diff --git a/Data/Field.hs b/Data/Field.hs
deleted file mode 100644
--- a/Data/Field.hs
+++ /dev/null
@@ -1,29 +0,0 @@
------------------------------------------------------------------------------
--- |
--- Module      :  Data.Field
--- Copyright   :  (c) Edward Kmett 2009
--- License     :  BSD-style
--- Maintainer  :  ekmett@gmail.com
--- Stability   :  experimental
--- Portability :  portable
---
------------------------------------------------------------------------------
-
-module Data.Field
-    ( module Data.Group.Multiplicative
-    , module Data.Ring
-    , Field
-    ) where
-
-import Data.Group.Multiplicative
-import Data.Ring
-import Data.Monoid.Self
-import Data.Monoid.FromString
-import Data.Monoid.Reducer
-
-class (Ring a, MultiplicativeGroup a) => Field a
-
-instance Field f => Field (Dual f)
-instance Field f => Field (Self f)
-instance Field f => Field (FromString f)
-instance Field f => Field (ReducedBy f s)
diff --git a/Data/Field/VectorSpace.hs b/Data/Field/VectorSpace.hs
deleted file mode 100644
--- a/Data/Field/VectorSpace.hs
+++ /dev/null
@@ -1,11 +0,0 @@
-{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, FlexibleContexts #-}
-module Data.Field.VectorSpace 
-    ( module Data.Field
-    , module Data.Ring.Module
-    , VectorSpace
-    ) where
-
-import Data.Field
-import Data.Ring.Module
-    
-class (Field f, Module f g) => VectorSpace f g
diff --git a/Data/Generator.hs b/Data/Generator.hs
--- a/Data/Generator.hs
+++ b/Data/Generator.hs
@@ -1,4 +1,4 @@
-{-# LANGUAGE UndecidableInstances, TypeOperators, FlexibleContexts, MultiParamTypeClasses, FlexibleInstances, TypeFamilies #-}
+{-# LANGUAGE UndecidableInstances, TypeOperators, FlexibleContexts, MultiParamTypeClasses, FlexibleInstances, TypeFamilies, CPP #-}
 
 -----------------------------------------------------------------------------
 -- |
@@ -36,17 +36,31 @@
     , reduceWith
     ) where
 
+#ifdef M_ARRAY
 import Data.Array 
-import Data.Word (Word8)
+#endif
+
+
+#ifdef M_TEXT
 import Data.Text (Text)
-import Data.Foldable (fold,foldMap)
 import qualified Data.Text as Text
+#endif
+
+
+#ifdef M_BYTESTRING
 import qualified Data.ByteString as Strict (ByteString, foldl')
 import qualified Data.ByteString.Char8 as Strict8 (foldl')
 import qualified Data.ByteString.Lazy as Lazy (ByteString, toChunks)
 import qualified Data.ByteString.Lazy.Char8 as Lazy8 (toChunks)
-import qualified Data.Sequence as Seq
+import Data.Word (Word8)
+#endif
+
+#ifdef M_FINGERTREE
 import Data.FingerTree (Measured, FingerTree)
+#endif
+
+#ifdef M_CONTAINERS
+import qualified Data.Sequence as Seq
 import Data.Sequence (Seq)
 import qualified Data.Set as Set
 import Data.Set (Set)
@@ -56,8 +70,13 @@
 import Data.IntMap (IntMap)
 import qualified Data.Map as Map
 import Data.Map (Map)
+#endif
 
+#ifdef M_PARALLEL
 import Control.Parallel.Strategies
+#endif
+
+import Data.Foldable (fold,foldMap)
 import Data.Monoid.Reducer
 
 -- | minimal definition 'mapReduce' or 'mapTo'
@@ -71,6 +90,7 @@
     mapTo f m = mappend m . mapReduce f
     mapFrom f = mappend . mapReduce f
 
+#ifdef M_BYTESTRING
 instance Generator Strict.ByteString where
     type Elem Strict.ByteString = Word8
     mapTo f = Strict.foldl' (\a -> snoc a . f)
@@ -78,19 +98,25 @@
 instance Generator Lazy.ByteString where
     type Elem Lazy.ByteString = Word8
     mapReduce f = fold . parMap rwhnf (mapReduce f) . Lazy.toChunks
+#endif
 
+#ifdef M_TEXT
 instance Generator Text where
     type Elem Text = Char
     mapTo f = Text.foldl' (\a -> snoc a . f)
+#endif
 
 instance Generator [c] where
     type Elem [c] = c
     mapReduce f = foldr (cons . f) mempty
 
+#ifdef M_FINGERTREE
 instance Measured v e => Generator (FingerTree v e) where
     type Elem (FingerTree v e) = e
     mapReduce f = foldMap (unit . f)
+#endif
 
+#ifdef M_CONTAINERS
 instance Generator (Seq c) where
     type Elem (Seq c) = c
     mapReduce f = foldMap (unit . f)
@@ -110,14 +136,18 @@
 instance Generator (Map k v) where
     type Elem (Map k v) = (k,v) 
     mapReduce f = mapReduce f . Map.toList
+#endif
 
+#ifdef M_ARRAY
 instance Ix i => Generator (Array i e) where
     type Elem (Array i e) = (i,e)
     mapReduce f = mapReduce f . assocs
+#endif
 
 -- | a 'Generator' transformer that asks only for the keys of an indexed container
 newtype Keys c = Keys { getKeys :: c } 
 
+#ifdef M_CONTAINERS
 instance Generator (Keys (IntMap v)) where
     type Elem (Keys (IntMap v)) = Int
     mapReduce f = mapReduce f . IntMap.keys . getKeys
@@ -125,14 +155,18 @@
 instance Generator (Keys (Map k v)) where
     type Elem (Keys (Map k v)) = k
     mapReduce f = mapReduce f . Map.keys . getKeys
+#endif
 
+#ifdef M_ARRAY
 instance Ix i => Generator (Keys (Array i e)) where
     type Elem (Keys (Array i e)) = i
     mapReduce f = mapReduce f . range . bounds . getKeys
+#endif
 
 -- | a 'Generator' transformer that asks only for the values contained in an indexed container
 newtype Values c = Values { getValues :: c } 
 
+#ifdef M_CONTAINERS
 instance Generator (Values (IntMap v)) where
     type Elem (Values (IntMap v)) = v
     mapReduce f = mapReduce f . IntMap.elems . getValues
@@ -140,15 +174,19 @@
 instance Generator (Values (Map k v)) where
     type Elem (Values (Map k v)) = v
     mapReduce f = mapReduce f . Map.elems . getValues
+#endif
 
+#ifdef M_ARRAY
 instance Ix i => Generator (Values (Array i e)) where
     type Elem (Values (Array i e)) = e
     mapReduce f = mapReduce f . elems . getValues
+#endif
 
 -- | a 'Generator' transformer that treats 'Word8' as 'Char'
 -- This lets you use a 'ByteString' as a 'Char' source without going through a 'Monoid' transformer like 'UTF8'
 newtype Char8 c = Char8 { getChar8 :: c } 
 
+#ifdef M_BYTESTRING
 instance Generator (Char8 Strict.ByteString) where
     type Elem (Char8 Strict.ByteString) = Char
     mapTo f m = Strict8.foldl' (\a -> snoc a . f) m . getChar8
@@ -156,17 +194,25 @@
 instance Generator (Char8 Lazy.ByteString) where
     type Elem (Char8 Lazy.ByteString) = Char
     mapReduce f = fold . parMap rwhnf (mapReduce f . Char8) . Lazy8.toChunks . getChar8
+#endif
 
 -- | Apply a 'Reducer' directly to the elements of a 'Generator'
 reduce :: (Generator c, Elem c `Reducer` m) => c -> m
 reduce = mapReduce id
+#ifdef M_BYTESTRING
 {-# SPECIALIZE reduce :: (Word8 `Reducer` m) => Strict.ByteString -> m #-}
 {-# SPECIALIZE reduce :: (Word8 `Reducer` m) => Lazy.ByteString -> m #-}
 {-# SPECIALIZE reduce :: (Char `Reducer` m) => Char8 Strict.ByteString -> m #-}
 {-# SPECIALIZE reduce :: (Char `Reducer` m) => Char8 Lazy.ByteString -> m #-}
+#endif
 {-# SPECIALIZE reduce :: (c `Reducer` m) => [c] -> m #-}
+#ifdef M_FINGERTREE
 {-# SPECIALIZE reduce :: (Generator (FingerTree v e), e `Reducer` m) => FingerTree v e -> m #-}
+#endif
+#ifdef M_TEXT
 {-# SPECIALIZE reduce :: (Char `Reducer` m) => Text -> m #-}
+#endif
+#ifdef M_CONTAINERS
 {-# SPECIALIZE reduce :: (e `Reducer` m) => Seq e -> m #-}
 {-# SPECIALIZE reduce :: (Int `Reducer` m) => IntSet -> m #-}
 {-# SPECIALIZE reduce :: (a `Reducer` m) => Set a -> m #-}
@@ -176,6 +222,7 @@
 {-# SPECIALIZE reduce :: (k `Reducer` m) => Keys (Map k v) -> m #-}
 {-# SPECIALIZE reduce :: (v `Reducer` m) => Values (IntMap v) -> m #-}
 {-# SPECIALIZE reduce :: (v `Reducer` m) => Values (Map k v) -> m #-}
+#endif
 
 mapReduceWith :: (Generator c, e `Reducer` m) => (m -> n) -> (Elem c -> e) -> c -> n
 mapReduceWith f g = f . mapReduce g
diff --git a/Data/Group.hs b/Data/Group.hs
--- a/Data/Group.hs
+++ b/Data/Group.hs
@@ -12,17 +12,23 @@
 -----------------------------------------------------------------------------
 
 module Data.Group 
-    ( module Data.Monoid.Additive
+    ( module Data.Monoid.Multiplicative
     , Group
     , gnegate
     , gsubtract
     , minus
+    , MultiplicativeGroup
+    , over
+    , under
+    , grecip
     ) where
 
-import Data.Monoid.Additive
+import Data.Monoid.Multiplicative
 import Data.Monoid.Self
+
+#ifdef X_OverloadedStrings
 import Data.Monoid.FromString
-import Data.Monoid.Reducer
+#endif
 
 infixl 6 `minus`
 
@@ -52,11 +58,57 @@
     gnegate = Self . gnegate . getSelf
     Self a `minus` Self b = Self (a `minus` b)
 
-instance Group a => Group (FromString a) where
-    gnegate = FromString . gnegate . getFromString
-    FromString a `minus` FromString b = FromString (a `minus` b)
+-- | Minimal definition over or grecip
+class Multiplicative g => MultiplicativeGroup g where
+    -- | @x / y@
+    over :: g -> g -> g
+    -- | @x \ y@
+    under :: g -> g -> g
+    grecip :: g -> g
 
+    x `under` y = grecip x `times` y
+    x `over` y = x `times` grecip y
+    grecip x = one `over` x
+
+instance MultiplicativeGroup g => Group (Log g) where
+    Log x `minus` Log y = Log (x `over` y)
+    Log x `gsubtract` Log y = Log (x `under` y)
+    gnegate (Log x) = Log (grecip x)
+
+instance Group g => MultiplicativeGroup (Exp g) where
+    Exp x `over` Exp y = Exp (x `minus` y)
+    Exp x `under` Exp y = Exp (x `gsubtract` y)
+    grecip (Exp x) = Exp (gnegate x)
+
+instance MultiplicativeGroup g => MultiplicativeGroup (Self g) where
+    Self x `over` Self y = Self (x `over` y)
+    Self x `under` Self y = Self (x `under` y)
+    grecip (Self x) = Self (grecip x)
+
+#ifdef M_REFLECTION
+instance MultiplicativeGroup g => MultiplicativeGroup (ReducedBy g s) where
+    Reduction x `over` Reduction y = Reduction (x `over` y)
+    Reduction x `under` Reduction y = Reduction (x `under` y)
+    grecip (Reduction x) = Reduction (grecip x)
+
 instance Group a => Group (ReducedBy a s) where
     gnegate = Reduction . gnegate . getReduction
     Reduction a `minus` Reduction b = Reduction (a `minus` b)
+    Reduction a `gsubtract` Reduction b = Reduction (a `gsubtract` b)
+#endif
+
+instance MultiplicativeGroup a => MultiplicativeGroup (Dual a) where
+    grecip = Dual . grecip . getDual
+
+#ifdef X_OverloadedStrings
+instance MultiplicativeGroup g => MultiplicativeGroup (FromString g) where
+    FromString x `over` FromString y = FromString (x `over` y)
+    FromString x `under` FromString y = FromString (x `under` y)
+    grecip (FromString x) = FromString (grecip x)
+
+instance Group a => Group (FromString a) where
+    gnegate = FromString . gnegate . getFromString
+    FromString a `minus` FromString b = FromString (a `minus` b)
+    FromString a `gsubtract` FromString b = FromString (a `gsubtract` b)
+#endif
 
diff --git a/Data/Group/Multiplicative.hs b/Data/Group/Multiplicative.hs
deleted file mode 100644
--- a/Data/Group/Multiplicative.hs
+++ /dev/null
@@ -1,56 +0,0 @@
------------------------------------------------------------------------------
--- |
--- Module      :  Data.Group.Multiplicative
--- Copyright   :  (c) Edward Kmett 2009
--- License     :  BSD-style
--- Maintainer  :  ekmett@gmail.com
--- Stability   :  experimental
--- Portability :  portable
---
------------------------------------------------------------------------------
-
-module Data.Group.Multiplicative 
-    ( module Data.Monoid.Multiplicative
-    , module Data.Group
-    , MultiplicativeGroup
-    , over
-    , under
-    , grecip
-    ) where
-
-import Data.Monoid.Multiplicative
-import Data.Group
-import Data.Monoid.Self
-import Data.Monoid.FromString
-import Data.Monoid.Reducer
-
-    
--- | Minimal definition over or grecip
-class Multiplicative g => MultiplicativeGroup g where
-    -- | @x / y@
-    over :: g -> g -> g
-    -- | @x \ y@
-    under :: g -> g -> g
-    grecip :: g -> g
-
-    x `under` y = grecip x `times` y
-    x `over` y = x `times` grecip y
-    grecip x = one `over` x
-
-instance MultiplicativeGroup g => MultiplicativeGroup (Self g) where
-    Self x `over` Self y = Self (x `over` y)
-    Self x `under` Self y = Self (x `under` y)
-    grecip (Self x) = Self (grecip x)
-
-instance MultiplicativeGroup g => MultiplicativeGroup (FromString g) where
-    FromString x `over` FromString y = FromString (x `over` y)
-    FromString x `under` FromString y = FromString (x `under` y)
-    grecip (FromString x) = FromString (grecip x)
-
-instance MultiplicativeGroup g => MultiplicativeGroup (ReducedBy g s) where
-    Reduction x `over` Reduction y = Reduction (x `over` y)
-    Reduction x `under` Reduction y = Reduction (x `under` y)
-    grecip (Reduction x) = Reduction (grecip x)
-
-instance MultiplicativeGroup a => MultiplicativeGroup (Dual a) where
-    grecip = Dual . grecip . getDual
diff --git a/Data/Group/Multiplicative/Sugar.hs b/Data/Group/Multiplicative/Sugar.hs
deleted file mode 100644
--- a/Data/Group/Multiplicative/Sugar.hs
+++ /dev/null
@@ -1,41 +0,0 @@
------------------------------------------------------------------------------
--- |
--- Module      :  Data.Group.Multiplicative.Sugar
--- Copyright   :  (c) Edward Kmett 2009
--- License     :  BSD-style
--- Maintainer  :  ekmett@gmail.com
--- Stability   :  experimental
--- Portability :  portable
---
--- Syntactic sugar for working with groups that conflicts with names from the "Prelude".
---
--- > import Prelude hiding ((-), (+), (*), (/), negate, subtract, recip)
--- > import Data.Group.Multiplicative.Sugar
---
------------------------------------------------------------------------------
-
-module Data.Group.Multiplicative.Sugar 
-    ( module Data.Monoid.Multiplicative.Sugar
-    , module Data.Group.Multiplicative
-    , module Data.Group.Sugar
-    , (/)
-    , (\\)
-    , recip
-    ) where
-
-import Data.Group.Multiplicative
-import Data.Monoid.Multiplicative.Sugar
-import Data.Group.Sugar
-import Prelude hiding ((-), (+), (*), (/), negate, subtract, recip)
-
-infixl 7 /
-infixr 7 \\
-
-(/) :: MultiplicativeGroup g => g -> g -> g
-(/) = over
-
-(\\) :: MultiplicativeGroup g => g -> g -> g
-(\\) = under
-
-recip :: MultiplicativeGroup g => g -> g
-recip = grecip
diff --git a/Data/Group/Sugar.hs b/Data/Group/Sugar.hs
--- a/Data/Group/Sugar.hs
+++ b/Data/Group/Sugar.hs
@@ -9,23 +9,30 @@
 --
 -- Syntactic sugar for working with groups that conflicts with names from the "Prelude".
 --
--- > import Prelude hiding ((-), (+), negate, subtract)
+-- > import Prelude hiding ((-), (+), (*), (/), (^), (^^), negate, subtract, recip)
 -- > import Data.Group.Sugar
 --
 -----------------------------------------------------------------------------
 
 module Data.Group.Sugar 
-    ( module Data.Monoid.Additive.Sugar
+    ( module Data.Monoid.Sugar
     , module Data.Group
     , (-)
     , negate
     , subtract
+    , (/)
+    , (.\.)
+    , (^^)
+    , recip
     ) where
 
-import Data.Monoid.Additive.Sugar
+import Data.Monoid.Sugar
+import Data.Group.Combinators as Group
 import Data.Group
-import Prelude hiding ((-), negate, subtract)
+import Prelude hiding ((-), (+), (*), (/), (^^), negate, subtract, recip)
 
