diff --git a/finite-field.cabal b/finite-field.cabal
--- a/finite-field.cabal
+++ b/finite-field.cabal
@@ -1,5 +1,5 @@
 Name:		finite-field
-Version:	0.4.0
+Version:	0.5.0
 License:	BSD3
 License-File:	COPYING
 Author:		Masahiro Sakai (masahiro.sakai@gmail.com)
@@ -7,7 +7,9 @@
 Category:	Math, Data
 Cabal-Version:	>= 1.10
 Synopsis:	Finite Fields
-Description:	Implementation of finite fields
+Description:
+  This is an implementation of finite fields.
+  Currently only prime fields are supported.
 Bug-Reports:	https://github.com/msakai/finite-field/issues
 Extra-Source-Files:
    README.md
@@ -23,7 +25,7 @@
 Library
   Hs-source-dirs: src
   Build-Depends:
-     base >=4 && <5, deepseq, type-level-numbers, algebra >=3.1
+     base >=4 && <5, template-haskell, deepseq, type-level-numbers, algebra >=3.1
   Default-Language: Haskell2010
   Other-Extensions:
      DeriveDataTypeable
@@ -31,7 +33,10 @@
      ScopedTypeVariables
      Rank2Types
      GADTs
+     TemplateHaskell
   Exposed-Modules:
+     Data.FiniteField
+     Data.FiniteField.Base
      Data.FiniteField.PrimeField
      Data.FiniteField.SomeNat
 
diff --git a/src/Data/FiniteField.hs b/src/Data/FiniteField.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/FiniteField.hs
@@ -0,0 +1,18 @@
+-----------------------------------------------------------------------------
+-- |
+-- module      :  Data.FiniteField
+-- Copyright   :  (c) Masahiro Sakai 2013
+-- License     :  BSD-style
+--
+-- Maintainer  :  masahiro.sakai@gmail.com
+-- Stability   :  provisional
+-- Portability :  portable
+--
+-----------------------------------------------------------------------------
+module Data.FiniteField
+  ( module Data.FiniteField.Base
+  , module Data.FiniteField.PrimeField
+  ) where
+
+import Data.FiniteField.Base
+import Data.FiniteField.PrimeField
diff --git a/src/Data/FiniteField/Base.hs b/src/Data/FiniteField/Base.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/FiniteField/Base.hs
@@ -0,0 +1,30 @@
+-----------------------------------------------------------------------------
+-- |
+-- module      :  Data.FiniteField.Base
+-- Copyright   :  (c) Masahiro Sakai 2013
+-- License     :  BSD-style
+--
+-- Maintainer  :  masahiro.sakai@gmail.com
+-- Stability   :  provisional
+-- Portability :  portable
+--
+-----------------------------------------------------------------------------
+module Data.FiniteField.Base
+  ( FiniteField (..)
+  ) where
+
+import Data.Ratio
+import qualified Numeric.Algebra as Alg
+
+-- | Type class for finite fields
+class Fractional k => FiniteField k where
+  -- | The order is number of elements of a finite field @k@.
+  -- It of the form @p^n@, where @p@ is  prime number called the characteristic
+  -- of the field, and @n@ is a positive integer.
+  order   :: k -> Integer
+
+  -- | The characteristic of a field, @p@.
+  char    :: k -> Integer
+
+  -- | The inverse of Frobenius endomorphism @x@ ↦ @x^p@.
+  pthRoot :: k -> k
diff --git a/src/Data/FiniteField/PrimeField.hs b/src/Data/FiniteField/PrimeField.hs
--- a/src/Data/FiniteField/PrimeField.hs
+++ b/src/Data/FiniteField/PrimeField.hs
@@ -1,4 +1,4 @@
-{-# LANGUAGE ScopedTypeVariables, MultiParamTypeClasses, DeriveDataTypeable #-}
+{-# LANGUAGE ScopedTypeVariables, MultiParamTypeClasses, DeriveDataTypeable, TemplateHaskell #-}
 {-# OPTIONS_GHC -Wall #-}
 -----------------------------------------------------------------------------
 -- |
@@ -8,9 +8,9 @@
 --
 -- Maintainer  :  masahiro.sakai@gmail.com
 -- Stability   :  provisional
--- Portability :  non-portable (ScopedTypeVariables, MultiParamTypeClasses, DeriveDataTypeable)
+-- Portability :  non-portable (ScopedTypeVariables, MultiParamTypeClasses, DeriveDataTypeable, TemplateHaskell)
 --
--- Finite field of prime order Fp.
+-- Finite field of prime order p, Fp = Z/pZ.
 --
 -- References:
 --
@@ -20,16 +20,21 @@
 module Data.FiniteField.PrimeField
   ( PrimeField
   , toInteger
+  -- * Template haskell utilities
+  -- $TH
+  , primeField
   ) where
 
 import Prelude hiding (toInteger)
 import Control.DeepSeq
 import Data.Ratio (denominator, numerator)
 import Data.Typeable
+import qualified Language.Haskell.TH as TH
 import qualified Numeric.Algebra as Alg
 import qualified TypeLevel.Number.Nat as TL
+import Data.FiniteField.Base
 
--- | Finite field of prime order Fp.
+-- | Finite field of prime order p, Fp = Z/pZ.
 --
 -- NB: Primality of @p@ is assumed, but not checked.
 newtype PrimeField p = PrimeField Integer deriving (Eq, Typeable)
@@ -78,6 +83,11 @@
   PrimeField a `max` PrimeField b = PrimeField (a `max` b)
   PrimeField a `min` PrimeField b = PrimeField (a `min` b)
 
+instance TL.Nat p => FiniteField (PrimeField p) where
+  order _   = TL.toInt (undefined :: p)
+  char _    = TL.toInt (undefined :: p)
+  pthRoot a = a
+
 -- ---------------------------------------------------------------------------
 
 instance TL.Nat p => Alg.Multiplicative (PrimeField p) where
@@ -127,8 +137,14 @@
 
 -- ---------------------------------------------------------------------------
 
-{-
-type GF2 = PrimeField (SuccessorTo (SuccessorTo Zero))
-type GF3 = PrimeField (SuccessorTo (SuccessorTo (SuccessorTo Zero)))
-type GF5 = PrimeField (SuccessorTo (SuccessorTo (SuccessorTo (SuccessorTo (SuccessorTo Zero)))))
--}
+-- | Create a PrimeField type
+primeField :: Integer -> TH.TypeQ
+primeField n
+  | n <= 0    = error "primeField: negative value"
+  | otherwise = [t| PrimeField $(TL.natT n) |]
+
+-- $TH
+-- Here is usage example for primeField:
+--
+-- > a :: $(primeField 15485867)
+-- > a = 1
diff --git a/test/TestPrimeField.hs b/test/TestPrimeField.hs
--- a/test/TestPrimeField.hs
+++ b/test/TestPrimeField.hs
@@ -1,14 +1,15 @@
 {-# LANGUAGE TemplateHaskell, ScopedTypeVariables #-}
 
+import Test.HUnit hiding (Test)
 import Test.QuickCheck
 import Test.Framework.TH
 import Test.Framework.Providers.QuickCheck2
+import Test.Framework.Providers.HUnit
 
 import Control.Monad
 import Data.Numbers.Primes (primes)
 
-import Data.FiniteField.PrimeField (PrimeField)
-import qualified Data.FiniteField.PrimeField as PrimeField
+import Data.FiniteField
 import Data.FiniteField.SomeNat (SomeNat (..))
 import qualified Data.FiniteField.SomeNat as SomeNat
 import TypeLevel.Number.Nat
@@ -106,11 +107,24 @@
       a /= 0 ==> a * (recip a) == 1
 
 -- ----------------------------------------------------------------------
+-- pthRoot
 
+prop_pthRoot =
+  forAll smallPrimes $ \(SomeNat (_ :: p)) ->
+    forAll arbitrary $ \(a :: PrimeField p) ->
+      pthRoot a ^ char a == a
+
+-- ----------------------------------------------------------------------
+
 prop_intToSomeNat = do
   forAll arbitrary $ \n ->
     case SomeNat.fromInteger (abs n) of
       SomeNat m -> abs n == toInt m
+
+case_primeFieldT = a @?= 1
+  where
+    a :: $(primeField 15485867)
+    a = 15485867 + 1
 
 ------------------------------------------------------------------------