算手続きを定義していくだけな感じ。
例によって追記したところだけコメントしてあります。
(define (apply-generic op . args) (let* ((type-tags (map type-tag args)) (proc (get op type-tags))) (if proc (apply proc (map contents args)) (error "No method for these types -- APPLY-GENERIC" (list op type-tags))))) (define (attach-tag type-tag contents) (if (eq? type-tag 'scheme-number) contents (cons type-tag contents))) (define (type-tag datum) (cond ((pair? datum) (car datum)) ((number? datum) 'scheme-number) (else (error "Bad tagged datum -- TYPE-TAG" datum)))) (define (contents datum) (cond ((pair? datum) (cdr datum)) ((number? datum) datum))) (define (square x) (* x x)) (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)) ;汎用ゼロ確認述語手続き=zero?を定義する。 (define (=zero? x) (apply-generic '=zero? x)) (define (install-scheme-number-package) (define (tag x) (attach-tag 'scheme-number x)) (put 'add '(scheme-number scheme-number) (lambda (x y) (tag (+ x y)))) (put 'sub '(scheme-number scheme-number) (lambda (x y) (tag (- x y)))) (put 'mul '(scheme-number scheme-number) (lambda (x y) (tag (* x y)))) (put 'div '(scheme-number scheme-number) (lambda (x y) (tag (/ x y)))) (put 'make 'scheme-number (lambda (x) (tag x))) (put 'equ? '(scheme-number scheme-number) (lambda (x y) (eq? x y))) ;scheme-number型のゼロ確認述語を定義して公開 (put '=zero? '(scheme-number) (lambda (x) (eq? 0 (contents x)))) 'done) (install-scheme-number-package) (define (make-scheme-number n) ((get 'make 'scheme-number) n)) (define (install-rational-package) (define (gcd a b) (if (= b 0) a (gcd b (remainder a b)))) (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 (tag x) (attach-tag 'rational 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 'make 'rational (lambda (n d) (tag (make-rat n d)))) (put 'equ? '(rational rational) (lambda (x y) (equal? x y))) ;rational型のゼロ確認述語を定義して公開 (put '=zero? '(rational) (lambda (x) (eq? 0 (numer x)))) 'done) (install-rational-package) (define (make-rational n d) ((get 'make 'rational) n d)) (define (install-rectangular-package) (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)))) (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)))) (put 'equ? '(rectangular rectangular) (lambda (x y) (equal? x y))) ;rectangular型のゼロ確認述語を定義して公開 (put '=zero? '(rectangular) (lambda (x) (and (eq? 0 (real-part x)) (eq? 0 (imag-part x))))) 'done) (install-rectangular-package) (define (install-polar-package) (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))) (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)))) (put 'equ? '(polar polar) (lambda (x y) (equal? x y))) ;polar型のゼロ確認述語を定義して公開 (put '=zero? '(polar) (lambda (x) (and (eq? 0 (magnitude x)) (eq? 0 (angle x))))) 'done) (install-polar-package) (define (install-complex-package) (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)) (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-mag-ang (* (magunitude z1) (magunitude z2)) (+ (angle z1) (angle z2)))) (define (div-complex z1 z2) (make-from-mag-ang (/ (magunitude z1) (magunitude z2)) (- (angle z1) (angle z2)))) (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)) (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 'real-part '(complex) real-part) (put 'imag-part '(complex) imag-part) (put 'magnitude '(complex) magnitude) (put 'angle '(complex) angle) (put 'equ? '(complex complex) (lambda (x y) (equal? x y))) ;complex型のゼロ確認述語を定義して公開 (put '=zero? '(complex) (lambda (x) (apply-generic '=zero? x))) 'done) (install-complex-package) (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)) (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))
但し、polar型のゼロ比較については、角度angleは2πの倍数ならゼロの扱いになる。けど、無理数なのでどうにもできない、というかどうにかするアイデアが沸かないし、この問題の本質と違うので保留。なので、ここでは角度が0の場合だけを考えてます。
では実験。
これもい〜んじゃないでしょうか?
gosh> (=zero? 0)
#t
gosh> (=zero? 1)
#f
gosh> (=zero? (make-scheme-number 0))
#t
gosh> (=zero? (make-scheme-number 1))
#f
gosh> (=zero? (make-rational 0 2))
#t
gosh> (=zero? (make-rational 1 2))
#f
gosh> (=zero? (make-complex-from-real-imag 1 2))
#f
gosh> (=zero? (make-complex-from-real-imag 0 2))
#f
gosh> (=zero? (make-complex-from-real-imag 0 0))
#t
gosh> (=zero? (make-complex-from-mag-ang 0 0))
#t
gosh> (=zero? (make-complex-from-mag-ang 0 1))
#f
gosh> (=zero? (make-complex-from-mag-ang 1 0))
#f
gosh>