diff --git a/defargs.cabal b/defargs.cabal
--- a/defargs.cabal
+++ b/defargs.cabal
@@ -1,6 +1,6 @@
 name: defargs
 category: type system
-version: 0.1
+version: 0.2
 license: BSD3
 license-file: LICENSE
 cabal-version: >= 1.10
@@ -12,7 +12,7 @@
 bug-reports: https://github.com/Kinokkory/defargs/issues
 copyright: (c) Yusuke Matsushita 2014
 synopsis:  default arguments in haskell
-description: Default arguments in Haskell.
+description: Default arguments in Haskell. More information can be found in <http://hackage.haskell.org/package/defargs the hackage's haddock> or the <http://kinokkory.github.io/defargs/ updated haddock>.
 
 build-type: Simple
 
diff --git a/src/Type/DefArgs.hs b/src/Type/DefArgs.hs
--- a/src/Type/DefArgs.hs
+++ b/src/Type/DefArgs.hs
@@ -26,8 +26,12 @@
     -- * Converters
     -- $converters
   , defarg, defargs2, defargs3, defargs4, defargs5
-  , defargs6, defargs7, defargs8, defargs9, defargs10) where
+  , defargs6, defargs7, defargs8, defargs9, defargs10
 
+    -- * Constraints
+  , DefArg, DefArgs2, DefArgs3, DefArgs4, DefArgs5
+  , DefArgs6, DefArgs7, DefArgs8, DefArgs9, DefArgs10) where
+
 import Type.Cluss
 
 -- | When used as an argument, 'Def' will be replaced with the corresponding default value by 'defarg', 'defargs2', ..., and 'defargs10'.
@@ -40,24 +44,38 @@
 (&) = Cons
 infixr 0 *, &
 
+type (=?) a = In [Type Def, Type a]
+
 -- core
-class DefArgs f as where
-  type P f as ::[*]
-  defargs' :: In (P f as) g => f -> as -> g
-instance DefArgs r Nil where
+class DefArgs' f as where
+  type P f as :: [*]
+  defargs' :: K f as g => f -> as -> g
+type K f as = In (P f as)
+instance DefArgs' r Nil where
   type P r Nil = '[Type r]
   defargs' x Nil = projI (
     x `andI`
     noneI :: AllOfI '[Type r])
-instance DefArgs f as => DefArgs (a -> f) (a * as) where
-  type P (a -> f) (a * as) = [Unary ((->) Def) (In (P f as)), Unary ((->) a) (In (P f as))]
-  defargs' f (Cons x xs) = projI (
-    (\Def -> defargs' (f x) xs) `andI1`
-    (\x' -> defargs' (f x') xs) `andI1`
+instance DefArgs' f as => DefArgs' (a -> f) (a * as) where
+  type P (a -> f) (a * as) = '[Binary (->) ((=?) a >|< K f as)]
+  defargs' f (Cons x xs) = projI ((projF (
+      (\Def -> defargs' (f x) xs) `andF`
+      (\x' -> defargs' (f x') xs) `andF`
+      noneF)) `andI2`
     noneI :: AllOfI (P (a -> f) (a * as)))
 
