Recursive type Problem

[NoahStoryM]

What version of Racket are you using?

Racket 7.7-1

What program did you run?

#lang typed/racket
(define-type Func (All (A) [-> Func A]))
(: test-func [-> Number Number])
(define test-func
  (λ (num)
    ((λ (func) num)
     (λ ([func : Func])
       (inst func Number)))))

What should have happened?

(test-func 0)   ; -> 0
(test-func 1)   ; -> 1
(test-func 2)   ; -> 2
(test-func 3)   ; -> 3
(test-func 4)   ; -> 4

And following codes work well:

#lang typed/racket
(define-type Func (All (A) [-> Func A]))
(: test-func [-> Number Number])
(define test-func
  (λ (num)
    ((λ (func) num)
     (λ ([func : (Func Number)])
       func))))

#lang typed/racket
(define-type Func (All (A) [-> Boolean Number Any A]))
(: test-func [-> Number Number])
(define test-func
  (λ (num)
    ((λ (func) num)
     (λ ([func : Func])
       (inst func Number)))))

If you got an error message, please include it here.

Type Checker: Cannot instantiate non-polymorphic type Func
  in: func