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10
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 132 (26 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...
Principles of Programming with Complex Objects and Collection Types
 Theoretical Computer Science
, 1995
"... 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. Th ..."
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Cited by 128 (28 self)
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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 welldefined operations, we find a number of close ...
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 54 (25 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...
Normal Forms And Conservative Extension Properties For Query Languages Over Collection Types
 Journal of Computer and System Sciences
, 1995
"... 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 outp ..."
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Cited by 27 (8 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 generali...
DomainIndependent Queries on Databases with External Functions
 in "LNCS 893: Proceedings of 5th International Conference on Database Theory," 177190
, 1995
"... We investigate queries in the presence of external functions with arbitrary inputs and outputs (atomic values, sets, nested sets etc). We propose a new notion of domain independence for queries with external functions which, in contrast to previous work, can also be applied to query languages with f ..."
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Cited by 13 (2 self)
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We investigate queries in the presence of external functions with arbitrary inputs and outputs (atomic values, sets, nested sets etc). We propose a new notion of domain independence for queries with external functions which, in contrast to previous work, can also be applied to query languages with fixpoints or other kinds of iterators. Next, we define two new notions of computable queries with external functions, and prove that they are equivalent, under the assumption that the external functions are total. Thus, our definition of computable queries with external functions is robust. Finally, based on the equivalence result, we give examples of complete query languages with external functions. A byproduct of the equivalence result is the fact that Relational Machines are complete for complex objects: it was known that they are not complete over flat relations. 1 Introduction Database functionalities are important both for practical and for theoretical purposes. E.g. the system O 2 of ...
The Restricted and Bounded Fixpoint Closures of the Nested Algebra are Equivalent
 In Proceedings of DBPL'95
, 1995
"... The nested model is an extension of the traditional, "flat" relational model in which relations can also have relationvalued entries. Its "default" query language, the nested algebra, is rather weak, unfortunately, since it is only a conservative extension of the traditional, "flat" relational algeb ..."
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Cited by 4 (1 self)
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The nested model is an extension of the traditional, "flat" relational model in which relations can also have relationvalued entries. Its "default" query language, the nested algebra, is rather weak, unfortunately, since it is only a conservative extension of the traditional, "flat" relational algebra, and thus can only express a small fraction of the polynomialtime queries. Therefore, it was proposed to extend the nested algebra with a leastfixpoint construct, but the resulting language turned out to be too powerful: many inherently exponential queries could also be expressed. Two polynomialtime restrictions of the leastfixpoint closure of the nested algebra were proposed: the restricted leastfixpoint closure (by Gyssens and Van Gucht) and the bounded fixpoint closure (by Suciu). Here, we prove that both restrictions are equivalent in expressive power. We also exhibit a proof technique, called type substitution, by which we reduce our result to its obvious counterpart in the "fla...
Tractable Iteration Mechanisms for Bag Languages
 in F. N. Afrati & P. Kolaitis, eds, `Database Theory  ICDT '97, 6th International Conference, Delphi
, 1997
"... . The goal of this paper is to study tractable iteration mechanisms for bags. The presence of duplicates in bags prevents iteration mechanisms developed in the context of sets to be directly applied to bags without losing tractability. We study two constructs for controlling tractability of iter ..."
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Cited by 2 (0 self)
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. The goal of this paper is to study tractable iteration mechanisms for bags. The presence of duplicates in bags prevents iteration mechanisms developed in the context of sets to be directly applied to bags without losing tractability. We study two constructs for controlling tractability of iteration over bags. The deflationary fixpoint construct keeps removing elements from a bag until a fixpoint is reached. The bounded fixpoint construct is an inflationary iteration mechanism that never exceeds some predefined bounding bag. We study these constructs in the context of a standard (nested) bag algebra. We show that the deflationary and bounded inflationary fixpoint constructs are equally expressive and strictly more expressive than their setbased counterparts. We also show that, unlike in the set case, the bag algebra with bounded fixpoint fails to capture all PTIME queries over databases with ordered domains. We then show that adding just one construct, which can be used...
Founded by Benjamin Franklin in 1740
, 1995
"... We investigate queries in the presence of external functions with arbitrary inputs and outputs (atomic values, sets, nested sets etc). We propose a new notion of domain independence for queries with external functions which, in contrast to previous work, can also be applied to query languages with x ..."
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We investigate queries in the presence of external functions with arbitrary inputs and outputs (atomic values, sets, nested sets etc). We propose a new notion of domain independence for queries with external functions which, in contrast to previous work, can also be applied to query languages with xpoints or other kinds of iterators. Next, we de ne two new notions of computable queries with external functions, and prove that they are equivalent, under the assumption that the external functions are total. Thus, our de nition of computable queries with external functions is robust. Finally, based on the equivalence result, we giveexamples of complete query languages with external functions. A byproduct of the equivalence result is the fact that Relational Machines are complete for complex objects: it was known that they are not complete over at relations. 1