250 research outputs found
Annotation and More Annotation: Some Problems Posed by (and to) Val Tannen
No full textAmong the many research accomplishments of Val Tannen, his work on provenance and semirings is probably the most widely known. In this paper, we discuss questions that arise when applying this general framework to the setting of curated databases, and in particular the setting where we can have multiple annotations on the same data, as well as annotations on annotations
Iterating on multiple collections in synchrony
No full textModern programming languages typically provide some form of comprehension syntax which renders programs manipulating collection types more readable and understandable. However, comprehension syntax corresponds to nested loops in general. There is no simple way of using it to express efficient general synchronized iterations on multiple ordered collections, such as linear-time algorithms for low-selectivity database joins. Synchrony fold is proposed here as a novel characterization of synchronized iteration. Central to this characterization is a monotonic isBefore predicate for relating the orderings on the two collections being iterated on and an antimonotonic canSee predicate for identifying matching pairs in the two collections to synchronize and act on. A restriction is then placed on Synchrony fold, cutting its extensional expressive power to match that of comprehension syntax, giving us Synchrony generator. Synchrony generator retains sufficient intensional expressive power for expressing efficient synchronized iteration on ordered collections. In particular, it is proved to be a natural generalization of the database merge join algorithm, extending the latter to more general database joins. Finally, Synchrony iterator is derived from Synchrony generator as a novel form of iterator. While Synchrony iterator has the same extensional and intensional expressive power as Synchrony generator, the former is better dovetailed with comprehension syntax. Thereby, algorithms requiring synchronized iterations on multiple ordered collections, including those for efficient general database joins, become expressible naturally in comprehension syntax
On the Impact of Provenance Semiring Theory on the Design of a Provenance-Aware Database System
No full textWe report on the impact that the theory of provenance semirings, developed by Val Tannen and his collaborators, has had on the design on a practical system for maintaining the provenance of query results over a relational database, namely ProvSQL
Tealeaves: Structured Monads for Generic First-Order Abstract Syntax Infrastructure
No full textVerifying the metatheory of a formal system in Coq involves a lot of tedious "infrastructural" reasoning about variable binders. We present Tealeaves, a generic framework for first-order representations of variable binding that can be used to develop this sort of infrastructure once and for all. Given a particular strategy for representing binders concretely, such as locally nameless or de Bruijn indices, Tealeaves allows developers to implement modules of generic infrastructure called backends that end users can simply instantiate to their own syntax. Our framework rests on a novel abstraction of first-order abstract syntax called a decorated traversable monad (DTM) whose equational theory provides reasoning principles that replace tedious induction on terms. To evaluate Tealeaves, we have implemented a multisorted locally nameless backend providing generic versions of the lemmas generated by LNgen. We discuss case studies where we instantiate this generic infrastructure to simply-typed and polymorphic lambda calculi, comparing our approach to other utilities
Lambda Calculus,Conservative Extension and Structural Induction
No full textThe issue of whether embedding algebraic theories in higher-order theories such as the simply typed and polymorphic lambda calculi is of interest in programming language design. The establishment of such a conservative extension result permits modularity in the verification of the correctness of datatype and function implementations. In earlier work [Breazu-Tannen & Meyer 1987a], [Breazu-Tannen & Meyer 1987b] and [Breazu-Tannen 1988], conservative extension results have been obtained for algebraic theories. However, in modelling inductive datatypes, the principle of structural induction needs to be admitted in the inference system, and the question of whether conservative extension holds in the presence of the principle of structural induction needs to be addressed. In this paper we look at the question of whether inductive algebraic theories are conservatively extended when embedded in the simply typed lambda calculus
Semiring Provenance for Fixed-Point Logic
No full textSemiring provenance is a successful approach, originating in database theory, to providing detailed information on how atomic facts combine to yield the result of a query. In particular, general provenance semirings of polynomials or formal power series provide precise descriptions of the evaluation strategies or "proof trees" for the query. By evaluating these descriptions in specific application semirings, one can extract practical information for instance about the confidence of a query or the cost of its evaluation.
This paper develops semiring provenance for very general logical languages featuring the full interaction between negation and fixed-point inductions or, equivalently, arbitrary interleavings of least and greatest fixed points. This also opens the door to provenance analysis applications for modal μ-calculus and temporal logics, as well as for finite and infinite model-checking games.
Interestingly, the common approach based on Kleene’s Fixed-Point Theorem for ω-continuous semirings is not sufficient for these general languages. We show that an adequate framework for the provenance analysis of full fixed-point logics is provided by semirings that are (1) fully continuous, and (2) absorptive. Full continuity guarantees that provenance values of least and greatest fixed-points are well-defined. Absorptive semirings provide a symmetry between least and greatest fixed-points and make sure that provenance values of greatest fixed points are informative.
We identify semirings of generalized absorptive polynomials S^{∞}[X] and prove universal properties that make them the most general appropriate semirings for our framework. These semirings have the further property of being (3) chain-positive, which is responsible for having truth-preserving interpretations that give non-zero values to all true formulae. We relate the provenance analysis of fixed-point formulae with provenance values of plays and strategies in the associated model-checking games. Specifically, we prove that the provenance value of a fixed point formula gives precise information on the evaluation strategies in these games
Different Differences in Semirings
No full textRelational algebra operates over relations under either set semantics or bag semantics. In 2007 Val Tannen extended the semantics of relational algebra to K-relations, where each tuple is annotated with a value from a semiring. However, only the positive fragment of the relational algebra can be interpreted over K-relations. The reason is that a semiring contains only the operations addition and multiplication, and does not have a difference operation. This paper explores three ways of adding a difference operator to a semiring: as a freely generated algebra, by using the natural order, or by an explicit construction using products and quotients. The paper consists of both a survey of results from the literature, and of some novel results
Integrating XML Data Sources using RDF/S Schemas: The ICS-FORTH Semantic Web Integration Middleware (SWIM)
No full textSemantic Web (SW) technology aims to facilitate the integration of legacy data sources spread worldwide. Despite the plethora of SW languages e.g., RDF/S, OWL recently proposed for
supporting large scale information interoperation, the vast majority of legacy sources still rely on relational databases RDB published on the
Web or corporate intranets as virtual XML. In this paper, we advocate a Datalog framework for mediating high level queries to relational and or
XML sources using community ontologies expressed in a SW language such as RDF/S. We describe the architecture and the reasoning services
of our SW integration middleware, called SWIM, and we present the main design choices and techniques for supporting powerful mappings between different data models, as well as reformulation and optimization of queries expressed against mediation schemas and views
m-tables: Representing Missing Data
No full textRepresentation systems have been widely used to capture different forms of incomplete data in various settings. However, existing representation systems are not expressive enough to handle the more complex scenarios of missing data that can occur in practice: these could vary from missing attribute values, missing a known number of tuples, or even missing an unknown number of tuples. In this work, we propose a new representation system called m-tables, that can represent many different types of missing data. We show that m-tables form a closed, complete and strong representation system under both set and bag semantics and are strictly more expressive than conditional tables under both the closed and open world assumptions. We further study the complexity of computing certain and possible answers in m-tables. Finally, we discuss how to "interpret" m-tables through a novel labeling scheme that marks a type of generalized tuples as certain or possible
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