How to return the Church number

Question

I want to change decimal encoding number to chruch encoding number ?

(define (encode n)
  (lambda(fn)(lambda(x) (funPower (fn n)x))))

What's wrong with my code? Thank you.

Answer 1

Data struct and hardware decided church number is so so slower than binary number.

#lang racket
; church-number->n : procedure -> number
(define (church-number->n cn)
  ((cn (λ (x) (+ 1 x))) 0))

; n->church-number : number -> procedure 
(define (n->church-number n)
  (local [(define zero (λ (f) (λ (x) x)))
          (define add-1
            (lambda (n)
              (lambda (f)
                (lambda (x) (f ((n f) x))))))
          (define (aux n cn)
            (if (= 0 n)
                cn
                (aux (- n 1) (add-1 cn))))]
    (aux n zero)))


;;; TEST
(church-number->n (n->church-number 101)) ; 101
(church-number->n (n->church-number (church-number->n (n->church-number 666)))) ; 666

; still slow than binary number
(church-number->n
 (compose (n->church-number 100) (n->church-number 5))) ; 500

(define mult
  (lambda (m)
    (lambda (n)
      (lambda (f)
        (lambda (x)
          ((m (n f)) x))))))

(church-number->n ((mult (n->church-number 100)) (n->church-number 5))) ; 500