Using Racket to implement operators in the lambda calculus for Church number.

church_number.rkt

#lang racket

(define zero
  (lambda (f)
    (lambda (x) x)))

(define (add-1 n)
  (lambda (f)
    (lambda(x) (f ((n f) x)))))

(define one
  (lambda (f)
    (lambda (x) (f x))))

(define two
  (lambda (f)
    (lambda (x) (f (f x)))))


(define three
  (lambda (f)
    (lambda (x) (f (f (f x))))))

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

(define (display-church-number n)
  (display "λfλx.")
  (display ((n (lambda (x) (cons "f" x))) "x"))
  (newline))

(display-church-number zero)

(display-church-number one)
(display-church-number (add-1 zero))

(display-church-number two)
(display-church-number (add-1 one))

(display-church-number three)
(display-church-number (add-1 two))