;; ----------------------------------------------------------------
;; Two ways to implement the non-negative integers in Racket.
;; Uncomment the definitions to try an implementation.
;; ----------------------------------------------------------------

#lang racket
(provide zero        ; a primitive value
         is-zero?    ; a predicate that recognizes zero
         next        ; a function that gives the next number
         previous)   ; a function that gives the previous number

;; ----------------------------------------------------------------
;; ... as Racket numbers.
;; ----------------------------------------------------------------

(define zero     0)
(define is-zero? zero?)
(define next     add1)
(define previous sub1)     ; problem at zero

;; ----------------------------------------------------------------
;; ... as Racket lists.  The list's length represents the number.
;; ----------------------------------------------------------------

;; (define zero     '())
;; (define is-zero? null?)
;; (define next     (lambda (n) (cons 1 n)))
;; (define previous rest)    ; problem at zero

;; ----------------------------------------------------------------
;; Using the non-negative integers, regardless of implementation.
;; ----------------------------------------------------------------

;; zero
;; (is-zero? zero)
;; (is-zero? (next zero))
;; (next (next (next zero)))

(require rackunit)
(check-equal? (next (next (previous (next (next zero)))))
              (next (next (next zero))))

; ----------------------------------------------------------------