diff --git a/sprout/functional/bind/bind.hpp b/sprout/functional/bind/bind.hpp
index 84c7dbf4..6e4436b2 100644
--- a/sprout/functional/bind/bind.hpp
+++ b/sprout/functional/bind/bind.hpp
@@ -14,6 +14,7 @@
 #include <sprout/tuple/tuple/get.hpp>
 #include <sprout/tuple/tuple/make_tuple.hpp>
 #include <sprout/type/algorithm/find_index_if.hpp>
+#include <sprout/type/algorithm/lower_bound_index.hpp>
 #include <sprout/type/integral_array.hpp>
 #include <sprout/functional/ref.hpp>
 #include <sprout/functional/mem_fn.hpp>
@@ -188,21 +189,14 @@ namespace sprout {
 			return sprout::tuples::get<I>(const_cast<sprout::tuples::tuple<Types...> const&>(tuple));
 		}
 
-		template<typename T, typename = void>
-		struct is_variadic_placeholder
-			: public std::integral_constant<
-				bool,
-				(sprout::is_placeholder<T>::value
-					<= sprout::is_placeholder<decltype(sprout::placeholders::_va)>::value
-					)
-			>
-		{};
-
 		struct is_variadic_placeholder_pred {
 		public:
 			template<typename T>
 			struct apply
-				: public sprout::detail::is_variadic_placeholder<T>
+				: public std::integral_constant<
+					bool,
+					(sprout::is_variadic_placeholder<T>::value > 0)
+				>
 			{};
 		};
 		template<typename Bounds, typename = void>
@@ -213,21 +207,9 @@ namespace sprout {
 			>
 		{};
 
-		template<typename T, typename = void>
-		struct tail_place
-			: public std::integral_constant<int, -1>
-		{};
 		template<typename T>
-		struct tail_place<
-			T,
-			typename std::enable_if<sprout::detail::is_variadic_placeholder<T>::value>::type
-		>
-			: public std::integral_constant<
-				int,
-				(sprout::is_placeholder<decltype(sprout::placeholders::_va)>::value
-					- sprout::is_placeholder<T>::value
-					)
-			>
+		struct tail_place
+			: public std::integral_constant<int, sprout::is_variadic_placeholder<T>::value - 1>
 		{};
 
 		template<typename T, std::size_t ArgSize, typename = void>
@@ -237,7 +219,7 @@ namespace sprout {
 		template<typename T, std::size_t ArgSize>
 		struct bound_size<
 			T, ArgSize,
-			typename std::enable_if<sprout::detail::is_variadic_placeholder<T>::value>::type
+			typename std::enable_if<(sprout::is_variadic_placeholder<T>::value > 0)>::type
 		>
 			: public std::integral_constant<
 				std::size_t,
@@ -292,39 +274,11 @@ namespace sprout {
 			: public sprout::make_index_tuple<sprout::detail::bounds_size<Bounds, ArgSize>::value>
 		{};
 
-		struct meta_less_ {
-		public:
-			template<typename T, typename U>
-			struct apply
-				: public std::integral_constant<bool, ((T::value) < (U::value))>
-			{};
-		};
-
-		template<std::size_t I, typename Tuple, typename T, typename Compare, typename = void>
-		struct lower_bound_index_impl
-			: public std::integral_constant<std::size_t, I>
-		{};
-		template<std::size_t I, typename Tuple, typename T, typename Compare>
-		struct lower_bound_index_impl<
-			I, Tuple, T, Compare,
-			typename std::enable_if<(I < sprout::tuples::tuple_size<Tuple>::value)>::type
-		>
-			: public std::conditional<
-				Compare::template apply<typename sprout::tuples::tuple_element<I, Tuple>::type, T>::type::value,
-				sprout::detail::lower_bound_index_impl<I + 1, Tuple, T, Compare>,
-				std::integral_constant<std::size_t, I>
-			>::type
-		{};
-		template<typename Tuple, typename T, typename Compare = sprout::detail::meta_less_>
-		struct lower_bound_index
-			: public sprout::detail::lower_bound_index_impl<0, Tuple, T, Compare>
-		{};
-
 		template<sprout::index_t I, typename Bounds, std::size_t ArgSize>
 		struct bound_position
 			: public std::integral_constant<
 				sprout::index_t,
-				(sprout::detail::lower_bound_index<
+				(sprout::types::lower_bound_index<
 					typename sprout::detail::bounds_partial_size<Bounds, ArgSize>::type,
 					std::integral_constant<std::size_t, I + 1>
 					>::type::value - 1
@@ -334,11 +288,15 @@ namespace sprout {
 
 		template<sprout::index_t I, typename Bounds, std::size_t ArgSize>
 		struct is_variadic_part
-			: public sprout::detail::is_variadic_placeholder<
-				typename sprout::tuples::tuple_element<
-					sprout::detail::bound_position<I, Bounds, ArgSize>::value,
-					Bounds
-				>::type
+			: public std::integral_constant<
+				bool,
+				(sprout::is_variadic_placeholder<
+						typename sprout::tuples::tuple_element<
+							sprout::detail::bound_position<I, Bounds, ArgSize>::value,
+							Bounds
+						>::type
+					>::value > 0
+					)
 			>
 		{};
 
@@ -730,7 +688,7 @@ namespace sprout {
 		template<sprout::index_t Index, typename BoundArg>
 		struct complete_placeholder<
 			Index, BoundArg,
-			typename std::enable_if<!(sprout::is_placeholder<BoundArg>::value == sprout::is_placeholder<decltype(sprout::placeholders::_)>::value)>::type
+			typename std::enable_if<!sprout::is_positional_placeholder<BoundArg>::value>::type
 		> {
 		public:
 			typedef BoundArg type;
@@ -738,7 +696,7 @@ namespace sprout {
 		template<sprout::index_t Index, typename BoundArg>
 		struct complete_placeholder<
 			Index, BoundArg,
-			typename std::enable_if<(sprout::is_placeholder<BoundArg>::value == sprout::is_placeholder<decltype(sprout::placeholders::_)>::value)>::type
+			typename std::enable_if<sprout::is_positional_placeholder<BoundArg>::value>::type
 		> {
 		public:
 			typedef sprout::placeholder<Index + 1> type;
diff --git a/sprout/functional/bind/placeholder.hpp b/sprout/functional/bind/placeholder.hpp
index a5a5be77..2fd07c6a 100644
--- a/sprout/functional/bind/placeholder.hpp
+++ b/sprout/functional/bind/placeholder.hpp
@@ -9,19 +9,22 @@ namespace sprout {
 	// placeholder
 	//
 	template<int N>
-	struct placeholder
-//		: public std::integral_constant<int, N>
-	{};
-	template<>
-	struct placeholder<-1>
-//		: public std::integral_constant<int, -1>
-	{
+	struct placeholder {};
+	//
+	// positional_placeholder
+	//
+	struct positional_placeholder {
 	public:
-		template<int N2>
-		SPROUT_CONSTEXPR operator sprout::placeholder<N2>() const {
-			return sprout::placeholder<N2>();
+		template<int N>
+		SPROUT_CONSTEXPR operator sprout::placeholder<N>() const {
+			return sprout::placeholder<N>();
 		}
 	};
+	//
+	// variadic_placeholder
+	//
+	template<int N>
+	struct variadic_placeholder {};
 
 	namespace placeholders {
 		namespace {
@@ -56,39 +59,39 @@ namespace sprout {
 			SPROUT_STATIC_CONSTEXPR sprout::placeholder<29> _29 = {};
 			SPROUT_STATIC_CONSTEXPR sprout::placeholder<30> _30 = {};
 
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-1> _ = {};
+			SPROUT_STATIC_CONSTEXPR sprout::positional_placeholder _ = {};
 
