y-combinator.clj

;; Step 1
(defn fact1 [n]
    (if (< n 2) 1 (* n (fact1 (- n 1)))))

(println (fact1 5))


;; Step 2
(def fact2
    ((fn [f]
         (fn [n]
             (if (< n 2) 1
                 (* n ((f f) (- n 1))))))
     (fn [f]
         (fn [n]
             (if (< n 2) 1
                 (* n ((f f) (- n 1))))))))

(println (fact2 5))


;; Step 3
(defn omega [f] (f f))

(def fact3
    (omega (fn [f]
                (fn [n] (if (< n 2) 1
                        (* n ((f f) (- n 1))))))))

(println (fact3 5))


;; Step 4
(def fact4
    (omega (fn [f]
                (let [g (fn [n] ((f f) n))]
                    (fn [n] (if (< n 2) 1
                            (* n (g (- n 1)))))))))

(println (fact4 5))


;; Step 5
(defn wrap
    [h]
    (omega (fn [f]
                (let [g (fn [n] ((f f) n))]
                     (h g)))))

(def fact5
    (wrap
        (fn [g]
            (fn [n]
                (if (< n 2) 1 (* n (g (- n 1))))))))

(println (fact5 5))


;; Step 6
(defn wrap6 [h] (omega (fn [f] (h (fn [n] ((f f) n))))))

(def fact6
    (wrap6
        (fn [g]
            (fn [n]
                (if (< n 2) 1 (* n (g (- n 1))))))))

(println (fact6 5))


;; Step 7
(defn Y [h]
    ((fn [f] (f f)) 
     (fn [f] (h (fn [n] ((f f) n))))))

(def fact7
    (Y (fn [g] (fn [n] (if (< n 2) 1
                           (* n (g (- n 1))))))))

(println (fact7 5))