diff --git a/opentheory-primitive.cabal b/opentheory-primitive.cabal
--- a/opentheory-primitive.cabal
+++ b/opentheory-primitive.cabal
@@ -1,5 +1,5 @@
 name: opentheory-primitive
-version: 1.3
+version: 1.4
 category: Formal Methods
 synopsis: Haskell primitives used by OpenTheory packages
 license: MIT
@@ -13,16 +13,13 @@
   Prelude to provide the core execution platform assumed by Haskell
   packages exported from formally verified OpenTheory packages.
 
-Library
+library
   build-depends:
     base >= 4.0 && < 5.0,
     random >= 1.0.1.1 && < 2.0,
     QuickCheck >= 2.4.0.1 && < 3.0
-
   hs-source-dirs: src
-
   ghc-options: -Wall
-
   exposed-modules:
     OpenTheory.Primitive.Byte
     OpenTheory.Primitive.Natural
@@ -30,14 +27,12 @@
     OpenTheory.Primitive.Word16
     OpenTheory.Primitive.Test
 
-Executable opentheory-primitive-test
+test-suite opentheory-primitive-test
+  type: exitcode-stdio-1.0
   build-depends:
     base >= 4.0 && < 5.0,
     random >= 1.0.1.1 && < 2,
     QuickCheck >= 2.4.0.1 && < 3.0
-
-  hs-source-dirs: src, testsrc
-
+  hs-source-dirs: src
   ghc-options: -Wall
-
-  main-is: Main.hs
+  main-is: Test.hs
diff --git a/src/OpenTheory/Primitive/Natural.hs b/src/OpenTheory/Primitive/Natural.hs
--- a/src/OpenTheory/Primitive/Natural.hs
+++ b/src/OpenTheory/Primitive/Natural.hs
@@ -8,21 +8,27 @@
 portability: portable
 -}
 module OpenTheory.Primitive.Natural
-  ( Natural )
+  ( Natural,
+    shiftLeft,
+    shiftRight )
 where
 
+import Data.Bits
 import qualified Test.QuickCheck
 
 newtype Natural =
     Natural { unNatural :: Integer }
-  deriving Eq
+  deriving (Eq, Ord)
 
-instance Show Natural where
-  show n = show (unNatural n)
+shiftLeft :: Natural -> Natural -> Natural
+shiftLeft (Natural x) k = Natural (shiftL x (fromIntegral k))
 
-instance Ord Natural where
-  compare x y = compare (unNatural x) (unNatural y)
+shiftRight :: Natural -> Natural -> Natural
+shiftRight (Natural x) k = Natural (shiftR x (fromIntegral k))
 
+instance Show Natural where
+  show x = show (unNatural x)
+
 instance Num Natural where
   x + y = Natural (unNatural x + unNatural y)
 
@@ -69,6 +75,33 @@
           in (Natural q, Natural r)
 
   toInteger = unNatural
+
+instance Data.Bits.Bits Natural where
+  x .&. y = Natural (unNatural x .&. unNatural y)
+
+  x .|. y = Natural (unNatural x .|. unNatural y)
+
+  xor x y = Natural (xor (unNatural x) (unNatural y))
+
+  complement _ = error "OpenTheory.Primitive.Natural.complement"
+
+  shift x k = Natural (shift (unNatural x) k)
+
+  shiftL x k = Natural (shiftL (unNatural x) k)
+
+  shiftR x k = Natural (shiftR (unNatural x) k)
+
+  rotate _ _ = error "OpenTheory.Primitive.Natural.rotate"
+
+  bitSize _ = error "OpenTheory.Primitive.Natural.bitSize"
+
+  isSigned _ = False
+
+  testBit x k = testBit (unNatural x) k
+
+  bit k = Natural (bit k)
+
+  popCount x = popCount (unNatural x)
 
 instance Test.QuickCheck.Arbitrary Natural where
   arbitrary = fmap fromRandomInteger Test.QuickCheck.arbitrary
diff --git a/src/Test.hs b/src/Test.hs
new file mode 100644
--- /dev/null
+++ b/src/Test.hs
@@ -0,0 +1,43 @@
+{- |
+Module: $Header$
+Description: Testing the OpenTheory standard theory library
+License: MIT
+
+Maintainer: Joe Leslie-Hurd <joe@gilith.com>
+Stability: provisional
+Portability: portable
+-}
+module Main
+  ( main )
+where
+
+import OpenTheory.Primitive.Natural
+import OpenTheory.Primitive.Test
+
+assertion0 :: Bool
+assertion0 = True
+
+assertion1 :: Bool
+assertion1 = (2 :: Natural) + 2 == 4
+
+proposition0 :: Bool -> Bool
+proposition0 p = p || not p
+
+proposition1 :: Natural -> Natural -> Bool
+proposition1 m n = m + n == n + m
+
+proposition2 :: Natural -> Natural -> Bool
+proposition2 n k = shiftLeft n k == (2 ^ k) * n
+
+proposition3 :: Natural -> Natural -> Bool
+proposition3 n k = shiftRight n k == n `div` (2 ^ k)
+
+main :: IO ()
+main =
+    do assert "Assertion 0:\n  T\n  " assertion0
+       assert "Assertion 1:\n  2 + 2 = 4\n  " assertion1
+       check "Proposition 0:\n  !p. p \\/ ~p\n  " proposition0
+       check "Proposition 1:\n  !m n. m + n = n + m\n  " proposition1
+       check "Proposition 2:\n  !n k. shiftLeft n k = 2 ^ k * n\n  " proposition2
+       check "Proposition 3:\n  !n k. shiftRight n k = n div 2 ^ k\n  " proposition3
+       return ()
diff --git a/testsrc/Main.hs b/testsrc/Main.hs
deleted file mode 100644
--- a/testsrc/Main.hs
+++ /dev/null
@@ -1,37 +0,0 @@
-{- |
-Module: $Header$
-Description: OpenTheory QuickCheck interface
-License: MIT
-
-Maintainer: Joe Leslie-Hurd <joe@gilith.com>
-Stability: provisional
-Portability: portable
-
-OpenTheory QuickCheck interface
--}
-module Main
-  ( main )
-where
-
-import OpenTheory.Primitive.Natural
-import OpenTheory.Primitive.Test
-
-assertion0 :: Bool
-assertion0 = True
-
-assertion1 :: Bool
-assertion1 = (2 :: Natural) + 2 == 4
-
-proposition0 :: Bool -> Bool
-proposition0 p = p || not p
-
-proposition1 :: Natural -> Natural -> Bool
-proposition1 m n = m + n == n + m
-
-main :: IO ()
-main =
-    do assert "Assertion 0:\n  T\n  " assertion0
-       assert "Assertion 1:\n  2 + 2 = 4\n  " assertion1
-       check "Proposition 0:\n  !p. p \\/ ~p\n  " proposition0
-       check "Proposition 1:\n  !m n. m + n = n + m\n  " proposition1
-       return ()