이 문제는 제곱을 하는 식을 만드는 문제입니다.

Louis Reasoner는 기존의 multiplier를 이용하여 이를 구현하려고 합니다.

하지만 이 프로시저는 문제가 있다고 합니다.

처음에는 문제점을 찾지 못했습니다.

그래서 직접 돌려보았습니다.

문제점 발견하였습니다.

문제점은 제곱근을 구하지 못합니다.

B에 16을 넣었을 때 A로 4가 나와야함에도 그렇게 동작하지 않습니다.

왜 이런가 살펴보니 multiplier의 한계였습니다.

여기서 m1과 m2를 구할 때 product와 m2 혹은 m1의 값이 필요합니다.

하지만, squarer를 구할 때 (multiplier a a b)를 사용하기에

a를 지우고 b에만 값을 설정하고 a를 구하려고 하면 m1, m2 모두 지워집니다.

따라서 이것으로는 구할 수 없습니다.

참조

해럴드 애빌슨, 김재우 역, <컴퓨터 프로그램의 구조와 해석>, 인사이트, 2007, pp. 382

(define true (= 0 0))
(define false (= 0 1))

;;;SECTION 3.3.5
(define (adder a1 a2 sum)
  (define (process-new-value)
    (cond ((and (has-value? a1) (has-value? a2))
           (set-value! sum
                       (+ (get-value a1) (get-value a2))
                       me))
          ((and (has-value? a1) (has-value? sum))
           (set-value! a2
                       (- (get-value sum) (get-value a1))
                       me))
          ((and (has-value? a2) (has-value? sum))
           (set-value! a1
                       (- (get-value sum) (get-value a2))
                       me))))
  (define (process-forget-value)
    (forget-value! sum me)
    (forget-value! a1 me)
    (forget-value! a2 me)
    (process-new-value))
  (define (me request)
    (cond ((eq? request 'I-have-a-value) 
           (process-new-value))
          ((eq? request 'I-lost-my-value)
           (process-forget-value))
          (else
           (error "Unknown request -- ADDER" request))))
  (connect a1 me)
  (connect a2 me)
  (connect sum me)
  me)

(define (inform-about-value constraint)
  (constraint 'I-have-a-value))

(define (inform-about-no-value constraint)
  (constraint 'I-lost-my-value))

(define (multiplier m1 m2 product)
  (define (process-new-value)
    (cond ((or (and (has-value? m1) (= (get-value m1) 0))
               (and (has-value? m2) (= (get-value m2) 0)))
           (set-value! product 0 me))
          ((and (has-value? m1) (has-value? m2))
           (set-value! product
                       (* (get-value m1) (get-value m2))
                       me))
          ((and (has-value? product) (has-value? m1))
           (set-value! m2
                       (/ (get-value product) (get-value m1))
                       me))
          ((and (has-value? product) (has-value? m2))
           (set-value! m1
                       (/ (get-value product) (get-value m2))
                       me))))
  (define (process-forget-value)
    (forget-value! product me)
    (forget-value! m1 me)
    (forget-value! m2 me)
    (process-new-value))
  (define (me request)
    (cond ((eq? request 'I-have-a-value)
           (process-new-value))
          ((eq? request 'I-lost-my-value)
           (process-forget-value))
          (else
           (error "Unknown request -- MULTIPLIER" request))))
  (connect m1 me)
  (connect m2 me)
  (connect product me)
  me)

(define (constant value connector)
  (define (me request)
    (error "Unknown request -- CONSTANT" request))
  (connect connector me)
  (set-value! connector value me)
  me)

(define (probe name connector)
  (define (print-probe value)
    (newline)
    (display "Probe: ")
    (display name)
    (display " = ")
    (display value))
  (define (process-new-value)
    (print-probe (get-value connector)))
  (define (process-forget-value)
    (print-probe "?"))
  (define (me request)
    (cond ((eq? request 'I-have-a-value)
           (process-new-value))
          ((eq? request 'I-lost-my-value)
           (process-forget-value))
          (else
           (error "Unknown request -- PROBE" request))))
  (connect connector me)
  me)

(define (make-connector)
  (let ((value false) (informant false) (constraints '()))
    (define (set-my-value newval setter)
      (cond ((not (has-value? me))
             (set! value newval)
             (set! informant setter)
             (for-each-except setter
                              inform-about-value
                              constraints))
            ((not (= value newval))
             (error "Contradiction" (list value newval)))
            (else 'ignored)))
    (define (forget-my-value retractor)
      (if (eq? retractor informant)
          (begin (set! informant false)
                 (for-each-except retractor
                                  inform-about-no-value
                                  constraints))
          'ignored))
    (define (connect new-constraint)
      (if (not (memq new-constraint constraints))
          (set! constraints
                (cons new-constraint constraints)))
      (if (has-value? me)
          (inform-about-value new-constraint))
      'done)
    (define (me request)
      (cond ((eq? request 'has-value?)
             (if informant true false))
            ((eq? request 'value) value)
            ((eq? request 'set-value!) set-my-value)
            ((eq? request 'forget) forget-my-value)
            ((eq? request 'connect) connect)
            (else (error "Unknown operation -- CONNECTOR"
                         request))))
    me))

(define (for-each-except exception procedure list)
  (define (loop items)
    (cond ((null? items) 'done)
          ((eq? (car items) exception) (loop (cdr items)))
          (else (procedure (car items))
                (loop (cdr items)))))
  (loop list))

(define (has-value? connector)
  (connector 'has-value?))

(define (get-value connector)
  (connector 'value))

(define (set-value! connector new-value informant)
  ((connector 'set-value!) new-value informant))

(define (forget-value! connector retractor)
  ((connector 'forget) retractor))

(define (connect connector new-constraint)
  ((connector 'connect) new-constraint))

; exercise 3.34
(define (squarer a b)
  (multiplier a a b))

; execute
(define A (make-connector))
(define B (make-connector))

(probe "Input A" A)
(probe "Output B" B)

(squarer A B)

(set-value! A 5 'user)
(forget-value! A 'user)
(set-value! B 16 'user)

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