+infixl 8 /
+infixr 8 .\.
 infixl 7 -
 
 (-) :: Group g => g -> g -> g
@@ -36,3 +43,15 @@
 
 subtract :: Group g => g -> g -> g
 subtract = gsubtract
+
+(/) :: MultiplicativeGroup g => g -> g -> g
+(/) = over
+
+(.\.) :: MultiplicativeGroup g => g -> g -> g
+(.\.) = under
+
+recip :: MultiplicativeGroup g => g -> g
+recip = grecip
+
+(^^) :: MultiplicativeGroup g => g -> Integer -> g
+g ^^ n = getLog (Group.replicate (Log g) n)
diff --git a/Data/Monoid/Additive/Sugar.hs b/Data/Monoid/Additive/Sugar.hs
deleted file mode 100644
--- a/Data/Monoid/Additive/Sugar.hs
+++ /dev/null
@@ -1,28 +0,0 @@
------------------------------------------------------------------------------
--- |
--- Module      :  Data.Monoid.Additive.Sugar
--- Copyright   :  (c) Edward Kmett 2009
--- License     :  BSD-style
--- Maintainer  :  ekmett@gmail.com
--- Stability   :  experimental
--- Portability :  portable
---
--- Syntactic sugar for working with a 'Monoid' that conflicts with names from the "Prelude".
---
--- > import Prelude hiding ((+))
--- > import Data.Monoid.Additive.Sugar
---
------------------------------------------------------------------------------
-
-module Data.Monoid.Additive.Sugar 
-    ( module Data.Monoid.Additive
-    , (+)
-    ) where
-
-import Data.Monoid.Additive
-import Prelude hiding ((+))
-
-infixl 6 + 
-
-(+) :: Monoid m => m -> m -> m 
-(+) = mappend
diff --git a/Data/Monoid/Applicative.hs b/Data/Monoid/Applicative.hs
--- a/Data/Monoid/Applicative.hs
+++ b/Data/Monoid/Applicative.hs
@@ -15,7 +15,6 @@
 
 module Data.Monoid.Applicative 
     ( module Data.Monoid.Reducer
-    , module Data.Ring.Semi.Near
     , module Data.Ring.Module
     , Traversal(Traversal,getTraversal)
     , Alt(Alt,getAlt)
@@ -25,7 +24,6 @@
 
 import Control.Applicative
 import Data.Monoid.Reducer
-import Data.Ring.Semi.Near
 import Data.Ring.Module
 import Control.Functor.Pointed
 
@@ -80,7 +78,7 @@
 -- | if @m@ is a 'Module' over @r@ and @f@ is a 'Applicative' then @f `App` m@ is a 'Module' over @r@ as well
 
 newtype App f m = App { getApp :: f m } 
-    deriving (Eq,Ord,Show,Read,Functor,Pointed,Applicative,Alternative,Copointed)
+    deriving (Eq,Ord,Show,Read,Functor,Applicative,Alternative,Pointed,Copointed)
 
 instance (Monoid m, Applicative f) => Monoid (f `App` m) where
     mempty = pure mempty
diff --git a/Data/Monoid/Combinators.hs b/Data/Monoid/Combinators.hs
--- a/Data/Monoid/Combinators.hs
+++ b/Data/Monoid/Combinators.hs
@@ -1,4 +1,4 @@
-{-# LANGUAGE UndecidableInstances, TypeOperators, FlexibleContexts, MultiParamTypeClasses, FlexibleInstances, TypeFamilies #-}
+{-# LANGUAGE UndecidableInstances, TypeOperators, FlexibleContexts, MultiParamTypeClasses, FlexibleInstances, TypeFamilies, CPP #-}
 
 -----------------------------------------------------------------------------
 -- |
@@ -22,14 +22,18 @@
       repeat
     , replicate
     , cycle
+#ifdef M_QUICKCHECK
     -- * QuickCheck Properties
     , prop_replicate_right_distributive
+#endif
     ) where
 
 import Prelude hiding (replicate, cycle, repeat)
 import Data.Monoid.Reducer
-import Test.QuickCheck
 
+#ifdef M_QUICKCHECK 
+import Test.QuickCheck
+#endif
 
 -- | A generalization of 'Data.List.cycle' to an arbitrary 'Monoid'. May fail to terminate for some values in some monoids.
 cycle :: Monoid m => m -> m
@@ -43,7 +47,7 @@
 -- <http://augustss.blogspot.com/2008/07/lost-and-found-if-i-write-108-in.html>
 replicate :: (Monoid m, Integral n) => m -> n -> m
 replicate x0 y0 
-    | y0 < 0 = mempty -- error "negative length"
+    | y0 < 0 = error "Data.Monoid.Combinators.replicate: negative length"
     | y0 == 0 = mempty
     | otherwise = f x0 y0
     where
@@ -57,6 +61,8 @@
             | otherwise = g (x `mappend` x) ((y - 1) `quot` 2) (x `mappend` z)
 {-# INLINE replicate #-}
 
+#ifdef M_QUICKCHECK
 prop_replicate_right_distributive :: (Eq m, Monoid m, Arbitrary m, Integral n) => m -> n -> n -> Bool
 prop_replicate_right_distributive m x y
     = replicate m (x + y) == replicate m x `mappend` replicate m y
+#endif
diff --git a/Data/Monoid/FromString.hs b/Data/Monoid/FromString.hs
--- a/Data/Monoid/FromString.hs
+++ b/Data/Monoid/FromString.hs
@@ -2,7 +2,7 @@
 
 -----------------------------------------------------------------------------
 -- |
--- Module      :  Data.Monoid.Additive
+-- Module      :  Data.Monoid.FromString
 -- Copyright   :  (c) Edward Kmett 2009
 -- License     :  BSD-style
 -- Maintainer  :  ekmett@gmail.com
@@ -23,7 +23,7 @@
 import Data.Generator
 import Data.Monoid.Reducer
 import Data.Monoid.Instances ()
-import GHC.Exts
+import Data.String
 
 data FromString m = FromString { getFromString :: m } 
 
diff --git a/Data/Monoid/Instances.hs b/Data/Monoid/Instances.hs
--- a/Data/Monoid/Instances.hs
+++ b/Data/Monoid/Instances.hs
@@ -1,4 +1,4 @@
-{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, UndecidableInstances, OverloadedStrings #-}
+{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, UndecidableInstances, OverloadedStrings, CPP #-}
 {-# OPTIONS_GHC -fno-warn-orphans #-}
 
 -----------------------------------------------------------------------------
@@ -27,33 +27,41 @@
 --
 -- * 'Monoid' instances for 'Int', 'Integer', and 'Ratio' using @(+,0)@
 --
+-- * 'Num' and 'Bits' instances for 'Bool' as a 'Boolean' `&&`/`||` 'SemiRing'
+--
 -- This module is automatically included everywhere this functionality is required
 -- within this package. You should only have to import this module yourself if you 
 -- want these instances for your own purposes.
 -----------------------------------------------------------------------------
 
-module Data.Monoid.Instances where
+module Data.Monoid.Instances () where
 
+#ifdef M_MTL
 import Control.Monad.Reader
-
 import qualified Control.Monad.RWS.Lazy as LRWS
 import qualified Control.Monad.RWS.Strict as SRWS
-
 import qualified Control.Monad.State.Lazy as LState
 import qualified Control.Monad.State.Strict as SState
-
 import Control.Monad.Writer
 import qualified Control.Monad.Writer.Strict as SWriter
+#endif
 
+#ifdef X_OverloadedStrings
 import Data.String
+#endif
 
+import Data.Bits
 import Data.Ratio
 
+#ifdef M_FINGERTREE
 import Data.FingerTree
+#endif
 
+#ifdef M_PARSEC
 import Text.Parsec.Prim
+#endif
 
--- orphan Monoid instances for Monad Transformers
+#ifdef M_MTL
 instance (MonadPlus m, Monoid w) => Monoid (SWriter.WriterT w m n) where
     mempty = mzero
     mappend = mplus
@@ -81,18 +89,21 @@
 instance MonadPlus m => Monoid (LState.StateT s m n) where
     mempty = mzero
     mappend = mplus
+#endif
 
--- orphan, which should be in Data.FingerTree
+#ifdef M_FINGERTREE
 instance Measured v a => Monoid (FingerTree v a) where
     mempty = empty
     mappend = (><)
+#endif
 
--- orphan, which should be in Parsec
+#ifdef M_PARSEC
 instance Stream s m t => Monoid (ParsecT s u m a) where
     mempty = mzero
     a `mappend` b = try a <|> b
+#endif
 
--- orphan, perhaps should be in Data.String
+#ifdef X_OverloadedStrings
 instance (IsString a, IsString b) => IsString (a,b) where
     fromString a = (fromString a, fromString a)
 
@@ -104,6 +115,7 @@
 
 instance (IsString a, IsString b, IsString c, IsString d, IsString e) => IsString (a,b,c,d,e) where
     fromString a = (fromString a, fromString a, fromString a, fromString a, fromString a)
+#endif
 
 instance Monoid Int where
     mempty = 0
@@ -116,3 +128,35 @@
 instance Integral m => Monoid (Ratio m) where
     mempty = 0
     mappend = (+)
+
+instance Monoid Bool where
+    mempty = 0
+    mappend = (||)
+
+-- boolean semiring
+instance Num Bool where
+    (+) = (||)
+    (*) = (&&)
+    x - y = x && not y
+    negate = not
+    abs = id
+    signum = id
+    fromInteger 0 = False
+    fromInteger _ = True
+
+instance Bits Bool where
+    (.&.)           = (&&)
+    (.|.)           = (||)
+    xor True True   = False
+    xor False False = False
+    xor _ _         = True
+    complement      = not
+    shiftL a b      = a && (b == 0)
+    shiftR a b      = a && (b == 0)
+    shift  a b      = a && (b == 0)
+    rotate a _      = a
+    bit             = (==0)
+    setBit a b      = a || (b == 0)
+    testBit a b     = a && (b == 0)
+    bitSize _       = 1
+    isSigned _      = False
diff --git a/Data/Monoid/Monad.hs b/Data/Monoid/Monad.hs
--- a/Data/Monoid/Monad.hs
+++ b/Data/Monoid/Monad.hs
@@ -15,7 +15,7 @@
 
 module Data.Monoid.Monad 
     ( module Data.Monoid.Reducer
-    , module Data.Ring.Semi.Near
+    , module Data.Ring.Module
     -- * Actions
     , Action(Action,getAction)
     , snocAction
@@ -28,7 +28,6 @@
 import Control.Applicative
 import Control.Functor.Pointed
 import Data.Monoid.Reducer
-import Data.Ring.Semi.Near
 import Data.Ring.Module
 import Control.Monad
 
diff --git a/Data/Monoid/Multiplicative.hs b/Data/Monoid/Multiplicative.hs
--- a/Data/Monoid/Multiplicative.hs
+++ b/Data/Monoid/Multiplicative.hs
@@ -41,41 +41,47 @@
     ) where
 
 import Control.Applicative
+import Data.Monoid.Additive
+import Data.Generator
+import Data.Monoid.Instances ()
+import Data.Monoid.Self
+import Data.Ratio
 
+#ifdef M_STM
 import Control.Concurrent.STM
+#endif
 
+#ifdef M_MTL
 import Control.Monad.Cont
 import Control.Monad.Identity
-
 import Control.Monad.Reader
-
 import qualified Control.Monad.RWS.Lazy as LRWS
 import qualified Control.Monad.RWS.Strict as SRWS
-
 import qualified Control.Monad.State.Lazy as LState
 import qualified Control.Monad.State.Strict as SState
-
 import qualified Control.Monad.Writer.Lazy as LWriter
 import qualified Control.Monad.Writer.Strict as SWriter
-
 import qualified Control.Monad.ST.Lazy as LST
 import qualified Control.Monad.ST.Strict as SST
+#endif
 
+#ifdef M_FINGERTREE
 import Data.FingerTree
-
-import Data.Monoid.Additive
-import Data.Monoid.FromString
-import Data.Generator
-import Data.Monoid.Instances ()
-import Data.Monoid.Self
-
-import Data.Ratio
+#endif
 
+#ifdef M_CONTAINERS
 import qualified Data.Sequence as Seq
 import Data.Sequence (Seq)
+#endif
 
+#ifdef M_PARSEC
 import Text.Parsec.Prim
+#endif
 
+#ifdef X_OverloadedStrings
+import Data.Monoid.FromString
+#endif
+
 class Multiplicative m where
     one :: m
     times :: m -> m -> m
@@ -102,144 +108,130 @@
     one = Exp mempty
     Exp a `times` Exp b = Exp (a `mappend` b)
 
--- simple monoid transformer instances
 instance Multiplicative m => Multiplicative (Self m) where
     one = Self one  
     Self a `times` Self b = Self (a `times` b)
 
-instance Multiplicative m => Multiplicative (FromString m) where
-    one = FromString one
-    FromString a `times` FromString b = FromString (a `times` b)
-
--- the goal of this is that I can make left seminearrings out of any 'Alternative' wrapped around a monoid
--- in particular its useful for containers
-
+-- Monad instances
 instance Monoid m => Multiplicative [m] where
     one = return mempty
     times = liftM2 mappend
+instance Monoid m => Multiplicative (Maybe m) where
+    one = return mempty
+    times = liftM2 mappend
+instance Monoid n => Multiplicative (IO n) where
+    one = return mempty
+    times = liftM2 mappend
+instance Monoid n => Multiplicative (SST.ST s n) where
+    one = return mempty
+    times = liftM2 mappend
+instance Monoid n => Multiplicative (LST.ST s n) where
+    one = return mempty
+    times = liftM2 mappend
 
+-- Applicative instances
+instance Monoid n => Multiplicative (ZipList n) where
+    one = pure mempty
+    times = liftA2 mappend
+
+instance Monoid m => Multiplicative (Const m a) where
+    one = pure undefined
+    times = liftA2 undefined
+
+-- Numeric instances
+instance Multiplicative Int where
+    one = 1
+    times = (*)
+
+instance Multiplicative Integer where
+    one = 1
+    times = (*)
+
+instance Integral m => Multiplicative (Ratio m) where
+    one = 1
+    times = (*)
+
+#ifdef M_CONTAINERS
 instance Monoid m => Multiplicative (Seq m) where
     one = return mempty
     times = liftM2 mappend
+#endif
 
+#ifdef M_FINGERTREE
 -- and things that can't quite be a Monad in Haskell
 instance (Measured v m, Monoid m) => Multiplicative (FingerTree v m) where
     one = singleton mempty
     xss `times` yss = getSelf $ mapReduce (flip fmap' yss . mappend) xss
-
--- but it can at least serve as a canonical multiplication for any monad. 
-instance Monoid m => Multiplicative (Maybe m) where
-    one = return mempty
-    times = liftM2 mappend
+#endif
 
+#ifdef M_MTL
 instance Monoid m => Multiplicative (Identity m) where
     one = return mempty
     times = liftM2 mappend
-
 instance (Monoid m) => Multiplicative (Cont r m) where
     one = return mempty
     times = liftM2 mappend
-
 instance (Monoid w, Monoid m) => Multiplicative (SRWS.RWS r w s m) where
     one = return mempty
     times = liftM2 mappend
-
 instance (Monoid w, Monoid m) => Multiplicative (LRWS.RWS r w s m) where
     one = return mempty
     times = liftM2 mappend
-
 instance Monoid m => Multiplicative (SState.State s m) where
     one = return mempty
     times = liftM2 mappend
-
 instance Monoid m => Multiplicative (LState.State s m) where
     one = return mempty
     times = liftM2 mappend
-
 instance Monoid m => Multiplicative (Reader e m) where
     one = return mempty
     times = liftM2 mappend
-
 instance (Monoid w, Monoid m) => Multiplicative (SWriter.Writer w m) where
     one = return mempty
     times = liftM2 mappend
-
 instance (Monoid w, Monoid m) => Multiplicative (LWriter.Writer w m) where
     one = return mempty
     times = liftM2 mappend
-
 instance (Monad m, Monoid n) => Multiplicative (ContT r m n) where
     one = return mempty 
     times = liftM2 mappend
-
 instance (Monad m, Monoid w, Monoid n) => Multiplicative (SRWS.RWST r w s m n) where 
     one = return mempty 
     times = liftM2 mappend
-
 instance (Monad m, Monoid w, Monoid n) => Multiplicative (LRWS.RWST r w s m n) where 
     one = return mempty 
     times = liftM2 mappend
-
 instance (Monad m, Monoid n) => Multiplicative (SState.StateT s m n) where
     one = return mempty
     times = liftM2 mappend
-
 instance (Monad m, Monoid n) => Multiplicative (LState.StateT s m n) where
     one = return mempty
     times = liftM2 mappend
-
 instance (Monad m, Monoid n) => Multiplicative (ReaderT e m n) where
     one = return mempty
     times = liftM2 mappend
-
 instance (Monad m, Monoid w, Monoid n) => Multiplicative (SWriter.WriterT w m n) where
     one = return mempty 
     times = liftM2 mappend
-
 instance (Monad m, Monoid w, Monoid n) => Multiplicative (LWriter.WriterT w m n) where
     one = return mempty 
     times = liftM2 mappend
-
-instance Monoid n => Multiplicative (IO n) where
-    one = return mempty
-    times = liftM2 mappend
-
-instance Monoid n => Multiplicative (SST.ST s n) where
-    one = return mempty
-    times = liftM2 mappend
-
-instance Monoid n => Multiplicative (LST.ST s n) where
-    one = return mempty
-    times = liftM2 mappend
+#endif
 
+#ifdef M_STM
 instance Monoid n => Multiplicative (STM n) where
     one = return mempty
     times = liftM2 mappend
+#endif
 
+#ifdef M_PARSEC
 instance (Stream s m t, Monoid n) => Multiplicative (ParsecT s u m n) where
     one = return mempty
     times = liftM2 mappend
-
--- Applicative instances
-
-instance Monoid n => Multiplicative (ZipList n) where
-    one = pure mempty
-    times = liftA2 mappend
-
-instance Monoid m => Multiplicative (Const m a) where
-    one = pure undefined
-    times = liftA2 undefined
-
--- Numeric instances
-instance Multiplicative Int where
-    one = 1
-    times = (*)
-
-instance Multiplicative Integer where
-    one = 1
-    times = (*)
-
-instance Integral m => Multiplicative (Ratio m) where
-    one = 1
-    times = (*)
+#endif
 
