A busy beaver in Scheme macros

beaver.scm

(define-syntax beaver
  (syntax-rules [a b c d quote]
    [(beaver lefts 0 rights 'a)
     (right  lefts 1 rights 'b)]
    [(beaver lefts 0 rights 'b)
     (left   lefts 1 rights 'a)]
    [(beaver '(lefts ...) 0 '(rights ...) 'c)
     '(lefts ... 1 rights ...)]
    [(beaver lefts 0 rights 'd)
     (right  lefts 1 rights 'd)]

    [(beaver lefts 1 rights 'a)
     (left   lefts 1 rights 'b)]
    [(beaver lefts 1 rights 'b)
     (left   lefts 0 rights 'c)]
    [(beaver lefts 1 rights 'c)
     (left   lefts 1 rights 'd)]
    [(beaver lefts 1 rights 'd)
     (right  lefts 0 rights 'a)]))

(define-syntax left
  (syntax-rules [quote]
    [(left   '(l lefts ...) new '(rights ...) next)
     (beaver '(lefts ...) l '(new rights ...) next)]
    [(left   '() new '(rights ...) next)
     (beaver '() 0 '(new rights ...) next)]))

(define-syntax right
  (syntax-rules [quote]
    [(right  '(lefts ...) new '(r rights ...) next)
     (beaver '(new lefts ...) r '(rights ...) next)]
    [(right  '(lefts ...) new '() next)
     (beaver '(new lefts ...) 0 '() next)]))