;; Data definition
;;
;; A NLON (short for Nested-List-of-Numbers) is one of
;;  - empty
;;  - (cons Number NLON)
;;  - (cons NLON NLON)

;; NLON examples
empty
(cons 4 (cons 5 empty))
(cons (cons 1 (cons 2 (cons 3 empty))) (cons 4 (cons 5 empty)))

#|
Note that these can be written more concisely using the list function.
Here are the same 3 examples written that way:
empty
(list 4 5)
(list (list 1 2 3) 4 5)
|#

#| Template for a function consuming an NLON
;; f : NLON -> ???
(define (f a-nlon)
  (cond
    [(empty? a-nlon) ... ]
    [(number? (first a-nlon)) ... (first a-nlon) ...
                              ... (f (rest a-nlon)) ... ]
    [(cons? (first a-nlon)) ... (f (first a-nlon)) ...
                            ... (f (rest a-nlon)) ... ]))
|#

;; add-all : NLON -> Number
;; adds up all numbers appearing in the given NLON
(define (add-all a-nlon)
  (cond
    [(empty? a-nlon) 0]
    [(number? (first a-nlon)) (+ (first a-nlon) (add-all (rest a-nlon)))]
    [(cons? (first a-nlon)) (+ (add-all (first a-nlon))
                               (add-all (rest a-nlon)))]))

;; Examples/tests of add-all
(= (add-all (list 4 5)) 9)
(= (add-all (list (list 1 2 3) 4 5)) 15)

;; flatten : NLON -> LON
;; creates a single list containing all the numbers in the NLON
(define (flatten a-nlon)
  (cond
    [(empty? a-nlon) empty]
    [(number? (first a-nlon)) (cons (first a-nlon) (flatten (rest a-nlon)))]
    [(cons? (first a-nlon)) (append (flatten (first a-nlon))
                                    (flatten (rest a-nlon)))]))

;; Examples/tests of flatten
(equal?
 (flatten (list 4 5))
 (list 4 5))

(equal?
 (flatten (list (list 1 2 3) 4 5))
 (list 1 2 3 4 5))