Asymmetric vs symmetric

To finish the theory part, we can rapidly discuss about the asymmetric and symmetric comparators in multiple dimensions. For their definition, refer to distance comparators.

On one side, the asymmetric comparator is easy to understand and predict. The dimensions are taken one by one to find the best match. The ambiguities can only come from a multiple inheritance of interfaces.
On the other side, the symmetric comparator is democratic. All the dimensions have the same weight in the final selection. However more democracy means more ambiguities and more difficulties to select one best match.

In search for best match, the multimethods given as example M3 and M4 have the same methods defined but have a different comparator. M4 will have an ambiguity while M3 won’t.

The choice of the type of comparator may not only guided by the ease to treat all the cases. The implementation of an operator that is fundamentally symmetric e.g. equals may deliberately choose the symmetric operator.

In EVL, the default distance comparator is the asymmetric comparator. We think that it is better to provide the easier comparator and avoid the user to resolve ambiguities. However it is possible to switch to the symmetric comparator as an implementation is provided.