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256> _va = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 1> _1tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 2> _2tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 3> _3tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 4> _4tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 5> _5tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 6> _6tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 7> _7tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 8> _8tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 9> _9tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 10> _10tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 11> _11tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 12> _12tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 13> _13tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 14> _14tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 15> _15tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 16> _16tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 17> _17tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 18> _18tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 19> _19tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 20> _20tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 21> _21tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 22> _22tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 23> _23tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 24> _24tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 25> _25tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 26> _26tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 27> _27tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 28> _28tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 29> _29tail = {};
-			SPROUT_STATIC_CONSTEXPR sprout::placeholder<-256 - 30> _30tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<0> _va = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<1> _1tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<2> _2tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<3> _3tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<4> _4tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<5> _5tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<6> _6tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<7> _7tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<8> _8tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<9> _9tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<10> _10tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<11> _11tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<12> _12tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<13> _13tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<14> _14tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<15> _15tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<16> _16tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<17> _17tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<18> _18tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<19> _19tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<20> _20tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<21> _21tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<22> _22tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<23> _23tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<24> _24tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<25> _25tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<26> _26tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<27> _27tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<28> _28tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<29> _29tail = {};
+			SPROUT_STATIC_CONSTEXPR sprout::variadic_placeholder<30> _30tail = {};
 		}	// anonymous-namespace
 	}	// namespace placeholders
 	using sprout::placeholders::_1;
@@ -163,10 +166,6 @@ namespace sprout {
 	struct is_placeholder
 		: public std::integral_constant<int, 0>
 	{};
-	template<int N>
-	struct is_placeholder<sprout::placeholder<N> >
-		: public std::integral_constant<int, N>
-	{};
 	template<typename T>
 	struct is_placeholder<T const>
 		: public sprout::is_placeholder<T>
@@ -179,6 +178,58 @@ namespace sprout {
 	struct is_placeholder<T const volatile>
 		: public sprout::is_placeholder<T>
 	{};
+	template<int N>
+	struct is_placeholder<sprout::placeholder<N> >
+		: public std::integral_constant<int, N>
+	{};
+
+	//
+	// is_positional_placeholder
+	//
+	template<typename T>
+	struct is_positional_placeholder
+		: public std::integral_constant<int, 0>
+	{};
+	template<typename T>
+	struct is_positional_placeholder<T const>
+		: public sprout::is_positional_placeholder<T>
+	{};
+	template<typename T>
+	struct is_positional_placeholder<T volatile>
+		: public sprout::is_positional_placeholder<T>
+	{};
+	template<typename T>
+	struct is_positional_placeholder<T const volatile>
+		: public sprout::is_positional_placeholder<T>
+	{};
+	template<>
+	struct is_positional_placeholder<sprout::positional_placeholder>
+		: public std::integral_constant<int, 1>
+	{};
+
+	//
+	// is_variadic_placeholder
+	//
+	template<typename T>
+	struct is_variadic_placeholder
+		: public std::integral_constant<int, 0>
+	{};
+	template<typename T>
+	struct is_variadic_placeholder<T const>
+		: public sprout::is_variadic_placeholder<T>
+	{};
+	template<typename T>
+	struct is_variadic_placeholder<T volatile>
+		: public sprout::is_variadic_placeholder<T>
+	{};
+	template<typename T>
+	struct is_variadic_placeholder<T const volatile>
+		: public sprout::is_variadic_placeholder<T>
+	{};
+	template<int N>
+	struct is_variadic_placeholder<sprout::variadic_placeholder<N> >
+		: public std::integral_constant<int, N + 1>
+	{};
 }	// namespace sprout
 
 #endif	// #ifndef SPROUT_FUNCTIONAL_BIND_PLACEHOLDER_HPP
diff --git a/sprout/type.hpp b/sprout/type.hpp
index ed428b39..6421f441 100644
--- a/sprout/type.hpp
+++ b/sprout/type.hpp
@@ -7,6 +7,7 @@
 #include <sprout/type/integral_array.hpp>
 #include <sprout/type/string.hpp>
 #include <sprout/type/rebind_types.hpp>
+#include <sprout/type/functional.hpp>
 #include <sprout/type/algorithm.hpp>
 #include <sprout/type/operation.hpp>
 
diff --git a/sprout/type/algorithm.hpp b/sprout/type/algorithm.hpp
index 16097cdd..32f0390d 100644
--- a/sprout/type/algorithm.hpp
+++ b/sprout/type/algorithm.hpp
@@ -4,5 +4,6 @@
 #include <sprout/config.hpp>
 #include <sprout/type/algorithm/find_index.hpp>
 #include <sprout/type/algorithm/find_index_if.hpp>
+#include <sprout/type/algorithm/lower_bound_index.hpp>
 
