Database queries and constraints via lifting problems

Previous work has demonstrated that categories are useful and expressive models for databases. In the present paper we build on that model, showing that certain queries and constraints correspond to lifting problems, as found in modern approaches to algebraic topology. In our formulation, each so-called SPARQL graph pattern query corresponds to a category-theoretic lifting problem, whereby the set of solutions to the query is precisely the set of lifts. We interpret constraints within the same formalism and then investigate some basic properties of queries and constraints. In particular, to any database $\pi$ we can associate a certain derived database \Qry(\pi) of queries on $\pi$. As an application, we explain how giving users access to certain parts of \Qry(\pi), rather than direct access to $\pi$, improves ones ability to manage the impact of schema evolution

Category Theory and Model-Driven Engineering: From Formal Semantics to Design Patterns and Beyond

There is a hidden intrigue in the title. CT is one of the most abstract mathematical disciplines, sometimes nicknamed "abstract nonsense". MDE is a recent trend in software development, industrially supported by standards, tools, and the status of a new "silver bullet". Surprisingly, categorical patterns turn out to be directly applicable to mathematical modeling of structures appearing in everyday MDE practice. Model merging, transformation, synchronization, and other important model management scenarios can be seen as executions of categorical specifications. Moreover, the paper aims to elucidate a claim that relationships between CT and MDE are more complex and richer than is normally assumed for "applied mathematics". CT provides a toolbox of design patterns and structural principles of real practical value for MDE. We will present examples of how an elementary categorical arrangement of a model management scenario reveals deficiencies in the architecture of modern tools automating the scenario.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

06472 Abstracts Collection - XQuery Implementation Paradigms

From 19.11.2006 to 22.11.2006, the Dagstuhl Seminar 06472 ``XQuery Implementation Paradigms'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Use-cases on evolution

This report presents a set of use cases for evolution and reactivity for data in the Web and Semantic Web. This set is organized around three different case study scenarios, each of them is related to one of the three different areas of application within Rewerse. Namely, the scenarios are: “The Rewerse Information System and Portal”, closely related to the work of A3 – Personalised Information Systems; “Organizing Travels”, that may be related to the work of A1 – Events, Time, and Locations; “Updates and evolution in bioinformatics data sources” related to the work of A2 – Towards a Bioinformatics Web

Compliance Using Metadata

Everybody talks about the data economy. Data is collected stored, processed and re-used. In the EU, the GDPR creates a framework with conditions (e.g. consent) for the processing of personal data. But there are also other legal provisions containing requirements and conditions for the processing of data. Even today, most of those are hard-coded into workflows or database schemes, if at all. Data lakes are polluted with unusable data because nobody knows about usage rights or data quality. The approach presented here makes the data lake intelligent. It remembers usage limitations and promises made to the data subject or the contractual partner. Data can be used as risk can be assessed. Such a system easily reacts on new requirements. If processing is recorded back into the data lake, the recording of this information allows to prove compliance. This can be shown to authorities on demand as an audit trail. The concept is best exemplified by the SPECIAL project https://specialprivacy.eu (Scalable Policy-aware Linked Data Architecture For PrivacyPrivacy, TransparencyTransparency and ComplianceCompliance). SPECIAL has several use cases, but the basic framework is applicable beyond those cases

Functorial Data Migration

In this paper we present a simple database definition language: that of categories and functors. A database schema is a small category and an instance is a set-valued functor on it. We show that morphisms of schemas induce three "data migration functors", which translate instances from one schema to the other in canonical ways. These functors parameterize projections, unions, and joins over all tables simultaneously and can be used in place of conjunctive and disjunctive queries. We also show how to connect a database and a functional programming language by introducing a functorial connection between the schema and the category of types for that language. We begin the paper with a multitude of examples to motivate the definitions, and near the end we provide a dictionary whereby one can translate database concepts into category-theoretic concepts and vice-versa.Comment: 30 page