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. 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 proffering a second factory. The 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 invoked factory.

Several points about this pattern are significant here: