Revamped partial function application

* moved internals into separate header i.e. the `detail` namespace relating to `Apply`
* implemented automatic alias selection by implementing aliae of the basic variadic `type` template alias in different base classes
** variadic partial application is implemented in `detail::apply_variadic`
*** `detail::apply_single` and `detail::apply_pair` define aliae to `detail::apply_variadic`'s `type` template alias
*** both restricted aliae derive from `detail::apply_variadic`
** `Apply` derives from any of the aliae defining base classes depending on the count of placeholders as determined by `detail::count_placeholders`
*** `Apply` is guaranteed to always be derived from `detail::apply_variadic` one way or the other
* changed functions, test cases and examples depending on `Apply` accordingly
** `Length` had to be reimplemented without `Apply` as it doesn't allow usage of aliae expecting a different count of arguments anymore
*** this is a advantage in the sense that core functionality of _TypeAsValue_ now doesn't depend on this complex partial application implementation anymore
*** such functionality may be reimplemented separately from `Apply`
* removed unnecessary `tav` namespace prefixes

8 files changed, 118 insertions, 64 deletions

diff --git a/example/prime/prime.cc b/example/prime/prime.cc
index f1771a6..3d5cced 100644
--- a/example/prime/prime.cc
+++ b/example/prime/prime.cc
@@ -2,6 +2,7 @@
 
 #include "type.h"
 #include "operation/math.h"
+#include "function/apply.h"
 
 #include "list/list.h"
 #include "list/operation/higher/filter.h"
@@ -30,7 +31,7 @@ template <
 	typename Base
 >
 using removeMultiplesOf = tav::Remove<
-	tav::Apply<isMultipleOf, tav::_0, Base>::template single_type,
+	tav::Apply<isMultipleOf, tav::_0, Base>::template type,
 	Candidates
 >;
 
diff --git a/src/function/apply.h b/src/function/apply.h
index 8e780e0..21364a8 100644
--- a/src/function/apply.h
+++ b/src/function/apply.h
@@ -1,43 +1,12 @@
 #ifndef TYPEASVALUE_SRC_FUNCTION_APPLY_H_
 #define TYPEASVALUE_SRC_FUNCTION_APPLY_H_
 
-#include <type_traits>
+#include "conditional/if.h"
 
-#include "list/list.h"
-#include "list/operation/nth.h"
+#include "detail/apply.h"
 
 namespace tav {
 
-namespace detail {
-
-struct placeholder_tag { };
-
-template <typename Type>
-using is_placeholder = tav::Boolean<
-	std::is_base_of<placeholder_tag, Type>::value
->;
-
-template <int Index>
-struct placeholder : placeholder_tag { };
-
-template <
-	typename Partials,
-	typename Argument
->
-struct resolve_placeholder {
-	typedef Argument type;
-};
-
-template <
-	typename Partials,
-	int      Index
->
-struct resolve_placeholder<Partials, placeholder<Index>> {
-	typedef typename Nth<Size<Index>, Partials>::type type;
-};
-
-}
-
 typedef detail::placeholder<0> _0;
 typedef detail::placeholder<1> _1;
 typedef detail::placeholder<2> _2;
@@ -47,24 +16,15 @@ template <
 	template<typename...> class Function,
 	typename...                 Arguments
 >
-struct Apply {
-	template <typename... Partials>
-	using variadic_type = Function<
-		typename detail::resolve_placeholder<
-			typename tav::List<Partials...>::type,
-			Arguments
-		>::type...
-	>;
-
-	template <typename Partial>
-	using single_type = variadic_type<Partial>;
-
-	template <typename Partial0, typename Partial1>
-	using pair_type = variadic_type<Partial0, Partial1>;
-
-	template <typename Partial0, typename Partial1, typename Partial2>
-	using triple_type = variadic_type<Partial0, Partial1, Partial2>;
-};
+struct Apply : If<
+	(detail::count_placeholders<Arguments...>::type::value > 2),
+	detail::apply_variadic<Function, Arguments...>,
+	typename If<
+		detail::count_placeholders<Arguments...>::type::value == 2,
+		detail::apply_pair<Function, Arguments...>,
+		detail::apply_single<Function, Arguments...>
+	>::type
+>::type { };
 
