Incremental View Maintenance For Collection Programming

In the context of incremental view maintenance (IVM), delta query derivation is an essential technique for speeding up the processing of large, dynamic datasets. The goal is to generate delta queries that, given a small change in the input, can update the materialized view more efficiently than via recomputation. In this work we propose the first solution for the efficient incrementalization of positive nested relational calculus (NRC+) on bags (with integer multiplicities). More precisely, we model the cost of NRC+ operators and classify queries as efficiently incrementalizable if their delta has a strictly lower cost than full re-evaluation. Then, we identify IncNRC+; a large fragment of NRC+ that is efficiently incrementalizable and we provide a semantics-preserving translation that takes any NRC+ query to a collection of IncNRC+ queries. Furthermore, we prove that incremental maintenance for NRC+ is within the complexity class NC0 and we showcase how recursive IVM, a technique that has provided significant speedups over traditional IVM in the case of flat queries [25], can also be applied to IncNRC+.Comment: 24 pages (12 pages plus appendix

Logische Grundlagen von Datenbanktransformationen für Datenbanken mit komplexen Typen

Database transformations consist of queries and updates which are two fundamental types of computations in any databases - the first provides the capability to retrieve data and the second is used to maintain databases in light of ever-changing application domains. With the rising popularity of web-based applications and service-oriented architectures, the development of database transformations must address new challenges, which frequently call for establishing a theoretical framework that unifies both queries and updates over complex-value databases. This dissertation aims to lay down the foundations for establishing a theoretical framework of database transformations in the context of complex-value databases. We shall use an approach that has successfully been used for the characterisation of sequential algorithms. The sequential Abstract State Machine (ASM) thesis captures semantics and behaviour of sequential algorithms. The thesis uses the similarity of general computations and database transformations for characterisation of the later by five postulates: sequential time postulate, abstract state postulate, bounded exploration postulate, background postulate, and the bounded non-determinism postulate. The last two postulates reflect the specific form of transformations for databases. The five postulates exactly capture database transformations. Furthermore, we provide a logical proof system for database transformations that is sound and complete.Datenbanktransformationen sind Anfragen an ein Datenbanksystem oder Modifikationen der Daten des Datenbanksystemes. Diese beiden grundlegenden Arten von Berechnungen auf Datenbanksystemen erlauben zum einem den Zugriff auf Daten und zum anderen die Pflege der Datenbank. Eine theoretische Fundierung von Datenbanktransformationen muss so flexibel sein, dass auch neue web-basierten Anwendungen und den neuen serviceorientierte Architekturen reflektiert sind, sowie auch die komplexeren Datenstrukturen. Diese Dissertation legt die Grundlagen für eine Theoriefundierung durch Datenbanktransformationen, die auch komplexe Datenstrukturen unterstützen. Wir greifen dabei auf einen Zugang zurück, der eine Theorie der sequentiellen Algorithmen bietet. Die sequentielle ASM-These (abstrakte Zustandsmaschinen) beschreibt die Semantik und das Verhalten sequentieller Algorithmen. Die Dissertation nutzt dabei die Gleichartigkeit von allgemeinen Berechnungen und Datenbanktransformationen zur Charakterisierung durch fünf Postulate bzw. Axiome: das Axiom der sequentiellen Ausführung, das Axiom einer abstrakten Charakterisierbarkeit von Zuständen, das Axiom der Begrenzbarkeit von Zustandsänderungen und Zustandssicht, das Axiom der Strukturierung von Datenbanken und das Axiom der Begrenzbarkeit des Nichtdeterminismus. Die letzten beiden Axiome reflektieren die spezifische Seite der Datenbankberechnungen. Die fünf Axiome beschreiben vollständig das Verhalten von Datenbanktransformationen. Weiterhin wird eine Beweiskalkül für Datenbanktransformationen entwickelt, der vollständig und korrekt ist

Well-definedness and semantic type-checking in the nested relational calculus and xquery

Abstract. Two natural decision problems regarding the XML query language XQuery are well-definedness and semantic type-checking. We study these problems in the setting of a relational fragment of XQuery. We show that well-definedness and semantic type-checking are undecidable, even in the positive-existential case. Nevertheless, for a “pure” variant of XQuery, in which no identification is made between an item and the singleton containing that item, the problems become decidable. We also consider the analogous problems in the setting of the nested relational calculus.

