diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,10 @@
+# 0.3
+* Adding Object
+* Rolled Control.Transformation into Control.Natural
+* Added RULES module
+* Required GHC 7.8 or greater
+* `Semigroup` instance for `(:~>)` on GHC 8.0 and up
+
 # 0.2
 * Require GHC 7.6 or greater
 * Exposed `~>` type synonym
diff --git a/README.md b/README.md
--- a/README.md
+++ b/README.md
@@ -1,3 +1,5 @@
 # natural-transformation [![Hackage version](https://img.shields.io/hackage/v/natural-transformation.svg?style=flat)](http://hackage.haskell.org/package/natural-transformation) [![Build Status](https://img.shields.io/travis/ku-fpg/natural-transformation.svg?style=flat)](https://travis-ci.org/ku-fpg/natural-transformation)
 
-A natural transformation transforms a container `f a` into another container `g a` while preserving the internal structure. Natural transformations act as functor morphisms in category theory. Technically, `f` and `g` should be functors, but we allow any correctly-shaped structure.
+A natural transformation transforms a container `f a` into another container `g a`. 
+Natural transformations act as functor morphisms in category theory. 
+Technically, `f` and `g` should be functors, but we allow any correctly-shaped structure.
diff --git a/natural-transformation.cabal b/natural-transformation.cabal
--- a/natural-transformation.cabal
+++ b/natural-transformation.cabal
@@ -1,9 +1,12 @@
 name:                natural-transformation
-version:             0.2
+version:             0.3
 synopsis:            A natural transformation package.
 description:         A natural transformation transforms a container @f a@ into another
-                     container @g a@ while preserving the internal structure. Natural
-                     transformations act as functor morphisms in category theory.
+                     container @g a@. Natural transformations act as functor morphisms
+                     in category theory.
+                     .
+                     The naming of '~>', ':~>' and '$$' were taken,
+                     with permission, from Edward Kmett's @indexed@ package.
 homepage:            https://github.com/ku-fpg/natural-transformation
 bug-reports:         https://github.com/ku-fpg/natural-transformation/issues
 license:             BSD3
@@ -15,6 +18,7 @@
 category:            Control
 build-type:          Simple
 extra-source-files:  CHANGELOG.md, README.md
+tested-with:         GHC == 7.8.4, GHC == 7.10.3
 cabal-version:       >= 1.10
 
 source-repository head
@@ -23,8 +27,10 @@
 
 library
   exposed-modules:     Control.Natural
-                       Control.Transformation
-  build-depends:       base >= 4.6 && < 5
+                       Control.Natural.RULES
+                       Control.Object
+                       
+  build-depends:       base >= 4.7 && < 5
   hs-source-dirs:      src
   default-language:    Haskell2010
   ghc-options:         -Wall
@@ -32,11 +38,11 @@
 test-suite natural-transformation-properties
   type:                exitcode-stdio-1.0
   main-is:             Properties.hs
-  build-depends:       base                   >= 4.6 && < 5
+  build-depends:       base                   >= 4.7 && < 5
                      , containers             >= 0.1 && < 0.6
-                     , natural-transformation == 0.2
+                     , natural-transformation == 0.3
                      , quickcheck-instances   >= 0.1 && < 0.4
-                     , tasty                  >= 0.8 && < 0.11
+                     , tasty                  >= 0.8 && < 0.12
                      , tasty-quickcheck       >= 0.8 && < 0.9
   hs-source-dirs:      tests
   default-language:    Haskell2010
diff --git a/src/Control/Natural.hs b/src/Control/Natural.hs
--- a/src/Control/Natural.hs
+++ b/src/Control/Natural.hs
@@ -1,22 +1,13 @@
 {-# LANGUAGE CPP #-}
+{-# LANGUAGE DeriveDataTypeable #-}
 {-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE FunctionalDependencies #-}
 {-# LANGUAGE GADTs #-}
-{-# LANGUAGE RankNTypes #-}
-{-# LANGUAGE TypeOperators #-}
-
-#if MIN_VERSION_base(4,7,0)
-# define LANGUAGE_PolyKinds
+{-# LANGUAGE MultiParamTypeClasses #-}
 {-# LANGUAGE PolyKinds #-}
-#endif
-
-#if __GLASGOW_HASKELL__ >= 708
-# define LANGUAGE_DeriveDataTypeable
-{-# LANGUAGE DeriveDataTypeable #-}
+{-# LANGUAGE RankNTypes #-}
 {-# LANGUAGE Safe #-}
-#else
-{-# LANGUAGE ScopedTypeVariables #-}
-{-# LANGUAGE Trustworthy #-}
-#endif
+{-# LANGUAGE TypeOperators #-}
 