--- the constraint
-type Good f d g = (DefArgs f d, In (P f d) g)
+-- the constraints
+type Good f d g = (DefArgs' f d, In (P f d) g)
+type DefArg r a a' = Good (a -> r) (a * Nil) (a' -> r)
+type DefArgs2 r a b a' b' = Good (a -> b -> r) (a * b * Nil) (a' -> b' -> r)
+type DefArgs3 r a b c a' b' c' = Good (a -> b -> c -> r) (a * b * c * Nil) (a' -> b' -> c' -> r)
+type DefArgs4 r a b c d a' b' c' d' = Good (a -> b -> c -> d -> r) (a * b * c * d * Nil) (a' -> b' -> c' -> d' -> r)
+type DefArgs5 r a b c d e a' b' c' d' e' = Good (a -> b -> c -> d -> e -> r) (a * b * c * d * e * Nil) (a' -> b' -> c' -> d' -> e' -> r)
+type DefArgs6 r a b c d e f a' b' c' d' e' f' = Good (a -> b -> c -> d -> e -> f -> r) (a * b * c * d * e * f * Nil) (a' -> b' -> c' -> d' -> e' -> f' -> r)
+type DefArgs7 r a b c d e f g a' b' c' d' e' f' g' = Good (a -> b -> c -> d -> e -> f -> g -> r) (a * b * c * d * e * f * g * Nil) (a' -> b' -> c' -> d' -> e' -> f' -> g' -> r)
+type DefArgs8 r a b c d e f g h a' b' c' d' e' f' g' h' = Good (a -> b -> c -> d -> e -> f -> g -> h -> r) (a * b * c * d * e * f * g * h * Nil) (a' -> b' -> c' -> d' -> e' -> f' -> g' -> h' -> r)
+type DefArgs9 r a b c d e f g h i a' b' c' d' e' f' g' h' i' = Good (a -> b -> c -> d -> e -> f -> g -> h -> i -> r) (a * b * c * d * e * f * g * h * i * Nil) (a' -> b' -> c' -> d' -> e' -> f' -> g' -> h' -> i' -> r)
+type DefArgs10 r a b c d e f g h i j a' b' c' d' e' f' g' h' i' j' = Good (a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> r) (a * b * c * d * e * f * g * h * i * j * Nil) (a' -> b' -> c' -> d' -> e' -> f' -> g' -> h' -> i' -> j' -> r)
 
 -- $converters
 -- Given a function, these converters provide every argument of the function with a default value.
@@ -68,25 +86,25 @@
 -- Internally, the judgment is made by <http://hackage.haskell.org/package/cluss cluss>.
 
