問題 2.85
オブジェクトを出来るだけ下げるdrop手続きを書いて、実装する方法を詳しく述べよ。
今回 scheme-real パッケージも実装しました。
drop 手続きの実装では、raise でも使用した *conversion-table* を使います。また、まとめて drop する drops 手続きも実装します。この drops 手続きを apply-generic に組み込みます。
以下全ソース
(define *table* '()) (define (get op type) (let ((item (filter (lambda (x) (and (eq? (car x) op) (equal? (cadr x) type))) *table*))) (if (null? item) #f (caddr (car item))))) (define (put op type item) (set! *table* (cons (list op type item) (filter (lambda (x) (not (and (eq? (car x) op) (equal? (cadr x) type)))) *table*)))) ;;;;; (define *coercion-table* '()) (define (get-coercion type1 type2) (let ((item (filter (lambda (x) (and (eq? (car x) type1) (eq? (cadr x) type2))) *coercion-table*))) (print ";;item=" item) (if (null? item) #f (caddr (car item))))) (define (put-coercion type1 type2 proc) (set! *coercion-table* (cons (list type1 type2 proc) (filter (lambda (x) (not (and (eq? (car x) type1) (eq? (cadr x) type2)))) *coercion-table*)))) ;;;;; (define *conversion-table* '()) (define (get-conversion conv type1) (let ((item (filter (lambda (x) (and (eq? (car x) conv) (eq? (cadr x) type1))) *conversion-table*))) (if (null? item) #f (caddr (car item))))) (define (put-conversion conv type proc) (set! *conversion-table* (cons (list conv type proc) (filter (lambda (x) (not (and (eq? (car x) conv) (eq? (cadr x) type)))) *conversion-table*)))) ;;;;; (define *height-table* '()) (define (get-height type) (let ((item (filter (lambda (x) (and (eq? (car x) type))) *height-table*))) (if (null? item) #f (cadr (car item))))) (define (put-height type height) (set! *height-table* (cons (list type height) (filter (lambda (x) (not (and (eq? (car x) type) (eq? (cadr x) height)))) *height-table*)))) ;;;;; (define (attach-tag type-tag contents) (if (or (eq? type-tag 'scheme-number) (eq? type-tag 'scheme-real)) contents (cons type-tag contents))) (define (type-tag datum) (cond ((exact-integer? datum) 'scheme-number) ((number? datum) 'scheme-real) ((pair? datum) (car datum)) (else (error "Bad tagged datum -- TYPE-TAG" datum)))) (define (contents datum) (cond ((number? datum) datum) ((pair? datum) (cdr datum)) (else (error "Bad tagged datum -- CONTENTS" datum)))) ;;;;; (define (convert-to-same-type arg1 arg2) (let ((type1 (type-tag arg1)) (type2 (type-tag arg2))) (let ((h1 (get-height type1)) (h2 (get-height type2))) (print ";;CONVERT-TO-SAME-TYPE arg1=" arg1 " arg2=" arg2) (cond ((< h1 h2) (convert-to-same-type (raise arg1) arg2)) ((> h1 h2) (convert-to-same-type arg1 (raise arg2))) (else (list arg1 arg2)))))) (define (apply-generic op . args) (let ((type-tags (map type-tag args))) (let ((proc (get op type-tags))) (print ";;APPLY-GENERIC op=" op " args=" args) (if proc (begin (print ";;APPLY proc=" proc " op=" op " args=" args) (drops (apply proc (map contents args)))) (if (= (length args) 2) (let ((type1 (car type-tags)) (type2 (cadr type-tags)) (a1 (car args)) (a2 (cadr args))) (if (eq? type1 type2) (error "op is not defined for the type -- APPLY-GENERIC" (list op type1)) (let ((conv-args (convert-to-same-type a1 a2))) (if conv-args (apply-generic op (car conv-args) (cadr conv-args)) (error "convert error -- APPLY-GENERIC" type1 type2)))))))))) (define (apply-generic-kai op . arguments) (define (arg1 args) (car args)) (define (arg2 args) (cadr args)) (define (iter args) (print ";;APPLY-GENERIC-KAI args=" args) (if (= (length args) 2) (apply-generic op (arg1 args) (arg2 args)) (let ((val (apply-generic op (arg1 args) (arg2 args)))) (iter (cons val (cddr args)))))) (iter (car arguments))) ;;;;; (define (install-scheme-number-package) ;; システムの他の部分へのインターフェース (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 'equ? '(scheme-number scheme-number) (lambda (x y) (tag (= x y)))) (put '=zero? '(scheme-number) (lambda (x) (zero? x))) (put 'exp '(scheme-number scheme-number) (lambda (x y) (tag (expt x y)))) (put 'make 'scheme-number (lambda (x) (tag x))) 'done) (define (install-scheme-real-package) ;; システムの他の部分へのインターフェース (define (tag x) (attach-tag 'scheme-real x)) (put 'add '(scheme-real scheme-real) (lambda (x y) (tag (+ x y)))) (put 'sub '(scheme-real scheme-real) (lambda (x y) (tag (- x y)))) (put 'mul '(scheme-real scheme-real) (lambda (x y) (tag (* x y)))) (put 'div '(scheme-real scheme-real) (lambda (x y) (tag (/ x y)))) (put 'equ? '(scheme-real scheme-real) (lambda (x y) (tag (= x y)))) (put '=zero? '(scheme-real) (lambda (x) (zero? x))) (put 'exp '(scheme-real scheme-real) (lambda (x y) (tag (expt x y)))) (put 'make 'scheme-real (lambda (x) (tag x))) 'done) (define (install-rational-package) ;; 内部手続き (define (numer x) (car x)) (define (denom x) (cdr x)) (define (make-rat n d) (if (= d 0) (error "zero denominator -- MAKE-RAT") (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? x