+#ifdef X_OverloadedStrings 
+instance Multiplicative m => Multiplicative (FromString m) where
+    one = FromString one
+    FromString a `times` FromString b = FromString (a `times` b)
+#endif
diff --git a/Data/Monoid/Multiplicative/Sugar.hs b/Data/Monoid/Multiplicative/Sugar.hs
deleted file mode 100644
--- a/Data/Monoid/Multiplicative/Sugar.hs
+++ /dev/null
@@ -1,30 +0,0 @@
------------------------------------------------------------------------------
--- |
--- Module      :  Data.Monoid.Multiplicative.Sugar
--- Copyright   :  (c) Edward Kmett 2009
--- License     :  BSD-style
--- Maintainer  :  ekmett@gmail.com
--- Stability   :  experimental
--- Portability :  portable
---
--- Syntactic sugar for working with a 'Multiplicative' monoids that conflicts with names from the "Prelude".
---
--- > import Prelude hiding ((+),(*))
--- > import Data.Monoid.Multiplicative.Sugar
---
------------------------------------------------------------------------------
-
-module Data.Monoid.Multiplicative.Sugar
-    ( module Data.Monoid.Additive.Sugar
-    , module Data.Monoid.Multiplicative
-    , (*)
-    ) where
-
-import Data.Monoid.Additive.Sugar
-import Data.Monoid.Multiplicative
-import Prelude hiding ((*))
-
-infixl 7 *
-
-(*) :: Multiplicative r => r -> r -> r
-(*) = times
diff --git a/Data/Monoid/Ord.hs b/Data/Monoid/Ord.hs
--- a/Data/Monoid/Ord.hs
+++ b/Data/Monoid/Ord.hs
@@ -28,7 +28,7 @@
 
 import Control.Functor.Pointed
 import Data.Monoid.Reducer (Reducer, unit, Monoid, mappend, mempty)
-import Data.Ring.Semi
+import Data.Ring
 
 -- | The 'Monoid' @('max','minBound')@
 newtype Max a = Max { getMax :: a } deriving (Eq,Ord,Show,Read,Bounded)
diff --git a/Data/Monoid/Reducer.hs b/Data/Monoid/Reducer.hs
--- a/Data/Monoid/Reducer.hs
+++ b/Data/Monoid/Reducer.hs
@@ -1,10 +1,10 @@
-{-# LANGUAGE UndecidableInstances , FlexibleContexts , MultiParamTypeClasses , FlexibleInstances , GeneralizedNewtypeDeriving, TypeOperators, ScopedTypeVariables #-}
+{-# LANGUAGE UndecidableInstances , FlexibleContexts , MultiParamTypeClasses , FlexibleInstances , GeneralizedNewtypeDeriving, TypeOperators, ScopedTypeVariables, CPP #-}
 
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Data.Monoid.Reducer
 -- Copyright   :  (c) Edward Kmett 2009
--- License     :  BSD-style
+-- License     :  BSD3
 -- Maintainer  :  ekmett@gmail.com
 -- Stability   :  experimental
 -- Portability :  non-portable (MPTCs)
@@ -33,30 +33,31 @@
 import Data.Monoid.Instances ()
 
 import Data.Foldable
+
+#ifdef M_FINGERTREE
 import Data.FingerTree
+#endif
 
+#ifdef M_CONTAINERS
 import qualified Data.Sequence as Seq
 import Data.Sequence (Seq)
-
 import qualified Data.Set as Set
 import Data.Set (Set)
-
 import qualified Data.IntSet as IntSet
 import Data.IntSet (IntSet)
-
 import qualified Data.IntMap as IntMap
 import Data.IntMap (IntMap)
-
-import Data.Reflection
-
 import qualified Data.Map as Map
-
 import Data.Map (Map)
+#endif
 
-import Text.Parsec.Prim
+#ifdef M_REFLECTION
+import Data.Reflection
+#endif
 
---import qualified Data.BitSet as BitSet
---import Data.BitSet (BitSet)
+#ifdef M_PARSEC
+import Text.Parsec.Prim
+#endif
 
 -- | This type may be best read infix. A @c `Reducer` m@ is a 'Monoid' @m@ that maps
 -- values of type @c@ through @unit@ to values of type @m@. A @c@-'Reducer' may also
@@ -155,14 +156,19 @@
 instance Reducer a (Last a) where
     unit = Last . Just
 
+#ifdef M_FINGERTREE
 instance Measured v a => Reducer a (FingerTree v a) where
     unit = singleton
     cons = (<|)
     snoc = (|>) 
+#endif
 
+#ifdef M_PARSEC
 instance (Stream s m t, c `Reducer` a) => Reducer c (ParsecT s u m a) where
     unit = return . unit
+#endif
 
+#ifdef M_CONTAINERS
 instance Reducer a (Seq a) where
     unit = Seq.singleton
     cons = (Seq.<|)
@@ -189,12 +195,9 @@
     unit = uncurry Map.singleton
     cons = uncurry Map.insert
     snoc = flip . uncurry . Map.insertWith $ const id
-
-{-
-instance Enum a => Reducer a (BitSet a) where
-    unit m = BitSet.insert m BitSet.empty
--}
+#endif
 
+#ifdef M_REFLECTION
 data (m `ReducedBy` s) = Reduction { getReduction :: m } 
 
 instance Monoid m => Monoid (m `ReducedBy` s) where
@@ -203,3 +206,4 @@
 
 instance (s `Reflects` (a -> m), Monoid m) => Reducer a (m `ReducedBy` s) where
     unit = Reduction . reflect (undefined :: s)
+#endif
diff --git a/Data/Monoid/Sugar.hs b/Data/Monoid/Sugar.hs
new file mode 100644
--- /dev/null
+++ b/Data/Monoid/Sugar.hs
@@ -0,0 +1,41 @@
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Data.Monoid.Additive.Sugar
+-- Copyright   :  (c) Edward Kmett 2009
+-- License     :  BSD-style
+-- Maintainer  :  ekmett@gmail.com
+-- Stability   :  experimental
+-- Portability :  portable
+--
+-- Syntactic sugar for working with a 'Monoid' and 'Multiplicative' instances 
+-- that conflicts with names from the "Prelude".
+--
+-- > import Prelude hiding ((+),(*),(^))
+-- > import Data.Monoid.Sugar
+--
+-----------------------------------------------------------------------------
+--
+module Data.Monoid.Sugar
+    ( module Data.Monoid.Multiplicative
+    , module Data.Ring.Semi.Natural
+    , (+)
+    , (*)
+    , (^)
+    ) where
+
+import Prelude hiding ((*),(^),(+))
+import Data.Monoid.Multiplicative
+import Data.Ring.Semi.Natural
+import qualified Data.Monoid.Combinators as Monoid
+
+infixl 6 + 
+infixl 7 *
+
+(+) :: Monoid m => m -> m -> m 
+(+) = mappend
+
+(*) :: Multiplicative r => r -> r -> r
+(*) = times
+
+(^) :: Multiplicative r => r -> Natural -> r
+r ^ n = getLog (Monoid.replicate (Log r) n)
diff --git a/Data/Ring.hs b/Data/Ring.hs
--- a/Data/Ring.hs
+++ b/Data/Ring.hs
@@ -1,3 +1,5 @@
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, UndecidableInstances #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Data.Ring
@@ -7,22 +9,146 @@
 -- Stability   :  experimental
 -- Portability :  portable (instances use MPTCs)
 --
+--
+-- Defines left- and right- seminearrings. Every 'MonadPlus' wrapped around
+-- a 'Monoid' qualifies due to the distributivity of (>>=) over 'mplus'.
+--
+-- See <http://conway.rutgers.edu/~ccshan/wiki/blog/posts/WordNumbers1/>
+--
 -----------------------------------------------------------------------------
 
 module Data.Ring
     ( module Data.Group
-    , module Data.Ring.Semi
+    , Ringoid
+    , LeftSemiNearRing
+    , RightSemiNearRing
+    , SemiRing
     , Ring
+    , DivisionRing
+    , Field
     ) where
 
 import Data.Group
-import Data.Ring.Semi
 import Data.Monoid.Self
+
+#ifdef X_OverloadedStrings
 import Data.Monoid.FromString
+#endif
 
-class (Group a, SemiRing a) => Ring a
+#ifdef M_MTL
+import Control.Monad.Reader
+import qualified Control.Monad.RWS.Lazy as LRWS
+import qualified Control.Monad.RWS.Strict as SRWS
+import qualified Control.Monad.State.Lazy as LState
+import qualified Control.Monad.State.Strict as SState
+import qualified Control.Monad.Writer.Lazy as LWriter
+import qualified Control.Monad.Writer.Strict as SWriter
+#endif
 
+#ifdef M_FINGERTREE
+import Data.FingerTree
+#endif
+
+#ifdef M_CONTAINERS
+import qualified Data.Sequence as Seq
+import Data.Sequence (Seq)
+#endif
+
+#ifdef M_PARSEC
+import Text.Parsec.Prim
+#endif
+
+#ifdef X_OverloadedStrings
+import Data.Monoid.FromString
+#endif
+
+-- | @0@ annihilates `times`
+class (Multiplicative m, Monoid m) => Ringoid m
+instance Ringoid Integer
+instance Ringoid Int
+instance Ringoid m => Ringoid (Self m)
+instance Ringoid m => Ringoid (Dual m)
+instance Monoid m => Ringoid [m]
+instance Monoid m => Ringoid (Maybe m)
+
+-- | @a * (b + c) = (a * b) + (a * c)@
+class Ringoid m => LeftSemiNearRing m 
+instance LeftSemiNearRing m => LeftSemiNearRing (Self m)
+instance RightSemiNearRing m => LeftSemiNearRing (Dual m)
+
+-- | @(a + b) * c = (a * c) + (b * c)@
+class Ringoid m => RightSemiNearRing m 
+instance RightSemiNearRing m => RightSemiNearRing (Self m)
+instance LeftSemiNearRing m => RightSemiNearRing (Dual m)
+instance Monoid m => RightSemiNearRing [m]
+instance Monoid m => RightSemiNearRing (Maybe m)
+
+-- | A 'SemiRing' is an instance of both 'Multiplicative' and 'Monoid' where 
+--   'times' distributes over 'plus'.
+class (RightSemiNearRing a, LeftSemiNearRing a) => SemiRing a
+instance SemiRing r => SemiRing (Self r)
+instance SemiRing r => SemiRing (Dual r)
+
+class (Group a, SemiRing a) => Ring a
 instance Ring r => Ring (Self r)
-instance Ring r => Ring (FromString r)
-instance Ring r => Ring (ReducedBy r s)
 instance Ring r => Ring (Dual r)
+
+class (Ring a, MultiplicativeGroup a) => DivisionRing a
+instance DivisionRing r => DivisionRing (Self r)
+instance DivisionRing r => DivisionRing (Dual r)
+
+class (Ring a, MultiplicativeGroup a) => Field a
+instance Field f => Field (Dual f)
+instance Field f => Field (Self f)
+
+#ifdef M_REFLECTION
+instance Ringoid m => Ringoid (ReducedBy m s)
+instance LeftSemiNearRing m => LeftSemiNearRing (ReducedBy m s)
+instance RightSemiNearRing m => RightSemiNearRing (ReducedBy m s)
+instance SemiRing r => SemiRing (ReducedBy r s)
+instance Ring r => Ring (ReducedBy r s)
+instance DivisionRing r => DivisionRing (ReducedBy r s)
+instance Field f => Field (ReducedBy f s)
+#endif
+
+#ifdef M_PARSEC
+instance (Stream s m t, Monoid a) => Ringoid (ParsecT s u m a)
+instance (Stream s m t, Monoid a) => RightSemiNearRing (ParsecT s u m a)
+#endif
+
+#ifdef M_MTL
+instance (MonadPlus m, Monoid n) => Ringoid (SState.StateT s m n)
+instance (MonadPlus m, Monoid n) => Ringoid (LState.StateT s m n)
+instance (MonadPlus m, Monoid n) => Ringoid (ReaderT e m n)
+instance (MonadPlus m, Monoid w, Monoid n) => Ringoid (SRWS.RWST r w s m n)
+instance (MonadPlus m, Monoid w, Monoid n) => Ringoid (LRWS.RWST r w s m n)
+instance (MonadPlus m, Monoid w, Monoid n) => Ringoid (SWriter.WriterT w m n)
+instance (MonadPlus m, Monoid w, Monoid n) => Ringoid (LWriter.WriterT w m n)
+instance (MonadPlus m, Monoid n) => RightSemiNearRing (SState.StateT s m n)
+instance (MonadPlus m, Monoid n) => RightSemiNearRing (LState.StateT s m n)
+instance (MonadPlus m, Monoid n) => RightSemiNearRing (ReaderT e m n)
+instance (MonadPlus m, Monoid w, Monoid n) => RightSemiNearRing (SRWS.RWST r w s m n)
+instance (MonadPlus m, Monoid w, Monoid n) => RightSemiNearRing (LRWS.RWST r w s m n)
+instance (MonadPlus m, Monoid w, Monoid n) => RightSemiNearRing (SWriter.WriterT w m n)
+instance (MonadPlus m, Monoid w, Monoid n) => RightSemiNearRing (LWriter.WriterT w m n)
+#endif
+
+#ifdef M_FINGERTREE
+instance (Measured v m, Monoid m) => Ringoid (FingerTree v m)
+instance (Measured v m, Monoid m) => RightSemiNearRing (FingerTree v m)
+#endif
+
+#ifdef M_CONTAINERS
+instance Monoid m => Ringoid (Seq m)
+instance Monoid m => RightSemiNearRing (Seq m)
+#endif
+
+#ifdef X_OverloadedStrings
+instance Ringoid m => Ringoid (FromString m)
+instance RightSemiNearRing m => RightSemiNearRing (FromString m)
+instance LeftSemiNearRing m => LeftSemiNearRing (FromString m)
+instance SemiRing r => SemiRing (FromString r)
+instance Ring r => Ring (FromString r)
+instance DivisionRing r => DivisionRing (FromString r)
+instance Field f => Field (FromString f)
+#endif
diff --git a/Data/Ring/Algebra.hs b/Data/Ring/Algebra.hs
deleted file mode 100644
--- a/Data/Ring/Algebra.hs
+++ /dev/null
@@ -1,14 +0,0 @@
-{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, FlexibleContexts #-}
-module Data.Ring.Algebra
-    ( module Data.Ring.Module
-    , RAlgebra
-    ) where
-
-import Data.Ring.Module
-
--- | Algebra over a (near) (semi) ring.
---
--- @r *. (x * y) = (r *. x) * y = x * (r *. y)@
---
--- @(x * y) .* r = y * (x .* r) = (y .* r) * x@
-class (r `Module` m, Multiplicative m) => RAlgebra r m 
diff --git a/Data/Ring/Boolean.hs b/Data/Ring/Boolean.hs
--- a/Data/Ring/Boolean.hs
+++ b/Data/Ring/Boolean.hs
@@ -9,39 +9,77 @@
 -- Stability   :  experimental
 -- Portability :  non-portable (MPTCs)
 --
--- A Boolean 'Ring' over 'Bool'. Note well that the 'mappend' of this ring is
--- symmetric difference and not disjunction like you might expect. To get that 
--- you should use use 'Ord' from "Data.Ring.Semi.Ord.Order" on 'Bool' to get the '&&'/'||'-based 
--- distributive-lattice 'SemiRing'
+-- A Boolean 'Ring' over any Bits instance. Note well that the 'mappend' of this ring is xor.
+-- You should use use 'Ord' from "Data.Ring.Semi.Ord.Order" on 'Bool' to get the '&&'/'||'-based 
+-- distributive-lattice 'SemiRing'.
+--
+-- Also note that @gnegate = id@ in a Boolean Ring!
 -----------------------------------------------------------------------------
 
 module Data.Ring.Boolean
     ( module Data.Ring
-    , BoolRing(BoolRing, getBoolRing)
+    , Boolean(Boolean, getBoolean)
     ) where
 
+import Data.Bits
 import Data.Ring
+import Data.Ring.Module
+import Data.Ring.Semi.Natural
 import Data.Monoid.Reducer
-import Test.QuickCheck
+import Test.QuickCheck hiding ((.&.))
 
