Abstract not found

Rule-based optimizers and optimizer generators use rules to specify query transformations. Rules act directly on query representations, which typically are based on query algebras. But most algebras complicate rule formulation, and rules over these algebras must often resort to calling to externally defined bodies of code. Code makes rules difficult to formulate, prove correct and reason about, and therefore compromises the effectiveness of rule-based systems. In this paper we present KOLA; a combinator-based algebra designed to simplify rule formulation. KOLA is not a user language, and KOLA's variable-free queries are difficult for humans to read. But KOLA is an effective internal algebra because its combinatorstyle makes queries manipulable and structurally revealing. As a result, rules over KOLA queries are easily expressed without the need for supplemental code. We illustrate this point, first by showing some transformations that despite their simplicity, require head and body rou...

Observing that networks are ubiquitous in applications for spatial databases, we define a new data model and query language that especially supports graph structures. This model integrates concepts of functional data modeling with order-sorted algebra. Besides object and data type hierar-chies graphs are available as an explicit modeling tool, and graph operations are part of the query lan-guage. Graphs have three classes of components, namely nodes, edges, and explicit paths. These are at the same time object types within the object type hierarchy and can be used like any other type. Explicit paths are useful because “real world ” objects often correspond to paths in a network. Further-more, a dynamic generalization concept is introduced to handle heterogeneous collections of objects in a query. In connection with spatial data types this leads to powerful modeling and querying capa-bilities for spatial databases, in particular for spatially embedded networks such as highways, rivers, public transport, and so forth. We use multi-level order-sorted algebra as a formal framework for the specification of our model. Roughly spoken, the first level algebra defines types and operations of the query language whereas the second level algebra defines kinds (collections of types) and type con-structors as functions between kinds and so provides the types that can be used at the first level.

We present a framework for semantic web applications based on constraint interchange and processing. At the core of the framework is a well-established semantic data model (P/FDM) with an associated expressive constraint language (Colan). To allow data instances to be transported across a network, we map our data model to the RDF Schema specification. To allow constraints to be transported, we define a Constraint Interchange Format (CIF) in the form of an RDF Schema for Colan, allowing each constraint to be defined as a resource in its own right. We show that, because Colan is essentially a syntactically-sugared form of first-order logic, and P/FDM is based on the widely-used extended ER model, our CIF is actually very widely applicable and reusable. Finally, we outline a set of services for constraint fusion and solving, which are particularly applicable to business-tobusiness e-commerce applications. All of these services can be accessed using the CIF.

A major challenge still facing the designers and implementors of database programming languages (DBPLs) is that of query optimisation. We investigate algebraic query optimisation for DBPLs in the context of a purely declarative functional language that supports sets as first-class objects. Since the language is computationally complete issues such as non-termination of expressions and construction of infinite data structures can be investigated, whilst its declarative nature allows the issue of side effects to be avoided and a rich set of equivalences to be developed. The language has a well-defined semantics which permits us to reason formally about the properties of expressions, such as their equivalence with other expressions and their termination. The support of a set bulk data type enables much prior work on the optimisation of relational languages to be utilised. In the paper we first give the syntax of an archetypal DBPL and briefly discuss its semantics. We then de...

The provision of more intelligent support for complex database applications is becoming an important research topic, and declaratively stated integrity constraints are increasingly being seen as a potential source of semantic information for such advanced DBMS's. However, despite much research e#ort, the problem of e#ciently compiling and checking a wide range of complex constraints has not yet been solved. And until it is solved, few database designers will be willing to sacrifice the performance of the every day database usage, in order to provide a complete semantic modelling of their application domain. In this paper, we describe the implementation of a constraint checking architecture and compiler, which have been designed to combine an expressive constraint language with e#cient run-time maintenance. While the current implementation does not yet achieve high e#ciency for all constraints, it has been designed with extensibility in mind and forms a solid platform from which to inv...

alexQdcs.kcl.ac.uk A major challenge still facing the designers and implementors of database programming languages (DBPLs) is that of query optimisa-tion. We investigate algebraic query optimi-sation techniques for DBPLs in the context of a purely declarative functional language that supports sets as first-class objects. Since the language is computationally complete issues such as non-termination of expressions and construction of infinite data structures can be investigated, whilst its declarative nature al-lows the issue of side effects to be avoided and a richer set of equivalences to be developed. The support of a set bulk data type enables much prior work on the optimisation of rela-tional languages to be utilised. Finally, the language has a well-defined semantics which permits us to reason formally about the prop erties of expressions, such as their equivalence with other expressions and their termination. 1

Abstract not found

Maps are a fundamental metaphor in GIS. We introduce several new operations on maps that go far beyond well-known operations like overlay or reclassification. In particular, we identify and generalize operations that are of practical interest for spatial analysis and that can be useful in many GIS applications. We give a precise definition of these operations based on a formal model of spatial partitions. This provides a theoretical foundation for maps which also serves as a specification for implementations.

In [CZ96], we argue that a combinator (i.e., variable-free) query algebra simplifies correctness proofs and implementations of query optimizers. But combinators make for poor query languages, and therefore translations from standard query languages (such as OQL [Cat93]) into some combinator form is required. In this paper, we present our translator that maps queries written in a variant of OQL (OQLdeB) into KOLA [Che95a]; our combinator-based query algebra. We introduce a denotational semantics for OQLdeB and define KOLA using an operational semantics that rewrites KOLA queries into OQLdeB . We then proceed to show the correctness of our translator by showing that translation produces a KOLA query whose OQLdeB equivalent has the same semantics as the original query. The significance of our work lies in its implications for the design of efficient and simply formalized query optimizers. With respect to formalization, we have used the Larch [GHG + 92] specification tool LSL to formally...