Ycombinator2

Ycombinator2.rkt

#lang racket


;(Y f) = fixpoint-of-f
;(f fixpoint-of-f) = fixpoint-of-f
;(Y f) = fixpoint-of-f = (f fixpoint-of-f)
;(Y f) = (f (Y f))
(define (Y f) (f (Y f)))

(define Y-lambda
  (lambda (f)
    (f (Y-lambda f))))

;; reverse use lambda to add a arg
(define Y-Strict
  (lambda (f)
    (f (lambda (x) ((Y-Strict f) x)))))

(define almost-factorial-half
  (lambda (f)
    (lambda (n)
      (if (= n 0)
          1
          (* n (f (- n 1)))))))
; why this can't work

(define identity (lambda (x) x))
(define factorial0 (almost-factorial-half identity))
(define factorial1
    (almost-factorial-half factorial0))

(define factorial2 (almost-factorial-half factorial1))
(define factorial3 (almost-factorial-half factorial2))

(define factorial-strict (Y-Strict almost-factorial-half))