-newtype BoolRing = BoolRing { getBoolRing :: Bool } deriving (Eq,Ord,Show,Read,Arbitrary,CoArbitrary)
+newtype Boolean a = Boolean { getBoolean :: a } deriving (Eq,Ord,Show,Read,Arbitrary,CoArbitrary)
 
-instance Monoid BoolRing where
-    mempty = BoolRing False
-    BoolRing a `mappend` BoolRing b = BoolRing ((a || b) && not (a && b))
+-- | @xor@
+instance Bits a => Monoid (Boolean a) where
+    mempty = Boolean 0  
+    Boolean a `mappend` Boolean b = Boolean ((a .|. b) .&. complement (a .&. b))
 
-instance Group BoolRing where
-    gnegate = BoolRing . not . getBoolRing
+-- | @id@, since @x `xor` x = zero@
+instance Bits a => Group (Boolean a) where
+    gnegate = Boolean . id . getBoolean
 
-instance Multiplicative BoolRing where
-    one = BoolRing True
-    BoolRing a `times` BoolRing b = BoolRing (a && b)
+-- | @and@
+instance Bits a => Multiplicative (Boolean a) where
+    one = Boolean (complement 0)
+    Boolean a `times` Boolean b = Boolean (a .&. b)
 
-instance Ringoid BoolRing
-instance LeftSemiNearRing BoolRing
-instance RightSemiNearRing BoolRing
-instance SemiRing BoolRing
-instance Ring BoolRing
+-- | the boolean ring (using symmetric difference as addition) is a ring
+instance Bits a => Ringoid (Boolean a)
+instance Bits a => LeftSemiNearRing (Boolean a)
+instance Bits a => RightSemiNearRing (Boolean a)
+instance Bits a => SemiRing (Boolean a)
+instance Bits a => Ring (Boolean a)
 
-instance Reducer Bool BoolRing where
-    unit = BoolRing
+-- | it reduces boolean values
+instance Bits a => Reducer a (Boolean a) where
+    unit = Boolean
+
+-- | every monoid is a module over the naturals, boolring is idempotent
+instance Bits a => Module Natural (Boolean a)
+instance Bits a => LeftModule Natural (Boolean a) where
+    0 *. _ = mempty
+    _ *. m = m
+instance Bits a => RightModule Natural (Boolean a) where
+    _ .* 0 = mempty
+    m .* _ = m
+instance Bits a => Bimodule Natural (Boolean a)
+
+-- | every group is a module over the integers, boolring is idempotent
+instance Bits a => Module Integer (Boolean a)
+instance Bits a => LeftModule Integer (Boolean a) where
+    0 *. _ = mempty
+    _ *. m = m
+instance Bits a => RightModule Integer (Boolean a) where
+    _ .* 0 = mempty
+    m .* _ = m
+instance Bits a => Bimodule Integer (Boolean a)
+
+-- | every ring is a module over itself
+instance Bits a => Module (Boolean a) (Boolean a)
+instance Bits a => LeftModule (Boolean a) (Boolean a) where 
+    (*.) = times
+instance Bits a => RightModule (Boolean a) (Boolean a) where 
+    (.*) = times
+instance Bits a => Bimodule (Boolean a) (Boolean a)
+instance Bits a => Normed (Boolean a) (Boolean a) where mabs = id
diff --git a/Data/Ring/Module.hs b/Data/Ring/Module.hs
--- a/Data/Ring/Module.hs
+++ b/Data/Ring/Module.hs
@@ -16,11 +16,17 @@
 
 module Data.Ring.Module 
     ( module Data.Ring
-    , LeftModule
-    , (*.)
-    , RightModule
-    , (.*)
+    -- * R-Modules
     , Module
+    , LeftModule, (*.)
+    , RightModule, (.*)
+    , Bimodule
+    -- * R-Normed Modules
+    , Normed, mabs
+    -- * Vector Spaces
+    , VectorSpace
+    -- * R-Algebras
+    , Algebra
     ) where
 
 import Data.Ring
@@ -28,17 +34,46 @@
 
 -- import qualified Data.Monoid.Combinators as Monoid
 
+
+class (Ringoid r, Monoid m) => Module r m where
+
 -- | @ (x * y) *. m = x * (y *. m) @
-class (Monoid r, Multiplicative r, Monoid m) => LeftModule r m where
+class (Module r m) => LeftModule r m where
     (*.) :: r -> m -> m
     
 -- | @ (m .* x) * y = m .* (x * y) @
-class (Monoid r, Multiplicative r, Monoid m) => RightModule r m where
+class (Module r m) => RightModule r m where
     (.*) :: m -> r -> m
 
 -- | @ (x *. m) .* y = x *. (m .* y) @
-class (LeftModule r m, RightModule r m) => Module r m 
+class (LeftModule r m, RightModule r m) => Bimodule r m 
 
+class (Field f, Module f g) => VectorSpace f g
+
+-- | An r-normed module m satisfies:
+--
+-- (1) @mabs m >= 0@
+--
+-- 2 @mabs m == zero{-_r-} => m == zero{-_m-}@
+--
+-- 3 @mabs (m + n) <= mabs m + mabs n@
+--
+-- 4 @r * mabs m = mabs (r *. m) -- if m is an r-LeftModule@
+--
+-- 5 @mabs m * r = mabs (m .* r) -- if m is an r-RightModule@
+class Module r m => Normed r m where
+    mabs :: m -> r
+
+-- | Algebra over a (near) (semi) ring.
+-- @r *. (x * y) = (r *. x) * y = x * (r *. y)@
+-- @(x * y) .* r = y * (x .* r) = (y .* r) * x@
+class (r `Bimodule` m, Multiplicative m) => Algebra r m 
+
+instance (Module r m, Module r n) => Module r (m,n)
+instance (Module r m, Module r n, Module r o) => Module r (m,n,o)
+instance (Module r m, Module r n, Module r o, Module r p) => Module r (m,n,o,p)
+instance (Module r m, Module r n, Module r o, Module r p, Module r q) => Module r (m,n,o,p,q)
+
 instance (LeftModule r m, LeftModule r n) => LeftModule r (m,n) where
     r *. (m,n) = (r *. m, r *. n)
 instance (LeftModule r m, LeftModule r n, LeftModule r o) => LeftModule r (m,n,o) where
@@ -57,11 +92,10 @@
 instance (RightModule r m, RightModule r n, RightModule r o, RightModule r p, RightModule r q ) => RightModule r (m,n,o,p,q) where
     (m,n,o,p,q) .* r = (m .* r, n .* r, o .* r, p .* r, q .* r)
 
-instance (Module r m, Module r n) => Module r (m,n)
-instance (Module r m, Module r n, Module r o) => Module r (m,n,o)
-instance (Module r m, Module r n, Module r o, Module r p) => Module r (m,n,o,p)
-instance (Module r m, Module r n, Module r o, Module r p, Module r q) => Module r (m,n,o,p,q)
-
+instance (Bimodule r m, Bimodule r n) => Bimodule r (m,n)
+instance (Bimodule r m, Bimodule r n, Bimodule r o) => Bimodule r (m,n,o)
+instance (Bimodule r m, Bimodule r n, Bimodule r o, Bimodule r p) => Bimodule r (m,n,o,p)
+instance (Bimodule r m, Bimodule r n, Bimodule r o, Bimodule r p, Bimodule r q) => Bimodule r (m,n,o,p,q)
 
 -- we want an absorbing 0, for that we need a seminearring and a notion of equality
 instance (HasUnionWith f, Ord r, Eq r, RightSemiNearRing r) => LeftModule r (UnionWith f r) where
diff --git a/Data/Ring/Module/AutomaticDifferentiation.hs b/Data/Ring/Module/AutomaticDifferentiation.hs
--- a/Data/Ring/Module/AutomaticDifferentiation.hs
+++ b/Data/Ring/Module/AutomaticDifferentiation.hs
@@ -26,10 +26,10 @@
 
 data D s r m = D r m deriving (Show,Read)
 
-lift :: (r `Module` m) => r -> D s r m
+lift :: (r `Bimodule` m) => r -> D s r m
 lift x = D x zero
 
-infinitesimal :: (r `Module` m, Ringoid m) => D s r m
+infinitesimal :: (r `Bimodule` m, Ringoid m) => D s r m
 infinitesimal = D zero one
 
 instance Eq r => Eq (D s r m) where
@@ -38,15 +38,15 @@
 instance Ord r => Ord (D s r m) where
     D x _ `compare` D y _ = compare x y
 
-instance (r `Module` m) => Monoid (D s r m) where
+instance (r `Bimodule` m) => Monoid (D s r m) where
     mempty = D mempty mempty
     D x m `mappend` D y n = D (x `mappend` y) (m `mappend` n)
 
-instance (r `Module` m) => Multiplicative (D s r m) where
+instance (r `Bimodule` m) => Multiplicative (D s r m) where
     one = D one zero
     D x m `times` D y n = D (x `times` y) (x *. n `plus` m .* y)
 
-instance (Group r, r `Module` m, Group m) => Group (D s r m) where
+instance (Group r, r `Bimodule` m, Group m) => Group (D s r m) where
     gnegate (D x m) = D (gnegate x) (gnegate m)
     D x m `minus` D y n = D (x `minus` y) (m `minus` n)
     D x m `gsubtract` D y n = D (x `gsubtract` y) (m `gsubtract` n)
@@ -64,13 +64,13 @@
     recip (D x x') = D (recip x) (-x'/x/x)
     fromRational x = D (fromRational x) 0
 
-instance (Ringoid r, r `Module` m) => Ringoid (D s r m)
-instance (LeftSemiNearRing r, Module r m) => LeftSemiNearRing (D s r m)
-instance (RightSemiNearRing r, Module r m) => RightSemiNearRing (D s r m)
-instance (SemiRing r, r `Module` m) => SemiRing (D s r m)
-instance (Ring r, r `Module` m, Group m) => Ring (D s r m)
+instance (Ringoid r, r `Bimodule` m) => Ringoid (D s r m)
+instance (LeftSemiNearRing r, Bimodule r m) => LeftSemiNearRing (D s r m)
+instance (RightSemiNearRing r, Bimodule r m) => RightSemiNearRing (D s r m)
+instance (SemiRing r, r `Bimodule` m) => SemiRing (D s r m)
+instance (Ring r, r `Bimodule` m, Group m) => Ring (D s r m)
 
-instance (r `Module` m, c `Reducer` r, c `Reducer` m) => Reducer c (D s r m) where
+instance (r `Bimodule` m, c `Reducer` r, c `Reducer` m) => Reducer c (D s r m) where
     unit c = D (unit c) (unit c)
     c `cons` D x m = D (c `cons` x) (c `cons` m)
     D x m `snoc` c = D (x `snoc` c) (m `snoc` c)
@@ -82,6 +82,6 @@
 instance (CoArbitrary r, CoArbitrary m) => CoArbitrary (D s r m) where
     coarbitrary (D r m) = coarbitrary r >< coarbitrary m
 
-d :: (r `Module` m, Ringoid m) => (forall s. D s r m -> D s r m) -> (r,m)
+d :: (r `Bimodule` m, Ringoid m) => (forall s. D s r m -> D s r m) -> (r,m)
 d f = (y,y') where D y y' = f infinitesimal
 
diff --git a/Data/Ring/Semi.hs b/Data/Ring/Semi.hs
deleted file mode 100644
--- a/Data/Ring/Semi.hs
+++ /dev/null
@@ -1,30 +0,0 @@
-{-# LANGUAGE MultiParamTypeClasses #-}
------------------------------------------------------------------------------
--- |
--- Module      :  Data.Ring.Semi
--- Copyright   :  (c) Edward Kmett 2009
--- License     :  BSD-style
--- Maintainer  :  ekmett@gmail.com
--- Stability   :  experimental
--- Portability :  non-portable (MPTCs)
---
---
------------------------------------------------------------------------------
-
-module Data.Ring.Semi
-    ( module Data.Ring.Semi.Near
-    , SemiRing
-    ) where
-
-import Data.Ring.Semi.Near
-import Data.Monoid.Self
-import Data.Monoid.FromString
-
--- | A 'SemiRing' is an instance of both 'Multiplicative' and 'Monoid' where 
---   'times' distributes over 'plus'.
-class (RightSemiNearRing a, LeftSemiNearRing a) => SemiRing a
-
-instance SemiRing r => SemiRing (Self r)
-instance SemiRing r => SemiRing (FromString r)
-instance SemiRing r => SemiRing (ReducedBy r s)
-instance SemiRing r => SemiRing (Dual r)
diff --git a/Data/Ring/Semi/BitSet.hs b/Data/Ring/Semi/BitSet.hs
--- a/Data/Ring/Semi/BitSet.hs
+++ b/Data/Ring/Semi/BitSet.hs
@@ -13,13 +13,14 @@
 -- Replacement for "Data.BitSet" extended to handle enumerations where fromEnum
 -- can return negative values, support efficient intersection and union
 -- and allow complementing of the set with respect to the bounds of the
--- enumeration
+-- enumeration. Treated as a Boolean semiring over `.&.`/`.|.`. To get a
+-- 'Boolean' 'Ring', use @'Boolean' ('BitSet' a)@.
 --
 -------------------------------------------------------------------------------
 
 module Data.Ring.Semi.BitSet
     ( module Data.Monoid.Reducer
-    , module Data.Ring.Semi
+    , module Data.Ring
     -- * BitSet
     , BitSet
     -- * Manipulation
@@ -43,15 +44,14 @@
     ) where
 
 import Prelude hiding ( null, exponent, toInteger, foldl, foldr, foldl1, foldr1 )
-import Data.Bits hiding ( complement )
-import qualified Data.Bits as Bits
+import Data.Bits
 import Data.Foldable hiding ( toList )
 import Data.Data
 import Data.Ring.Semi.Natural
-import Data.Ring.Semi
+import Data.Ring
 import Data.Monoid.Reducer
 import Data.Generator
-import Data.Ring.Algebra
+import Data.Ring.Module
 import Text.Read
 import Text.Show
 
@@ -128,23 +128,18 @@
 
 -- | /O(d)/ A 'BitSet' containing every member of the enumeration of @a@.
 full :: (Enum a, Bounded a) => BitSet a
-full = complement empty 
+full = complement' empty 
 {-# INLINE full #-}
 
--- | /O(d)/ Complements a 'BitSet' with respect to the bounds of @a@. Preserves order of 'null' and 'size'
-complement :: (Enum a, Bounded a) => BitSet a -> BitSet a 
-complement r@(BS a b c l h m _ f) = BS (Bits.complement b) (Bits.complement a) (Bits.complement c) l h (Bits.complement m) u f where
-    u = (fromEnum (minBound `asArgTypeOf` r), fromEnum (maxBound `asArgTypeOf` r))
-{-# INLINE complement #-}
 
 -- | /O(d)/ unsafe internal method: complement a set that has already been complemented at least once.
 recomplement :: BitSet a -> BitSet a 
-recomplement (BS a b c l h m u f) = BS (Bits.complement b) (Bits.complement a) (Bits.complement c) l h (Bits.complement m) u f
+recomplement (BS a b c l h m u f) = BS (complement b) (complement a) (complement c) l h (complement m) u f
 {-# INLINE recomplement #-}
 
 -- | /O(d)/ unsafe internal method: complement a set that has already been complemented at least once.
 pseudoComplement :: BitSet a -> (Int,Int) -> BitSet a 
-pseudoComplement (BS a b c l h m _ f) u = BS (Bits.complement b) (Bits.complement a) (Bits.complement c) l h (Bits.complement m) u f
+pseudoComplement (BS a b c l h m _ f) u = BS (complement b) (complement a) (complement c) l h (complement m) u f
 {-# INLINE pseudoComplement #-}
 
 -- | /O(d * n)/ Make a 'BitSet' from a list of items.
@@ -184,7 +179,7 @@
 -- | /O(d)/ Delete a single item from the 'BitSet'. Preserves order of 'null' and 'size'
 delete :: Enum a => a -> BitSet a -> BitSet a
 delete x r@(BS a b c l h m u _) 
-    | m < 0, e < l = bs (a+1) (b+1) (c+1) e h (shiftL m (l - e) .&. Bits.complement 1) u
+    | m < 0, e < l = bs (a+1) (b+1) (c+1) e h (shiftL m (l - e) .&. complement 1) u
     | m < 0, e > h = bs (a+1) (b+1) (c+1) l p (clearBit m p) u
     | b == 0       = r
     | a == -1      = pseudoComplement (singleton x) u
@@ -269,7 +264,7 @@
     | h' < l = x
     | otherwise = bs (max (a - b') 0) a (recount m'') l h m'' u''
     where 
-        m'' = m .&. shift (Bits.complement m') (l' - l)
+        m'' = m .&. shift (complement m') (l' - l)
 {-# INLINE diff #-}
 
 -- | /O(d)/ Remove all elements present in the second bitset from the first
@@ -317,7 +312,7 @@
 -- | /O(d)/
 recount :: Integer -> Int
 recount !n 
-    | n < 0     = Bits.complement (recount (Bits.complement n))
+    | n < 0     = complement (recount (complement n))
     | otherwise = recount' 0 0 
     where
         h = hwm n
@@ -404,20 +399,62 @@
 instance (Bounded a, Enum a) => SemiRing (BitSet a)
 
 -- idempotent monoid
+instance Enum a => Module Natural (BitSet a)
 instance Enum a => LeftModule Natural (BitSet a) where
     0 *. _ = empty
     _ *. m = m
 instance Enum a => RightModule Natural (BitSet a) where
     _ .* 0 = empty
     m .* _ = m
-instance Enum a => Module Natural (BitSet a)
+instance Enum a => Bimodule Natural (BitSet a)
+instance (Bounded a, Enum a) => Algebra Natural (BitSet a)
 
+instance (Bounded a, Enum a) => Module (BitSet a) (BitSet a)
 instance (Bounded a, Enum a) => LeftModule (BitSet a) (BitSet a) where (*.) = times
 instance (Bounded a, Enum a) => RightModule (BitSet a) (BitSet a) where (.*) = times
-instance (Bounded a, Enum a) => Module (BitSet a) (BitSet a)
-
-instance (Bounded a, Enum a) => RAlgebra Natural (BitSet a)
+instance (Bounded a, Enum a) => Bimodule (BitSet a) (BitSet a)
+instance (Bounded a, Enum a) => Algebra (BitSet a) (BitSet a)
     
 instance Generator (BitSet a) where
     type Elem (BitSet a) = a
     mapReduce f = mapReduce f . toList
+
+instance (Show a, Bounded a, Enum a) => Num (BitSet a) where
+    (+) = union
+    (-) = difference
+    (*) = intersection
+    fromInteger m = r where
+        r = BS c c c 0 (hwm m) m u toEnum where
+        c = recount m
+        u = (fromEnum (minBound `asArgTypeOf` r), fromEnum (maxBound `asArgTypeOf` r))
+    abs b | mantissa b < 0 = recomplement b
+          | otherwise = b
+    signum = error "BitSet.signum undefined"
+
+instance (Show a, Bounded a, Enum a) => Bits (BitSet a) where
+    (.&.) = intersection
+    (.|.) = union
+    a `xor` b = (a .|. b) .&. complement (a .&. b)
+
+    -- | /O(d)/ Complements a 'BitSet' with respect to the bounds of @a@. Preserves order of 'null' and 'size'
+    complement r@(BS a b c l h m _ _) = BS (complement b) (complement a) (complement c) l h (complement m) u toEnum where
+        u = (fromEnum (minBound `asArgTypeOf` r), fromEnum (maxBound `asArgTypeOf` r))
+    {-# INLINE complement #-}
+    {-
+    shift (BS a b c l h m _ f) n = BS a b c ((l + r) `max` uh) ((h + r) `max` uh) m (ul,uh) toEnum) where
+        ul = fromEnum (minBound `asArgTypeOf` r)
+        uh = fromEnum (maxBound `asArgTypeOf` r)
+    -}
+    shift = error "BitSet.shift undefined"
+    rotate = error "BitSet.rotate undefined"
+    bit = singleton . toEnum
+    setBit s b = s `union` singleton (toEnum b)
+    clearBit s b = s `difference` singleton (toEnum b)
+    complementBit s b = s `xor` singleton (toEnum b)
+    testBit s b = member (toEnum b) s 
+    bitSize r = fromEnum (maxBound `asArgTypeOf` r) - fromEnum (minBound `asArgTypeOf` r)
+    isSigned _ = True
+
+complement' :: (Bounded a, Enum a) => BitSet a -> BitSet a
+complement' r@(BS a b c l h m _ _) = BS (complement b) (complement a) (complement c) l h (complement m) u toEnum where
+    u = (fromEnum (minBound `asArgTypeOf` r), fromEnum (maxBound `asArgTypeOf` r))
diff --git a/Data/Ring/Semi/Kleene.hs b/Data/Ring/Semi/Kleene.hs
--- a/Data/Ring/Semi/Kleene.hs
+++ b/Data/Ring/Semi/Kleene.hs
@@ -1,10 +1,10 @@
 module Data.Ring.Semi.Kleene 
-    ( module Data.Ring.Semi
+    ( module Data.Ring
     , KleeneAlgebra
     , star
     ) where
 
