diff --git a/Data/IntTrie.hs b/Data/IntTrie.hs
--- a/Data/IntTrie.hs
+++ b/Data/IntTrie.hs
@@ -23,6 +23,7 @@
 import Control.Applicative
 import Data.Bits
 import Data.Function (fix)
+import Data.Monoid (Monoid(..))
 
 -- | A trie from integers to values of type a. 
 -- 
@@ -38,6 +39,10 @@
     pure x = fix (\g -> BitTrie x g g)
     ~(BitTrie f fl fr) <*> ~(BitTrie x xl xr) = BitTrie (f x) (fl <*> xl) (fr <*> xr)
 
+instance Monoid a => Monoid (BitTrie a) where
+    mempty = pure mempty
+    mappend = liftA2 mappend
+
 instance Functor IntTrie where
     fmap f ~(IntTrie neg z pos) = IntTrie (fmap f neg) (f z) (fmap f pos)
 
@@ -46,16 +51,20 @@
     IntTrie fneg fz fpos <*> IntTrie xneg xz xpos = 
         IntTrie (fneg <*> xneg) (fz xz) (fpos <*> xpos)
 
+instance Monoid a => Monoid (IntTrie a) where
+    mempty = pure mempty
+    mappend = liftA2 mappend
+
 -- | Apply the trie to an argument.  This is the semantic map.
 apply :: (Ord b, Num b, Bits b) => IntTrie a -> b -> a
-apply ~(IntTrie neg z pos) x =
+apply (IntTrie neg z pos) x =
     case compare x 0 of
         LT -> applyPositive neg (-x)
         EQ -> z
         GT -> applyPositive pos x
 
 applyPositive :: (Num b, Bits b) => BitTrie a -> b -> a
-applyPositive ~(BitTrie one even odd) x
+applyPositive (BitTrie one even odd) x
     | x == 1 = one
     | testBit x 0 = applyPositive odd (x `shiftR` 1)
     | otherwise   = applyPositive even (x `shiftR` 1)
diff --git a/data-inttrie.cabal b/data-inttrie.cabal
--- a/data-inttrie.cabal
+++ b/data-inttrie.cabal
@@ -1,7 +1,7 @@
 Name: data-inttrie
 Description:
     A simple lazy, infinite trie from integers.
-Version: 0.0.9
+Version: 0.1.0
 Stability: experimental
 Synopsis: A lazy, infinite trie of integers.
 License: BSD3