diff --git a/syndicate/bag.rkt b/syndicate/bag.rkt
index 984a651..4e4aca8 100644
--- a/syndicate/bag.rkt
+++ b/syndicate/bag.rkt
@@ -1,21 +1,29 @@
 #lang racket/base
 ;; Bags and Deltas (which are Bags where item-counts can be negative).
 
-(provide make-bag
+(provide make-bag ;; mutable
+         bag ;; immutable
          bag-change!
+         bag-change
          bag-ref
          bag-clear!
          bag-member?
          in-bag
-         in-bag/count)
+         in-bag/count
+         set->bag)
 
-;; A `(Bagof X)` is a `(MutableHash X Nat)`, where the `Nat` against
-;; an `X` is its replication count in the bag.
+(require racket/set)
+
+;; A `(MutableBagof X)` is a `(MutableHash X Nat)`, where the `Nat`
+;; against an `X` is its replication count in the bag.
 ;;
-;; A `(Deltaof X)` is a `(MutableHash X Int)`, just like a `(Bagof X)`
-;; except the replication counts can be negative.
+;; A `(Bagof X)` is similar, but immutable.
+;;
+;; A `(Deltaof X)` is a `(MutableHash X Int)`, just like a
+;; `(MutableBagof X)` except the replication counts can be negative.
 
 (define make-bag make-hash)
+(define bag hash)
 
 (define (bag-change! b x delta)
   (define old-count (bag-ref b x))
@@ -26,6 +34,15 @@
       (begin (hash-set! b x new-count)
              (if (zero? old-count) 'absent->present 'present->present))))
 
+(define (bag-change b x delta)
+  (define old-count (bag-ref b x))
+  (define new-count (+ old-count delta))
+  (if (zero? new-count)
+      (values (hash-remove b x)
+              (if (zero? old-count) 'absent->absent 'present->absent))
+      (values (hash-set b x new-count)
+              (if (zero? old-count) 'absent->present 'present->present))))
+
 (define (bag-ref b x)
   (hash-ref b x 0))
 
@@ -34,3 +51,7 @@
 
 (define-syntax-rule (in-bag piece ...) (in-hash-keys piece ...))
 (define-syntax-rule (in-bag/count piece ...) (in-hash piece ...))
+
+(define (set->bag s)
+  (for/hash [(e (in-set s))]
+    (values e 1)))