-import Data.Ring.Semi
+import Data.Ring
 
 class SemiRing r => KleeneAlgebra r where
     star :: r -> r
diff --git a/Data/Ring/Semi/Natural.hs b/Data/Ring/Semi/Natural.hs
--- a/Data/Ring/Semi/Natural.hs
+++ b/Data/Ring/Semi/Natural.hs
@@ -15,16 +15,17 @@
 -----------------------------------------------------------------------------
 
 module Data.Ring.Semi.Natural
-    ( module Data.Ring.Semi
+    ( module Data.Ring
     , Natural
-    , natural
+    , toNatural
+    , fromNatural
     ) where
 
 import Prelude hiding (id,(.))
 import Numeric (readDec, showInt)
 import Control.Applicative
 import Control.Monad
-import Data.Ring.Semi
+import Data.Ring
 import qualified Data.Monoid.Combinators as Monoid
 -- import Data.Word
 import Data.Monoid.Monad
@@ -32,16 +33,26 @@
 import Data.Monoid.Multiplicative
 import Data.Monoid.Categorical
 import Data.Monoid.Self
-import Data.Monoid.FromString
 import Data.Monoid.Lexical.SourcePosition
 import Data.Monoid.Lexical.UTF8.Decoder
 import Data.Generator.Free
+
+#ifdef M_CONTAINERS
+-- used with Seq
 import Data.Generator.Compressive.RLE
 import Data.Sequence (Seq)
+#endif
 
-natural :: Integer -> Natural
-natural = fromInteger
+#ifdef X_OverloadedStrings
+import Data.Monoid.FromString
+#endif
 
+toNatural :: Integer -> Natural
+toNatural = fromInteger
+
+fromNatural :: Ringoid r => Natural -> r
+fromNatural = Monoid.replicate one . getNatural
+
 newtype Natural = Natural { getNatural :: Integer } 
     deriving (Eq,Ord)
 
@@ -172,11 +183,6 @@
 instance Monoid m => RightModule Natural (Dual m) where (.*) = Monoid.replicate
 instance Monoid m => Module Natural (Dual m)
 
--- FromString
-instance Monoid m => LeftModule  Natural (FromString m) where (*.) = flip Monoid.replicate
-instance Monoid m => RightModule Natural (FromString m) where (.*) = Monoid.replicate
-instance Monoid m => Module Natural (FromString m)
-
 -- Self
 instance Monoid m => LeftModule  Natural (Self m) where (*.) = flip Monoid.replicate
 instance Monoid m => RightModule Natural (Self m) where (.*) = Monoid.replicate
@@ -187,11 +193,6 @@
 instance RightModule Natural (Free a) where (.*) = Monoid.replicate
 instance Module Natural (Free a)
 
--- RLE Seq
-instance Eq a => LeftModule  Natural (RLE Seq a) where (*.) = flip Monoid.replicate
-instance Eq a => RightModule Natural (RLE Seq a) where (.*) = Monoid.replicate
-instance Eq a => Module Natural (RLE Seq a)
-
 -- Categorical
 instance Category k => LeftModule Natural  (GEndo k a) where (*.) = flip Monoid.replicate
 instance Category k => RightModule Natural (GEndo k a) where (.*) = Monoid.replicate
@@ -246,6 +247,19 @@
 instance Multiplicative m => RightModule Natural (Log m) where (.*) = Monoid.replicate
 instance Multiplicative m => Module Natural (Log m) 
 
+#ifdef M_CONTAINERS
+-- RLE Seq
+instance Eq a => LeftModule  Natural (RLE Seq a) where (*.) = flip Monoid.replicate
+instance Eq a => RightModule Natural (RLE Seq a) where (.*) = Monoid.replicate
+instance Eq a => Module Natural (RLE Seq a)
+#endif
+
+#ifdef X_OverloadedStrings
+-- FromString
+instance Monoid m => LeftModule  Natural (FromString m) where (*.) = flip Monoid.replicate
+instance Monoid m => RightModule Natural (FromString m) where (.*) = Monoid.replicate
+instance Monoid m => Module Natural (FromString m)
+#endif
 
 -- TODO
 --
diff --git a/Data/Ring/Semi/Near.hs b/Data/Ring/Semi/Near.hs
deleted file mode 100644
--- a/Data/Ring/Semi/Near.hs
+++ /dev/null
@@ -1,93 +0,0 @@
-{-# OPTIONS_GHC -fno-warn-orphans #-}
-{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, UndecidableInstances #-}
-
------------------------------------------------------------------------------
--- |
--- Module      :  Data.Ring.Semi.Near
--- Copyright   :  (c) Edward Kmett 2009
--- License     :  BSD-style
--- Maintainer  :  ekmett@gmail.com
--- Stability   :  experimental
--- Portability :  portable (instances use MPTCs)
---
--- Defines left- and right- seminearrings. Every 'MonadPlus' wrapped around
--- a 'Monoid' qualifies due to the distributivity of (>>=) over 'mplus'.
---
--- See <http://conway.rutgers.edu/~ccshan/wiki/blog/posts/WordNumbers1/>
---
------------------------------------------------------------------------------
-
-module Data.Ring.Semi.Near
-    ( module Data.Monoid.Multiplicative
-    , Ringoid
-    , LeftSemiNearRing
-    , RightSemiNearRing
-    ) where
-
-import Control.Monad.Reader
-
-import qualified Control.Monad.RWS.Lazy as LRWS
-import qualified Control.Monad.RWS.Strict as SRWS
-
-import qualified Control.Monad.State.Lazy as LState
-import qualified Control.Monad.State.Strict as SState
-
-import qualified Control.Monad.Writer.Lazy as LWriter
-import qualified Control.Monad.Writer.Strict as SWriter
-
-import Data.Monoid.Multiplicative
-import Data.FingerTree
-import Data.Monoid.FromString
-import Data.Monoid.Self
-import Data.Generator
-
-import qualified Data.Sequence as Seq
-import Data.Sequence (Seq)
-
-import Text.Parsec.Prim
-
--- | @0@ annihilates `times`
-class (Multiplicative m, Monoid m) => Ringoid m
-instance Ringoid m => Ringoid (Self m)
-instance Ringoid m => Ringoid (FromString m)
-instance Ringoid m => Ringoid (ReducedBy m s)
-instance Ringoid m => Ringoid (Dual m)
-instance (Measured v m, Monoid m) => Ringoid (FingerTree v m)
-instance Monoid m => Ringoid [m]
-instance Monoid m => Ringoid (Maybe m)
-instance Monoid m => Ringoid (Seq m)
-instance (Stream s m t, Monoid a) => Ringoid (ParsecT s u m a)
-instance (MonadPlus m, Monoid n) => Ringoid (SState.StateT s m n)
-instance (MonadPlus m, Monoid n) => Ringoid (LState.StateT s m n)
-instance (MonadPlus m, Monoid n) => Ringoid (ReaderT e m n)
-instance (MonadPlus m, Monoid w, Monoid n) => Ringoid (SRWS.RWST r w s m n)
-instance (MonadPlus m, Monoid w, Monoid n) => Ringoid (LRWS.RWST r w s m n)
-instance (MonadPlus m, Monoid w, Monoid n) => Ringoid (SWriter.WriterT w m n)
-instance (MonadPlus m, Monoid w, Monoid n) => Ringoid (LWriter.WriterT w m n)
-
--- | @a * (b + c) = (a * b) + (a * c)@
-class Ringoid m => LeftSemiNearRing m 
-instance LeftSemiNearRing m => LeftSemiNearRing (Self m)
-instance LeftSemiNearRing m => LeftSemiNearRing (FromString m)
-instance LeftSemiNearRing m => LeftSemiNearRing (ReducedBy m s)
-instance RightSemiNearRing m => LeftSemiNearRing (Dual m)
-
--- | @(a + b) * c = (a * c) + (b * c)@
-class Ringoid m => RightSemiNearRing m 
-instance RightSemiNearRing m => RightSemiNearRing (Self m)
-instance RightSemiNearRing m => RightSemiNearRing (FromString m)
-instance RightSemiNearRing m => RightSemiNearRing (ReducedBy m s)
-instance LeftSemiNearRing m => RightSemiNearRing (Dual m)
-instance (Measured v m, Monoid m) => RightSemiNearRing (FingerTree v m)
-instance Monoid m => RightSemiNearRing [m]
-instance Monoid m => RightSemiNearRing (Maybe m)
-instance Monoid m => RightSemiNearRing (Seq m)
-instance (Stream s m t, Monoid a) => RightSemiNearRing (ParsecT s u m a)
-instance (MonadPlus m, Monoid n) => RightSemiNearRing (SState.StateT s m n)
-instance (MonadPlus m, Monoid n) => RightSemiNearRing (LState.StateT s m n)
-instance (MonadPlus m, Monoid n) => RightSemiNearRing (ReaderT e m n)
-instance (MonadPlus m, Monoid w, Monoid n) => RightSemiNearRing (SRWS.RWST r w s m n)
-instance (MonadPlus m, Monoid w, Monoid n) => RightSemiNearRing (LRWS.RWST r w s m n)
-instance (MonadPlus m, Monoid w, Monoid n) => RightSemiNearRing (SWriter.WriterT w m n)
-instance (MonadPlus m, Monoid w, Monoid n) => RightSemiNearRing (LWriter.WriterT w m n)
-
diff --git a/Data/Ring/Semi/Near/Trie.hs b/Data/Ring/Semi/Near/Trie.hs
--- a/Data/Ring/Semi/Near/Trie.hs
+++ b/Data/Ring/Semi/Near/Trie.hs
@@ -1,20 +1,16 @@
 {-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, FlexibleContexts #-}
 module Data.Ring.Semi.Near.Trie 
-    ( module Data.Ring.Semi.Near
+    ( module Data.Ring
     , Trie(Trie, total, label, children)
     , singleton
     , empty
     , null
     ) where
     
-
 import Data.Map (Map)
 import qualified Data.Map as Map
---import Data.Monoid.Multiplicative
---import Data.Monoid.Reducer
 import Data.Monoid.Union hiding (empty)
---import Data.Ring.Module
-import Data.Ring.Semi.Near
+import Data.Ring
 import Prelude hiding (null)
 
 singleton :: (Ord c, c `Reducer` m) => c -> Trie c m 
diff --git a/Data/Ring/Semi/Ord.hs b/Data/Ring/Semi/Ord.hs
--- a/Data/Ring/Semi/Ord.hs
+++ b/Data/Ring/Semi/Ord.hs
@@ -12,20 +12,33 @@
 ------------------------------------------------------------------------
 
 module Data.Ring.Semi.Ord
-    ( module Data.Ring.Semi
+    ( module Data.Ring
     , Order(Order,getOrder)
     , Priority(MinBound,Priority,MaxBound)
     ) where
 
-import Test.QuickCheck
 -- import Control.Applicative
 import Control.Functor.Pointed
-import Data.Ring.Semi
+import Data.Ring
 import Data.Monoid.Ord
 import Data.Monoid.Reducer
 
+#ifdef M_QUICKCHECK
+import Test.QuickCheck
+#endif
+
 -- | A 'SemiRing' using a type's built-in Bounded instance.
-newtype Order a = Order { getOrder :: a } deriving (Eq,Ord,Read,Show,Bounded,Arbitrary,CoArbitrary)
+newtype Order a = Order { getOrder :: a } deriving 
+    ( Eq
+    , Ord
+    , Read
+    , Show
+    , Bounded
+#ifdef M_QUICKCHECK
+    , Arbitrary
+    , CoArbitrary
+#endif
+    )
 
 instance (Bounded a, Ord a) => Monoid (Order a) where
     mappend = max
@@ -78,6 +91,7 @@
   _          `max` MaxBound   = MaxBound
   MaxBound   `max` _          = MaxBound
 
+#ifdef M_QUICKCHECK
 instance Arbitrary a => Arbitrary (Priority a) where
   arbitrary = frequency [ (1 ,return MinBound)
                         , (10, fmap Priority arbitrary)
@@ -90,6 +104,7 @@
   coarbitrary MinBound     = variant (0 :: Int)
   coarbitrary (Priority a) = variant (1 :: Int) . coarbitrary a
   coarbitrary MaxBound     = variant (2 :: Int)
+#endif
 
 instance Ord a => Monoid (Priority a) where
     mappend = max
diff --git a/Data/Ring/Semi/Tropical.hs b/Data/Ring/Semi/Tropical.hs
--- a/Data/Ring/Semi/Tropical.hs
+++ b/Data/Ring/Semi/Tropical.hs
@@ -12,18 +12,24 @@
 
 module Data.Ring.Semi.Tropical
     ( module Data.Monoid.Reducer
-    , module Data.Ring.Semi
+    , module Data.Ring
     -- * Tropical Semirings
     , infinity
     , Tropical(Tropical,getTropical)
     ) where
 
-import Test.QuickCheck
 import Control.Functor.Pointed
-import Data.Monoid.Reducer (Reducer, unit, Monoid, mappend, mempty)
-import Data.Ring.Semi
+import Data.Monoid.Reducer
+import Data.Monoid.Combinators as Monoid
+import Data.Ring.Semi.Natural
+import Data.Ring
+import Data.Ring.Module
 import Data.Monoid.Ord hiding (infinity)
 
+#ifdef M_QUICKCHECK
+import Test.QuickCheck
+#endif
+
 infinity :: Tropical a
 infinity = Tropical Nothing
 
@@ -34,12 +40,19 @@
 --
 --   <http://hal.archives-ouvertes.fr/docs/00/11/37/79/PDF/Tropical.pdf>
 
-newtype Tropical a = Tropical { getTropical :: Maybe a } 
-    deriving (Eq,Show,Read,Arbitrary,CoArbitrary)
+newtype Tropical a = Tropical { getTropical :: Maybe a } deriving 
+    ( Eq
+    , Show
+    , Read
+#ifdef M_QUICKCHECK
+    , Arbitrary
+    , CoArbitrary
+#endif
+    )
 
 instance Ord a => Ord (Tropical a) where
     Tropical Nothing  `compare` Tropical Nothing  = EQ
-    Tropical Nothing  `compare` _                    = GT
+    Tropical Nothing  `compare` _                 = GT
     _                 `compare` Tropical Nothing  = LT
     Tropical (Just a) `compare` Tropical (Just b) = a `compare` b
 
