#lang sicp

(define (stream-car stream) 
  (car stream))
(define (stream-cdr stream) 
  (force (cdr stream)))
(define (display-stream-first-n s n)
  (if (and (not (stream-null? s)) (> n 0))
    (begin 
      (display-line (stream-car s))
      (display-stream-first-n (stream-cdr s) (- n 1)))))
(define (display-line x)
  (newline)
  (display x))

(define (integers-starting-from n)
  (cons-stream 
   n (integers-starting-from (+ n 1))))
(define integers (integers-starting-from 1))
(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))))))

(define (negate-series S) (stream-map - S))

(define (add-streams s1 s2)
  (stream-map + s1 s2))
(define (mul-streams s1 s2)
  (stream-map * s1 s2))
(define (scale-stream S m) 
  (stream-map (lambda (x) (* x m)) S))
(define (mul-series s1 s2)
  (add-streams 
    (scale-stream s2 (stream-car s1))
    (cons-stream 0 (mul-series (stream-cdr s1) s2))))

(define (invert-unit-series S)
  (if (not (= 1 (stream-car S)))
    (error "In invert-unit-series first element is not 1!")
    (let ((SR (stream-cdr S)))
      (define X 
        (cons-stream 1 (negate-series (mul-series SR X))))
      X)))

; 1+ x + x^2 + x^3 + ... == {1, 1, 1, 1, ...}
; == 1/(1-x), so inverting this should give us {1, -1, 0, 0, ...}

(define ones 
  (cons-stream 1 ones))

(display-line "1/(1-x)")
(display-stream-first-n ones 8)

(display-line "(invert-unit-series 1/(1-x))")
(display-stream-first-n (invert-unit-series ones) 8)


;; (define (integrate-series S)
;;   (stream-map / S integers))
;; 
;; (define exp-series
;;   (cons-stream
;;    1 (integrate-series exp-series)))
;; (define cosine-series
;;   (cons-stream 1 (integrate-series (negate-series sine-series))))
;; (define sine-series
;;   (cons-stream 0 (integrate-series cosine-series)))
;; (define sum-squared-stream
;;   (add-streams (mul-series sine-series sine-series)
;;                (mul-series cosine-series cosine-series)))
;; 
;; (display-line "cos^2+sin^2 series:")
;; (display-stream-first-n sum-squared-stream 8)
;;