diff --git a/typed-racket-lib/typed-racket/types/generalize.rkt b/typed-racket-lib/typed-racket/types/generalize.rkt
index f1f62c42..cab68b18 100644
--- a/typed-racket-lib/typed-racket/types/generalize.rkt
+++ b/typed-racket-lib/typed-racket/types/generalize.rkt
@@ -31,6 +31,9 @@
         [(? (lambda (t) (subtype t -Char))) -Char]
         [(? (lambda (t) (subtype t -ExtFlonum))) -ExtFlonum]
         [(Listof: _) t*]
+        [(Immutable-HashTable: k v) (-HT k v)]
+        [(Mutable-HashTable: k v) (-HT k v)]
+        [(Weak-HashTable: k v) (-HT k v)]
         [(Pair: t1 (== -Null)) (-lst t1)]
         [(MPair: t1 (== -Null)) (-mlst t1)]
         [(or (Pair: t1 t2) (MPair: t1 t2))
diff --git a/typed-racket-test/unit-tests/typecheck-tests.rkt b/typed-racket-test/unit-tests/typecheck-tests.rkt
index 3589580f..7991da67 100644
--- a/typed-racket-test/unit-tests/typecheck-tests.rkt
+++ b/typed-racket-test/unit-tests/typecheck-tests.rkt
@@ -3970,6 +3970,51 @@
        [tc-e (let ([a (inst cons Integer Integer)])
                (cons #f #f))
              (-pair -False -False)]
+       ;; TR github issue 573
+       ;; make sure immutable hash tables generalize to just hash
+       [tc-e (let ()
+               (define h1 (hash))
+
+               (: hfun (-> (HashTable Any Any) (HashTable Any Any)))
+               (define (hfun h) h)
+
+               (define h2
+                 (for/fold : (HashTable Any Any)
+                   ([h h1])
+                   ([_ (in-range 3)])
+                   (hfun h)))
+               (void))
+             -Void]
+       ;; TR github issue 573
+       ;; make sure mutable hash tables generalize to just hash
+       [tc-e (let ()
+               (define h1 (make-hash '()))
+
+               (: hfun (-> (HashTable Any Any) (HashTable Any Any)))
+               (define (hfun h) h)
+
+               (define h2
+                 (for/fold : (HashTable Any Any)
+                   ([h h1])
+                   ([_ (in-range 3)])
+                   (hfun h)))
+               (void))
+             -Void]
+       ;; TR github issue 573
+       ;; make sure weak hash tables generalize to just hash
+       [tc-e (let ()
+               (define h1 (make-weak-hash '()))
+
+               (: hfun (-> (HashTable Any Any) (HashTable Any Any)))
+               (define (hfun h) h)
+
+               (define h2
+                 (for/fold : (HashTable Any Any)
+                   ([h h1])
+                   ([_ (in-range 3)])
+                   (hfun h)))
+               (void))
+             -Void]
        )
 
   (test-suite