 {-|
 Module:      Control.Natural
@@ -25,21 +16,29 @@
 Maintainer:  Andy Gill
 Stability:   Experimental
 
-A data type for natural transformations.
+A data type and class for natural transformations.
 -}
-module Control.Natural ((~>)(), (:~>)(..)) where
+module Control.Natural
+  ( -- * Type Synonym for a Natural Transformation
+    type (~>)
+    -- * Newtype for a Natural Transformation
+  , (:~>)(..)
+    -- * Class for Natural Transformations
+  , Transformation(..)
+  ) where
 
-#if defined(LANGUAGE_PolyKinds)
 import qualified Control.Category as C (Category(..))
-#endif
 
 #if !(MIN_VERSION_base(4,8,0))
 import           Data.Monoid (Monoid(..))
 #endif
+#if MIN_VERSION_base(4,9,0)
+import           Data.Semigroup (Semigroup(..))
+#endif
 import           Data.Typeable
 
 ---------------------------------------------------------------------------
--- Code adapted, with permission, from Edward Kmett's @indexed@ package.
+-- Naming of ~>, :~> and $$ are taken (with permission) from Edward Kmett's @indexed@ package.
 ---------------------------------------------------------------------------
 
 infixr 0 ~>
@@ -49,27 +48,31 @@
 infixr 0 :~>, $$
 -- | A natural transformation suitable for storing in a container.
 newtype f :~> g = Nat { ($$) :: f ~> g }
-#if defined(LANGUAGE_DeriveDataTypeable)
   deriving Typeable
-#else
-instance (Typeable1 f, Typeable1 g) => Typeable (f :~> g) where
-    typeOf _ = mkTyConApp natTyCon [typeOf1 (undefined :: f a), typeOf1 (undefined :: g a)]
 
-natTyCon :: TyCon
-# if MIN_VERSION_base(4,4,0)
-natTyCon = mkTyCon3 "natural-transformation" "Control.Natural" ":~>"
-# else
-natTyCon = mkTyCon ":~>"
-# endif
-{-# NOINLINE natTyCon #-}
-#endif
-
-#if defined(LANGUAGE_PolyKinds)
 instance C.Category (:~>) where
     id = Nat id
     Nat f . Nat g = Nat (f . g)
+
+#if MIN_VERSION_base(4,9,0)
+instance f ~ g => Semigroup (f :~> g) where
+    Nat f <> Nat g = Nat (f . g)
 #endif
 
