Abstract

While the relational data model and many of its extensions have proven to be of considerable importance to many database applications, it has become clear that some advanced systems require more flexible structures and query languages. The expression of queries based on the occurrence of substructures on instance level (i.e., pattern matchings) requires constructs which cannot be expressed easily in the traditional models.

In this article, we introduce an object-oriented data model which solves these shortcomings. The instances of this data model will be represented by typed graphs. Both scheme and data will be defined entirely in terms of categorical constructs; pattern matching of graphs will be realized by morphisms in a suitable graph category. These morphisms will be used to define a powerful query and update language, which is capable of querying and restructuring the database in a natural and elegant way. Finally, we show that this query language is able to express the relational database operators, functional abstraction and transitive closure.

It will become clear that the categorical approach provides a solid basis for data modeling because it offers a unifying, theoretical framework. The abstractive power of the categorical framework creates an environment which sheds new light upon existing concepts and is the source of many interesting generalizations. The capability to make abstraction of low-level details, moreover, will often simplify the proofs of many theorems which would be rather involved and confusing in the traditional frameworks.

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