; This is the "Example" from R7RS-little

(define (integrate-system system-derivative
                          initial-state
                          h)
  (let ((next (runge-kutta-4 system-derivative h)))
    (letrec ((states
               (cons initial-state
                     (delay (map-streams next
                                         states)))))
      states)))

(define (runge-kutta-4 f h)
  (let ((*h (scale-vector h))
        (*2 (scale-vector 2))
        (*1/2 (scale-vector (/ 1 2)))
        (*1/6 (scale-vector (/ 1 6))))
    (lambda (y)
      ;; y is a system state
      (let* ((k0 (*h (f y)))
             (k1 (*h (f (add-vectors y (*1/2 k0)))))
             (k2 (*h (f (add-vectors y (*1/2 k1)))))
             (k3 (*h (f (add-vectors y k2)))))
        (add-vectors y
            (*1/6 (add-vectors k0
                               (*2 k1)
                               (*2 k2)
                               k3)))))))

(define (elementwise f)
  (lambda vectors
    (generate-vector
      (vector-length (car vectors))
      (lambda (i)
        (apply f
               (map (lambda (v) (vector-ref v i))
                    vectors))))))

(define (generate-vector size proc)
  (let ((ans (make-vector size)))
    (letrec ((loop
               (lambda (i)
                 (cond ((= i size) ans)
                       (else
                         (vector-set! ans i (proc i))
                         (loop (+ 1 i)))))))
      (loop 0))))

(define add-vectors (elementwise +))

(define (scale-vector s)
  (elementwise (lambda (x) (* x s))))

(define (map-streams f s)
  (cons (f (head s))
        (delay (map-streams f (tail s)))))

(define head car)
(define (tail stream)
  (force (cdr stream)))

; Ok, now the actual example

(define (damped-oscillator R L C)
  (lambda (state)
    (let ((Vc (vector-ref state 0))
          (Il (vector-ref state 1)))
      (vector (- 0 (+ (/ Vc (* R C)) (/ Il C)))
              (/ Vc L)))))

(define the-states
  (integrate-system
    (damped-oscillator 10000 1000 .001)
    '#(1 0)
    .01))

(display the-states)