Start of a proposed Concepts framework enabled by traits, addressing issue #180

GTSAM-Concepts.md

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+GTSAM Concepts
+==============
+
+Concepts define (see [Generic Programming Techniques](http://www.boost.org/community/generic_programming.html))
+
+* associated types
+* valid expressions
+* invariants
+* complexity guarantees
+
+GTSAM Types start with Uppercase, e.g., `gtsam::Point2`, and are models of the concepts MANIFOLD, GROUP, LIE_GROUP, VECTOR_SPACE
+
+`gtsam::traits` is our way to associate these concepts with types. We will not use Eigen-style or STL-style traits, that define many properties at once. Rather, we use boost::mpl style meta-programming functions to facilitate meta-programming.
+
+Traits allow us to play with types that are outside GTSAM control, e.g., `Eigen::VectorXd`.
+
+The naming conventions are as follows:
+
+* Types: `gtsam::traits::SomeAssociatedType<T>::type`, i.e., they are MixedCase and define a `type`, for example:
+    
+      template<>
+      gtsam::traits::TangentVector<Point2> {
+        typedef Vector2 type;
+      }
+    
+* Values: `gtsam::traits::someValue<T>::value`, i.e., they are mixedCase starting with a lowercase letter and define a `value`, but also a `value_type`. For example:
+    
+      template<>
+      gtsam::traits::dimension<Point2> {
+        static const int value = 2;
+        typedef const int value_type; // const ?
+      }
+    
+* Functors: `gtsam::traits::someFunctor<T>`, i.e., they are mixedCase starting with a lowercase letter and define a functor type
+    
+      template<>
+      gtsam::traits::retract<Point2> {
+        Point2 operator()(const Point2& p, const Vector2& v) {
+        	return Point2(p.x()+v[0], p.y()+v[1]);
+        }
+      }
+    
+  The above is still up in the air, can we not point to a function somewhere? Or a method?
+  
+Concepts are associated with a tag.
+
+Manifold
+--------
+
+`gtsam::tags::manifold_tag`
+
+`gtsam::traits::structure_tag<T>`
+
+* associated types: DefaultChart
+* valid expressions: dimension
+
+Chart
+-----
+
+
+Group
+-----
+
+Lie Group
+---------
+
+Vector Space
+------------
+
+Examples
+--------
+
+An example of implementing a Manifold is here:
+
+
+    namespace gtsam {
+      namespace traits {
+      
+      // types:
+      template<typename T>
+      struct SomeAssociatedType<T>::type
+      
+      }
+    }
+
+
+