Lesson 7.6: Solution set semantics

In Lesson 7.1, we learned how patterns in TypeQL queries are resolved as a set of simultaneous constraints. With that in mind, let’s consider the following Fetch query, which is intended to list books and the promotions they are in.

This query does not in fact achieve the desired result. The third statement in the match clause specifies that $book is in a promotion-inclusion.

Because the constraints in a pattern must be simultaneously satisfied, this means that if a book is not in any promotion, then it will not be returned. This query does not actually list books and the promotions they are in, rather it lists only books that are in promotions. We’ll see how we can retrieve all books plus any promotions they are in by using subqueries in Lesson 8.2.

When composing a query pattern from individual statements, it is important to remember that each constraint must be satisfied individually in order for the whole pattern to be satisfied simultaneously. If we do not bear this in mind, we can run into issues like this where our intent does not match the query we have written.

Another important aspect of a pattern is the dependencies between its constraints, and how they affect the result set. If two statements in a pattern share a variable, then there is a dependency between them. Let’s consider the statements in the match clause of the previous query:

We can see that statement (1) and (3) are interdependent because they share $book, and that (2) and (3) are also interdependent because they share $promotion. This in turn means that (1) and (2) are also interdependent as they share a mutual dependency. In short, all the statements in the pattern are interdependent. Now, what if we remove statement (3)?

Without statement (3), statements (1) and (2) are now completely independent. When a query pattern can be split into independent sub-patterns, as we could with this one, then there is no constraint that links the sub-patterns. TypeDB then resolves each sub-pattern against the schema independently, and all possible combinations of data matching each sub-pattern are returned. In this particular example, the first sub-pattern would match every book once, the second sub-pattern would match every promotion once, and then every possible combination of book and promotion would be returned, even if nothing relates them. This behaviour is roughly equivalent to a cross join in SQL.

If a query pattern is incorrectly constructed, leading to multiple independent sub-patterns, queries can have significantly more results than intended. For this reason, it is important to ensure that dependencies between statements in query patterns are correctly constrained to achieve the intended purpose of the query. As a general rule, almost all queries should have fully interdependent patterns. We will see an example of how this applies to write queries later in this lesson.

If a query pattern can match multiple data instances for multiple variables, then one result will be returned for each permutation of these data instances. Consider the following Fetch query, which retrieves pairs of books that have been ordered together.

If we run this query, every pair of books will be returned twice. Let’s examine a couple of the results.

These two results represent the same pair of books, but The Odyssey is matched as $book-1 in one of them and as $book-2 in the other, and vice versa for One Hundred Years of Solitude. This occurs because the constraints on $book-1 and $book-2 are completely symmetrical, so they can each be resolved to the same set of data instances.

In many cases, this kind of result duplication can be avoided by leveraging key attributes. We saw how we can define them in Lesson 5.3. Books own key attributes of type isbn-13. If we modify our query to ensure state that the ISBN-13 of $book-1 must be greater than the ISBN-13 of $book-2, then each pair of books will only be returned once.

Because all books must have exactly one ISBN-13, and no two books can have the same one, then the ordering constraint will always be satisfied only once for each pair of duplicated results. This guarantees that the results will not be duplicated, without otherwise modifying the results. We can even omit the negated identity statement, as the ordering constraint ensures it must necessarily be satisfied.

So far in this lesson, we have only examined the effects of solution set semantics on data reads, but it is also important to consider how they affect data writes. Let’s consider an example. In the following Insert query, we add every book in the Holiday Sale 2023 to an order.

Let’s remove the constraint featuring the promotion-inclusion relation, as we did in one of the previous queries.

Now the constraint on $book is independent of the constraints on $promotion. This query will now add one of every book to the order, regardless of whether it is in the promotion or not. Here we can see how not using a fully interdependent query pattern can lead to unintended results.

When designing write queries, a good way to check that they will function as intended is to check the data that will be matched in the match clause with a read query. For the query above, we could use the following query to check the ISBNs of books that will be added to the order: