In Racket 7.9 CS, the type quotient/remainder includes a case (-> Integer Fixnum (values Integer Fixnum)), but remainder's corresponding case is (-> Integer Fixnum Integer). There may be other, similar inconsistencies.
As an example, this program works:
#lang typed/racket
(: my-remainder (-> Integer Fixnum Fixnum))
(define (my-remainder x y)
(define-values [q r]
(quotient/remainder x y))
r)
whereas this version fails to typecheck:
#lang typed/racket
(: my-remainder (-> Integer Fixnum Fixnum))
(define (my-remainder x y)
(remainder x y))