(∩ struct-type (→ t)) can't be used as a function, needs annotation

What version of Racket are you using?

6.6.0.5

What program did you run?

#lang typed/racket

(define-struct foo ())

(λ ([x : (∩ foo (→ foo))])
  (x) ;; <==================== fails
  ((ann x (→ foo))))

What should have happened?

The program should typecheck without the need for the annotation, since the ∩ guarantees that x is already the right type.

The use case for this is to have define-struct/exec instances which behave transparently as functions too, once #430 is solved.

Note that if the type of x is (∩ Number (→ foo)) instead of (∩ foo (→ foo)), the program compiles fine, but the function's argument type gets reduced to Nothing (which is likely correct in this case).

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

Type Checker: Cannot apply expression of type (∩ foo (-> foo)), since it is not a function type in: (x)