 -- converters
-defarg :: Good (a -> r) (a * Nil) (a' -> r) => (a -> r) -> a -> (a' -> r)
+defarg :: DefArg r a a' => (a -> r) -> a -> (a' -> r)
 defarg f x = defargs' f (x & Nil)
-defargs2 :: Good (a -> b -> r) (a * b * Nil) (a' -> b' -> r) => (a -> b -> r) -> a -> b -> (a' -> b' -> r)
+defargs2 :: DefArgs2 r a b a' b' => (a -> b -> r) -> a -> b -> (a' -> b' -> r)
 defargs2 f x x2 = defargs' f (x & x2 & Nil)
-defargs3 :: Good (a -> b -> c -> r) (a * b * c * Nil) (a' -> b' -> c' -> r) => (a -> b -> c -> r) -> a -> b -> c -> (a' -> b' -> c' -> r)
+defargs3 :: DefArgs3 r a b c a' b' c' => (a -> b -> c -> r) -> a -> b -> c -> (a' -> b' -> c' -> r)
 defargs3 f x x2 x3 = defargs' f (x & x2 & x3 & Nil)
-defargs4 :: Good (a -> b -> c -> d -> r) (a * b * c * d * Nil) (a' -> b' -> c' -> d' -> r) => (a -> b -> c -> d -> r) -> a -> b -> c -> d -> (a' -> b' -> c' -> d' -> r)
+defargs4 :: DefArgs4 r a b c d a' b' c' d' => (a -> b -> c -> d -> r) -> a -> b -> c -> d -> (a' -> b' -> c' -> d' -> r)
 defargs4 f x x2 x3 x4 = defargs' f (x & x2 & x3 & x4 & Nil)
-defargs5 :: Good (a -> b -> c -> d -> e -> r) (a * b * c * d * e * Nil) (a' -> b' -> c' -> d' -> e' -> r) => (a -> b -> c -> d -> e -> r) -> a -> b -> c -> d -> e -> (a' -> b' -> c' -> d' -> e' -> r)
+defargs5 :: DefArgs5 r a b c d e a' b' c' d' e' => (a -> b -> c -> d -> e -> r) -> a -> b -> c -> d -> e -> (a' -> b' -> c' -> d' -> e' -> r)
 defargs5 f x x2 x3 x4 x5 = defargs' f (x & x2 & x3 & x4 & x5 & Nil)
-defargs6 :: Good (a -> b -> c -> d -> e -> f -> r) (a * b * c * d * e * f * Nil) (a' -> b' -> c' -> d' -> e' -> f' -> r) => (a -> b -> c -> d -> e -> f -> r) -> a -> b -> c -> d -> e -> f -> (a' -> b' -> c' -> d' -> e' -> f' -> r)
+defargs6 :: DefArgs6 r a b c d e f a' b' c' d' e' f' => (a -> b -> c -> d -> e -> f -> r) -> a -> b -> c -> d -> e -> f -> (a' -> b' -> c' -> d' -> e' -> f' -> r)
 defargs6 f x x2 x3 x4 x5 x6 = defargs' f (x & x2 & x3 & x4 & x5 & x6 & Nil)
-defargs7 :: Good (a -> b -> c -> d -> e -> f -> g -> r) (a * b * c * d * e * f * g * Nil) (a' -> b' -> c' -> d' -> e' -> f' -> g' -> r) => (a -> b -> c -> d -> e -> f -> g -> r) -> a -> b -> c -> d -> e -> f -> g -> (a' -> b' -> c' -> d' -> e' -> f' -> g' -> r)
+defargs7 :: DefArgs7 r a b c d e f g a' b' c' d' e' f' g' => (a -> b -> c -> d -> e -> f -> g -> r) -> a -> b -> c -> d -> e -> f -> g -> (a' -> b' -> c' -> d' -> e' -> f' -> g' -> r)
 defargs7 f x x2 x3 x4 x5 x6 x7 = defargs' f (x & x2 & x3 & x4 & x5 & x6 & x7 & Nil)
-defargs8 :: Good (a -> b -> c -> d -> e -> f -> g -> h -> r) (a * b * c * d * e * f * g * h * Nil) (a' -> b' -> c' -> d' -> e' -> f' -> g' -> h' -> r) => (a -> b -> c -> d -> e -> f -> g -> h -> r) -> a -> b -> c -> d -> e -> f -> g -> h -> (a' -> b' -> c' -> d' -> e' -> f' -> g' -> h' -> r)
+defargs8 :: DefArgs8 r a b c d e f g h a' b' c' d' e' f' g' h' => (a -> b -> c -> d -> e -> f -> g -> h -> r) -> a -> b -> c -> d -> e -> f -> g -> h -> (a' -> b' -> c' -> d' -> e' -> f' -> g' -> h' -> r)
 defargs8 f x x2 x3 x4 x5 x6 x7 x8 = defargs' f (x & x2 & x3 & x4 & x5 & x6 & x7 & x8 & Nil)
-defargs9 :: Good (a -> b -> c -> d -> e -> f -> g -> h -> i -> r) (a * b * c * d * e * f * g * h * i * Nil) (a' -> b' -> c' -> d' -> e' -> f' -> g' -> h' -> i' -> r) => (a -> b -> c -> d -> e -> f -> g -> h -> i -> r) -> a -> b -> c -> d -> e -> f -> g -> h -> i -> (a' -> b' -> c' -> d' -> e' -> f' -> g' -> h' -> i' -> r)
+defargs9 :: DefArgs9 r a b c d e f g h i a' b' c' d' e' f' g' h' i' => (a -> b -> c -> d -> e -> f -> g -> h -> i -> r) -> a -> b -> c -> d -> e -> f -> g -> h -> i -> (a' -> b' -> c' -> d' -> e' -> f' -> g' -> h' -> i' -> r)
 defargs9 f x x2 x3 x4 x5 x6 x7 x8 x9 = defargs' f (x & x2 & x3 & x4 & x5 & x6 & x7 & x8 & x9 & Nil)
-defargs10 :: Good (a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> r) (a * b * c * d * e * f * g * h * i * j * Nil) (a' -> b' -> c' -> d' -> e' -> f' -> g' -> h' -> i' -> j' -> r) => (a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> r) -> a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> (a' -> b' -> c' -> d' -> e' -> f' -> g' -> h' -> i' -> j' -> r)
+defargs10 :: DefArgs10 r a b c d e f g h i j a' b' c' d' e' f' g' h' i' j' => (a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> r) -> a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> (a' -> b' -> c' -> d' -> e' -> f' -> g' -> h' -> i' -> j' -> r)
 defargs10 f x x2 x3 x4 x5 x6 x7 x8 x9 x10 = defargs' f (x & x2 & x3 & x4 & x5 & x6 & x7 & x8 & x9 & x10 & Nil)
 
 -- $example