J. Van Den Bussche and J. Paredaens. The expressive power of structured values in pure OODB's. In Proc. 10th Symp. on Principles of Database Systems, 291-299, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... , to denote the restriction of Pom Alg without the operation . We next study the properties and dependencies of the different operations. We first consider the duplicate elimination operator. Note that this operator received much attention in the context of object oriented languages [AK89, BP91] It was shown in particular that it plays an important role to get complete languages. This operation is also very significant in the context of ordered types. The next propositions shows the limitations of Pom Alg ffl n . For that we introduce the notion of series parallel pomsets. ....

J. Van Den Bussche and J. Paredaens. The expressive power of structured values in pure OODB's. In Proc. 10th Symp. on Principles of Database Systems, 291-299, 1991.

....get the expressive power of nested relational algebra the Relative Powerset operation should be added. If one wishes complex objects with variant types, Disjoint Union with UAUn should be added as well. The Partition operation is the diagram formalization of the abstraction operation studied in [12]. Thus, their results can be immediately transferred into the sketch framework. On the other hand, expressiveness of different collections of diagram operations has been studied intensively in the mathematical category theory in the framework of toposes. Briefly, a topos is a category possessing ....

J. Van den Bussche and J. Paredaens. The expressive power of structured values in pure OODB's. In 1991 ACM Symposium on Principles of Database Systems, pages 291--299, 1991.

....notation PALG , to denote the restriction of PALG without the operation . We next study the properties and dependencies of the different operations. We first consider the duplicate elimination operator. Note that this operator received much attention in the context of object oriented languages [AK89, BP91]. It was shown in particular that it plays an important role to get complete languages. This operation is also very significant in the context of ordered types. The next propositions shows the limitations of PALG ffl n . Proposition 4.1 PALG ffl n can construct only series parallel pomsets. ....

J. Van Den Bussche and J. Paredaens. The expressive power of structured values in pure oodb's. In Proc. 10th Symp. on Principles of Database Systems, 1991.

....in each of these lists. As count statements can be (unefficiently) expressed in pure CQL, the above argument also provides an alternative, constructive proof of Theorem 4.4. Furthermore, it should be noted that the proof of Theorem 5.1 heavily relies on the use of the abstraction operation. In [20] it was shown that the use of abstraction is necessary for the faithful representation of sets in CQL. We conjecture that abstraction is equally crucial for the simulation of count. Most importantly, Theorem 5.1 shows that, in the absence of order, a very limited form of non determinism is ....

J. Van den Bussche and J. Paredaens. The expressive power of structured values in pure OODB's. In Proc. 10th ACM Symp. Principles of Database Systems, 291--299. 1991.

....schema simulating complex objects In Fig. 5 it is shown how complex object types might be simulated within an object schema. Such a simulation means adding abstract object identity but making no use of it. In the case of complex objects it is not possible for there to be shallow equal objects [6], e.g. two different SUPPLIERs with the same values in all components. In principle, this is possible in the object model, because in an object schema instance SUPPLIERs are primarily represented by abstract object identifiers, and not by (tuple) values. However, by specifying all attributes as ....

J. Van den Bussche and J. Paredaens. The expressive power of structured values in pure OODB's. In Proc. 10th ACM Symp. Principles of Database Syst., pages 291--299, 1991.

....to be a tractable alternative to explicit powerset construction. Other means of avoiding duplicates, such as total order, equality axioms, or copy elimination, are also discussed. Extended and revised version of a paper presented at the Tenth ACM Symposium on Principles of Database Systems [VP91]. y Research Assistant of the Belgian National Fund for Scientific Research. 1 Introduction In the past decade, there has been a lot of interest in database systems allowing a more direct representation of complex data structures than possible in standard relational systems. Recent work in ....

J. Van den Bussche and J. Paredaens. The expressive power of structured values in pure OODB's. In Proceedings of the Tenth ACM Symposium on Principles of Database Systems, pages 291-- 299. ACM Press, 1991.

....use of the four other basic operations. However, we now introduce a general abstraction operation, that allows making abstraction of objects according to several common properties at a time. For the proof that this operation can be simulated using the operations defined in Section 2, we refer to [6]. For an illustration of this operation we refer to Figure 26, illustrating control structures. K L a # not K ass ass K L a # K ass a K L a # not K ass ass a K L a # not K ass # K # false Figure 22: Body of a method for the conversion of cardinality edges, part 1 K # false K ass L a K # ....

