Intersection type example not typechecking, but it (probably?) should

[rfindler]

This program:

#lang typed/racket
(: g (∩ (-> Integer Integer)
        (-> Boolean Boolean)))
(define (g x)
  (if (exact-integer? x)
      5
      #f))

produces this error:

Welcome to DrRacket, version 8.3.900 [cs].
Language: typed/racket, with debugging; memory limit: 128 MB.
. Type Checker: type mismatch
  expected: (∩ (-> Boolean Boolean) (-> Integer Integer))
  given: (-> Any (U False Positive-Byte) : Integer) in: (define (g x) (if (exact-integer? x) 5 #f))

but it seems like, if the rule for intersection types is this,

 e : τ1      e : τ2
 ------------------
   e : τ1 ∩ τ2

then it should, because these two programs both type check:

#lang typed/racket
(: g (-> Integer Integer))
(define (g x)
  (if (exact-integer? x)
      5
      #f))

#lang typed/racket
(: g (-> Boolean Boolean))
(define (g x)
  (if (exact-integer? x)
      5
      #f))