 }
 
diff --git a/src/function/detail/apply.h b/src/function/detail/apply.h
new file mode 100644
index 0000000..bf60be1
--- /dev/null
+++ b/src/function/detail/apply.h
@@ -0,0 +1,86 @@
+#ifndef TYPEASVALUE_SRC_FUNCTION_DETAIL_APPLY_H_
+#define TYPEASVALUE_SRC_FUNCTION_DETAIL_APPLY_H_
+
+#include <type_traits>
+
+#include "list/list.h"
+#include "list/operation/nth.h"
+#include "list/operation/higher/query.h"
+
+namespace tav {
+namespace detail {
+
+struct placeholder_tag { };
+
+template <typename Type>
+using is_placeholder = tav::Boolean<
+	std::is_base_of<placeholder_tag, Type>::value
+>;
+
+template <int Index>
+struct placeholder : placeholder_tag { };
+
+template <
+	typename Partials,
+	typename Argument
+>
+struct resolve_placeholder {
+	typedef Argument type;
+};
+
+template <
+	typename Partials,
+	int      Index
+>
+struct resolve_placeholder<Partials, placeholder<Index>> {
+	typedef typename Nth<Size<Index>, Partials>::type type;
+};
+
+template <typename... Arguments>
+using count_placeholders = Count<
+	is_placeholder,
+	typename List<Arguments...>::type
+>;
+
+template <
+	template<typename...> class Function,
+	typename...                 Arguments
+>
+struct apply_variadic {
+	template <typename... Partials>
+	using type = Function<
+		typename resolve_placeholder<
+			typename tav::List<Partials...>::type,
+			Arguments
+		>::type...
+	>;
+};
+
+template <
+	template<typename...> class Function,
+	typename...                 Arguments
+>
+struct apply_single : apply_variadic<Function, Arguments...> {
+	template <typename Partial0>
+	using type = typename apply_variadic<
+		Function,
+		Arguments...
+	>::template type<Partial0>;
+};
+
+template <
+	template<typename...> class Function,
+	typename...                 Arguments
+>
+struct apply_pair : apply_variadic<Function, Arguments...> {
+	template <typename Partial0, typename Partial1>
+	using type = typename apply_variadic<
+		Function,
+		Arguments...
+	>::template type<Partial0, Partial1>;
+};
+
+}
+}
+
+#endif  // TYPEASVALUE_SRC_FUNCTION_DETAIL_APPLY_H_
diff --git a/src/list/operation/basic.h b/src/list/operation/basic.h
index cbbe22c..b4aa35a 100644
--- a/src/list/operation/basic.h
+++ b/src/list/operation/basic.h
@@ -2,17 +2,24 @@
 #define TYPEASVALUE_SRC_LIST_OPERATION_BASIC_H_
 
 #include "higher/fold.h"
-#include "function/apply.h"
 #include "operation/math.h"
 
 namespace tav {
 
-template <typename Pair>
-using Length = Fold<
-	Apply<Add, Size<1>, _1>::pair_type,
-	Size<0>,
-	Pair
->;
+template <typename Cons>
+class Length {
+	private:
+		template <typename, typename Accumulated>
+		using accumulate = Add<Size<1>, Accumulated>;
+
+	public:
+		typedef typename Fold<
+			accumulate,
+			Size<0>,
+			Cons
+		>::type type;
+
+};
 
 }
 
diff --git a/src/list/operation/contains.h b/src/list/operation/contains.h
index 51d7d9f..458acc0 100644
--- a/src/list/operation/contains.h
+++ b/src/list/operation/contains.h
@@ -12,7 +12,7 @@ template <
 	typename List
 >
 using Contains = Any<
-	Apply<EqualValue, tav::_0, Element>::template single_type,
+	Apply<EqualValue, _0, Element>::template type,
 	List
 >;
 
diff --git a/src/list/operation/delete.h b/src/list/operation/delete.h
index 2ff674c..a524667 100644
--- a/src/list/operation/delete.h
+++ b/src/list/operation/delete.h
@@ -12,7 +12,7 @@ template <
 	typename List
 >
 using Delete = Remove<
-	Apply<EqualValue, tav::_0, Element>::template single_type,
+	Apply<EqualValue, _0, Element>::template type,
 	List
 >;
 
diff --git a/src/list/operation/higher/sort.h b/src/list/operation/higher/sort.h
index f9146d6..5bc30c6 100644
--- a/src/list/operation/higher/sort.h
+++ b/src/list/operation/higher/sort.h
@@ -18,7 +18,7 @@ class Sort {
 		using pivot = typename Nth<index, Sequence>::type;
 
 		using partitions = typename Partition<
-			Apply<Comparator, pivot, tav::_0>::template single_type,
+			Apply<Comparator, pivot, _0>::template type,
 			typename DeleteNth<index, Sequence>::type
 		>::type;
 
diff --git a/test.cc b/test.cc
index 931d8f1..2bf9e09 100644
--- a/test.cc
+++ b/test.cc
@@ -999,7 +999,7 @@ static_assert(
 			tav::Multiply,
 			tav::Int<21>,
 			tav::_0
-		>::single_type<
+		>::type<
 			tav::Int<2>
 		>::type
 	>::value,
@@ -1014,7 +1014,7 @@ static_assert(
 				tav::Add,
 				tav::_0,
 				tav::Int<10>
-			>::single_type,
+			>::type,
 			tav::List<tav::Int<0>, tav::Int<2>, tav::Int<4>>::type
 		>::type
 	>::value,