diff --git a/CMakeLists.txt b/CMakeLists.txt
index b042b02..3589530 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -23,6 +23,7 @@ link_libraries( alepha )
 # The subdirs to build
 add_subdirectory( Meta )
 add_subdirectory( Atomic )
+add_subdirectory( Functional )
 add_subdirectory( Proof )
 add_subdirectory( Memory )
 add_subdirectory( IOStreams )
diff --git a/Concepts.h b/Concepts.h
index 9e021bd..33e97c3 100644
--- a/Concepts.h
+++ b/Concepts.h
@@ -214,6 +214,13 @@ namespace Alepha::Hydrogen  ::detail::  Concepts_m
 		template< typename T >
 		concept UnaryFunction= Functional< T > and function_traits< T >::args_size == 1;
 
+		template< typename T, typename Signature >
+		concept Function= ConvertibleTo< T, std::function< Signature > >;
+
+		template< typename T, typename ReturnType >
+		concept FunctionReturning= Functional< T >
+				and ConvertibleTo< typename function_traits< T >::return_type, ReturnType >;
+
 		template< typename T >
 		concept StandardLayout= std::is_standard_layout_v< T >;
 
diff --git a/Functional/CMakeLists.txt b/Functional/CMakeLists.txt
new file mode 100644
index 0000000..8802363
--- /dev/null
+++ b/Functional/CMakeLists.txt
@@ -0,0 +1 @@
+add_subdirectory( composition.test )
diff --git a/Functional/composition.h b/Functional/composition.h
new file mode 100644
index 0000000..530bbe9
--- /dev/null
+++ b/Functional/composition.h
@@ -0,0 +1,137 @@
+static_assert( __cplusplus >= 2023'02 );
+
+#pragma once
+
+#include <Alepha/Alepha.h>
+
+#include <tuple>
+
+#include <Alepha/Concepts.h>
+
+namespace Alepha::Hydrogen::Functional  ::detail::  composition_m
+{
+	inline namespace exports
+	{
+		constexpr struct
+		{
+			template< typename T >
+			constexpr T
+			operator() ( T t ) const
+			{
+				return t;
+			}
+		} ident;
+
+		/*!
+		 * Functional Composition utilities.
+		 *
+		 * All utilities herein use value/copy semantics.  This is both because 
+		 * it makes it easier to implement, and because functional programming typically
+		 * eschews reference and move semantics.
+		 */
+	}
+
+	template< typename Outer, typename Inner, typename ReturnType, typename TupleOfArguments >
+	struct Composed;
+
+	template< typename Outer, typename Inner, typename ReturnType, typename ... Args >
+	struct Composed< Outer, Inner, ReturnType, std::tuple< Args... > >
+	{
+		using outer_type= Outer;
+		using inner_type= Inner;
+
+		using return_type= ReturnType;
+
+		Outer outer;
+		Inner inner;
+
+		return_type
+		operator() ( Args ... args )
+		{
+			return outer( inner( std::forward< Args >( args )... ) );
+		}
+	};
+
+	template< typename Intermediate, typename ReturnType >
+	auto
+	compose( Concepts::Function< ReturnType ( Intermediate ) > auto outer, Concepts::FunctionReturning< Intermediate > auto inner )
+	{
+		using inner_traits= function_traits< decltype( inner ) >;
+		using params= typename inner_traits::args_type;
+
+		return Composed< decltype( outer ), decltype( inner ), ReturnType, params >{ std::move( outer ), std::move( inner ) };
+	}
+
+	namespace exports
+	{
+		inline auto
+		operator * ( decltype( ident ), decltype( ident ) )
+		{
+			return ident;
+		}
+
+		inline auto
+		operator * ( decltype( ident ), Concepts::Functional auto inner )
+		{
+			using Intermediate= typename function_traits< decltype( inner ) >::return_type;
+
+			return []( Intermediate intermediate ) { return intermediate; } * inner;
+		}
+
+		/*!
