sicp 2.86

sicp_2_86

;-------------put-get-----------------------------------------
(define global-array '())
 
(define (make-entry k v) (list k v))
(define (key entry) (car entry))
(define (value entry) (cadr entry))
 
(define (put op type item)
  (define (put-helper k array)
    (cond ((null? array) (list(make-entry k item)))
          ((equal? (key (car array)) k) array)
          (else (cons (car array) (put-helper k (cdr array))))))
  (set! global-array (put-helper (list op type) global-array)))
 
(define (get op type)
  (define (get-helper k array)
    (cond ((null? array) #f)
          ((equal? (key (car array)) k) (value (car array)))
          (else (get-helper k (cdr array)))))
  (get-helper (list op type) global-array))
 
;-------------put-get-coercion-----------------------------------------
(define coercion-registry '())
(define (put-coercion t1 t2 fn) (set! coercion-registry (cons (list t1 t2 fn) coercion-registry)))
(define (get-coercion t1 t2)
  (define (rec entry . reg)
    (define t1-entry car)
    (define t2-entry cadr)
    (define fn-entry caddr)
    (cond ((and (eq? t1 (t1-entry entry))
                (eq? t2 (t2-entry entry))) (fn-entry entry))
          ((null? reg) #f)
          (else (apply rec reg))))
  (apply rec coercion-registry))
;-------------tag type----------------------------------------
(define (type-tag datum)
  (cond ((pair? datum) (car datum))
        ((number? datum) 'scheme-number)
        (else (error "Bad tagged datum -- TYPE-TAG" datum))))
 
(define (contents datum)
  (cond ((pair? datum) (cdr datum))
        ((number? datum) datum)
        (else (error "Bad tagged datum -- CONTENTS" datum))))
 
(define (attach-tag type-tag contents)
      (cons type-tag contents))
;-------------------------------------------------------------
 
(define (apply-generic op . args)
  (define (rise-to a type)
    (cond
      ((eq? (type-tag a) type) a)
      (else (raise1 a))
     )
    )
  (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 THIS TYPE3"
                           (list op type-tags)))
                (if (eq? (rise-to a1 type2) #f) (rise-to a2 type1) (rise-to a1 type2))
                )
              (error "NO METHOD FOR THIS TYPE2"
                     (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 (equ? x y) (apply-generic 'equ? x y))
(define (=zero? x) (apply-generic '=zero? x))
(define (raise1 x) (apply-generic 'raise1 x))
(define (project x) (apply-generic 'project x))
 (define (sine x) (apply-generic 'sine x)) 
 (define (cosine x) (apply-generic cosine x)) 
;-------------------------------------------
(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)))
(put 'equ? '(scheme-number scheme-number) (lambda (x y) (= x y)))
(put '=zero? '(scheme-number) (lambda (x) (= x 0)))
(put 'raise1 '(scheme-number) (lambda (x) (make-rational x 1)))
  (put 'raise1 'scheme-number (lambda (x) (make-rational x 1)))
 (put 'sine 'scheme-number 
      (lambda (x) (tag (sin x)))) 
 (put 'cosine 'scheme-number 
      (lambda (x) (tag (cos x)))) 
'done)
;----------
(define (make-scheme-number n)
((get 'make 'scheme-number) n))
;-------------------------------------------
(define (install-rational-package)
;; âíóòðåííèå ïðîöåäóðû
(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))))
;; interface
(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))))
(put '=zero? '(rational)
     (lambda (x) (and (= (numer x) 0) (= (denom x) 0))))
(put 'raise1'(rational)
       (lambda (r) (make-real (/ (numer r) (denom r)))))
(put 'project '(rational)
      (lambda (x) (make-scheme-number (round (/ (numer x) (denom x)))))) 
(put 'project 'rational 
      (lambda (x) (make-scheme-number (round (/ (numer x) (denom  x)))) ))
(put 'equ? '(rational rational)
(lambda (x y)  (and (= (numer x) (numer y)) (= (denom x) (denom y)))))
(put 'sine '(rational) (lambda (x) (attach-tag 'rational (sin (/ (car x) (cdr x))))))
(put 'cosine '(rational) (lambda (x) (attach-tag 'rational (cos (/ (car x) (cdr x))))))
  
