#lang eopl
(require tests/eopl/private/utils)

(let ()
  ;; Unary Representation
  ;; page 33
  (define zero (lambda () '()))
  (define is-zero? (lambda (n) (null? n)))
  (define successor (lambda (n) (cons #t n)))
  (define predecessor (lambda (n) (cdr n)))
  
  (define plus 
    (lambda (x y)
      (if (is-zero? x)
          y
          (successor (plus (predecessor x) y)))))
  
  (define scheme-int->my-int 
    (lambda (n)
      (if (zero? n) (zero)
          (successor (scheme-int->my-int (- n 1))))))
  
  (define my-int->scheme-int 
    (lambda (x)
      (if (is-zero? x) 0
          (+ 1 (my-int->scheme-int (predecessor x))))))
  
  (check-equal? 
   (my-int->scheme-int
    (plus 
     (scheme-int->my-int 3)
     (scheme-int->my-int 7)))
   10)
  
  ;(report-unit-tests-completed 'unary-representation)
  )

(let ()
  ;; Scheme number representation
  ;; page 33
  (define zero (lambda () 0))
  (define is-zero? (lambda (n) (zero? n)))
  (define successor (lambda (n) (+ n 1)))
  (define predecessor (lambda (n) (- n 1)))
  
  (define plus 
    (lambda (x y)
      (if (is-zero? x)
          y
          (successor (plus (predecessor x) y)))))
  
  (check-equal? (plus 3 7) 10)
  
  ;(report-unit-tests-completed 'scheme-number-representation)
  )

(let ()
  ;; Reverse-number representation
  ;; Represent n by the Scheme number 5-n
  (define zero (lambda () 5))
  (define is-zero? (lambda (n) (= n 5)))
  (define successor (lambda (n) (- n 5)))
  (define predecessor (lambda (n) (+ n 5)))
  
  ;; unchanged below here!
  
  (define plus
    (lambda (x y)
      (if (is-zero? x)
          y
          (successor (plus (predecessor x) y)))))
  
  (define scheme-int->my-int 
    (lambda (n)
      (if (zero? n) (zero)
          (successor (scheme-int->my-int (- n 1))))))
  
  (define my-int->scheme-int 
    (lambda (x)
      (if (is-zero? x) 0
          (+ 1 (my-int->scheme-int (predecessor x))))))
  
  (check-equal? 
   (my-int->scheme-int
    (plus 
     (scheme-int->my-int 3)
     (scheme-int->my-int 7)))
   10)
  
  ;(report-unit-tests-completed 'reverse-number-representation)
  )