## 2015年7月9日木曜日

### Scheme - データによる抽象の構築(汎用演算システム(異なる型のデータの統合(同じ型, 強制型変換, 任意の個数の引数)))

その他参考書籍

コード(Emacs)

``` (begin (define print (lambda (x) (display x) (newline))) (define error (lambda (message value) (display message) (display " ") (display value) (newline))) (define for-each (lambda (proc items) (if (not (null? items)) (begin (proc (car items)) (for-each proc (cdr items)))))) (define gcd (lambda (a b) (if (= b 0) a (gcd b (remainder a b))))) (define inc (lambda (n) (+ n 1))) (define square (lambda (x) (* x x))) (define sqrt (lambda (x) (define sqrt-iter (lambda (guess x) (if (good-enough? guess x) guess (sqrt-iter (improve guess x) x)))) (define good-enough? (lambda (guess x) (< (abs (- (square guess) x)) 0.001))) (define improve (lambda (guess x) (average guess (/ x guess)))) (sqrt-iter 1.0 x))) (define average (lambda (x y) (/ (+ x y) 2))) (define abs (lambda (x) (if (< x 0) (* -1 x) x))) (define map (lambda (proc items) (if (null? items) (quote ()) (cons (proc (car items)) (map proc (cdr items)))))) (define accumulate (lambda (combiner null-value term a next b) (define inner (lambda (x result) (if (> x b) result (inner (next x) (combiner (term x) result))))) (inner a null-value))) (define expt (lambda (base n) (define (iter n result) (if (= n 0) result (iter (- n 1) (* result base)))) (iter n 1))) (define (factorial n) (define (iter product counter) (if (> counter n) product (iter (* counter product) (+ counter 1)))) (iter 1 1)) (define sin (lambda (x) (accumulate + 0.0 (lambda (n) (let ((a (+ (* 2 n) 1))) (* (/ (expt -1 n) (factorial a)) (expt x a)))) 0 inc 10))) (define cos (lambda (x) (accumulate + 0.0 (lambda (n) (let ((a (* 2 n))) (* (/ (expt -1 n) (factorial a)) (expt x a)))) 0 inc 10))) (define make-table (lambda () (let ((local-table (list (quote *table*)))) (define assoc (lambda (key records) (cond ((null? records) #f) ((equal? key (caar records)) (car records)) (else (assoc key (cdr records)))))) (define lookup (lambda (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! (lambda (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))))) (quote ok))) (define dispatch (lambda (m) (cond ((eq? m (quote lookup-proc)) lookup) ((eq? m (quote insert-proc!)) insert!) (else (error "Unknown operation -- TABLE" m))))) dispatch))) (define operation-table (make-table)) (define get (operation-table (quote lookup-proc))) (define put (operation-table (quote insert-proc!))) (define attach-tag (lambda (type-tag contents) (cons type-tag contents))) (define type-tag (lambda (datum) (if (pair? datum) (car datum) (error "Bad tagged datum -- TYPE-TAG" datum)))) (define contents (lambda (datum) (if (pair? datum) (cdr datum) (else error "Bad tagged datum -- CONTENTS" datum)))) (define type-table (make-table)) (define get-coercion (type-table (quote lookup-proc))) (define put-coercion (type-table (quote insert-proc!))) (define scheme-number->complex (lambda (n) (make-complex-from-real-imag (contents n) 0))) (define scheme-number->rational (lambda (n) (make-rational (contents n) 1))) (put-coercion (quote scheme-number) (quote complex) scheme-number->complex) (put-coercion (quote scheme-number) (quote rational) scheme-number->rational) ;; b. 同じ型の引数の強制型変換について何かをすべきだというLouis は正しくない ;; 可変個引数の手続きの定義はまだ kscheme に実装してないから、明示的にリストを渡す (define apply-generic (lambda (op args) (let ((type-tags (map type-tag args))) (define iter1 (lambda (args types type) (if (null? args) (quote ()) (let ((t (type-tag (car args)))) (if (eq? t type) (cons (car args) (iter1 (cdr args) (cdr types) type)) (let ((t->type (get-coercion t type))) (if t->type (cons (t->type (car args)) (iter1 (cdr args) (cdr types) type)) (quote ())))))))) (define iter (lambda (args types) (if (null? types) (error "No method for these types" (list op type-tags)) (let ((type (car types))) (let ((args1 (iter1 args types type))) (if (= (length args) (length args1)) (let ((proc (get op (map type-tag args1)))) (if proc (apply proc (map contents args1)) (iter args (cdr types)))) (iter args (cdr types)))))))) (iter args type-tags)))) (define add (lambda (x y) (apply-generic (quote add) (list x y)))) (define sub (lambda (x y) (apply-generic (quote sub) (list x