The Y combinator for applicative-order evaluation and its CPS-transformed version

gistfile1.scm

(define Y
  (lambda (f)
    (let [(A (lambda (x) (f (lambda (y) ((x x) y)))))]
      (A A))))

(define (factF self)
  (lambda (n)
    (if (= n 0)
      1
      (* n (self (- n 1))))))

(define fact (Y factF))

(display (fact 5)) (newline)

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(define (Y-cps f k-f)
  (let [(A (lambda (x k-x)
              (f (lambda (y k-y) (x x (lambda (v-xx) (v-xx y k-y)))) k-x)))]
    (A A k-f)))

(define (factF-cps self k)
  (k (lambda (n k-n)
      (if (= n 0)
        (k-n 1)
        (self (- n 1) (lambda (res) (k-n (* n res))))))))

(define (fact-cps k) (Y-cps factF-cps k))

(fact-cps (lambda (f) (f 5 display))) (newline)