 instance f ~ g => Monoid (f :~> g) where
     mempty = Nat id
     mappend (Nat f) (Nat g) = Nat (f . g)
+
+infix 0 #
+-- | A (natural) transformation is inside @t@, and contains @f@ and @g@
+-- (typically 'Functor's).
+--
+-- The order of arguments allows the use of @GeneralizedNewtypeDeriving@ to wrap
+-- a ':~>', but maintain the 'Transformation' constraint. Thus, @#@ can be used
+-- on abstract data types.
+class Transformation f g t | t -> f g where
+    -- | The invocation method for a natural transformation.
+    (#) :: t -> f a -> g a
+
+instance Transformation f g (f :~> g) where
+    Nat f # g = f g
diff --git a/src/Control/Natural/RULES.hs b/src/Control/Natural/RULES.hs
new file mode 100644
--- /dev/null
+++ b/src/Control/Natural/RULES.hs
@@ -0,0 +1,32 @@
+{-# LANGUAGE FunctionalDependencies #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE Trustworthy #-}
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+{-|
+Module:      Control.Transformation.RULES
+Copyright:   (C) 2015 The University of Kansas
+License:     BSD-style (see the file LICENSE)
+Maintainer:  Andy Gill
+Stability:   Experimental
+
+= GHC RULE for Natural Transformation
+
+
+@
+  RULES "natural free theorem" [~]
+     forall h (r :: (Functor f, Functor g, Transformation f g t) => t) .
+       fmap h . (r \#) = (r #) . fmap h
+@
+
+-}
+module Control.Natural.RULES () where
+
+import Control.Natural
+
+{-# RULES "natural free theorem" [~]
+     forall h (r :: (Functor f, Functor g, Transformation f g t) => t) .
+       fmap h . (r #) = (r #) . fmap h
+  #-}
+
diff --git a/src/Control/Object.hs b/src/Control/Object.hs
new file mode 100644
--- /dev/null
+++ b/src/Control/Object.hs
@@ -0,0 +1,25 @@
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE Safe #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE RankNTypes #-}
+
+{-|
+Module:      Control.Object
+Copyright:   (C) 2015 The University of Kansas
+License:     BSD-style (see the file LICENSE)
+Maintainer:  Andy Gill
+Stability:   Experimental
+
+An Object type, which is a natural transformation into the 'IO' monad.
+-}
+
+module Control.Object (Object(..), (#)) where
+
+import Control.Natural
+
+-- | An 'Object' is a natural transformation from a given 'Functor' 'f', to 'IO'.
+newtype Object f = Object (f ~> IO)
+
+instance Transformation f IO (Object f) where
+    Object f # g = Nat f # g
diff --git a/src/Control/Transformation.hs b/src/Control/Transformation.hs
deleted file mode 100644
--- a/src/Control/Transformation.hs
+++ /dev/null
@@ -1,42 +0,0 @@
-{-# LANGUAGE CPP #-}
-{-# LANGUAGE FlexibleInstances #-} 
-{-# LANGUAGE FunctionalDependencies #-}
-{-# LANGUAGE MultiParamTypeClasses #-}
-{-# LANGUAGE Safe #-}
-{-# LANGUAGE TypeOperators #-}
-
-#if MIN_VERSION_base(4,7,0)
-{-# LANGUAGE PolyKinds #-}
-#endif
-
-{-|
-Module:      Control.Transformation
-Copyright:   (C) 2015 The University of Kansas
-License:     BSD-style (see the file LICENSE)
-Maintainer:  Andy Gill
-Stability:   Experimental
-
-A type class for transformations.
--}
-module Control.Transformation (Transformation(..)) where
-
-import Control.Natural ((:~>)(..))
-
-infixr 0 #
--- | A (natural) transformation is inside @t@, and contains @f@ and @g@
--- (typically 'Functor's).
--- 
--- The order of arguments allows the use of @GeneralizedNewtypeDeriving@ to wrap
--- a ':~>', but maintain the 'Transformation' constraint. Thus, @#@ can be used
--- on abstract data types.
-class Transformation f g t | t -> f g where
-    -- | The invocation method for a natural transformation.
-    (#) :: t -> f a -> g a
-
--- {-# RULES "natural free theorem" [~] 
---     forall h (r :: (Functor f, Functor g, Transformation f g t) => t) . 
---     fmap h . (r #) = (r #) . fmap h 
---   #-}
-
-instance Transformation f g (f :~> g) where
-    Nat f # g = f g
diff --git a/tests/Properties.hs b/tests/Properties.hs
--- a/tests/Properties.hs
+++ b/tests/Properties.hs
@@ -11,8 +11,7 @@
 -}
 module Main (main) where
 
-import Control.Natural ((:~>)(..))
-import Control.Transformation (Transformation(..))
+import Control.Natural
 
 import Data.Foldable (toList)
 #if !(MIN_VERSION_base(4,8,0))