#lang racket

(require "stream-base.rkt")

; stream examples

; some operations on streams

; add two streams together, pairwise
(define (add-streams s1 s2)
  (s-map + s1 s2))

; apply an operation (op v e) to each element e of the stream
(define (op-on-stream op v s)
  (s-map (lambda (e) (op v e)) s) )

; infinite streams

; a function that recursively generates an stream of integers starting
; at n
(define (integers-starting-from n)
  (s-cons n (integers-starting-from (+ n 1))))

; the natural numbers
(define naturals (integers-starting-from 0))

; true if a divides b evenly
(define (divides? a b) (= (remainder b a) 0))

; true if x is evenly divisible by y
(define (divisible? x y) (= (remainder x y) 0))

; the stream consisting of any natural number not divisible by 7
(define no-sevens
  (s-filter (lambda (x) (not (divisible? x 7))) naturals))

; generate the fibonacci stream with initial terms a, b
; note the recursive generator function 
(define (fibgen a b) (s-cons a (fibgen b (+ a b))))

; the usual fibonacci stream
(define fibs (fibgen 0 1))