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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 ...
An Extended Algebra for Constraint Databases
 IEEE Transactions on Knowledge and Data Engineering
, 1999
"... Constraint relational databases use constraints to both model and query data. A constraint relation contains a finite set of generalized tuples. Each generalized tuple is represented by a conjunction of constraints on a given logical theory and, depending on the logical theory and the specific conju ..."
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Cited by 20 (3 self)
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Constraint relational databases use constraints to both model and query data. A constraint relation contains a finite set of generalized tuples. Each generalized tuple is represented by a conjunction of constraints on a given logical theory and, depending on the logical theory and the specific conjunction of constraints, it may possibly represent an infinite set of relational tuples. For their characteristics, constraint databases are well suited to model multidimensional and structured data, like spatial and temporal data. The definition of an algebra for constraint relational databases is important in order to make constraint databases a practical technology. In this paper, we extend the previously defined constraint algebra (called generalized relational algebra). First, we show that the relational model is not the only possible semantic reference model for constraint relational databases and we show how constraint relations can be interpreted under the nested relational model. Then...
Constructibility and Decidability versus Domain Independence and Absoluteness
"... We develop a unified framework for dealing with constructibility and absoluteness in set theory, decidability of relations in effective structures (like the natural numbers), and domain independence of queries in database theory. Our framework and results suggest that domainindependence and absolut ..."
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Cited by 4 (2 self)
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We develop a unified framework for dealing with constructibility and absoluteness in set theory, decidability of relations in effective structures (like the natural numbers), and domain independence of queries in database theory. Our framework and results suggest that domainindependence and absoluteness might be the key notions in a general theory of constructibility, predicativity, and computability. 1
Safety Signatures for Firstorder Languages and Their Applications
 In FirstOrder Logic Revisited (Hendricks et all,, eds.), 3758, Logos Verlag
, 2004
"... ..."
Modeling and Language Support for the Management of
 in: Proceedings of the 16th International Conference on Scientific and Statistical Database Management (SSDBM’04), IEEE Computer Society
, 2004
"... In our days knowledge extraction methods are able to produce artifacts (also called patterns) that concisely represent data. Patterns are usually quite heterogeneous and require adhoc processing techniques. So far, little emphasis has been posed on developing an overall integrated environment for u ..."
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In our days knowledge extraction methods are able to produce artifacts (also called patterns) that concisely represent data. Patterns are usually quite heterogeneous and require adhoc processing techniques. So far, little emphasis has been posed on developing an overall integrated environment for uniformly representing and querying different types of patterns. Within the larger context of modelling, storing, and querying patterns, in this paper, we: (a) formally define the logical foundations for the global setting of pattern management through a model that covers data, patterns and their intermediate mappings; (b) present a pattern specification language for pattern management along with safety restrictions; and (c) introduce queries and query operators and identify interesting query classes.
Institute for Research in Cognitive Science Parallel Programming Languages for Collections Ph.D. Dissertation
, 1995
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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
Functional Query Languages with Categorical Types A dissertation
, 2013
"... We study three categorytheoretic types in the context of functional query languages – typed λcalculi extended with additional operations for bulk data processing. The types we study are • The type of propositions. By adding this type to the simply typed λcalculus, we obtain higherorder logic. We ..."
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We study three categorytheoretic types in the context of functional query languages – typed λcalculi extended with additional operations for bulk data processing. The types we study are • The type of propositions. By adding this type to the simply typed λcalculus, we obtain higherorder logic. We prove that every hereditarily domainindependent higherorder logic program can be translated into the nested relational algebra, thereby giving a higherorder generalization of Codd’s theorem. • The dependent identity type. By adding identity types to the nested relational calculus we obtain a language where embedded dependencies are firstclass objects that can be manipulated by the programmer and used for optimization. We prove that the chase rewriting procedure is sound for this language. • The type of finitely presented categories. In the functorial data model, database schemas are finitely presented categories, and every database instance over a schema C is a functor from C to the category of sets. We define FQL, the first query