We investigate the properties of a simple programming language whose main computational engine is structural recursion on sets. We describe a progression of sublanguages in this paradigm that (1) have increasing expressive power, and (2) illustrate robust conceptual restrictions thus exhibiting interesting additional properties. These properties suggest that we consider our sublanguages as candidates for "query languages". Viewing query languages as restrictions of our more general programming language has several advantages. First, there is no "impedance mismatch" problem; the query languages are already there, so they share common semantic foundation with the general language. Second, we suggest a uniform characterization of nested relational and complex-object algebras in terms of some surprisingly simple operators; and we can make comparisons of expressiveness in a general framework. Third, we exhibit differences in expressive power that are not always based on complexity arguments...

We present a new principle for the development of database query languages that the primitive operations should be organized around types. Viewing a relational database as consisting of sets of records, this principle dictates that we should investigate separately operations for records and sets. There are two immediate advantages of this approach, which is partly inspired by basic ideas from category theory. First, it provides a language for structures in which record and set types may be freely combined: nested relations or complex objects. Second, the fundamental operations for sets are closely related to those for other "collection types" such as bags or lists, and this suggests how database languages may be uniformly extended to these new types. The most general operation on sets, that of structural recursion, is one in which not all programs are welldefined. In looking for limited forms of this operation that always give rise to well-defined operations, we find a number of close ...

This paper presents structural recursion as the basis of the syntax and semantics of query languages for semistructured data and XML. We describe a simple and powerful query language based on pattern matching and show that it can be expressed using structural recursion, which is introduced as a top-down, recursive function, similar to the way XSL is defined on XML trees. On cyclic data, structural recursion can be defined in two equivalent ways: as a recursive function which evaluates the data top-down and remembers all its calls to avoid infinite loops, or as a bulk evaluation which processes the entire data in parallel using only traditional relational algebra operators. The latter makes it possible for optimization techniques in relational queries to be applied to structural recursion. We show that the composition of two structural recursion queries can be expressed as a single such query, and this is used as the basis of an optimization method for mediator systems. Several other fo...

We show how structured data stored in files can benefit from standard database technology and in particular be queried and updated using database languages. We introduce the notion of structuring schema which consists of a grammar annotated with database programs and of a database schema. We study the translation from structured strings to databases, and the converse. We adapt optimization techniques from relational databases to our context. 1 Introduction Database systems are concerned with structured data. Unfortunately, data is often stored in an unstructured manner (e.g., in files) even when it does have a strong internal structure (e.g., electronic documents or programs) . In this paper, we consider how data stored as strings can benefit from standard database technology and in particular be queried and updated using database languages. In actual systems, data is often stored as string for obvious historical reasons. The problem that we are considering is thus very general. Tools...

Data of interest to biomedical researchers associated with the Human Genome Project (HGP) is stored all over the world in a number of different electronic data formats and accessible through a varietyof interfaces and retrieval languages. These data sources include conventional relational databases with SQL interfaces, formatted text files on top of which indexing is provided for efficient retrieval (ASN.1-Entrez), and binary files that can be interpreted textually or graphically via special purpose interfaces (ACeDB). Researchers within the HGP wanttocombine data from these different data sources, add value through sophisticated data analysis techniques (such as the biosequence comparison software BLAST and FASTA), and view it using special purpose scientific visualization tools. However, currently there are no commercial tools for enabling such an integrated digital library, and a fundamental barrier to developing such tools appears to be one of language design and optimization: The data f...

Scientific data of importance to biologists in the Human Genome Project resides not only in conventional databases, but in structured files maintained in a number of different formats (e.g. ASN.1 and ACE) as well as sequence analysis packages (e.g. BLAST and FASTA). These formats and packages contain a number of data types not found in conventional databases, such as lists and variants, and may be deeply nested. We present in this paper techniques for querying and transforming such data, and illustrate their use in a prototype system developed in conjunction with the Human Genome Center for Chromosome 22. We also describe optimizations performed by the system, a crucial issue for bulk data. 1 Introduction The goal of the Human Genome Project (HGP) is to sequence the 24 distinct chromosomes comprising the human genome. Much of the information associated with the HGP resides not in conventional databases, but in files that have been formatted according to a variety of conventions. These...

We define a standard of effectiveness for a database calculus relative to a query language. Effectiveness judges suitability to serve as a processing framework for the query language, and comprises aspects of coverage, manipulability and efficient evaluation. We present the monoid calculus, and argue its effectiveness for object-oriented query languages, exemplified by OQL of ODMG-93. The monoid calculus readily captures such features as multiple collection types, aggregations, arbitrary composition of type constructors and nested query expressions. We also show how to extend the monoid calculus to deal with vectors and arrays in more expressive ways than current query languages do, and illustrate how it can handle identity and updates. 1 Introduction A much-touted advantage of the relational data model is the existence of a formal calculus and algebra to model database queries. In practice, these formalisms fail to model many of the features present in commercial query languages (e.g...

Bags, i.e. sets with duplicates, are often used to implement relations in database systems. In this paper, we study the expressive power of algebras for manipulating bags. The algebra we present is a simple extension of the nested relation algebra. Our aim is to investigate how the use of bags in the language extends its expressive power, and increases its complexity. We consider two main issues, namely (i) the impact of the depth of bag nesting on the expressive power, and (ii) the complexity and the expressive power induced by the algebraic operations. We show that the bag algebra is more expressive than the nested relation algebra (at all levels of nesting), and that the difference may be subtle. We establish a hierarchy based on the structure of algebra expressions. This hierarchy is shown to be highly related to the properties of the powerset operator. Invited to a special issue of the Journal of Computer and System Sciences selected from ACM Princ. of Database Systems,...

Strong normalization results are obtained for a general language for collection types. An induced normal form for sets and bags is then used to show that the class of functions whose input has height (that is, the maximal depth of nestings of sets/bags/lists in the complex object) at most i and output has height at most o definable in a nested relational query language without powerset operator is independent of the height of intermediate expressions used. Our proof holds regardless of whether the language is used for querying sets, bags, or lists, even in the presence of variant types. Moreover, the normal forms are useful in a general approach to query optimization. Paredaens and Van Gucht proved a similar result for the special case when i = o = 1. Their result is complemented by Hull and Su who demonstrated the failure of independence when powerset operator is present and i = o = 1. The theorem of Hull and Su was generalized to all i and o by Grumbach and Vianu. Our result genera...

This paper concentrates on query unnesting (also known as query decorrelation), an optimization that, even though improves performance considerably, is not treated properly (if at all) by most OODB systems. Our framework generalizes many unnesting techniques proposed recently in the literature and is capable of removing any form of query nesting using a very simple and efficient algorithm. The simplicity of our method is due to the use of the monoid comprehension calculus as an intermediate form for OODB queries. The monoid comprehension calculus treats operations over multiple collection types, aggregates, and quantifiers in a similar way, resulting in a uniform way of unnesting queries, regardless of their type of nesting.