There are a few situations where Keykos provides a partial ordering among instances of the some particular type. This is a common pattern that needs elaboration. See this note for further applications of this pattern.

Perhaps the factory was the first type to provide a comparison operation between objects of the type. This introduction to the factory defines “discreet” in terms of a set of holes. For discreetness fewer holes are better (more discreet). There is an order on a factory that accepts a key to another factory which queries the first as to the relative merits of the second. The paranoid factory user invokes the first factory (that he has prior reason to trust) proffering a second factory. The first factory performs a set inclusion test on the respective hole sets and replies firstly whether the proffered factory was indeed a real factory, and if so whether there are holes in the proffered factory that are not in the first factory.

Several points about this pattern are significant here: