Y Combinator (http://blog.tomtung.com/2012/10/yet-another-y-combinator-tutorial/)

combinators.groovy

def Y = { f ->
  { x -> x(x) } { x -> f { y -> x(x)(y) } }
}

def triangular = Y { f ->
  { n -> n == 0 ? 0 : n + f(n - 1) }
}

triangular(3000)

combinators.rkt

(define U
  (λ (f) (f f)))

(define Θ
  ((λ (f) (f f))
   (λ (g) (λ (f)
            (f (λ (x)
                 (((g g) f) x)))))))

(define F
  (λ (f)
    (U (λ (self)
         (f (λ (x)
              ((self self) x)))))))

(define G
  (λ (f)
    (f (λ (x)
         ((G f) x)))))

(define Y
  (λ (f)
    ((λ (g) (g g))
     (λ (g)
       (f (λ (x) ((g g) x)))))))

(define mk-len
  (λ (rlen)
    (λ (lst)
      (cond
        [(empty? lst) 0]
        [else (+ 1 (rlen (rest lst)))]))))

(module+ test
  (require rackunit)
  (check = ((Θ mk-len) '(1 2 3 4 5)) 5)
  (check = ((F mk-len) '(1 2 3 4 5)) 5)
  (check = ((G mk-len) '(1 2 3 4 5)) 5)
  (check = ((Y mk-len) '(1 2 3 4 5)) 5))