diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,10 @@
+# 0.4
+* Rename `Nat` constructor to `NT`
+* Rename `run` to `unwrapNT`
+* Rename `nat` to `wrapNT`
+* Backport the `Semigroup` instance for `(:~>)` by conditionally depending on
+  the `semigroups` package
+
 # 0.3.1
 * Adding `run` and `nat`.
 
diff --git a/LICENSE b/LICENSE
--- a/LICENSE
+++ b/LICENSE
@@ -1,4 +1,4 @@
-Copyright (c) 2015, The University of Kansas
+Copyright (c) 2015-2016, The University of Kansas
 
 All rights reserved.
 
diff --git a/natural-transformation.cabal b/natural-transformation.cabal
--- a/natural-transformation.cabal
+++ b/natural-transformation.cabal
@@ -1,5 +1,5 @@
 name:                natural-transformation
-version:             0.3.1
+version:             0.4
 synopsis:            A natural transformation package.
 description:         A natural transformation transforms a container @f a@ into another
                      container @g a@. Natural transformations act as functor morphisms
@@ -14,23 +14,26 @@
 stability:           Provisional
 author:              Andy Gill
 maintainer:          Andy Gill <andygill@ku.edu>
-copyright:           Copyright (c) 2015 The University of Kansas
+copyright:           Copyright (c) 2015-2016 The University of Kansas
 category:            Control
 build-type:          Simple
 extra-source-files:  CHANGELOG.md, README.md
-tested-with:         GHC == 7.8.4, GHC == 7.10.3
+tested-with:         GHC == 7.8.4, GHC == 7.10.3, GHC == 8.0.1
 cabal-version:       >= 1.10
 
 source-repository head
   type:                git
-  location:            git://github.com/ku-fpg/natural-transformation
+  location:            https://github.com/ku-fpg/natural-transformation
 
 library
   exposed-modules:     Control.Natural
                        Control.Natural.RULES
                        Control.Object
-                       
-  build-depends:       base >= 4.7 && < 5
+
+  build-depends:       base       >= 4.7  && < 5
+  if !impl(ghc >= 8.0)
+    build-depends:     semigroups >= 0.16 && < 0.19
+
   hs-source-dirs:      src
   default-language:    Haskell2010
   ghc-options:         -Wall
@@ -40,7 +43,7 @@
   main-is:             Properties.hs
   build-depends:       base                   >= 4.7 && < 5
                      , containers             >= 0.1 && < 0.6
-                     , natural-transformation == 0.3.1
+                     , natural-transformation == 0.4
                      , quickcheck-instances   >= 0.1 && < 0.4
                      , tasty                  >= 0.8 && < 0.12
                      , tasty-quickcheck       >= 0.8 && < 0.9
diff --git a/src/Control/Natural.hs b/src/Control/Natural.hs
--- a/src/Control/Natural.hs
+++ b/src/Control/Natural.hs
@@ -24,8 +24,8 @@
     -- * Type Synonym for a Natural Transformation
   , type (~>)
     -- * Conversion functions between the newtype and the synonym
-  , run
-  , nat
+  , wrapNT
+  , unwrapNT
     -- * Class for Natural Transformations
   , Transformation(..)
   ) where
@@ -35,9 +35,7 @@
 #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
 
 ---------------------------------------------------------------------------
@@ -50,21 +48,19 @@
 
 infixr 0 :~>, $$
 -- | A natural transformation suitable for storing in a container.
-newtype f :~> g = Nat { ($$) :: f ~> g }
+newtype f :~> g = NT { ($$) :: f ~> g }
   deriving Typeable
 
 instance C.Category (:~>) where
-    id = Nat id
-    Nat f . Nat g = Nat (f . g)
+    id = NT id
+    NT f . NT g = NT (f . g)
 
-#if MIN_VERSION_base(4,9,0)
 instance f ~ g => Semigroup (f :~> g) where
-    Nat f <> Nat g = Nat (f . g)
-#endif
+    NT f <> NT g = NT (f . g)
 
 instance f ~ g => Monoid (f :~> g) where
-    mempty = Nat id
-    mappend (Nat f) (Nat g) = Nat (f . g)
+    mempty = NT id
+    mappend = (<>)
 
 infix 0 #
 -- | A (natural) transformation is inside @t@, and contains @f@ and @g@
@@ -78,14 +74,17 @@
     (#) :: t -> forall a . f a -> g a
 
 instance Transformation f g (f :~> g) where
-    Nat f # g = f g
+    NT f # g = f g
 
--- | 'run' is the nonfix version of @#@. It is used to break natural
---   transformation wrappers, including ':~>'.
-run :: Transformation f g t => t -> (forall a . f a -> g a)
-run = (#)
+-- | 'wrapNT' builds our natural transformation abstraction out of
+-- a natural transformation function.
+--
+-- An alias to 'NT' provided for symmetry with 'unwrapNT'.
+--
+wrapNT :: (forall a . f a -> g a) -> f :~> g
+wrapNT = NT
 
--- | 'nat' builds our natural transformation abstraction out of
---    a natural transformation function.
-nat :: (forall a . f a -> g a) -> f :~> g
-nat = Nat
+-- | 'unwrapNT' is the nonfix version of @#@. It is used to break natural
+--   transformation wrappers, including ':~>'.
+unwrapNT :: Transformation f g t => t -> (forall a . f a -> g a)
+unwrapNT = (#)
diff --git a/src/Control/Object.hs b/src/Control/Object.hs
--- a/src/Control/Object.hs
+++ b/src/Control/Object.hs
@@ -22,4 +22,4 @@
 newtype Object f = Object (f ~> IO)
 
 instance Transformation f IO (Object f) where
-    Object f # g = Nat f # g
+    Object f # g = NT f # g
diff --git a/tests/Properties.hs b/tests/Properties.hs
--- a/tests/Properties.hs
+++ b/tests/Properties.hs
@@ -58,19 +58,19 @@
 
 -- | A natural transformations from lists to lists that 'reverse's.
 listReverseNT :: [] :~> []
-listReverseNT = Nat reverse
+listReverseNT = NT reverse
 
 -- | A natural transformation from lists to lists that shifts all elements to the left,
 -- moving the head element to the back.
 listShiftNT :: [] :~> []
-listShiftNT = Nat $ \l -> case l of
+listShiftNT = NT $ \l -> case l of
                                []     -> []
                                (x:xs) -> xs ++ [x]
 
 -- | A natural transformation from lists to 'Seq's.
 listSeqNT :: [] :~> Seq
-listSeqNT = Nat fromList
+listSeqNT = NT fromList
 
 -- | A natural transformation from 'Seq's to lists.
 seqListNT :: Seq :~> []
-seqListNT = Nat toList
+seqListNT = NT toList