diff --git a/copilot-language.cabal b/copilot-language.cabal
--- a/copilot-language.cabal
+++ b/copilot-language.cabal
@@ -1,6 +1,6 @@
 cabal-version:       >=1.10
 name:                copilot-language
-version:             0.2
+version:             0.3
 synopsis:            A Haskell-embedded DSL for monitoring hard real-time
                      distributed systems.
 description:         Blah blah blah...
diff --git a/src/Copilot/Language.hs b/src/Copilot/Language.hs
--- a/src/Copilot/Language.hs
+++ b/src/Copilot/Language.hs
@@ -2,7 +2,7 @@
 -- Copyright © 2011 National Institute of Aerospace / Galois, Inc.
 --------------------------------------------------------------------------------
 
--- |
+-- | Main Copilot language export file.
 
 module Copilot.Language
   ( module Data.Int
diff --git a/src/Copilot/Language/Operators/BitWise.hs b/src/Copilot/Language/Operators/BitWise.hs
--- a/src/Copilot/Language/Operators/BitWise.hs
+++ b/src/Copilot/Language/Operators/BitWise.hs
@@ -5,36 +5,34 @@
 {-# OPTIONS_GHC -fno-warn-orphans #-}
 
 module Copilot.Language.Operators.BitWise
-  ( Bits ( (.&.), complement, (.|.) )
+  ( Bits ((.&.), complement, (.|.))
   , (.^.)
   , (.<<.)
   , (.>>.)
   ) where
 
-import Copilot.Core ( Typed, typeOf )
+import Copilot.Core (Typed, typeOf)
 import qualified Copilot.Core as Core
 import Copilot.Language.Stream
 import qualified Prelude as P
 import Data.Bits
 
-instance ( Typed a, Bits a ) => Bits ( Stream a ) where
-  (.&.)      = Op2 ( Core.BwAnd typeOf )
-  complement = Op1 ( Core.BwNot typeOf )
-  (.|.)      = Op2 ( Core.BwOr  typeOf )
-  xor        = Op2 ( Core.BwXor typeOf )
+instance (Typed a, Bits a) => Bits (Stream a) where
+  (.&.)      = Op2 (Core.BwAnd typeOf)
+  complement = Op1 (Core.BwNot typeOf)
+  (.|.)      = Op2 (Core.BwOr  typeOf)
+  xor        = Op2 (Core.BwXor typeOf)
   shiftL     = P.error "shiftL undefined, for left-shifting use .<<."
   shiftR     = P.error "shiftR undefined, for right-shifting use .>>."
   rotate     = P.error "tbd: rotate"
   bitSize    = P.error "tbd: bitSize"
   isSigned   = P.error "tbd: issigned"
 
-
 -- Avoid redefinition of the Operators.Boolean xor
-(.^.) :: ( Bits a ) => a -> a -> a
+(.^.) :: Bits a => a -> a -> a
 (.^.) = xor
 
-
-(.<<.), (.>>.) :: ( Bits a, Typed a, Typed b, P.Integral b ) =>
-                    Stream a -> Stream b -> Stream a
-(.<<.) = Op2 ( Core.BwShiftL typeOf typeOf )
-(.>>.) = Op2 ( Core.BwShiftR typeOf typeOf )
+(.<<.), (.>>.) :: (Bits a, Typed a, Typed b, P.Integral b) 
+               => Stream a -> Stream b -> Stream a
+(.<<.) = Op2 (Core.BwShiftL typeOf typeOf)
+(.>>.) = Op2 (Core.BwShiftR typeOf typeOf)
diff --git a/src/Copilot/Language/Operators/Boolean.hs b/src/Copilot/Language/Operators/Boolean.hs
--- a/src/Copilot/Language/Operators/Boolean.hs
+++ b/src/Copilot/Language/Operators/Boolean.hs
@@ -28,7 +28,7 @@
 false :: Stream Bool
 false = constant False
 
-infix 4 &&
+infixr 4 &&
 
 (&&) :: Stream Bool -> Stream Bool -> Stream Bool
 (Const False) && _ = false
@@ -37,7 +37,7 @@
 x && (Const True)  = x
 x && y             = Op2 Core.And x y
 
-infix 4 ||
+infixr 4 ||
 
 (||) :: Stream Bool -> Stream Bool -> Stream Bool
 (Const True) || _  = true
diff --git a/src/Copilot/Language/Operators/Integral.hs b/src/Copilot/Language/Operators/Integral.hs
--- a/src/Copilot/Language/Operators/Integral.hs
+++ b/src/Copilot/Language/Operators/Integral.hs
@@ -7,12 +7,17 @@
 module Copilot.Language.Operators.Integral
   ( div
   , mod
+  , (^)
   ) where
 
 import Copilot.Core (Typed, typeOf)
 import qualified Copilot.Core as Core
+import Copilot.Language.Operators.BitWise ((.<<.))
 import Copilot.Language.Stream
+
+import qualified Data.Bits as B
 import qualified Prelude as P
+import Data.List (foldl', replicate)
 
