問題 2.84
問題 2.83 の raise 演算を使って apply-generic 手続きを修正し、本節で論じたように順次に高めていく方法で、引数を同じ型になるまで、強制変換するようにせよ。
raise を使用する convert-to-same-type 手続きを用意し、これを apply-generic に組み込みます。
型の階層は height-table を用意して、これに定義します。
(put-height 'scheme-number 10) (put-height 'rational 20) (put-height 'complex 30)
値は適当ですが、値の大小関係は重要です。
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 (eq? type-tag 'scheme-number)
contents
(cons type-tag contents)))
(define (type-tag datum)
(cond ((number? datum) 'scheme-number)
((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)
(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-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)
((get '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->rational n)
(make-rational (contents n) 1))
(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->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))))
;;;;;
(put-height 'scheme-number 10)
(put-height 'rational 20)
(put-height 'complex 30)
;;;;;
(install-scheme-number-package)
(install-rational-package)
(install-rectangular-package)
(install-polar-package)
(install-complex-package)