'done)
(define (make-rational n d)
((get 'make 'rational) n d))
;------------------real-------------------------------
(define (install-real-package)
  (define (tag x)
    (attach-tag 'real x))    
  (put 'add '(real real)
       (lambda (x y) (tag (+ x y))))
  (put 'sub '(real real)
       (lambda (x y) (tag (- x y))))
  (put 'mul '(real real)
       (lambda (x y) (tag (* x y))))
  (put 'div '(real real)
       (lambda (x y) (tag (/ x y))))
  (put 'equ? '(real real) =)
  (put '=zero? '(real)
       (lambda (x) (= 0 x)))
  (put 'make 'real
       (lambda (x) (if (real? x)
                       (tag x)
                       (error "non-real value" x))))
   (put 'raise1 '(real)
       (lambda (r) (make-complex-from-real-imag r 0)))
  
   (put 'project 'real 
      (lambda (x)  
        (let ((rat (rationalize  
                     (inexact->exact x) 1/100))) 
          (make-rational 
            (numerator rat) 
            (denominator rat))))) 
  'done)
 
(define (make-real n)
  ((get 'make 'real) n))
;-----------------------------------------------------
(define (install-polar-package)
;; âíóòðåííèå ïðîöåäóðû
(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)))
;; èíòåðôåéñ ê îñòàëüíîé ñèñòåìå
(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))))
 (put 'sine 'rational 
      (lambda (x) (tag (sin x)))) 
 (put 'cosine 'rational 
      (lambda (x) (tag (cos x)))) 
'done)
;-----------------------------------------------------
(define (install-rectangular-package)
;; âíóòðåííèå ïðîöåäóðû
(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))))
;; èíòåðôåéñ ê îñòàëüíîé ñèñòåìå
(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-complex-package)
;; ïðîöåäóðû, èìïîðòèðóåìûå èç äåêàðòîâà
;; è ïîëÿðíîãî ïàêåòîâ
(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))
;; âíóòðåííèå ïðîöåäóðû
(define (add-complex z1 z2) 
   (make-from-real-imag (add (real-part z1) (real-part z2)) 
                        (add (imag-part z1) (imag-part z2)))) 
 (define (sub-complex z1 z2) 
   (make-from-real-imag (sub (real-part z1) (real-part z2)) 
                        (sub (imag-part z1) (imag-part z2)))) 
 (define (mul-complex z1 z2) 
   (make-from-mag-ang (mul (magnitude z1) (magnitude z2)) 
                      (add (angle z1) (angle z2)))) 
 (define (div-complex z1 z2) 
   (make-from-mag-ang (div (magnitude z1) (magnitude z2)) 
                      (sub (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))
;; èíòåðôåéñ ê îñòàëüíîé ñèñòåìå
(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 '=zero? '(complex) (lambda (x) (and (= (real-part x) 0) (= (imag-part x) 0))))
(put 'equ? '(complex complex)
(lambda (x y)  (and (= (real-part x) (real-part y)) (= (imag-part x) (imag-part y)))))
  (put 'project '(complex) 
      (lambda (x) (make-real (real-part x)))) 
'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))
 
;----------------corrections-------------------------
(define (scheme-number->complex n)
(make-complex-from-real-imag (contents n) 0))
 
(put-coercion 'scheme-number 'complex scheme-number->complex)
 
(define (scheme-number->rational n)
(make-rational (contents n) 1))
 
(put-coercion 'scheme-number 'rational scheme-number->rational)
 
;------------------------------------------------------
(install-polar-package)
(install-rectangular-package)
(install-scheme-number-package)
(install-rational-package)
(install-real-package)
(install-complex-package)
 
(sine (make-rational 4 1))
(add (make-complex-from-real-imag (make-rational 4 1) (make-rational 4 1))
   (make-complex-from-real-imag (make-rational 4 1) (make-rational 4 1))
   )
;(type-tag 1)


;results:
;(rational . -0.7568024953079282)
;(complex rectangular (rational 8 . 1) rational 8 . 1)