Recursive types in Typed Racket

rec.rkt

#lang typed/racket

(define-type Hungry (Rec X (Natural -> X)))

(: f Hungry)
(define (f _) f)

(define-type (Stream X) (Rec A (Void -> (List Natural A))))

; U-combinator (self application)
(: U (∀ [T] (Rec X (X -> T)) -> T))
(define (U f) (f f))

; Y-combinator
(: fix (∀ [T] (T -> T) -> T))
(define (fix f)
  (U (λ ([x : (Rec A (A -> T))]) (f (x x)))))