; COSC 152
; Fall 2005
; Dennis Brylow
;
; Lecture 4 Demo
; Implementing a number system without numbers.

(define is-zero?
  (lambda (x) (null? x)))

(define succ
  (lambda (x) (cons '() x)))

(define pred
  (lambda (x)
    (if (is-zero? x)
        x
        (cdr x) )))

(define add
  (lambda (x y)
    (if (is-zero? x)
        y
        (add (pred x) (succ y))
    )))
; See The Little Schemer for more functions like
; subtraction, multiplication, division, exponentiation, etc.


; And now some functions to translate back and forth between
;  the native Scheme representation of numbers and my new
;  list-based representation of numbers.
(define translate
  (lambda (x)
    (if (zero? x) 
        '()
        (cons '() (translate (- x 1))))))

(define untranslate
  (lambda (x)
    (if (is-zero? x)
        0
        (+ 1 (untranslate (cdr x))))))