Bad optimization with (if (pair? rest) …) on polymorphic rest argument (unsound)

What version of Racket are you using?

6.6.0.1

What program did you run?

#lang typed/racket
((λ #:∀ (A ...) [rest : A ... A]
   (if (pair? rest)
       #t
       #f))
 1)
; => #f

What should have happened?

The result should be #t, but the program outputs #f. When typing this expression at the REPL, we can see racket incorrectly inferred the return type is False.

Without the (if … #t #f), the program outputs #t as expected:

#lang typed/racket
((λ #:∀ (A ...) [rest : A ... A]
   (pair? rest))
 1)
; => #t

Also, when using a regular Any * rest argument instead of the polymorphic A ... A, the result is correct:

#lang typed/racket
((λ [rest : Any *]
   (if (pair? rest)
       #t
       #f))
 1)
; => #t

I couldn't find a way to turn this into unsafe behaviour, so the problem is "just" incorrect results.

Start by running the Typed Racket examples in the issue and compare the inferred return type with the runtime result. Investigate the optimization or type-inference path for polymorphic rest arguments and the pair? test behavior. Done means the example returns #t and is no longer inferred as False, while the existing Any * behavior remains correct.