みんな大好き汎用算術演算の続き！
問題 2.81
a. Louisの強制型変換手続きが設定されると、型で表に見つからない手続きに対して呼び出されると、何が起きるか。
1) complex に exp 手続きは無いため、apply-generic の proc は常に #f となる 2) complex 同士は強制型変換するようにしているので complex 同士の強制型変換を行う。 3) 1 に戻る これを延々と繰り返す無限ループに陥いる。
b. 同じ型の引数の強制型変換について何かすべきだというLouisは正しいか。それともこのままapply-genericは正しく働くか。
そもそも同じ型同士の変換は意味が無い。 また、すべてのパッケージに exp を実装しなければならなくなり面倒である。 (exp を実装しなくてもよいパッケージもあるかも知れない。この場合どうするのか。) さらに未実装のパッケージがあれば無限ループに陥いる。 以上から Louis の実装は良いとは言えない。
c. 二つの引数が同じ型を持っていれば、強制型変換を試みないように、apply-genericを修正せよ。
(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 "Attempting to coerce the same type -- APPLY-GENERIC" type1 type2)
(let ((t1->t2 (get-coercion type1 type2))
(t2->t1 (get-coercion type2 type1)))
(cond (t1->t2
(begin
(print ";COERCION t1->t2 type1=" type1 " type2=" type2)
(apply-generic op (t1->t2 a1) a2)))
(t2->t1
(begin
(print ";COERCION t2->t1 type1=" type1 " type2=" type2)
(apply-generic op a1 (t2->t1 a2))))
(else
(error "No method for these types -- APPLY-GENERIC"
(list op type-tags)))))))
(error
"No method for these types -- APPLY-GENERIC"
(list op type-tags)))))))同じ型を強制変換しようとした場合はエラーにします。
問題 2.82
多くの引数を持つ一般の場合に、強制型変換が使えるよう、apply-genericをどう一般化すればよいか示せ。
以下戦略。
add の引数を 3 つ以上指定できるようにする。 先頭の 2 つの add を試み、型変換が必要ならば行う 先頭の 2 つを取り除き、結果を先頭の値とする。 引数が 2 個未満になるまでくりかえす。 例 (add 2 3 (scheme-number->complex 10) 100) (add 2 3 (scheme-number->complex 10) 100) この場合は scheme-number 型同士なので型変換は行わず、 (add 2 3) を評価して 5 を得る。 (add 5 (scheme-number->complex 10) 100) 同様に先頭 2 つの add を試みる。型変換が必要となるので先頭の 5 を complex rectangular に変換する。 (add '(complex rectangular 5 . 0) '(complex rectangular 10 . 0) を評価し、 '(complex rectangular 15 . 0) を得る。 (add '(complex rectangular 15 . 0) 100) これも同様に 100 を complex rectangular に型変換する。 (add '(complex rectangular 15 . 0) '(complex rectangular 100 . 0) を評価する。 '(complex rectangular 115 . 0) が計算結果となる。
多引数対応版ソースコード。
(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)
(equal? (cadr x) type2)))
*coercion-table*)))
(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)
(equal? (cadr x) type2))))
*coercion-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 (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 ((t1->t2 (get-coercion type1 type2))
(t2->t1 (get-coercion type2 type1)))
(cond (t1->t2
(begin
(print ";;COERCION t1->t2 type1=" type1 " type2=" type2)
(apply-generic op (t1->t2 a1) a2)))
(t2->t1
(begin
(print ";;COERCION t2->t1 type1=" type1 " type2=" type2)
(apply-generic op a1 (t2->t1 a2))))
(else
(error "No method for these types -- APPLY-GENERIC"
(list op type-tags)))))))
(error
"No method for these types -- APPLY-GENERIC"
(list op type-tags)))))))
(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)
;;;;;
(install-scheme-number-package)
(install-rational-package)
(install-rectangular-package)
(install-polar-package)
(install-complex-package)add 手続きのみ 3 つ以上の引数に対応しています。
問題 2.83
その型のオブジェクトを塔の中で一レベル高める手続きを設計せよ。 (複素数を除く)各型に働く汎用raise演算はどう設計するか。
強制型変換用のテーブル conversion-table を用意して、各型の上下関係、つまり raise で変換できる型を定義します。
raise 手続きはこのテーブルを参照して型のレベルを 1 つぶん上げます。
以下ソース
(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 (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 (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 ((t1->t2 (get-coercion type1 type2))
(t2->t1 (get-coercion type2 type1)))
(cond (t1->t2
(begin
(print ";;COERCION t1->t2 type1=" type1 " type2=" type2)
(apply-generic op (t1->t2 a1) a2)))
(t2->t1
(begin
(print ";;COERCION t2->t1 type1=" type1 " type2=" type2)
(apply-generic op a1 (t2->t1 a2))))
(else
(error "No method for these types -- APPLY-GENERIC"
(list op type-tags)))))))
(error
"No method for these types -- APPLY-GENERIC"
(list op type-tags)))))))
(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))))
(if proc
(proc x)
(error "cannot raise -- RAISE" x))))
;;;;;
(install-scheme-number-package)
(install-rational-package)
(install-rectangular-package)
(install-polar-package)
(install-complex-package)
