diff --git a/utils.rkt b/utils.rkt
index 7e0259e..8001dcc 100644
--- a/utils.rkt
+++ b/utils.rkt
@@ -8,11 +8,13 @@
          (for-syntax racket/list))
 
 (provide
- ;; Functions with contracts
+ ;; Functions
  (contract-out [eval-with (-> variable-mapping? any/c any)]
-               [extract-symbols (-> any/c list?)])
- ;; Functions without contracts
- variable-mapping? hash-pred
+               [extract-symbols (-> any/c list?)]
+               [variable-mapping? (-> any/c boolean?)]
+               [hash-pred (->* (hash?)
+                               (#:key-pred any/c #:val-pred any/c)
+                               boolean?)])
  ;; Syntax
  auto-hash-ref/explicit auto-hash-ref/:)