@@ -72,3 +85,13 @@
 instance (Ord a, Num a) => LeftSemiNearRing (Tropical a)
 instance (Ord a, Num a) => RightSemiNearRing (Tropical a)
 instance (Ord a, Num a) => SemiRing (Tropical a)
+
+instance (Ord a, Num a) => Module (Tropical a) (Tropical a)
+instance (Ord a, Num a) => LeftModule (Tropical a) (Tropical a) where (*.) = times
+instance (Ord a, Num a) => RightModule (Tropical a) (Tropical a) where (.*) = times
+instance (Ord a, Num a) => Bimodule (Tropical a) (Tropical a)
+
+instance (Ord a, Num a) => Module Natural (Tropical a)
+instance (Ord a, Num a) => LeftModule Natural (Tropical a) where (*.) = flip Monoid.replicate
+instance (Ord a, Num a) => RightModule Natural (Tropical a) where (.*) = Monoid.replicate
+instance (Ord a, Num a) => Bimodule Natural (Tropical a)
diff --git a/Data/Ring/Sugar.hs b/Data/Ring/Sugar.hs
deleted file mode 100644
--- a/Data/Ring/Sugar.hs
+++ /dev/null
@@ -1,23 +0,0 @@
------------------------------------------------------------------------------
--- |
--- Module      :  Data.Ring.Sugar
--- Copyright   :  (c) Edward Kmett 2009
--- License     :  BSD-style
--- Maintainer  :  ekmett@gmail.com
--- Stability   :  experimental
--- Portability :  portable
---
--- Syntactic sugar for working with rings that conflicts with names from the "Prelude".
---
--- > import Prelude hiding ((-), (+), (*), negate, subtract)
--- > import Data.Ring.Sugar
---
------------------------------------------------------------------------------
-
-module Data.Ring.Sugar 
-    ( module Data.Monoid.Multiplicative.Sugar
-    , module Data.Ring.Semi.Near
-    ) where
-
-import Data.Monoid.Multiplicative.Sugar
-import Data.Ring.Semi.Near
diff --git a/Data/Set/Unboxed.hs b/Data/Set/Unboxed.hs
deleted file mode 100644
--- a/Data/Set/Unboxed.hs
+++ /dev/null
@@ -1,1258 +0,0 @@
-{-# LANGUAGE TypeFamilies, CPP, ViewPatterns #-}
-
-{------------------------------------------------------------------------------
--- |
--- Module      :  Data.Set.Unboxed
--- Copyright   :  (c) Edward Kmett 2009
---                (c) Daan Leijen 2002
--- License     :  BSD-style
--- Maintainer  :  ekmett@gmail.com
--- Stability   :  experimental
--- Portability :  non-portable (type families, view patterns)
---
--- An efficient implementation of sets.
---
--- Since many function names (but not the type name) clash with
--- "Prelude" names, this module is usually imported @qualified@, e.g.
---
--- >  import Data.Set.Unboxed (USet)
--- >  import qualified Data.Set.Unboxed as USet
---
--- The implementation of 'USet' is based on /size balanced/ binary trees (or
--- trees of /bounded balance/) as described by:
---
---    * Stephen Adams, \"/Efficient sets: a balancing act/\",
---  Journal of Functional Programming 3(4):553-562, October 1993,
---  <http://www.swiss.ai.mit.edu/~adams/BB/>.
---
---    * J. Nievergelt and E.M. Reingold,
---  \"/Binary search trees of bounded balance/\",
---  SIAM journal of computing 2(1), March 1973.
---
--- Note that the implementation is /left-biased/ -- the elements of a
--- first argument are always preferred to the second, for example in
--- 'union' or 'insert'.  Of course, left-biasing can only be observed
--- when equality is an equivalence relation instead of structural
--- equality.
---
--- Modified from "Data.Set" to use type families for automatic boxing.
------------------------------------------------------------------------------
--}
-
-module Data.Set.Unboxed ( 
-            -- * Set type
-              USet          -- instance Eq,Ord,Show,Read,Data,Typeable
-            , US
-
-            -- * Operators
-            , (\\)
-
-            -- * Query
-            , null
-            , size
-            , member
-            , notMember
-            , isSubsetOf
-            , isProperSubsetOf
-            
-            -- * Construction
-            , empty
-            , singleton
-            , insert
-            , delete
-            
-            -- * Combine
-            , union, unions
-            , difference
-            , intersection
-            
-            -- * Filter
-            , filter
-            , partition
-            , split
-            , splitMember
-
-            -- * Map
-            , map
-            , mapMonotonic
-
-            -- * Fold
-            , fold
-
-            -- * Min\/Max
-            , findMin
-            , findMax
-            , deleteMin
-            , deleteMax
-            , deleteFindMin
-            , deleteFindMax
-            , maxView
-            , minView
-
-            -- * Conversion
-
-            -- ** List
-            , elems
-            , toList
-            , fromList
-            
-            -- ** Ordered list
-            , toAscList
-            , fromAscList
-            , fromDistinctAscList
-                        
-            -- * Debugging
-            , showTree
-            , showTreeWith
-            , valid
-            ) where
-
-import Prelude hiding (filter,foldr,null,map)
-import qualified Data.List as List
-import Data.Monoid (Monoid(..))
-import Data.Generator.Combinators (Generator,Elem,foldMap, mapReduce)
-#ifndef __GLASGOW_HASKELL__
-import Data.Typeable (Typeable, typeOf, typeOfDefault)
-#endif
-import Data.Typeable (Typeable1(..), TyCon, mkTyCon, mkTyConApp)
-import Data.Word
-import Data.Int
-
-{-
--- just for testing
-import Test.QuickCheck 
-import Data.List (nub,sort)
-import qualified Data.List as List
--}
-
-#if __GLASGOW_HASKELL__
-import Text.Read
-import Data.Data (Data(..), mkNorepType, gcast1)
-#endif
-
-{--------------------------------------------------------------------
-  Operators
---------------------------------------------------------------------}
-infixl 9 \\ --
-
--- | /O(n+m)/. See 'difference'.
-(\\) :: (US a, Ord a) => USet a -> USet a -> USet a
-m1 \\ m2 = difference m1 m2
-
-{--------------------------------------------------------------------
-  Sets are size balanced trees
---------------------------------------------------------------------}
-type Size     = Int
-
--- | A set of values @a@.
-data Set a    = Tip 
-              | Bin {-# UNPACK #-} !Size a !(USet a) !(USet a) 
-
--- smart unboxed types
-class US a where
-    data USet a
-    view :: USet a -> Set a
-    {-# INLINE view #-}
-    tip :: USet a
-    {-# INLINE tip #-}
-    bin :: Size -> a -> USet a -> USet a -> USet a
-    {-# INLINE bin #-}
-
-
-instance (US a, Ord a) => Monoid (USet a) where
-    mempty  = empty
-    mappend = union
-    mconcat = unions
-
-{-
-instance US a => Generator (USet a) where
-    type Elem (USet a) = a
-    mapReduce _ (view -> Tip) = mempty
-    mapReduce f (view -> Bin _s k l r) = mapReduce f l `mappend` f k `mappend` mapReduce f r
--}
-
-#if __GLASGOW_HASKELL__
-
-{--------------------------------------------------------------------
-  A Data instance  
---------------------------------------------------------------------}
-
--- This instance preserves data abstraction at the cost of inefficiency.
--- We omit reflection services for the sake of data abstraction.
-
-{-
-instance (US a, Data a, Ord a) => Data (USet a) where
-  gfoldl f z set = z fromList `f` (toList set)
-  toConstr _     = error "toConstr"
-  gunfold _ _    = error "gunfold"
-  dataTypeOf _   = mkNorepType "Data.Set.Set"
-  dataCast1 f    = gcast1 f
--}
-
-#endif
-
-{--------------------------------------------------------------------
-  Query
---------------------------------------------------------------------}
--- | /O(1)/. Is this the empty set?
-null :: US a => USet a -> Bool
-null (view -> Tip) = True
-null (view -> Bin {}) = False
-
--- | /O(1)/. The number of elements in the set.
-size :: US a => USet a -> Int
-size (view -> Tip) = 0
-size (view -> Bin sz _ _ _) = sz
-
--- | /O(log n)/. Is the element in the set?
-member :: (US a, Ord a) => a -> USet a -> Bool
-member x (view -> Tip) = False
-member x (view -> Bin _ y l r) = 
-    case compare x y of
-        LT -> member x l
-        GT -> member x r
-        EQ -> True       
-
--- | /O(log n)/. Is the element not in the set?
-notMember :: (US a, Ord a) => a -> USet a -> Bool
-notMember x t = not $ member x t
-
-{--------------------------------------------------------------------
-  Construction
---------------------------------------------------------------------}
--- | /O(1)/. The empty set.
-empty :: US a => USet a
-empty = tip
-
--- | /O(1)/. Create a singleton set.
-singleton :: US a => a -> USet a
-singleton x = bin 1 x tip tip
-
-{--------------------------------------------------------------------
-  Insertion, Deletion
---------------------------------------------------------------------}
--- | /O(log n)/. Insert an element in a set.
--- If the set already contains an element equal to the given value,
--- it is replaced with the new value.
-insert :: (US a, Ord a) => a -> USet a -> USet a
-insert x (view -> Tip)          = singleton x
-insert x (view -> Bin sz y l r) = case compare x y of
-   LT -> balance y (insert x l) r
-   GT -> balance y l (insert x r)
-   EQ -> bin sz x l r
-
--- | /O(log n)/. Delete an element from a set.
-delete :: (US a, Ord a) => a -> USet a -> USet a
-delete x (view -> Tip)         = tip
-delete x (view -> Bin _ y l r) = case compare x y of
-    LT -> balance y (delete x l) r
-    GT -> balance y l (delete x r)
-    EQ -> glue l r
-
-{--------------------------------------------------------------------
-  Subset
---------------------------------------------------------------------}
--- | /O(n+m)/. Is this a proper subset? (ie. a subset but not equal).
-isProperSubsetOf :: (US a, Ord a) => USet a -> USet a -> Bool
-isProperSubsetOf s1 s2
-    = (size s1 < size s2) && (isSubsetOf s1 s2)
-
--- | /O(n+m)/. Is this a subset?
--- @(s1 `isSubsetOf` s2)@ tells whether @s1@ is a subset of @s2@.
-isSubsetOf :: (US a, Ord a) => USet a -> USet a -> Bool
-isSubsetOf t1 t2 = (size t1 <= size t2) && (isSubsetOfX t1 t2)
-
-isSubsetOfX :: (US a, Ord a) => USet a -> USet a -> Bool
-isSubsetOfX (view -> Tip) _         = True
-isSubsetOfX _ (view -> Tip)         = False
-isSubsetOfX (view -> Bin _ x l r) t = found && isSubsetOfX l lt && isSubsetOfX r gt
-  where
-    (lt,found,gt) = splitMember x t
-
-
-{--------------------------------------------------------------------
-  Minimal, Maximal
---------------------------------------------------------------------}
--- | /O(log n)/. The minimal element of a set.
-findMin :: US a => USet a -> a
-findMin (view -> Bin _ x (view -> Tip) _) = x
-findMin (view -> Bin _ _ l _)   = findMin l
-findMin (view -> Tip)           = error "Set.findMin: empty set has no minimal element"
-
--- | /O(log n)/. The maximal element of a set.
-findMax :: US a => USet a -> a
-findMax (view -> Bin _ x _ (view -> Tip))  = x
-findMax (view -> Bin _ _ _ r)    = findMax r
-findMax (view -> Tip)            = error "Set.findMax: empty set has no maximal element"
-
--- | /O(log n)/. Delete the minimal element.
-deleteMin :: US a => USet a -> USet a
-deleteMin (view -> Bin _ _ (view -> Tip) r) = r
-deleteMin (view -> Bin _ x l r)   = balance x (deleteMin l) r
-deleteMin (view -> Tip)           = tip
-
--- | /O(log n)/. Delete the maximal element.
-deleteMax :: US a => USet a -> USet a
-deleteMax (view -> Bin _ _ l (view -> Tip)) = l
-deleteMax (view -> Bin _ x l r)   = balance x l (deleteMax r)
-deleteMax (view -> Tip)           = tip
-
-{--------------------------------------------------------------------
-  Union. 
---------------------------------------------------------------------}
--- | The union of a list of sets: (@'unions' == 'foldl' 'union' 'empty'@).
-unions :: (US a, Ord a) => [USet a] -> USet a
-unions ts
-  = foldlStrict union empty ts
-
-
--- | /O(n+m)/. The union of two sets, preferring the first set when
--- equal elements are encountered.
--- The implementation uses the efficient /hedge-union/ algorithm.
--- Hedge-union is more efficient on (bigset `union` smallset).
-union :: (US a, Ord a) => USet a -> USet a -> USet a
-union (view -> Tip) t2  = t2
-union t1 (view -> Tip)  = t1
-union t1 t2 = hedgeUnion (const LT) (const GT) t1 t2
-
-hedgeUnion :: (US a, Ord a) => (a -> Ordering) -> (a -> Ordering) -> USet a -> USet a -> USet a
-hedgeUnion _     _     t1 (view -> Tip)                    = t1
-hedgeUnion cmplo cmphi (view -> Tip) (view -> Bin _ x l r) = join x (filterGt cmplo l) (filterLt cmphi r)
-hedgeUnion cmplo cmphi (view -> Bin _ x l r) t2            = join x (hedgeUnion cmplo cmpx l (trim cmplo cmpx t2)) (hedgeUnion cmpx cmphi r (trim cmpx cmphi t2))
-  where
-    cmpx = compare x
-
-{--------------------------------------------------------------------
-  Difference
---------------------------------------------------------------------}
--- | /O(n+m)/. Difference of two sets. 
--- The implementation uses an efficient /hedge/ algorithm comparable with /hedge-union/.
-difference :: (US a, Ord a) => USet a -> USet a -> USet a
-difference (view -> Tip) _   = tip
-difference t1 (view -> Tip)  = t1
-difference t1 t2   = hedgeDiff (const LT) (const GT) t1 t2
-
-hedgeDiff :: (US a, Ord a) => (a -> Ordering) -> (a -> Ordering) -> USet a -> USet a -> USet a
-hedgeDiff _ _ (view -> Tip) _ = tip
-hedgeDiff cmplo cmphi (view -> Bin _ x l r) (view -> Tip) = join x (filterGt cmplo l) (filterLt cmphi r)
-hedgeDiff cmplo cmphi t (view -> Bin _ x l r) = merge (hedgeDiff cmplo cmpx (trim cmplo cmpx t) l) (hedgeDiff cmpx cmphi (trim cmpx cmphi t) r)
-  where
-    cmpx = compare x
-
-{--------------------------------------------------------------------
-  Intersection
---------------------------------------------------------------------}
--- | /O(n+m)/. The intersection of two sets.
--- Elements of the result come from the first set, so for example
---
--- > import qualified Data.Set as S
--- > data AB = A | B deriving Show
--- > instance Ord AB where compare _ _ = EQ
--- > instance Eq AB where _ == _ = True
--- > main = print (S.singleton A `S.intersection` S.singleton B,
--- >               S.singleton B `S.intersection` S.singleton A)
---
--- prints @(fromList [A],fromList [B])@.
-intersection :: (US a, Ord a) => USet a -> USet a -> USet a
-intersection (view -> Tip) _ = tip
-intersection _ (view -> Tip) = tip
-intersection t1@(view -> Bin s1 x1 l1 r1) t2@(view -> Bin s2 x2 l2 r2) =
-   if s1 >= s2 then
-      let (lt,found,gt) = splitLookup x2 t1
-          tl            = intersection lt l2
-          tr            = intersection gt r2
-      in case found of
-      Just x -> join x tl tr
-      Nothing -> merge tl tr
-   else let (lt,found,gt) = splitMember x1 t2
-            tl            = intersection l1 lt
-            tr            = intersection r1 gt
-        in if found then join x1 tl tr
-           else merge tl tr
-
-{--------------------------------------------------------------------
-  Filter and partition
---------------------------------------------------------------------}
--- | /O(n)/. Filter all elements that satisfy the predicate.
-filter :: (US a, Ord a) => (a -> Bool) -> USet a -> USet a
-filter _ (view -> Tip) = tip
-filter p (view -> Bin _ x l r)
-  | p x       = join x (filter p l) (filter p r)
-  | otherwise = merge (filter p l) (filter p r)
-
--- | /O(n)/. Partition the set into two sets, one with all elements that satisfy
--- the predicate and one with all elements that don't satisfy the predicate.
--- See also 'split'.
-partition :: (US a, Ord a) => (a -> Bool) -> USet a -> (USet a,USet a)
-partition _ (view -> Tip) = (tip,tip)
-partition p (view -> Bin _ x l r)
-  | p x       = (join x l1 r1,merge l2 r2)
-  | otherwise = (merge l1 r1,join x l2 r2)
-  where
-    (l1,l2) = partition p l
-    (r1,r2) = partition p r
-
-{----------------------------------------------------------------------
-  Map
-----------------------------------------------------------------------}
-
--- | /O(n*log n)/. 
--- @'map' f s@ is the set obtained by applying @f@ to each element of @s@.
--- 
--- It's worth noting that the size of the result may be smaller if,
--- for some @(x,y)@, @x \/= y && f x == f y@
-
-map :: (US a, US b, Ord a, Ord b) => (a->b) -> USet a -> USet b
-map f = fromList . List.map f . toList
-
--- | /O(n)/. The 
---
--- @'mapMonotonic' f s == 'map' f s@, but works only when @f@ is monotonic.
--- /The precondition is not checked./
--- Semi-formally, we have:
--- 
--- > and [x < y ==> f x < f y | x <- ls, y <- ls] 
--- >                     ==> mapMonotonic f s == map f s
--- >     where ls = toList s
-
-mapMonotonic :: (US a, US b) => (a->b) -> USet a -> USet b
-mapMonotonic _ (view -> Tip) = tip
-mapMonotonic f (view -> Bin sz x l r) = bin sz (f x) (mapMonotonic f l) (mapMonotonic f r)
-
-
-{--------------------------------------------------------------------
-  Fold
---------------------------------------------------------------------}
--- | /O(n)/. Fold over the elements of a set in an unspecified order.
-fold :: US a => (a -> b -> b) -> b -> USet a -> b
-fold f z s = foldr f z s
-
--- | /O(n)/. Post-order fold.
-foldr :: US a => (a -> b -> b) -> b -> USet a -> b
-foldr _ z (view -> Tip)         = z
-foldr f z (view -> Bin _ x l r) = foldr f (f x (foldr f z r)) l
-
-{--------------------------------------------------------------------
-  List variations 
---------------------------------------------------------------------}
--- | /O(n)/. The elements of a set.
-elems :: US a => USet a -> [a]
-elems = toList
-
-{--------------------------------------------------------------------
-  Lists 
---------------------------------------------------------------------}
--- | /O(n)/. Convert the set to a list of elements.
-toList :: US a => USet a -> [a]
-toList = toAscList
-
--- | /O(n)/. Convert the set to an ascending list of elements.
-toAscList :: US a => USet a -> [a]
-toAscList = foldr (:) []
-
-
--- | /O(n*log n)/. Create a set from a list of elements.
-fromList :: (US a, Ord a) => [a] -> USet a 
-fromList = foldlStrict ins empty
-  where
-    ins t x = insert x t
-
-{--------------------------------------------------------------------
-  Building trees from ascending/descending lists can be done in linear time.
-  
-  Note that if [xs] is ascending that: 
-    fromAscList xs == fromList xs
---------------------------------------------------------------------}
--- | /O(n)/. Build a set from an ascending list in linear time.
--- /The precondition (input list is ascending) is not checked./
-fromAscList :: (US a, Eq a) => [a] -> USet a 
-fromAscList xs
-  = fromDistinctAscList (combineEq xs)
-  where
-  -- [combineEq xs] combines equal elements with [const] in an ordered list [xs]
-  combineEq xs'
-    = case xs' of
-        []     -> []
-        [x]    -> [x]
-        (x:xx) -> combineEq' x xx
-
-  combineEq' z [] = [z]
-  combineEq' z (x:xs')
-    | z==x      =   combineEq' z xs'
-    | otherwise = z:combineEq' x xs'
-
-
--- | /O(n)/. Build a set from an ascending list of distinct elements in linear time.
--- /The precondition (input list is strictly ascending) is not checked./
-fromDistinctAscList :: US a => [a] -> USet a 
-fromDistinctAscList xs
-  = build const (length xs) xs
-  where
-    -- 1) use continutations so that we use heap space instead of stack space.
-    -- 2) special case for n==5 to build bushier trees. 
-    build c 0 xs'  = c tip xs'
-    build c 5 xs'  = case xs' of
-                       (x1:x2:x3:x4:x5:xx) 
-                            -> c (bin_ x4 (bin_ x2 (singleton x1) (singleton x3)) (singleton x5)) xx
-                       _ -> error "fromDistinctAscList build 5"
-    build c n xs'  = seq nr $ build (buildR nr c) nl xs'
-                   where
-                     nl = n `div` 2
-                     nr = n - nl - 1
-
-    buildR n c l (x:ys) = build (buildB l x c) n ys
-    buildR _ _ _ []     = error "fromDistinctAscList buildR []"
-    buildB l x c r zs   = c (bin_ x l r) zs
-
-{--------------------------------------------------------------------
-  Eq converts the set to a list. In a lazy setting, this 
-  actually seems one of the faster methods to compare two trees 
-  and it is certainly the simplest :-)
---------------------------------------------------------------------}
-instance (US a, Eq a) => Eq (USet a) where
-  t1 == t2  = (size t1 == size t2) && (toAscList t1 == toAscList t2)
-
-{--------------------------------------------------------------------
-  Ord 
---------------------------------------------------------------------}
-
-instance (US a, Ord a) => Ord (USet a) where
-    compare s1 s2 = compare (toAscList s1) (toAscList s2) 
-
-{--------------------------------------------------------------------
-  Show
---------------------------------------------------------------------}
-instance (US a, Show a) => Show (USet a) where
-  showsPrec p xs = showParen (p > 10) $
-    showString "fromList " . shows (toList xs)
-
-{-
-XXX unused code
-
-showSet :: (Show a) => [a] -> ShowS
-showSet []     
-  = showString "{}" 
-showSet (x:xs) 
-  = showChar '{' . shows x . showTail xs
-  where
-    showTail []       = showChar '}'
-    showTail (x':xs') = showChar ',' . shows x' . showTail xs'
--}
-
-{--------------------------------------------------------------------
-  Read
---------------------------------------------------------------------}
-instance (US a, Read a, Ord a) => Read (USet a) where
-#ifdef __GLASGOW_HASKELL__
-  readPrec = parens $ prec 10 $ do
-    Ident "fromList" <- lexP
-    xs <- readPrec
-    return (fromList xs)
-
-  readListPrec = readListPrecDefault
-#else
-  readsPrec p = readParen (p > 10) $ \ r -> do
-    ("fromList",s) <- lex r
-    (xs,t) <- reads s
-    return (fromList xs,t)
-#endif
-
-{--------------------------------------------------------------------
-  Typeable/Data
---------------------------------------------------------------------}
-
--- #include "Typeable.h"
--- INSTANCE_TYPEABLE1(Set,setTc,"Set")
-
-{--------------------------------------------------------------------
-  Utility functions that return sub-ranges of the original
-  tree. Some functions take a comparison function as argument to
-  allow comparisons against infinite values. A function [cmplo x]
-  should be read as [compare lo x].
-
-  [trim cmplo cmphi t]  A tree that is either empty or where [cmplo x == LT]
-                        and [cmphi x == GT] for the value [x] of the root.
-  [filterGt cmp t]      A tree where for all values [k]. [cmp k == LT]
-  [filterLt cmp t]      A tree where for all values [k]. [cmp k == GT]
-
-  [split k t]           Returns two trees [l] and [r] where all values
-                        in [l] are <[k] and all keys in [r] are >[k].
-  [splitMember k t]     Just like [split] but also returns whether [k]
-                        was found in the tree.
---------------------------------------------------------------------}
-
-{--------------------------------------------------------------------
-  [trim lo hi t] trims away all subtrees that surely contain no
-  values between the range [lo] to [hi]. The returned tree is either
-  empty or the key of the root is between @lo@ and @hi@.
---------------------------------------------------------------------}
-trim :: US a => (a -> Ordering) -> (a -> Ordering) -> USet a -> USet a
-trim _     _     (view -> Tip) = tip
-trim cmplo cmphi t@(view -> Bin _ x l r)
-  = case cmplo x of
-      LT -> case cmphi x of
-              GT -> t
-              _  -> trim cmplo cmphi l
-      _  -> trim cmplo cmphi r
-
-{--------------------------------------------------------------------
-  [filterGt x t] filter all values >[x] from tree [t]
-  [filterLt x t] filter all values <[x] from tree [t]
---------------------------------------------------------------------}
-filterGt :: US a => (a -> Ordering) -> USet a -> USet a
-filterGt _ (view -> Tip) = tip
-filterGt cmp (view -> Bin _ x l r)
-  = case cmp x of
-      LT -> join x (filterGt cmp l) r
-      GT -> filterGt cmp r
-      EQ -> r
-      
-filterLt :: US a => (a -> Ordering) -> USet a -> USet a
-filterLt _ (view -> Tip) = tip
-filterLt cmp (view -> Bin _ x l r)
-  = case cmp x of
-      LT -> filterLt cmp l
-      GT -> join x l (filterLt cmp r)
-      EQ -> l
-
-
-{--------------------------------------------------------------------
-  Split
---------------------------------------------------------------------}
--- | /O(log n)/. The expression (@'split' x set@) is a pair @(set1,set2)@
--- where @set1@ comprises the elements of @set@ less than @x@ and @set2@
--- comprises the elements of @set@ greater than @x@.
-split :: (US a, Ord a) => a -> USet a -> (USet a,USet a)
-split _ (view -> Tip) = (tip,tip)
-split x (view -> Bin _ y l r)
-  = case compare x y of
-      LT -> let (lt,gt) = split x l in (lt,join y gt r)
-      GT -> let (lt,gt) = split x r in (join y l lt,gt)
-      EQ -> (l,r)
-
--- | /O(log n)/. Performs a 'split' but also returns whether the pivot
--- element was found in the original set.
-splitMember :: (US a, Ord a) => a -> USet a -> (USet a,Bool,USet a)
-splitMember x t = let (l,m,r) = splitLookup x t in
-     (l,maybe False (const True) m,r)
-
--- | /O(log n)/. Performs a 'split' but also returns the pivot
--- element that was found in the original set.
-splitLookup :: (US a, Ord a) => a -> USet a -> (USet a,Maybe a,USet a)
-splitLookup _ (view -> Tip) = (tip,Nothing,tip)
-splitLookup x (view -> Bin _ y l r)
-   = case compare x y of
-       LT -> let (lt,found,gt) = splitLookup x l in (lt,found,join y gt r)
-       GT -> let (lt,found,gt) = splitLookup x r in (join y l lt,found,gt)
-       EQ -> (l,Just y,r)
-
-{--------------------------------------------------------------------
-  Utility functions that maintain the balance properties of the tree.
-  All constructors assume that all values in [l] < [x] and all values
-  in [r] > [x], and that [l] and [r] are valid trees.
-  
-  In order of sophistication:
-    [Bin sz x l r]    The type constructor.
-    [bin_ x l r]      Maintains the correct size, assumes that both [l]
-                      and [r] are balanced with respect to each other.
-    [balance x l r]   Restores the balance and size.
-                      Assumes that the original tree was balanced and
-                      that [l] or [r] has changed by at most one element.
-    [join x l r]      Restores balance and size. 
-
-  Furthermore, we can construct a new tree from two trees. Both operations
-  assume that all values in [l] < all values in [r] and that [l] and [r]
-  are valid:
-    [glue l r]        Glues [l] and [r] together. Assumes that [l] and
-                      [r] are already balanced with respect to each other.
-    [merge l r]       Merges two trees and restores balance.
-
-  Note: in contrast to Adam's paper, we use (<=) comparisons instead
-  of (<) comparisons in [join], [merge] and [balance]. 
-  Quickcheck (on [difference]) showed that this was necessary in order 
-  to maintain the invariants. It is quite unsatisfactory that I haven't 
-  been able to find out why this is actually the case! Fortunately, it 
-  doesn't hurt to be a bit more conservative.
---------------------------------------------------------------------}
-
-{--------------------------------------------------------------------
-  Join 
---------------------------------------------------------------------}
-join :: US a => a -> USet a -> USet a -> USet a
-join x (view -> Tip) r  = insertMin x r
-join x l (view -> Tip)  = insertMax x l
-join x l@(view -> Bin sizeL y ly ry) r@(view -> Bin sizeR z lz rz)
-  | delta*sizeL <= sizeR  = balance z (join x l lz) rz
-  | delta*sizeR <= sizeL  = balance y ly (join x ry r)
-  | otherwise             = bin_ x l r
-
-
--- insertMin and insertMax don't perform potentially expensive comparisons.
-insertMax,insertMin :: US a => a -> USet a -> USet a 
-insertMax x t
-  = case view t of
-      Tip -> singleton x
-      Bin _ y l r
-          -> balance y l (insertMax x r)
-             
-insertMin x t
-  = case view t of
-      Tip -> singleton x
-      Bin _ y l r
-          -> balance y (insertMin x l) r
-             
-{--------------------------------------------------------------------
-  [merge l r]: merges two trees.
---------------------------------------------------------------------}
-merge :: US a => USet a -> USet a -> USet a
-merge (view -> Tip) r   = r
-merge l (view -> Tip)   = l
-merge l@(view -> Bin sizeL x lx rx) r@(view -> Bin sizeR y ly ry)
-  | delta*sizeL <= sizeR = balance y (merge l ly) ry
-  | delta*sizeR <= sizeL = balance x lx (merge rx r)
-  | otherwise            = glue l r
-
-{--------------------------------------------------------------------
-  [glue l r]: glues two trees together.
-  Assumes that [l] and [r] are already balanced with respect to each other.
---------------------------------------------------------------------}
-glue :: US a => USet a -> USet a -> USet a
-glue (view -> Tip) r = r
-glue l (view -> Tip) = l
-glue l r   
-  | size l > size r = let (m,l') = deleteFindMax l in balance m l' r
-  | otherwise       = let (m,r') = deleteFindMin r in balance m l r'
-
-
--- | /O(log n)/. Delete and find the minimal element.
--- 
--- > deleteFindMin set = (findMin set, deleteMin set)
-
-deleteFindMin :: US a => USet a -> (a,USet a)
-deleteFindMin t 
-  = case view t of
-      Bin _ x (view -> Tip) r -> (x,r)
-      Bin _ x l r   -> let (xm,l') = deleteFindMin l in (xm,balance x l' r)
-      Tip           -> (error "Set.deleteFindMin: can not return the minimal element of an empty set", tip)
-
--- | /O(log n)/. Delete and find the maximal element.
--- 
--- > deleteFindMax set = (findMax set, deleteMax set)
-deleteFindMax :: US a => USet a -> (a,USet a)
-deleteFindMax t
-  = case view t of
-      Bin _ x l (view -> Tip) -> (x,l)
-      Bin _ x l r   -> let (xm,r') = deleteFindMax r in (xm,balance x l r')
-      Tip           -> (error "Set.deleteFindMax: can not return the maximal element of an empty set", tip)
-
--- | /O(log n)/. Retrieves the minimal key of the set, and the set
--- stripped of that element, or 'Nothing' if passed an empty set.
-minView :: US a => USet a -> Maybe (a, USet a)
-minView (view -> Tip) = Nothing
-minView x = Just (deleteFindMin x)
-
--- | /O(log n)/. Retrieves the maximal key of the set, and the set
--- stripped of that element, or 'Nothing' if passed an empty set.
-maxView :: US a => USet a -> Maybe (a, USet a)
-maxView (view -> Tip) = Nothing
-maxView x = Just (deleteFindMax x)
-
-{--------------------------------------------------------------------
-  [balance x l r] balances two trees with value x.
-  The sizes of the trees should balance after decreasing the
-  size of one of them. (a rotation).
-
-  [delta] is the maximal relative difference between the sizes of
-          two trees, it corresponds with the [w] in Adams' paper,
-          or equivalently, [1/delta] corresponds with the $\alpha$
-          in Nievergelt's paper. Adams shows that [delta] should
-          be larger than 3.745 in order to garantee that the
-          rotations can always restore balance.         
-
-  [ratio] is the ratio between an outer and inner sibling of the
-          heavier subtree in an unbalanced setting. It determines
-          whether a double or single rotation should be performed
-          to restore balance. It is correspondes with the inverse
-          of $\alpha$ in Adam's article.
-
-  Note that:
-  - [delta] should be larger than 4.646 with a [ratio] of 2.
-  - [delta] should be larger than 3.745 with a [ratio] of 1.534.
-  
-  - A lower [delta] leads to a more 'perfectly' balanced tree.
-  - A higher [delta] performs less rebalancing.
-
-  - Balancing is automatic for random data and a balancing
-    scheme is only necessary to avoid pathological worst cases.
-    Almost any choice will do in practice
-    
-  - Allthough it seems that a rather large [delta] may perform better 
-    than smaller one, measurements have shown that the smallest [delta]
-    of 4 is actually the fastest on a wide range of operations. It
-    especially improves performance on worst-case scenarios like
-    a sequence of ordered insertions.
-
-  Note: in contrast to Adams' paper, we use a ratio of (at least) 2
-  to decide whether a single or double rotation is needed. Allthough
-  he actually proves that this ratio is needed to maintain the
-  invariants, his implementation uses a (invalid) ratio of 1. 
-  He is aware of the problem though since he has put a comment in his 
-  original source code that he doesn't care about generating a 
-  slightly inbalanced tree since it doesn't seem to matter in practice. 
-  However (since we use quickcheck :-) we will stick to strictly balanced 
-  trees.
---------------------------------------------------------------------}
-delta,ratio :: Int
-delta = 4
-ratio = 2
-
-balance :: US a => a -> USet a -> USet a -> USet a
-balance x l r
-  | sizeL + sizeR <= 1    = bin sizeX x l r
-  | sizeR >= delta*sizeL  = rotateL x l r
-  | sizeL >= delta*sizeR  = rotateR x l r
-  | otherwise             = bin sizeX x l r
-  where
-    sizeL = size l
-    sizeR = size r
-    sizeX = sizeL + sizeR + 1
-
--- rotate
-rotateL :: US a => a -> USet a -> USet a -> USet a
-rotateL x l r@(view -> Bin _ _ ly ry)
-  | size ly < ratio*size ry = singleL x l r
-  | otherwise               = doubleL x l r
-rotateL _ _ (view -> Tip) = error "rotateL Tip"
-
-rotateR :: US a => a -> USet a -> USet a -> USet a
-rotateR x l@(view -> Bin _ _ ly ry) r
-  | size ry < ratio*size ly = singleR x l r
-  | otherwise               = doubleR x l r
-rotateR _ (view -> Tip) _ = error "rotateL Tip"
-
--- basic rotations
-singleL, singleR :: US a => a -> USet a -> USet a -> USet a
-singleL x1 t1 (view -> Bin _ x2 t2 t3)  = bin_ x2 (bin_ x1 t1 t2) t3
-singleL _  _  (view -> Tip)             = error "singleL"
-singleR x1 (view -> Bin _ x2 t1 t2) t3  = bin_ x2 t1 (bin_ x1 t2 t3)
-singleR _ (view -> Tip)             _   = error "singleR"
-
-doubleL, doubleR :: US a => a -> USet a -> USet a -> USet a
-doubleL x1 t1 (view -> Bin _ x2 (view -> Bin _ x3 t2 t3) t4) = bin_ x3 (bin_ x1 t1 t2) (bin_ x2 t3 t4)
-doubleL _ _ _ = error "doubleL"
-doubleR x1 (view -> Bin _ x2 t1 (view -> Bin _ x3 t2 t3)) t4 = bin_ x3 (bin_ x2 t1 t2) (bin_ x1 t3 t4)
-doubleR _ _ _ = error "doubleR"
-
-
-{--------------------------------------------------------------------
-  The bin constructor maintains the size of the tree
---------------------------------------------------------------------}
-bin_ :: US a => a -> USet a -> USet a -> USet a
-bin_ x l r
-  = bin (size l + size r + 1) x l r
-
-
-{--------------------------------------------------------------------
-  Utilities
---------------------------------------------------------------------}
-foldlStrict :: (a -> b -> a) -> a -> [b] -> a
-foldlStrict f z xs
-  = case xs of
-      []     -> z
-      (x:xx) -> let z' = f z x in seq z' (foldlStrict f z' xx)
-
-
-{--------------------------------------------------------------------
-  Debugging
---------------------------------------------------------------------}
--- | /O(n)/. Show the tree that implements the set. The tree is shown
--- in a compressed, hanging format.
-showTree :: (US a, Show a) => USet a -> String
-showTree s
-  = showTreeWith True False s
-
-
-{- | /O(n)/. The expression (@showTreeWith hang wide map@) shows
- the tree that implements the set. If @hang@ is
- @True@, a /hanging/ tree is shown otherwise a rotated tree is shown. If
- @wide@ is 'True', an extra wide version is shown.
-
-> Set> putStrLn $ showTreeWith True False $ fromDistinctAscList [1..5]
-> 4
-> +--2
-> |  +--1
-> |  +--3
-> +--5
-> 
-> Set> putStrLn $ showTreeWith True True $ fromDistinctAscList [1..5]
-> 4
-> |
-> +--2
-> |  |
-> |  +--1
-> |  |
-> |  +--3
-> |
-> +--5
-> 
-> Set> putStrLn $ showTreeWith False True $ fromDistinctAscList [1..5]
-> +--5
-> |
-> 4
-> |
-> |  +--3
-> |  |
-> +--2
->    |
->    +--1
-
--}
-showTreeWith :: (US a, Show a) => Bool -> Bool -> USet a -> String
-showTreeWith hang wide t
-  | hang      = (showsTreeHang wide [] t) ""
-  | otherwise = (showsTree wide [] [] t) ""
-
-showsTree :: (US a, Show a) => Bool -> [String] -> [String] -> USet a -> ShowS
-showsTree wide lbars rbars t
-  = case view t of
-      Tip -> showsBars lbars . showString "|\n"
-      Bin _ x (view -> Tip) (view -> Tip)
-          -> showsBars lbars . shows x . showString "\n" 
-      Bin _ x l r
-          -> showsTree wide (withBar rbars) (withEmpty rbars) r .
-             showWide wide rbars .
-             showsBars lbars . shows x . showString "\n" .
-             showWide wide lbars .
-             showsTree wide (withEmpty lbars) (withBar lbars) l
-
-showsTreeHang :: (US a, Show a) => Bool -> [String] -> USet a -> ShowS
-showsTreeHang wide bars t
-  = case view t of
-      Tip -> showsBars bars . showString "|\n" 
-      Bin _ x (view -> Tip) (view -> Tip) 
-          -> showsBars bars . shows x . showString "\n" 
-      Bin _ x l r
-          -> showsBars bars . shows x . showString "\n" . 
-             showWide wide bars .
-             showsTreeHang wide (withBar bars) l .
-             showWide wide bars .
-             showsTreeHang wide (withEmpty bars) r
-
-showWide :: Bool -> [String] -> String -> String
-showWide wide bars 
-  | wide      = showString (concat (reverse bars)) . showString "|\n" 
-  | otherwise = id
-
-showsBars :: [String] -> ShowS
-showsBars bars
-  = case bars of
-      [] -> id
-      _  -> showString (concat (reverse (tail bars))) . showString node
-
-node :: String
-node           = "+--"
-
-withBar, withEmpty :: [String] -> [String]
-withBar bars   = "|  ":bars
-withEmpty bars = "   ":bars
-
-{--------------------------------------------------------------------
-  Assertions
---------------------------------------------------------------------}
--- | /O(n)/. Test if the internal set structure is valid.
-valid :: (US a, Ord a) => USet a -> Bool
-valid t
-  = balanced t && ordered t && validsize t
-
-ordered :: (US a, Ord a) => USet a -> Bool
-ordered t
-  = bounded (const True) (const True) t
-  where
-    bounded lo hi t'
-      = case view t' of
-          Tip         -> True
-          Bin _ x l r -> (lo x) && (hi x) && bounded lo (<x) l && bounded (>x) hi r
-
-balanced :: US a => USet a -> Bool
-balanced t
-  = case view t of
-      Tip         -> True
-      Bin _ _ l r -> (size l + size r <= 1 || (size l <= delta*size r && size r <= delta*size l)) &&
-                     balanced l && balanced r
-
-validsize :: US a => USet a -> Bool
-validsize t
-  = (realsize t == Just (size t))
-  where
-    realsize t'
-      = case view t' of
-          Tip          -> Just 0
-          Bin sz _ l r -> case (realsize l,realsize r) of
-                            (Just n,Just m)  | n+m+1 == sz  -> Just sz
-                            _                -> Nothing
-
-{-
-{--------------------------------------------------------------------
-  Testing
---------------------------------------------------------------------}
-testTree :: [Int] -> USet Int
-testTree xs   = fromList xs
-test1 = testTree [1..20]
-test2 = testTree [30,29..10]
-test3 = testTree [1,4,6,89,2323,53,43,234,5,79,12,9,24,9,8,423,8,42,4,8,9,3]
-
-{--------------------------------------------------------------------
-  QuickCheck
---------------------------------------------------------------------}
-
-{-
-qcheck prop
-  = check config prop
-  where
-    config = Config
-      { configMaxTest = 500
-      , configMaxFail = 5000
-      , configSize    = \n -> (div n 2 + 3)
-      , configEvery   = \n args -> let s = show n in s ++ [ '\b' | _ <- s ]
-      }
--}
-
-
-{--------------------------------------------------------------------
-  Arbitrary, reasonably balanced trees
---------------------------------------------------------------------}
-instance (US a, Enum a) => Arbitrary (USet a) where
-  arbitrary = sized (arbtree 0 maxkey)
-            where maxkey  = 10000
-
-arbtree :: (US a, Enum a) => Int -> Int -> Int -> Gen (USet a)
-arbtree lo hi n
-  | n <= 0        = return tip
-  | lo >= hi      = return tip
-  | otherwise     = do{ i  <- choose (lo,hi)
-                      ; m  <- choose (1,30)
-                      ; let (ml,mr)  | m==(1::Int)= (1,2)
-                                     | m==2       = (2,1)
-                                     | m==3       = (1,1)
-                                     | otherwise  = (2,2)
-                      ; l  <- arbtree lo (i-1) (n `div` ml)
-                      ; r  <- arbtree (i+1) hi (n `div` mr)
-                      ; return (bin_ (toEnum i) l r)
-                      }  
-
-
-{--------------------------------------------------------------------
-  Valid tree's
---------------------------------------------------------------------}
-forValid :: (US a, Enum a,Show a,Testable b) => (USet a -> b) -> Property
-forValid f
-  = forAll arbitrary $ \t -> 
---    classify (balanced t) "balanced" $
-    classify (size t == 0) "empty" $
-    classify (size t > 0  && size t <= 10) "small" $
-    classify (size t > 10 && size t <= 64) "medium" $
-    classify (size t > 64) "large" $
-    balanced t ==> f t
-
-forValidIntTree :: Testable a => (USet Int -> a) -> Property
-forValidIntTree f
-  = forValid f
-
-forValidUnitTree :: Testable a => (USet Int -> a) -> Property
-forValidUnitTree f
-  = forValid f
-
-
-prop_Valid 
-  = forValidUnitTree $ \t -> valid t
-
-{--------------------------------------------------------------------
-  Single, Insert, Delete
---------------------------------------------------------------------}
-prop_Single :: Int -> Bool
-prop_Single x
-  = (insert x empty == singleton x)
-
-prop_InsertValid :: Int -> Property
-prop_InsertValid k
-  = forValidUnitTree $ \t -> valid (insert k t)
-
-prop_InsertDelete :: Int -> USet Int -> Property
-prop_InsertDelete k t
-  = not (member k t) ==> delete k (insert k t) == t
-
-prop_DeleteValid :: Int -> Property
-prop_DeleteValid k
-  = forValidUnitTree $ \t -> 
-    valid (delete k (insert k t))
-
-{--------------------------------------------------------------------
-  Balance
---------------------------------------------------------------------}
-prop_Join :: Int -> Property 
-prop_Join x
-  = forValidUnitTree $ \t ->
-    let (l,r) = split x t
-    in valid (join x l r)
-
-prop_Merge :: Int -> Property 
-prop_Merge x
-  = forValidUnitTree $ \t ->
-    let (l,r) = split x t
-    in valid (merge l r)
-
-
-{--------------------------------------------------------------------
-  Union
---------------------------------------------------------------------}
-prop_UnionValid :: Property
-prop_UnionValid
-  = forValidUnitTree $ \t1 ->
-    forValidUnitTree $ \t2 ->
-    valid (union t1 t2)
-
-prop_UnionInsert :: Int -> USet Int -> Bool
-prop_UnionInsert x t
-  = union t (singleton x) == insert x t
-
-prop_UnionAssoc :: USet Int -> USet Int -> USet Int -> Bool
-prop_UnionAssoc t1 t2 t3
-  = union t1 (union t2 t3) == union (union t1 t2) t3
-
-prop_UnionComm :: USet Int -> USet Int -> Bool
-prop_UnionComm t1 t2
-  = (union t1 t2 == union t2 t1)
-
-
-prop_DiffValid
-  = forValidUnitTree $ \t1 ->
-    forValidUnitTree $ \t2 ->
-    valid (difference t1 t2)
-
-prop_Diff :: [Int] -> [Int] -> Bool
-prop_Diff xs ys
-  =  toAscList (difference (fromList xs) (fromList ys))
-    == List.sort ((List.\\) (nub xs)  (nub ys))
-
-prop_IntValid
-  = forValidUnitTree $ \t1 ->
-    forValidUnitTree $ \t2 ->
-    valid (intersection t1 t2)
-
-prop_Int :: [Int] -> [Int] -> Bool
-prop_Int xs ys
-  =  toAscList (intersection (fromList xs) (fromList ys))
-    == List.sort (nub ((List.intersect) (xs)  (ys)))
-
-{--------------------------------------------------------------------
-  Lists
---------------------------------------------------------------------}
-prop_Ordered
-  = forAll (choose (5,100)) $ \n ->
-    let xs = [0..n::Int]
-    in fromAscList xs == fromList xs
-
-prop_List :: [Int] -> Bool
-prop_List xs
-  = (sort (nub xs) == toList (fromList xs))
--}
-
-
-newtype Boxed a = Boxed a
-instance US (Boxed a) where
-    data USet (Boxed a) = BoxedTip | BoxedBin {-# UNPACK #-} !Size (Boxed a) !(USet (Boxed a)) !(USet (Boxed a))
-    view BoxedTip = Tip
-    view (BoxedBin s i l r) = Bin s i l r
-    tip = BoxedTip
-    bin = BoxedBin
-
-instance US Char where
-    data USet Char = CharTip | CharBin {-# UNPACK #-} !Size {-# UNPACK #-} !Char !(USet Char) !(USet Char)
-    view CharTip = Tip
-    view (CharBin s i l r) = Bin s i l r
-    tip = CharTip
-    bin = CharBin
-instance US Int where
-    data USet Int = IntTip | IntBin {-# UNPACK #-} !Size {-# UNPACK #-} !Int !(USet Int) !(USet Int)
-    view IntTip = Tip
-    view (IntBin s i l r) = Bin s i l r
-    tip = IntTip
-    bin = IntBin
-
-instance US Integer where
-    data USet Integer = IntegerTip | IntegerBin {-# UNPACK #-} !Size {-# UNPACK #-} !Integer !(USet Integer) !(USet Integer)
-    view IntegerTip = Tip
-    view (IntegerBin s i l r) = Bin s i l r
-    tip = IntegerTip
-    bin = IntegerBin
-
-instance US Int8 where
-    data USet Int8 = Int8Tip | Int8Bin {-# UNPACK #-} !Size {-# UNPACK #-} !Int8 !(USet Int8) !(USet Int8)
-    view Int8Tip = Tip
-    view (Int8Bin s i l r) = Bin s i l r
-    tip = Int8Tip
-    bin = Int8Bin
-
-instance US Int16 where
-    data USet Int16 = Int16Tip | Int16Bin {-# UNPACK #-} !Size {-# UNPACK #-} !Int16 !(USet Int16) !(USet Int16)
-    view Int16Tip = Tip
-    view (Int16Bin s i l r) = Bin s i l r
-    tip = Int16Tip
-    bin = Int16Bin
-
-instance US Int32 where
-    data USet Int32 = Int32Tip | Int32Bin {-# UNPACK #-} !Size {-# UNPACK #-} !Int32 !(USet Int32) !(USet Int32)
-    view Int32Tip = Tip
-    view (Int32Bin s i l r) = Bin s i l r
-    tip = Int32Tip
-    bin = Int32Bin
-
-instance US Int64 where
-    data USet Int64 = Int64Tip | Int64Bin {-# UNPACK #-} !Size {-# UNPACK #-} !Int64 !(USet Int64) !(USet Int64)
-    view Int64Tip = Tip
-    view (Int64Bin s i l r) = Bin s i l r
-    tip = Int64Tip
-    bin = Int64Bin
-
-instance US Word8 where
-    data USet Word8 = Word8Tip | Word8Bin {-# UNPACK #-} !Size {-# UNPACK #-} !Word8 !(USet Word8) !(USet Word8)
-    view Word8Tip = Tip
-    view (Word8Bin s i l r) = Bin s i l r
-    tip = Word8Tip
-    bin = Word8Bin
-
-instance US Word16 where
-    data USet Word16 = Word16Tip | Word16Bin {-# UNPACK #-} !Size {-# UNPACK #-} !Word16 !(USet Word16) !(USet Word16)
-    view Word16Tip = Tip
-    view (Word16Bin s i l r) = Bin s i l r
-    tip = Word16Tip
-    bin = Word16Bin
-
-instance US Word32 where
-    data USet Word32 = Word32Tip | Word32Bin {-# UNPACK #-} !Size {-# UNPACK #-} !Word32 !(USet Word32) !(USet Word32)
-    view Word32Tip = Tip
-    view (Word32Bin s i l r) = Bin s i l r
-    tip = Word32Tip
-    bin = Word32Bin
-
-instance US Word64 where
-    data USet Word64 = Word64Tip | Word64Bin {-# UNPACK #-} !Size {-# UNPACK #-} !Word64 !(USet Word64) !(USet Word64)
-    view Word64Tip = Tip
-    view (Word64Bin s i l r) = Bin s i l r
-    tip = Word64Tip
-    bin = Word64Bin
-
-instance US Double where
-    data USet Double = DoubleTip | DoubleBin {-# UNPACK #-} !Size {-# UNPACK #-} !Double !(USet Double) !(USet Double)
-    view DoubleTip = Tip
-    view (DoubleBin s i l r) = Bin s i l r
-    tip = DoubleTip
-    bin = DoubleBin
-
-instance US Float where
-    data USet Float = FloatTip | FloatBin {-# UNPACK #-} !Size {-# UNPACK #-} !Float !(USet Float) !(USet Float)
-    view FloatTip = Tip
-    view (FloatBin s i l r) = Bin s i l r
-    tip = FloatTip
-    bin = FloatBin
-
diff --git a/monoids.cabal b/monoids.cabal
--- a/monoids.cabal
+++ b/monoids.cabal
@@ -1,5 +1,5 @@
 name:		    monoids
-version:	    0.1.33
+version:	    0.1.36
 license:	    BSD3
 license-file:   LICENSE
 author:		    Edward A. Kmett
@@ -11,72 +11,137 @@
 description:    Monoids, specialized containers and a general map/reduce framework
 copyright:      (c) 2009 Edward A. Kmett
 build-type:     Simple
-cabal-version:  >=1.2
+cabal-version:  >=1.2.3
 