Bidirectional data transformation by calculation

MAPi Doctoral Programme in Computer ScienceThe advent of bidirectional programming, in recent years, has led to the development of a vast number of approaches from various computer science disciplines. These are often based on domain-specific languages in which a program can be read both as a forward and a backward transformation that satisfy some desirable consistency properties. Despite the high demand and recognized potential of intrinsically bidirectional languages, they have still not matured to the point of mainstream adoption. This dissertation contemplates some usually disregarded features of bidirectional transformation languages that are vital for deployment at a larger scale. The first concerns efficiency. Most of these languages provide a rich set of primitive combinators that can be composed to build more sophisticated transformations. Although convenient, such compositional languages are plagued by inefficiency and their optimization is mandatory for a serious application. The second relates to configurability. As update translation is inherently ambiguous, users shall be allowed to control the choice of a suitable strategy. The third regards genericity. Writing a bidirectional transformation typically implies describing the concrete steps that convert values in a source schema to values a target schema, making it impractical to express very complex transformations, and practical tools shall support concise and generic coding patterns. We first define a point-free language of bidirectional transformations (called lenses), characterized by a powerful set of algebraic laws. Then, we tailor it to consider additional parameters that describe updates, and use them to refine the behavior of intricate lenses between arbitrary data structures. On top, we propose the Multifocal framework for the evolution of XML schemas. A Multifocal program describes a generic schema-level transformation, and has a value-level semantics defined using the point-free lens language. Its optimization employs the novel algebraic lens calculus.O advento da programação bidirecional, nos últimos anos, fez surgir inúmeras abordagens em diversas disciplinas de ciências da computação, geralmente baseadas em linguagens de domínio específico em que um programa representa uma transformação para a frente ou para trás, satisfazendo certas propriedades de consistência desejáveis. Apesar do elevado potencial de linguagens intrinsicamente bidirecionais, estas ainda não amadureceram o suficiente para serem correntemente utilizadas. Esta dissertação contempla algumas características de linguagens bidirecionais usualmente negligenciadas, mas vitais para um desenvolvimento em mais larga escala. A primeira refere-se à eficiência. A maioria destas linguagens fornece um conjunto rico de combinadores primitivos que podem ser utilizados para construir transformações mais sofisticadas que, embora convenientes, são cronicamente ineficientes, exigindo ser otimizadas para uma aplicação séria. A segunda diz respeito à configurabilidade. Sendo a tradução de modificações inerentemente ambígua, os utilizadores devem poder controlar a escolha de uma estratégia adequada. A terceira prende-se com a genericidade. Escrever uma transformação bidirecional implica tipicamente descrever os passos que convertem um modelo noutro diferente, enquanto que ferramentas práticas devem suportar padrões concisos e genéricos de forma a poderem expressar transformações muito complexas. Primeiro, definimos uma linguagem de transformações bidirecionais (intituladas de lentes), livre de variáveis, caracterizada por um poderoso conjunto de leis algébricas. De seguida, adaptamo-la para receber parâmetros que descrevem modificações, e usamo-los para refinar lentes intrincadas entre estruturas de dados arbitrárias. Por cima, propomos a plataforma Multifocal para a evolução de modelos XML. Um programa Multifocal descreve uma transformação genérica de modelos, cuja semântica ao nível dos valores e consequente otimização é definida em função da linguagem de lentes

Equivalence of Queries with Nested Aggregation

Query equivalence is a fundamental problem within database theory. The correctness of all forms of logical query rewriting—join minimization, view flattening, rewriting over materialized views, various semantic optimizations that exploit schema dependencies, federated query processing and other forms of data integration—requires proving that the final executed query is equivalent to the original user query. Hence, advances in the theory of query equivalence enable advances in query processing and optimization. In this thesis we address the problem of deciding query equivalence between conjunctive SQL queries containing aggregation operators that may be nested. Our focus is on understanding the interaction between nested aggregation operators and the other parts of the query body, and so we model aggregation functions simply as abstract collection constructors. Hence, the precise language that we study is a conjunctive algebraic language that constructs complex objects from databases of flat relations. Using an encoding of complex objects as flat relations, we reduce the query equivalence problem for this algebraic language to deciding equivalence between relational encodings output by traditional conjunctive queries (not containing aggregation). This encoding-equivalence cleanly unifies and generalizes previous results for deciding equivalence of conjunctive queries evaluated under various processing semantics. As part of our study of aggregation operators that can construct empty sub-collections—so-called “scalar” aggregation—we consider query equivalence for conjunctive queries extended with a left outer join operator, a very practical class of queries for which the general equivalence problem has never before been analyzed. Although we do not completely solve the equivalence problem for queries with outer joins or with scalar aggregation, we do propose useful sufficient conditions that generalize previously known results for restricted classes of queries. Overall, this thesis offers new insight into the fundamental principles governing the behaviour of nested aggregation

Well-definedness and semantic type-checking in the nested relational calculus and xquery

The well-definedness problem for a programming language consists of checking, given an expression and an input type, whether the semantics of the expression is defined for all inputs adhering to the input type. A related problem is the semantic type-checking problem which consists of checking, given an expression, an input type, and an output type whether the expression always returns outputs adhering to the output type on inputs adhering to the input type. Both problems are undecidable for general-purpose programming languages. In this paper we study these problems for the Nested Relational Calculus, a specific-purpose database query language. We also investigate how these problems behave in the presence of programming language features such as singleton coercion and type tests.