;; starting code for Homework 18 exercises
;;
;; this code is written in Ruse
;;
;;-----------------------------------------------------------------
;; we wrote this code in class

;; returns the nth element of stream s
(def nth
  (fun (n s) :
    (if (n == 0)
        then (zcar s)
        else (nth (n - 1) (zcdr s)))))

;; builds an ordinary list of the first n elements of stream s
(def get-first
  (fun (n s) :
    (if (n == 0)
        then nil
	;; must use cons here to build an ordinary list
        else (cons (zcar s) (get-first (n - 1) (zcdr s))))))

;; prints the first n elements of stream s, one element per line
(def print-first
  (fun (n s) :
    (if (n == 0)
        then (print "...")
        else (do (print (zcar s))
		 (print-first (n - 1) (zcdr s))))))

;; creates a stream of constant values of n
(def constant-stream
  (fun (n) :
    (zcons n (constant-stream n))))

;; creates a stream of ascending numbers beginning with n
(def ascending-stream
  (fun (n) :
    (zcons n (ascending-stream (n + 1)))))

;; applies a one-argument function f to all elements of stream s
(def zmap
  (fun (f s) :
    (zcons (f (zcar s)) (zmap f (zcdr s)))))

(def add1 (fun (n) : (n + 1)))

;; the stream of natural numbers: (0 1 2 3 4 5 ...)
(def nats (zcons 0 (zmap add1 nats)))

;; combines corresponding elements of two streams using addition
(def add-streams
  (fun (s1 s2) :
    (zcons ((zcar s1) + (zcar s2))
           (add-streams (zcdr s1) (zcdr s2)))))

;; combines corresponding elements of two streams using multiplication
(def multiply-streams
  (fun (s1 s2) :
    (zcons ((zcar s1) * (zcar s2))
           (multiply-streams (zcdr s1) (zcdr s2)))))

;;-----------------------------------------------------------------
;; your new Ruse code goes here