y)))) (define mul (lambda (x y) (apply-generic (quote mul) (list x y)))) (define mul3 (lambda (x y z) (apply-generic (quote mul3) (list x y z)))) (define div (lambda (x y) (apply-generic (quote div) (list x y)))) (define equ? (lambda (x y) (apply-generic (quote equ?) (list x y)))) (define =zero? (lambda (x) (apply-generic (quote =zero?) (list x)))) (define real-part (lambda (z) (apply-generic (quote real-part) (list z)))) (define imag-part (lambda (z) (apply-generic (quote imag-part) (list z)))) (define magnitude (lambda (z) (apply-generic (quote magnitude) (list z)))) (define angle (lambda (z) (apply-generic (quote angle) (list z)))) (define make-from-real-imag (lambda (real imag) ((get (quote make-from-real-imag) (quote complex)) real imag))) (define make-from-mag-ang (lambda (mag ang) ((get (quote make-from-mag-ang) (quote complex)) mag ang))) (define install-scheme-number-package (lambda () (define tag (lambda (x) (attach-tag (quote scheme-number) x))) (put (quote add) (quote (scheme-number scheme-number)) (lambda (x y) (tag (+ x y)))) (put (quote sub) (quote (scheme-number scheme-number)) (lambda (x y) (tag (- x y)))) (put (quote mul) (quote (scheme-number scheme-number)) (lambda (x y) (tag (* x y)))) (put (quote div) (quote (scheme-number scheme-number)) (lambda (x y) (tag (/ x y)))) (put (quote equ?) (quote (scheme-number scheme-number)) (lambda (x y) (= x y))) (put (quote =zero?) (quote (scheme-number)) (lambda (x) (= x 0))) (put (quote exp) (quote (scheme-number scheme-number)) (lambda (x y) (tag (expt x y)))) (put (quote make) (quote scheme-number) (lambda (x) (tag x))) (quote done))) (define make-scheme-number (lambda (n) ((get (quote make) (quote scheme-number)) n))) (define exp (lambda (x y) (apply-generic (quote exp) (list x y)))) (define install-rational-package (lambda () (define numer car) (define denom cdr) (define make-rat (lambda (n d) (let ((g (gcd n d))) (cons (/ n g) (/ d g))))) (define add (lambda (x y) (make-rat (+ (* numer x) (denom y) (* (numer y) (denom x))) (* (denom x) (denom y))))) (define sub (lambda (x y) (make-rat (- (* numer x) (denom y) (* numer y) (denom y)) (* (denom x) (denom y))))) (define mul (lambda (x y) (make-rat (* (numer x) (numer y)) (* (denom x) (denom y))))) (define mul3 (lambda (x y z) (make-rat (* (* (numer x) (numer y)) (numer z)) (* (* (denom x) (denom y)) (denom z))))) (define div (lambda (x y) (make-rat (* (numer x) (denom y)) (* (denom x) (numer y))))) (define equ? (lambda (x y) (and (= (numer x) (numer y)) (= (denom x) (denom y))))) (define =zero? (lambda (x) (and (= (numer x) 0)))) (define tag (lambda (x) (attach-tag (quote rational) x))) (put (quote add) (quote (rational rational)) (lambda (x y) (tag (add x y)))) (put (quote sub) (quote (rational rational)) (lambda (x y) (tag (sub x y)))) (put (quote mul) (quote (rational rational)) (lambda (x y) (tag (mul x y)))) (put (quote mul3) (quote (rational rational rational)) (lambda (x y z) (tag (mul3 x y z)))) (put (quote div) (quote (rational rational)) (lambda (x y) (tag (div x y)))) (put (quote make) (quote rational) (lambda (n d) (tag (make-rat n d)))) (put (quote equ?) (quote (rational rational)) equ?) (put (quote =zero?) (quote (rational)) =zero?) (quote done))) (define make-rational (lambda (n d) ((get (quote make) (quote rational)) n d))) (define install-rectangular-package (lambda () (define real-part (lambda (z) (car z))) (define imag-part (lambda (z) (cdr z))) (define make-from-real-imag (lambda (x y) (cons x y))) (define magnitude (lambda (z) (sqrt (+ (square (real-part z)) (square (imag-part z)))))) (define angle (lambda (z) (atan (imag-part z) (real-part z)))) (define make-from-mag-ang (lambda (r a) (cons (* r (cos a)) (* r (sin a))))) (define equ? (lambda (z1 z2) (and (= (real-part z1) (real-part z2)) (= (imag-part z1) (imag-part z2))))) (define =zero? (lambda (z) (and (= (real-part z) 0) (= (imag-part z) 0)))) (define tag (lambda (x) (attach-tag (quote rectangular) x))) (put (quote real-part) (quote (rectangular)) real-part) (put (quote imag-part) (quote (rectangular)) imag-part) (put (quote magnitude) (quote (rectangular)) magnitude) (put (quote angle) (quote (rectangular)) angle) (put (quote make-from-real-imag) (quote rectangular) (lambda (x y) (tag (make-from-real-imag x y)))) (put (quote make-from-mag-ang) (quote rectangular) (lambda (r a) (tag (make-from-mag-ang r a)))) (put (quote equ?) (quote (rectangular rectangular)) equ?) (put (quote =zero?) (quote (rectangular)) =zero?) (quote done))) (define install-polar-package (lambda () (define magnitude (lambda (z) (car z))) (define angle (lambda (z) (cdr z))) (define make-from-mag-ang (lambda (r a) (cons r a))) (define real-part (lambda (z) (* (magnitude z) (cos (angle z))))) (define imag-part (lambda (z) (* (magnitude z) (sin (angle z))))) (define make-from-real-imag (lambda (x y) (cons (sqrt (+ (square x) (square y))) (atan y x)))) (define equ? (lambda (z1 z2) (and (= (real-part z1) (real-part z2)) (= (imag-part z1) (imag-part z2))))) (define =zero? (lambda (z) (and (= (real-part z) 0) (= (imag-part z) 0)))) (define tag (lambda (x) (attach-tag (quote polar) x))) (put (quote real-part) (quote (polar)) real-part) (put (quote imag-part) (quote (polar)) imag-part) (put (quote magnitude) (quote (polar)) magnitude) (put (quote angle) (quote (polar)) angle) (put (quote make-from-real-imag) (quote polar) (lambda (x y) (tag (make-from-real-imag x y)))) (put (quote make-from-mag-ang) (quote polar) (lambda (r a) (tag (make-from-mag-ang r a)))) (put (quote equ?) (quote (polar polar)) equ?) (put (quote =zero?) (quote (polar)) =zero?) (quote done))) (define install-complex-package (lambda () (define make-from-real-imag (lambda (x y) ((get (quote make-from-real-imag) (quote rectangular)) x y))) (define make-from-mag-ang (lambda (r a) ((get (quote make-from-mag-ang) (quote polar)) r a))) (define add-complex (lambda (z1 z2) (make-from-real-imag (+ (real-part z1) (real-part z2)) (+ (imag-part z1) (imag-part z2))))) (define sub-complex (lambda (z1 z2) (make-from-real-imag (- (real-part z1) (real-part z2)) (- (imag-part z1) (imag-part z2))))) (define mul-complex (lambda (z1 z2) (make-from-mag-ang (* (magnitude z1) (magnitude z2)) (+ (angle z1) (angle z2))))) (define div-complex (lambda (z1 z2) (make-from-mag-ang (/ (magnitude z1) (magnitude z2)) (- (angle z1) (angle z2))))) (define equ? (lambda (z1 z2) (and (= (real-part z1) (real-part z2)) (= (imag-part z1) (imag-part z2))))) (define =zero? (lambda (z) (and (= (real-part z) 0) (= (imag-part z) 0)))) (define tag (lambda (z) (attach-tag (quote complex) z))) (put (quote add) (quote (complex complex)) (lambda (z1 z2) (tag (add-complex z1 z2)))) (put (quote sub) (quote (complex complex)) (lambda (z1 z2) (tag (sub-complex z1 z2)))) (put (quote mul) (quote (complex complex)) (lambda (z1 z2) (tag (mul-complex z1 z2)))) (put (quote div) (quote (complex complex)) (lambda (z1 z2) (tag (div-complex z1 z2)))) (put (quote make-from-real-imag) (quote complex) (lambda (x y) (tag (make-from-real-imag x y)))) (put (quote make-from-mag-ang) (quote complex) (lambda (r a) (tag (make-from-mag-ang r a)))) (put (quote real-part) (quote (complex)) real-part) (put (quote imag-part) (quote (complex)) imag-part) (put (quote magnitude) (quote (complex)) magnitude) (put (quote angle) (quote (complex)) angle) (put (quote equ?) (quote (complex complex)) equ?) (put (quote =zero?) (quote (complex)) =zero?) (quote done))) (install-scheme-number-package) (install-rational-package) (install-rectangular-package) (install-polar-package) (install-complex-package) (define r1 (make-rational 1 2)) (define r2 (make-rational 3 4)) (define r3 (make-rational 5 6)) (print (mul3 r1 r2 r3)) ; 1/2 * 3/4 * 5/6 = 5/16 (print (mul3 r1 r2 (make-scheme-number 10))) ; 1/2 * 3/4 * 10 = 15/4 (print (mul3 r1 (make-scheme-number 10) r3)) ; 1/2 * 10 * 5/6 = 25/6 (print (mul3 (make-scheme-number 10) r2 r3)) ; 10 * 3/4 * 5/6 = 25/4 (quote done)) ;; 出力結果が意図した通りではなかった。。kscheme の実装に問題があるっぽい. ;; ただ、Gauche でもエラーが発生したから、この scheme のコード自体にも問題があるかも。 ;; とりあえず先に進むことに。 ;; この戦略は、拡大型に高めるのではなく、降ろすことにより演算できる場合は、まだ十分に一般的ではない。 ```

```\$ kscheme sample82.scm
(rational 5/16 . 1)
(rational 15/4 . 1)
(rational 25/6 . 1)
(rational 25/4 . 1)
done
\$ gosh sample82.scm
(rational 5 . 16)
(rational 15 . 4)
(rational 25.0 . 6.0)
gosh: "error": pair required, but got ()
\$```