#lang racket
(define (square x) (* x x))
;put get實現
(define *op-table* (make-hash))
(define (put op type proc)
(hash-set! *op-table* (list op type) proc))
(define (get op type)
(hash-ref *op-table* (list op type) #f))
(define *type-coercion* (make-hash))
(define (put-coercion type1 type2 proc)
(hash-set! *type-coercion* (list type1 type2) proc))
(define (get-coercion type1 type2)
(hash-ref *type-coercion* (list type1 type2) #f))
(define (scheme-number->scheme-number n) n)
(define (complex->complex z) z)
(put-coercion 'scheme-number 'scheme-number scheme-number->scheme-number)
(put-coercion 'complex 'complex complex->complex)
(define (attach-tag type-tag contents)
(cond ((eq? type-tag 'scheme-number) contents)
(else (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 (apply-generic op . args)
(let ((type-tags (map type-tag args)))
(let ((proc (get op type-tags)))
(if proc
(apply proc (map contents args))
(if (= (length args) 2)
(let ((type1 (car type-tags))
(type2 (cadr type-tags))
(a1 (car args))
(a2 (cadr args)))
(let ((t1->t2 (get-coercion type1 type2))
(t2->t1 (get-coercion type2 type1)))
(cond (t1->t2
(apply-generic op (t1->t2 1) a2))
(t2->t1
(apply-generic op a1 (t2->t1 a2)))
(else
(error "No method for these types"
(list op type-tags))))))
(error "No method for these types"
(list op type-tags)))))))
(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 (real-part x) (apply-generic 'real-part x))
(define (imag-part x) (apply-generic 'imag-part x))
(define (magnitude x) (apply-generic 'magnitude x))
(define (angle x) (apply-generic 'angle x))
(define (exp x y) (apply-generic 'exp x y))
(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 'exp '(scheme-number scheme-number)
(lambda (x y) (tag (expt x y))))
(put 'make 'scheme-number
(lambda (x) (tag x)))
'done)
(define (make-scheme-number n)
((get 'make 'scheme-number) n))
(define (install-rational-package)
(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))))
'done)
(define (make rational n d)
((get 'make 'rational) n d))
(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 (* (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))))
(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)
'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))
(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))))
'done)
(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))))
'done)
(install-scheme-number-package)
(install-rational-package)
(install-complex-package)
(install-rectangular-package)
(install-polar-package)
(define complex-A (make-complex-from-real-imag 1 2))
(define complex-B (make-complex-from-real-imag 3 4))
(exp complex-A complex-B)
a）程序陷入死循環，因爲兩個參數類型一樣，經過轉化後，兩個類型還是一樣，而且又找不到合適的操作過程執行，所以程序一直循環。
b）沒有糾正，而且添加同類型的強制，會讓程序陷入死循環，本來沒添加強制之前，程序會直接找不到過程而退出。
c）添加兩個類型一樣的判斷，如果兩個類型一樣，則直接報錯，顯示找不到方法，完整過程如下。
#lang racket
(define (square x) (* x x))
;put get實現
(define *op-table* (make-hash))
(define (put op type proc)
(hash-set! *op-table* (list op type) proc))
(define (get op type)
(hash-ref *op-table* (list op type) #f))
(define *type-coercion* (make-hash))
(define (put-coercion type1 type2 proc)
(hash-set! *type-coercion* (list type1 type2) proc))
(define (get-coercion type1 type2)
(hash-ref *type-coercion* (list type1 type2) #f))
(define (scheme-number->scheme-number n) n)
(define (complex->complex z) z)
(put-coercion 'scheme-number 'scheme-number scheme-number->scheme-number)
(put-coercion 'complex 'complex complex->complex)
(define (attach-tag type-tag contents)
(cond ((eq? type-tag 'scheme-number) contents)
(else (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 (apply-generic op . args)
(let ((type-tags (map type-tag args)))
(let ((proc (get op type-tags)))
(if proc
(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 "No method for these types"
(list op type-tags))
(let ((t1->t2 (get-coercion type1 type2))
(t2->t1 (get-coercion type2 type1)))
(cond (t1->t2
(apply-generic op (t1->t2 a1) a2))
(t2->t1
(apply-generic op a1 (t2->t1 a2)))
(else
(error "No method for these types"
(list op type-tags)))))))
(error "No method for these types"
(list op type-tags)))))))
(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 (real-part x) (apply-generic 'real-part x))
(define (imag-part x) (apply-generic 'imag-part x))
(define (magnitude x) (apply-generic 'magnitude x))
(define (angle x) (apply-generic 'angle x))
(define (exp x y) (apply-generic 'exp x y))
(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 'exp '(scheme-number scheme-number)
(lambda (x y) (tag (expt x y))))
(put 'make 'scheme-number
(lambda (x) (tag x)))
'done)
(define (make-scheme-number n)
((get 'make 'scheme-number) n))
(define (install-rational-package)
(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))))
'done)
(define (make rational n d)
((get 'make 'rational) n d))
(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 (* (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))))
(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)
'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))
(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))))
'done)
(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))))
'done)
(install-scheme-number-package)
(install-rational-package)
(install-complex-package)
(install-rectangular-package)
(install-polar-package)
(define complex-A (make-complex-from-real-imag 1 2))
(define complex-B (make-complex-from-real-imag 3 4))
(exp complex-A complex-B)
運行結果
'done
'done
'done
'done
'done
. . No method for these types (exp (complex complex))