이 문제는 i≤j의 조건 없이 모든 정수(i, j)의 스트림을 만들도록

pair 프로시저를 수정하는 문제입니다.

잘 되는군요.^^

위와 같은 스트림을 만드는 것입니다.

따라서 기존에 행렬을 만들 때 행과 열을 동시에 옮겼기에

이번에는 행만을 움직이도록 하였습니다.

여기서 행은 S가 되고 열은 T가 되기에 (stream-cdr t)에서 t로 바꾸었습니다.

참조

해럴드 애빌슨, 김재우 역, <컴퓨터 프로그램의 구조와 해석>, 인사이트, 2007, pp. 445

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

(define (cons-stream a b)
  (cons a (delay b)))
(define the-empty-stream '())
(define stream-null? null?)
(define (stream-car stream) (car stream))
(define (stream-cdr stream) (force (cdr stream)))

; section 3.5
(define (stream-ref s n)
  (if (= n 0)
      (stream-car s)
      (stream-ref (stream-cdr s) (- n 1))))

(define (stream-for-each proc s)
  (if (stream-null? s)
      'done
      (begin (proc (stream-car s))
             (stream-for-each proc (stream-cdr s)))))

(define (display-stream s)
  (stream-for-each display-line s))

(define (display-line x)
  (newline)
  (display x))

(define (stream-enumerate-interval low high)
  (if (> low high)
      the-empty-stream
      (cons-stream
       low
       (stream-enumerate-interval (+ low 1) high))))

(define (stream-filter pred stream)
  (cond ((stream-null? stream) the-empty-stream)
        ((pred (stream-car stream))
         (cons-stream (stream-car stream)
                      (stream-filter pred
                                     (stream-cdr stream))))
        (else (stream-filter pred (stream-cdr stream)))))

(define (memo-proc proc)
  (let ((already-run? false) (result false))
    (lambda ()
      (if (not already-run?)
          (begin (set! result (proc))
                 (set! already-run? true)
                 result)
          result))))

(define (scale-stream stream factor)
  (stream-map (lambda (x) (* x factor)) stream))

; exercise 3.50
(define (stream-map proc . argstreams)
  (if (stream-null? (car argstreams))
      the-empty-stream
      (cons-stream
       (apply proc (map stream-car argstreams))
       (apply stream-map
              (cons proc (map stream-cdr argstreams))))))

;;;SECTION 3.5.2
(define (add-streams s1 s2)
  (stream-map + s1 s2))

(define ones (cons-stream 1 ones))
(define integers (cons-stream 1 (add-streams ones integers)))

; exercise 3.54
(define (mul-streams s1 s2)
  (stream-map * s1 s2))

; exercise 3.55
(define (partial-sums S)
  (cons-stream (stream-car S) (add-streams (stream-cdr S)
                                           (partial-sums S))))

; exercise 3.56
(define (merge s1 s2)
  (cond ((stream-null? s1) s2)
        ((stream-null? s2) s1)
        (else
         (let ((s1car (stream-car s1))
               (s2car (stream-car s2)))
           (cond ((< s1car s2car)
                  (cons-stream s1car (merge (stream-cdr s1) s2)))
                 ((> s1car s2car)
                  (cons-stream s2car (merge s1 (stream-cdr s2))))
                 (else
                  (cons-stream s1car
                               (merge (stream-cdr s1)
                                      (stream-cdr s2)))))))))

; print-stream-n
(define (print-stream-n S n)
  (define (iter i)
    (if (= i n)
        'done
        (begin (display (stream-ref S i))
               (display "   ")
               (if (= (remainder (+ i 1) 5) 0)
                   (newline))
               (iter (+ i 1)))))
  (iter 0))

; exercise 3.59
(define (div-streams s1 s2)
  (stream-map / s1 s2))

(define (integrate-series coff_stm)
  (let ((integrate_s (cons-stream 1 ; 상수 c
                                  (div-streams coff_stm integers))))
    (stream-cdr integrate_s)))

(define exp-series
  (cons-stream 1 (integrate-series exp-series)))
(define cosine-series
  (cons-stream 1
               (integrate-series (scale-stream sine-series -1))))
(define sine-series
  (cons-stream 0
               (integrate-series cosine-series)))

; exercise 3.60
(define (mul-series s1 s2)
  (cons-stream (* (stream-car s1) (stream-car s2))
               (add-streams (mul-series (stream-cdr s1) s2)
                            (scale-stream (stream-cdr s2) (stream-car s1)))))
; exercise 3.61
(define (invert-unit-series S)
  (define X
    (cons-stream 1
                 (scale-stream (mul-series (stream-cdr S) X) -1)))
  X)

; exercise 3.62
; s1 / s2
(define (div-series s1 s2)
  (if (= 0 (stream-car s2))
      (error "Divide by zero" s2)
      (mul-series s1 (invert-unit-series s2))))

; exercise 3.63
(define (sqrt-improve guess x)
  (average guess (/ x guess)))

(define (average x y)
  (/ (+ x y) 2))

(define (sqrt-stream x)
  (define guesses
    (cons-stream 1.0
                 (stream-map (lambda (guess)
                               (sqrt-improve guess x))
                             guesses)))
  guesses)

; exercise 3.64
(define (stream-limit stm tolerance)
  (let ((element1 (stream-car stm)) ; 앞의 원소
        (element2 (stream-car (stream-cdr stm)))) ; 뒤의 원소
    (if (< (abs (- element1 element2)) tolerance)
        element2
        (stream-limit (stream-cdr stm) tolerance))))
(define (sqrt x tolerance)
  (stream-limit (sqrt-stream x) tolerance))

; exercise 3.65
(define ln2-stream
  (partial-sums (ln2-summands 1)))
(define (ln2-summands n)
  (cons-stream (/ 1.0 n)
               (stream-map - (ln2-summands (+ n 1)))))

(define (euler-transform s)
  (let ((s0 (stream-ref s 0))           ; Sn-1
        (s1 (stream-ref s 1))           ; Sn
        (s2 (stream-ref s 2)))          ; Sn+1
    (cons-stream (- s2 (/ (square (- s2 s1))
                          (+ s0 (* -2 s1) s2)))
                 (euler-transform (stream-cdr s)))))

(define (make-tableau transform s)
  (cons-stream s
               (make-tableau transform
                             (transform s))))

(define (accelerated-sequence transform s)
  (stream-map stream-car
              (make-tableau transform s)))

(define (square x) (* x x))

; section 3.5.3
(define (interleave s1 s2)
  (if (stream-null? s1)
      s2
      (cons-stream (stream-car s1)
                   (interleave s2 (stream-cdr s1)))))

; exercise 3.66
(define a (pairs integers integers))

; exercise 3.67
(define (pairs s t)
  (cons-stream
   (list (stream-car s) (stream-car t))
   (interleave
    (stream-map (lambda (x) (list (stream-car s) x))
                (stream-cdr t))
    (pairs (stream-cdr s) t))))

; execute
(define a (pairs integers integers))
(print-stream-n a 100)

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