Jan Van den Bussche and Jan Paredaens. On the expressive power of structured values in pure OODB's. In Proceedings of the Tenth ACM Symposium on Principles of Database Systems, pages 291--299. ACM Press, 1991.

....language As a final variation on our main theorem, we consider the language obtained by omitting the operation for adding nodes with outgoing non functional edges. Let us call this language GOOD . Since it has been shown that this operation cannot be expressed using the other four operations [14], the set of transformations that can be expressed using this restricted language is a strict subset of the set of transformations expressible in the full GOOD language. As for the theorem, this implies that the property, requiring the existence of an extension morphism, has to be strengthened. ....

Jan Van den Bussche and Jan Paredaens. On the expressive power of structured values in pure OODB's. In Proceedings of the Tenth ACM Symposium on Principles of Database Systems, pages 291--299. ACM Press, 1991.

....Also known as the complex object, nested relational, NF 2 , or unnormalized model. object creation and edge addition as basic statements and closing off under composition and while loops. This language subsumes many object based query languages proposed in the literature. However, it is known [20] that if we insist on duplicate free representations, there are very simple collections of set values that are inexpressible in OBQL. For example, the query asking for all subsets of two elements of a given class is not expressible without duplicates. Duplicate free representations have a number ....

....considered in [15] is an explicit powerset operation. An alternative, considered in [8] is the abstraction operation, which provides a quotient construction, creating a unique representative for each equivalence class of duplicate objects. These two options for enriching OBQL are equivalent [20]. In the present paper, we are motivated by the observation that in many practical applications, the set values appearing in the database have bounded cardinality: their cardinality is often known to be bounded by a fixed natural number m. For example, we might know in advance that each student ....

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J. Van den Bussche and J. Paredaens. The expressive power of structured values in pure OODB's. In Proceedings of the Tenth ACM Symposium on Principles of Database Systems, pages 291--299. ACM Press, 1991.

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J. Van den Bussche and J. Paredaens. The expressive power of structured values in pure OODB's. In Proceedings of the Tenth ACM Symposium on Principles of Database Systems, pages 291--299. ACM Press, 1991.

....that abstraction over functional properties is expressible using the other GOOD operations introduced in this section. Furthermore, abstraction over multiple properties can always be reduced to abstraction over one single property. More details on the expressive power of abstraction are given in [32]. 3.6 Methods As in any high level programming language, it is useful to incorporate in the GOOD transformation language, a programming construct to allow the grouping of a sequence of other operations. Furthermore, the object oriented approach in software engineering advocates the principle of ....

....[28] Nested relations are represented in an analogous manner as standard relations, now using also multivalued edges. The abstraction operation is needed in this case to obtain faithful simulations of relation valued attributes, meaning that duplicate relations can be eliminated (see also [32]) Again, the details of the simulation are left to the reader. The full language with methods is sufficiently strong to simulate arbitrary Turing Machines; this can be shown using well known techniques (e.g. 34] Finally, on the most general level, one may ask exactly which graph ....

J. Van den Bussche and J. Paredaens. The expressive power of structured values in pure OODB's. In Proceedings of the Tenth ACM Symposium on Principles of Database Systems, pages 291--299. ACM Press, 1991.

....new . The language RA new provides a basic and general object creation mechanism in function of tuples. Essentially this same mechanism is provided by many other query languages with object creating capabilities that have been proposed in the literature [3, 5, 6, 16, 17, 18, 22] Some languages [3, 16, 22, 26] provide also object creation in function of sets. We will not 3 Note that for any query Q, Q(I; J) implies adom(I) adom(J) explicitly need this capability to prove our results, but will return to it in Section 6. While we know that an object creating query must be non deterministic, it is ....

....can be thus expressed 3. In the present paper, we have focused on object creation in function of tuples (the new operation. Object creation in function of sets has also been considered in the literature; a simple and uniform operation providing this functionality is the abstraction operation [16, 26]. One among the many equivalent ways to define this operation is as follows. Let I 2 inst(S) and R 2 S with a(R) 2. If the binary relation I(R) is not an equivalence relation, then the application of abstr(R) to I is undefined. Otherwise, assume Z 1 ; Z k is an enumeration of the ....

[Article contains additional citation context not shown here]

J. Van den Bussche and J. Paredaens. The expressive power of structured values in pure OODB's. In Proceedings of the Tenth ACM Symposium on Principles of Database Systems, pages 291--299. ACM Press, 1991.

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