+-- packages we can extend with new instances
+flag bytestring
+  description: Data.ByteString is available (bytestring)
+
+flag fingertree
+  description: Data.Fingertree is available (fingertree)
+
+flag parallel
+  description: Control.Parallel.Strategies is available (parallel)
+  
+flag stm
+  description: Control.Concurrent.STM is available (stm)
+
+flag QuickCheck
+  description: Test.QuickCheck is available (QuickCheck)
+ 
+flag text
+  description: Data.Text is available (text)
+
+flag reflection
+  description: Data.Reflection is available (reflection)
+
+flag parsec
+  description: Text.Parsec is available (parsec >= 3)
+
+flag mtl
+  description: Control.Monad.* is available (mtl)
+
+-- optional extensions
+flag overloaded-strings
+  description: OverloadedStrings extension is available (extension)
+
+-- compilation options
+flag optimize
+  description: Enable optimizations 
+  default: False
+
 library
   build-depends: 
-    base >= 4 && < 4.2,
-    containers >= 0.2 && < 0.3, 
-    text >= 0.1 && < 0.2, 
-    parsec >= 3.0 && < 3.1,
-    fingertree >= 0.0 && < 0.1, 
-    bytestring >= 0.9 && < 1.0, 
-    category-extras >= 0.53 && < 0.60, 
-    parallel >= 1.1 && < 1.2, 
-    mtl >= 1.0 && < 1.2, 
-    stm >= 2.1 && < 2.2, 
-    bitset >= 1.0 && < 1.1, 
-    QuickCheck >= 2.1 && < 2.2, 
+    base >= 4 && < 4.2, 
+    category-extras >= 0.53 && < 0.60,
     array >= 0.2 && < 0.3,
-    reflection >= 0.1 && < 0.2
+    containers >= 0.2 && < 0.3
+
+  extensions:
+    CPP
+
   exposed-modules:
-    Data.Field
-    Data.Field.VectorSpace
+    Data.Generator
+    Data.Generator.Combinators
+    Data.Generator.Compressive.LZ78
+    Data.Generator.Compressive.RLE
+    Data.Generator.Free
     Data.Group
     Data.Group.Combinators
-    Data.Group.Multiplicative
-    Data.Group.Multiplicative.Sugar
     Data.Group.Sugar
     Data.Monoid.Additive
-    Data.Monoid.Additive.Sugar
     Data.Monoid.Applicative
     Data.Monoid.Categorical
     Data.Monoid.Combinators
-    Data.Monoid.FromString
-    Data.Generator
-    Data.Generator.Combinators
-    Data.Generator.Compressive.LZ78
-    Data.Generator.Compressive.RLE
-    Data.Generator.Free
     Data.Monoid.Instances
     Data.Monoid.Lexical.SourcePosition
     Data.Monoid.Lexical.UTF8.Decoder
     Data.Monoid.Lexical.Words
     Data.Monoid.Monad
     Data.Monoid.Multiplicative
-    Data.Monoid.Multiplicative.Sugar
     Data.Monoid.Ord
     Data.Monoid.Reducer
     Data.Monoid.Reducer.Char
     Data.Monoid.Reducer.With
     Data.Monoid.Self
+    Data.Monoid.Sugar
     Data.Monoid.Union
     Data.Ring
-    Data.Ring.Algebra
     Data.Ring.Boolean
     Data.Ring.FromNum
-    Data.Ring.ModularArithmetic
     Data.Ring.Module
     Data.Ring.Module.AutomaticDifferentiation
-    Data.Ring.Semi
     Data.Ring.Semi.BitSet
     Data.Ring.Semi.Kleene
-    Data.Ring.Semi.Near
     Data.Ring.Semi.Near.Trie
     Data.Ring.Semi.Natural
     Data.Ring.Semi.Ord
     Data.Ring.Semi.Tropical
-    Data.Ring.Sugar
-    Data.Set.Unboxed
 
