The Object methods equals and hashValue define an equivalence relation
among objects. Similarly, the Comparable method compareTo defines an ordering.

The Comparator interface defines a way to impose an external ordering among
objects. Why isn't there similarly a way to impose an external equivalence
relation among objects?

I have some nontrivial applications in which I'd like to look at a set of
objects from different points of view (that is, under different equivalence
relations at different points in my code), but the absence of an externally
imposable equivalence relation forces me to wrap all the objects in order
to view them under a different equivlence relation. If I'm lucky then the
two default equivalence relations (identity and natural) may be just what I
need, but I suspect not.

If there were an externally imposable equivalence relation, it would be
an interface with two methods:
     interface Equivalence {
int hashValue(Object);
boolean equals(Object, Object);
     }

Two standard (and trivial) instances would be provided: the identity
equivalence relation and the natural equivalence relation.

I believe separating things this way makes it much easier to have a number
of interesting variants on maps and sets without providing wholly new
implementations. If the constructors are static factories, we would still
have the flexibility to fully specialize the implementation for performance
when one of the two standard equivalence relations is given to the static
constructor.

This kind of functionality can be added without making any of the existing
classes obsolete.