ycombinator.scm

;; Derivation of the Y combinator following Jim Weirich's approach.

(define fact-improver
  (lambda (partial)
    (lambda (n) (if (= n 0) 1 (* n (partial (- n 1)))))))

(define err
  (lambda () (error "Should not be called")))

(define fx-naive
  (fact-improver (fact-improver (fact-improver (fact-improver err)))))

(display (fx-naive 3))
(newline)


(define Y
  (lambda (f)
    ((lambda (x)
       (x x))
     (lambda (x)
       (f
	(lambda (n) ((x x) n)))))))

(define f (lambda (code)
	    (lambda (n) (if (= n 0) 1 (* n (code (- n 1)))))))
(define fx (Y f))

(display (fx 15))
(newline)