;; The first three lines of this file were inserted by DrRacket. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-beginner-reader.ss" "lang")((modname lect21-natnum) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ())))

; func-for-natnum : natNum -> ???
(define (func-for-natnum n)
  (cond [(zero? n)      (...)]
        [(positive? n)  (...(func-for-natnum (sub1 n)))]))


; countdown : natNum -> string
(define (countdown n)
  (cond [(zero? n)      "liftoff!"]
        [(positive? n)  (string-append (number->string n)
                                       ", "
                                       (countdown (sub1 n)))]))


(check-expect (countdown 0) "liftoff!")
(check-expect (countdown 1) "1, liftoff!")
(check-expect (countdown 3) "3, 2, 1, liftoff!")
(check-expect (countdown 4) "4, 3, 2, 1, liftoff!")

(check-expect (nums-down-from 0)
              (cons 0 empty))

(check-expect (nums-down-from 3)
              (cons 3 (cons 2 (cons 1 (cons 0 empty)))))

(check-expect (nums-down-from 4)
              (cons 4 (cons 3 (cons 2 (cons 1 (cons 0 empty))))))

; nums-down-from : natNum -> cons
;
(define (nums-down-from n)
  (cond [(zero? n)      (cons 0 empty)]
        [(positive? n)  (cons n (nums-down-from (sub1 n)))]))


(define (k-nums-up-to k n)
  (cond [(zero? k)      (cons n empty)]
        [(positive? n)  (cons (- n k) (k-nums-up-to (sub1 k) n))]))

(define (nums-up-to n) (k-nums-up-to n n))

#;(define (nums-up-to n)
  (cond [(zero? n)      (cons 0 empty)]
        [(positive? n)  (snoc n (nums-down-from (sub1 n)))]))

(check-expect (nums-up-to 4)
              (cons 0 (cons 1 (cons 2 (cons 3 (cons 4 empty))))))
(check-expect (nums-up-to 3)
              (cons 0 (cons 1 (cons 2 (cons 3 empty)))))
(check-expect (nums-up-to 0)
              (cons 0 empty))





(define (sum-up-to n)
  (cond [(zero? n)      0]
        [(positive? n)  (+ n (sum-up-to (sub1 n)))]))




; sum-up-to : natNum -> number
; Return 0+1+2+3+...+n.
;
(check-expect (sum-up-to 0) 0)
(check-expect (sum-up-to 1) 1)
(check-expect (sum-up-to 2) 3)
(check-expect (sum-up-to 3) 6)
(check-expect (sum-up-to 4) 10)