 --------------------------------------------------------------------------------
 
@@ -27,5 +32,14 @@
 (Const 0) `mod` _         = (Const 0)
 (Const x) `mod` (Const y) = Const (x `P.mod` y)
 x `mod` y = Op2 (Core.Mod typeOf) x y
+
+(^) :: (Typed a, Typed b, P.Num a, B.Bits a, P.Integral b) 
+    => Stream a -> Stream b -> Stream a
+(Const 0) ^ _          = Const 0
+(Const 1) ^ _          = Const 1
+(Const x) ^ (Const y)  = Const (x P.^ y)
+(Const 2) ^ y          = (Const 2) .<<. y
+x ^ (Const y)          = foldl' ((P.*)) (Const 1) (replicate (P.fromIntegral y) x)
+_ ^ _                  = Core.badUsage "in ^: in x ^ y, either x must be the constant 2, or y must be a constant.  (Do not confuse ^ with bitwise XOR (.^.) or with ** for exponentation of floats/doubles.)"
 
 --------------------------------------------------------------------------------
diff --git a/src/Copilot/Language/Operators/Mux.hs b/src/Copilot/Language/Operators/Mux.hs
--- a/src/Copilot/Language/Operators/Mux.hs
+++ b/src/Copilot/Language/Operators/Mux.hs
@@ -2,7 +2,7 @@
 -- Copyright © 2011 National Institute of Aerospace / Galois, Inc.
 --------------------------------------------------------------------------------
 
--- |
+-- | if-then-else.
 
 module Copilot.Language.Operators.Mux
   ( mux
diff --git a/src/Copilot/Language/Prelude.hs b/src/Copilot/Language/Prelude.hs
--- a/src/Copilot/Language/Prelude.hs
+++ b/src/Copilot/Language/Prelude.hs
@@ -15,6 +15,7 @@
   , div, mod
   , (<=), (>=), (<), (>)
   , (&&)
+  , (^)
   , (||)
   , const
   , drop
diff --git a/src/Copilot/Language/Stream.hs b/src/Copilot/Language/Stream.hs
--- a/src/Copilot/Language/Stream.hs
+++ b/src/Copilot/Language/Stream.hs
@@ -22,63 +22,27 @@
 --------------------------------------------------------------------------------
 
 data Stream :: * -> * where
-  Append
-    :: Typed a
-    => [a]
-    -> Maybe (Stream Bool)
-    -> Stream a
-    -> Stream a
-  Const
-    :: Typed a
-    => a
-    -> Stream a
-  Drop
-    :: Typed a
-    => Int
-    -> Stream a
-    -> Stream a
-  Extern
-    :: Typed a
-    => String
-    -> Maybe [a]
-    -> Stream a
-  ExternFun
-    :: Typed a
-    => String
-    -> [FunArg]
-    -> Maybe (Stream a)
-    -> Stream a
-  ExternArray
-    :: (Typed a, Typed b, Integral a)
-    => String
-    -> Stream a
-    -> Int
-    -> Maybe [[b]]
-    -> Stream b
-  Local
-    :: (Typed a, Typed b)
-    => Stream a
-    -> (Stream a -> Stream b)
-    -> Stream b
-  Var
-    :: Typed a
-    => String
-    -> Stream a
-  Op1
-    :: (Typed a, Typed b)
-    => Core.Op1 a b
-    -> Stream a -> Stream b
-  Op2
-    :: (Typed a, Typed b, Typed c)
-    => Core.Op2 a b c
-    -> Stream a -> Stream b -> Stream c
-  Op3
-    :: (Typed a, Typed b, Typed c, Typed d)
-    => Core.Op3 a b c d
-    -> Stream a
-    -> Stream b
-    -> Stream c
-    -> Stream d
+  Append      :: Typed a 
+              => [a] -> Maybe (Stream Bool) -> Stream a -> Stream a
+  Const       :: Typed a => a -> Stream a
+  Drop        :: Typed a
+              => Int -> Stream a -> Stream a
+  Extern      :: Typed a
+              => String -> Maybe [a] -> Stream a
+  ExternFun   :: Typed a 
+              => String -> [FunArg] -> Maybe (Stream a) -> Stream a
+  ExternArray :: (Typed a, Typed b, Integral a)
+              => String -> Stream a -> Int -> Maybe [[b]] -> Stream b
+  Local       :: (Typed a, Typed b) 
+              => Stream a -> (Stream a -> Stream b) -> Stream b
+  Var         :: Typed a 
+              => String -> Stream a
+  Op1         :: (Typed a, Typed b)
+              => Core.Op1 a b -> Stream a -> Stream b
+  Op2         :: (Typed a, Typed b, Typed c)
+              => Core.Op2 a b c -> Stream a -> Stream b -> Stream c
+  Op3         :: (Typed a, Typed b, Typed c, Typed d)
+              => Core.Op3 a b c d -> Stream a -> Stream b -> Stream c -> Stream d
 
 --------------------------------------------------------------------------------