+		 * Function composition operator.
+		 *
+		 * This is a C++ notation equivalent to the `∘` operator in mathematics
+		 * for functions.  Just as `f( g( x ) )` is `( f ∘ g )( x )`, the C++
+		 * equivalent notation is `( f * g )( x )`.
+		 */
+		inline auto
+		operator * ( Concepts::UnaryFunction auto outer, Concepts::Functional auto inner )
+		{
+			using Intermediate= typename function_traits< decltype( inner ) >::return_type;
+			using ReturnType= typename function_traits< decltype( inner ) >::return_type;
+
+			return compose< Intermediate, ReturnType >( std::move( outer ), std::move( inner ) );
+		}
+
+		inline auto
+		operator >> ( decltype( ident ), decltype( ident ) )
+		{
+			return ident;
+		}
+
+		inline auto
+		operator >> ( Concepts::Functional auto first, decltype( ident ) )
+		{
+			return ident * first;
+		}
+
+		/*!
+		 * Ordered function composition operator.
+		 *
+		 * While `(f * g * h)( x )` preserves the order in the
+		 * notation `f( g( h( x ) ) )`, sometimes it's desirable to
+		 * write the composition in "first, then" style syntax.  This
+		 * example would be `h`, then `g`, then `f`.  For this purpose,
+		 * `operator >>` has been overloaded bewteen two functions to
+		 * permit simple examples such as:
+		 *
+		 * `( first >> second >> third )( arg )`
+		 *
+		 * This operator uses the same underpinnings as the `operator *`,
+		 * and thus both syntaxes (and captures of their combinations) can
+		 * be mixed and matched.
+		 */
+
+		inline auto
+		operator >> ( Concepts::Functional auto first, Concepts::Functional auto then )
+		{
+			return then * first;
+		}
+	}
+}
+
+namespace Alepha::Hydrogen::Functional::inline exports::inline composition_m
+{
+	using namespace detail::composition_m::exports;
+}
diff --git a/Functional/composition.test/0.cc b/Functional/composition.test/0.cc
new file mode 100644
index 0000000..5a9250f
--- /dev/null
+++ b/Functional/composition.test/0.cc
@@ -0,0 +1,48 @@
+static_assert( __cplusplus >= 2023'02 );
+
+#include <Alepha/Functional/composition.h>
+
+#include <Alepha/Testing/test.h>
+
+#include <Alepha/Utility/enroll.h>
+
+namespace
+{
+	using namespace Alepha::Testing::exports;
+
+
+	auto init= Alepha::Utility::enroll <=[]
+	{
+		"smoke test"_test <=[]( Environment test )
+		{
+			using namespace Alepha::Functional::exports::composition_m;
+
+			auto i= ident * ident;
+
+			auto add_two= []( const int x )
+			{
+				return x + 2;
+			};
+
+			auto mult_two= []( const int x ) { return x * 2; };
+
+			auto add_two_then_mult_two= mult_two * add_two;
+
+			test.expect( add_two_then_mult_two( 1 ) == 6 );
+		};
+
+		"compose test"_test <=[]( Environment test )
+		{
+			using namespace Alepha::Functional::exports::composition_m;
+
+			auto add= []( const int x, const int y )
+			{
+				return x + y;
+			};
+
+			auto mult3= []( const int x ) { return x * 3; };
+
+			test.expect( ( add >> mult3 )( 2, 1 ) == 9 );
+		};
+	};
+}
diff --git a/Functional/composition.test/CMakeLists.txt b/Functional/composition.test/CMakeLists.txt
new file mode 100644
index 0000000..b099603
--- /dev/null
+++ b/Functional/composition.test/CMakeLists.txt
@@ -0,0 +1 @@
+unit_test( 0 )
diff --git a/Testing/test.h b/Testing/test.h
index 7124949..d069477 100644
--- a/Testing/test.h
+++ b/Testing/test.h
@@ -138,6 +138,7 @@ namespace Alepha::Hydrogen::Testing
 			};
 
 			using TestState= TestStateCore &;
+			using Environment= TestState;
 		}
 
 		inline auto