計算機プログラムの構造と解釈 第二版 P113 問題2.78
type-tag
contents
attach-tag
この三つの手続きを書き換える問題。
どう書き換えるかというと、
普通の数字(なんていうんだ?lispのリテラル?): 1とか2とか
と
システムで考えてきたscheme-number: (scheme-number 1) とか(scheme-number 2)
を同等に扱えればよいと。
敵を知り、自分を知れば百戦危うからずと言います。
ま、これで敵は分かった。自分はどうだ?
type-tagの定義はこんな感じ
(define (type-tag datum) (if (pair? datum) (car datum) (error "Bad tagged datum -- TYPE-TAG" datum)))
なんか引数が入ってきたら、そのタグを返してる感じだな。
普通の1とか、2とかはpair?で引っかかってエラーになるね。
という事はだ、1とか2が入ってきたら、scheme-numberを返すようにすりゃ良さそうだ。
contentsの定義
(define (contents datum) (if (pair? datum) (cdr datum) (error "Bad tagged datum -- CONTENTS" datum)))
なるほどcdr使ってるから、タグ以外の場所だな。値を渡すって感じか。
1とか2とかだったら、そのまま1とか渡せば良いかな。
attach-tagの定義
(define (attach-tag type-tag contents) (cons type-tag contents))
なんか今までと逆パターンな感じだな。今までは数字入れたらタグ返すとかだったけど、
多分、type-tagとしてscheme-numberきてもシカトする感じだな。
なぜなら、scheme-numberは普通の数字でもう大丈夫だから。
そんな感じで実装
p110-p113_1.scm
#!/usr/local/bin/gosh ;; -*- coding: utf-8 -*- ;;; 3.3.3 put & get (define (make-table) (let ((local-table (list '*table*))) (define (lookup key-1 key-2) (let ((subtable (assoc key-1 (cdr local-table)))) (if subtable (let ((record (assoc key-2 (cdr subtable)))) (if record (cdr record) #f)) #f))) (define (insert! key-1 key-2 value) (let ((subtable (assoc key-1 (cdr local-table)))) (if subtable (let ((record (assoc key-2 (cdr subtable)))) (if record (set-cdr! record value) (set-cdr! subtable (cons (cons key-2 value) (cdr subtable))))) (set-cdr! local-table (cons (list key-1 (cons key-2 value)) (cdr local-table))))) 'ok) (define (dispatch m) (cond ((eq? m 'lookup-proc) lookup) ((eq? m 'insert-proc!) insert!) (else (error "Unknown operation -- TABLE" m)))) dispatch)) (define operation-table (make-table)) (define get (operation-table 'lookup-proc)) (define put (operation-table 'insert-proc!)) ;;P107 apply-generic (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)) (error "No method for these types -- APPLY-GENERIC" (list op type-tags)))))) ;; data with type tag (define (attach-tag type-tag contents) (cons type-tag contents)) (define (type-tag datum) (if (pair? datum) (car datum) (error "Bad tagged datum -- TYPE-TAG" datum))) (define (contents datum) (if (pair? datum) (cdr datum) (error "Bad tagged datum -- CONTENTS" datum))) ;;2.5.1 (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)) ;;問題2.77の変更 (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 (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))) 'done) (define (make-scheme-number n) ((get 'make 'scheme-number) n)) ;;有理数パッケージ (define (install-rational-package) ;;内部手続き (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)))) ;;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 'make 'rational (lambda (n d) (tag (make-rat n d)))) 'done) (define (make-rational n d) ((get 'make 'rational) n d)) ;;複素数表現 (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)))) ;;問題2.77の変更 ;;システムの他の部分へのインターフェース (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)) ;; 直交座標表現 (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 (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 '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-real-mag-ang r a)))) 'done) ;;極座標表現 (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 (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イス (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 '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)
2-78.scm
#!/usr/local/bin/gosh ;; -*- coding: utf-8 -*- (use ggc.debug.trace) (use math.mt-random) (define nil '()) (define nl newline) (define disp display) (define (square x) (* x x)) (load "./p110-p113_1.scm") (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 (attach-tag type-tag contents) (cond ((eq? 'scheme-number type-tag) contents) (else (cons type-tag contents)))) (install-scheme-number-package) (install-complex-package) (install-rectangular-package) (define z (make-complex-from-real-imag 3 4)) (define i (make-scheme-number 5)) ;; main (define (main args) (disp z)(nl) (disp i)(nl) (disp 5)(nl) (nl) (disp (type-tag z))(nl) (disp (type-tag i))(nl) (disp (type-tag 5))(nl) (nl) (disp (contents z))(nl) (disp (contents i))(nl) (disp (contents 5))(nl) (nl) (disp (contents z))(nl) (disp (contents i))(nl) (disp (contents 5))(nl) (nl) (disp (add (make-scheme-number 5) 5))(nl) 0)
実行
(complex rectangular 3 . 4) 5 5 complex scheme-number scheme-number (rectangular 3 . 4) 5 5 (rectangular 3 . 4) 5 5 10
できた。