+  if flag (bytestring)
+    build-depends: bytestring >= 0.9 && < 1.0 
+    cpp-options: -DM_BYTESTRING=1
+
+  if flag (fingertree)
+    build-depends: fingertree >= 0.0 && < 0.1
+    cpp-options: -DM_FINGERTREE=1
+
+  if flag (parallel)
+    build-depends: parallel >= 1.1 && < 1.2
+    cpp-options: -DM_PARALLEL=1
+
+  if flag (text)
+    build-depends: text >= 0.1 && < 0.2
+    cpp-options: -DM_TEXT=1
+
+  if flag (stm)
+    build-depends: stm >= 2.1 && < 2.2
+    cpp-options: -DM_STM=1
+
+  if flag (QuickCheck)
+    build-depends: QuickCheck >= 2.1 && < 2.2
+    cpp-options: -DM_QUICKCHECK=1
+
+  if flag (reflection)
+    build-depends: reflection >= 0.1 && < 0.2
+    cpp-options: -DM_REFLECTION=1
+    exposed-modules: Data.Ring.ModularArithmetic
+
+  if flag (parsec)
+    build-depends: parsec >= 3.0 && < 3.1
+    cpp-options: -DM_PARSEC=3
+
+  if flag (overloaded-strings)
+    extensions: OverloadedStrings
+    cpp-options: -DX_OverloadedStrings=1
+    exposed-modules: Data.Monoid.FromString
+
+  if flag (mtl) 
+    build-depends: mtl >= 1.0 && < 1.2 
+    cpp-options: -DM_MTL=1
+    
   ghc-options: -Wall -fno-warn-duplicate-exports
+  cpp-options -DM_ARRAY=1 -DM_CONTAINERS=1
+
+  if flag (optimize)
+    ghc-options: -funbox-strict-fields -O2 -fdicts-cheap