We propose a SSReflect library for logic programming in the Datalog setting. As part of this work, we give a first mechanization of standard Datalog and of its extension with stratified negation. The library contains a formalization of the model theoretical and fixpoint semantics of the languages, implemented through bottom-up and, respectively, through stratified evaluation procedures. We provide corresponding soundness, termination, completeness and model minimality proofs. To this end, we rely on the Coq proof assistant and SSReflect. In this context, we also construct a preliminary framework for dealing with stratified programs. We consider this to be a necessary first step towards the certification of security-aware data-centric applications.

Abstract. In this article, we propose a Coq formalization of the relational data model which underlies relational database systems. More precisely, we present and formalize the data definition part of the model including integrity constraints. We model two different query language formalisms: relational algebra and conjunctive queries. We also present logical query optimization and prove the main "database theorems": algebraic equivalences, the homomorphism theorem and conjunctive query minimization.

Ensuring the success of big graph processing for the next decade and beyond.

We employ the Coq proof assistant to develop a mechanically-certified framework for evaluating graph queries and incrementally maintaining materialized graph instances, also called views. The language we use for defining queries and views is Regular Datalog (RD) – a notable fragment of non-recursive Datalog that can express complex navigational queries, with transitive closure as native operator. We first design and encode the theory of RD and then mechanize a RD-specific evaluation algorithm capable of fine-grained, incremental graph view computation, which we prove sound with respect to the declarative RD semantics. By using the Coq extraction mechanism, we test an OCaml version of the verified engine on a set of preliminary benchmarks. Our development is particularly focused on leveraging existing verification and notational techniques to: a) define mechanized properties that can be easily understood by logicians and database researchers and b) attain formal verification with limited effort. Our work is the first step towards a unified, machine-verified, formal framework for dynamic graph query languages and their evaluation engines.

We report on a community effort between industry and academia to shape the future of property graph constraints. The standardization for a property graph query language is currently underway through the ISO Graph Query Language (GQL) project. Our position is that this project should pay close attention to schemas and constraints, and should focus next on key constraints.The main purposes of keys are enforcing data integrity and allowing the referencing and identifying of objects. Motivated by use cases from our industry partners, we argue that key constraints should be able to have different modes, which are combinations of basic restriction that require the key to be exclusive, mandatory, and singleton. Moreover, keys should be applicable to nodes, edges, and properties since these all can represent valid real-life entities. Our result is PG-Keys, a flexible and powerful framework for defining key constraints, which fulfills the above goals.PG-Keys is a design by the Linked Data Benchmark Council's Property Graph Schema Working Group, consisting of members from industry, academia, and ISO GQL standards group, intending to bring the best of all worlds to property graph practitioners. PG-Keys aims to guide the evolution of the standardization efforts towards making systems more useful, powerful, and expressive.

Threshold queries are an important class of queries that only require computing or counting answers up to a specified threshold value. To the best of our knowledge, threshold queries have been largely disregarded in the research literature, which is surprising considering how common they are in practice. In this paper, we present a deep theoretical analysis of threshold query evaluation and show that thresholds can be used to significantly improve the asymptotic bounds of state-of-the-art query evaluation algorithms. We also empirically show that threshold queries are significant in practice. In surprising contrast to conventional wisdom, we found important scenarios in real-world data sets in which users are interested in computing the results of queries up to a certain threshold, independent of a ranking function that orders the query results.

No abstract

We employ the Coq proof assistant to develop a mechanically-certified framework for evaluating graph queries and incrementally maintaining materialized graph instances, also called views. The language we use for defining queries and views is Regular Datalog (RD) -a notable fragment of non-recursive Datalog that can express complex navigational queries, with transitive closure as native operator. We first design and encode the theory of RD and then mechanize a RD-specific evaluation algorithm capable of fine-grained, incremental graph view computation, which we prove sound with respect to the declarative RD semantics. By using the Coq extraction mechanism, we test an OCaml version of the verified engine on a set of preliminary benchmarks. Our development is particularly focused on leveraging existing verification and notational techniques to: a) define mechanized properties that can be easily understood by logicians and database researchers and b) attain formal verification with limited effort. Our work is the first step towards a unified, machine-verified, formal framework for dynamic graph query languages and their evaluation engines.