Haskell Curry's Y Combinator

ycombinator.clj

;; https://en.wikipedia.org/wiki/Fixed-point_combinator#Fixed-point_combinators_in_lambda_calculus

(defn ycombinator [f]
  ((fn [x]
     (x x))
   (fn [x]
     (f (fn [y]
          ((x x) y))))))

(defn factorial [f]
  (fn [n]
    (if (zero? n)
      1
      (* n (f (dec n))))))

((ycombinator factorial) 5) ;; => 120

(defn fib [f]
  (fn [n]
    (cond (zero? n) 0
          (= 1 n)   1
          :else     (+ (f (dec n)) (f (- n 2))))))

((ycombinator fib) 20) ;; => 6765