Church numbers and pairs in Clojure (WIP)

church.clj

; This uses only fn and def in Clojure to create non-negative integers and pairs.
; (This restricts the language to only using lambda calculus.)



; Church numerals

(defn succ [n]
  (fn [f]
    (fn [x]
      (f ((n f) x)))))

(def zero
  (fn [f]
    (fn [x] x)))

(def one (succ zero))

(defn plus [a b]
  (fn [f]
    (fn [x]
      ((a f) ((b f) x)))))

; Church pairs

(defn cns [x y]
  (fn [m]
    (m x y)))

(defn car [c]
  (c (fn [x y] x)))

(defn cdr [c]
  (c (fn [x y] y)))

; Display functions
; N.B. - These "cheat" a little so we can see what we're working with

(defn display-church-num [f]
  (when (not (nil? f))
    (println ((f inc) 0))))


(defn display-church-list [lst]
  (loop [lst lst]
    (when (not (nil? lst))
      (display-church-num (car lst))
      (recur (cdr lst)))))

; testing
(display-church-list (cns one (cns zero (cns (succ one) nil))))