 #endif	// #ifndef SPROUT_TYPE_ALGORITHM_HPP
diff --git a/sprout/type/algorithm/lower_bound_index.hpp b/sprout/type/algorithm/lower_bound_index.hpp
new file mode 100644
index 00000000..79a0e341
--- /dev/null
+++ b/sprout/type/algorithm/lower_bound_index.hpp
@@ -0,0 +1,39 @@
+#ifndef SPROUT_TYPE_ALGORITHM_LOWER_BOUND_INDEX_HPP
+#define SPROUT_TYPE_ALGORITHM_LOWER_BOUND_INDEX_HPP
+
+#include <cstddef>
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/type/functional/less.hpp>
+#include <sprout/type/tuple.hpp>
+
+namespace sprout {
+	namespace types {
+		namespace detail {
+			template<std::size_t I, typename Tuple, typename T, typename Compare, typename = void>
+			struct lower_bound_index_impl
+				: public std::integral_constant<std::size_t, I>
+			{};
+			template<std::size_t I, typename Tuple, typename T, typename Compare>
+			struct lower_bound_index_impl<
+				I, Tuple, T, Compare,
+				typename std::enable_if<(I < sprout::tuples::tuple_size<Tuple>::value)>::type
+			>
+				: public std::conditional<
+					Compare::template apply<typename sprout::tuples::tuple_element<I, Tuple>::type, T>::type::value,
+					sprout::types::detail::lower_bound_index_impl<I + 1, Tuple, T, Compare>,
+					std::integral_constant<std::size_t, I>
+				>::type
+			{};
+		}	// namespace detail
+		//
+		// lower_bound_index
+		//
+		template<typename Tuple, typename T, typename Compare = sprout::types::less_>
+		struct lower_bound_index
+			: public sprout::types::detail::lower_bound_index_impl<0, Tuple, T, Compare>
+		{};
+	}	// namespace types
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_TYPE_ALGORITHM_LOWER_BOUND_INDEX_HPP
diff --git a/sprout/type/functional.hpp b/sprout/type/functional.hpp
new file mode 100644
index 00000000..3c0f3a4c
--- /dev/null
+++ b/sprout/type/functional.hpp
@@ -0,0 +1,7 @@
+#ifndef SPROUT_TYPE_FUNCTIONAL_HPP
+#define SPROUT_TYPE_FUNCTIONAL_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/type/functional/less.hpp>
+
+#endif	// #ifndef SPROUT_TYPE_FUNCTIONAL_HPP
diff --git a/sprout/type/functional/less.hpp b/sprout/type/functional/less.hpp
new file mode 100644
index 00000000..6151c296
--- /dev/null
+++ b/sprout/type/functional/less.hpp
@@ -0,0 +1,30 @@
+#ifndef SPROUT_TYPE_FUNCTIONAL_LESS_HPP
+#define SPROUT_TYPE_FUNCTIONAL_LESS_HPP
+
+#include <type_traits>
+#include <sprout/config.hpp>
+
+namespace sprout {
+	namespace types {
+		//
+		// less
+		//
+		template<typename T, typename U>
+		struct less
+			: public std::integral_constant<bool, ((T::value) < (U::value))>
+		{};
+
+		//
+		// less_
+		//
+		struct less_ {
+		public:
+			template<typename T, typename U>
+			struct apply
+				: public sprout::types::less<T, U>
+			{};
+		};
+	}	// namespace types
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_TYPE_FUNCTIONAL_LESS_HPP