Let’s begin by adding the following rule to our schema to make locating relations transitive, which we first encountered in Lesson 5.4.

With this rule defined, we can use the following patterns to describe things that are located in a particular country:

It’s very easy to write a polymorphic pattern that describes states or cities located in a particular country.

Here the type of $x is determined to be locating:located, so instances of state and city are returned as they can be cast into this role. Now, what happens if we want to polymorphically query for everything located in the country? Well, we must use the following pattern instead.

Here we need a disjunction. This is due to the fact that publishing cannot be cast into locating:located, so we need to make a special case for it using the second branch of the disjunction. When querying them individually, the patterns for states and cities were structurally identical, while the pattern for publications was different. This means that we cannot query all three together using a structurally common pattern.

Essentially, we are using two different interfaces to represent common behaviour: the locating:location interface and the publishing:location interface. This is a bad practice in PERA model design, as it would be in application model design. While it is not too much of a problem at this stage, it has the potential to grow much more prevalent if we do not build the model’s interfaces in an extensible manner.

In order to eliminate the interface redundancy, we must choose which to keep. Between locating:location and publishing:location, the former is the more general-purpose interface. We will keep that interface, and change the way we record the locations where books are published to use it as well. Let’s begin by examining the section of the current schema used for publishing information.

We need to choose an object type to play the locating:located role. The entity type publisher would be a very poor choice.

Publishers can publish different books in different cities, and if we record the publishing location on the publisher, we won’t be able to tell which book was published in which city. Consider if we chose this approach and then inserted, for example, the following data from the dataset.

If we were to then query the location that one of the books was published, we’d get two results back.

This occurs because both publisher and city have functional dependencies on book, but there is no functional dependency between city and publisher. As a result, we can’t use publisher as the roleplayer because the data model will store the data in a lossy manner, as we have just seen.

Moving to the next option for the new roleplayer of locating:located, the entity type book is a reasonable choice.

We won’t run into the issue we do with publisher as there is a functional dependency of city on book. But this feels semantically odd. If we chose this approach, then the above query for a book’s publication city would become the following.

While this model would not incur data loss, it is strange to talk about the location of a book as if it is somehow fixed, and the intent of the query is not immediately obvious as there is no mention of the book’s publication. In fact, there is a better choice.

In this case, the best option is to make the relation type publishing the roleplayer of location:located.

Because publishing is an object type, it can implement any interface like an entity type can. And because it depends functionally on book (by definition), doing so does not incur information loss. Here we have created a nested relation type: a relation type in which another relation type plays a role. Now we can query for a book’s publication city in the following manner.

With this model, we do not incur information loss, and the intent of the query is clear. If we return to our polymorphic pattern from earlier, it will now match instances of city, state, and publishing for $x, as they can all be upcast to location:located!

When we extend the model to include more concepts with locations, we should always make them play locating:located. In this way, this polymorphic query will always be able to find everything in a given location. If we would like to restrict the list of things returned, we can always place further constraints on the type of $x.

Nested relation types are an advanced feature of the PERA model. They can be difficult to deal with, and so should be used with caution. Notably, the strategies we explored in Lesson 4.3 for deleting entities and relations cannot be applied universally if there are nested relations in the schema. However, nested relations are also an extremely powerful tool, as we will see in Lesson 12.1, where we will explore the full type-theoretic capabilities of the PERA model.