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Naturally Embedded Query Languages
 LNCS 646: Proceedings of 4th International Conference on Database Theory
, 1992
"... 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 inte ..."
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Cited by 144 (32 self)
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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 complexobject 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...
Normal Forms and Conservative Properties for Query Languages over Collection Types
 In Proceedings of 12th ACM Symposium on Principles of Database Systems
, 1993
"... 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 out ..."
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Cited by 66 (31 self)
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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...
Towards Tractable Algebras for Bags
, 1993
"... 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 ..."
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Cited by 62 (5 self)
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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,...
Deciding Containment for Queries with Complex Objects and Aggregations
, 1997
"... We address the problem of query containment and query equivalence for complex objects. We show that for a certain conjunctive query language for complex objects, query containment and weak query equivalence are decidable. Our results have two consequences. First, when the answers of the two queries ..."
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Cited by 46 (7 self)
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We address the problem of query containment and query equivalence for complex objects. We show that for a certain conjunctive query language for complex objects, query containment and weak query equivalence are decidable. Our results have two consequences. First, when the answers of the two queries are guaranteed not to contain empty sets, then weak equivalence coincides with equivalence, and our result answers partially an open problem about the equivalence of nest; unnest queries for complex objects [GPG90]. Second, we derive an NPcomplete algorithm for checking the equivalence of certain conjunctive queries with grouping and aggregates. Our results rely on a translation of the containment and equivalence conditions for complex objects into novel conditions on conjunctive queries, which we call simulation and strong simulation. These conditions are more complex than containment of conjunctive queries, because they involve arbitrary numbers of quantifier alternations. We prove that c...
New Techniques for Studying Set Languages, Bag Languages and Aggregate Functions
, 1994
"... We provide new techniques for the analysis of the expressive power of query languages for nested collections. These languages may use set or bag semantics and may be further complicated by the presence of aggregate functions. We exhibit certain classes of graphs and prove that the properties of thes ..."
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Cited by 44 (28 self)
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We provide new techniques for the analysis of the expressive power of query languages for nested collections. These languages may use set or bag semantics and may be further complicated by the presence of aggregate functions. We exhibit certain classes of graphs and prove that the properties of these graphs that can be tested in such languages are either finite or cofinite. This result settles the conjectures of Grumbach, Milo, and Paredaens that parity test, transitive closure, and balanced binary tree test are not expressible in bag languages like the PTIME fragment of BALG of Grumbach and Milo and BQL of Libkin and Wong. Moreover, it implies that many recursive queries, including simple ones like the test for a chain, cannot be expressed in a nested relational language even when aggregate functions are available. In an attempt to generalize the finitecofiniteness result, we study the bounded degree property which says that the number of distinct in and outdegrees in the output of...
A SemiMonad for SemiStructured Data
, 2001
"... . This document proposes an algebra for XML Query. The algebra has been submitted to the W3C XML Query Working Group. A novel feature of the algebra is the use of regularexpression types, similar in power to DTDs or XML Schemas, and closely related to Hasoya and Pierce's work on Xduce. The ite ..."
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Cited by 44 (3 self)
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. This document proposes an algebra for XML Query. The algebra has been submitted to the W3C XML Query Working Group. A novel feature of the algebra is the use of regularexpression types, similar in power to DTDs or XML Schemas, and closely related to Hasoya and Pierce's work on Xduce. The iteration construct is based on the notion of a monad, and involves novel typing rules not encountered elsewhere. 1 Introduction This document proposes an algebra for XML Query. This work builds on long standing traditions in the database community. In particular, we have been inspired by systems such as SQL, OQL, and nested relational algebra (NRA). We have also been inspired by systems such as Quilt, UnQL, XDuce, XMLQL, XPath, XQL, XSLT, and YATL. We give citations for all these systems below. In the database world, it is common to translate a query language into an algebra; this happens in SQL, OQL, and NRA, among others. The purpose of the algebra is twofold. First, the algebra is used to give...
An Algebra for XML Query
, 2000
"... . This document proposes an algebra for XML Query. The algebra has been submitted to the W3C XML Query Working Group. A novel feature of the algebra is the use of regularexpression types, similar in power to DTDs or XML Schemas, and closely related to Hasoya, Pierce, and Vouillon's work on Xdu ..."
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Cited by 38 (1 self)
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. This document proposes an algebra for XML Query. The algebra has been submitted to the W3C XML Query Working Group. A novel feature of the algebra is the use of regularexpression types, similar in power to DTDs or XML Schemas, and closely related to Hasoya, Pierce, and Vouillon's work on Xduce. The iteration construct involves novel typing rules not encountered elsewhere (even in Xduce). 1 Introduction This document proposes an algebra for XML Query. This work builds on long standing traditions in the database community. In particular, we have been inspired by systems such as SQL, OQL, and nested relational algebra (NRA). We have also been inspired by systems such as Quilt, UnQL, XDuce, XMLQL, XPath, XQL, and YATL. We give citations for all these systems below. In the database world, it is common to translate a query language into an algebra; this happens in SQL, OQL, and NRA, among others. The purpose of the algebra is twofold. First, the algebra is used to give a semantics for t...
Aggregate functions, conservative extension, and linear orders
 In Proceedings of 4th International Workshop on Database Programming Languages
, 1993
"... Practical database query languages are usually equipped with some aggregate functions. For example, \ nd mean of column " can be expressed in SQL. However, the manner in which aggregate functions were introduced in these query languages leaves something to be desired. BreazuTannen, Buneman, a ..."
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Cited by 35 (28 self)
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Practical database query languages are usually equipped with some aggregate functions. For example, \ nd mean of column " can be expressed in SQL. However, the manner in which aggregate functions were introduced in these query languages leaves something to be desired. BreazuTannen, Buneman, and Wong [3] introduced a nested relational languageNRC(=) based on monads [16, 24] and structural recursion [1, 2]. It was shown in Wong [27] that this language is equivalent to the nested relational algebras of Thomas and Fischer [22], Schek and Scholl [20], and Colby [4]. NRC(=) enjoys certain advantages over these languages: it is naturally embedded in functional languages, it is readily extensible, and it has a compact equational theory. Therefore, it is used in this report as a basis for investigating aggregate functions. In section 2, the nested relational calculus NRC(=) is described. It is then endowed with rational numbers, rational arithmetic, and a summation operator. The augmented language,NRC(Q; +; ; ; ; P; =), is able to express a variety