church.rkt

#lang scheme

;; church encoded zero
(define c-zero
  (lambda (f x) x))

;; church encoded one
(define (add-1 cn)
  (lambda (f x) (f (cn f x))))

;; addition of chruch numerals
(define (c-add cn cm)
  (lambda (f x) (cn f (cm f x))))

;; mulitplication of church numerals
(define (c-mult cn cm)
  (lambda (f x) (cn (lambda (x) (cm f x)) x)))

;; exponential of chrurch numerals
(define (c-exp cn cm)
  (lambda (f x) (error "to do"))

;; convert from church numeral to literal
(define (to-Nat cn)
  (cn add1 0))