y) (and (= (numer x) (numer y)) (= (denom x) (denom y)))) (define (=zero? x) (zero? (numer x))) ;; システムの他の部分へのインターフェース (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 'equ? '(rational rational) (lambda (x y) (equ? x y))) (put '=zero? '(rational) (lambda (x) (=zero? x))) (put 'numer '(rational) numer) (put 'denom '(rational) denom) (put 'make 'rational (lambda (n d) (tag (make-rat n d)))) 'done) (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 (equ? z1 z2) (and (= (real-part z1) (real-part z2)) (= (imag-part z1) (imag-part z2)))) (define (=zero? z) (and (zero? (real-part z)) (zero? (imag-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ーフェース (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 'equ? '(rectangular rectangular) (lambda (z1 z2) (equ? z1 z2))) (put '=zero? '(rectangular) (lambda (z) (=zero? z))) (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) (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 (equ? z1 z2) (and (= (magnitude z1) (magnitude z2)) (= (angle z1) (angle z2)))) (define (=zero? z) (zero? (magnitude 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ーフェース (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 'equ? '(polar polar) (lambda (z1 z2) (equ? z1 z2))) (put '=zero? '(polar) (lambda (z) (=zero? z))) (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) (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-mag-ang (* (magnitude z1) (magnitude z2)) (+ (angle z1) (angle z2)))) (define (div-complex z1 z2) (make-from-mag-ang (/ (magnitude z1) (magnitude z2)) (- (angle z1) (angle z2)))) ;; システムの他の部分へのインターフェース (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 'real-part '(complex) real-part) (put 'imag-part '(complex) imag-part) (put 'magnitude '(complex) magnitude) (put 'angle '(complex) angle) (put 'equ? '(complex complex) equ?) (put '=zero? '(complex) =zero?) 'done) ;;;;; (define (add x . y) (apply-generic-kai 'add (cons 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 (numer r) (apply-generic 'numer r)) (define (denom r) (apply-generic 'denom r)) (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 (make-scheme-number n) (if (exact-integer? n) ((get 'make 'scheme-number) n) ((get 'make 'scheme-real) n))) (define (make-scheme-real n) (make-scheme-number n)) (define (make-rational n d) ((get 'make 'rational) n d)) (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 (equ? x y) (apply-generic 'equ? x y)) (define (=zero? x) (apply-generic '=zero? x)) (define (exp x y) (apply-generic 'exp x y)) ;;;;; (define (scheme-number->real n) (make-scheme-real (contents n))) (define (scheme-number->rational n) (make-rational (contents n) 1)) (define (rational->scheme-real rat) (make-scheme-real (/. (numer rat) (denom rat)))) (define (scheme-real->complex r) (make-complex-from-real-imag (contents r) 0)) (define (scheme-number->complex n) (make-complex-from-real-imag (contents n) 0)) (define (rational->complex rat) (make-complex-from-real-imag (/ (numer rat) (denom rat)) 0)) (put-coercion 'scheme-number 'rational scheme-number->rational) (put-coercion 'scheme-number 'complex scheme-number->complex) (put-coercion 'rational 'complex rational->complex) ;;;;; (put-conversion 'raise 'scheme-number scheme-number->rational) (put-conversion 'raise 'rational rational->scheme-real) (put-conversion 'raise 'scheme-real scheme-real->complex) (define (raise x) (let ((proc (get-conversion 'raise (type-tag x)))) (print ";;RAISE x=" x) (if proc (proc x) (error "cannot raise -- RAISE" x)))) ;;;;; (define (rational->scheme-number rat) (if (= (denom rat) 1) (make-scheme-number (numer rat)) rat)) (define (scheme-real->rational real) (let ((s (string-split (number->string (inexact->exact real)) "/"))) (if (= (length s) 2) (make-rational (string->number (car s)) (string->number (cadr s))) (make-rational (string->number (car s)) 1)))) (define (complex->scheme-real z) (if (= (imag-part z) 0) (make-scheme-real (* 1.0 (real-part z))) z)) (put-conversion 'drop 'rational rational->scheme-number) (put-conversion 'drop 'scheme-real scheme-real->rational) (put-conversion 'drop 'complex complex->scheme-real) (define (drop x) (let ((proc (get-conversion 'drop (type-tag x)))) (print ";;DROP x=" x) (if proc (proc x) x))) (define (drops x) (let* ((old-type (type-tag x)) (new-type-x (drop x)) (new-type (type-tag new-type-x))) (if (eq? old-type new-type) x (drops new-type-x)))) ;;;;; (put-height 'scheme-number 10) (put-height 'rational 20) (put-height 'scheme-real 30) (put-height 'complex 40) ;;;;; (install-scheme-number-package) (install-scheme-real-package) (install-rational-package) (install-rectangular-package) (install-polar-package) (install-complex-package)
なお、drops 手続きには問題があります。次の問題をやるときに修正します。
