; We can define:


(define (y* f)
  ((lambda (g) (f (lambda () (g g))))
   (lambda (g) (f (lambda () (g g))))))

; This y operator must be used slightly differently, however.
; The kernel f must be called in place to extract the function
; because this y operator was derived by a call-by-name
; transformation from the original one -- see ! lines below.

(define (++ x y)
  ((y* (lambda (f)
	 (lambda (x y)
	   (if (zero? x)
	       y
	       ((f) (-1+ x) (1+ y))))))
   x
   y))

(define (fib* k)
  ((y* (lambda (f)
	 (lambda (n)
	   (cond ((zero? n) 1)
		 ((zero? (-1+ n)) 1)
		 (else
		  (++ ((f) (-1+ n))
		      ((f) (-1+ (-1+ n)))))))))
   k))

(define (app l1 l2)
  ((y* (lambda (f)
	 (lambda (l1 l2)
	   (cond ((eq? () l1) l2)
		 (else
		  (cons (car l1)
			((f) (cdr l1) l2)))))))	;!
   l1
   l2))