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

ARDI: automatic generation of RDFS models from heterogeneous data sources

The current wealth of information, typically known as Big Data, generates a large amount of available data for organisations. Data Integration provides foundations to query disparate data sources as if they were integrated into a single source. However, current data integration tools are far from being useful for most organisations due to the heterogeneous nature of data sources, which represents a challenge for current frameworks. To enable data integration of highly heterogeneous and disparate data sources, this paper proposes a method to extract the schema from semi-structured (such as JSON and XML) and structured (such as relational) data sources, and generate an equivalent RDFS representation. The output of our method complements current frameworks and reduces the manual workload required to represent the input data sources in terms of the integration canonical data model. Our approach consists of production rules at the meta-model level that guarantee the correctness of the model translations. Finally, a tool for implementing our approach has been developed.Peer ReviewedPostprint (author's final draft

An Open Challenge Problem Repository for Systems Supporting Binders

A variety of logical frameworks support the use of higher-order abstract syntax in representing formal systems; however, each system has its own set of benchmarks. Even worse, general proof assistants that provide special libraries for dealing with binders offer a very limited evaluation of such libraries, and the examples given often do not exercise and stress-test key aspects that arise in the presence of binders. In this paper we design an open repository ORBI (Open challenge problem Repository for systems supporting reasoning with BInders). We believe the field of reasoning about languages with binders has matured, and a common set of benchmarks provides an important basis for evaluation and qualitative comparison of different systems and libraries that support binders, and it will help to advance the field.Comment: In Proceedings LFMTP 2015, arXiv:1507.0759

The schema coercion problem

Journal ArticleOver the past decade, the ability to incorporate data from a wide variety of sources has become increasingly important to database users. To meet this need, significant effort has been expended in automatic database schema manipulation. However, to date this effort has focused on two aspects of this problem: schema integration and schema evolution. Schema integration results in a unified view of several databases, while schema evolution enhances an existing database design to represent additional information. This work defines and addresses a third problem, schema coercion, which defines a mapping from one database to another. This paper presents an overview of the problems associated with schema coercion and how they correspond to the problems encountered by schema integration and schema evolution. In addition, our approach to this problem is outlined. The feasibility of this approach is demonstrated by a tool which reduces the human interaction required at all steps in the integration process. The database schemata are automatically read and converted into corresponding ER representations. Then, a correspondence identification heuristic is used to identify similar concepts, and create mappings between them. Finally, a program is generated to perform the data transfer. This tool has successfully been used to coerce the Haemophilus and Methanococcus genomes from the Genbank ASN.l database to the Utah Center for Human Genome Research database. Our comprehensive approach to addressing the schema coercion problem has proven extremely valuable in reducing the interaction required to define coercions, particularly when the heuristics are unsuccessful

Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality

We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts published in a same volume. Part II is dedicated to the relation between logic and information system, within the scope of Kolmogorov algorithmic information theory. We present a recent application of Kolmogorov complexity: classification using compression, an idea with provocative implementation by authors such as Bennett, Vitanyi and Cilibrasi. This stresses how Kolmogorov complexity, besides being a foundation to randomness, is also related to classification. Another approach to classification is also considered: the so-called "Google classification". It uses another original and attractive idea which is connected to the classification using compression and to Kolmogorov complexity from a conceptual point of view. We present and unify these different approaches to classification in terms of Bottom-Up versus Top-Down operational modes, of which we point the fundamental principles and the underlying duality. We look at the way these two dual modes are used in different approaches to information system, particularly the relational model for database introduced by Codd in the 70's. This allows to point out diverse forms of a fundamental duality. These operational modes are also reinterpreted in the context of the comprehension schema of axiomatic set theory ZF. This leads us to develop how Kolmogorov's complexity is linked to intensionality, abstraction, classification and information system.Comment: 43 page