peano in scheme

peano.scm

; O is a natural number.
(define zero 'zero)

; For every number n, (succ n) is a natural number.
(define (succ n)
    (lambda () n))

; A few numbers
(define one
  (succ zero))
(define two
  (succ one))
(define three
  (succ two))
(define four
  (succ three))

; Equality
(define (are-equal? a b)
  (cond ((and (eq? a zero)
             (eq? b zero)) #t)
        ((or (eq? a zero)
             (eq? b zero)) #f)
        (else (are-equal? (a) (b)))))

; Addition
(define (add a b) 
  (define (add-recur a b)
      (succ (add a (b))))
    (if (eq? b zero) a
        (add-recur a b)))