As proposed on the list:

- rename EvalBeforeAssignBit to MayAliasBit
- make .lazy() remove the MayAliasBit only, and mark it as deprecated
- add a NoAlias pseudo expression, and MatrixBase::noalias() function
Todo:
- we have to decide whether += and -= assume no aliasing by default ?
- once we agree on the API: update the Sparse module and the unit tests respectively.

Eigen/src/Core/util/Constants.h

@@ -76,8 +76,10 @@ const unsigned int EvalBeforeNestingBit = 0x2;
 
 /** \ingroup flags
   *
-  * means the expression should be evaluated before any assignement */
-const unsigned int EvalBeforeAssigningBit = 0x4;
+  * Means the expression cannot be evaluated safely if the result alias one
+  * of the operands of the expression. Therefore it should be evaluated
+  * before any assignement. */
+const unsigned int MayAliasBit = 0x4;
 
 /** \ingroup flags
   *
@@ -182,7 +184,7 @@ const unsigned int SparseBit = 0x1000;
 // list of flags that are inherited by default
 const unsigned int HereditaryBits = RowMajorBit
                                   | EvalBeforeNestingBit
-                                  | EvalBeforeAssigningBit
+                                  | MayAliasBit
                                   | SparseBit;
 
 // Possible values for the Mode parameter of part()

Eigen/src/Core/util/ForwardDeclarations.h

@@ -35,6 +35,7 @@ template<typename _Scalar, int _Rows, int _Cols,
          int _MaxRows = _Rows, int _MaxCols = _Cols> class Matrix;
 
 template<typename ExpressionType, unsigned int Added, unsigned int Removed> class Flagged;
+template<typename ExpressionType> class NoAlias;
 template<typename ExpressionType> class NestByValue;
 template<typename ExpressionType> class SwapWrapper;
 template<typename MatrixType> class Minor;