diff --git a/src/Data/TypeFun.hs b/src/Data/TypeFun.hs
--- a/src/Data/TypeFun.hs
+++ b/src/Data/TypeFun.hs
@@ -1,13 +1,15 @@
+-- | Emulation of type-level functions.
 module Data.TypeFun (
 
     -- * Type-level functions in general
     TypeFun (type Domain),
     App,
 
-    -- * Specific type-level functions
+    -- * Construction of type-level functions
     Id (Id),
     Const (Const),
     (:->) ((:->)),
+    FunMap,
 
     -- * Utilities
     WrappedApp (WrapApp),
@@ -18,6 +20,11 @@
 
     import Data.Kind as Kind
 
+    {-NOTE:
+        At the value level, type-level function representations contain other /representations/ but
+        nothing else.
+    -}
+
     -- * Type-level functions in general
     {-|
         Type-level functions are represented by types. @TypeFun@ is the class of all type-level
@@ -37,12 +44,12 @@
     -}
     type family App fun arg
 
-    -- * Specific type-level functions
+    -- * Construction of type-level functions
     infixr 1 :->
 
     {-|
         A type @Id /d/@ represents the type-level identity function whose domain is represented
-        by /d/.
+        by @/d/@.
     -}
     data Id dom = Id dom
 
@@ -54,9 +61,9 @@
 
     {-|
         A type @Const /d/ /v/@ represents the constant type-level function whose domain is
-        represented by /d/, and whose result is @/v/@.
+        represented by @/d/@, and whose result is @/v/@.
     -}
-    data Const dom val = Const dom val
+    data Const dom val = Const dom
 
     instance (Kind dom) => TypeFun (Const dom val) where
 
@@ -65,7 +72,8 @@
     type instance App (Const dom val) arg = val
 
     {-|
-        A type @/f/ :-> /f'/@ represents the type-level function @\\arg -> (/f/ arg -> /f'/ arg)@.
+        A type @/f/ :-> /f'/@ represents the type-level function @\\arg -> ('App' /f/ arg -> 'App'
+        /f'/ arg)@.
     -}
     data fun :-> fun' = fun :-> fun'
 
@@ -74,6 +82,18 @@
         type Domain (fun :-> fun') = Domain fun
 
     type instance App (fun :-> fun') arg = App fun arg -> App fun' arg
+
+    {-|
+        If @/t/@ is a type of kind @* -> *@, and @/f/@ is the representation of a
+        type-level function, @FunMap /t/ /f/@ represents the function @\\arg -> /t/ (App /f/ arg)@.
+    -}
+    data FunMap (trans :: * -> *) fun = FunMap fun
+
+    instance (TypeFun fun) => TypeFun (FunMap trans fun) where
+
+        type Domain (FunMap trans fun) = Domain fun
+
+    type instance App (FunMap trans fun) arg = trans (App fun arg)
 
     -- * Utilities
     -- |A data type that is isomorphic to the type synonym family 'App'.
diff --git a/type-functions.cabal b/type-functions.cabal
--- a/type-functions.cabal
+++ b/type-functions.cabal
@@ -1,5 +1,5 @@
 Name:          type-functions
-Version:       0.1.0.0
+Version:       0.2.0.0
 Cabal-Version: >= 1.2.3
 Build-Type:    Simple
 License:       BSD3
@@ -10,13 +10,16 @@
 Stability:     provisional
 Homepage:      http://community.haskell.org/~jeltsch/type-functions/
 Bug-Reports:   jeltsch@tu-cottbus.de
-Package-URL:   http://hackage.haskell.org/packages/archive/type-functions/0.0.0.0/type-functions-0.0.0.0.tar.gz
+Package-URL:   http://hackage.haskell.org/packages/archive/type-functions/0.2.0.0/type-functions-0.2.0.0.tar.gz
 Synopsis:      Emulation of type-level functions
 Description:   This package supports emulation of type-level functions using defunctionalization.
                All functions whose domain is a subkind of @*@ and whose codomain is @*@
                itself can be represented.
+               .
+               For detailed information, please refer to Subsection 3.2 of the paper
+               /Generic Record Combinators with Static Type Checking/.
 Category:      Type System
-Tested-With:   GHC == 6.10.4
+Tested-With:   GHC == 6.12.1
 
 Library
     Build-Depends:   base  >= 3.0   && < 4.1,