diff --git a/src/Data/TotalMap.hs b/src/Data/TotalMap.hs
--- a/src/Data/TotalMap.hs
+++ b/src/Data/TotalMap.hs
@@ -12,7 +12,7 @@
 -- a default value. Has Applicative and Monad instances (unlike "Data.Map").
 ----------------------------------------------------------------------
 
-module Data.TotalMap (TMap,fromPartial,(!),tabulate,trim,intersectionPartialWith) where
+module Data.TotalMap (TMap,fromPartial,(!),tabulate,trim,intersectionPartialWith,codomain) where
 
 import Data.Monoid (Monoid(..),(<>))
 import Control.Applicative (Applicative(..),liftA2,(<$>))
@@ -62,6 +62,10 @@
    M.intersectionWith f am bm
    `M.union`
    fmap (f ad) bm
+
+-- | Witness the finiteness of the support concretely by giving its image.
+codomain :: Ord v => TMap k v -> Set v
+codomain (TMap dflt m) = S.fromList (dflt : M.elems m)
 
 {--------------------------------------------------------------------
     Instances
diff --git a/total-map.cabal b/total-map.cabal
--- a/total-map.cabal
+++ b/total-map.cabal
@@ -1,11 +1,11 @@
 Name:                total-map
-Version:             0.0.5
+Version:             0.0.6
 Cabal-Version:       >= 1.6
 Synopsis:            Finitely represented /total/ maps
 Category:            Data
 Description:
-  Finitely represented /total/ maps. Represented by as a partial map and a default value.
-  Has Applicative and Monad instances (unlike Data.Map).
+  Finitely represented /total/ maps. Represented by as a partial map and
+  a default value. Has Applicative and Monad instances (unlike Data.Map).
 Author:              Conal Elliott
 Maintainer:          conal@conal.net
 Copyright:           (c) 2012 by Conal Elliott