Scheme: Understanding Continuation-Passing-Style the Easiest Way, with the example of Fibonacci

; Fibonacci 

(define (fibo i)
  (if (= i 0)
      1
      (* i (fibo (- i 1)))))

; Rewrite in if-then-else form

(define (ite i cond kSucc kFail)
  (if (cond i)
      (kSucc i)
      (kFail i)))

(define (fiboIte i)
  (ite
   i
   (lambda (i) (= i 0))
   (lambda (x) 1)
   (lambda (i) (* i (fiboIte (- i 1))))))

; Continuation-Passing-Style

(define (cont i) (lambda (k) (k i)))

(define (iteCont iCont kCond kSucc kFail)
  (if (iCont kCond)
      (iCont kSucc)
      (iCont kFail)))

(define (fiboCont i)
  (iteCont
   (cont i)
   (lambda (i) (= i 0))
   (lambda (x) 1)
   (lambda (i) (* i (fiboIte (- i 1))))))